Finite Group Databasebeta

← #11670761

Subgroups — #11670761

Order 768.

2682 conjugacy classes of subgroups.

The subgroup lattice has 1436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5779C211yesmaximal, characteristic, complemented
2C2×#5768C211yesmaximal, characteristic, complemented
3#86356C211yesmaximal, characteristic, complemented
4#85901C211yesmaximal, characteristic, complemented
5C3×#3046C211yesmaximal, characteristic, complemented
6#83981C211yesmaximal, characteristic, complemented
7#83913C211yesmaximal, characteristic, complemented
8#83403C211yesmaximal, characteristic, complemented
9#82558C211yesmaximal, characteristic, complemented
10#80631C212yesmaximal, complemented
11#80629C212yesmaximal, complemented
12#80567C212yesmaximal, complemented
13#80556C212yesmaximal, complemented
14#80501C212yesmaximal, complemented
15#80489C212yesmaximal, complemented
16#80447C212yesmaximal, complemented
17#80445C212yesmaximal, complemented
18#79089C211yesmaximal, characteristic, complemented
19#79074C211yesmaximal, characteristic, complemented
20#78890C211yesmaximal, characteristic, complemented
21#78885C211yesmaximal, characteristic, complemented
22C2×#4816C211yesmaximal, characteristic, complemented
23#78795C211yesmaximal, characteristic, complemented
24#61064—31nomaximal, Sylow
25C2×#1010C2211yescharacteristic, complemented
26C2×D3×#41C2211yescharacteristic
27C2×D3×#41C2211yescharacteristic
28C2×#1007C2211yescharacteristic, complemented
29C2×C3×#137C2211yescharacteristic, complemented
30C2×C3×#135C2211yescharacteristic
31C3×#536C2211yescharacteristic, complemented
32C3×#520C2211yescharacteristic, complemented
33#5833C2211yescharacteristic, complemented
34C2×#951C2211yescharacteristic, complemented
35C2×#950C2211yescharacteristic
36C2×#950C2211yescharacteristic
37C2×#946C2211yescharacteristic
38C22×#216C2211yescharacteristic, complemented
39C2×#942C2211yescharacteristic, complemented
40#5779—28no—
41#5768—28no—
42C2×#918C2211yescharacteristic
43C2×#918C2211yescharacteristic
44C2×#918C2212yescomplemented
45C2×D3×Q16C2212yescomplemented
46C2×#916C2212yescomplemented
47C2×#915C2211yescharacteristic
48C2×#915C2211yescharacteristic
49C2×#915C2212yescomplemented
50C2×#914C2211yescharacteristic
51C2×#914C2211yescharacteristic
52C2×#911C2211yescharacteristic
53C2×#911C2211yescharacteristic
54C2×#909C2211yescharacteristic, complemented
55C2×#907C2211yescharacteristic, complemented
56C2×#904C2211yescharacteristic
57C22×ΓL(1,𝔽25)C2211yescharacteristic
58#5727C2212yescomplemented
59#5726C2212yes—
60#5677C2212yes—
61#5676C2212yescomplemented
62#5655—22no—
63#5654—22no—
64#5629—21no—
65#5628—21no—
66#5627—21no—
67D3×C22⋊Q8—21no—
68#5576C2212yes—
69Q8×D12C2212yescomplemented
70#5555—22no—
71#5555C2212yes—
72#5554—22no—
73#5554C2212yescomplemented
74#5526—21no—
75#5526C2211yescharacteristic, complemented
76#5524—21no—
77#5524C2211yescharacteristic
78#5523C2211yescharacteristic, complemented
79#5510—21no—
80#5510C2211yescharacteristic, complemented
81C2×#897—21no—
82C2×#897C2211yescharacteristic
83C3×#464C2212yescomplemented
84C3×#463C2212yescomplemented
85C3×#462C2212yescomplemented
86C3×#461C2212yescomplemented
87C3×#424C2211yescharacteristic, complemented
88C3×#417C2211yescharacteristic, complemented
89C2×C3×#103C2211yescharacteristic, complemented
90#5232C2211yescharacteristic, complemented
91#5187C2212yes—
92#5186C2212yescomplemented
93#5186C2212yescomplemented
94#5173C2212yes—
95#5173C2212yescomplemented
96#5170C2212yescomplemented
97#5169C2212yescomplemented
98#5158C2212yescomplemented
99#5133C2211yescharacteristic, complemented
100#5126C2211yescharacteristic
101#5110C2211yescharacteristic, complemented
102C2×#816C2211yescharacteristic, complemented
103#5092C2212yescomplemented
104#5086C2212yescomplemented
105#5060C2212yescomplemented
106#5059C2212yescomplemented
107#5030C2212yescomplemented
108C4×#215C2212yescomplemented
