Finite Group Databasebeta

← #33978987

Subgroups — #33978987

Order 18688.

1870 conjugacy classes of subgroups.

The subgroup lattice has 1772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623889C211yesmaximal, characteristic, complemented
2#22623525C211yesmaximal, characteristic, complemented
3#22623017C211yesmaximal, characteristic, complemented
4#22622995C211yesmaximal, characteristic, complemented
5#22622779C211yesmaximal, characteristic, complemented
6#22622697C211yesmaximal, characteristic, complemented
7#22622100C211yesmaximal, characteristic, complemented
8#22622068C211yesmaximal, characteristic, complemented
9#22621993C211yesmaximal, characteristic, complemented
10#22621965C211yesmaximal, characteristic, complemented
11#22621827C211yesmaximal, characteristic, complemented
12#22621674C211yesmaximal, characteristic, complemented
13#22621634C211yesmaximal, characteristic, complemented
14#22621509C211yesmaximal, characteristic, complemented
15#22621498C211yesmaximal, characteristic, complemented
16#22621468C211yesmaximal, characteristic, complemented
17#22621430C211yesmaximal, characteristic, complemented
18#22621331C211yesmaximal, characteristic, complemented
19#22621277C211yesmaximal, characteristic, complemented
20#22621252C211yesmaximal, characteristic, complemented
21#22620966C211yesmaximal, characteristic, complemented
22#22620915C211yesmaximal, characteristic, complemented
23#22620897C211yesmaximal, characteristic, complemented
24#22620105C211yesmaximal, characteristic, complemented
25#22620035C211yesmaximal, characteristic, complemented
26#22619945C211yesmaximal, characteristic, complemented
27#22619420C211yesmaximal, characteristic, complemented
28#22619384C211yesmaximal, characteristic, complemented
29C2×#17988808C211yesmaximal, characteristic, complemented
30#22619054C211yesmaximal, characteristic, complemented
31C73×#3297C211yesmaximal, characteristic, complemented
32C2×#14556620C2211yescharacteristic, complemented
33C2×#14556615C2211yescharacteristic
34C2×#14556613C2211yescharacteristic, complemented
35C2×#14556611C2211yescharacteristic, complemented
36C22×Dic292C2211yescharacteristic, complemented
37C22×#11924016C2211yescharacteristic
38#17989321—21no—
39#17989320C2211yescharacteristic
40#17989320C2211yescharacteristic, complemented
41#17989314C2211yescharacteristic, complemented
42#17989306C2211yescharacteristic
43#17989305C2211yescharacteristic, complemented
44#17989304—21no—
45#17989301—21no—
46#17989286—21no—
47#17989285C2211yescharacteristic
48#17989280—21no—
49#17989265—21no—
50#17989263—21no—
51#17989255C2211yescharacteristic, complemented
52#17989250C2211yescharacteristic
53#17989246C2211yescharacteristic
54#17989246C2211yescharacteristic, complemented
55#17989244C2211yescharacteristic
56#17989243C2211yescharacteristic
57#17989234C2211yescharacteristic
58#17989224—21no—
59D4×C22⋊D73C2211yescharacteristic
60#17989205—21no—
61#17989172—21no—
62#17989169—21no—
63#17989133C2211yescharacteristic
64#17989132—21no—
65#17989132C2211yescharacteristic, complemented
66#17989123C2211yescharacteristic
67#17989122C2211yescharacteristic, complemented
68#17989120—21no—
69#17989119C2211yescharacteristic
70#17989118C2211yescharacteristic
71#17989118C2211yescharacteristic, complemented
72#17989114—21no—
73C2×#14556578C2211yescharacteristic
74#124×D73C2211yescharacteristic
75#17989060—21no—
76#17989055C2211yescharacteristic, complemented
77C4×#11924027—21no—
78C4×#11924027C2211yescharacteristic
79C4×#11924027C2211yescharacteristic, complemented
80C2×#14556556C2211yescharacteristic, complemented
81#17988978C2211yescharacteristic, complemented
82#17988975C2211yescharacteristic
83#17988975C2211yescharacteristic
84#17988975C2211yescharacteristic, complemented
85#17988971C2211yescharacteristic, complemented
86#17988969C2211yescharacteristic
87#17988954C2211yescharacteristic, complemented
88#17988950C2211yescharacteristic
89#17988945C2211yescharacteristic
90#17988945C2211yescharacteristic, complemented
91#17988944C2211yescharacteristic, complemented
92#17988930C2211yescharacteristic, complemented
93#17988928C2211yescharacteristic, complemented
94#17988909C2211yescharacteristic
95#17988905C2211yescharacteristic
96#17988893C2211yescharacteristic, complemented
97#17988893C2211yescharacteristic, complemented
98#17988893C2211yescharacteristic, complemented
99#17988891C2211yescharacteristic, complemented
100#17988886C2211yescharacteristic, complemented
101#17988885C2211yescharacteristic
102#17988885C2211yescharacteristic, complemented
103#17988880C2211yescharacteristic, complemented
104#17988876C2211yescharacteristic, complemented
105#17988846C2211yescharacteristic, complemented
106#17988839C2211yescharacteristic
107#17988834C2211yescharacteristic, complemented
108#17988832C2211yescharacteristic
109#17988828C2211yescharacteristic, complemented
110#17988823C2211yescharacteristic
111#17988821C2211yescharacteristic
112#17988818C2211yescharacteristic, complemented
113#17988814C2211yescharacteristic
114#17988814C2211yescharacteristic, complemented
115#17988812C2211yescharacteristic, complemented
116#17988812C2211yescharacteristic, complemented
117#17988810C2211yescharacteristic, complemented
118#17988810C2211yescharacteristic, complemented
119#17988808C2211yescharacteristic
120#17988808C2211yescharacteristic
121#17988808C2211yescharacteristic
122#17988808C2211yescharacteristic
123#17988808C2211yescharacteristic, complemented
124#17988808C2211yescharacteristic, complemented
125#17988808C2211yescharacteristic, complemented
126#17988808C2211yescharacteristic, complemented
127#17988808C2211yescharacteristic, complemented
