Finite Group Databasebeta

← #33969108

Subgroups — #33969108

Order 18688.

1890 conjugacy classes of subgroups.

The subgroup lattice has 1760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22624042C211yesmaximal, characteristic, complemented
2#22623961C211yesmaximal, characteristic, complemented
3#22622972C211yesmaximal, characteristic, complemented
4#22622874C211yesmaximal, characteristic, complemented
5#22622687C211yesmaximal, characteristic, complemented
6#22622655C211yesmaximal, characteristic, complemented
7#22622488C211yesmaximal, characteristic, complemented
8#22622435C211yesmaximal, characteristic, complemented
9#22622429C211yesmaximal, characteristic, complemented
10#22622188C211yesmaximal, characteristic, complemented
11#22622171C211yesmaximal, characteristic, complemented
12#22622110C211yesmaximal, characteristic, complemented
13#22622075C211yesmaximal, characteristic, complemented
14#22621959C211yesmaximal, characteristic, complemented
15#22621934C211yesmaximal, characteristic, complemented
16#22621546C211yesmaximal, characteristic, complemented
17#22621419C211yesmaximal, characteristic, complemented
18#22621419C211yesmaximal, characteristic, complemented
19#22620612C211yesmaximal, characteristic, complemented
20#22620575C211yesmaximal, characteristic, complemented
21#22620522C211yesmaximal, characteristic, complemented
22#22620175C211yesmaximal, characteristic, complemented
23#22620136C211yesmaximal, characteristic, complemented
24#22620121C211yesmaximal, characteristic, complemented
25#22620080C211yesmaximal, characteristic, complemented
26#22620073C211yesmaximal, characteristic, complemented
27#22618914C211yesmaximal, characteristic, complemented
28#22618790C211yesmaximal, characteristic, complemented
29#22618762C211yesmaximal, characteristic, complemented
30C4×#14556618C211yesmaximal, characteristic, complemented
31C73×#3126C211yesmaximal, characteristic, complemented
32C2×#14556618C2211yescharacteristic
33C2×#14556618C2211yescharacteristic
34C22×#11924015C2211yescharacteristic
35#17989322—21no—
36#17989322C2211yescharacteristic, complemented
37#17989313C2211yescharacteristic, complemented
38#17989301C2211yescharacteristic
39#17989300—21no—
40#17989300C2211yescharacteristic, complemented
41#17989293C2211yescharacteristic
42#17989290C2211yescharacteristic
43#17989284C2211yescharacteristic
44#17989282—21no—
45#17989281—21no—
46#17989281C2211yescharacteristic, complemented
47#17989278—21no—
48#17989278C2211yescharacteristic, complemented
49#17989259C2211yescharacteristic, complemented
50#17989257C2211yescharacteristic
51#17989248C2211yescharacteristic, complemented
52#17989248C2211yescharacteristic, complemented
53#17989234—21no—
54#17989229—21no—
55#17989226—21no—
56#17989222C2211yescharacteristic
57#17989221C2211yescharacteristic
58#17989221C2211yescharacteristic
59#17989209—21no—
60#17989209C2211yescharacteristic, complemented
61#17989192—21no—
62#17989192C2211yescharacteristic, complemented
63#17989188C2211yescharacteristic
64#17989173—21no—
65#17989169—21no—
66#17989134C2211yescharacteristic
67#17989124—21no—
68#17989124C2211yescharacteristic, complemented
69#17989115—21no—
70#17989115C2211yescharacteristic
71#17989095—21no—
72#121×D73—21no—
73#17989069C2211yescharacteristic, complemented
74#17989061C2211yescharacteristic
75#17989059C2211yescharacteristic
76C4×#11924029C2211yescharacteristic, complemented
77C4×D4×D73C2211yescharacteristic
78#17988995C2211yescharacteristic, complemented
79#17988994C2211yescharacteristic, complemented
80#17988986C2211yescharacteristic, complemented
81#17988973C2211yescharacteristic, complemented
82#17988973C2211yescharacteristic, complemented
83#17988963C2211yescharacteristic, complemented
84#17988953C2211yescharacteristic, complemented
85#17988951C2211yescharacteristic, complemented
86#17988950C2211yescharacteristic, complemented
87#17988948C2211yescharacteristic, complemented
88#17988943C2211yescharacteristic, complemented
89#17988932C2211yescharacteristic, complemented
90#17988927C2211yescharacteristic, complemented
91#17988916C2211yescharacteristic, complemented
92#17988914C2211yescharacteristic, complemented
93#17988913C2211yescharacteristic, complemented
94#17988912C2211yescharacteristic, complemented
95#17988912C2211yescharacteristic, complemented
96#17988910C2211yescharacteristic, complemented
97#17988907C2211yescharacteristic, complemented
98#17988902C2211yescharacteristic, complemented
99#17988899C2211yescharacteristic, complemented
100#17988896C2211yescharacteristic, complemented
101#17988890C2211yescharacteristic
102#17988889C2211yescharacteristic, complemented
103#17988888C2211yescharacteristic
104#17988888C2211yescharacteristic, complemented
105#17988886C2211yescharacteristic, complemented
106#17988876C2211yescharacteristic
107#17988870C2211yescharacteristic, complemented
108#17988866C2211yescharacteristic, complemented
109#17988865C2211yescharacteristic, complemented
110#17988841C2211yescharacteristic, complemented
111#17988839C2211yescharacteristic, complemented
112#17988839C2211yescharacteristic, complemented
113#17988838C2211yescharacteristic, complemented
114#17988838C2211yescharacteristic, complemented
115#17988836C2211yescharacteristic, complemented
116#17988836C2211yescharacteristic, complemented
117#17988830C2211yescharacteristic, complemented
118#17988824C2211yescharacteristic, complemented
119#17988821C2211yescharacteristic, complemented
120#17988821C2211yescharacteristic, complemented
121#17988813C2211yescharacteristic, complemented
122#17988805C2211yescharacteristic
123#17988805C2211yescharacteristic
124#17988804C2211yescharacteristic, complemented
125#17988804C2211yescharacteristic, complemented
126#17988785C2211yescharacteristic, complemented
127#17988785C2211yescharacteristic, complemented
128#17988783C2211yescharacteristic
