Finite Group Databasebeta

← #33979778

Subgroups — #33979778

Order 18688.

1860 conjugacy classes of subgroups.

The subgroup lattice has 1790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22624526C211yesmaximal, characteristic, complemented
2#22623870C211yesmaximal, characteristic, complemented
3#22622939C211yesmaximal, characteristic, complemented
4#22622686C211yesmaximal, characteristic, complemented
5#22622576C211yesmaximal, characteristic, complemented
6#22622239C211yesmaximal, characteristic, complemented
7#22622206C211yesmaximal, characteristic, complemented
8#22622189C211yesmaximal, characteristic, complemented
9#22622062C211yesmaximal, characteristic, complemented
10#22621897C211yesmaximal, characteristic, complemented
11#22621788C211yesmaximal, characteristic, complemented
12#22621633C211yesmaximal, characteristic, complemented
13#22621546C211yesmaximal, characteristic, complemented
14#22621540C211yesmaximal, characteristic, complemented
15#22621537C211yesmaximal, characteristic, complemented
16#22621455C211yesmaximal, characteristic, complemented
17#22621425C211yesmaximal, characteristic, complemented
18#22621375C211yesmaximal, characteristic, complemented
19#22621339C211yesmaximal, characteristic, complemented
20#22621330C211yesmaximal, characteristic, complemented
21#22621035C211yesmaximal, characteristic, complemented
22#22620976C211yesmaximal, characteristic, complemented
23#22620902C211yesmaximal, characteristic, complemented
24#22620173C211yesmaximal, characteristic, complemented
25#22620143C211yesmaximal, characteristic, complemented
26#22619982C211yesmaximal, characteristic, complemented
27#22619473C211yesmaximal, characteristic, complemented
28#22619438C211yesmaximal, characteristic, complemented
29#22619393C211yesmaximal, characteristic, complemented
30#22619083C211yesmaximal, characteristic, complemented
31C73×#3401C211yesmaximal, characteristic, complemented
32C2×#14556618C2211yescharacteristic
33C2×#14556618C2211yescharacteristic
34C2×#14556618C2211yescharacteristic, complemented
35C2×#14556615C2211yescharacteristic
36C2×#14556614C2211yescharacteristic
37C2×SD16×D73C2211yescharacteristic, complemented
38#17989333—21no—
39#17989328—21no—
40#17989322C2211yescharacteristic, complemented
41#17989297C2211yescharacteristic, complemented
42#17989288—21no—
43#17989287C2211yescharacteristic
44#17989282—21no—
45#17989278C2211yescharacteristic, complemented
46#17989267—21no—
47#17989266—21no—
48#17989261—21no—
49#17989259C2211yescharacteristic
50#17989249C2211yescharacteristic, complemented
51#17989245C2211yescharacteristic
52#17989242C2211yescharacteristic
53#17989240C2211yescharacteristic, complemented
54#17989232C2211yescharacteristic, complemented
55#17989230C2211yescharacteristic
56#17989230C2211yescharacteristic
57#17989230C2211yescharacteristic, complemented
58#17989229—21no—
59#17989222C2211yescharacteristic, complemented
60#17989206C2211yescharacteristic, complemented
61#17989195C2211yescharacteristic, complemented
62#17989192—21no—
63#17989191C2211yescharacteristic
64#17989188C2211yescharacteristic, complemented
65#17989180—21no—
66#17989178—21no—
67#17989177—21no—
68#17989176—21no—
69#17989171—21no—
70#17989162C2211yescharacteristic, complemented
71#17989155C2211yescharacteristic, complemented
72#17989136C2211yescharacteristic, complemented
73#17989124C2211yescharacteristic
74#17989124C2211yescharacteristic, complemented
75#17989116C2211yescharacteristic, complemented
76#17989096—21no—
77#123×D73—21no—
78#17989069C2211yescharacteristic
79#17989059C2211yescharacteristic, complemented
80C4×D4×D73C2211yescharacteristic, complemented
81#17988969C2211yescharacteristic, complemented
82#17988969C2211yescharacteristic, complemented
83#17988963C2211yescharacteristic
84#17988952C2211yescharacteristic, complemented
85#17988947C2211yescharacteristic, complemented
86#17988942C2211yescharacteristic, complemented
87#17988941C2211yescharacteristic, complemented
88#17988941C2211yescharacteristic, complemented
89#17988937C2211yescharacteristic, complemented
90#17988921C2211yescharacteristic, complemented
91#17988921C2211yescharacteristic, complemented
92#17988919C2211yescharacteristic, complemented
93#17988913C2211yescharacteristic, complemented
94#17988910C2211yescharacteristic, complemented
95#17988907C2211yescharacteristic, complemented
96#17988896C2211yescharacteristic, complemented
97#17988895C2211yescharacteristic, complemented
98#17988894C2211yescharacteristic, complemented
99#17988894C2211yescharacteristic, complemented
100#17988889C2211yescharacteristic, complemented
101#17988888C2211yescharacteristic, complemented
102#17988886C2211yescharacteristic, complemented
103#17988885C2211yescharacteristic, complemented
104#17988877C2211yescharacteristic, complemented
105#17988868C2211yescharacteristic, complemented
106#17988842C2211yescharacteristic, complemented
107#17988839C2211yescharacteristic
108#17988839C2211yescharacteristic, complemented
109#17988836C2211yescharacteristic, complemented
110#17988832C2211yescharacteristic, complemented
111#17988830C2211yescharacteristic, complemented
112#17988830C2211yescharacteristic, complemented
113#17988830C2211yescharacteristic, complemented
114#17988820C2211yescharacteristic
115#17988819C2211yescharacteristic, complemented
116#17988815C2211yescharacteristic, complemented
117#17988813C2211yescharacteristic, complemented
118#17988811C2211yescharacteristic, complemented
119#17988805C2211yescharacteristic
120#17988804C2211yescharacteristic, complemented
121#17988804C2211yescharacteristic, complemented
122#17988803C2211yescharacteristic
123#17988803C2211yescharacteristic, complemented
124#17988802C2211yescharacteristic, complemented
125#17988802C2211yescharacteristic, complemented
126#17988799C2211yescharacteristic
127#17988799C2211yescharacteristic
128#17988799C2211yescharacteristic, complemented
129#17988799C2211yescharacteristic, complemented
130#17988795C2211yescharacteristic, complemented
131#17988791C2211yescharacteristic, complemented
