Finite Group Databasebeta

← #11910012

Subgroups — #11910012

Order 1152.

2216 conjugacy classes of subgroups.

The subgroup lattice has 1378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596024C211yesmaximal, characteristic, complemented
2C3×#5541C211yesmaximal, characteristic, complemented
3C3×#5538C211yesmaximal, characteristic, complemented
4#10595251C212yesmaximal, complemented
5#10595212C212yesmaximal, complemented
6#10594990C211yesmaximal, characteristic, complemented
7#10594955C211yesmaximal, characteristic, complemented
8#10594954C211yesmaximal, characteristic, complemented
9#10594916C211yesmaximal, characteristic, complemented
10#10594916C211yesmaximal, characteristic, complemented
11#10594843C211yesmaximal, characteristic, complemented
12#10594838C211yesmaximal, characteristic, complemented
13#10594814C211yesmaximal, characteristic, complemented
14#10594476C212yesmaximal, complemented
15#10594465C212yesmaximal, complemented
16#10594157C212yesmaximal, complemented
17#10594109C212yesmaximal, complemented
18#10594106C212yesmaximal, complemented
19#10594032C212yesmaximal, complemented
20#10593989C211yesmaximal, characteristic, complemented
21#10593963C211yesmaximal, characteristic, complemented
22#10593885C211yesmaximal, characteristic, complemented
23#10593852C211yesmaximal, characteristic, complemented
24#86843—31nomaximal
25#86130—31nomaximal
26C2×#3828C2211yescharacteristic
27C2×#3828C2211yescharacteristic
28C2×D3×Dic6C2211yescharacteristic
29C32×C4×D4C2211yescharacteristic
30#64149C2212yes—
31#64139C2211yescharacteristic
32#64139C2211yescharacteristic
33#64102C2212yes—
34#64093C2212yes—
35#64093C2212yes—
36#64083C2211yescharacteristic
37C4×#634C2211yescharacteristic
38C3×#939C2211yescharacteristic
39C3×#935C2211yescharacteristic
40C3×#935C2212yes—
41C3×C4×#67C2211yescharacteristic
42C3×C4×#67C2211yescharacteristic
43C3×#926C2211yescharacteristic
44C3×#926C2211yescharacteristic
45C2×C3×C4⋊Dic3C2211yescharacteristic
46C3×#924C2211yescharacteristic
47C3×#924C2211yescharacteristic
48C2×C3×C4×Dic3C2211yescharacteristic
49C3×#898C2211yescharacteristic
50C3×#889C2211yescharacteristic
51C3×#889C2212yes—
52C3×#886C2211yescharacteristic
53C3×#885C2211yescharacteristic
54C3×#879C2211yescharacteristic
55C3×#879C2212yes—
56C3×#878C2211yescharacteristic
57C3×#877C2212yes—
58C3×#872C2211yescharacteristic
59C3×#870C2211yescharacteristic
60C3×C4×Dic6C2211yescharacteristic
61C3×C4×Dic6C2211yescharacteristic
62#63978C2212yes—
63#63975C2212yes—
64#63971C2212yes—
65#63971C2212yes—
66#63966C2212yes—
67#63958C2212yes—
68#63953C2212yes—
69#63953C2212yes—
70#63953C2212yes—
71#63953C2212yes—
72#63952C2212yes—
73#63952C2212yes—
74#63952C2212yes—
75#63952C2212yes—
76#63952C2212yes—
77#63952C2212yes—
78#63918C2211yescharacteristic
79#63910C2212yes—
80#63910C2212yes—
81#63909C2211yescharacteristic
82#63909C2211yescharacteristic
83#63900C2212yes—
84#63897C2212yes—
85#63897C2212yes—
86#63897C2212yes—
87#63897C2212yes—
88#63895C2212yes—
89#63894C2211yescharacteristic
90#63894C2211yescharacteristic
91#63894C2212yes—
92#63894C2211yescharacteristic
93#63894C2211yescharacteristic
94C4×#624C2212yes—
95#63881C2212yes—
96#63881C2212yes—
97#63878C2212yes—
98#63877C2212yes—
99#63874C2212yes—
100#63870C2212yes—
101#63869C2211yescharacteristic
102#63868C2212yes—
103#63865C2212yes—
104#63865C2212yes—
105#63864C2212yes—
106#63864C2211yescharacteristic
107#63864C2211yescharacteristic
108#63854C2212yes—
109#63852C2212yes—
110#63849C2212yes—
111#63848C2212yes—
112#63848C2212yes—
113#63847C2212yes—
114#63844C2211yescharacteristic
115#63844C2211yescharacteristic
116#63844C2211yescharacteristic