129#17988783C2211yescharacteristic, complemented
130#17988781C2211yescharacteristic, complemented
131#17988781C2211yescharacteristic, complemented
132#17988736C2211yescharacteristic
133#17988736C2211yescharacteristic
134#17988735C2211yescharacteristic, complemented
135#17988735C2211yescharacteristic, complemented
136#17988731C2211yescharacteristic, complemented
137#17988731C2211yescharacteristic, complemented
138#17988723C2211yescharacteristic
139#17988723C2211yescharacteristic
140#17988722C2211yescharacteristic
141#17988722C2211yescharacteristic
142#17988716C2211yescharacteristic, complemented
143#17988714C2211yescharacteristic, complemented
144#17988700C2211yescharacteristic
145#17988700C2211yescharacteristic, complemented
146#17988698C2211yescharacteristic
147#17988697C2211yescharacteristic, complemented
148#17988697C2211yescharacteristic, complemented
149#17988696C2211yescharacteristic, complemented
150#17988696C2211yescharacteristic, complemented
151#17988690C2211yescharacteristic
152#17988690C2211yescharacteristic
153#17988688C2211yescharacteristic, complemented
154#17988685C2211yescharacteristic
155#17988685C2211yescharacteristic
156#17988685C2211yescharacteristic, complemented
157#17988685C2211yescharacteristic, complemented
158SD16×Dic73C2211yescharacteristic, complemented
159C4×#11924015C2211yescharacteristic
160C4×#11924015C2211yescharacteristic
161C4×#11924015C2211yescharacteristic, complemented
162C4×#11924015C2211yescharacteristic, complemented
163C4×D584C2211yescharacteristic
164C4×D584C2211yescharacteristic, complemented
165#17988669C2211yescharacteristic
166C4×#11924013C2211yescharacteristic, complemented
167C4×#11924013C2211yescharacteristic, complemented
168#17988664C2211yescharacteristic, complemented
169#17988662C2211yescharacteristic, complemented
170#17988661C2211yescharacteristic, complemented
171#17988657C2211yescharacteristic, complemented
172#17988655C2211yescharacteristic, complemented
173#17988655C2211yescharacteristic, complemented
174#17988646C2211yescharacteristic, complemented
175#17988642C2211yescharacteristic, complemented
176#17988628C2211yescharacteristic, complemented
177#17988626C2211yescharacteristic, complemented
178#17988623C2211yescharacteristic, complemented
179#17988596C2211yescharacteristic, complemented
180#17988591C2211yescharacteristic
181#17988590C2211yescharacteristic
182#17988587C2211yescharacteristic, complemented
183#17988582C2211yescharacteristic, complemented
184#102×D73C2211yescharacteristic
185#17988544C2211yescharacteristic, complemented
186#17988543C2211yescharacteristic, complemented
187C4×#11924011C2211yescharacteristic, complemented
188#540×C73C2211yescharacteristic
189#519×C73C2211yescharacteristic, complemented
190#482×C73C2211yescharacteristic, complemented
191#482×C73C2211yescharacteristic, complemented
192#479×C73C2211yescharacteristic, complemented
193#479×C73C2211yescharacteristic, complemented
194#460×C73C2211yescharacteristic, complemented
195#460×C73C2211yescharacteristic, complemented
196#448×C73C2211yescharacteristic, complemented
197#448×C73C2211yescharacteristic, complemented
198#440×C73C2211yescharacteristic, complemented
199#440×C73C2211yescharacteristic, complemented
200C4×SD16×C73C2211yescharacteristic, complemented
201C4×SD16×C73C2211yescharacteristic, complemented
202#433×C73C2211yescharacteristic, complemented
203C2×#11924029C2311yescharacteristic
204C2×#11924029C2311yescharacteristic
205C2×#11924028—21no—
206C2×#11924027—21no—
207C22×D292C2311yescharacteristic
208C2×D4×D73—21no—
209C2×D4×D73—21no—
210C2×D4×D73—21no—
211C2×D4×D73C2311yescharacteristic
212C2×D4×D73C2311yescharacteristic
213C22×C4×D73—21no—
214#14556618—24no—
215#14556618—24no—
216C2×#11924015—24no—
217C2×#11924015C2311yescharacteristic
218C2×#11924015C2311yescharacteristic
219C2×#11924015C2311yescharacteristic
220C2×#11924015C2311yescharacteristic
221C2×D584C2311yescharacteristic
222C2×D584C2311yescharacteristic
223C2×D584C2311yescharacteristic
224C2×D584C2311yescharacteristic
225C2×#11924013C2311yescharacteristic
226C2×#11924013C2311yescharacteristic
227C2×#11924013C2311yescharacteristic
228C2×#11924013C2311yescharacteristic
229C2×#11924012C2311yescharacteristic
230C2×#11924011C2311yescharacteristic
231C2×#11924011C2311yescharacteristic
232C2×#11924011C2311yescharacteristic
233C22×#10596831C2311yescharacteristic
234C2×C8×D73C2311yescharacteristic
235#14556590—21no—
236#14556590C2311yescharacteristic
237#14556590C2311yescharacteristic
238#14556588—21no—
239#14556588C2311yescharacteristic
240#14556587C2311yescharacteristic
241#14556587C2311yescharacteristic
242#14556586—21no—
243#14556586—21no—
244#14556586D411yescharacteristic
245#14556585—21no—
246#14556585—21no—
247#14556585—21no—
248#14556584—21no—
249#14556584D411yescharacteristic
250#14556583—21no—
251#14556583C2311yescharacteristic
252#14556582—21no—
253#14556582C2311yescharacteristic
254#14556582C2311yescharacteristic
255#14556581—21no—
256#14556581D411yescharacteristic
257#14556580—21no—
258#14556580—21no—
259#14556580C2311yescharacteristic
260#14556580C2311yescharacteristic
261#14556579—21no—
262#14556579—21no—
263#14556579—21no—
264#14556578—21no—
265#14556577—21no—
266#14556577—21no—
267#14556577—21no—
268#14556577D411yescharacteristic
269#14556576—21no—
270#14556576—21no—
271#14556576—21no—
272#14556576—21no—
273#14556576—21no—
274#14556576—21no—
275#14556576—21no—
276#14556576—21no—
277#14556576D411yescharacteristic
278#14556574—21no—
279#14556573—21no—
280#14556573—21no—
281#14556573D411yescharacteristic
282#14556572—21no—
283#14556571—21no—
284#14556569—21no—
285#14556569—21no—
286#14556569—21no—
287#14556569D411yescharacteristic
288#14556567—21no—
289#14556567—21no—
290#14556567C2311yescharacteristic
291#14556567C2311yescharacteristic
292#14556566—21no—
293#14556566—21no—
294#14556566—21no—
295#14556566C2311yescharacteristic