132#17988790C2211yescharacteristic, complemented
133#17988790C2211yescharacteristic, complemented
134#17988789C2211yescharacteristic, complemented
135#17988787C2211yescharacteristic, complemented
136#17988785C2211yescharacteristic, complemented
137#17988784C2211yescharacteristic, complemented
138#17988783C2211yescharacteristic
139#17988781C2211yescharacteristic
140#17988780C2211yescharacteristic, complemented
141#17988780C2211yescharacteristic, complemented
142#17988752C2211yescharacteristic
143#17988748C2211yescharacteristic
144#17988748C2211yescharacteristic, complemented
145#17988748C2211yescharacteristic, complemented
146#17988746C2211yescharacteristic, complemented
147#17988741C2211yescharacteristic, complemented
148#17988736C2211yescharacteristic, complemented
149#17988731C2211yescharacteristic
150#17988731C2211yescharacteristic, complemented
151#17988731C2211yescharacteristic, complemented
152#17988731C2211yescharacteristic, complemented
153#17988729C2211yescharacteristic
154#17988724C2211yescharacteristic, complemented
155#17988722C2211yescharacteristic
156#17988722C2211yescharacteristic, complemented
157#17988719C2211yescharacteristic
158#17988719C2211yescharacteristic, complemented
159#17988719C2211yescharacteristic, complemented
160Q8×#10596831C2211yescharacteristic, complemented
161#17988700C2211yescharacteristic, complemented
162#17988689C2211yescharacteristic, complemented
163C4×#11924018C2211yescharacteristic, complemented
164C4×#11924015C2211yescharacteristic, complemented
165C4×#11924015C2211yescharacteristic, complemented
166C4×D584C2211yescharacteristic
167C4×#11924013C2211yescharacteristic
168C4×#11924013C2211yescharacteristic, complemented
169C4×#11924013C2211yescharacteristic, complemented
170#17988666C2211yescharacteristic, complemented
171#17988664C2211yescharacteristic, complemented
172#17988664C2211yescharacteristic, complemented
173#17988660C2211yescharacteristic, complemented
174#17988660C2211yescharacteristic, complemented
175#17988652C2211yescharacteristic, complemented
176#17988649C2211yescharacteristic, complemented
177#17988649C2211yescharacteristic, complemented
178#17988638C2211yescharacteristic, complemented
179#17988612C2211yescharacteristic, complemented
180#17988612C2211yescharacteristic, complemented
181#17988609C2211yescharacteristic, complemented
182#17988594C2211yescharacteristic, complemented
183#17988587C2211yescharacteristic, complemented
184#17988587C2211yescharacteristic, complemented
185#17988585C2211yescharacteristic, complemented
186#17988582C2211yescharacteristic, complemented
187#102×D73C2211yescharacteristic, complemented
188#559×C73C2211yescharacteristic, complemented
189#556×C73C2211yescharacteristic, complemented
190#497×C73C2211yescharacteristic, complemented
191#496×C73C2211yescharacteristic
192#495×C73C2211yescharacteristic, complemented
193#464×C73C2211yescharacteristic, complemented
194#464×C73C2211yescharacteristic, complemented
195#463×C73C2211yescharacteristic, complemented
196#463×C73C2211yescharacteristic, complemented
197#461×C73C2211yescharacteristic, complemented
198#460×C73C2211yescharacteristic, complemented
199#446×C73C2211yescharacteristic, complemented
200#442×C73C2211yescharacteristic, complemented
201#441×C73C2211yescharacteristic, complemented
202C4×SD16×C73C2211yescharacteristic, complemented
203C2×#11924029C2311yescharacteristic
204C2×#11924029C2311yescharacteristic
205C2×#11924029C2311yescharacteristic
206C2×#11924029C2311yescharacteristic
207C2×#11924028—21no—
208C2×#11924027C2311yescharacteristic
209C2×Q8×D73C2311yescharacteristic
210C2×D4×D73—21no—
211C2×D4×D73C2311yescharacteristic
212C2×D4×D73C2311yescharacteristic
213C2×D4×D73C2311yescharacteristic
214C22×C4×D73—21no—
215#14556618—42no—
216#14556618—42no—
217#14556618—42no—
218#14556615—42no—
219#14556614—42no—
220C2×#11924018C2311yescharacteristic
221C2×#11924017C2311yescharacteristic
222C2×#11924016C2311yescharacteristic
223C2×#11924016C2311yescharacteristic
224C2×#11924015C2311yescharacteristic
225C2×#11924015C2311yescharacteristic
226C2×#11924015C2311yescharacteristic
227C2×#11924015C2311yescharacteristic
228SD16×D73—42no—
229C2×D584C2311yescharacteristic
230C2×D584C2311yescharacteristic
231C2×#11924013C2311yescharacteristic
232C2×#11924013C2311yescharacteristic
233C2×#11924013C2311yescharacteristic
234C2×#11924013C2311yescharacteristic
235C2×#11924013C2311yescharacteristic
236C2×#11924011C2311yescharacteristic
237C2×#11924011C2311yescharacteristic
238C2×#11924011C2311yescharacteristic
239C2×#11924011C2311yescharacteristic
240C2×C8×D73C2311yescharacteristic
241C2×C8×D73C2311yescharacteristic
242#14556591C2311yescharacteristic
243#14556589C2311yescharacteristic
244#14556588—21no—
245#14556588C2311yescharacteristic
246#14556587C2311yescharacteristic
247#14556586—21no—
248#14556586—21no—
249#14556586D411yescharacteristic
250#14556586D411yescharacteristic
251#14556585—21no—
252#14556585—21no—
253#14556584—21no—
254#14556584—21no—
255#14556584—21no—
256#14556583—21no—
257#14556583C2311yescharacteristic
258#14556583C2311yescharacteristic
259#14556582D411yescharacteristic
260#14556582C2311yescharacteristic
261#14556581—21no—
262#14556581—21no—
263#14556580—21no—
264#14556580D411yescharacteristic
265#14556580C2311yescharacteristic
266#14556579—21no—
267#14556579C2311yescharacteristic
268#14556579C2311yescharacteristic
269#14556577—21no—
270#14556577—21no—
271#14556576—21no—
272#14556576—21no—
273#14556576—21no—
274#14556576—21no—
275#14556576—21no—
276#14556576—21no—
277#14556576—21no—
278#14556576—21no—
279#14556576D411yescharacteristic
280#14556576D411yescharacteristic
281#14556575—21no—
282#14556575—21no—
283#14556574—21no—
284#14556574—21no—
285#14556573—21no—
286#14556573—21no—
287#14556573—21no—
288#14556573—21no—
289#14556573—21no—
290#14556573—21no—
291#14556573—21no—
292#14556572—21no—
293#14556572—21no—
294#14556571—21no—
295#14556571C2311yescharacteristic
296#14556570—21no—
297#14556569—21no—
298#14556569—21no—
299#14556569—21no—