128#17988806C2211yescharacteristic
129#17988805C2211yescharacteristic, complemented
130#17988804C2211yescharacteristic, complemented
131#17988802C2211yescharacteristic, complemented
132#17988802C2211yescharacteristic, complemented
133#17988801C2211yescharacteristic
134#17988801C2211yescharacteristic, complemented
135#17988800C2211yescharacteristic
136#17988800C2211yescharacteristic
137#17988800C2211yescharacteristic, complemented
138#17988796C2211yescharacteristic, complemented
139#17988791C2211yescharacteristic, complemented
140#17988786C2211yescharacteristic
141#17988785C2211yescharacteristic, complemented
142#17988781C2211yescharacteristic
143#17988781C2211yescharacteristic, complemented
144#17988751C2211yescharacteristic, complemented
145#17988751C2211yescharacteristic, complemented
146#17988750C2211yescharacteristic, complemented
147#17988749C2211yescharacteristic, complemented
148#17988744C2211yescharacteristic, complemented
149#17988742C2211yescharacteristic, complemented
150#17988739C2211yescharacteristic
151#17988730C2211yescharacteristic
152#17988730C2211yescharacteristic, complemented
153#17988729C2211yescharacteristic
154#17988728C2211yescharacteristic
155#17988728C2211yescharacteristic, complemented
156#17988727C2211yescharacteristic, complemented
157#17988725C2211yescharacteristic, complemented
158#17988722C2211yescharacteristic
159#17988721C2211yescharacteristic
160#17988717C2211yescharacteristic, complemented
161#17988714C2211yescharacteristic, complemented
162#17988696C2211yescharacteristic
163#17988693C2211yescharacteristic, complemented
164#17988691C2211yescharacteristic, complemented
165#17988691C2211yescharacteristic, complemented
166#17988686C2211yescharacteristic, complemented
167#17988686C2211yescharacteristic, complemented
168#17988686C2211yescharacteristic, complemented
169#17988684C2211yescharacteristic
170C4×Dic292C2211yescharacteristic, complemented
171C4×#11924016C2211yescharacteristic, complemented
172C4×#11924016C2211yescharacteristic, complemented
173#17988658C2211yescharacteristic
174#17988658C2211yescharacteristic, complemented
175#17988655C2211yescharacteristic
176#17988655C2211yescharacteristic, complemented
177D4×#10596831C2211yescharacteristic, complemented
178#17988641C2211yescharacteristic, complemented
179#17988641C2211yescharacteristic, complemented
180#17988638C2211yescharacteristic, complemented
181#17988609C2211yescharacteristic, complemented
182C2×#14556520C2211yescharacteristic, complemented
183C2×#14556520C2211yescharacteristic, complemented
184#17988594C2211yescharacteristic, complemented
185#17988590C2211yescharacteristic
186#17988581C2211yescharacteristic, complemented
187C2×#14556514C2211yescharacteristic, complemented
188#553×C73C2211yescharacteristic, complemented
189#546×C73C2211yescharacteristic
190#488×C73C2211yescharacteristic
191#484×C73C2211yescharacteristic, complemented
192#482×C73C2211yescharacteristic
193#478×C73C2211yescharacteristic, complemented
194#466×C73C2211yescharacteristic
195#465×C73C2211yescharacteristic, complemented
196#463×C73C2211yescharacteristic
197#449×C73C2211yescharacteristic, complemented
198#447×C73C2211yescharacteristic
199C4×D8×C73C2211yescharacteristic, complemented
200C8×D4×C73C2211yescharacteristic, complemented
201#416×C73C2211yescharacteristic, complemented
202C2×#102×C73C2211yescharacteristic
203C2×#11924028C2311yescharacteristic
204C2×#11924028C2311yescharacteristic
205C2×#11924027—21no—
206C2×#11924027D411yescharacteristic
207C2×#11924027C2311yescharacteristic
208C22×Dic146C2311yescharacteristic
209C22×Dic146C2311yescharacteristic
210C2×Q8×D73C2311yescharacteristic
211C22×C22⋊D73—21no—
212C2×D4×D73C2311yescharacteristic
213#14556620—42no—
214#14556615—42no—
215#14556613—42no—
216#14556611—42no—
217C2×Dic292—42no—
218C2×Dic292C2311yescharacteristic
219C2×Dic292C2311yescharacteristic
220C2×Dic292C2311yescharacteristic
221C2×Dic292C2311yescharacteristic
222C2×#11924018C2311yescharacteristic
223C2×#11924018C2311yescharacteristic
224C2×#11924017C2311yescharacteristic
225C2×#11924017C2311yescharacteristic
226C2×#11924017C2311yescharacteristic
227C2×#11924017C2311yescharacteristic
228C2×#11924016—42no—
229C2×#11924016C2311yescharacteristic
230C2×#11924016C2311yescharacteristic
231C2×#11924016C2311yescharacteristic
232C2×#11924016C2311yescharacteristic
233C2×#11924016C2311yescharacteristic
234C2×#11924016C2311yescharacteristic
235C2×#11924015C2311yescharacteristic
236C2×D584C2311yescharacteristic
237C2×#11924013C2311yescharacteristic
238C2×#11924013C2311yescharacteristic
239C2×#11924013C2311yescharacteristic
240C2×#11924011C2311yescharacteristic
241C2×#11924011C2311yescharacteristic
242C22×#10596831C2311yescharacteristic
243C22×#10596831C2311yescharacteristic
244#14556590—21no—
245#14556590—21no—
246#14556590C2311yescharacteristic
247#14556589C2311yescharacteristic
248#14556587—21no—
249#14556587C2311yescharacteristic
250#14556587C2311yescharacteristic
251#14556586—21no—
252#14556586—21no—
253#14556586—21no—
254#14556585—21no—
255#14556584—21no—
256#14556584—21no—
257#14556584—21no—
258#14556584—21no—
259#14556584—21no—
260#14556584—21no—
261#14556582C2311yescharacteristic
262#14556582C2311yescharacteristic
263#14556581—21no—
264#14556581—21no—
265#14556580C2311yescharacteristic
266#14556579C2311yescharacteristic
267#14556579C2311yescharacteristic
268#14556578—21no—
269#14556578—21no—
270#14556578—21no—
271#14556578C2311yescharacteristic
272#14556578C2311yescharacteristic
273#14556578C2311yescharacteristic
274#14556578C2311yescharacteristic
275#14556578C2311yescharacteristic
276#14556577—21no—
277#14556577—21no—
278#14556577—21no—
279#14556577—21no—