296#14556566C2311yescharacteristic
297#14556566C2311yescharacteristic
298#14556566C2311yescharacteristic
299#14556565—21no—
300#14556565—21no—
301#14556565—21no—
302#14556565C2311yescharacteristic
303#14556565C2311yescharacteristic
304#14556564—21no—
305#14556564—21no—
306#14556564—21no—
307#14556564—21no—
308#14556564—21no—
309#14556564—21no—
310#14556564—21no—
311#14556564—21no—
312#14556564D411yescharacteristic
313#14556563—21no—
314#14556563—21no—
315#14556563—21no—
316#14556562—21no—
317#14556562—21no—
318#14556562—21no—
319#14556562C2311yescharacteristic
320#14556562C2311yescharacteristic
321#14556561—21no—
322#14556561—21no—
323#14556559—21no—
324#14556559—21no—
325#14556559—21no—
326#14556559—21no—
327Q8×Dic73C2311yescharacteristic
328Q8×Dic73C2311yescharacteristic
329C4×Dic146—21no—
330C4×Dic146C2311yescharacteristic
331C4×D292—21no—
332C4×D292—21no—
333C4×D292—21no—
334C4×D292—21no—
335C4×D292—21no—
336C4×D292—21no—
337C4×D292C2311yescharacteristic
338C4×D292C2311yescharacteristic
339C4×D292C2311yescharacteristic
340C4×D292C2311yescharacteristic
341C4×D292C2311yescharacteristic
342C4×D292C2311yescharacteristic
343C4×D292C2311yescharacteristic
344D4×Dic73C2311yescharacteristic
345D4×Dic73C2311yescharacteristic
346#14556553—21no—
347#14556553—21no—
348#14556553—21no—
349#14556553—21no—
350#14556553—21no—
351#14556553C2311yescharacteristic
352#14556553C2311yescharacteristic
353#14556553C2311yescharacteristic
354#14556553C2311yescharacteristic
355C4×C22⋊D73—21no—
356C4×C22⋊D73—21no—
357C4×C22⋊D73—21no—
358C4×C22⋊D73—21no—
359C4×C22⋊D73—21no—
360C4×C22⋊D73C2311yescharacteristic
361C4×C22⋊D73C2311yescharacteristic
362#14556551—21no—
363#14556551—21no—
364#14556551—21no—
365#14556550C2311yescharacteristic
366#14556549—21no—
367#14556549C2311yescharacteristic
368#14556549C2311yescharacteristic
369#14556548—21no—
370#14556548—21no—
371#14556548—21no—
372#14556548—21no—
373#14556548C2311yescharacteristic
374#14556547—21no—
375C4⋊C4×D73—21no—
376C4⋊C4×D73—21no—
377C4⋊C4×D73C2311yescharacteristic
378C4⋊C4×D73C2311yescharacteristic
379C2×#11924005—21no—
380C22⋊C4×D73—21no—
381C22⋊C4×D73—21no—
382C22⋊C4×D73—21no—
383C22⋊C4×D73—21no—
384C42×D73—21no—
385C42×D73C2311yescharacteristic
386#14556525C2311yescharacteristic
387#14556525C2311yescharacteristic
388#14556524C2311yescharacteristic
389#14556524C2311yescharacteristic
390#14556524C2311yescharacteristic
391#14556524C2311yescharacteristic
392#14556523C2311yescharacteristic
393#14556523C2311yescharacteristic
394#14556522C2311yescharacteristic
395#14556522C2311yescharacteristic
396#14556522C2311yescharacteristic
397#14556522C2311yescharacteristic
398#14556520C2311yescharacteristic
399#14556520C2311yescharacteristic
400#14556520C2311yescharacteristic
401#14556520C2311yescharacteristic
402#14556515C2311yescharacteristic
403#14556515C2311yescharacteristic
404#14556515C2311yescharacteristic
405#14556515C2311yescharacteristic
406#14556513C2311yescharacteristic
407#14556513C2311yescharacteristic
408#14556513C2311yescharacteristic
409#14556513C2311yescharacteristic
410#14556513C2311yescharacteristic
411#14556513C2311yescharacteristic
412#14556513C2311yescharacteristic
413#14556513C2311yescharacteristic
414#14556512C2311yescharacteristic
415#14556512C2311yescharacteristic
416#14556512C2311yescharacteristic
417#14556512C2311yescharacteristic
418#14556511C2311yescharacteristic
419#14556511C2311yescharacteristic
420#14556511C2311yescharacteristic
421#14556511C2311yescharacteristic
422#14556511C2311yescharacteristic
423#14556511C2311yescharacteristic
424#14556511C2311yescharacteristic
425#14556511C2311yescharacteristic
426#14556503C2311yescharacteristic
427#14556503C2311yescharacteristic
428#14556503C2311yescharacteristic
429#14556503C2311yescharacteristic
430#14556502C2311yescharacteristic
431#14556502C2311yescharacteristic
432#14556501C2311yescharacteristic
433#14556501C2311yescharacteristic
434#14556501C2311yescharacteristic
435C4×#10596831C2311yescharacteristic
436C4×#10596831C2311yescharacteristic
437C8×Dic73C2311yescharacteristic
438C22×Q8×C73C2311yescharacteristic
439C2×SD16×C73C2311yescharacteristic
440C2×SD16×C73C2311yescharacteristic
441C2×SD16×C73C2311yescharacteristic
442C2×SD16×C73C2311yescharacteristic
443#127×C73C2311yescharacteristic
444#125×C73C2311yescharacteristic
445#123×C73—21no—
446#123×C73—21no—
447#121×C73—21no—
448#121×C73—21no—
449#121×C73C2311yescharacteristic
450#121×C73C2311yescharacteristic
451C4×Q8×C73—21no—
452C4×Q8×C73—21no—
453C4×Q8×C73C2311yescharacteristic
454C4×Q8×C73C2311yescharacteristic
455C4×Q8×C73C2311yescharacteristic
456C4×Q8×C73C2311yescharacteristic
457C4×D4×C73C2311yescharacteristic
458C4×D4×C73C2311yescharacteristic
459#117×C73—21no—
460#117×C73—21no—
461#117×C73C2311yescharacteristic
462#117×C73C2311yescharacteristic
463#107×C73C2311yescharacteristic
464#107×C73C2311yescharacteristic
465#106×C73C2311yescharacteristic
466#106×C73C2311yescharacteristic
467C4⋊C8×C73C2311yescharacteristic
468C4⋊C8×C73C2311yescharacteristic
469#103×C73C2311yescharacteristic
470#103×C73C2311yescharacteristic
471#103×C73C2311yescharacteristic
472#103×C73C2311yescharacteristic
473#102×C73C2311yescharacteristic
474#102×C73C2311yescharacteristic
475#102×C73C2311yescharacteristic
476#102×C73C2311yescharacteristic
477C22⋊C8×C73C2311yescharacteristic
478C22⋊C8×C73C2311yescharacteristic
479#97×C73C2311yescharacteristic
480C4×C8×C73C2311yescharacteristic
481C23×D73—21no—
482C23×D73—21no—
483C23×D73—21no—
484#11924029—22no—
485#11924029—22no—
486#11924029—41no—
487#11924029—41no—
488#11924028—82no—
489#11924027—82no—
490C2×Dic146—21no—
491C2×Dic146—21no—
492C2×Dic146C2×D411yescharacteristic
493C2×D292—22no—
494C2×D292—21no—
495C2×D292—21no—
496C2×D292—21no—
497C2×D292—21no—
498C2×D292—21no—
499C2×D292—21no—
500C2×D292—21no—
501C2×D292—21no—
502C2×D292—21no—
503C2×D292—41no—