117Dic3×Dic6C2211yescharacteristic
118#63841C2211yescharacteristic
119#63839C2212yes—
120#63838C2212yes—
121#63838C2212yes—
122#63837C2212yes—
123#63836C2212yes—
124#63836C2212yes—
125C3×#552—31no—
126C3×#529—31no—
127#5710—32no—
128#5709—32no—
129#5706—32no—
130#5706—32no—
131#5697—31no—
132#5693—32no—
133#5693—32no—
134#5691—32no—
135#5685—31no—
136#5670—32no—
137#5664—32no—
138#5664—32no—
139#5663—32no—
140#5661—32no—
141#5643—31no—
142#5640—32no—
143#5633—31no—
144#5633—31no—
145#5624—31no—
146#5615—32no—
147#5585—31no—
148#5585—31no—
149#5572—31no—
150#5567—31no—
151#5565—31no—
152#5563—31no—
153#5553—31no—
154#5553—31no—
155#5553—61no—
156#5552—31no—
157#5552—31no—
158#5541D311yescharacteristic, complemented
159#5538D311yescharacteristic, complemented
160#5535—31no—
161#5534—31no—
162#5532—31no—
163#5532—32no—
164#5528—32no—
165#5523—31no—
166#5522—31no—
167#5516—31no—
168#5514—31no—
169#5504—31no—
170#5479—31no—
171C4×#235—31no—
172C2×C32×D4C2311yescharacteristic
173C22×C32×C4C2311yescharacteristic
174C22×C32×C4C2311yescharacteristic
175C2×#638C2312yes—
176C2×#638C2312yes—
177C2×#638C2312yes—
178C2×#638C2312yes—
179#3828—24no—
180#3828—24no—
181C2×C4⋊(C3⋊D3)C2311yescharacteristic
182C2×C4⋊(C3⋊D3)C2311yescharacteristic
183C2×C4⋊(C3⋊D3)C2312yes—
184C2×C4⋊(C3⋊D3)C2312yes—
185C2×C4×C3⋊D3C2312yes—
186C2×C4×C3⋊D3C2312yes—
187C2×#634C2311yescharacteristic
188C2×C3×#67C2311yescharacteristic
189C2×C3×#67C2311yescharacteristic
190C22×C3×Dic3C2312yes—
191C22×C3×Dic3C2311yescharacteristic
192C22×C3×Dic3C2311yescharacteristic
193C2×C3×C4×D3C2311yescharacteristic
194C2×C3×Dic6C2311yescharacteristic
195C2×C3×Dic6C2311yescharacteristic
196C2×#627C2312yes—
197C2×#627C2312yes—
198C2×#626C2312yes—
199C2×#626C2312yes—
200C2×#624C2312yes—
201C2×#624C2312yes—
202C2×#624C2312yes—
203C2×#624C2312yes—
204C2×D3×Dic3C2312yes—
205D3×Dic6—24no—
206C32×C4⋊C4C2311yescharacteristic
207C32×C22⋊C4C2311yescharacteristic
208C32×C22⋊C4C2311yescharacteristic
209C32×C42C2311yescharacteristic
210#3752C2312yes—
211#3752C2312yes—
212C4⋊(C3⋊Dic3)C2311yescharacteristic
213#3750C2312yes—
214C4×C3⋊Dic3C2312yes—
215C3×#217C2312yes—
216C3×#217C2311yescharacteristic
217C3×#217C2312yes—
218C3×#217C2312yes—
219C3×#217C2311yescharacteristic
220C3×#217C2311yescharacteristic
221C3×#217C2311yescharacteristic
222C3×(C2×D3)⋊C4C2311yescharacteristic
223C3×(C2×D3)⋊C4C2311yescharacteristic
224C3×(C2×D3)⋊C4C2311yescharacteristic
225C3×(C2×D3)⋊C4C2311yescharacteristic
226C3×C4⋊Dic3C2311yescharacteristic
227C3×C4⋊Dic3C2311yescharacteristic
228C3×C4⋊Dic3C2312yes—
229C3×C4⋊Dic3C2311yescharacteristic
230C3×C4⋊Dic3C2311yescharacteristic
231C3×C4⋊Dic3C2311yescharacteristic
232C3×C4⋊Dic3C2311yescharacteristic
233C3×Dic3⋊C4C2312yes—
234C3×Dic3⋊C4C2312yes—
235C3×Dic3⋊C4C2311yescharacteristic
236C3×Dic3⋊C4C2311yescharacteristic
237C3×Dic3⋊C4C2312yes—
238C3×Dic3⋊C4C2311yescharacteristic
239C3×Dic3⋊C4C2311yescharacteristic
240C3×Dic3⋊C4C2312yes—
241C3×Dic3⋊C4C2312yes—
242C3×Dic3⋊C4C2311yescharacteristic
243C3×Dic3⋊C4C2311yescharacteristic
244C3×C4×Dic3C2312yes—
245C3×C4×Dic3C2312yes—
246C3×C4×Dic3C2311yescharacteristic
247C3×C4×Dic3C2311yescharacteristic
248C3×C4×Dic3C2311yescharacteristic
249C3×C4×Dic3C2311yescharacteristic
250C3×C4×Dic3C2311yescharacteristic
251#3724C2312yes—
252#3724C2312yes—
253#3724C2312yes—
254#3724C2312yes—
255Dic3⋊Dic3C2312yes—
256Dic3⋊Dic3C2312yes—
257Dic3⋊Dic3C2312yes—
258#3722C2312yes—
259#3722C2312yes—
260#3722C2312yes—
261#3722C2312yes—
262#3722C2312yes—
263#3722C2312yes—
264#3722C2312yes—
265#3722C2312yes—
266#3722C2312yes—
267#3722C2312yes—
268(C2×D3)⋊Dic3C2312yes—
269Dic32C2312yes—