280#14556577—21no—
281#14556577—21no—
282#14556577—21no—
283#14556577—21no—
284#14556577—21no—
285#14556576—21no—
286#14556576—21no—
287#14556575—21no—
288#14556574—21no—
289#14556574—21no—
290#14556573—21no—
291#14556573—21no—
292#14556573—21no—
293#14556573—21no—
294#14556572—21no—
295#14556572—21no—
296#14556571C2311yescharacteristic
297#14556571C2311yescharacteristic
298#14556570—21no—
299#14556570C2311yescharacteristic
300#14556570C2311yescharacteristic
301#14556569—21no—
302#14556569—21no—
303#14556569—21no—
304#14556568—21no—
305#14556568—21no—
306#14556568—21no—
307#14556566C2311yescharacteristic
308#14556565—21no—
309#14556565C2311yescharacteristic
310#14556565C2311yescharacteristic
311#14556564—21no—
312#14556563—21no—
313#14556563—21no—
314#14556563—21no—
315#14556563—21no—
316#14556563—21no—
317#14556563—21no—
318#14556563—21no—
319#14556563—21no—
320#14556562—21no—
321#14556562—21no—
322#14556562C2311yescharacteristic
323#14556560—21no—
324#14556559—21no—
325#14556559—21no—
326Q8×Dic73C2311yescharacteristic
327C4×Dic146—21no—
328C4×Dic146C2311yescharacteristic
329C4×Dic146C2311yescharacteristic
330C4×Dic146C2311yescharacteristic
331#14556556—21no—
332#14556556—21no—
333#14556556—21no—
334#14556556D411yescharacteristic
335#14556556C2311yescharacteristic
336#14556556C2311yescharacteristic
337#14556556C2311yescharacteristic
338#14556556C2311yescharacteristic
339#14556556C2311yescharacteristic
340#14556556C2311yescharacteristic
341D4×Dic73—21no—
342D4×Dic73—21no—
343D4×Dic73—21no—
344D4×Dic73D411yescharacteristic
345D4×Dic73C2311yescharacteristic
346D4×Dic73C2311yescharacteristic
347#14556553—21no—
348#14556553C2311yescharacteristic
349#14556553C2311yescharacteristic
350#14556553C2311yescharacteristic
351C4×C22⋊D73—21no—
352C4×C22⋊D73—21no—
353C4×C22⋊D73—21no—
354C4×C22⋊D73—21no—
355C4×C22⋊D73—21no—
356C4×C22⋊D73—21no—
357C4×C22⋊D73—21no—
358C4×C22⋊D73—21no—
359C4×C22⋊D73C2311yescharacteristic
360C4×C22⋊D73C2311yescharacteristic
361#14556551—21no—
362#14556551—21no—
363#14556551—21no—
364#14556551—21no—
365#14556551—21no—
366#14556551—21no—
367#14556551—21no—
368#14556551—21no—
369#14556551—21no—
370#14556551D411yescharacteristic
371#14556551D411yescharacteristic
372#14556550—21no—
373#14556549—21no—
374#14556549—21no—
375#14556549D411yescharacteristic
376#14556549C2311yescharacteristic
377#14556548—21no—
378#14556547—21no—
379#14556547—21no—
380#14556547—21no—
381#14556547—21no—
382#14556547D411yescharacteristic
383#14556547D411yescharacteristic
384C2×#11924007—21no—
385C2×C22⋊Dic73—21no—
386C2×C22⋊Dic73—21no—
387C22⋊C4×D73—21no—
388C22⋊C4×D73—21no—
389C22⋊C4×D73—21no—
390C2×C4×Dic73—21no—
391C2×C4×Dic73—21no—
392C2×C4×Dic73C2311yescharacteristic
393C2×C4×Dic73C2311yescharacteristic
394C42×D73—21no—
395C42×D73C2311yescharacteristic
396#14556525C2311yescharacteristic
397#14556524C2311yescharacteristic
398#14556522C2311yescharacteristic
399#14556522C2311yescharacteristic
400#14556522C2311yescharacteristic
401C4⋊#10596831C2311yescharacteristic
402#14556520C2311yescharacteristic
403#14556520C2311yescharacteristic
404#14556520C2311yescharacteristic
405#14556520C2311yescharacteristic
406#14556520C2311yescharacteristic
407#14556520C2311yescharacteristic
408#14556520C2311yescharacteristic
409#14556520C2311yescharacteristic
410#14556516C2311yescharacteristic
411#14556516C2311yescharacteristic
412#14556516C2311yescharacteristic
413#14556516C2311yescharacteristic
414#14556515C2311yescharacteristic
415#14556514C2311yescharacteristic
416#14556514C2311yescharacteristic
417#14556514C2311yescharacteristic
418#14556514C2311yescharacteristic
419#14556514C2311yescharacteristic
420#14556514C2311yescharacteristic
421#14556514C2311yescharacteristic
422#14556514C2311yescharacteristic
423#14556513C2311yescharacteristic
424#14556513C2311yescharacteristic
425#14556512C2311yescharacteristic
426#14556512C2311yescharacteristic
427#14556512C2311yescharacteristic
428#14556511C2311yescharacteristic
429#14556511C2311yescharacteristic
430#14556511C2311yescharacteristic
431#14556511C2311yescharacteristic
432C22⋊#10596831C2311yescharacteristic
433C22⋊#10596831C2311yescharacteristic
434#14556503C2311yescharacteristic
435#14556503C2311yescharacteristic
436#14556501C2311yescharacteristic
437#14556501C2311yescharacteristic
438#14556501C2311yescharacteristic
439#14556501C2311yescharacteristic
440C4×#10596831C2311yescharacteristic
441C2×#41×C73C2311yescharacteristic
442C22×D4×C73C2311yescharacteristic
443C2×SD16×C73C2311yescharacteristic
444C2×D8×C73C2311yescharacteristic
445C2×D8×C73C2311yescharacteristic
446C22×C8×C73C2311yescharacteristic
447C22×C8×C73C2311yescharacteristic
448#126×C73—21no—
449#125×C73C2311yescharacteristic
450#124×C73C2311yescharacteristic
451#123×C73—21no—
452#123×C73—21no—
453C22⋊Q8×C73C2311yescharacteristic
454#121×C73—21no—
455#121×C73—21no—
456#121×C73C2311yescharacteristic
457#121×C73C2311yescharacteristic
458#121×C73C2311yescharacteristic
459#120×C73—21no—
460C4×D4×C73—21no—
461C4×D4×C73C2311yescharacteristic
462C4×D4×C73C2311yescharacteristic
463C4×D4×C73C2311yescharacteristic
464#117×C73C2311yescharacteristic
465C2×C4⋊C4×C73C2311yescharacteristic
466C2×C22⋊C4×C73—21no—
467#107×C73C2311yescharacteristic
468#107×C73C2311yescharacteristic
469#106×C73C2311yescharacteristic
470C4⋊C8×C73C2311yescharacteristic
471#103×C73C2311yescharacteristic
472#103×C73C2311yescharacteristic
473#103×C73C2311yescharacteristic
474#102×C73C2311yescharacteristic
475#102×C73C2311yescharacteristic
476#102×C73C2311yescharacteristic
477#102×C73C2311yescharacteristic
478#102×C73C2311yescharacteristic
479#102×C73C2311yescharacteristic
480#102×C73C2311yescharacteristic