300#14556569—21no—
301#14556568—21no—
302#14556568—21no—
303#14556567—21no—
304#14556567D411yescharacteristic
305#14556567C2311yescharacteristic
306#14556567C2311yescharacteristic
307#14556567C2311yescharacteristic
308#14556567C2311yescharacteristic
309#14556566—21no—
310#14556566—21no—
311#14556566—21no—
312#14556566—21no—
313#14556566D411yescharacteristic
314#14556566C2311yescharacteristic
315#14556566C2311yescharacteristic
316#14556565—21no—
317#14556565—21no—
318#14556564—21no—
319#14556564—21no—
320#14556564—21no—
321#14556564—21no—
322#14556564—21no—
323#14556564—21no—
324#14556564—21no—
325#14556564—21no—
326#14556564—21no—
327#14556564—21no—
328#14556563—21no—
329#14556563—21no—
330#14556562—21no—
331#14556562C2311yescharacteristic
332#14556562C2311yescharacteristic
333#14556562C2311yescharacteristic
334#14556562C2311yescharacteristic
335#14556562C2311yescharacteristic
336#14556561—21no—
337#14556561—21no—
338#14556561—21no—
339#14556561—21no—
340#14556561—21no—
341#14556561—21no—
342#14556559—21no—
343#14556559—21no—
344Q8×Dic73C2311yescharacteristic
345C4×Dic146C2311yescharacteristic
346C4×D292—21no—
347C4×D292—21no—
348C4×D292—21no—
349C4×D292—21no—
350C4×D292C2311yescharacteristic
351C4×D292C2311yescharacteristic
352C4×D292C2311yescharacteristic
353C4×D292C2311yescharacteristic
354C4×D292C2311yescharacteristic
355C4×D292C2311yescharacteristic
356C4×D292C2311yescharacteristic
357C4×D292C2311yescharacteristic
358D4×Dic73C2311yescharacteristic
359D4×Dic73C2311yescharacteristic
360#14556553—21no—
361#14556553—21no—
362#14556553C2311yescharacteristic
363C4×C22⋊D73—21no—
364C4×C22⋊D73—21no—
365C4×C22⋊D73—21no—
366#14556551—21no—
367#14556551—21no—
368#14556551—21no—
369#14556551—21no—
370#14556551—21no—
371#14556551—21no—
372#14556549C2311yescharacteristic
373#14556548—21no—
374#14556548—21no—
375#14556548—21no—
376#14556548C2311yescharacteristic
377#14556548C2311yescharacteristic
378#14556547—21no—
379C4⋊C4×D73—21no—
380C4⋊C4×D73—21no—
381C4⋊C4×D73—21no—
382C4⋊C4×D73C2311yescharacteristic
383C4⋊C4×D73C2311yescharacteristic
384C2×#11924005—21no—
385C2×#11924005—21no—
386C22⋊C4×D73—21no—
387C22⋊C4×D73—21no—
388C22⋊C4×D73—21no—
389C22⋊C4×D73—21no—
390C22⋊C4×D73—21no—
391C42×D73C2311yescharacteristic
392#14556525C2311yescharacteristic
393#14556525C2311yescharacteristic
394#14556524C2311yescharacteristic
395#14556524C2311yescharacteristic
396#14556523C2311yescharacteristic
397#14556522C2311yescharacteristic
398#14556522C2311yescharacteristic
399C4⋊#10596831C2311yescharacteristic
400C4⋊#10596831C2311yescharacteristic
401C4⋊#10596831C2311yescharacteristic
402#14556520C2311yescharacteristic
403#14556520C2311yescharacteristic
404#14556520C2311yescharacteristic
405#14556520C2311yescharacteristic
406#14556516C2311yescharacteristic
407#14556516C2311yescharacteristic
408#14556516C2311yescharacteristic
409#14556515C2311yescharacteristic
410#14556515C2311yescharacteristic
411#14556515C2311yescharacteristic
412#14556515C2311yescharacteristic
413#14556515C2311yescharacteristic
414#14556515C2311yescharacteristic
415#14556515C2311yescharacteristic
416#14556514C2311yescharacteristic
417#14556513C2311yescharacteristic
418#14556513C2311yescharacteristic
419#14556513C2311yescharacteristic
420#14556513C2311yescharacteristic
421#14556513C2311yescharacteristic
422#14556513C2311yescharacteristic
423#14556513C2311yescharacteristic
424#14556512C2311yescharacteristic
425#14556512C2311yescharacteristic
426#14556512C2311yescharacteristic
427#14556512C2311yescharacteristic
428#14556512C2311yescharacteristic
429#14556511C2311yescharacteristic
430#14556511C2311yescharacteristic
431#14556511C2311yescharacteristic
432#14556503C2311yescharacteristic
433#14556503C2311yescharacteristic
434#14556503C2311yescharacteristic
435#14556503C2311yescharacteristic
436#14556503C2311yescharacteristic
437#14556503C2311yescharacteristic
438C4×#10596831C2311yescharacteristic
439C4×#10596831C2311yescharacteristic
440C4×#10596831C2311yescharacteristic
441C2×Q16×C73C2311yescharacteristic
442C2×Q16×C73C2311yescharacteristic
443C2×SD16×C73C2311yescharacteristic
444C2×SD16×C73C2311yescharacteristic
445C2×SD16×C73C2311yescharacteristic
446C2×SD16×C73C2311yescharacteristic
447C2×SD16×C73C2311yescharacteristic
448C2×D8×C73C2311yescharacteristic
449C2×D8×C73C2311yescharacteristic
450C4⋊Q8×C73C2311yescharacteristic
451#127×C73C2311yescharacteristic
452#126×C73—21no—
453#126×C73—21no—
454#124×C73—21no—
455#124×C73C2311yescharacteristic
456#124×C73C2311yescharacteristic
457#124×C73C2311yescharacteristic
458#124×C73C2311yescharacteristic
459#123×C73—21no—
460#123×C73—21no—
461C22⋊Q8×C73—21no—
462C4×Q8×C73C2311yescharacteristic
463C4×Q8×C73C2311yescharacteristic
464C4×Q8×C73C2311yescharacteristic
465C4×Q8×C73C2311yescharacteristic
466C4×D4×C73—21no—
467C4×D4×C73C2311yescharacteristic
468C4×D4×C73C2311yescharacteristic
469C4×D4×C73C2311yescharacteristic
470#117×C73—21no—
471#106×C73C2311yescharacteristic
472C4⋊C8×C73C2311yescharacteristic
473C4⋊C8×C73C2311yescharacteristic
474C4⋊C8×C73C2311yescharacteristic
475#103×C73C2311yescharacteristic
476#103×C73C2311yescharacteristic
477#103×C73C2311yescharacteristic
478#102×C73C2311yescharacteristic
479#102×C73C2311yescharacteristic
480#102×C73C2311yescharacteristic
481#97×C73C2311yescharacteristic
482#97×C73C2311yescharacteristic
483C4×C8×C73C2311yescharacteristic
484C23×D73—21no—
485C23×D73—21no—
486C23×D73—21no—
487#11924029—22no—
488#11924029—41no—
489#11924029—41no—
490#11924029—41no—
491#11924029—41no—
492#11924029—41no—
493#11924029—41no—
494#11924029—41no—
495#11924028—82no—
496#11924027—41no—
497#11924027—41no—
498C2×Dic146—21no—
499C2×Dic146—21no—
500C2×Dic146C2411yescharacteristic
501Q8×D73—41no—
502Q8×D73—41no—
503C2×D292—21no—
504C2×D292—21no—
505C2×D292—21no—
506C2×D292—21no—
507C2×D292—21no—
508C2×D292—21no—
509C2×D292—21no—
510C2×D292—21no—
511C2×D292C2×D411yescharacteristic
512C2×D292C2×D411yescharacteristic
513C2×D292C2×D411yescharacteristic
514C2×D292C2411yescharacteristic