109C4×#214C2212yescomplemented
110#5014C2212yescomplemented
111#4997C2211yescharacteristic, complemented
112#4966C2211yescharacteristic, complemented
113C2×#808C2211yescharacteristic, complemented
114#4849C2212yescomplemented
115#4845C2212yescomplemented
116#4844C2212yescomplemented
117#4841C2212yescomplemented
118#4838C2212yescomplemented
119#4838C2212yescomplemented
120#4836C2212yescomplemented
121#4836C2212yescomplemented
122#4816C2212yescomplemented
123#4816C2212yescomplemented
124#4816C2212yescomplemented
125#4816C2212yescomplemented
126#4816C2212yescomplemented
127#4810C2212yescomplemented
128#4809C2212yescomplemented
129#4809C2212yescomplemented
130#4808C2212yes—
131#4808C2212yescomplemented
132#4807C2212yescomplemented
133#4806C2212yescomplemented
134#4783C2212yes—
135#4782C2212yescomplemented
136#4778C2212yescomplemented
137#4776C2212yescomplemented
138C2×#578—31no—
139C2×#575—31no—
140#3489—31no—
141#3489—31no—
142#3276—32no—
143#3276—32no—
144#3275—32no—
145#3275—32no—
146#3270—32no—
147#3270—32no—
148#3267—32no—
149#3267—32no—
150#3156—31no—
151#3060—31no—
152C2×#470—31no—
153#3046—31no—
154#3046D311yescharacteristic, complemented
155#3013—31no—
156#3013—31no—
157#3007—31no—
158#3007—31no—
159#2952—31no—
160#2930—31no—
161C2×C3×#41C2311yescharacteristic
162C2×C3×#41C2311yescharacteristic
163C22×C3×Q8C2311yescharacteristic
164#1010—24no—
165#1010—42no—
166D3×#41—24no—
167D3×#41—24no—
168D3×#41—42no—
169D3×#41—42no—
170#1007—24no—
171#1007—42no—
172C2×#239—21no—
173C2×#239C2312yes—
174C2×#239C2311yescharacteristic
175C2×#239C2311yescharacteristic
176C2×D3×Q8—21no—
177C2×D3×Q8C2312yes—
178C2×D3×Q8C2312yes—
179C2×D3×Q8C2311yescharacteristic
180C2×D3×Q8C2311yescharacteristic
181C2×#237—22no—
182C2×#237—21no—
183C2×#237—21no—
184C2×#237C2312yes—
185C2×#237C2311yescharacteristic
186C2×#237C2311yescharacteristic
187C2×D3×D4—21no—
188C2×D3×D4—21no—
189C2×D3×D4C2311yescharacteristic
190C2×D3×D4C2311yescharacteristic
191C2×#235—22no—
192C2×#235—21no—
193C2×#235—21no—
194C2×#235—21no—
195C2×#235C2311yescharacteristic
196C2×#235C2311yescharacteristic
197C2×#235C2311yescharacteristic
198C22×C4×D3—21no—
199C22×C4×D3—21no—
200C22×C4×D3C2311yescharacteristic
201C22×Dic6—21no—
202C22×Dic6C2311yescharacteristic
203C3×#137—24no—
204C3×#135—24no—
205C2×C3×Q16C2311yescharacteristic
206C2×C3×Q16C2312yes—
207C2×C3×SD16C2311yescharacteristic
208C2×C3×SD16C2311yescharacteristic
209C2×C3×SD16C2312yes—
210C2×C3×D8C2311yescharacteristic
211C2×C3×M16C2311yescharacteristic
212C22×C3×C8C2311yescharacteristic
213C3×C4⋊Q8C2312yes—
214C3×#124C2312yes—
215C3×#123—22no—
216C3×C22⋊Q8—21no—
217C3×C22⋊Q8—21no—
218C3×C4×Q8C2312yes—
219C3×C4×D4—22no—
220C3×C4×D4C2312yes—
221C3×#117—21no—
222C3×#117C2311yescharacteristic
223C2×C3×C4⋊C4—21no—
224C2×C3×C4⋊C4C2311yescharacteristic
225#951—42no—
226#950—24no—
227#950D418yescomplemented
228#946—21no—
229#946—21no—
230#946C2312yes—
231#946C2312yes—
232#946C2312yes—
233C2×#216—24no—
234C2×#216C2311yescharacteristic
235C2×#216C2312yes—
236C2×#216C2312yes—
237C2×#216C2312yes—
238C2×#216C2312yes—
239C2×#216C2311yescharacteristic
240#942—42no—
241C2×#215C2311yescharacteristic
242C2×#215C2312yes—
243C2×#215C2311yescharacteristic
244#939—22no—
245#938C2312yes—
246C2×#214C2311yescharacteristic
247C2×#214C2312yes—
248C2×#214C2311yescharacteristic
249C2×#213C2311yescharacteristic
250C2×#213C2311yescharacteristic
251#930—22no—
252#930—22no—
253#930—21no—
254#930—22no—
255C2×(C2×D3)⋊C4—21no—
256C2×(C2×D3)⋊C4—21no—
257C2×(C2×D3)⋊C4—22no—
258C2×C4⋊Dic3—21no—
259C2×C4⋊Dic3—22no—
260C2×C4⋊Dic3C2311yescharacteristic
261#924—21no—
262C2×Dic3⋊C4—21no—
263C2×#208C2311yescharacteristic
264C22×C3⋊C8C2311yescharacteristic
265#918—24no—
266#918—24no—
267#918—28no—
268D3×Q16—28no—
269#916—28no—
270#915—24no—
271#915—24no—
272#915—28no—
273#914—24no—
274#914—24no—
275#911—24no—
276#911—24no—
277#909—24no—
278#907—24no—