481C22⋊C8×C73C2311yescharacteristic
482C22⋊C8×C73C2311yescharacteristic
483C4×C8×C73C2311yescharacteristic
484C23×D73—21no—
485#11924028—22no—
486#11924028—41no—
487#11924028—41no—
488#11924028—41no—
489#11924027—22no—
490#11924027—41no—
491#11924027—42no—
492#11924027—44no—
493C2×Dic146—22no—
494C2×Dic146—21no—
495C2×Dic146—21no—
496C2×Dic146—21no—
497C2×Dic146—21no—
498C2×Dic146—41no—
499C2×Dic146—41no—
500C2×Dic146—41no—
501C2×Dic146C2×D411yescharacteristic
502C2×Dic146C2411yescharacteristic
503C2×Dic146C2411yescharacteristic
504C2×Dic146C2411yescharacteristic
505C2×Dic146C2411yescharacteristic
506Q8×D73—41no—
507Q8×D73—41no—
508C2×D292—21no—
509C2×D292C2411yescharacteristic
510C2×D292C2411yescharacteristic
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⋊D73—21no—
520C2×C22⋊D73—21no—
521C2×C22⋊D73—21no—
522C2×C22⋊D73—44no—
523C2×C22⋊D73C2×D411yescharacteristic
524C2×C22⋊D73C2×D411yescharacteristic
525D4×D73—41no—
526D4×D73—41no—
527C22×Dic73—21no—
528C22×Dic73—21no—
529C22×Dic73—21no—
530C22×Dic73—21no—
531C22×Dic73—21no—
532C22×Dic73C2×D411yescharacteristic
533C22×Dic73C2×D411yescharacteristic
534C22×Dic73C2×D411yescharacteristic
535C22×Dic73C2×D411yescharacteristic
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×D73C2×D411yescharacteristic
543C2×C4×D73C2×D411yescharacteristic
544C2×C4×D73C2411yescharacteristic
545Dic292—22no—
546Dic292—22no—
547Dic292—41no—
548Dic292—41no—
549#11924018—22no—
550#11924018—41no—
551#11924017—22no—
552#11924017—41no—
553#11924017—41no—
554#11924017—41no—
555#11924016—22no—
556#11924016—22no—
557#11924016—41no—
558#11924016—41no—
559#11924016—41no—
560#11924016—41no—
561#11924015—41no—
562D584—41no—
563#11924013—41no—
564#11924013—41no—
565#11924013—41no—
566#11924011—41no—
567#11924011—41no—
568C2×#10596831—41no—
569C2×#10596831—41no—
570C2×#10596831C2411yescharacteristic
571C2×#10596831C2411yescharacteristic
572C2×#10596831C2411yescharacteristic
573C2×#10596831C2411yescharacteristic
574C4⋊Dic73—21no—
575C4⋊Dic73—21no—
576C4⋊Dic73—21no—
577C4⋊Dic73—21no—
578C4⋊Dic73—21no—
579C4⋊Dic73C2×D411yescharacteristic
580C4⋊Dic73C2411yescharacteristic
581C4⋊Dic73C2411yescharacteristic
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#11924007—21no—
592#11924007—21no—
593#11924007—21no—
594#11924007—21no—
595#11924007—21no—
596#11924007—21no—
597#11924007C2×D411yescharacteristic
598#11924007C2×D411yescharacteristic
599#11924007C2×D411yescharacteristic
600#11924007C2×D411yescharacteristic
601C22⋊Dic73—21no—
602C22⋊Dic73—21no—
603C22⋊Dic73—21no—
604C22⋊Dic73—21no—
605C22⋊Dic73—21no—
606C22⋊Dic73—21no—
607C22⋊Dic73—21no—
608C22⋊Dic73—21no—
609C22⋊Dic73—21no—
610C22⋊Dic73—21no—
611C22⋊Dic73—21no—
612C22⋊Dic73—21no—
613C22⋊Dic73—21no—
614C22⋊Dic73—21no—
615C22⋊Dic73—21no—
616C22⋊Dic73C2×D411yescharacteristic
617C22⋊Dic73C2×D411yescharacteristic
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#11924005C2×D411yescharacteristic
634#11924005C2×D411yescharacteristic
635C4×Dic73—21no—
636C4×Dic73—21no—
637C4×Dic73—21no—
638C4×Dic73—21no—
639C4×Dic73—21no—
640C4×Dic73—21no—
641C4×Dic73—21no—
642C4×Dic73—21no—
643C4×Dic73—21no—
644C4×Dic73—21no—
645C4×Dic73C2×D411yescharacteristic
646C4×Dic73C2×D411yescharacteristic
647C4×Dic73C2×D411yescharacteristic
648C4×Dic73C2×D411yescharacteristic
649C4×Dic73C2×D411yescharacteristic
650C4×Dic73C2×D411yescharacteristic
651C4×Dic73C2411yescharacteristic
652C4×Dic73C2411yescharacteristic
653C4×Dic73C2411yescharacteristic
654C24×C73—21no—
655#41×C73—41no—
656#41×C73—41no—
657C2×Q8×C73C2411yescharacteristic
658C2×D4×C73—21no—
659C2×D4×C73—21no—
660C2×D4×C73—21no—
661C2×D4×C73—21no—
662C2×D4×C73—21no—
663C2×D4×C73—41no—
664C2×D4×C73—41no—
665C2×D4×C73C2×D411yescharacteristic
666C2×D4×C73C2411yescharacteristic
667C2×D4×C73C2411yescharacteristic
668C2×D4×C73C2411yescharacteristic
669C22×C4×C73—21no—
670C22×C4×C73—21no—
671C22×C4×C73—21no—
672C22×C4×C73—21no—
673C22×C4×C73C2411yescharacteristic
674C22×C4×C73C2411yescharacteristic
675SD16×C73—41no—
676D8×C73—41no—
677D8×C73—41no—
678C2×C8×C73—41no—
679C2×C8×C73—41no—
680C2×C8×C73C2411yescharacteristic
681C2×C8×C73C2411yescharacteristic
682C2×C8×C73C2411yescharacteristic
683C2×C8×C73C2411yescharacteristic
684C4⋊C4×C73—21no—
685C4⋊C4×C73—21no—
686C4⋊C4×C73—21no—
687C4⋊C4×C73—21no—
688C4⋊C4×C73C2×D411yescharacteristic
689C4⋊C4×C73C2411yescharacteristic
690C4⋊C4×C73C2411yescharacteristic
691C4⋊C4×C73C2411yescharacteristic
692C4⋊C4×C73C2411yescharacteristic
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—
700C22⋊C4×C73—21no—
701C22⋊C4×C73—21no—
702C22⋊C4×C73C2×D411yescharacteristic
703C22⋊C4×C73C2×D411yescharacteristic
704C42×C73—21no—
705C42×C73C2411yescharacteristic
706C23×C73—21no—
707C23×C73—21no—
708C23×C73—21no—
709C23×C73—42no—
710C23×C73—81no—
711C23×C73—81no—
712C23×C73C22×D411yescharacteristic
713C23×C73C22×D411yescharacteristic
714C22×D73—21no—
715C22×D73—21no—
716C22×D73—42no—
717C22×D73—81no—
718C22×D73—81no—
719C22×D73C22×D411yescharacteristic
720Q8×C73—21no—
721Q8×C73—21no—
722D4×C73—22no—
723D4×C73—21no—
724D4×C73—21no—
725D4×C73—21no—
726D4×C73—21no—
727D4×C73—21no—
728D4×C73—21no—
729D4×C73—42no—
730D4×C73—81no—
731D4×C73—81no—
732D4×C73—81no—
733D4×C73—81no—
734C2×C4×C73—21no—
735C2×C4×C73—21no—
736C2×C4×C73—21no—
737C2×C4×C73—21no—
738C2×C4×C73—21no—
739C2×C4×C73—21no—
740C2×C4×C73—21no—
741C2×C4×C73—21no—
742C2×C4×C73—21no—
743C2×C4×C73—81no—
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×C73C2511yescharacteristic
752C22⋊D73—22no—
753C22⋊D73—41no—
754C22⋊D73—42no—
755C22⋊D73—42no—
756C22⋊D73—42no—
757C22⋊D73—42no—
758C22⋊D73—42no—
759C22⋊D73—42no—
760C22⋊D73—42no—
761C22⋊D73—81no—