515C2×D292C2411yescharacteristic
516C2×D292C2411yescharacteristic
517C2×C22⋊D73—21no—
518C2×C22⋊D73—21no—
519C2×C22⋊D73—21no—
520C2×C22⋊D73—21no—
521C2×C22⋊D73—21no—
522C2×C22⋊D73—21no—
523C2×C22⋊D73—21no—
524C2×C22⋊D73—21no—
525C2×C22⋊D73—21no—
526C2×C22⋊D73—21no—
527C2×C22⋊D73—21no—
528D4×D73—22no—
529D4×D73—22no—
530D4×D73—41no—
531D4×D73—41no—
532D4×D73—41no—
533D4×D73—41no—
534D4×D73—82no—
535C22×Dic73—21no—
536C22×Dic73—21no—
537C22×Dic73—21no—
538C2×C4×D73—21no—
539C2×C4×D73—21no—
540C2×C4×D73—21no—
541C2×C4×D73—21no—
542C2×C4×D73—21no—
543C2×C4×D73—21no—
544C2×C4×D73—21no—
545C2×C4×D73—21no—
546C2×C4×D73—21no—
547C2×C4×D73—21no—
548C2×C4×D73—21no—
549C2×C4×D73—21no—
550C2×C4×D73—21no—
551C2×C4×D73—82no—
552C2×C4×D73C2×D411yescharacteristic
553C2×C4×D73C2×D411yescharacteristic
554C2×C4×D73C2411yescharacteristic
555C2×C4×D73C2411yescharacteristic
556C2×C4×D73C2411yescharacteristic
557#11924018—41no—
558#11924017—22no—
559#11924016—41no—
560#11924016—41no—
561#11924015—22no—
562#11924015—22no—
563#11924015—41no—
564#11924015—41no—
565D584—22no—
566D584—22no—
567#11924013—22no—
568#11924013—41no—
569#11924013—41no—
570#11924013—41no—
571#11924013—41no—
572#11924011—41no—
573#11924011—41no—
574#11924011—41no—
575#11924011—41no—
576C2×#10596831C2411yescharacteristic
577C2×#10596831C2411yescharacteristic
578C2×#10596831C2411yescharacteristic
579C2×#10596831C2411yescharacteristic
580C8×D73—41no—
581C8×D73—41no—
582C4⋊Dic73—21no—
583C4⋊Dic73—21no—
584C4⋊Dic73—21no—
585C4⋊Dic73—21no—
586C4⋊Dic73C2×D411yescharacteristic
587C4⋊Dic73C2×D411yescharacteristic
588C4⋊Dic73C2×D411yescharacteristic
589C4⋊Dic73C2411yescharacteristic
590C4⋊Dic73C2411yescharacteristic
591C4⋊Dic73C2411yescharacteristic
592C4⋊Dic73C2411yescharacteristic
593#11924007—21no—
594#11924007—21no—
595#11924007—21no—
596#11924007—21no—
597#11924007—21no—
598#11924007—21no—
599#11924007—21no—
600#11924007—21no—
601#11924007—21no—
602#11924007—21no—
603#11924007—21no—
604#11924007—21no—
605#11924007—21no—
606#11924007—21no—
607#11924007C2×D411yescharacteristic
608#11924007C2×D411yescharacteristic
609#11924007C2×D411yescharacteristic
610#11924007C2×D411yescharacteristic
611C22⋊Dic73—21no—
612C22⋊Dic73—21no—
613C22⋊Dic73—21no—
614C22⋊Dic73—21no—
615C22⋊Dic73—21no—
616C22⋊Dic73—21no—
617C22⋊Dic73—21no—
618#11924005—21no—
619#11924005—21no—
620#11924005—21no—
621#11924005—21no—
622#11924005—21no—
623#11924005—21no—
624#11924005—21no—
625#11924005—21no—
626#11924005—21no—
627#11924005—21no—
628#11924005—21no—
629#11924005—21no—
630#11924005—21no—
631#11924005—21no—
632#11924005—21no—
633#11924005—21no—
634#11924005—21no—
635#11924005—21no—
636#11924005—21no—
637#11924005—21no—
638#11924005C2×D411yescharacteristic
639#11924005C2×D411yescharacteristic
640#11924005C2×D411yescharacteristic
641#11924005C2×D411yescharacteristic
642#11924005C2×D411yescharacteristic
643#11924005C2×D411yescharacteristic
644#11924005C2×D411yescharacteristic
645#11924005C2×D411yescharacteristic
646#11924005C2×D411yescharacteristic
647#11924005C2×D411yescharacteristic
648C4×Dic73—21no—
649C4×Dic73—21no—
650C4×Dic73—21no—
651C4×Dic73C2×D411yescharacteristic
652C4×Dic73C2×D411yescharacteristic
653C4×Dic73C2411yescharacteristic
654C2×Q8×C73C2×D411yescharacteristic
655C2×Q8×C73C2411yescharacteristic
656C2×Q8×C73C2411yescharacteristic
657C2×Q8×C73C2411yescharacteristic
658C2×D4×C73—21no—
659C2×D4×C73—21no—
660C2×D4×C73C2411yescharacteristic
661C2×D4×C73C2411yescharacteristic
662C2×D4×C73C2411yescharacteristic
663C22×C4×C73—21no—
664C22×C4×C73—21no—
665C22×C4×C73—21no—
666Q16×C73—41no—
667Q16×C73—41no—
668SD16×C73—41no—
669SD16×C73—41no—
670SD16×C73—41no—
671SD16×C73—41no—
672SD16×C73—41no—
673D8×C73—41no—
674D8×C73—41no—
675C2×C8×C73C2411yescharacteristic
676C2×C8×C73C2411yescharacteristic
677C2×C8×C73C2411yescharacteristic
678C2×C8×C73C2411yescharacteristic
679C4⋊C4×C73—21no—
680C4⋊C4×C73—21no—
681C4⋊C4×C73—21no—
682C4⋊C4×C73—21no—
683C4⋊C4×C73—21no—
684C4⋊C4×C73C2×D411yescharacteristic
685C4⋊C4×C73C2×D411yescharacteristic
686C4⋊C4×C73C2×D411yescharacteristic
687C4⋊C4×C73C2411yescharacteristic
688C4⋊C4×C73C2411yescharacteristic
689C22⋊C4×C73—21no—
690C22⋊C4×C73—21no—
691C22⋊C4×C73—21no—
692C22⋊C4×C73—21no—
693C22⋊C4×C73—21no—
694C22⋊C4×C73—21no—
695C22⋊C4×C73—21no—
696C22⋊C4×C73—21no—
697C22⋊C4×C73—21no—
698C22⋊C4×C73—21no—
699C22⋊C4×C73—21no—
700C42×C73—21no—
701C42×C73—21no—
702C42×C73—21no—
703C42×C73C2411yescharacteristic
704C42×C73C2411yescharacteristic
705C42×C73C2411yescharacteristic
706C23×C73—21no—
707C23×C73—21no—
708C23×C73—21no—
709C22×D73—21no—
710C22×D73—21no—
711C22×D73—21no—
712C22×D73—42no—
713C22×D73—42no—
714C22×D73—42no—
715C22×D73—81no—
716C22×D73—81no—
717C22×D73—81no—
718C22×D73—81no—
719C22×D73—81no—
720C22×D73—81no—
721C22×D73C22×D411yescharacteristic
722C22×D73C22×D411yescharacteristic
723C22×D73C22×D411yescharacteristic
724Q8×C73—21no—
725Q8×C73—21no—
726Q8×C73—21no—
727Q8×C73—21no—
728Q8×C73—21no—
729Q8×C73—21no—
730Q8×C73—41no—
731D4×C73—21no—
732D4×C73—21no—
733D4×C73—21no—
734D4×C73—21no—
735D4×C73—21no—
736D4×C73—21no—
737D4×C73—81no—
738D4×C73—81no—
739C2×C4×C73—21no—
740C2×C4×C73—21no—
741C2×C4×C73—21no—
742C2×C4×C73—21no—
743C2×C4×C73—21no—
744C2×C4×C73—81no—
745C2×C4×C73—81no—
746C2×C4×C73—81no—
747C2×C4×C73C22×D411yescharacteristic
748C2×C4×C73C22×D411yescharacteristic
749C2×C4×C73C22×D411yescharacteristic
750C2×C4×C73C22×D411yescharacteristic
751C2×C4×C73C22×D411yescharacteristic
752C2×C4×C73C22×D411yescharacteristic
753C2×C4×C73C2511yescharacteristic
754C22⋊D73—42no—
755C22⋊D73—42no—
756C22⋊D73—42no—
757C22⋊D73—81no—
758C22⋊D73—81no—
759C22⋊D73—81no—
760C22⋊D73—81no—
761C22⋊D73—81no—
762C22⋊D73—81no—
763C22⋊D73—81no—
764C22⋊D73—81no—
765C2×Dic73—21no—
766C2×Dic73—21no—
767C2×Dic73—21no—
768C2×Dic73—21no—
769C2×Dic73—21no—
770C2×Dic73—81no—
771C2×Dic73—81no—
772C2×Dic73—81no—
773C2×Dic73C22×D411yescharacteristic
774C2×Dic73C22×D411yescharacteristic
775C2×Dic73C22×D411yescharacteristic
776C2×Dic73C22×D411yescharacteristic