270Dic32C2312yes—
271Dic32C2312yes—
272Dic32C2312yes—
273Dic32C2312yes—
274#3524—91noSylow
275C2×D3×Q8—31no—
276C2×#235—31no—
277C2×#235—31no—
278C2×#235—31no—
279C2×#235—31no—
280C2×#235—61no—
281C2×#235—61no—
282C22×Dic6—31no—
283C3×#126—31no—
284C3×#126—31no—
285C3×#126—32no—
286C3×#125—32no—
287C3×#125—31no—
288C3×#125—31no—
289C3×#124—31no—
290C3×#123—32no—
291C3×#123—31no—
292C3×#123—31no—
293C3×C22⋊Q8—31no—
294C3×C22⋊Q8—31no—
295C3×C22⋊Q8—31no—
296C3×#121—31no—
297C3×C4×Q8—31no—
298C3×C4×Q8—31no—
299C3×C4×D4—21no—
300C3×C4×D4—31no—
301C3×C4×D4—31no—
302C3×C4×D4C2×D311yescharacteristic
303C3×C4×D4C2×D311yescharacteristic
304C3×#117—31no—
305C3×#117—31no—
306C3×#117—32no—
307C3×#117—31no—
308C2×C3×C4⋊C4—31no—
309C2×C3×C42—31no—
310#947—31no—
311#947—31no—
312#947—32no—
313Q8×Dic3—31no—
314#944—32no—
315#940—32no—
316#940—32no—
317#940—62no—
318#939—32no—
319#939—32no—
320#939—32no—
321#939C2×D311yescharacteristic
322#938—32no—
323#935C2×D311yescharacteristic
324#935C2×D312yes—
325#930—31no—
326#930—31no—
327#930—31no—
328#930—31no—
329#930—32no—
330#930—31no—
331#930—31no—
332#930—61no—
333#930—61no—
334#929—32no—
335C4×#67—32no—
336C4×#67—32no—
337C4×#67—32no—
338C4×#67—32no—
339C4×#67—32no—
340C4×#67—32no—
341C4×#67C2×D311yescharacteristic
342C4×#67C2×D311yescharacteristic
343#926—31no—
344#926C2×D311yescharacteristic
345#926C2×D311yescharacteristic
346C2×C4⋊Dic3C2×D311yescharacteristic
347#924C2×D311yescharacteristic
348#924C2×D311yescharacteristic
349C2×C4×Dic3C2×D311yescharacteristic
350#898—32no—
351#898—32no—
352#898—32no—
353#898—32no—
354#898—32no—
355#898C2×D311yescharacteristic
356#897—32no—
357#896—32no—
358#896—32no—
359#896—32no—
360#896—32no—
361#896—32no—
362#895—31no—
363#895—31no—
364#895—32no—
365#895—32no—
366#894—32no—
367#894—32no—
368#894—32no—
369#894—32no—
370#894—32no—
371#894—32no—
372#894—32no—
373#894—32no—
374#894—32no—
375#893—32no—
376#893—32no—
377#893—32no—
378#893—32no—
379#893—31no—
380#893—32no—
381#893—31no—
382#893—31no—
383#893—31no—
384#893—62no—
385#892—31no—
386#892—32no—
387#892—32no—
388#892—32no—
389#892—32no—
390#892—32no—
391D3×C4⋊C4—32no—
392D3×C4⋊C4—32no—
393#890—31no—
394#889—32no—
395#889—32no—
396#889—32no—
397#889—32no—
398#889C2×D311yescharacteristic
399#889C2×D312yes—
400#888—32no—
401#888—31no—
402#887—32no—
403#887—32no—
404#887—32no—
405#887—32no—
406#887—31no—
407#887—31no—
408#887—32no—
409#887—31no—
410#886—32no—
411#886C2×D311yescharacteristic
412#885—32no—
413#885—32no—
414#885—32no—
415#885—32no—
416#885—32no—
417#885—32no—
418#885—32no—
419#885—32no—
420#885—32no—
421#885C2×D311yescharacteristic
422#884—32no—
423#884—32no—
424#884—32no—
425#884—32no—
426#884—32no—
427#884—32no—
428#884—32no—
429#884—32no—
430#884—32no—
431#884—62no—
432#884—62no—
433#883—32no—
434#883—32no—
435#883—32no—
436#67⋊C4—32no—
437#67⋊C4—32no—
438#67⋊C4—32no—
439#67⋊C4—32no—
440#67⋊C4—32no—
441#67⋊C4—32no—
442#67⋊C4—32no—
443#67⋊C4—32no—
444#879C2×D312yes—
445#879C2×D311yescharacteristic
446#878C2×D311yescharacteristic
447#877—32no—
448#877—32no—
449#877C2×D312yes—
450#876—32no—
451#875—32no—
452#875—31no—
453#875—31no—
454#875—32no—
455#874—31no—
456#874—31no—
457#874—61no—
458C4×D12—32no—
459C4×D12—31no—
460C4×D12—31no—
461C4×D12—31no—
462C4×D12—31no—
463#872—32no—
464#872—32no—
465#872—32no—
466#872—32no—
467#872—32no—
468#872C2×D311yescharacteristic
469C42×D3—32no—
470C42×D3—32no—
471#870—31no—
472#870C2×D311yescharacteristic
473#869—31no—
474C4×Dic6—31no—
475C4×Dic6—31no—
476C4×Dic6—31no—
477C4×Dic6—31no—
478C4×Dic6—31no—
479C4×Dic6—31no—
480C4×Dic6—32no—
481C4×Dic6—61no—
482C4×Dic6C2×D311yescharacteristic