504C2×D292C2×D411yescharacteristic
505C2×D292C2411yescharacteristic
506C2×D292C2411yescharacteristic
507C2×D292C2411yescharacteristic
508C2×D292C2411yescharacteristic
509C2×C22⋊D73—21no—
510C2×C22⋊D73—21no—
511C2×C22⋊D73—21no—
512C2×C22⋊D73—21no—
513C2×C22⋊D73—21no—
514C2×C22⋊D73—21no—
515C2×C22⋊D73—21no—
516C2×C22⋊D73—21no—
517C2×C22⋊D73—21no—
518C2×C22⋊D73—21no—
519C2×C22⋊D73C2×D411yescharacteristic
520C2×C22⋊D73C2×D411yescharacteristic
521D4×D73—22no—
522D4×D73—22no—
523D4×D73—41no—
524D4×D73—41no—
525D4×D73—82no—
526D4×D73—82no—
527D4×D73—82no—
528C22×Dic73—21no—
529C22×Dic73—21no—
530C2×C4×D73—21no—
531C2×C4×D73—21no—
532C2×C4×D73—21no—
533C2×C4×D73—21no—
534C2×C4×D73—21no—
535C2×C4×D73—21no—
536C2×C4×D73—21no—
537C2×C4×D73—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—82no—
545C2×C4×D73C2×D411yescharacteristic
546C2×C4×D73C2×D411yescharacteristic
547C2×C4×D73C2411yescharacteristic
548C2×C4×D73C2411yescharacteristic
549#11924015—22no—
550#11924015—22no—
551#11924015—22no—
552#11924015#4114yescomplemented
553D584—22no—
554D584—22no—
555D584—41no—
556D584—41no—
557#11924013—22no—
558#11924013—22no—
559#11924013—41no—
560#11924013—41no—
561#11924012—41no—
562#11924011—22no—
563#11924011—22no—
564#11924011—41no—
565C2×#10596831—22no—
566C2×#10596831C2411yescharacteristic
567C2×#10596831C2411yescharacteristic
568C2×#10596831C2411yescharacteristic
569C2×#10596831C2411yescharacteristic
570C8×D73—41no—
571C4⋊Dic73—21no—
572C4⋊Dic73—21no—
573C4⋊Dic73—21no—
574C4⋊Dic73—21no—
575C4⋊Dic73C2×D411yescharacteristic
576C4⋊Dic73C2×D411yescharacteristic
577C4⋊Dic73C2411yescharacteristic
578C4⋊Dic73C2411yescharacteristic
579C4⋊Dic73C2411yescharacteristic
580C4⋊Dic73C2411yescharacteristic
581#11924007—21no—
582#11924007—21no—
583#11924007—21no—
584#11924007—21no—
585#11924007—21no—
586#11924007—21no—
587#11924007—21no—
588#11924007—21no—
589#11924007—21no—
590#11924007—21no—
591#11924007C2×D411yescharacteristic
592#11924007C2×D411yescharacteristic
593#11924007C2×D411yescharacteristic
594#11924007C2×D411yescharacteristic
595#11924007C2×D411yescharacteristic
596#11924007C2×D411yescharacteristic
597C22⋊Dic73—21no—
598C22⋊Dic73—21no—
599C22⋊Dic73—21no—
600C22⋊Dic73—21no—
601C22⋊Dic73—21no—
602C22⋊Dic73C2×D411yescharacteristic
603C22⋊Dic73C2×D411yescharacteristic
604#11924005—21no—
605#11924005—21no—
606#11924005—21no—
607#11924005—21no—
608#11924005—21no—
609#11924005—21no—
610#11924005—21no—
611#11924005—21no—
612#11924005—21no—
613#11924005—21no—
614#11924005—21no—
615#11924005—21no—
616#11924005—21no—
617#11924005—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#11924005C2×D411yescharacteristic
629#11924005C2×D411yescharacteristic
630#11924005C2×D411yescharacteristic
631#11924005C2×D411yescharacteristic
632#11924005C2×D411yescharacteristic
633#11924005C2×D411yescharacteristic
634C4×Dic73—21no—
635C4×Dic73—21no—
636C4×Dic73—21no—
637C4×Dic73—21no—
638C4×Dic73—21no—
639C4×Dic73C2×D411yescharacteristic
640C4×Dic73C2×D411yescharacteristic
641C4×Dic73C2411yescharacteristic
642C4×Dic73C2411yescharacteristic
643C2×Q8×C73—21no—
644C2×Q8×C73—22no—
645C2×Q8×C73—41no—
646C2×Q8×C73C2411yescharacteristic
647C2×Q8×C73C2411yescharacteristic
648C2×D4×C73—21no—
649C2×D4×C73—21no—
650C2×D4×C73—21no—
651C2×D4×C73—21no—
652C2×D4×C73C2411yescharacteristic
653C2×D4×C73C2411yescharacteristic
654C22×C4×C73—21no—
655C22×C4×C73—21no—
656C22×C4×C73—21no—
657C22×C4×C73C2411yescharacteristic
658SD16×C73—22no—
659SD16×C73—22no—
660SD16×C73—41no—
661SD16×C73—41no—
662C2×C8×C73C2411yescharacteristic
663C2×C8×C73C2411yescharacteristic
664C2×C8×C73C2411yescharacteristic
665C2×C8×C73C2411yescharacteristic
666C4⋊C4×C73—21no—
667C4⋊C4×C73—21no—
668C4⋊C4×C73—21no—
669C4⋊C4×C73—21no—
670C4⋊C4×C73—21no—
671C4⋊C4×C73—21no—
672C4⋊C4×C73C2×D411yescharacteristic
673C4⋊C4×C73C2×D411yescharacteristic
674C4⋊C4×C73C2411yescharacteristic
675C4⋊C4×C73C2411yescharacteristic
676C4⋊C4×C73C2411yescharacteristic
677C4⋊C4×C73C2411yescharacteristic
678C22⋊C4×C73—21no—
679C22⋊C4×C73—21no—
680C22⋊C4×C73—21no—
681C22⋊C4×C73—21no—
682C22⋊C4×C73—21no—
683C22⋊C4×C73C2×D411yescharacteristic
684C22⋊C4×C73C2×D411yescharacteristic
685C42×C73—21no—
686C42×C73—21no—
687C42×C73—21no—
688C42×C73—21no—
689C42×C73—21no—
690C42×C73C2411yescharacteristic
691C42×C73C2411yescharacteristic
692C23×C73—21no—
693C23×C73—21no—
694C23×C73C22×D411yescharacteristic
695C22×D73—21no—
696C22×D73—21no—
697C22×D73—21no—
698C22×D73—21no—
699C22×D73—42no—
700C22×D73—42no—
701C22×D73—42no—
702C22×D73—42no—
703C22×D73—81no—
704C22×D73—81no—
705C22×D73—81no—
706C22×D73—81no—
707C22×D73—81no—
708C22×D73C22×D411yescharacteristic
709C22×D73C22×D411yescharacteristic
710Q8×C73—21no—
711Q8×C73—21no—
712Q8×C73—21no—
713Q8×C73—42no—
714Q8×C73C2×#4112yes—
715D4×C73—21no—
716D4×C73—21no—
717D4×C73—21no—
718D4×C73—21no—
719D4×C73—81no—
720D4×C73—81no—
721D4×C73—81no—
722D4×C73—81no—
723C2×C4×C73—21no—
724C2×C4×C73—21no—
725C2×C4×C73—21no—
726C2×C4×C73—21no—
727C2×C4×C73—21no—
728C2×C4×C73—21no—
729C2×C4×C73—21no—
730C2×C4×C73—21no—
731C2×C4×C73—42no—
732C2×C4×C73—81no—
733C2×C4×C73—81no—
734C2×C4×C73C22×D411yescharacteristic
735C2×C4×C73C22×D411yescharacteristic
736C2×C4×C73C22×D411yescharacteristic
737C2×C4×C73C22×D411yescharacteristic
738C2×C4×C73C22×D411yescharacteristic
739C2×C4×C73C2511yescharacteristic
740C22⋊D73—41no—
741C22⋊D73—41no—
742C22⋊D73—42no—
743C22⋊D73—42no—
744C22⋊D73—42no—
745C22⋊D73—42no—
746C22⋊D73—81no—
747C22⋊D73—81no—
748C22⋊D73—81no—
749C22⋊D73—81no—
750C22⋊D73—81no—
751C22⋊D73—81no—
752C2×Dic73—21no—
753C2×Dic73—21no—
754C2×Dic73—21no—
755C2×Dic73—21no—
756C2×Dic73—42no—
757C2×Dic73—81no—
758C2×Dic73C22×D411yescharacteristic
759C2×Dic73C22×D411yescharacteristic
760C2×Dic73C22×D411yescharacteristic
761C2×Dic73C22×D411yescharacteristic
762C2×Dic73C22×D411yescharacteristic
763C2×Dic73C22×D411yescharacteristic
764D292—21no—