777C2×Dic73C22×D411yescharacteristic
778D292—21no—
779D292—21no—
780D292—21no—
781D292—21no—
782D292—21no—
783D292—41no—
784D292—41no—
785D292—41no—
786D292—42no—
787D292—81no—
788D292—81no—
789D292—81no—
790D292—81no—
791D292—81no—
792D292—81no—
793D292—81no—
794D292H(5,𝔽2)12yes—
795C4×D73—21no—
796C4×D73—21no—
797C4×D73—21no—
798C4×D73—21no—
799C4×D73—21no—
800C4×D73—21no—
801C4×D73—41no—
802C4×D73—41no—
803C4×D73—42no—
804C4×D73—42no—
805C4×D73—81no—
806C4×D73—81no—
807C4×D73—81no—
808C4×D73—81no—
809C4×D73—81no—
810C4×D73—81no—
811C4×D73—81no—
812C4×D73—81no—
813C4×D73—81no—
814C4×D73—81no—
815C4×D73—81no—
816Dic146—21no—
817Dic146—21no—
818Dic146—81no—
819Dic146—81no—
820C8×C73—21no—
821C8×C73—21no—
822C8×C73—21no—
823C8×C73—21no—
824#10596831—21no—
825#10596831—21no—
826#10596831—21no—
827#10596831—21no—
828C22×C73—41no—
829C22×C73—41no—
830C22×C73—41no—
831C22×C73—41no—
832C22×C73—41no—
833C22×C73—41no—
834C22×C73—41no—
835C22×C73—41no—
836C22×C73—41no—
837C22×C73C23×D411yescharacteristic
838C2×D73—21no—
839C2×D73—21no—
840C2×D73—21no—
841C2×D73—21no—
842C2×D73—21no—
843C2×D73—21no—
844C2×D73—21no—
845C2×D73—21no—
846C2×D73—21no—
847C2×D73—22no—
848C2×D73—41no—
849C2×D73—41no—
850C2×D73—41no—
851C2×D73—41no—
852C2×D73—41no—
853C2×D73—41no—
854C2×D73—41no—
855C2×D73—41no—
856C2×D73—84no—
857C2×D73—162no—
858C2×D73—162no—
859C4×C73—21no—
860C4×C73—21no—
861C4×C73—21no—
862C4×C73—21no—
863C4×C73—21no—
864C4×C73—21no—
865C4×C73—41no—
866C4×C73—41no—
867C4×C73—41no—
868C4×C73—41no—
869C4×C73—41no—
870C4×C73C2×H(5,𝔽2)11yescharacteristic
871C4×C73#58511yescharacteristic
872Dic73—21no—
873Dic73—21no—
874Dic73—21no—
875Dic73—21no—
876Dic73—21no—
877Dic73—41no—
878Dic73—41no—
879Dic73—41no—
880Dic73—41no—
881Dic73—41no—
882#62027—731nomaximal, Sylow
883C2×C73—81no—
884C2×C73—81no—
885C2×C73—81no—
886C2×C73#348811yescharacteristic
887C2×C73#358411yescharacteristic
888C2×C73#358511yescharacteristic
889D73—41no—
890D73—41no—
891D73—41no—
892D73—42no—
893D73—81no—
894D73—81no—
895#3562—731no—
896#3513—731no—
897#3401D7311yescharacteristic, complemented
898#3396—731no—
899#3370—731no—
900#3360—731no—
901#3330—731no—
902#3327—731no—
903#3326—731no—
904#3317—731no—
905#3306—731no—
906#3297—731no—
907#3282—731no—
908#3274—731no—
909#3273—731no—
910#3273—731no—
911#3267—731no—
912#3265—731no—
913#3260—731no—
914#3257—731no—
915#3256—731no—
916#3225—731no—
917#3220—731no—
918#3212—731no—
919#3122—731no—
920#3120—731no—
921#3105—731no—
922#3045—731no—
923#3042—731no—
924#3036—731no—
925#2993—731no—
926C73#6202711yescharacteristic, complemented, Sylow
927C2×AGL(1,ℤ/8)—731no—
928C2×AGL(1,ℤ/8)—731no—
929C2×AGL(1,ℤ/8)—731no—
930C2×AGL(1,ℤ/8)—731no—
931C2×#135—731no—
932C22×SD16—731no—
933#562—1461no—
934#560—1461no—
935#559—731no—
936#559C2×D7311yescharacteristic, complemented
937#556C2×D7311yescharacteristic, complemented
938#554—731no—
939#553—731no—
940#553—1461no—
941#553—1461no—
942#552—731no—
943#551—1461no—
944#551—1461no—
945#551—1461no—
946#550—731no—
947#548—731no—
948#548—731no—
949#547—731no—
950#547—731no—
951#546—731no—
952#546—731no—
953#546—731no—
954#546—731no—
955#546—1461no—
956D42—731no—
957#542—731no—
958#541—731no—
959#540—731no—
960#540—731no—
961#540—1461no—
962#539—1461no—
963#539—1461no—
964#538—1461no—
965#538—1461no—
966#538—1461no—
967#536—731no—
968#535—731no—
969#532—731no—
970#529—731no—
971#529—731no—
972#529—731no—
973#525—1461no—
974C2×#123—1461no—
975#520—731no—
976#518—731no—
977C2×C4×D4—731no—
978#497C2×D7311yescharacteristic, complemented
979#496C2×D7311yescharacteristic
980#495—731no—
981#495—731no—
982#495C2×D7311yescharacteristic, complemented
983#493—731no—
984#490—731no—
985#489—731no—
986#488—731no—
987#488—731no—
988#488—731no—
989#487—731no—
990#484—731no—
991#484—731no—
992#483—731no—
993#482—731no—
994#482—731no—
995#481—731no—
996#479—731no—
997#479—731no—
998#479—731no—
999#479—731no—
1000#478—731no—
1001#478—731no—
1002#478—731no—
1003#478—731no—
1004#476—731no—
1005#474—731no—
1006#470—731no—
1007#469—731no—
1008#469—731no—
1009#468—731no—
1010#468—731no—
1011#468—731no—
1012#468—731no—
1013#468—731no—
1014#466—731no—
1015#465—731no—
1016#465—731no—
1017#465—731no—
1018#464—731no—
1019#464C2×D7311yescharacteristic, complemented
1020#464C2×D7311yescharacteristic, complemented
1021#463—731no—
1022#463—731no—
1023#463—731no—
1024#463—731no—
1025#463—731no—
1026#463—731no—
1027#463—731no—
1028#463—731no—
1029#463—731no—
1030#463—731no—
1031#463—731no—
1032#463C2×D7311yescharacteristic, complemented
1033#463C2×D7311yescharacteristic, complemented
1034#462—731no—
1035#461—731no—
1036#461—731no—
1037#461—731no—
1038#461—731no—
1039#461C2×D7311yescharacteristic, complemented
1040#460—731no—
1041#460—731no—
1042#460—731no—
1043#460C2×D7311yescharacteristic, complemented
1044#459—731no—
1045#459—731no—
1046#459—731no—
1047#459—731no—
1048#452—731no—
1049#452—731no—
1050#452—731no—
1051#452—731no—
1052#452—731no—
1053#451—731no—
1054#450—731no—
1055#449—731no—
1056#449—731no—
1057#449—731no—
1058#449—731no—
1059#449—731no—
1060#448—731no—
1061#447—731no—
1062#447—731no—
1063#447—731no—
1064#447—731no—
1065#447—731no—
1066#446C2×D7311yescharacteristic, complemented
1067C8×Q8—731no—
1068#442—731no—
1069#442C2×D7311yescharacteristic, complemented
1070#441C2×D7311yescharacteristic, complemented
1071#440—731no—
1072C4×Q16—731no—
1073C4×SD16—731no—
1074C4×SD16—731no—
1075C4×SD16C2×D7311yescharacteristic, complemented
1076C4×D8—731no—
1077C4×D8—731no—
1078C4×D8—731no—
1079C4×D8—731no—
1080#436—731no—
1081#436—731no—
1082#436—731no—
1083#435—731no—
1084#435—731no—
1085C8×D4—731no—
1086#433—731no—
1087#433—731no—
1088#431—731no—
1089#424—731no—
1090#424—731no—
1091#423—731no—
1092#419—731no—
1093#417—731no—
1094#417—731no—
1095#417—731no—
1096#416—731no—
1097C2×#102—731no—
1098C2×#41—731no—
1099C2×#41—731no—
1100C2×#41—731no—
1101C2×#41—731no—
1102C2×#41—731no—
1103C2×#41—1461no—
1104C22×Q8—731no—
1105C22×D4—731no—
1106C22×D4—731no—
1107C22×D4—731no—
1108C22×D4—1461no—
1109C23×C4—1461no—