483C4×Dic6C2×D311yescharacteristic
484C23×C32C2411yescharacteristic
485C23×C32C2411yescharacteristic
486C22×C3⋊D3C2412yes—
487C22×C3⋊D3C2412yes—
488C22×C3×D3C2411yescharacteristic
489C32×D4—41no—
490C2×C32×C4—22no—
491C2×C32×C4—22no—
492C2×C32×C4C2411yescharacteristic
493C2×C32×C4C2411yescharacteristic
494C2×C32×C4C2411yescharacteristic
495C2×C32×C4C2411yescharacteristic
496C2×C32×C4C2411yescharacteristic
497#638—24no—
498#638—24no—
499#638—42no—
500#638—42no—
501C2×C3⋊Dic3C2412yes—
502C2×C3⋊Dic3C2412yes—
503C4⋊(C3⋊D3)—22no—
504C4⋊(C3⋊D3)—22no—
505C4⋊(C3⋊D3)—42no—
506C4⋊(C3⋊D3)—42no—
507C4×C3⋊D3—24no—
508C4×C3⋊D3—24no—
509#634#4114yes—
510C3×#67—41no—
511C3×#67—41no—
512C2×C3×Dic3—41no—
513C2×C3×Dic3—42no—
514C2×C3×Dic3—41no—
515C2×C3×Dic3C2412yes—
516C2×C3×Dic3C2411yescharacteristic
517C2×C3×Dic3C2411yescharacteristic
518C2×C3×Dic3C2411yescharacteristic
519C2×C3×Dic3C2411yescharacteristic
520C2×C3×Dic3C2411yescharacteristic
521C2×C3×Dic3C2412yes—
522C2×C3×Dic3C2412yes—
523C2×C3×Dic3C2412yes—
524C2×C3×Dic3C2411yescharacteristic
525C2×C3×Dic3C2411yescharacteristic
526C3×C4×D3—22no—
527C3×Dic6—22no—
528C3×Dic6—41no—
529#627—24no—
530#627—42no—
531#626—42no—
532#626—42no—
533#624—42no—
534#624—42no—
535#624—42no—
536#624—42no—
537D3×Dic3—24no—
538#559—91no—
539#559—92no—
540#557—91no—
541#555—91no—
542#555—92no—
543#553—91no—
544#553—92no—
545#552—31no—
546#552—92no—
547#550—91no—
548#548—91no—
549#548—91no—
550#542—91no—
551#542—92no—
552#540—91no—
553#540—92no—
554#529—31no—
555#529—91no—
556#529—92no—
557#529—92no—
558#520—91no—
559#519—91no—
560C4×#41—91no—
561C2×C3×Q8—31no—
562C2×C3×Q8—31no—
563C2×C3×D4—21no—
564C2×C3×D4—31no—
565C2×C3×D4—31no—
566C2×C3×D4C22×D311yescharacteristic
567C2×C3×D4C22×D311yescharacteristic
568C22×C3×C4—21no—
569C22×C3×C4—21no—
570C22×C3×C4—31no—
571C22×C3×C4—32no—
572C22×C3×C4—31no—
573C22×C3×C4—31no—
574C22×C3×C4C22×D311yescharacteristic
575C22×C3×C4C22×D311yescharacteristic
576C22×C3×C4C22×D311yescharacteristic
577C22×C3×C4C22×D311yescharacteristic
578C2×#67—32no—
579C2×#67—32no—
580C2×#67—32no—
581C2×#67—32no—
582C2×#67—32no—
583C2×#67—32no—
584C2×#67—32no—
585C2×#67—32no—
586C2×#67—32no—
587C2×#67—32no—
588C2×#67—62no—
589C2×#67—62no—
590C2×#67—62no—
591C2×#67—62no—
592C2×#67C22×D311yescharacteristic
593C2×#67C22×D311yescharacteristic
594C22×Dic3—32no—
595C22×Dic3C22×D312yes—
596C22×Dic3C22×D311yescharacteristic
597C22×Dic3C22×D311yescharacteristic
598D3×Q8—64no—
599#235—64no—
600#235—64no—
601#235—64no—
602#235—64no—
603#235—124no—
604#235—124no—
605C2×D12—31no—
606C2×D12—31no—
607C2×D12—31no—
608C2×D12—31no—
609C2×D12—32no—
610C2×D12—32no—
611C2×D12—32no—
612C2×D12—32no—
613C2×D12—32no—
614C2×D12—32no—
615C2×D12—62no—
616C2×D12—61no—
617C2×D12—61no—
618C2×D12—62no—
619C2×C4×D3—32no—
620C2×C4×D3—32no—
621C2×C4×D3—32no—
622C2×C4×D3—32no—
623C2×C4×D3—32no—
624C2×C4×D3—32no—
625C2×C4×D3—32no—
626C2×C4×D3—32no—
627C2×C4×D3—32no—
628C2×C4×D3—32no—
629C2×C4×D3—32no—
630C2×C4×D3—32no—
631C2×C4×D3—32no—
632C2×C4×D3—62no—
633C2×C4×D3—62no—
634C2×C4×D3C22×D311yescharacteristic
635C2×Dic6—31no—
636C2×Dic6—31no—
637C2×Dic6—32no—
638C2×Dic6—32no—
639C2×Dic6—32no—
640C2×Dic6—32no—
641C2×Dic6—61no—
642C2×Dic6—64no—
643C2×Dic6C22×D311yescharacteristic
644C2×Dic6C22×D311yescharacteristic
645C3×C4⋊C4—21no—
646C3×C4⋊C4—31no—
647C3×C4⋊C4—31no—
648C3×C4⋊C4—31no—
649C3×C4⋊C4—31no—
650C3×C4⋊C4—32no—
651C3×C4⋊C4—31no—
652C3×C4⋊C4—31no—
653C3×C4⋊C4—32no—
654C3×C4⋊C4—32no—
655C3×C4⋊C4—31no—
656C3×C4⋊C4—31no—
657C3×C4⋊C4—31no—
658C3×C4⋊C4—32no—
659C3×C4⋊C4—31no—
660C3×C4⋊C4—31no—
661C3×C4⋊C4—32no—
662C3×C4⋊C4—32no—
663C3×C4⋊C4—31no—