279C2×Dic12C2311yescharacteristic
280C2×Dic12C2312yes—
281#904—24no—
282C2×D24C2311yescharacteristic
283C2×#204C2311yescharacteristic
284C2×#204C2311yescharacteristic
285C2×#204C2312yes—
286C2×ΓL(1,𝔽25)—24no—
287C2×ΓL(1,𝔽25)C2311yescharacteristic
288C2×ΓL(1,𝔽25)C2311yescharacteristic
289C2×ΓL(1,𝔽25)C2311yescharacteristic
290C2×ΓL(1,𝔽25)C2311yescharacteristic
291C2×ΓL(1,𝔽25)C2312yes—
292C2×D3×C8C2312yes—
293#897—21no—
294#897—21no—
295#897—21no—
296#897—21no—
297#897—21no—
298#897—22no—
299#897—22no—
300#897—22no—
301#897D411yescharacteristic
302#897D411yescharacteristic
303#897C2312yes—
304#897C2312yes—
305#897C2312yes—
306#896—22no—
307#896—22no—
308#895—22no—
309#895—21no—
310#895—22no—
311#895D411yescharacteristic
312#895D411yescharacteristic
313#895C2312yes—
314#894—22no—
315#894—22no—
316#893—22no—
317#892—21no—
318D3×C4⋊C4—21no—
319D3×C4⋊C4—22no—
320#888—22no—
321#886—22no—
322#886—22no—
323#886—22no—
324#886—22no—
325#886D412yes—
326#885—22no—
327#884—22no—
328#884—22no—
329#883—22no—
330#882—22no—
331#882—22no—
332#882D412yes—
333#67⋊C4—22no—
334#67⋊C4—22no—
335D3×C22⋊C4—22no—
336#878—22no—
337#875—22no—
338#875C2312yes—
339C4×D12—22no—
340C4×D12—22no—
341C4×D12C2312yes—
342C4×D12C2312yes—
343C4×D12C2312yes—
344#869—22no—
345#869C2312yes—
346C4×Dic6C2312yes—
347C3×C4⋊C8C2312yes—
348C3×C4⋊C8C2312yes—
349C3×#103C2312yes—
350C3×#103C2312yes—
351C3×#103C2312yes—
352C3×#102C2312yes—
353#835C2312yes—
354#832C2312yes—
355#821C2312yes—
356(C2×D3)⋊C8C2312yes—
357(C2×D3)⋊C8C2312yes—
358(C2×D3)⋊C8C2312yes—
359(C2×D3)⋊C8C2312yes—
360#816C2312yes—
361#816C2312yes—
362#816C2312yes—
363#810C2312yes—
364#809C2312yes—
365#808C2312yes—
366#808C2312yes—
367#803C2312yes—
368C4×C3⋊C8C2312yes—
369C2×2−1+4—31no—
370C2×2−1+4—31no—
371C22×#41—31no—
372C22×#41—31no—
373#578—68no—
374#575—68no—
375C2×#137—31no—
376C2×#137—31no—
377C2×#137—31no—
378C2×#137—31no—
379C2×#137—32no—
380C2×#137—31no—
381C2×#137—31no—
382C2×#137—32no—
383C2×#137—31no—
384C2×#137C2×D311yescharacteristic, complemented
385C2×AGL(1,ℤ/8)—31no—
386C2×AGL(1,ℤ/8)—31no—
387C2×AGL(1,ℤ/8)—31no—
388C2×AGL(1,ℤ/8)—31no—
389C2×#135—31no—
390C2×#135—31no—
391C2×#135—32no—
392C2×#135—31no—
393C2×#135C2×D311yescharacteristic
394C22×Q16—31no—
395C22×Q16—32no—
396C2×#131—31no—
397C22×M16—31no—
398D4×Q8—32no—
399D4×Q8—32no—
400#548—32no—
401#548—32no—
402#547—32no—
403#547—32no—
404#547—62no—
405#547—62no—
406#546—32no—
407#546—32no—
408#546—62no—
409#546—62no—
410#537—31no—
411#537—31no—
412#537—61no—
413#537—61no—
414#536—31no—
415#536—61no—
416#536—61no—
417#536C2×D311yescharacteristic, complemented
418#525—31no—
419#525—61no—
420#525—61no—
421C2×C22⋊Q8—31no—
422C2×C22⋊Q8—31no—
423C2×C22⋊Q8—61no—
424C2×C22⋊Q8—61no—
425#520—31no—
426#520C2×D311yescharacteristic, complemented
427#497—32no—
428#497—32no—
429#495—32no—
430#494—32no—
431#470—32no—
432#470—32no—
433#470—32no—
434#470—32no—
435#470—32no—
436#469—32no—
437#465—32no—
438#465—32no—
439#464—32no—
440#464C2×D312yescomplemented
441#463—32no—
442#463C2×D312yescomplemented
443#462—32no—
444#462C2×D312yescomplemented
445#461—32no—
446#461C2×D312yescomplemented
447#452—32no—
448#452—32no—
449#452—32no—
450#452—32no—
451#452—32no—
452#452—32no—
453#451—32no—
454#451—32no—
455#451—32no—
456#451—32no—
457#450—32no—
458#450—32no—
459#449—32no—
460#449—32no—
461#448—32no—
462#448—32no—
463#442—32no—
464#441—32no—
465C4×SD16—32no—
466C4×SD16—32no—
467#436—32no—
468#436—32no—
469#435—32no—
470#435—32no—
471C2×#106—31no—
472#424C2×D311yescharacteristic, complemented
473#417—31no—
474#417—31no—
475#417—31no—
476#417C2×D311yescharacteristic, complemented
477C2×#103—31no—
478C2×#103C2×D311yescharacteristic, complemented
479#408—31no—
480#407—31no—
481#405—31no—
482C23×D3—21no—
483C23×D3—21no—
484C23×D3C2×D411yescharacteristic
485C3×#41—22no—
486C3×#41—22no—
487C3×#41—22no—
488C3×#41C2×D414yes—
489C2×C3×Q8—21no—
490C2×C3×Q8—22no—