1110AGL(1,ℤ/8)—2922no—
1111AGL(1,ℤ/8)—2922no—
1112AGL(1,ℤ/8)—2922no—
1113AGL(1,ℤ/8)—2922no—
1114#135—2922no—
1115C2×Q16—731no—
1116C2×Q16C22×D7311yescharacteristic
1117C2×Q16C22×D7311yescharacteristic
1118C2×SD16—2922no—
1119C2×SD16—731no—
1120C2×SD16—731no—
1121C2×SD16—731no—
1122C2×SD16—731no—
1123C2×SD16—731no—
1124C2×SD16—731no—
1125C2×SD16—731no—
1126C2×SD16C22×D7311yescharacteristic
1127C2×SD16C22×D7311yescharacteristic
1128C2×SD16C22×D7311yescharacteristic
1129C2×SD16C22×D7311yescharacteristic
1130C2×SD16C22×D7311yescharacteristic
1131C2×D8—731no—
1132C2×D8—731no—
1133C2×D8—731no—
1134C2×D8—731no—
1135C2×D8—731no—
1136C2×D8—731no—
1137C2×D8—731no—
1138C2×D8C22×D7311yescharacteristic
1139C2×D8C22×D7311yescharacteristic
1140C2×M16—731no—
1141C2×M16—731no—
1142C2×M16—731no—
1143C2×M16—731no—
1144C22×C8—731no—
1145C22×C8—731no—
1146C4⋊Q8—731no—
1147C4⋊Q8—731no—
1148C4⋊Q8C22×D7311yescharacteristic
1149#127—731no—
1150#127—731no—
1151#127—1461no—
1152#127C22×D7311yescharacteristic
1153#126—21no—
1154#126—21no—
1155#126—731no—
1156#126—731no—
1157#126—1461no—
1158#126—1461no—
1159#126—1461no—
1160#126—1461no—
1161#126—1461no—
1162#126—1461no—
1163#126—1461no—
1164#125—731no—
1165#125—731no—
1166#125—731no—
1167#125—731no—
1168#125—1461no—
1169#125—1461no—
1170#125—1461no—
1171#124—21no—
1172#124—731no—
1173#124—731no—
1174#124—731no—
1175#124—731no—
1176#124—1461no—
1177#124—1461no—
1178#124—1461no—
1179#124—1461no—
1180#124C22×D7311yescharacteristic
1181#124C22×D7311yescharacteristic
1182#124C22×D7311yescharacteristic
1183#124C22×D7311yescharacteristic
1184#123—21no—
1185#123—21no—
1186#123—731no—
1187#123—731no—
1188#123—1461no—
1189#123—1461no—
1190#123—1461no—
1191#123—1461no—
1192#123—1461no—
1193#123—1461no—
1194#123—1461no—
1195#123—1461no—
1196#123—1461no—
1197#123—1461no—
1198#123—1461no—
1199#123—1461no—
1200#123—1461no—
1201#123—1461no—
1202#123—1461no—
1203#123—1461no—
1204#123—1461no—
1205#123—1461no—
1206#123—1461no—
1207#123—1461no—
1208#123—1461no—
1209C22⋊Q8—21no—
1210C22⋊Q8—731no—
1211C22⋊Q8—731no—
1212C22⋊Q8—731no—
1213C22⋊Q8—731no—
1214C22⋊Q8—731no—
1215C22⋊Q8—731no—
1216C22⋊Q8—1461no—
1217C22⋊Q8—1461no—
1218C22⋊Q8—1461no—
1219C22⋊Q8—1461no—
1220C22⋊Q8—1461no—
1221C22⋊Q8—1461no—
1222C22⋊Q8—1461no—
1223C22⋊Q8—1461no—
1224C22⋊Q8—1461no—
1225#121—731no—
1226#121—731no—
1227#121—731no—
1228#121—731no—
1229#121—731no—
1230#121—731no—
1231#121—731no—
1232#121—731no—
1233#121—1461no—
1234#121—1461no—
1235#121—1461no—
1236#121—1461no—
1237#121—1461no—
1238#121—1461no—
1239#121—1461no—
1240#121—1461no—
1241#121—1461no—
1242#121—1461no—
1243#121—1461no—
1244#121—1461no—
1245#121—1461no—
1246#121—1461no—
1247#121—1461no—
1248#121—1461no—
1249#121—1461no—
1250#121—1461no—
1251#121—1461no—
1252#120—1461no—
1253#120—1461no—
1254#120—1461no—
1255#120—1461no—
1256#120—1461no—
1257#120—1461no—
1258#120—1461no—
1259#120—1461no—
1260C4×Q8—731no—
1261C4×Q8—731no—
1262C4×Q8C22×D7311yescharacteristic
1263C4×Q8C22×D7311yescharacteristic
1264C4×Q8C22×D7311yescharacteristic
1265C4×Q8C22×D7311yescharacteristic
1266C4×D4—21no—
1267C4×D4—731no—
1268C4×D4—731no—
1269C4×D4—731no—
1270C4×D4—731no—
1271C4×D4—731no—
1272C4×D4—731no—
1273C4×D4—731no—
1274C4×D4—731no—
1275C4×D4—731no—
1276C4×D4—731no—
1277C4×D4—731no—
1278C4×D4—1461no—
1279C4×D4—1461no—
1280C4×D4—1461no—
1281C4×D4—1461no—
1282C4×D4—1461no—
1283C4×D4—1461no—
1284C4×D4—1461no—
1285C4×D4—1461no—
1286C4×D4—1461no—
1287C4×D4—1461no—
1288C4×D4—1461no—
1289C4×D4—1461no—
1290C4×D4—1461no—
1291C4×D4—1461no—
1292C4×D4—1461no—
1293C4×D4C22×D7311yescharacteristic
1294C4×D4C22×D7311yescharacteristic
1295C4×D4C22×D7311yescharacteristic
1296#117—21no—
1297#117—731no—
1298#117—731no—
1299#117—731no—
1300#117—1461no—
1301#117—1461no—
1302#117—1461no—
1303#117—1461no—
1304C2×C4⋊C4—731no—
1305C2×C4⋊C4—731no—
1306C2×C4⋊C4—1461no—
1307C2×C4⋊C4—1461no—
1308C2×C4⋊C4—1461no—
1309C2×C22⋊C4—1461no—
1310C2×C22⋊C4—1461no—
1311C2×C22⋊C4—1461no—
1312C2×C22⋊C4—1461no—
1313C2×C22⋊C4—1461no—
1314C2×C22⋊C4—1461no—
1315C2×C22⋊C4—1461no—
1316C2×C42—731no—
1317#107—731no—
1318#107—731no—
1319#107—731no—
1320#107—731no—
1321#106—731no—
1322#106—731no—
1323#106—731no—
1324#106C22×D7311yescharacteristic
1325C4⋊C8—731no—
1326C4⋊C8—731no—
1327C4⋊C8—731no—
1328C4⋊C8—731no—
1329C4⋊C8—731no—
1330C4⋊C8—731no—
1331C4⋊C8—731no—
1332C4⋊C8C22×D7311yescharacteristic
1333C4⋊C8C22×D7311yescharacteristic
1334C4⋊C8C22×D7311yescharacteristic
1335#103—731no—
1336#103—731no—
1337#103—731no—
1338#103—731no—
1339#103—731no—
1340#103—731no—
1341#103—731no—
1342#103—731no—
1343#103—731no—
1344#103—731no—
1345#103—731no—
1346#103C22×D7311yescharacteristic
1347#103C22×D7311yescharacteristic
1348#103C22×D7311yescharacteristic
1349#102—731no—
1350#102—731no—
1351#102—731no—
1352#102—731no—
1353#102—731no—
1354#102—731no—
1355#102—731no—
1356#102—731no—
1357#102—731no—
1358#102—731no—
1359#102—731no—
1360#102—731no—
1361#102—731no—
1362#102—731no—
1363#102—731no—
1364#102C22×D7311yescharacteristic
1365#102C22×D7311yescharacteristic
1366#102C22×D7311yescharacteristic
1367C22⋊C8—731no—
1368C22⋊C8—731no—
1369C22⋊C8—731no—
1370C22⋊C8—731no—
1371C22⋊C8—731no—
1372C22⋊C8—731no—
1373#97C22×D7311yescharacteristic
1374#97C22×D7311yescharacteristic
1375C4×C8—731no—
1376C4×C8—731no—
1377C4×C8—731no—
1378C4×C8C22×D7311yescharacteristic
1379C24—1461no—
1380C24—1461no—
1381C24—1461no—
1382#41—2921no—
1383#41—2921no—
1384#41—2921no—
1385#41—2921no—
1386#41—2921no—
1387#41—2921no—
1388#41—2921no—
1389#41—2921no—
1390#41—2921no—
1391#41—5842no—
1392#41—1462no—
1393C2×Q8—2921no—
1394C2×Q8—2921no—
1395C2×Q8—731no—
1396C2×Q8—1461no—
1397C2×Q8—1461no—
1398C2×Q8D4×D7311yescharacteristic
1399C2×Q8C23×D7311yescharacteristic
1400C2×Q8C23×D7311yescharacteristic
1401C2×Q8C23×D7311yescharacteristic
1402C2×D4—21no—
1403C2×D4—21no—
1404C2×D4—2921no—
1405C2×D4—2921no—
1406C2×D4—2921no—
1407C2×D4—2921no—
1408C2×D4—5842no—
1409C2×D4—731no—
1410C2×D4—731no—
1411C2×D4—731no—
1412C2×D4—731no—
1413C2×D4—731no—
1414C2×D4—731no—