664C3×C4⋊C4C22×D311yescharacteristic
665C3×C4⋊C4C22×D311yescharacteristic
666C3×C22⋊C4—21no—
667C3×C22⋊C4—21no—
668C3×C22⋊C4—31no—
669C3×C22⋊C4—32no—
670C3×C22⋊C4—31no—
671C3×C22⋊C4—31no—
672C3×C22⋊C4—32no—
673C3×C22⋊C4—32no—
674C3×C22⋊C4—31no—
675C3×C22⋊C4—31no—
676C3×C22⋊C4—31no—
677C3×C22⋊C4—31no—
678C3×C22⋊C4—31no—
679C3×C22⋊C4C22×D311yescharacteristic
680C3×C22⋊C4C22×D311yescharacteristic
681C3×C22⋊C4C22×D311yescharacteristic
682C3×C22⋊C4C22×D311yescharacteristic
683C3×C42—21no—
684C3×C42—31no—
685C3×C42—31no—
686C3×C42—31no—
687C3×C42—32no—
688C3×C42—31no—
689C3×C42—32no—
690C3×C42—31no—
691C3×C42C22×D311yescharacteristic
692C3×C42C22×D311yescharacteristic
693#217—32no—
694#217C22×D312yes—
695#217C22×D311yescharacteristic
696#217C22×D311yescharacteristic
697#217C22×D311yescharacteristic
698#217C22×D312yes—
699#217C22×D312yes—
700#217C22×D311yescharacteristic
701(C2×D3)⋊C4—32no—
702(C2×D3)⋊C4—32no—
703(C2×D3)⋊C4—32no—
704(C2×D3)⋊C4—32no—
705(C2×D3)⋊C4—32no—
706(C2×D3)⋊C4—32no—
707(C2×D3)⋊C4—32no—
708(C2×D3)⋊C4—32no—
709(C2×D3)⋊C4—32no—
710(C2×D3)⋊C4—32no—
711(C2×D3)⋊C4—32no—
712(C2×D3)⋊C4—32no—
713(C2×D3)⋊C4—32no—
714(C2×D3)⋊C4—32no—
715(C2×D3)⋊C4—32no—
716(C2×D3)⋊C4—32no—
717(C2×D3)⋊C4—32no—
718(C2×D3)⋊C4—32no—
719(C2×D3)⋊C4—32no—
720(C2×D3)⋊C4—32no—
721(C2×D3)⋊C4—32no—
722(C2×D3)⋊C4—32no—
723(C2×D3)⋊C4—32no—
724(C2×D3)⋊C4—32no—
725(C2×D3)⋊C4—32no—
726(C2×D3)⋊C4—62no—
727(C2×D3)⋊C4—62no—
728(C2×D3)⋊C4C22×D311yescharacteristic
729(C2×D3)⋊C4C22×D311yescharacteristic
730(C2×D3)⋊C4C22×D311yescharacteristic
731(C2×D3)⋊C4C22×D311yescharacteristic
732C4⋊Dic3—31no—
733C4⋊Dic3—31no—
734C4⋊Dic3—32no—
735C4⋊Dic3—32no—
736C4⋊Dic3—32no—
737C4⋊Dic3—61no—
738C4⋊Dic3C22×D311yescharacteristic
739C4⋊Dic3C22×D311yescharacteristic
740C4⋊Dic3C22×D311yescharacteristic
741C4⋊Dic3C22×D311yescharacteristic
742C4⋊Dic3C22×D311yescharacteristic
743C4⋊Dic3C22×D312yes—
744C4⋊Dic3C22×D311yescharacteristic
745Dic3⋊C4—32no—
746Dic3⋊C4—32no—
747Dic3⋊C4—32no—
748Dic3⋊C4—32no—
749Dic3⋊C4—32no—
750Dic3⋊C4—32no—
751Dic3⋊C4—32no—
752Dic3⋊C4—32no—
753Dic3⋊C4—32no—
754Dic3⋊C4—32no—
755Dic3⋊C4—32no—
756Dic3⋊C4—32no—
757Dic3⋊C4—32no—
758Dic3⋊C4—62no—
759Dic3⋊C4C22×D311yescharacteristic
760Dic3⋊C4C22×D312yes—
761Dic3⋊C4C22×D311yescharacteristic
762Dic3⋊C4C22×D311yescharacteristic
763Dic3⋊C4C22×D312yes—
764Dic3⋊C4C22×D312yes—
765Dic3⋊C4C22×D311yescharacteristic
766Dic3⋊C4C22×D312yes—
767Dic3⋊C4C22×D311yescharacteristic
768Dic3⋊C4C22×D311yescharacteristic
769Dic3⋊C4C22×D312yes—
770C4×Dic3—32no—
771C4×Dic3—32no—
772C4×Dic3—32no—
773C4×Dic3—32no—
774C4×Dic3—32no—
775C4×Dic3—32no—
776C4×Dic3—32no—
777C4×Dic3—32no—
778C4×Dic3—32no—
779C4×Dic3—32no—
780C4×Dic3—32no—
781C4×Dic3—32no—
782C4×Dic3—62no—
783C4×Dic3C22×D312yes—
784C4×Dic3C22×D311yescharacteristic
785C4×Dic3C22×D311yescharacteristic
786C4×Dic3C22×D311yescharacteristic
787C4×Dic3C22×D312yes—
788C4×Dic3C22×D311yescharacteristic
789C4×Dic3C22×D311yescharacteristic
790C22×C32—21no—
791C22×C32—21no—
792C22×C32—21no—
793C22×C32—21no—
794C22×C32—21no—
795C22×C32—21no—
796C22×C32C2511yescharacteristic
797C2×C3⋊D3—22no—
798C2×C3⋊D3—22no—
799C2×C3⋊D3—22no—
800C2×C3⋊D3—22no—
801C2×C3⋊D3—22no—
802C2×C3⋊D3—22no—
803C2×C3×D3—21no—
804C2×C3×D3—21no—
805C2×C3×D3—21no—
806C32×C4—21no—
807C32×C4—21no—
808C32×C4—21no—
809C32×C4—21no—
810C32×C4C2×#4112yes—
811C3⋊Dic3—22no—
812C3⋊Dic3C2×#4114yes—
813C3×Dic3—22no—
814C3×Dic3—21no—
815C3×Dic3—22no—
816C3×Dic3—21no—
817C3×Dic3—21no—
818C3×Dic3—21no—
819C3×Dic3—21no—
820C3×Dic3—22no—
821C3×Dic3—22no—
822C3×Dic3—21no—
823C3×Dic3—21no—
824C2×#41—91no—
825C2×#41—91no—
826C22×Q8—91no—
827C4⋊Q8—91no—
828C4⋊Q8—92no—
829#127—92no—
830#127—91no—