762C22⋊D73—81no—
763C22⋊D73—81no—
764C22⋊D73—81no—
765C2×Dic73—22no—
766C2×Dic73—21no—
767C2×Dic73—21no—
768C2×Dic73—21no—
769C2×Dic73—21no—
770C2×Dic73—21no—
771C2×Dic73—21no—
772C2×Dic73—41no—
773C2×Dic73—41no—
774C2×Dic73—41no—
775C2×Dic73—42no—
776C2×Dic73—42no—
777C2×Dic73—42no—
778C2×Dic73—42no—
779C2×Dic73—81no—
780C2×Dic73C22×D411yescharacteristic
781C2×Dic73C22×D411yescharacteristic
782C2×Dic73C22×D411yescharacteristic
783C2×Dic73C22×D411yescharacteristic
784C2×Dic73C22×D411yescharacteristic
785C2×Dic73C22×D411yescharacteristic
786C2×Dic73C22×D411yescharacteristic
787D292—21no—
788D292—21no—
789D292—21no—
790D292—21no—
791D292—81no—
792C4×D73—21no—
793C4×D73—21no—
794C4×D73—41no—
795C4×D73—41no—
796C4×D73—42no—
797C4×D73—42no—
798C4×D73—81no—
799C4×D73—81no—
800C4×D73—81no—
801C4×D73—81no—
802Dic146—21no—
803Dic146—21no—
804Dic146—21no—
805Dic146—21no—
806Dic146—21no—
807Dic146—21no—
808Dic146—21no—
809Dic146—41no—
810Dic146—42no—
811Dic146—42no—
812Dic146—81no—
813Dic146—81no—
814Dic146H(5,𝔽2)12yes—
815C8×C73—21no—
816C8×C73—21no—
817C8×C73—21no—
818C8×C73—21no—
819#10596831—21no—
820#10596831—21no—
821#10596831—21no—
822#10596831—21no—
823C22×C73—21no—
824C22×C73—21no—
825C22×C73—21no—
826C22×C73—21no—
827C22×C73—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×C73—162no—
838C22×C73#57512yes—
839C22×C73C23×D411yescharacteristic
840C2×D73—21no—
841C2×D73—21no—
842C2×D73—21no—
843C2×D73—41no—
844C2×D73—41no—
845C2×D73—41no—
846C2×D73—41no—
847C2×D73—41no—
848C2×D73—41no—
849C2×D73—162no—
850C4×C73—21no—
851C4×C73—21no—
852C4×C73—21no—
853C4×C73—21no—
854C4×C73—41no—
855C4×C73—41no—
856C4×C73—41no—
857C4×C73—41no—
858C4×C73—41no—
859C4×C73C2×H(5,𝔽2)11yescharacteristic
860C4×C73#58511yescharacteristic
861Dic73—21no—
862Dic73—21no—
863Dic73—21no—
864Dic73—22no—
865Dic73—21no—
866Dic73—21no—
867Dic73—21no—
868Dic73—21no—
869Dic73—41no—
870Dic73—41no—
871Dic73—41no—
872Dic73—41no—
873Dic73—41no—
874#61992—731nomaximal, Sylow
875C2×C73—22no—
876C2×C73—41no—
877C2×C73—81no—
878C2×C73—81no—
879C2×C73—81no—
880C2×C73#348811yescharacteristic
881C2×C73C2×#57511yescharacteristic
882C2×C73#358411yescharacteristic
883D73—41no—
884D73—81no—
885D73—81no—
886#3514—731no—
887#3480—731no—
888#3403—731no—
889#3401—731no—
890#3377—731no—
891#3371—731no—
892#3320—731no—
893#3318—731no—
894#3313—731no—
895#3311—731no—
896#3301—731no—
897#3297D7311yescharacteristic, complemented
898#3285—731no—
899#3282—731no—
900#3271—731no—
901#3270—731no—
902#3268—731no—
903#3265—731no—
904#3256—731no—
905#3250—731no—
906#3247—731no—
907#3219—731no—
908#3213—731no—
909#3211—731no—
910#3117—731no—
911#3111—731no—
912#3102—731no—
913#3040—731no—
914#3035—731no—
915C2×#464—731no—
916#2990—731no—
917C73#6199211yescharacteristic, complemented, Sylow
918C2×#137—731no—
919C2×AGL(1,ℤ/8)—731no—
920C2×#135—731no—
921C2×#135—731no—
922C22×Q16—731no—
923C22×SD16—731no—
924#559—731no—
925#559—731no—
926#559—1461no—
927#557—731no—
928#556—731no—
929#556—731no—
930#556—1461no—
931#555—1461no—
932#553—731no—
933#553—1461no—
934#553—1461no—
935#553C2×D7311yescharacteristic, complemented
936#551—1461no—
937#551—1461no—
938#550—731no—
939D4×Q8—731no—
940#548—731no—
941#548—731no—
942#548—731no—
943#548—731no—
944#546—731no—
945#546—1461no—
946#546C2×D7311yescharacteristic
947D42—731no—
948#542—1461no—
949#538—1461no—
950#538—1461no—
951#532—731no—
952#532—731no—
953#532—1461no—
954#529—731no—
955#529—731no—
956#529—731no—
957#529—731no—
958#529—731no—
959#529—1461no—
960#529—1461no—
961C2×#124—731no—
962C2×#124—731no—
963#518—1461no—
964C4×#41—731no—
965C4×#41—731no—
966C4×#41—731no—
967C4×#41—1461no—
968C2×C4×Q8—731no—
969#497—731no—
970#496—731no—
971#496—731no—
972#496—731no—
973#495—731no—
974#495—731no—
975#491—731no—
976#490—731no—
977#489—731no—
978#489—731no—
979#488—731no—
980#488C2×D7311yescharacteristic
981#485—731no—
982#485—731no—
983#484C2×D7311yescharacteristic, complemented
984#482—731no—
985#482C2×D7311yescharacteristic
986#481—731no—
987#479—731no—
988#479—731no—
989#479—731no—
990#479—731no—
991#478—731no—
992#478—731no—
993#478—731no—
994#478C2×D7311yescharacteristic, complemented
995#477—731no—
996#476—731no—
997#470—731no—
998#469—731no—
999#468—731no—
1000#468—731no—
1001#467—731no—
1002#466—731no—
1003#466—731no—
1004#466C2×D7311yescharacteristic
1005#465—731no—
1006#465—731no—
1007#465—731no—
1008#465C2×D7311yescharacteristic, complemented
1009#464—731no—
1010#464—731no—
1011#464—731no—
1012#464—731no—
1013#464—731no—
1014#464—731no—
1015#464—731no—
1016#464—731no—
1017#464—731no—
1018#464—731no—
1019#464—731no—
1020#464—731no—
1021#464—731no—
1022#464—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
1033#462—731no—
1034#461—731no—
1035#460—731no—
1036#460—731no—
1037#459—731no—
1038#459—731no—
1039#452—731no—
1040#452—731no—
1041#452—731no—
1042#452—731no—
1043#451—731no—
1044#451—731no—
1045#450—731no—
1046#449—731no—
1047#449—731no—
1048#449—731no—
1049#449C2×D7311yescharacteristic, complemented
1050#448—731no—
1051#448—731no—
1052#448—731no—
1053#448—731no—
1054#447—731no—
1055#447—731no—
1056#447C2×D7311yescharacteristic
1057#446—731no—
1058#446—731no—
1059#442—731no—
1060#441—731no—
1061#441—731no—
1062#441—731no—
1063#440—731no—
1064#440—731no—
1065#440—731no—
1066#440—731no—
1067C4×Q16—731no—
1068C4×SD16—731no—
1069C4×SD16—731no—
1070C4×D8C2×D7311yescharacteristic, complemented
1071#435—731no—
1072#435—731no—
1073#435—731no—
1074#435—731no—
1075C8×D4—731no—
1076C8×D4C2×D7311yescharacteristic, complemented
1077#432—731no—
1078#432—731no—
1079#431—731no—
1080#423—731no—
1081C2×C4⋊C8—731no—
1082C2×C4⋊C8—731no—
1083#419—731no—
1084#418—731no—