1415C2×D4—1461no—
1416C2×D4—1461no—
1417C2×D4—1461no—
1418C2×D4—1461no—
1419C2×D4—1461no—
1420C2×D4—1461no—
1421C2×D4—1461no—
1422C2×D4—1461no—
1423C2×D4—1461no—
1424C2×D4—1461no—
1425C2×D4—1461no—
1426C2×D4—1462no—
1427C2×D4—1462no—
1428C2×D4—1461no—
1429C2×D4—1461no—
1430C2×D4—1461no—
1431C2×D4—1461no—
1432C2×D4—1461no—
1433C2×D4—1461no—
1434C2×D4—1461no—
1435C2×D4—1461no—
1436C2×D4C23×D7311yescharacteristic
1437C2×D4C23×D7311yescharacteristic
1438C2×D4C23×D7311yescharacteristic
1439C22×C4—21no—
1440C22×C4—21no—
1441C22×C4—21no—
1442C22×C4—5842no—
1443C22×C4—731no—
1444C22×C4—731no—
1445C22×C4—731no—
1446C22×C4—731no—
1447C22×C4—731no—
1448C22×C4—1461no—
1449C22×C4—1461no—
1450C22×C4—1461no—
1451C22×C4—1461no—
1452C22×C4—1461no—
1453C22×C4—1461no—
1454C22×C4—1461no—
1455C22×C4—1461no—
1456C22×C4—1461no—
1457C22×C4—1461no—
1458C22×C4—1461no—
1459C22×C4—1461no—
1460C22×C4—1461no—
1461C22×C4—1461no—
1462C22×C4—1461no—
1463C22×C4—1461no—
1464Q16—41no—
1465Q16—41no—
1466Q16—2921no—
1467SD16—41no—
1468SD16—41no—
1469SD16—41no—
1470SD16—41no—
1471SD16—41no—
1472SD16—2921no—
1473SD16—2921no—
1474SD16—2921no—
1475SD16—2921no—
1476SD16—1462no—
1477SD16—1462no—
1478SD16—1462no—
1479D8—41no—
1480D8—41no—
1481D8—2921no—
1482D8—2921no—
1483D8—2921no—
1484D8—2921no—
1485D8—1462no—
1486D8—1462no—
1487D8—1462no—
1488M16—2921no—
1489M16—2921no—
1490M16—2921no—
1491M16—2921no—
1492C2×C8—2921no—
1493C2×C8—2921no—
1494C2×C8—731no—
1495C2×C8—731no—
1496C2×C8—731no—
1497C2×C8—731no—
1498C2×C8C23×D7311yescharacteristic
1499C2×C8C23×D7311yescharacteristic
1500C2×C8C23×D7311yescharacteristic
1501C2×C8C23×D7311yescharacteristic
1502C4⋊C4—21no—
1503C4⋊C4—21no—
1504C4⋊C4—21no—
1505C4⋊C4—21no—
1506C4⋊C4—21no—
1507C4⋊C4—731no—
1508C4⋊C4—731no—
1509C4⋊C4—731no—
1510C4⋊C4—731no—
1511C4⋊C4—731no—
1512C4⋊C4—731no—
1513C4⋊C4—731no—
1514C4⋊C4—731no—
1515C4⋊C4—731no—
1516C4⋊C4—731no—
1517C4⋊C4—731no—
1518C4⋊C4—1461no—
1519C4⋊C4—1461no—
1520C4⋊C4—1461no—
1521C4⋊C4—1461no—
1522C4⋊C4—1461no—
1523C4⋊C4—1461no—
1524C4⋊C4—1461no—
1525C4⋊C4—1461no—
1526C4⋊C4—1461no—
1527C4⋊C4—1461no—
1528C4⋊C4—1461no—
1529C4⋊C4—1461no—
1530C4⋊C4—1461no—
1531C4⋊C4—1461no—
1532C4⋊C4—1461no—
1533C4⋊C4—1461no—
1534C4⋊C4—1461no—
1535C4⋊C4—1461no—
1536C4⋊C4D4×D7311yescharacteristic
1537C4⋊C4D4×D7311yescharacteristic
1538C4⋊C4D4×D7311yescharacteristic
1539C4⋊C4C23×D7311yescharacteristic
1540C4⋊C4C23×D7311yescharacteristic
1541C22⋊C4—21no—
1542C22⋊C4—21no—
1543C22⋊C4—21no—
1544C22⋊C4—21no—
1545C22⋊C4—21no—
1546C22⋊C4—21no—
1547C22⋊C4—21no—
1548C22⋊C4—21no—
1549C22⋊C4—21no—
1550C22⋊C4—21no—
1551C22⋊C4—21no—
1552C22⋊C4—731no—
1553C22⋊C4—731no—
1554C22⋊C4—731no—
1555C22⋊C4—731no—
1556C22⋊C4—731no—
1557C22⋊C4—731no—
1558C22⋊C4—731no—
1559C22⋊C4—731no—
1560C22⋊C4—731no—
1561C22⋊C4—731no—
1562C22⋊C4—1461no—
1563C22⋊C4—1461no—
1564C22⋊C4—1461no—
1565C22⋊C4—1461no—
1566C22⋊C4—1461no—
1567C22⋊C4—1461no—
1568C22⋊C4—1461no—
1569C22⋊C4—1461no—
1570C22⋊C4—1461no—
1571C22⋊C4—1461no—
1572C22⋊C4—1461no—
1573C22⋊C4—1461no—
1574C22⋊C4—1461no—
1575C22⋊C4—1461no—
1576C22⋊C4—1461no—
1577C22⋊C4—1461no—
1578C22⋊C4—1461no—
1579C22⋊C4—1461no—
1580C22⋊C4—1461no—
1581C22⋊C4—1461no—
1582C22⋊C4—1461no—
1583C22⋊C4—1461no—
1584C22⋊C4—1461no—
1585C22⋊C4—1461no—
1586C22⋊C4—1461no—
1587C22⋊C4—1461no—
1588C22⋊C4—1461no—
1589C42—21no—
1590C42—21no—
1591C42—21no—
1592C42—731no—
1593C42—731no—
1594C42—731no—
1595C42—1461no—
1596C42—1461no—
1597C42—1461no—
1598C42C23×D7311yescharacteristic
1599C42C23×D7311yescharacteristic
1600C42C23×D7311yescharacteristic
1601C23—21no—
1602C23—21no—
1603C23—21no—
1604C23—2922no—
1605C23—2922no—
1606C23—2922no—
1607C23—5841no—
1608C23—5841no—
1609C23—5841no—
1610C23—5841no—
1611C23—5841no—
1612C23—5841no—
1613C23—731no—
1614C23—731no—
1615C23—731no—
1616C23—1461no—
1617C23—1461no—
1618C23—1461no—
1619Q8—21no—
1620Q8—21no—
1621Q8—21no—
1622Q8—21no—
1623Q8—21no—
1624Q8—21no—
1625Q8—41no—
1626Q8—5841no—
1627Q8—5841no—
1628Q8—1461no—
1629Q8—1461no—
1630D4—21no—
1631D4—21no—
1632D4—21no—
1633D4—21no—
1634D4—21no—
1635D4—21no—
1636D4—81no—
1637D4—81no—
1638D4—2921no—
1639D4—2921no—
1640D4—2921no—
1641D4—2922no—
1642D4—2922no—
1643D4—2922no—
1644D4—2922no—
1645D4—5841no—
1646D4—5841no—
1647D4—5841no—
1648D4—5841no—
1649D4—5841no—
1650D4—5841no—
1651D4—5841no—
1652D4—5841no—
1653D4—5841no—
1654D4—5841no—
1655D4—5841no—
1656D4—5841no—
1657D4—5841no—
1658D4—5841no—
1659D4—5841no—
1660D4—732no—
1661D4—1461no—
1662D4—1461no—
1663D4—1461no—
1664D4—1461no—
1665D4—1461no—
1666C2×C4—21no—
1667C2×C4—21no—
1668C2×C4—21no—
1669C2×C4—21no—
1670C2×C4—21no—
1671C2×C4—81no—
1672C2×C4—81no—
1673C2×C4—81no—
1674C2×C4—2921no—
1675C2×C4—2921no—
1676C2×C4—2922no—
1677C2×C4—2922no—
1678C2×C4—5841no—
1679C2×C4—5841no—
1680C2×C4—5841no—
1681C2×C4—5841no—
1682C2×C4—5841no—
1683C2×C4—5841no—
1684C2×C4—5841no—
1685C2×C4—5841no—
1686C2×C4—5841no—
1687C2×C4—5841no—
1688C2×C4—5841no—
1689C2×C4—5841no—
1690C2×C4—5841no—
1691C2×C4—5841no—
1692C2×C4—731no—
1693C2×C4—731no—
1694C2×C4—731no—
1695C2×C4—731no—
1696C2×C4—731no—
1697C2×C4—1461no—
1698C2×C4—1461no—
1699C2×C4—1461no—
1700C2×C4—1461no—
1701C2×C4—1461no—
1702C2×C4—1461no—
1703C2×C4—1461no—
1704C2×C4—1461no—
1705C2×C4—1461no—
1706C2×C4—1461no—
1707C2×C4—1461no—
1708C2×C4C2×D4×D7311yescharacteristic
1709C2×C4C2×D4×D7311yescharacteristic
1710C2×C4C2×D4×D7311yescharacteristic
1711C2×C4C2×D4×D7311yescharacteristic
1712C2×C4C2×D4×D7311yescharacteristic
1713C2×C4C2×D4×D7311yescharacteristic
1714C2×C4C24×D7311yescharacteristic
1715C8—21no—
1716C8—21no—
1717C8—21no—
1718C8—21no—
1719C8—1461no—
1720C8—1461no—
1721C8—1461no—
1722C8—1461no—
1723C22—41no—
1724C22—41no—
1725C22—41no—
1726C22—41no—
1727C22—41no—
1728C22—41no—
1729C22—41no—
1730C22—41no—
1731C22—41no—
1732C22—2921no—
1733C22—2921no—
1734C22—2921no—
1735C22—2921no—
1736C22—2921no—
1737C22—2921no—
1738C22—2921no—
1739C22—2921no—
1740C22—5844no—
1741C22—11682no—
1742C22—11682no—
1743C22—1462no—
1744C22—1461no—
1745C22—1461no—
1746C22—1461no—
1747C22—1461no—
1748C22—1461no—
1749C22—1461no—