831#126—31no—
832#126—31no—
833#126—32no—
834#126—92no—
835#126—92no—
836#126—92no—
837#125—31no—
838#125—32no—
839#125—31no—
840#125—91no—
841#125—92no—
842#125—92no—
843#124—31no—
844#124—92no—
845#124—91no—
846#124—91no—
847#124—92no—
848#124—92no—
849#124—92no—
850#124—92no—
851#124—92no—
852#123—31no—
853#123—32no—
854#123—31no—
855#123—92no—
856#123—92no—
857#123—92no—
858#123—92no—
859#123—92no—
860#123—92no—
861#123—92no—
862C22⋊Q8—31no—
863C22⋊Q8—31no—
864C22⋊Q8—31no—
865C22⋊Q8—92no—
866C22⋊Q8—92no—
867C22⋊Q8—92no—
868#121—31no—
869#121—92no—
870#121—92no—
871#121—92no—
872#121—92no—
873#121—92no—
874#121—91no—
875#121—91no—
876#121—92no—
877#121—91no—
878#121—91no—
879#121—92no—
880#121—92no—
881C4×Q8—31no—
882C4×Q8—31no—
883C4×Q8—91no—
884C4×Q8—91no—
885C4×Q8—92no—
886C4×Q8—91no—
887C4×Q8—91no—
888C4×Q8—92no—
889C4×Q8—92no—
890C4×Q8—91no—
891C4×D4—31no—
892C4×D4—31no—
893C4×D4—91no—
894C4×D4—91no—
895C4×D4—91no—
896C4×D4—91no—
897C4×D4—92no—
898C4×D4—92no—
899C4×D4—92no—
900C4×D4—92no—
901C4×D4—92no—
902C4×D4—92no—
903C4×D4—92no—
904C4×D4—92no—
905C4×D4—92no—
906C4×D4—92no—
907C4×D4D3211yescharacteristic
908#117—31no—
909#117—31no—
910#117—32no—
911#117—31no—
912#117—92no—
913#117—92no—
914#117—92no—
915#117—92no—
916#117—92no—
917#117—92no—
918#117—91no—
919C2×C4⋊C4—31no—
920C2×C4⋊C4—92no—
921C2×C42—31no—
922C2×C42—92no—
923C23×C3—21no—
924C23×C3—21no—
925C23×C3—31no—
926C23×C3C23×D311yescharacteristic
927C23×C3C23×D311yescharacteristic
928C23×C3C23×D311yescharacteristic
929C23×C3C23×D311yescharacteristic
930C22×D3—32no—
931C22×D3—32no—
932C22×D3—32no—
933C22×D3—32no—
934C22×D3—62no—
935C22×D3—62no—
936C22×D3C23×D311yescharacteristic
937C3×Q8—62no—
938C3×Q8—121no—
939C3×D4—41no—
940C3×D4—41no—
941C3×D4—42no—
942C3×D4—121no—
943C3×D4—121no—
944C2×C3×C4—22no—
945C2×C3×C4—22no—
946C2×C3×C4—22no—
947C2×C3×C4—22no—
948C2×C3×C4—21no—
949C2×C3×C4—21no—
950C2×C3×C4—21no—
951C2×C3×C4—21no—
952C2×C3×C4—21no—
953C2×C3×C4—31no—
954C2×C3×C4—31no—
955C2×C3×C4—31no—
956C2×C3×C4—32no—
957C2×C3×C4—31no—
958C2×C3×C4—31no—
959C2×C3×C4—32no—
960C2×C3×C4—32no—
961C2×C3×C4—32no—
962C2×C3×C4—31no—
963C2×C3×C4—31no—
964C2×C3×C4—42no—
965C2×C3×C4—42no—
966C2×C3×C4—62no—
967C2×C3×C4—121no—
968C2×C3×C4—122no—
969C2×C3×C4—121no—
970C2×C3×C4C23×D311yescharacteristic
971C2×C3×C4C23×D311yescharacteristic
972C2×C3×C4C23×D311yescharacteristic
973C2×C3×C4C23×D311yescharacteristic
974C2×C3×C4C23×D311yescharacteristic
975C2×C3×C4C23×D311yescharacteristic
976C2×C3×C4C23×D311yescharacteristic
977C2×C3×C4C23×D311yescharacteristic
978C2×C3×C4C23×D311yescharacteristic
979C2×C3×C4C23×D311yescharacteristic
980#67—41no—
981#67—41no—
982#67—64no—
983#67—64no—
984#67—64no—
985#67—64no—
986#67—124no—
987#67—124no—
988#67—122no—
989#67—122no—
990#67—122no—
991#67—122no—
992#67—122no—
993#67—122no—
994#67—242no—
995#67—242no—
996C2×Dic3—32no—
997C2×Dic3—32no—
998C2×Dic3—32no—
999C2×Dic3—32no—
1000C2×Dic3—41no—
1001C2×Dic3—41no—
1002C2×Dic3—42no—
1003C2×Dic3—62no—
1004C2×Dic3—62no—
1005C2×Dic3—64no—
1006C2×Dic3C23×D311yescharacteristic
1007C2×Dic3C23×D311yescharacteristic
1008C2×Dic3C23×D312yes—
1009C2×Dic3C23×D311yescharacteristic
1010C2×Dic3C23×D311yescharacteristic
1011C2×Dic3C23×D311yescharacteristic
1012C2×Dic3C23×D312yes—
1013C2×Dic3C23×D312yes—
1014C2×Dic3C23×D312yes—
1015C2×Dic3C23×D311yescharacteristic
1016C2×Dic3C23×D311yescharacteristic
1017D12—62no—
1018D12—62no—
1019D12—62no—
1020D12—62no—
1021D12—122no—
1022D12—122no—
1023D12—122no—
1024D12—122no—
1025D12—122no—
1026D12—122no—
1027D12—124no—
1028D12—122no—
1029D12—122no—
1030D12—242no—
1031C4×D3—22no—
1032C4×D3—64no—