765D292—21no—
766D292—21no—
767D292—21no—
768D292—21no—
769D292—21no—
770D292—21no—
771D292—41no—
772D292—42no—
773D292—42no—
774D292—42no—
775D292—42no—
776D292—81no—
777D292—81no—
778D292—81no—
779D292—81no—
780D292—81no—
781D292C2×#4112yes—
782C4×D73—21no—
783C4×D73—21no—
784C4×D73—21no—
785C4×D73—21no—
786C4×D73—41no—
787C4×D73—41no—
788C4×D73—42no—
789C4×D73—42no—
790C4×D73—42no—
791C4×D73—81no—
792C4×D73—81no—
793C4×D73—81no—
794C4×D73—81no—
795C4×D73—81no—
796C4×D73—81no—
797C4×D73—81no—
798C4×D73—81no—
799C4×D73—81no—
800C4×D73—81no—
801C4×D73—81no—
802Dic146—41no—
803Dic146—81no—
804Dic146—81no—
805C8×C73—21no—
806C8×C73—21no—
807C8×C73—21no—
808C8×C73—21no—
809#10596831—21no—
810#10596831—21no—
811#10596831—21no—
812#10596831C2×#4112yes—
813C22×C73—21no—
814C22×C73—21no—
815C22×C73—21no—
816C22×C73—41no—
817C22×C73—41no—
818C22×C73—41no—
819C22×C73—41no—
820C22×C73—41no—
821C22×C73—41no—
822C22×C73C23×D411yescharacteristic
823C2×D73—21no—
824C2×D73—21no—
825C2×D73—21no—
826C2×D73—21no—
827C2×D73—21no—
828C2×D73—21no—
829C2×D73—22no—
830C2×D73—41no—
831C2×D73—41no—
832C2×D73—41no—
833C2×D73—41no—
834C2×D73—41no—
835C2×D73—41no—
836C2×D73—41no—
837C2×D73—41no—
838C2×D73—41no—
839C2×D73—41no—
840C2×D73—41no—
841C2×D73—84no—
842C2×D73—162no—
843C2×D73—162no—
844C4×C73—21no—
845C4×C73—21no—
846C4×C73—21no—
847C4×C73—21no—
848C4×C73—22no—
849C4×C73—21no—
850C4×C73—41no—
851C4×C73—41no—
852C4×C73—41no—
853C4×C73—41no—
854C4×C73—41no—
855C4×C73C22×#4111yescharacteristic
856C4×C73#58511yescharacteristic
857Dic73—21no—
858Dic73—21no—
859Dic73—21no—
860Dic73—21no—
861Dic73—21no—
862Dic73—21no—
863Dic73—41no—
864Dic73—41no—
865Dic73—41no—
866Dic73—41no—
867#61504—731nomaximal, Sylow
868C2×C73—41no—
869C2×C73—81no—
870C2×C73—81no—
871C2×C73D4×#4111yescharacteristic
872C2×C73#358511yescharacteristic
873C2×C73#358511yescharacteristic
874D73—41no—
875D73—41no—
876D73—42no—
877D73—81no—
878D73—81no—
879D73—81no—
880#3524—731no—
881#3519—731no—
882#3399—731no—
883#3388—731no—
884#3370—731no—
885#3368—731no—
886#3351—731no—
887#3347—731no—
888#3347—731no—
889#3326—731no—
890#3325—731no—
891#3321—731no—
892#3318—731no—
893#3310—731no—
894#3309—731no—
895#3274—731no—
896#3265—731no—
897#3265—731no—
898#3179—731no—
899#3176—731no—
900#3171—731no—
901#3126D7311yescharacteristic, complemented
902#3122—731no—
903#3119—731no—
904#3118—731no—
905#3115—731no—
906#3114—731no—
907#2967—731no—
908#2949—731no—
909#2946—731no—
910C4×AGL(1,ℤ/8)—731no—
911C73#6150411yescharacteristic, complemented, Sylow
912C2×AGL(1,ℤ/8)—731no—
913C2×AGL(1,ℤ/8)—731no—
914C22×SD16—731no—
915#559—731no—
916#559—1461no—
917#557—731no—
918#555—731no—
919#555—731no—
920#555—1461no—
921#554—731no—
922#553—731no—
923#553—731no—
924#553—731no—
925#553—1461no—
926#553—1461no—
927#552—731no—
928#552—1461no—
929#550—731no—
930#550—731no—
931#548—731no—
932#548—731no—
933#546—1461no—
934#546—1461no—
935#546—1461no—
936D42—731no—
937D42—731no—
938D42—731no—
939#542—731no—
940#542—1461no—
941#540—731no—
942#540—731no—
943#540—1461no—
944#540C2×D7311yescharacteristic
945#538—1461no—
946#538—1461no—
947#532—731no—
948#529—731no—
949#529—731no—
950#529—1461no—
951#529—1461no—
952#525—1461no—
953C2×#121—1461no—
954#520—731no—
955#519C2×D7311yescharacteristic, complemented
956#518—731no—
957#518—731no—
958C4×#41—731no—
959C2×C4×D4—731no—
960#501—731no—
961#501—731no—
962#499—731no—
963#496—731no—
964#496—731no—
965#493—731no—
966#490—731no—
967#490—731no—
968#490—731no—
969#489—731no—
970#488—731no—
971#486—731no—
972#485—731no—
973#483—731no—
974#482—731no—
975#482—731no—
976#482—731no—
977#482—731no—
978#482—731no—
979#482C2×D7311yescharacteristic, complemented
980#482C2×D7311yescharacteristic, complemented
981#481—731no—
982#480—731no—
983#480—731no—
984#479—731no—
985#479C2×D7311yescharacteristic, complemented
986#479C2×D7311yescharacteristic, complemented
987#478—731no—
988#478—731no—
989#478—731no—
990#478—731no—
991#478—731no—
992#476—731no—
993#475—731no—
994#474—731no—
995#474—731no—
996#469—731no—
997#469—731no—
998#469—731no—
999#469—731no—
1000#469—731no—
1001#468—731no—
1002#468—731no—
1003#468—731no—
1004#466—731no—
1005#466—731no—
1006#466—731no—
1007#465—731no—
1008#463—731no—
1009#463—731no—
1010#463—731no—
1011#463—731no—
1012#460—731no—
1013#460—731no—
1014#460C2×D7311yescharacteristic, complemented
1015#460C2×D7311yescharacteristic, complemented
1016#459—731no—
1017#459—731no—
1018#459—731no—
1019#459—731no—
1020#450—731no—
1021#450—731no—
1022#449—731no—
1023#449—731no—
1024#449—731no—
1025#449—731no—
1026#448C2×D7311yescharacteristic, complemented
1027#448C2×D7311yescharacteristic, complemented
1028#447—731no—
1029#447—731no—
1030#447—731no—
1031#447—731no—
1032#446—731no—
1033#446—731no—
1034#442—731no—
1035#442—731no—
1036#442—731no—
1037#442—731no—
1038#442—731no—
1039#442—731no—
1040#442—731no—
1041#440—731no—
1042#440—731no—
1043#440—731no—
1044#440—731no—
1045#440—731no—
1046#440—731no—
1047#440—731no—
1048#440C2×D7311yescharacteristic, complemented
1049#440C2×D7311yescharacteristic, complemented
1050C4×SD16—731no—
1051C4×SD16—731no—
1052C4×SD16—731no—
1053C4×SD16—731no—
1054C4×SD16—731no—
1055C4×SD16C2×D7311yescharacteristic, complemented
1056C4×SD16C2×D7311yescharacteristic, complemented
1057C4×D8—731no—
1058C4×D8—731no—
1059C4×D8—731no—
1060C4×D8—731no—
1061C4×D8—731no—
1062#436—731no—
1063#436—731no—
1064#435—731no—
1065#435—731no—
1066#435—731no—
1067#435—731no—
1068#433—731no—
1069#433C2×D7311yescharacteristic, complemented
1070#432—731no—
1071#428—731no—
1072#428—731no—
1073#427—731no—
1074#419—731no—
1075#418—731no—
1076#418—731no—
1077#417—731no—
1078#416—731no—
1079C2×#102—731no—
1080#405—731no—
1081#405—731no—
1082C4×M16—731no—
1083C2×#41—731no—
1084C2×#41—731no—
1085C2×#41—1461no—
1086C2×#41—1461no—
1087C22×Q8C22×D7311yescharacteristic
1088C22×D4—731no—