1085#416—731no—
1086#416C2×D7311yescharacteristic, complemented
1087C2×#103—731no—
1088C2×#102C2×D7311yescharacteristic
1089C2×#41—731no—
1090C2×#41—731no—
1091C2×#41—731no—
1092C2×#41—731no—
1093C2×#41—1461no—
1094C2×#41C22×D7311yescharacteristic
1095C22×Q8—731no—
1096C22×Q8—731no—
1097C22×Q8—731no—
1098C22×D4—731no—
1099C22×D4—1461no—
1100C22×D4C22×D7311yescharacteristic
1101#137—2922no—
1102AGL(1,ℤ/8)—2922no—
1103#135—2922no—
1104#135—2922no—
1105C2×Q16—2922no—
1106C2×Q16—731no—
1107C2×Q16—731no—
1108C2×Q16—731no—
1109C2×Q16—731no—
1110C2×Q16—731no—
1111C2×Q16—731no—
1112C2×SD16—2922no—
1113C2×SD16—731no—
1114C2×SD16—731no—
1115C2×SD16—731no—
1116C2×SD16—731no—
1117C2×SD16—731no—
1118C2×SD16—731no—
1119C2×SD16—731no—
1120C2×SD16—731no—
1121C2×SD16—731no—
1122C2×SD16—731no—
1123C2×SD16—731no—
1124C2×SD16C22×D7311yescharacteristic
1125C2×D8—731no—
1126C2×D8—731no—
1127C2×D8—731no—
1128C2×D8—731no—
1129C2×D8C22×D7311yescharacteristic
1130C2×D8C22×D7311yescharacteristic
1131C2×M16—731no—
1132C2×M16—731no—
1133C22×C8—731no—
1134C22×C8—731no—
1135C22×C8C22×D7311yescharacteristic
1136C22×C8C22×D7311yescharacteristic
1137C4⋊Q8—731no—
1138C4⋊Q8—731no—
1139C4⋊Q8—1461no—
1140C4⋊Q8—1461no—
1141#127—731no—
1142#127—731no—
1143#127—1461no—
1144#126—21no—
1145#126—1461no—
1146#126—1461no—
1147#126—1461no—
1148#126—1461no—
1149#126—1461no—
1150#126—1461no—
1151#126—1461no—
1152#126—1461no—
1153#126—1461no—
1154#126—1461no—
1155#125—731no—
1156#125—731no—
1157#125—1461no—
1158#125—1461no—
1159#125C22×D7311yescharacteristic
1160#124—731no—
1161#124—731no—
1162#124—731no—
1163#124—731no—
1164#124—731no—
1165#124—731no—
1166#124—731no—
1167#124—731no—
1168#124—1461no—
1169#124—1461no—
1170#124—1461no—
1171#124—1461no—
1172#124—1461no—
1173#124—1461no—
1174#124—1461no—
1175#124—1461no—
1176#124—1461no—
1177#124—1461no—
1178#124—1461no—
1179#124—1461no—
1180#124C22×D7311yescharacteristic
1181#123—21no—
1182#123—21no—
1183#123—1461no—
1184#123—1461no—
1185#123—1461no—
1186#123—1461no—
1187#123—1461no—
1188#123—1461no—
1189#123—1461no—
1190#123—1461no—
1191#123—1461no—
1192#123—1461no—
1193#123—1461no—
1194C22⋊Q8—731no—
1195C22⋊Q8—731no—
1196C22⋊Q8—731no—
1197C22⋊Q8—731no—
1198C22⋊Q8—1461no—
1199C22⋊Q8—1461no—
1200C22⋊Q8—1461no—
1201C22⋊Q8—1461no—
1202C22⋊Q8—1461no—
1203C22⋊Q8—1461no—
1204C22⋊Q8—1461no—
1205C22⋊Q8C22×D7311yescharacteristic
1206#121—21no—
1207#121—21no—
1208#121—731no—
1209#121—731no—
1210#121—731no—
1211#121—731no—
1212#121—1461no—
1213#121—1461no—
1214#121—1461no—
1215#121—1461no—
1216#121—1461no—
1217#121—1461no—
1218#121—1461no—
1219#121—1461no—
1220#121—1461no—
1221#121—1461no—
1222#121—1461no—
1223#121—1461no—
1224#121C22×D7311yescharacteristic
1225#121C22×D7311yescharacteristic
1226#121C22×D7311yescharacteristic
1227#120—21no—
1228#120—1461no—
1229#120—1461no—
1230#120—1461no—
1231C4×Q8—731no—
1232C4×Q8—731no—
1233C4×Q8—731no—
1234C4×Q8—731no—
1235C4×Q8—731no—
1236C4×Q8—731no—
1237C4×Q8—731no—
1238C4×Q8—731no—
1239C4×Q8—731no—
1240C4×Q8—731no—
1241C4×Q8—731no—
1242C4×Q8—1461no—
1243C4×Q8—1461no—
1244C4×Q8—1461no—
1245C4×Q8—1461no—
1246C4×D4—21no—
1247C4×D4—731no—
1248C4×D4—731no—
1249C4×D4—731no—
1250C4×D4—731no—
1251C4×D4—731no—
1252C4×D4—731no—
1253C4×D4—731no—
1254C4×D4—731no—
1255C4×D4—731no—
1256C4×D4—731no—
1257C4×D4—1461no—
1258C4×D4—1461no—
1259C4×D4—1461no—
1260C4×D4—1461no—
1261C4×D4—1461no—
1262C4×D4—1461no—
1263C4×D4—1461no—
1264C4×D4—1461no—
1265C4×D4—1461no—
1266C4×D4—1461no—
1267C4×D4—1461no—
1268C4×D4—1461no—
1269C4×D4—1461no—
1270C4×D4—1461no—
1271C4×D4—1461no—
1272C4×D4—1461no—
1273C4×D4—1461no—
1274C4×D4—1461no—
1275C4×D4—1461no—
1276C4×D4—1461no—
1277C4×D4—1461no—
1278C4×D4C22×D7311yescharacteristic
1279C4×D4C22×D7311yescharacteristic
1280C4×D4C22×D7311yescharacteristic
1281#117—731no—
1282#117—731no—
1283#117—731no—
1284#117—731no—
1285#117—1461no—
1286#117—1461no—
1287#117—1461no—
1288#117—1461no—
1289#117—1461no—
1290#117—1461no—
1291#117—1461no—
1292#117—1461no—
1293#117C22×D7311yescharacteristic
1294C2×C4⋊C4—1461no—
1295C2×C4⋊C4C22×D7311yescharacteristic
1296C2×C22⋊C4—21no—
1297C2×C22⋊C4—1461no—
1298C2×C22⋊C4—1461no—
1299C2×C22⋊C4—1461no—
1300C2×C22⋊C4—1461no—
1301C2×C22⋊C4—1461no—
1302C2×C42—731no—
1303C2×C42—731no—
1304C2×C42—731no—
1305C2×C42—1461no—
1306C2×C42—1461no—
1307C2×C42—1461no—
1308#107—731no—
1309#107—731no—
1310#107C22×D7311yescharacteristic
1311#107C22×D7311yescharacteristic
1312#106—731no—
1313#106—731no—
1314#106—731no—
1315#106C22×D7311yescharacteristic
1316C4⋊C8—731no—
1317C4⋊C8—731no—
1318C4⋊C8—731no—
1319C4⋊C8—731no—
1320C4⋊C8—731no—
1321C4⋊C8—731no—
1322C4⋊C8—731no—
1323C4⋊C8—731no—
1324C4⋊C8—731no—
1325C4⋊C8C22×D7311yescharacteristic
1326#103—731no—
1327#103—731no—
1328#103—731no—
1329#103—731no—
1330#103—731no—
1331#103—731no—
1332#103—731no—
1333#103—731no—
1334#103—731no—
1335#103—731no—
1336#103—731no—
1337#103—731no—
1338#103—731no—
1339#103C22×D7311yescharacteristic
1340#103C22×D7311yescharacteristic
1341#103C22×D7311yescharacteristic
1342#102—731no—
1343#102—731no—
1344#102—731no—
1345#102—731no—
1346#102—731no—
1347#102—731no—
1348#102—731no—
1349#102—731no—
1350#102—731no—
1351#102C22×D7311yescharacteristic
1352#102C22×D7311yescharacteristic
1353#102C22×D7311yescharacteristic
1354#102C22×D7311yescharacteristic
1355#102C22×D7311yescharacteristic
1356#102C22×D7311yescharacteristic
1357#102C22×D7311yescharacteristic
1358C22⋊C8—731no—
1359C22⋊C8—731no—
1360C22⋊C8—731no—
1361C22⋊C8—731no—
1362C22⋊C8C22×D7311yescharacteristic
1363C22⋊C8C22×D7311yescharacteristic
1364#97—731no—
1365#97—731no—
1366#97—731no—
1367#97—731no—
1368C4×C8—731no—
1369C4×C8C22×D7311yescharacteristic