491C2×C3×Q8—22no—
492C2×C3×Q8C2412yes—
493C2×C3×Q8C2411yescharacteristic
494C2×C3×Q8C2411yescharacteristic
495C2×C3×D4—21no—
496C2×C3×D4—21no—
497C2×C3×D4C2411yescharacteristic
498C2×C3×D4C2411yescharacteristic
499C22×C3×C4—21no—
500C22×C3×C4—21no—
501C22×C3×C4—21no—
502C22×C3×C4—21no—
503C22×C3×C4—22no—
504C22×C3×C4C2411yescharacteristic
505C2×#67—21no—
506C2×#67—21no—
507C2×#67—22no—
508C2×#67—21no—
509C2×#67—21no—
510C2×#67—22no—
511C2×#67—21no—
512C2×#67—21no—
513C2×#67C2×D412yes—
514C22×Dic3—21no—
515C22×Dic3—21no—
516C22×Dic3—21no—
517C22×Dic3—21no—
518C22×Dic3—22no—
519C22×Dic3C2×D411yescharacteristic
520#239—22no—
521#239—22no—
522#239—24no—
523#239—42no—
524#239—41no—
525#239—41no—
526#239—44no—
527D3×Q8—22no—
528D3×Q8—24no—
529D3×Q8—24no—
530D3×Q8—22no—
531D3×Q8—42no—
532D3×Q8—41no—
533D3×Q8—41no—
534D3×Q8—42no—
535D3×Q8—44no—
536#237—22no—
537#237—24no—
538#237—22no—
539#237—41no—
540#237—41no—
541#237—42no—
542#237—44no—
543#237—44no—
544#237—48no—
545D3×D4—22no—
546D3×D4—22no—
547D3×D4—41no—
548D3×D4—41no—
549D3×D4—44no—
550D3×D4—44no—
551#235—22no—
552#235—22no—
553#235—22no—
554#235—22no—
555#235—22no—
556#235—44no—
557#235—44no—
558#235—44no—
559#235—48no—
560#235C2×D414yes—
561C2×D12—21no—
562C2×D12—22no—
563C2×D12—21no—
564C2×D12—22no—
565C2×D12C2×D411yescharacteristic
566C2×D12C2×D412yes—
567C2×D12C2×D412yes—
568C2×D12C2411yescharacteristic
569C2×D12C2411yescharacteristic
570C2×C4×D3—21no—
571C2×C4×D3—22no—
572C2×C4×D3—22no—
573C2×C4×D3—22no—
574C2×C4×D3—21no—
575C2×C4×D3—22no—
576C2×C4×D3—21no—
577C2×C4×D3—21no—
578C2×C4×D3—21no—
579C2×C4×D3—22no—
580C2×C4×D3—21no—
581C2×C4×D3—22no—
582C2×C4×D3—44no—
583C2×C4×D3—44no—
584C2×C4×D3C2×D411yescharacteristic
585C2×C4×D3C2×D411yescharacteristic
586C2×C4×D3C2412yes—
587C2×C4×D3C2411yescharacteristic
588C2×C4×D3C2411yescharacteristic
589C2×Dic6—22no—
590C2×Dic6—22no—
591C2×Dic6—21no—
592C2×Dic6—21no—
593C2×Dic6—22no—
594C2×Dic6—22no—
595C2×Dic6—21no—
596C2×Dic6—44no—
597C2×Dic6C2×D411yescharacteristic
598C2×Dic6C2411yescharacteristic
599C2×Dic6C2412yes—
600C2×Dic6C2411yescharacteristic
601C3×Q16—24no—
602C3×Q16—22no—
603C3×SD16—22no—
604C3×SD16—22no—
605C3×SD16—24no—
606C3×D8—22no—
607C3×M16—22no—
608C2×C3×C8—22no—
609C2×C3×C8C2411yescharacteristic
610C2×C3×C8C2411yescharacteristic
611C2×C3×C8C2412yes—
612C3×C4⋊C4—22no—
613C3×C4⋊C4—22no—
614C3×C4⋊C4—21no—
615C3×C4⋊C4—22no—
616C3×C4⋊C4C2×D411yescharacteristic
617C3×C4⋊C4C2×D411yescharacteristic
618C3×C4⋊C4C2412yes—
619C3×C22⋊C4—22no—
620C3×C22⋊C4—22no—
621C3×C22⋊C4—22no—
622C3×C22⋊C4C2×D412yes—
623C3×C42—22no—
624C3×C42C2412yes—
625#217—22no—
626#216—24no—
627#216—22no—
628#216—24no—
629#216—42no—
630#216—42no—
631#216C2×D414yes—
632#215—22no—
633#215—42no—
634#215C2×D414yes—
635#214—22no—
636#214—42no—
637#214C2×D414yes—
638#213—22no—
639#213C2×D414yes—
640(C2×D3)⋊C4—22no—
641(C2×D3)⋊C4—22no—
642(C2×D3)⋊C4—22no—
643(C2×D3)⋊C4—22no—
644(C2×D3)⋊C4—22no—
645(C2×D3)⋊C4—22no—
646(C2×D3)⋊C4—22no—
647(C2×D3)⋊C4—22no—
648(C2×D3)⋊C4—22no—
649(C2×D3)⋊C4—22no—
650(C2×D3)⋊C4C2×D412yes—
651(C2×D3)⋊C4C2×D412yes—
652(C2×D3)⋊C4C2×D412yes—
653(C2×D3)⋊C4C2×D412yes—
654C4⋊Dic3—22no—
655C4⋊Dic3—22no—
656C4⋊Dic3—21no—
657C4⋊Dic3—22no—
658C4⋊Dic3—22no—
659C4⋊Dic3—22no—
660C4⋊Dic3C2×D412yes—
661C4⋊Dic3C2×D412yes—
662C4⋊Dic3C2412yes—
663Dic3⋊C4—22no—
664Dic3⋊C4—22no—
665Dic3⋊C4—22no—
666Dic3⋊C4—22no—
667C4×Dic3—22no—
668#208—22no—
669C2×C3⋊C8C2×D414yes—
670C2×C3⋊C8C2412yes—
671C2×C3⋊C8C2411yescharacteristic
672C2×C3⋊C8C2411yescharacteristic
673Dic12—22no—
674Dic12—24no—
675D24—22no—
676#204—22no—
677#204—24no—
678#204—22no—
679ΓL(1,𝔽25)—22no—
680ΓL(1,𝔽25)—22no—
681ΓL(1,𝔽25)—22no—
682ΓL(1,𝔽25)—22no—
683ΓL(1,𝔽25)—24no—
684D3×C8—24no—
6852−1+4—64no—
6862−1+4—64no—
6872−1+4—122no—
6882−1+4—122no—
689C2×#41—31no—
690C2×#41—32no—
691C2×#41—31no—
692C2×#41—31no—
693C2×#41—32no—
694C2×#41—31no—
695C2×#41—31no—
696C2×#41—31no—
697C2×#41—31no—