1089C22×D4—731no—
1090C22×D4—731no—
1091C22×D4—1461no—
1092C22×D4—1461no—
1093C22×D4—1461no—
1094C23×C4—1461no—
1095AGL(1,ℤ/8)—1464no—
1096AGL(1,ℤ/8)—1464no—
1097C2×SD16—731no—
1098C2×SD16—731no—
1099C2×SD16—731no—
1100C2×SD16—731no—
1101C2×SD16—1464no—
1102C2×SD16C22×D7311yescharacteristic
1103C2×SD16C22×D7311yescharacteristic
1104C2×SD16C22×D7311yescharacteristic
1105C2×SD16C22×D7311yescharacteristic
1106C2×D8—731no—
1107C2×D8—731no—
1108C2×D8—731no—
1109C2×D8—731no—
1110C2×D8—731no—
1111C2×D8—731no—
1112C2×D8—731no—
1113C2×D8—731no—
1114C2×M16—731no—
1115C2×M16—731no—
1116C2×M16—731no—
1117C2×M16—731no—
1118C22×C8—731no—
1119C22×C8—731no—
1120C4⋊Q8—731no—
1121C4⋊Q8—731no—
1122C4⋊Q8—1461no—
1123#127—731no—
1124#127—731no—
1125#127—731no—
1126#127—1461no—
1127#127C22×D7311yescharacteristic
1128#126—731no—
1129#126—731no—
1130#126—1461no—
1131#126—1461no—
1132#126—1461no—
1133#126—1461no—
1134#126—1461no—
1135#126—1461no—
1136#125—731no—
1137#125—731no—
1138#125—731no—
1139#125—731no—
1140#125—1461no—
1141#125—1461no—
1142#125—1461no—
1143#125C22×D7311yescharacteristic
1144#124—731no—
1145#124—731no—
1146#124—731no—
1147#124—1461no—
1148#124—1461no—
1149#124—1461no—
1150#124—1461no—
1151#124—1461no—
1152#124—1461no—
1153#124—1461no—
1154#124—1461no—
1155#124—1461no—
1156#123—21no—
1157#123—21no—
1158#123—731no—
1159#123—731no—
1160#123—1461no—
1161#123—1461no—
1162#123—1461no—
1163#123—1461no—
1164#123—1461no—
1165#123—1461no—
1166#123—1461no—
1167#123—1461no—
1168#123—1461no—
1169#123—1461no—
1170#123—1461no—
1171#123—1461no—
1172C22⋊Q8—731no—
1173C22⋊Q8—731no—
1174C22⋊Q8—731no—
1175C22⋊Q8—1461no—
1176C22⋊Q8—1461no—
1177C22⋊Q8—1461no—
1178C22⋊Q8—1461no—
1179C22⋊Q8—1461no—
1180C22⋊Q8—1461no—
1181#121—21no—
1182#121—21no—
1183#121—731no—
1184#121—731no—
1185#121—731no—
1186#121—731no—
1187#121—731no—
1188#121—731no—
1189#121—731no—
1190#121—731no—
1191#121—731no—
1192#121—1461no—
1193#121—1461no—
1194#121—1461no—
1195#121—1461no—
1196#121—1461no—
1197#121—1461no—
1198#121—1461no—
1199#121—1461no—
1200#121—1461no—
1201#121—1461no—
1202#121—1461no—
1203#121—1461no—
1204#121—1461no—
1205#121—1461no—
1206#121—1461no—
1207#121—1461no—
1208#121—1461no—
1209#121—1461no—
1210#121—1461no—
1211#121—1461no—
1212#121C22×D7311yescharacteristic
1213#121C22×D7311yescharacteristic
1214#120—1461no—
1215#120—1461no—
1216#120—1461no—
1217#120—1461no—
1218#120—1461no—
1219#120—1461no—
1220C4×Q8—21no—
1221C4×Q8—21no—
1222C4×Q8—731no—
1223C4×Q8—731no—
1224C4×Q8—731no—
1225C4×Q8—1461no—
1226C4×Q8C22×D7311yescharacteristic
1227C4×Q8C22×D7311yescharacteristic
1228C4×Q8C22×D7311yescharacteristic
1229C4×Q8C22×D7311yescharacteristic
1230C4×D4—731no—
1231C4×D4—731no—
1232C4×D4—731no—
1233C4×D4—731no—
1234C4×D4—731no—
1235C4×D4—731no—
1236C4×D4—731no—
1237C4×D4—731no—
1238C4×D4—731no—
1239C4×D4—731no—
1240C4×D4—731no—
1241C4×D4—731no—
1242C4×D4—731no—
1243C4×D4—731no—
1244C4×D4—731no—
1245C4×D4—1461no—
1246C4×D4—1461no—
1247C4×D4—1461no—
1248C4×D4—1461no—
1249C4×D4—1461no—
1250C4×D4—1461no—
1251C4×D4—1461no—
1252C4×D4—1461no—
1253C4×D4—1461no—
1254C4×D4—1461no—
1255C4×D4—1461no—
1256C4×D4—1461no—
1257C4×D4—1461no—
1258C4×D4—1461no—
1259C4×D4—1461no—
1260C4×D4—1461no—
1261C4×D4—1461no—
1262C4×D4—1461no—
1263C4×D4—1461no—
1264C4×D4C22×D7311yescharacteristic
1265C4×D4C22×D7311yescharacteristic
1266#117—21no—
1267#117—21no—
1268#117—731no—
1269#117—731no—
1270#117—731no—
1271#117—731no—
1272#117—1461no—
1273#117—1461no—
1274#117—1461no—
1275#117—1461no—
1276#117—1461no—
1277#117—1461no—
1278#117C22×D7311yescharacteristic
1279#117C22×D7311yescharacteristic
1280C2×C4⋊C4—731no—
1281C2×C4⋊C4—731no—
1282C2×C4⋊C4—1461no—
1283C2×C4⋊C4—1461no—
1284C2×C22⋊C4—1461no—
1285C2×C22⋊C4—1461no—
1286C2×C22⋊C4—1461no—
1287C2×C22⋊C4—1461no—
1288C2×C22⋊C4—1461no—
1289C2×C42—731no—
1290C2×C42—1461no—
1291#107—731no—
1292#107—731no—
1293#107—731no—
1294#107—731no—
1295#107—731no—
1296#107—731no—
1297#107C22×D7311yescharacteristic
1298#107C22×D7311yescharacteristic
1299#106—731no—
1300#106—731no—
1301#106—731no—
1302#106—731no—
1303#106—731no—
1304#106—731no—
1305#106C22×D7311yescharacteristic
1306#106C22×D7311yescharacteristic
1307C4⋊C8—731no—
1308C4⋊C8—731no—
1309C4⋊C8—731no—
1310C4⋊C8—731no—
1311C4⋊C8C22×D7311yescharacteristic
1312C4⋊C8C22×D7311yescharacteristic
1313#103—731no—
1314#103—731no—
1315#103—731no—
1316#103—731no—
1317#103C22×D7311yescharacteristic
1318#103C22×D7311yescharacteristic
1319#103C22×D7311yescharacteristic
1320#103C22×D7311yescharacteristic
1321#102—731no—
1322#102—731no—
1323#102—731no—
1324#102—731no—
1325#102—731no—
1326#102—731no—
1327#102—731no—
1328#102—731no—
1329#102—731no—
1330#102—731no—
1331#102—731no—
1332#102—731no—
1333#102—731no—
1334#102—731no—
1335#102—731no—
1336#102—731no—
1337#102—731no—
1338#102—731no—
1339#102—731no—
1340#102—731no—
1341#102C22×D7311yescharacteristic
1342#102C22×D7311yescharacteristic
1343#102C22×D7311yescharacteristic
1344#102C22×D7311yescharacteristic
1345C22⋊C8—731no—
1346C22⋊C8—731no—
1347C22⋊C8—731no—
1348C22⋊C8—731no—
1349C22⋊C8C22×D7311yescharacteristic
1350C22⋊C8C22×D7311yescharacteristic
1351#97—731no—
1352#97—731no—
1353#97—731no—
1354#97—731no—
1355#97—731no—
1356#97C22×D7311yescharacteristic
1357C4×C8—731no—
1358C4×C8—731no—
1359C4×C8—731no—
1360C4×C8C22×D7311yescharacteristic
1361C24—1461no—
1362C24—1461no—
1363C24—1461no—
1364#41—2921no—
1365#41—2921no—
1366#41—5842no—
1367#41—5842no—
1368#41—1462no—
1369#41—1462no—
1370C2×Q8—21no—
1371C2×Q8—22no—
1372C2×Q8—41no—
1373C2×Q8—731no—
1374C2×Q8—1461no—
1375C2×Q8—1461no—
1376C2×Q8C23×D7311yescharacteristic
1377C2×Q8C23×D7311yescharacteristic
1378C2×D4—21no—
1379C2×D4—21no—
1380C2×D4—21no—
1381C2×D4—21no—
1382C2×D4—2921no—
1383C2×D4—2921no—
1384C2×D4—2921no—
1385C2×D4—5842no—
1386C2×D4—5842no—
1387C2×D4—5842no—
1388C2×D4—731no—
1389C2×D4—731no—
1390C2×D4—731no—