1370C24—21no—
1371C24—1461no—
1372#41—41no—
1373#41—41no—
1374#41—2921no—
1375#41—2921no—
1376#41—2921no—
1377#41—2921no—
1378#41—2922no—
1379#41—2924no—
1380#41—1462no—
1381#41—1462no—
1382C2×Q8—2921no—
1383C2×Q8—2921no—
1384C2×Q8—2921no—
1385C2×Q8—2921no—
1386C2×Q8—2921no—
1387C2×Q8—731no—
1388C2×Q8—731no—
1389C2×Q8—731no—
1390C2×Q8—731no—
1391C2×Q8—731no—
1392C2×Q8—1462no—
1393C2×Q8—1461no—
1394C2×Q8—1461no—
1395C2×Q8—1461no—
1396C2×Q8—1461no—
1397C2×Q8C23×D7311yescharacteristic
1398C2×D4—21no—
1399C2×D4—21no—
1400C2×D4—21no—
1401C2×D4—21no—
1402C2×D4—21no—
1403C2×D4—41no—
1404C2×D4—41no—
1405C2×D4—2924no—
1406C2×D4—2921no—
1407C2×D4—2921no—
1408C2×D4—731no—
1409C2×D4—731no—
1410C2×D4—731no—
1411C2×D4—731no—
1412C2×D4—1461no—
1413C2×D4—1461no—
1414C2×D4—1461no—
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×D4D4×D7311yescharacteristic
1425C2×D4C23×D7311yescharacteristic
1426C2×D4C23×D7311yescharacteristic
1427C2×D4C23×D7311yescharacteristic
1428C22×C4—21no—
1429C22×C4—21no—
1430C22×C4—21no—
1431C22×C4—21no—
1432C22×C4—731no—
1433C22×C4—731no—
1434C22×C4—731no—
1435C22×C4—731no—
1436C22×C4—731no—
1437C22×C4—731no—
1438C22×C4—731no—
1439C22×C4—1461no—
1440C22×C4—1461no—
1441C22×C4—1461no—
1442C22×C4—1461no—
1443C22×C4—1461no—
1444C22×C4—1461no—
1445C22×C4—1461no—
1446C22×C4—1461no—
1447C22×C4—1461no—
1448C22×C4—1461no—
1449C22×C4—1461no—
1450C22×C4C23×D7311yescharacteristic
1451C22×C4C23×D7311yescharacteristic
1452Q16—2921no—
1453Q16—2921no—
1454Q16—2921no—
1455Q16—1462no—
1456Q16—1462no—
1457Q16—1462no—
1458SD16—41no—
1459SD16—2921no—
1460SD16—2921no—
1461SD16—2921no—
1462SD16—2921no—
1463SD16—2921no—
1464SD16—2921no—
1465SD16—2921no—
1466SD16—2921no—
1467SD16—1462no—
1468SD16—1462no—
1469SD16—1462no—
1470D8—41no—
1471D8—41no—
1472D8—2921no—
1473D8—2921no—
1474D8—2921no—
1475D8—2921no—
1476M16—2921no—
1477M16—2921no—
1478C2×C8—41no—
1479C2×C8—41no—
1480C2×C8—2921no—
1481C2×C8—2921no—
1482C2×C8—731no—
1483C2×C8—731no—
1484C2×C8—731no—
1485C2×C8—731no—
1486C2×C8C23×D7311yescharacteristic
1487C2×C8C23×D7311yescharacteristic
1488C2×C8C23×D7311yescharacteristic
1489C2×C8C23×D7311yescharacteristic
1490C4⋊C4—21no—
1491C4⋊C4—21no—
1492C4⋊C4—21no—
1493C4⋊C4—21no—
1494C4⋊C4—731no—
1495C4⋊C4—731no—
1496C4⋊C4—731no—
1497C4⋊C4—731no—
1498C4⋊C4—731no—
1499C4⋊C4—731no—
1500C4⋊C4—731no—
1501C4⋊C4—1461no—
1502C4⋊C4—1461no—
1503C4⋊C4—1461no—
1504C4⋊C4—1461no—
1505C4⋊C4—1461no—
1506C4⋊C4—1461no—
1507C4⋊C4—1461no—
1508C4⋊C4—1461no—
1509C4⋊C4—1461no—
1510C4⋊C4—1461no—
1511C4⋊C4—1461no—
1512C4⋊C4—1461no—
1513C4⋊C4—1461no—
1514C4⋊C4—1461no—
1515C4⋊C4—1461no—
1516C4⋊C4—1461no—
1517C4⋊C4—1461no—
1518C4⋊C4—1461no—
1519C4⋊C4—1461no—
1520C4⋊C4—1461no—
1521C4⋊C4D4×D7311yescharacteristic
1522C4⋊C4C23×D7311yescharacteristic
1523C4⋊C4C23×D7311yescharacteristic
1524C4⋊C4C23×D7311yescharacteristic
1525C4⋊C4C23×D7311yescharacteristic
1526C22⋊C4—21no—
1527C22⋊C4—21no—
1528C22⋊C4—21no—
1529C22⋊C4—21no—
1530C22⋊C4—21no—
1531C22⋊C4—21no—
1532C22⋊C4—21no—
1533C22⋊C4—21no—
1534C22⋊C4—21no—
1535C22⋊C4—731no—
1536C22⋊C4—731no—
1537C22⋊C4—731no—
1538C22⋊C4—731no—
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⋊C4—1461no—
1555C22⋊C4—1461no—
1556C22⋊C4—1461no—
1557C22⋊C4—1461no—
1558C22⋊C4—1461no—
1559C22⋊C4—1461no—
1560C22⋊C4—1461no—
1561C22⋊C4—1461no—
1562C22⋊C4—1461no—
1563C22⋊C4—1461no—
1564C22⋊C4—1461no—
1565C22⋊C4—1461no—
1566C22⋊C4—1461no—
1567C22⋊C4—1461no—
1568C22⋊C4—1461no—
1569C22⋊C4D4×D7311yescharacteristic
1570C22⋊C4D4×D7311yescharacteristic
1571C42—21no—
1572C42—731no—
1573C42—731no—
1574C42—731no—
1575C42—731no—
1576C42—731no—
1577C42—731no—
1578C42—731no—
1579C42—731no—
1580C42—731no—
1581C42—1461no—
1582C42—1461no—
1583C42—1461no—
1584C42—1461no—
1585C42—1461no—
1586C42—1461no—
1587C42—1461no—
1588C42—1461no—
1589C42—1461no—
1590C42—1461no—
1591C42C23×D7311yescharacteristic
1592C23—21no—
1593C23—21no—
1594C23—21no—
1595C23—42no—
1596C23—81no—
1597C23—81no—
1598C23—2922no—
1599C23—5841no—
1600C23—5841no—
1601C23—731no—
1602C23—1461no—
1603C23—1461no—
1604C23C2×D4×D7311yescharacteristic
1605C23C2×D4×D7311yescharacteristic
1606Q8—21no—
1607Q8—21no—
1608Q8—2922no—
1609Q8—2921no—
1610Q8—2922no—
1611Q8—5841no—
1612Q8—5841no—
1613Q8—732no—
1614Q8—1461no—
1615Q8—1461no—
1616Q8—1461no—
1617Q8—1461no—
1618Q8—1461no—
1619Q8—1461no—
1620Q8—1461no—
1621D4—22no—
1622D4—21no—
1623D4—21no—
1624D4—21no—
1625D4—21no—
1626D4—21no—
1627D4—21no—
1628D4—42no—
1629D4—81no—
1630D4—81no—
1631D4—81no—
1632D4—81no—
1633D4—2922no—
1634D4—2922no—
1635D4—2922no—
1636D4—2922no—
1637D4—2921no—
1638D4—2922no—
1639D4—2922no—
1640D4—2922no—
1641D4—5841no—
1642D4—5841no—
1643D4—5841no—
1644D4—5841no—
1645D4—5841no—
1646D4—1462no—
1647D4—1461no—
1648D4—1461no—
1649D4—1461no—
1650D4—1461no—
1651C2×C4—21no—
1652C2×C4—21no—
1653C2×C4—21no—
1654C2×C4—21no—
1655C2×C4—21no—
1656C2×C4—21no—
1657C2×C4—21no—
1658C2×C4—21no—
1659C2×C4—21no—
1660C2×C4—81no—
1661C2×C4—81no—
1662C2×C4—81no—
1663C2×C4—81no—
1664C2×C4—2922no—
1665C2×C4—2921no—
1666C2×C4—2921no—
1667C2×C4—2922no—
1668C2×C4—2922no—
1669C2×C4—2922no—
1670C2×C4—2922no—
1671C2×C4—2921no—
1672C2×C4—2921no—
1673C2×C4—2921no—
1674C2×C4—2922no—
1675C2×C4—5841no—
1676C2×C4—5841no—
1677C2×C4—5841no—
1678C2×C4—5841no—
1679C2×C4—5841no—
1680C2×C4—731no—
1681C2×C4—731no—
1682C2×C4—731no—
1683C2×C4—731no—
1684C2×C4—731no—
1685C2×C4—731no—
1686C2×C4—731no—
1687C2×C4—1461no—
1688C2×C4—1461no—
1689C2×C4—1461no—
1690C2×C4—1461no—
1691C2×C4—1461no—
1692C2×C4—1462no—
1693C2×C4—1461no—
1694C2×C4—1461no—
1695C2×C4—1461no—
1696C2×C4C2×D4×D7311yescharacteristic
1697C2×C4C2×D4×D7311yescharacteristic
1698C2×C4C2×D4×D7311yescharacteristic