698C2×#41—61no—
699C2×#41—61no—
700C2×#41—61no—
701C2×#41—62no—
702C2×#41—61no—
703C2×#41—61no—
704C2×#41—62no—
705C2×#41—61no—
706C2×#41—64no—
707C2×#41—64no—
708C2×#41—122no—
709C2×#41—122no—
710C2×#41C22×D311yescharacteristic
711C2×#41C22×D311yescharacteristic
712C22×Q8—32no—
713C22×Q8—32no—
714C22×Q8—31no—
715C22×Q8—31no—
716C22×Q8—31no—
717C22×Q8—61no—
718C22×Q8—61no—
719C22×Q8C22×D311yescharacteristic
720C22×D4—31no—
721C22×D4—31no—
722C22×D4—61no—
723C22×D4—61no—
724C23×C4—31no—
725C23×C4—61no—
726C23×C4—61no—
727#137—24no—
728#137—64no—
729#137—64no—
730#137—68no—
731#137—64no—
732#137—64no—
733#137—68no—
734#137—64no—
735#137—122no—
736#137—122no—
737AGL(1,ℤ/8)—64no—
738AGL(1,ℤ/8)—64no—
739AGL(1,ℤ/8)—64no—
740AGL(1,ℤ/8)—64no—
741#135—24no—
742#135—38no—
743#135—64no—
744#135—64no—
745#135—68no—
746C2×Q16—31no—
747C2×Q16—32no—
748C2×Q16—32no—
749C2×Q16—31no—
750C2×Q16—32no—
751C2×Q16—32no—
752C2×Q16—32no—
753C2×Q16—31no—
754C2×Q16—64no—
755C2×Q16—68no—
756C2×Q16C22×D312yes—
757C2×Q16C22×D311yescharacteristic
758C2×SD16—31no—
759C2×SD16—31no—
760C2×SD16—31no—
761C2×SD16—31no—
762C2×SD16—32no—
763C2×SD16—32no—
764C2×SD16—31no—
765C2×SD16—31no—
766C2×SD16—32no—
767C2×SD16C22×D312yes—
768C2×SD16C22×D311yescharacteristic
769C2×SD16C22×D311yescharacteristic
770C2×D8—31no—
771C2×D8—31no—
772C2×D8—31no—
773C2×D8C22×D311yescharacteristic
774#131—64no—
775C2×M16—31no—
776C2×M16—31no—
777C2×M16—31no—
778C2×M16—31no—
779C2×M16—31no—
780C2×M16—32no—
781C2×M16—64no—
782C2×M16C22×D311yescharacteristic
783C22×C8—31no—
784C22×C8—32no—
785C22×C8C22×D311yescharacteristic
786C4⋊Q8—32no—
787C4⋊Q8—62no—
788C4⋊Q8—62no—
789C4⋊Q8C22×D312yes—
790#124—32no—
791#124—62no—
792#124—62no—
793#124C22×D312yes—
794#123—22no—
795#123—32no—
796#123—62no—
797#123—62no—
798#123—62no—
799#123—62no—
800#123—62no—
801#123—62no—
802#123—62no—
803C22⋊Q8—21no—
804C22⋊Q8—21no—
805C22⋊Q8—31no—
806C22⋊Q8—31no—
807C22⋊Q8—32no—
808C22⋊Q8—32no—
809C22⋊Q8—32no—
810C22⋊Q8—32no—
811C22⋊Q8—32no—
812C22⋊Q8—32no—
813C22⋊Q8—62no—
814C22⋊Q8—62no—
815C22⋊Q8—62no—
816C22⋊Q8—62no—
817C22⋊Q8—62no—
818C22⋊Q8—62no—
819C22⋊Q8—61no—
820C22⋊Q8—61no—
821C22⋊Q8—61no—
822C22⋊Q8—61no—
823C22⋊Q8—61no—
824C22⋊Q8—61no—
825C22⋊Q8—61no—
826C22⋊Q8—61no—
827#121—31no—
828#121—31no—
829#121—32no—
830#121—32no—
831#121—62no—
832#121—62no—
833#121—62no—
834#121—61no—
835#121—62no—
836#121—62no—
837#121—61no—
838#121—62no—
839#121—62no—
840#121—62no—
841#120—32no—
842#120—62no—
843#120—62no—
844C4×Q8—32no—
845C4×Q8C22×D312yes—
846C4×D4—22no—
847C4×D4—32no—
848C4×D4—32no—
849C4×D4—32no—
850C4×D4—62no—
851C4×D4—62no—
852C4×D4—62no—
853C4×D4—62no—
854C4×D4—62no—
855C4×D4C22×D312yes—
856#117—21no—
857#117—61no—
858#117C22×D311yescharacteristic
859C2×C4⋊C4—21no—
860C2×C4⋊C4—31no—
861C2×C4⋊C4—62no—
862C2×C4⋊C4—62no—
863C2×C4⋊C4—61no—
864C2×C4⋊C4—61no—
865C2×C4⋊C4—61no—
866C2×C4⋊C4C22×D311yescharacteristic
867C2×C22⋊C4—62no—
868C2×C22⋊C4—62no—
869C2×C22⋊C4—61no—
870C2×C22⋊C4—61no—
871#106—32no—
872#106—32no—
873C4⋊C8C22×D312yes—
874C4⋊C8C22×D312yes—
875#103—32no—
876#103—32no—
877#103—32no—
878#103—32no—
879#103—32no—
880#103C22×D312yes—
881#103C22×D312yes—
882#103C22×D312yes—
883#102—32no—
884#102—32no—
885#102—32no—
886#102C22×D312yes—
887C22⋊C8—32no—
888C22⋊C8—32no—
889C22⋊C8—32no—
890C22⋊C8—32no—
891#97—32no—
892C4×C8—32no—
893C23×C3—21no—
894C23×C3—21no—
895C23×C3C22×D411yescharacteristic
896C22×D3—21no—
897C22×D3—22no—
898C22×D3—21no—
899C22×D3—41no—
900C22×D3—41no—
901C22×D3—42no—
902C22×D3—42no—
903C22×D3—42no—
904C22×D3—42no—
905C22×D3—81no—
906C22×D3—81no—
907C22×D3C22×D411yescharacteristic
908C22×D3C22×D411yescharacteristic
909C22×D3C22×D412yes—
910C3×Q8—21no—
911C3×Q8—21no—
912C3×Q8—22no—
913C3×Q8—22no—
914C3×Q8—21no—
915C3×Q8—42no—
916C3×Q8C22×D412yes—
917C3×D4—24no—
918C3×D4—21no—
919C3×D4—21no—
920C3×D4—21no—
921C3×D4—42no—
922C3×D4C22×D412yes—
923C2×C3×C4—21no—
924C2×C3×C4—24no—