1033C4×D3—64no—
1034C4×D3—64no—
1035C4×D3—64no—
1036C4×D3—64no—
1037C4×D3—124no—
1038C4×D3—124no—
1039C4×D3—122no—
1040C4×D3—122no—
1041C4×D3—122no—
1042C4×D3—122no—
1043C4×D3—122no—
1044C4×D3—122no—
1045C4×D3—122no—
1046C4×D3—122no—
1047Dic6—22no—
1048Dic6—34no—
1049Dic6—34no—
1050Dic6—41no—
1051Dic6—64no—
1052Dic6—64no—
1053Dic6—64no—
1054Dic6—122no—
1055Dic6—122no—
1056C2×C32—41no—
1057C2×C32—41no—
1058C2×C32C22×#4111yescharacteristic
1059C2×C32#58511yescharacteristic
1060C2×C32#58511yescharacteristic
1061C3⋊D3—42no—
1062C3⋊D3—42no—
1063C3×D3—41no—
1064#41—184no—
1065#41—184no—
1066C2×Q8—31no—
1067C2×Q8—31no—
1068C2×Q8—92no—
1069C2×Q8—92no—
1070C2×Q8—91no—
1071C2×Q8—184no—
1072C2×D4—31no—
1073C2×D4—31no—
1074C2×D4—92no—
1075C2×D4—92no—
1076C2×D4—92no—
1077C2×D4—92no—
1078C2×D4—92no—
1079C2×D4—92no—
1080C2×D4—91no—
1081C2×D4—91no—
1082C2×D4—92no—
1083C2×D4—92no—
1084C2×D4C2×D3211yescharacteristic
1085C22×C4—31no—
1086C22×C4—31no—
1087C22×C4—32no—
1088C22×C4—31no—
1089C22×C4—92no—
1090C22×C4—92no—
1091C22×C4—92no—
1092C22×C4—92no—
1093C22×C4—92no—
1094C22×C4—92no—
1095C22×C4—92no—
1096C22×C4C2×D3211yescharacteristic
1097C22×C4C2×D3211yescharacteristic
1098C4⋊C4—32no—
1099C4⋊C4—31no—
1100C4⋊C4—31no—
1101C4⋊C4—31no—
1102C4⋊C4—31no—
1103C4⋊C4—32no—
1104C4⋊C4—31no—
1105C4⋊C4—31no—
1106C4⋊C4—31no—
1107C4⋊C4—32no—
1108C4⋊C4—31no—
1109C4⋊C4—32no—
1110C4⋊C4—31no—
1111C4⋊C4—31no—
1112C4⋊C4—32no—
1113C4⋊C4—31no—
1114C4⋊C4—31no—
1115C4⋊C4—32no—
1116C4⋊C4—92no—
1117C4⋊C4—92no—
1118C4⋊C4—92no—
1119C4⋊C4—92no—
1120C4⋊C4—92no—
1121C4⋊C4—92no—
1122C4⋊C4—92no—
1123C4⋊C4—92no—
1124C4⋊C4—91no—
1125C4⋊C4C2×D3211yescharacteristic
1126C22⋊C4—31no—
1127C22⋊C4—32no—
1128C22⋊C4—31no—
1129C22⋊C4—32no—
1130C22⋊C4—31no—
1131C22⋊C4—31no—
1132C22⋊C4—32no—
1133C22⋊C4—31no—
1134C22⋊C4—31no—
1135C22⋊C4—31no—
1136C22⋊C4—31no—
1137C22⋊C4—92no—
1138C22⋊C4—92no—
1139C22⋊C4—92no—
1140C22⋊C4—92no—
1141C22⋊C4—92no—
1142C22⋊C4—92no—
1143C22⋊C4—92no—
1144C22⋊C4—92no—
1145C22⋊C4—92no—
1146C22⋊C4—92no—
1147C22⋊C4—92no—
1148C22⋊C4—92no—
1149C22⋊C4—92no—
1150C22⋊C4C2×D3211yescharacteristic
1151C22⋊C4C2×D3211yescharacteristic
1152C42—31no—
1153C42—31no—
1154C42—31no—
1155C42—31no—
1156C42—32no—
1157C42—32no—
1158C42—31no—
1159C42—92no—
1160C42—92no—
1161C42—92no—
1162C42—92no—
1163C42—92no—
1164C42—92no—
1165C42C2×D3211yescharacteristic
1166C22×C3—21no—
1167C22×C3—21no—
1168C22×C3—21no—
1169C22×C3—21no—
1170C22×C3—21no—
1171C22×C3—21no—
1172C22×C3—21no—
1173C22×C3—21no—
1174C22×C3—21no—
1175C22×C3—21no—
1176C22×C3—21no—
1177C22×C3—21no—
1178C22×C3—21no—
1179C22×C3—41no—
1180C22×C3—41no—
1181C22×C3—41no—
1182C22×C3—41no—
1183C22×C3—41no—
1184C22×C3—41no—
1185C22×C3—61no—
1186C22×C3—61no—
1187C22×C3—61no—
1188C22×C3C24×D311yescharacteristic
1189C22×C3C24×D311yescharacteristic
1190C2×D3—21no—
1191C2×D3—21no—
1192C2×D3—21no—
1193C2×D3—62no—
1194C2×D3—62no—
1195C2×D3—62no—
1196C2×D3—62no—
1197C2×D3—62no—
1198C2×D3—62no—
1199C2×D3—62no—
1200C2×D3—62no—
1201C2×D3—62no—
1202C2×D3—62no—
1203C2×D3—62no—
1204C2×D3—62no—
1205C2×D3—122no—
1206C2×D3—122no—
1207C2×D3—122no—
1208C2×D3—122no—
1209C2×D3—122no—
1210C2×D3—122no—
1211C3×C4—22no—
1212C3×C4—21no—
1213C3×C4—21no—
1214C3×C4—21no—
1215C3×C4—21no—
1216C3×C4—21no—
1217C3×C4—21no—
1218C3×C4—21no—
1219C3×C4—21no—
1220C3×C4—22no—
1221C3×C4—41no—
1222C3×C4—41no—
1223C3×C4—41no—
1224C3×C4—61no—
1225C3×C4—62no—
1226C3×C4—62no—
1227C3×C4—61no—
1228C3×C4—61no—
1229C3×C4—62no—
1230C3×C4—61no—
1231C3×C4—62no—
1232C3×C4—61no—
1233C3×C4—61no—
1234C3×C4—61no—
1235C3×C4D3×#4112yes—
1236C3×C4D3×#4112yes—
1237Dic3—22no—
1238Dic3—21no—
1239Dic3—21no—
1240Dic3—21no—
1241Dic3—22no—