1391C2×D4—731no—
1392C2×D4—731no—
1393C2×D4—731no—
1394C2×D4—731no—
1395C2×D4—1461no—
1396C2×D4—1461no—
1397C2×D4—1461no—
1398C2×D4—1462no—
1399C2×D4—1461no—
1400C2×D4—1461no—
1401C2×D4—1461no—
1402C2×D4—1461no—
1403C2×D4—1461no—
1404C2×D4—1461no—
1405C2×D4—1461no—
1406C2×D4—1461no—
1407C2×D4—1461no—
1408C2×D4—1462no—
1409C2×D4—1462no—
1410C2×D4—1461no—
1411C2×D4—1461no—
1412C2×D4—1461no—
1413C2×D4—1461no—
1414C2×D4—1461no—
1415C2×D4—1461no—
1416C2×D4—1461no—
1417C2×D4C23×D7311yescharacteristic
1418C2×D4C23×D7311yescharacteristic
1419C22×C4—21no—
1420C22×C4—21no—
1421C22×C4—21no—
1422C22×C4—5842no—
1423C22×C4—731no—
1424C22×C4—731no—
1425C22×C4—731no—
1426C22×C4—731no—
1427C22×C4—1461no—
1428C22×C4—1461no—
1429C22×C4—1461no—
1430C22×C4—1461no—
1431C22×C4—1461no—
1432C22×C4—1461no—
1433C22×C4—1461no—
1434C22×C4—1461no—
1435C22×C4—1461no—
1436C22×C4—1461no—
1437C22×C4—1461no—
1438C22×C4—1461no—
1439C22×C4—1461no—
1440C22×C4—1461no—
1441C22×C4—1461no—
1442C22×C4—1461no—
1443C22×C4C23×D7311yescharacteristic
1444SD16—22no—
1445SD16—22no—
1446SD16—41no—
1447SD16—41no—
1448SD16—734no—
1449SD16—1462no—
1450SD16—1462no—
1451SD16—1462no—
1452D8—2921no—
1453D8—2921no—
1454D8—2921no—
1455D8—2921no—
1456D8—1462no—
1457D8—1462no—
1458D8—1462no—
1459D8—1462no—
1460M16—2921no—
1461M16—2921no—
1462M16—1462no—
1463M16—1462no—
1464C2×C8—2921no—
1465C2×C8—731no—
1466C2×C8—731no—
1467C2×C8—731no—
1468C2×C8—731no—
1469C2×C8—1462no—
1470C2×C8C23×D7311yescharacteristic
1471C2×C8C23×D7311yescharacteristic
1472C2×C8C23×D7311yescharacteristic
1473C2×C8C23×D7311yescharacteristic
1474C4⋊C4—21no—
1475C4⋊C4—21no—
1476C4⋊C4—21no—
1477C4⋊C4—21no—
1478C4⋊C4—21no—
1479C4⋊C4—21no—
1480C4⋊C4—731no—
1481C4⋊C4—731no—
1482C4⋊C4—731no—
1483C4⋊C4—731no—
1484C4⋊C4—731no—
1485C4⋊C4—731no—
1486C4⋊C4—731no—
1487C4⋊C4—731no—
1488C4⋊C4—731no—
1489C4⋊C4—731no—
1490C4⋊C4—731no—
1491C4⋊C4—731no—
1492C4⋊C4—1461no—
1493C4⋊C4—1461no—
1494C4⋊C4—1461no—
1495C4⋊C4—1461no—
1496C4⋊C4—1461no—
1497C4⋊C4—1461no—
1498C4⋊C4—1461no—
1499C4⋊C4—1461no—
1500C4⋊C4—1461no—
1501C4⋊C4—1461no—
1502C4⋊C4—1461no—
1503C4⋊C4—1461no—
1504C4⋊C4—1461no—
1505C4⋊C4—1461no—
1506C4⋊C4D4×D7311yescharacteristic
1507C4⋊C4D4×D7311yescharacteristic
1508C4⋊C4C23×D7311yescharacteristic
1509C4⋊C4C23×D7311yescharacteristic
1510C4⋊C4C23×D7311yescharacteristic
1511C4⋊C4C23×D7311yescharacteristic
1512C22⋊C4—21no—
1513C22⋊C4—21no—
1514C22⋊C4—21no—
1515C22⋊C4—21no—
1516C22⋊C4—21no—
1517C22⋊C4—731no—
1518C22⋊C4—731no—
1519C22⋊C4—731no—
1520C22⋊C4—731no—
1521C22⋊C4—731no—
1522C22⋊C4—731no—
1523C22⋊C4—731no—
1524C22⋊C4—731no—
1525C22⋊C4—1461no—
1526C22⋊C4—1461no—
1527C22⋊C4—1461no—
1528C22⋊C4—1461no—
1529C22⋊C4—1461no—
1530C22⋊C4—1461no—
1531C22⋊C4—1461no—
1532C22⋊C4—1461no—
1533C22⋊C4—1461no—
1534C22⋊C4—1461no—
1535C22⋊C4—1461no—
1536C22⋊C4—1461no—
1537C22⋊C4—1461no—
1538C22⋊C4—1461no—
1539C22⋊C4—1461no—
1540C22⋊C4—1461no—
1541C22⋊C4—1461no—
1542C22⋊C4—1461no—
1543C22⋊C4—1461no—
1544C22⋊C4—1461no—
1545C22⋊C4—1461no—
1546C22⋊C4—1461no—
1547C22⋊C4—1461no—
1548C22⋊C4—1461no—
1549C22⋊C4—1461no—
1550C22⋊C4—1461no—
1551C22⋊C4—1461no—
1552C22⋊C4—1461no—
1553C22⋊C4—1461no—
1554C22⋊C4D4×D7311yescharacteristic
1555C22⋊C4D4×D7311yescharacteristic
1556C42—21no—
1557C42—21no—
1558C42—21no—
1559C42—21no—
1560C42—21no—
1561C42—731no—
1562C42—731no—
1563C42—731no—
1564C42—731no—
1565C42—1461no—
1566C42—1461no—
1567C42—1461no—
1568C42—1461no—
1569C42—1461no—
1570C42C23×D7311yescharacteristic
1571C42C23×D7311yescharacteristic
1572C23—21no—
1573C23—21no—
1574C23—2922no—
1575C23—2922no—
1576C23—2922no—
1577C23—2922no—
1578C23—5841no—
1579C23—5841no—
1580C23—5841no—
1581C23—5841no—
1582C23—5841no—
1583C23—731no—
1584C23—731no—
1585C23—1461no—
1586C23—1461no—
1587C23—1461no—
1588C23—1461no—
1589C23C2×D4×D7311yescharacteristic
1590Q8—21no—
1591Q8—21no—
1592Q8—21no—
1593Q8—42no—
1594Q8—2921no—
1595Q8—5841no—
1596Q8—5841no—
1597Q8#41×D7312yes—
1598D4—21no—
1599D4—21no—
1600D4—21no—
1601D4—21no—
1602D4—81no—
1603D4—81no—
1604D4—81no—
1605D4—81no—
1606D4—2922no—
1607D4—2922no—
1608D4—2922no—
1609D4—2921no—
1610D4—2922no—
1611D4—2922no—
1612D4—2921no—
1613D4—2921no—
1614D4—2922no—
1615D4—2922no—
1616D4—2922no—
1617D4—5841no—
1618D4—5841no—
1619D4—5841no—
1620D4—5841no—
1621D4—5841no—
1622D4—5841no—
1623D4—5841no—
1624D4—5841no—
1625D4—5841no—
1626D4—5841no—
1627D4—5841no—
1628D4—732no—
1629D4—1461no—
1630D4—1461no—
1631D4—1461no—
1632D4—1461no—
1633D4—1461no—
1634D4—1461no—
1635D4—1461no—
1636C2×C4—21no—
1637C2×C4—21no—
1638C2×C4—21no—
1639C2×C4—21no—
1640C2×C4—21no—
1641C2×C4—21no—
1642C2×C4—21no—
1643C2×C4—21no—
1644C2×C4—42no—
1645C2×C4—81no—
1646C2×C4—81no—
1647C2×C4—2922no—
1648C2×C4—2922no—
1649C2×C4—2921no—
1650C2×C4—2921no—
1651C2×C4—2922no—
1652C2×C4—2922no—
1653C2×C4—5841no—
1654C2×C4—5841no—
1655C2×C4—5841no—
1656C2×C4—5841no—
1657C2×C4—5841no—
1658C2×C4—5841no—
1659C2×C4—5841no—
1660C2×C4—5841no—
1661C2×C4—5841no—
1662C2×C4—5841no—
1663C2×C4—5841no—
1664C2×C4—5841no—
1665C2×C4—731no—
1666C2×C4—731no—
1667C2×C4—731no—
1668C2×C4—731no—
1669C2×C4—731no—
1670C2×C4—731no—
1671C2×C4—1461no—
1672C2×C4—1461no—
1673C2×C4—1461no—
1674C2×C4—1461no—
1675C2×C4—1461no—
1676C2×C4—1461no—
1677C2×C4—1461no—
1678C2×C4—1461no—
1679C2×C4C2×D4×D7311yescharacteristic
1680C2×C4C2×D4×D7311yescharacteristic
1681C2×C4C2×D4×D7311yescharacteristic
1682C2×C4C2×D4×D7311yescharacteristic
1683C2×C4C2×D4×D7311yescharacteristic
1684C2×C4C24×D7311yescharacteristic
1685C8—21no—
1686C8—21no—
1687C8—21no—
1688C8—21no—
1689C8—732no—
1690C8—1461no—
1691C8—1461no—
1692C8—1461no—
1693C22—21no—
1694C22—21no—
1695C22—21no—
1696C22—41no—
1697C22—41no—
1698C22—41no—
1699C22—41no—
1700C22—41no—
1701C22—41no—
1702C22—2921no—
1703C22—2921no—
1704C22—2921no—
1705C22—2921no—
1706C22—2921no—
1707C22—2921no—
1708C22—2921no—
1709C22—2921no—
1710C22—2921no—
1711C22—2921no—
1712C22—2921no—