925C2×C3×C4—22no—
926C2×C3×C4—21no—
927C2×C3×C4—22no—
928C2×C3×C4—42no—
929C2×C3×C4—42no—
930C2×C3×C4—82no—
931C2×C3×C4—81no—
932C2×C3×C4C22×D412yes—
933C2×C3×C4C22×D412yes—
934C2×C3×C4C22×D411yescharacteristic
935C2×C3×C4C22×D412yes—
936C2×C3×C4H(5,𝔽2)12yes—
937C2×C3×C4C2511yescharacteristic
938#67—24no—
939#67—24no—
940#67—42no—
941#67—42no—
942#67—42no—
943#67—42no—
944#67—44no—
945#67—42no—
946#67—82no—
947C2×Dic3—22no—
948C2×Dic3—21no—
949C2×Dic3—22no—
950C2×Dic3—21no—
951C2×Dic3—22no—
952C2×Dic3—42no—
953C2×Dic3—44no—
954C2×Dic3—42no—
955C2×Dic3—42no—
956C2×Dic3—81no—
957C2×Dic3C22×D411yescharacteristic
958C2×Dic3C22×D411yescharacteristic
959C2×Dic3C22×D412yes—
960D12—22no—
961D12—21no—
962D12—21no—
963D12—21no—
964D12—42no—
965D12—42no—
966D12—42no—
967D12—42no—
968D12—44no—
969D12—82no—
970D12C22×D412yes—
971C4×D3—22no—
972C4×D3—22no—
973C4×D3—24no—
974C4×D3—22no—
975C4×D3—21no—
976C4×D3—21no—
977C4×D3—21no—
978C4×D3—21no—
979C4×D3—22no—
980C4×D3—42no—
981C4×D3—42no—
982C4×D3—42no—
983C4×D3—44no—
984C4×D3—44no—
985C4×D3—42no—
986C4×D3—44no—
987C4×D3—42no—
988C4×D3—82no—
989Dic6—22no—
990Dic6—21no—
991Dic6—21no—
992Dic6—22no—
993Dic6—22no—
994Dic6—21no—
995Dic6—42no—
996Dic6—44no—
997Dic6—44no—
998Dic6—42no—
999Dic6—42no—
1000Dic6C22×D412yes—
1001C3×C8—22no—
1002C3×C8—21no—
1003C3×C8—21no—
1004C3⋊C8—22no—
1005C3⋊C8C22×D412yes—
1006C3⋊C8C22×D412yes—
1007C24—31no—
1008C24—61no—
1009C24—61no—
1010#41—22no—
1011#41—22no—
1012#41—22no—
1013#41—34no—
1014#41—62no—
1015#41—62no—
1016#41—62no—
1017#41—62no—
1018#41—64no—
1019#41—62no—
1020#41—62no—
1021#41—64no—
1022#41—62no—
1023#41—62no—
1024#41—62no—
1025#41—124no—
1026#41—124no—
1027#41—124no—
1028#41—128no—
1029#41—121no—
1030#41—121no—
1031#41—122no—
1032#41—124no—
1033#41—124no—
1034#41—121no—
1035#41—121no—
1036#41—122no—
1037#41—124no—
1038#41—128no—
1039#41D3×D414yes—
1040C2×Q8—21no—
1041C2×Q8—22no—
1042C2×Q8—22no—
1043C2×Q8—31no—
1044C2×Q8—31no—
1045C2×Q8—32no—
1046C2×Q8—31no—
1047C2×Q8—62no—
1048C2×Q8—62no—
1049C2×Q8—61no—
1050C2×Q8—61no—
1051C2×Q8—61no—
1052C2×Q8—64no—
1053C2×Q8—62no—
1054C2×Q8—64no—
1055C2×Q8—62no—
1056C2×Q8—62no—
1057C2×Q8—62no—
1058C2×Q8—124no—
1059C2×Q8—121no—
1060C2×Q8—121no—
1061C2×Q8—122no—
1062C2×Q8—122no—
1063C2×Q8—124no—
1064C2×Q8C23×D312yes—
1065C2×Q8C23×D311yescharacteristic
1066C2×Q8C23×D311yescharacteristic
1067C2×D4—21no—
1068C2×D4—21no—
1069C2×D4—32no—
1070C2×D4—31no—
1071C2×D4—32no—
1072C2×D4—32no—
1073C2×D4—31no—
1074C2×D4—31no—
1075C2×D4—62no—
1076C2×D4—61no—
1077C2×D4—61no—
1078C2×D4—62no—
1079C2×D4—61no—
1080C2×D4—61no—
1081C2×D4—62no—
1082C2×D4—61no—
1083C2×D4—62no—
1084C2×D4—62no—
1085C2×D4—61no—
1086C2×D4—61no—
1087C2×D4—61no—
1088C2×D4—62no—
1089C2×D4—121no—
1090C2×D4—121no—
1091C2×D4—124no—
1092C2×D4—124no—
1093C2×D4C23×D311yescharacteristic
1094C2×D4C23×D311yescharacteristic
1095C22×C4—21no—
1096C22×C4—21no—
1097C22×C4—21no—
1098C22×C4—21no—
1099C22×C4—22no—
1100C22×C4—31no—
1101C22×C4—31no—
1102C22×C4—31no—
1103C22×C4—32no—
1104C22×C4—31no—
1105C22×C4—31no—
1106C22×C4—62no—
1107C22×C4—61no—
1108C22×C4—61no—
1109C22×C4—62no—
1110C22×C4—62no—
1111C22×C4—61no—
1112C22×C4—61no—
1113C22×C4—62no—
1114C22×C4—61no—
1115C22×C4—61no—
1116C22×C4—61no—
1117C22×C4—62no—
1118C22×C4—62no—
1119C22×C4—61no—
1120C22×C4—61no—
1121C22×C4—61no—
1122C22×C4—62no—
1123C22×C4—124no—
1124C22×C4—124no—
1125C22×C4C23×D311yescharacteristic
1126Q16—24no—
1127Q16—22no—
1128Q16—34no—
1129Q16—64no—
1130Q16—62no—
1131Q16—64no—
1132Q16—64no—
1133Q16—62no—
1134Q16—122no—
1135Q16—122no—
1136SD16—22no—
1137SD16—22no—
1138SD16—24no—
1139SD16—34no—
1140SD16—34no—
1141SD16—62no—
1142SD16—64no—
1143SD16—62no—
1144SD16—62no—
1145SD16—62no—
1146SD16—122no—
1147SD16—122no—
1148D8—22no—
1149D8—34no—
1150D8—62no—
1151D8—62no—
1152M16—22no—
1153M16—62no—
1154M16—62no—
1155M16—62no—
1156M16—62no—
1157M16—64no—
1158M16—62no—
1159C2×C8—22no—
1160C2×C8—34no—