1242Dic3—21no—
1243Dic3—21no—
1244Dic3—21no—
1245Dic3—21no—
1246Dic3—22no—
1247Dic3—22no—
1248Dic3—34no—
1249Dic3—34no—
1250Dic3—64no—
1251Dic3—62no—
1252Dic3—62no—
1253Dic3—122no—
1254C32#352411yescharacteristic, complemented, Sylow
1255C23—31no—
1256C23—92no—
1257C23—92no—
1258C23C22×D3211yescharacteristic
1259C23C22×D3211yescharacteristic
1260Q8—62no—
1261Q8—94no—
1262Q8—121no—
1263Q8—184no—
1264Q8—362no—
1265D4—41no—
1266D4—121no—
1267D4—121no—
1268D4—184no—
1269D4—184no—
1270D4—182no—
1271D4—182no—
1272D4—362no—
1273D4—362no—
1274D4—362no—
1275D4—362no—
1276D4—362no—
1277D4—362no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—31no—
1281C2×C4—31no—
1282C2×C4—31no—
1283C2×C4—32no—
1284C2×C4—31no—
1285C2×C4—31no—
1286C2×C4—32no—
1287C2×C4—32no—
1288C2×C4—31no—
1289C2×C4—31no—
1290C2×C4—32no—
1291C2×C4—62no—
1292C2×C4—92no—
1293C2×C4—92no—
1294C2×C4—121no—
1295C2×C4—122no—
1296C2×C4—121no—
1297C2×C4—184no—
1298C2×C4—184no—
1299C2×C4—184no—
1300C2×C4—362no—
1301C2×C4—362no—
1302C2×C4—362no—
1303C2×C4—362no—
1304C2×C4C22×D3211yescharacteristic
1305C2×C4C22×D3211yescharacteristic
1306C2×C4C22×D3211yescharacteristic
1307C2×C4C22×D3211yescharacteristic
1308C2×C4C22×D3211yescharacteristic
1309C2×C3—21no—
1310C2×C3—21no—
1311C2×C3—21no—
1312C2×C3—41no—
1313C2×C3—41no—
1314C2×C3—41no—
1315C2×C3—41no—
1316C2×C3—81no—
1317C2×C3—81no—
1318C2×C3—121no—
1319C2×C3C2×D3×#4111yescharacteristic
1320C2×C3C2×D3×#4111yescharacteristic
1321C2×C3#596411yescharacteristic
1322C2×C3#596411yescharacteristic
1323C2×C3#596411yescharacteristic
1324C2×C3#596811yescharacteristic
1325D3—41no—
1326D3—122no—
1327D3—122no—
1328D3—122no—
1329D3—122no—
1330D3—242no—
1331D3—242no—
1332C22—21no—
1333C22—21no—
1334C22—21no—
1335C22—21no—
1336C22—21no—
1337C22—21no—
1338C22—61no—
1339C22—61no—
1340C22—61no—
1341C22—182no—
1342C22—182no—
1343C22—182no—
1344C22—182no—
1345C22—182no—
1346C22—182no—
1347C22C23×D3211yescharacteristic
1348C4—21no—
1349C4—21no—
1350C4—21no—
1351C4—21no—
1352C4—61no—
1353C4—61no—
1354C4—62no—
1355C4—62no—
1356C4—61no—
1357C4—61no—
1358C4—62no—
1359C4—61no—
1360C4—61no—
1361C4—62no—
1362C4—61no—
1363C4—94no—
1364C4—182no—
1365C4#6431212yes—
1366C3—21no—
1367C3#8613011yescharacteristic, complemented
1368C3#8684311yescharacteristic, complemented
1369C2—41no—
1370C2—41no—
1371C2—121no—
1372C2—362no—
1373C2—362no—
1374C2#1059666911yescharacteristic
1375C2C2×#6431211yescharacteristic
1376C2#1059669711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×D4C22
hypercenterC4×D4D32
hypocenterC32#3524
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10596024C2semidirect
2. C3×#5541C2semidirect
3. C3×#5538C2semidirect
4. #10595251C2semidirect
5. #10595212C2semidirect
6. #10594990C2semidirect
7. #10594955C2semidirect
8. #10594954C2semidirect
9. #10594916C2semidirect
10. #10594916C2semidirect
11. #10594843C2semidirect
12. #10594838C2semidirect
13. #10594814C2semidirect
14. #10594476C2semidirect
15. #10594465C2semidirect
16. #10594157C2semidirect
17. #10594109C2semidirect
18. #10594106C2semidirect
19. #10594032C2semidirect
20. #10593989C2semidirect
21. #10593963C2semidirect
22. #10593885C2semidirect
23. #10593852C2semidirect
158. #5541D3semidirect
159. #5538D3semidirect
1254. C32#3524semidirect
1367. C3#86130semidirect
1368. C3#86843semidirect

Maximal subgroups

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

subgroupindex
#105960242
C3×#55412
C3×#55382
#105952512
#105952122
#105949902
#105949552
#105949542
#105949162
#105948432
#105948382
#105948142
#105944762
#105944652
#105941572
#105941092
#105941062
#105940322
#105939892
#105939632
#105938852
#105938522
#868433
#861303