1699C2×C4C2×D4×D7311yescharacteristic
1700C2×C4C24×D7311yescharacteristic
1701C8—21no—
1702C8—21no—
1703C8—21no—
1704C8—21no—
1705C8—1461no—
1706C8—1461no—
1707C8—1461no—
1708C8—1461no—
1709C22—21no—
1710C22—21no—
1711C22—21no—
1712C22—21no—
1713C22—21no—
1714C22—41no—
1715C22—41no—
1716C22—41no—
1717C22—41no—
1718C22—41no—
1719C22—41no—
1720C22—41no—
1721C22—41no—
1722C22—41no—
1723C22—162no—
1724C22—2921no—
1725C22—2921no—
1726C22—2921no—
1727C22—2921no—
1728C22—2921no—
1729C22—2921no—
1730C22—11682no—
1731C22—1461no—
1732C22—1461no—
1733C22—1461no—
1734C22#1798938412yes—
1735C22C22×D4×D7311yescharacteristic
1736C4—21no—
1737C4—21no—
1738C4—21no—
1739C4—21no—
1740C4—41no—
1741C4—41no—
1742C4—41no—
1743C4—41no—
1744C4—41no—
1745C4—2921no—
1746C4—2921no—
1747C4—2921no—
1748C4—2921no—
1749C4—2921no—
1750C4—1462no—
1751C4—1461no—
1752C4—1461no—
1753C4—1461no—
1754C4—1461no—
1755C4—1461no—
1756C4—1461no—
1757C4—1461no—
1758C4H(5,𝔽2)×D7311yescharacteristic
1759C4#1798942311yescharacteristic
1760C2—22no—
1761C2—41no—
1762C2—81no—
1763C2—81no—
1764C2—81no—
1765C2—2921no—
1766C2—5841no—
1767C2—5841no—
1768C2#2262359411yescharacteristic
1769C2C2×#1798938411yescharacteristic
1770C2#2262469911yescharacteristic
subgroupG/H
centerC22C22×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC73×#3297C2
socleC22×C73C23×D4
hypercenter#3297D73
hypocenterC73#61992
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3297

Complements

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

NH ≅ G/Ntype
1. #22623889C2semidirect
2. #22623525C2semidirect
3. #22623017C2semidirect
4. #22622995C2semidirect
5. #22622779C2semidirect
6. #22622697C2semidirect
7. #22622100C2semidirect
8. #22622068C2semidirect
9. #22621993C2semidirect
10. #22621965C2semidirect
11. #22621827C2semidirect
12. #22621674C2semidirect
13. #22621634C2semidirect
14. #22621509C2semidirect
15. #22621498C2semidirect
16. #22621468C2semidirect
17. #22621430C2semidirect
18. #22621331C2semidirect
19. #22621277C2semidirect
20. #22621252C2semidirect
21. #22620966C2semidirect
22. #22620915C2semidirect
23. #22620897C2semidirect
24. #22620105C2semidirect
25. #22620035C2semidirect
26. #22619945C2semidirect
27. #22619420C2semidirect
28. #22619384C2semidirect
29. C2×#17988808C2semidirect
30. #22619054C2semidirect
31. C73×#3297C2semidirect
32. C2×#14556620C22semidirect
34. C2×#14556613C22semidirect
35. C2×#14556611C22semidirect
36. C22×Dic292C22semidirect
40. #17989320C22semidirect
41. #17989314C22semidirect
43. #17989305C22semidirect
51. #17989255C22semidirect
54. #17989246C22semidirect
65. #17989132C22semidirect
67. #17989122C22semidirect
71. #17989118C22semidirect
76. #17989055C22semidirect
79. C4×#11924027C22semidirect
80. C2×#14556556C22semidirect
81. #17988978C22semidirect
84. #17988975C22semidirect
85. #17988971C22semidirect
87. #17988954C22semidirect
90. #17988945C22semidirect
91. #17988944C22semidirect
92. #17988930C22semidirect
93. #17988928C22semidirect
96. #17988893C22semidirect
97. #17988893C22semidirect
98. #17988893C22semidirect
99. #17988891C22semidirect
100. #17988886C22semidirect
102. #17988885C22semidirect
103. #17988880C22semidirect
104. #17988876C22semidirect
105. #17988846C22semidirect
107. #17988834C22semidirect
109. #17988828C22semidirect
112. #17988818C22semidirect
114. #17988814C22semidirect
115. #17988812C22semidirect
116. #17988812C22semidirect
117. #17988810C22semidirect
118. #17988810C22semidirect
123. #17988808C22semidirect
124. #17988808C22semidirect
125. #17988808C22semidirect
126. #17988808C22semidirect
127. #17988808C22semidirect
129. #17988805C22semidirect
130. #17988804C22semidirect
131. #17988802C22semidirect
132. #17988802C22semidirect
134. #17988801C22semidirect
137. #17988800C22semidirect
138. #17988796C22semidirect
139. #17988791C22semidirect
141. #17988785C22semidirect
143. #17988781C22semidirect
144. #17988751C22semidirect
145. #17988751C22semidirect
146. #17988750C22semidirect
147. #17988749C22semidirect
148. #17988744C22semidirect
149. #17988742C22semidirect
152. #17988730C22semidirect
155. #17988728C22semidirect
156. #17988727C22semidirect
157. #17988725C22semidirect
160. #17988717C22semidirect
161. #17988714C22semidirect
163. #17988693C22semidirect
164. #17988691C22semidirect
165. #17988691C22semidirect
166. #17988686C22semidirect
167. #17988686C22semidirect
168. #17988686C22semidirect
170. C4×Dic292C22semidirect
171. C4×#11924016C22semidirect
172. C4×#11924016C22semidirect
174. #17988658C22semidirect
176. #17988655C22semidirect
177. D4×#10596831C22semidirect
178. #17988641C22semidirect
179. #17988641C22semidirect
180. #17988638C22semidirect
181. #17988609C22semidirect
182. C2×#14556520C22semidirect
183. C2×#14556520C22semidirect
184. #17988594C22semidirect
186. #17988581C22semidirect
187. C2×#14556514C22semidirect
188. #553×C73C22semidirect
191. #484×C73C22semidirect
193. #478×C73C22semidirect
195. #465×C73C22semidirect
197. #449×C73C22semidirect
199. C4×D8×C73C22semidirect
200. C8×D4×C73C22semidirect
201. #416×C73C22semidirect
897. #3297D73semidirect
917. C73#61992semidirect
935. #553C2×D73semidirect
983. #484C2×D73semidirect
994. #478C2×D73semidirect
1008. #465C2×D73semidirect
1049. #449C2×D73semidirect
1070. C4×D8C2×D73semidirect
1076. C8×D4C2×D73semidirect
1086. #416C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226238892
#226235252
#226230172
#226229952
#226227792
#226226972
#226221002
#226220682
#226219932
#226219652
#226218272
#226216742
#226216342
#226215092
#226214982
#226214682
#226214302
#226213312
#226212772
#226212522
#226209662
#226209152
#226208972
#226201052
#226200352
#226199452
#226194202
#226193842
C2×#179888082
#226190542
C73×#32972
#6199273