1161C2×C8—31no—
1162C2×C8—31no—
1163C2×C8—32no—
1164C2×C8—64no—
1165C2×C8C23×D312yes—
1166C2×C8C23×D311yescharacteristic
1167C2×C8C23×D311yescharacteristic
1168C4⋊C4—21no—
1169C4⋊C4—22no—
1170C4⋊C4—22no—
1171C4⋊C4—22no—
1172C4⋊C4—32no—
1173C4⋊C4—32no—
1174C4⋊C4—32no—
1175C4⋊C4—62no—
1176C4⋊C4—62no—
1177C4⋊C4—62no—
1178C4⋊C4—62no—
1179C4⋊C4—62no—
1180C4⋊C4—62no—
1181C4⋊C4—61no—
1182C4⋊C4—62no—
1183C4⋊C4—62no—
1184C4⋊C4—62no—
1185C4⋊C4D3×D411yescharacteristic
1186C4⋊C4D3×D411yescharacteristic
1187C4⋊C4C23×D312yes—
1188C22⋊C4—22no—
1189C22⋊C4—22no—
1190C22⋊C4—22no—
1191C22⋊C4—32no—
1192C22⋊C4—32no—
1193C22⋊C4—32no—
1194C22⋊C4—32no—
1195C22⋊C4—62no—
1196C22⋊C4—62no—
1197C22⋊C4—62no—
1198C22⋊C4—62no—
1199C22⋊C4—62no—
1200C22⋊C4—62no—
1201C22⋊C4—62no—
1202C22⋊C4—62no—
1203C22⋊C4—62no—
1204C22⋊C4—62no—
1205C22⋊C4—62no—
1206C22⋊C4D3×D412yes—
1207C42—22no—
1208C42—62no—
1209C42C23×D312yes—
1210C22×C3—21no—
1211C22×C3—21no—
1212C22×C3—22no—
1213C22×C3—41no—
1214C22×C3—41no—
1215C22×C3—41no—
1216C22×C3—41no—
1217C22×C3—41no—
1218C22×C3D4212yes—
1219C22×C3C23×D411yescharacteristic
1220C2×D3—21no—
1221C2×D3—21no—
1222C2×D3—22no—
1223C2×D3—22no—
1224C2×D3—21no—
1225C2×D3—21no—
1226C2×D3—21no—
1227C2×D3—21no—
1228C2×D3—22no—
1229C2×D3—22no—
1230C2×D3—41no—
1231C2×D3—41no—
1232C2×D3—41no—
1233C2×D3—41no—
1234C2×D3—41no—
1235C2×D3—82no—
1236C2×D3—84no—
1237C2×D3—84no—
1238C3×C4—22no—
1239C3×C4—22no—
1240C3×C4—22no—
1241C3×C4—42no—
1242C3×C4—41no—
1243C3×C4—42no—
1244C3×C4D4212yes—
1245C3×C4C23×D411yescharacteristic
1246C3×C4C2×H(5,𝔽2)11yescharacteristic
1247Dic3—22no—
1248Dic3—22no—
1249Dic3—21no—
1250Dic3—21no—
1251Dic3—42no—
1252Dic3—42no—
1253Dic3—41no—
1254C23—21no—
1255C23—21no—
1256C23—31no—
1257C23—31no—
1258C23—32no—
1259C23—61no—
1260C23—62no—
1261C23—61no—
1262C23—121no—
1263C23—121no—
1264C23—122no—
1265C23—122no—
1266C23—122no—
1267C23—122no—
1268C23—241no—
1269C23—241no—
1270C23C2×D3×D411yescharacteristic
1271Q8—21no—
1272Q8—21no—
1273Q8—22no—
1274Q8—22no—
1275Q8—21no—
1276Q8—32no—
1277Q8—42no—
1278Q8—61no—
1279Q8—62no—
1280Q8—61no—
1281Q8—62no—
1282Q8—62no—
1283Q8—61no—
1284Q8—124no—
1285Q8—122no—
1286Q8—124no—
1287Q8—122no—
1288Q8—122no—
1289Q8C2×D3×D412yes—
1290D4—24no—
1291D4—21no—
1292D4—21no—
1293D4—21no—
1294D4—32no—
1295D4—42no—
1296D4—64no—
1297D4—64no—
1298D4—61no—
1299D4—61no—
1300D4—61no—
1301D4—62no—
1302D4—122no—
1303D4—122no—
1304D4—122no—
1305D4—122no—
1306D4—124no—
1307D4—122no—
1308D4—122no—
1309D4—122no—
1310D4—122no—
1311D4—124no—
1312D4—122no—
1313D4—242no—
1314D4—242no—
1315D4C2×D3×D412yes—
1316C2×C4—21no—
1317C2×C4—24no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—21no—
1321C2×C4—32no—
1322C2×C4—31no—
1323C2×C4—31no—
1324C2×C4—42no—
1325C2×C4—42no—
1326C2×C4—61no—
1327C2×C4—62no—
1328C2×C4—62no—
1329C2×C4—61no—
1330C2×C4—61no—
1331C2×C4—61no—
1332C2×C4—61no—
1333C2×C4—62no—
1334C2×C4—62no—
1335C2×C4—62no—
1336C2×C4—64no—
1337C2×C4—62no—
1338C2×C4—62no—
1339C2×C4—61no—
1340C2×C4—82no—
1341C2×C4—81no—
1342C2×C4—122no—
1343C2×C4—122no—
1344C2×C4—124no—
1345C2×C4—122no—
1346C2×C4—122no—
1347C2×C4—124no—
1348C2×C4—124no—
1349C2×C4—122no—
1350C2×C4—122no—
1351C2×C4—124no—
1352C2×C4—122no—
1353C2×C4—122no—
1354C2×C4—242no—
1355C2×C4—241no—
1356C2×C4C2×D3×D412yes—
1357C2×C4C2×D3×D412yes—
1358C2×C4C2×D3×D412yes—
1359C2×C4C2×D3×D411yescharacteristic
1360C2×C4#100912yes—
1361C2×C4C24×D311yescharacteristic
1362C8—21no—
1363C8—21no—
1364C8—22no—
1365C8—32no—
1366C8—32no—
1367C8—62no—
1368C2×C3—22no—
1369C2×C3—42no—
1370C2×C3—81no—
1371C2×C3C2×D4211yescharacteristic
1372C2×C3#358611yescharacteristic
1373C2×C3#358611yescharacteristic
1374D3—42no—
1375D3—41no—
1376D3—41no—
1377D3—42no—
1378D3—81no—
1379C22—21no—
1380C22—21no—
1381C22—22no—
1382C22—41no—
1383C22—41no—
1384C22—41no—
1385C22—41no—
1386C22—41no—
1387C22—61no—
1388C22—62no—
1389C22—61no—
1390C22—61no—
1391C22—62no—
1392C22—61no—