1713C22—5844no—
1714C22—11682no—
1715C22—11682no—
1716C22—1461no—
1717C22—1461no—
1718C22—1462no—
1719C22—1461no—
1720C22—1461no—
1721C22—1461no—
1722C22—1461no—
1723C22C22×D4×D7311yescharacteristic
1724C4—21no—
1725C4—22no—
1726C4—21no—
1727C4—21no—
1728C4—21no—
1729C4—21no—
1730C4—41no—
1731C4—41no—
1732C4—41no—
1733C4—41no—
1734C4—41no—
1735C4—2921no—
1736C4—2921no—
1737C4—2921no—
1738C4—2921no—
1739C4—1461no—
1740C4—1461no—
1741C4—1461no—
1742C4—1461no—
1743C4—1461no—
1744C4—1461no—
1745C4C2×#41×D7311yescharacteristic
1746C4#1798942311yescharacteristic
1747C2—41no—
1748C2—81no—
1749C2—81no—
1750C2—2922no—
1751C2—2921no—
1752C2—2921no—
1753C2—5841no—
1754C2—5841no—
1755C2—5841no—
1756C2#2262341411yescharacteristic
1757C2#2262470911yescharacteristic
1758C2#2262470911yescharacteristic
subgroupG/H
centerC22C22×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC73×#3126C2
socleC22×C73C23×D4
hypercenter#3126D73
hypocenterC73#61504
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ #117 ◁ #3126

Complements

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

NH ≅ G/Ntype
1. #22624042C2semidirect
2. #22623961C2semidirect
3. #22622972C2semidirect
4. #22622874C2semidirect
5. #22622687C2semidirect
6. #22622655C2semidirect
7. #22622488C2semidirect
8. #22622435C2semidirect
9. #22622429C2semidirect
10. #22622188C2semidirect
11. #22622171C2semidirect
12. #22622110C2semidirect
13. #22622075C2semidirect
14. #22621959C2semidirect
15. #22621934C2semidirect
16. #22621546C2semidirect
17. #22621419C2semidirect
18. #22621419C2semidirect
19. #22620612C2semidirect
20. #22620575C2semidirect
21. #22620522C2semidirect
22. #22620175C2semidirect
23. #22620136C2semidirect
24. #22620121C2semidirect
25. #22620080C2semidirect
26. #22620073C2semidirect
27. #22618914C2semidirect
28. #22618790C2semidirect
29. #22618762C2semidirect
30. C4×#14556618C2semidirect
31. C73×#3126C2semidirect
36. #17989322C22semidirect
37. #17989313C22semidirect
40. #17989300C22semidirect
46. #17989281C22semidirect
48. #17989278C22semidirect
49. #17989259C22semidirect
51. #17989248C22semidirect
52. #17989248C22semidirect
60. #17989209C22semidirect
62. #17989192C22semidirect
68. #17989124C22semidirect
73. #17989069C22semidirect
76. C4×#11924029C22semidirect
78. #17988995C22semidirect
79. #17988994C22semidirect
80. #17988986C22semidirect
81. #17988973C22semidirect
82. #17988973C22semidirect
83. #17988963C22semidirect
84. #17988953C22semidirect
85. #17988951C22semidirect
86. #17988950C22semidirect
87. #17988948C22semidirect
88. #17988943C22semidirect
89. #17988932C22semidirect
90. #17988927C22semidirect
91. #17988916C22semidirect
92. #17988914C22semidirect
93. #17988913C22semidirect
94. #17988912C22semidirect
95. #17988912C22semidirect
96. #17988910C22semidirect
97. #17988907C22semidirect
98. #17988902C22semidirect
99. #17988899C22semidirect
100. #17988896C22semidirect
102. #17988889C22semidirect
104. #17988888C22semidirect
105. #17988886C22semidirect
107. #17988870C22semidirect
108. #17988866C22semidirect
109. #17988865C22semidirect
110. #17988841C22semidirect
111. #17988839C22semidirect
112. #17988839C22semidirect
113. #17988838C22semidirect
114. #17988838C22semidirect
115. #17988836C22semidirect
116. #17988836C22semidirect
117. #17988830C22semidirect
118. #17988824C22semidirect
119. #17988821C22semidirect
120. #17988821C22semidirect
121. #17988813C22semidirect
124. #17988804C22semidirect
125. #17988804C22semidirect
126. #17988785C22semidirect
127. #17988785C22semidirect
129. #17988783C22semidirect
130. #17988781C22semidirect
131. #17988781C22semidirect
134. #17988735C22semidirect
135. #17988735C22semidirect
136. #17988731C22semidirect
137. #17988731C22semidirect
142. #17988716C22semidirect
143. #17988714C22semidirect
145. #17988700C22semidirect
147. #17988697C22semidirect
148. #17988697C22semidirect
149. #17988696C22semidirect
150. #17988696C22semidirect
153. #17988688C22semidirect
156. #17988685C22semidirect
157. #17988685C22semidirect
158. SD16×Dic73C22semidirect
161. C4×#11924015C22semidirect
162. C4×#11924015C22semidirect
164. C4×D584C22semidirect
166. C4×#11924013C22semidirect
167. C4×#11924013C22semidirect
168. #17988664C22semidirect
169. #17988662C22semidirect
170. #17988661C22semidirect
171. #17988657C22semidirect
172. #17988655C22semidirect
173. #17988655C22semidirect
174. #17988646C22semidirect
175. #17988642C22semidirect
176. #17988628C22semidirect
177. #17988626C22semidirect
178. #17988623C22semidirect
179. #17988596C22semidirect
182. #17988587C22semidirect
183. #17988582C22semidirect
185. #17988544C22semidirect
186. #17988543C22semidirect
187. C4×#11924011C22semidirect
189. #519×C73C22semidirect
190. #482×C73C22semidirect
191. #482×C73C22semidirect
192. #479×C73C22semidirect
193. #479×C73C22semidirect
194. #460×C73C22semidirect
195. #460×C73C22semidirect
196. #448×C73C22semidirect
197. #448×C73C22semidirect
198. #440×C73C22semidirect
199. #440×C73C22semidirect
200. C4×SD16×C73C22semidirect
201. C4×SD16×C73C22semidirect
202. #433×C73C22semidirect
552. #11924015#41semidirect
901. #3126D73semidirect
911. C73#61504semidirect
955. #519C2×D73semidirect
979. #482C2×D73semidirect
980. #482C2×D73semidirect
985. #479C2×D73semidirect
986. #479C2×D73semidirect
1014. #460C2×D73semidirect
1015. #460C2×D73semidirect
1026. #448C2×D73semidirect
1027. #448C2×D73semidirect
1048. #440C2×D73semidirect
1049. #440C2×D73semidirect
1055. C4×SD16C2×D73semidirect
1056. C4×SD16C2×D73semidirect
1069. #433C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226240422
#226239612
#226229722
#226228742
#226226872
#226226552
#226224882
#226224352
#226224292
#226221882
#226221712
#226221102
#226220752
#226219592
#226219342
#226215462
#226214192
#226206122
#226205752
#226205222
#226201752
#226201362
#226201212
#226200802
#226200732
#226189142
#226187902
#226187622
C4×#145566182
C73×#31262
#6150473