1750C22—1461no—
1751C22—1461no—
1752C22—1461no—
1753C22C22×D4×D7311yescharacteristic
1754C4—21no—
1755C4—21no—
1756C4—21no—
1757C4—21no—
1758C4—21no—
1759C4—21no—
1760C4—41no—
1761C4—41no—
1762C4—41no—
1763C4—41no—
1764C4—41no—
1765C4—2921no—
1766C4—2921no—
1767C4—2921no—
1768C4—2921no—
1769C4—2921no—
1770C4—1461no—
1771C4—1461no—
1772C4—1461no—
1773C4—1461no—
1774C4—1461no—
1775C4H(5,𝔽2)×D7311yescharacteristic
1776C4#1798942311yescharacteristic
1777C2—81no—
1778C2—81no—
1779C2—81no—
1780C2—2922no—
1781C2—2921no—
1782C2—2921no—
1783C2—2921no—
1784C2—5841no—
1785C2—5841no—
1786C2#2262359911yescharacteristic
1787C2#2262470411yescharacteristic
1788C2#2262470911yescharacteristic
subgroupG/H
centerC22C22×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC73×#3401C2
socleC22×C73C23×D4
hypercenter#3401D73
hypocenterC73#62027
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #3401

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #22624526C2semidirect
2. #22623870C2semidirect
3. #22622939C2semidirect
4. #22622686C2semidirect
5. #22622576C2semidirect
6. #22622239C2semidirect
7. #22622206C2semidirect
8. #22622189C2semidirect
9. #22622062C2semidirect
10. #22621897C2semidirect
11. #22621788C2semidirect
12. #22621633C2semidirect
13. #22621546C2semidirect
14. #22621540C2semidirect
15. #22621537C2semidirect
16. #22621455C2semidirect
17. #22621425C2semidirect
18. #22621375C2semidirect
19. #22621339C2semidirect
20. #22621330C2semidirect
21. #22621035C2semidirect
22. #22620976C2semidirect
23. #22620902C2semidirect
24. #22620173C2semidirect
25. #22620143C2semidirect
26. #22619982C2semidirect
27. #22619473C2semidirect
28. #22619438C2semidirect
29. #22619393C2semidirect
30. #22619083C2semidirect
31. C73×#3401C2semidirect
34. C2×#14556618C22semidirect
37. C2×SD16×D73C22semidirect
40. #17989322C22semidirect
41. #17989297C22semidirect
45. #17989278C22semidirect
50. #17989249C22semidirect
53. #17989240C22semidirect
54. #17989232C22semidirect
57. #17989230C22semidirect
59. #17989222C22semidirect
60. #17989206C22semidirect
61. #17989195C22semidirect
64. #17989188C22semidirect
70. #17989162C22semidirect
71. #17989155C22semidirect
72. #17989136C22semidirect
74. #17989124C22semidirect
75. #17989116C22semidirect
79. #17989059C22semidirect
80. C4×D4×D73C22semidirect
81. #17988969C22semidirect
82. #17988969C22semidirect
84. #17988952C22semidirect
85. #17988947C22semidirect
86. #17988942C22semidirect
87. #17988941C22semidirect
88. #17988941C22semidirect
89. #17988937C22semidirect
90. #17988921C22semidirect
91. #17988921C22semidirect
92. #17988919C22semidirect
93. #17988913C22semidirect
94. #17988910C22semidirect
95. #17988907C22semidirect
96. #17988896C22semidirect
97. #17988895C22semidirect
98. #17988894C22semidirect
99. #17988894C22semidirect
100. #17988889C22semidirect
101. #17988888C22semidirect
102. #17988886C22semidirect
103. #17988885C22semidirect
104. #17988877C22semidirect
105. #17988868C22semidirect
106. #17988842C22semidirect
108. #17988839C22semidirect
109. #17988836C22semidirect
110. #17988832C22semidirect
111. #17988830C22semidirect
112. #17988830C22semidirect
113. #17988830C22semidirect
115. #17988819C22semidirect
116. #17988815C22semidirect
117. #17988813C22semidirect
118. #17988811C22semidirect
120. #17988804C22semidirect
121. #17988804C22semidirect
123. #17988803C22semidirect
124. #17988802C22semidirect
125. #17988802C22semidirect
128. #17988799C22semidirect
129. #17988799C22semidirect
130. #17988795C22semidirect
131. #17988791C22semidirect
132. #17988790C22semidirect
133. #17988790C22semidirect
134. #17988789C22semidirect
135. #17988787C22semidirect
136. #17988785C22semidirect
137. #17988784C22semidirect
140. #17988780C22semidirect
141. #17988780C22semidirect
144. #17988748C22semidirect
145. #17988748C22semidirect
146. #17988746C22semidirect
147. #17988741C22semidirect
148. #17988736C22semidirect
150. #17988731C22semidirect
151. #17988731C22semidirect
152. #17988731C22semidirect
154. #17988724C22semidirect
156. #17988722C22semidirect
158. #17988719C22semidirect
159. #17988719C22semidirect
160. Q8×#10596831C22semidirect
161. #17988700C22semidirect
162. #17988689C22semidirect
163. C4×#11924018C22semidirect
164. C4×#11924015C22semidirect
165. C4×#11924015C22semidirect
168. C4×#11924013C22semidirect
169. C4×#11924013C22semidirect
170. #17988666C22semidirect
171. #17988664C22semidirect
172. #17988664C22semidirect
173. #17988660C22semidirect
174. #17988660C22semidirect
175. #17988652C22semidirect
176. #17988649C22semidirect
177. #17988649C22semidirect
178. #17988638C22semidirect
179. #17988612C22semidirect
180. #17988612C22semidirect
181. #17988609C22semidirect
182. #17988594C22semidirect
183. #17988587C22semidirect
184. #17988587C22semidirect
185. #17988585C22semidirect
186. #17988582C22semidirect
187. #102×D73C22semidirect
188. #559×C73C22semidirect
189. #556×C73C22semidirect
190. #497×C73C22semidirect
192. #495×C73C22semidirect
193. #464×C73C22semidirect
194. #464×C73C22semidirect
195. #463×C73C22semidirect
196. #463×C73C22semidirect
197. #461×C73C22semidirect
198. #460×C73C22semidirect
199. #446×C73C22semidirect
200. #442×C73C22semidirect
201. #441×C73C22semidirect
202. C4×SD16×C73C22semidirect
897. #3401D73semidirect
926. C73#62027semidirect
936. #559C2×D73semidirect
937. #556C2×D73semidirect
978. #497C2×D73semidirect
982. #495C2×D73semidirect
1019. #464C2×D73semidirect
1020. #464C2×D73semidirect
1032. #463C2×D73semidirect
1033. #463C2×D73semidirect
1039. #461C2×D73semidirect
1043. #460C2×D73semidirect
1066. #446C2×D73semidirect
1069. #442C2×D73semidirect
1070. #441C2×D73semidirect
1075. C4×SD16C2×D73semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#226245262
#226238702
#226229392
#226226862
#226225762
#226222392
#226222062
#226221892
#226220622
#226218972
#226217882
#226216332
#226215462
#226215402
#226215372
#226214552
#226214252
#226213752
#226213392
#226213302
#226210352
#226209762
#226209022
#226201732
#226201432
#226199822
#226194732
#226194382
#226193932
#226190832
C73×#34012
#6202773