1393C22—61no—
1394C22—61no—
1395C22—62no—
1396C22—62no—
1397C22—121no—
1398C22—121no—
1399C22—121no—
1400C22—121no—
1401C22—121no—
1402C22—242no—
1403C22—244no—
1404C22—244no—
1405C22#560912yes—
1406C22C22×D3×D411yescharacteristic
1407C4—22no—
1408C4—22no—
1409C4—22no—
1410C4—42no—
1411C4—41no—
1412C4—42no—
1413C4—61no—
1414C4—61no—
1415C4—62no—
1416C4—62no—
1417C4—122no—
1418C4—121no—
1419C4—122no—
1420C4#560912yes—
1421C4C22×D3×D411yescharacteristic
1422C4C2×#100911yescharacteristic
1423C3#6106411yescharacteristic, complemented, Sylow
1424C2—22no—
1425C2—42no—
1426C2—81no—
1427C2—121no—
1428C2—121no—
1429C2—122no—
1430C2—122no—
1431C2—241no—
1432C2C2×#560911yescharacteristic
1433C2#8720811yescharacteristic
1434C2#8721111yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3046C2
socleC22×C3C23×D4
hypercenter#3046D3
hypocenterC3#61064
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #117 ◁ #3046

Complements

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

NH ≅ G/Ntype
1. C2×#5779C2semidirect
2. C2×#5768C2semidirect
3. #86356C2semidirect
4. #85901C2semidirect
5. C3×#3046C2semidirect
6. #83981C2semidirect
7. #83913C2semidirect
8. #83403C2semidirect
9. #82558C2semidirect
10. #80631C2semidirect
11. #80629C2semidirect
12. #80567C2semidirect
13. #80556C2semidirect
14. #80501C2semidirect
15. #80489C2semidirect
16. #80447C2semidirect
17. #80445C2semidirect
18. #79089C2semidirect
19. #79074C2semidirect
20. #78890C2semidirect
21. #78885C2semidirect
22. C2×#4816C2semidirect
23. #78795C2semidirect
25. C2×#1010C22semidirect
28. C2×#1007C22semidirect
29. C2×C3×#137C22semidirect
31. C3×#536C22semidirect
32. C3×#520C22semidirect
33. #5833C22semidirect
34. C2×#951C22semidirect
38. C22×#216C22semidirect
39. C2×#942C22semidirect
44. C2×#918C22semidirect
45. C2×D3×Q16C22semidirect
46. C2×#916C22semidirect
49. C2×#915C22semidirect
54. C2×#909C22semidirect
55. C2×#907C22semidirect
58. #5727C22semidirect
61. #5676C22semidirect
69. Q8×D12C22semidirect
73. #5554C22semidirect
75. #5526C22semidirect
78. #5523C22semidirect
80. #5510C22semidirect
83. C3×#464C22semidirect
84. C3×#463C22semidirect
85. C3×#462C22semidirect
86. C3×#461C22semidirect
87. C3×#424C22semidirect
88. C3×#417C22semidirect
89. C2×C3×#103C22semidirect
90. #5232C22semidirect
92. #5186C22semidirect
93. #5186C22semidirect
95. #5173C22semidirect
96. #5170C22semidirect
97. #5169C22semidirect
98. #5158C22semidirect
99. #5133C22semidirect
101. #5110C22semidirect
102. C2×#816C22semidirect
103. #5092C22semidirect
104. #5086C22semidirect
105. #5060C22semidirect
106. #5059C22semidirect
107. #5030C22semidirect
108. C4×#215C22semidirect
109. C4×#214C22semidirect
110. #5014C22semidirect
111. #4997C22semidirect
112. #4966C22semidirect
113. C2×#808C22semidirect
114. #4849C22semidirect
115. #4845C22semidirect
116. #4844C22semidirect
117. #4841C22semidirect
118. #4838C22semidirect
119. #4838C22semidirect
120. #4836C22semidirect
121. #4836C22semidirect
122. #4816C22semidirect
123. #4816C22semidirect
124. #4816C22semidirect
125. #4816C22semidirect
126. #4816C22semidirect
127. #4810C22semidirect
128. #4809C22semidirect
129. #4809C22semidirect
131. #4808C22semidirect
132. #4807C22semidirect
133. #4806C22semidirect
135. #4782C22semidirect
136. #4778C22semidirect
137. #4776C22semidirect
154. #3046D3semidirect
227. #950D4semidirect
384. C2×#137C2×D3semidirect
417. #536C2×D3semidirect
426. #520C2×D3semidirect
440. #464C2×D3semidirect
442. #463C2×D3semidirect
444. #462C2×D3semidirect
446. #461C2×D3semidirect
472. #424C2×D3semidirect
476. #417C2×D3semidirect
478. C2×#103C2×D3semidirect
1423. C3#61064semidirect

Maximal subgroups

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

subgroupindex
C2×#57792
C2×#57682
#863562
#859012
C3×#30462
#839812
#839132
#834032
#825582
#806312
#806292
#805672
#805562
#805012
#804892
#804472
#804452
#790892
#790742
#788902
#788852
C2×#48162
#787952
#610643