Finite Group Databasebeta

← #11909336

Subgroups — #11909336

Order 1152.

2365 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596162C211yesmaximal, characteristic, complemented
2C3×#5694C212yesmaximal, complemented
3#10594643C214yesmaximal, complemented
4#10594627C212yesmaximal, complemented
5D3×#897C212yesmaximal, complemented
6#10594616C212yesmaximal, complemented
7#10594581C211yesmaximal, characteristic, complemented
8#10594571C212yesmaximal, complemented
9#10594530C211yesmaximal, characteristic, complemented
10#10594526C211yesmaximal, characteristic, complemented
11#10594512C211yesmaximal, characteristic, complemented
12#10594511C212yesmaximal, complemented
13#10594484C212yesmaximal, complemented
14#10594440C214yesmaximal, complemented
15C4×#3802C211yesmaximal, characteristic, complemented
16#10593899C212yesmaximal, complemented
17#10593882C211yesmaximal, characteristic, complemented
18#86839—32nomaximal
19C2×#3802C2211yescharacteristic
20C2×C4×D32C2212yes—
21C2×#3799C2212yescomplemented
22C2×#3798C2212yes—
23C2×D3×Dic6C2212yescomplemented
24C32×#125C2211yescharacteristic, complemented
25#64107C2212yescomplemented
26#64106C2211yescharacteristic
27#64104C2211yescharacteristic
28#64103C2212yes—
29#64102C2212yes—
30#64102C2211yescharacteristic, complemented
31#64101C2212yescomplemented
32#64096C2211yescharacteristic, complemented
33#64084C2211yescharacteristic, complemented
34C42×C3⋊D3C2211yescharacteristic
35C3×#898C2214yescomplemented
36C3×#897C2212yescomplemented
37C3×#897C2212yescomplemented
38C3×#894C2214yes—
39C3×#892C2212yescomplemented
40C3×#892C2214yescomplemented
41C3×D3×C4⋊C4C2212yescomplemented
42C3×#890C2214yescomplemented
43C3×C4×D12C2212yes—
44C3×C4×Dic6C2212yescomplemented
45#63923C2214yes—
46#63921C2212yes—
47D3×(C2×D3)⋊C4C2214yes—
48#63919C2212yescomplemented
49#63919C2211yescharacteristic, complemented
50C4×#627C2212yescomplemented
51C4×#627C2212yescomplemented
52#63915C2212yes—
53#63912C2212yes—
54#63909C2212yescomplemented
55#63902C2211yescharacteristic
56#63902C2212yes—
57#63902C2211yescharacteristic
58C4×#625C2211yescharacteristic
59C4×#625C2211yescharacteristic
60#63900C2211yescharacteristic
61#63900C2212yescomplemented
62#63899C2214yescomplemented
63#63898C2212yes—
64#63895C2214yes—
65#63895C2214yescomplemented
66#63894C2214yes—
67#63893C2214yescomplemented
68#63890C2214yescomplemented
69D3×C4⋊Dic3C2214yescomplemented
70#63886C2214yes—
71#63880C2214yescomplemented
72#63880C2214yescomplemented
73#63874C2212yes—
74#63873C2211yescharacteristic, complemented
75#63871C2212yes—
76#63870C2212yescomplemented
77#63865C2212yes—
78#63865C2212yescomplemented
79#63859C2214yescomplemented
80#63857C2212yescomplemented
81#63854C2214yescomplemented
82#63852C2214yescomplemented
83#63850C2214yescomplemented
84C3×#552—32no—
85#5710—34no—
86#5705—34no—
87#5694D312yescomplemented
88#5692—34no—
89#5691—32no—
90#5691—61no—
91#5690—34no—
92#5665—34no—
93#5654—34no—
94#5632—32no—
95#5631—32no—
96#5627—32no—
97D3×C22⋊Q8—32no—
98#5578—32no—
99#5576—32no—
100#5552—32no—
101C4×D3×D4—32no—
102#5533—32no—
103#5527—34no—
104#5524—32no—
105#5523—34no—
106C2×#897—32no—
107#5507—32no—
108C22×D32C2312yes—
109C2×C4⋊(C3⋊D3)C2311yescharacteristic
110C2×C4⋊(C3⋊D3)C2312yes—
111C2×C4×C3⋊D3C2312yes—
112C2×C4×C3⋊D3C2311yescharacteristic
113C2×C4×C3⋊D3C2311yescharacteristic
114C2×C4×C3⋊D3C2311yescharacteristic
115C2×#634C2311yescharacteristic
116C2×C3×D12C2312yes—
117C2×C3×C4×D3C2314yes—
118C2×C3×C4×D3C2312yes—
119C2×C3×C4×D3C2312yes—
120C2×C3×Dic6C2312yes—
121C2×#627C2312yes—
122C2×#627C2314yes—
123C2×#626C2314yes—
124C2×#626C2314yes—
125C2×#625C2311yescharacteristic
126C2×#625C2311yescharacteristic
127C2×#624C2314yes—
128C2×#624C2312yes—
129C2×D3×Dic3C2314yes—
130C2×D3×Dic3C2312yes—
131C2×D3×Dic3C2312yes—
132#3802—24no—
133C4×D32—44no—
134#3799—44no—
135#3798—28no—
136D3×Dic6—44no—
137C32×C4⋊C4C2312yes—
138C32×C4⋊C4C2311yescharacteristic
139C32×C4⋊C4C2311yescharacteristic
140C32×C4⋊C4C2312yes—
141C32×C42C2311yescharacteristic
142#3752C2312yes—
143#3752C2312yes—
144#3752C2312yes—
145#3752C2312yes—
146#3752C2312yes—
147C4⋊(C3⋊Dic3)C2312yes—
148#3750C2312yes—
149C4×C3⋊Dic3C2311yescharacteristic
150C4×C3⋊Dic3C2311yescharacteristic
151C4×C3⋊Dic3C2311yescharacteristic
152C4×C3⋊Dic3C2312yes—
153C3×(C2×D3)⋊C4C2312yes—
154C3×(C2×D3)⋊C4C2314yes—
155C3×(C2×D3)⋊C4C2314yes—
156C3×(C2×D3)⋊C4C2314yes—
157C3×(C2×D3)⋊C4C2312yes—
158C3×C4⋊Dic3C2312yes—
159C3×C4⋊Dic3C2314yes—
160C3×C4⋊Dic3C2314yes—
161C3×C4⋊Dic3C2312yes—
162C3×Dic3⋊C4C2314yes—
163C3×Dic3⋊C4C2314yes—
164C3×C4×Dic3C2314yes—
165C3×C4×Dic3C2314yes—
166#3724C2312yes—
167#3724C2312yes—
168#3724C2312yes—
169#3724C2311yescharacteristic
170#3724C2311yescharacteristic
171Dic3⋊Dic3C2314yes—
172Dic3⋊Dic3C2314yes—
173#3722C2314yes—
174#3722C2314yes—
175(C2×D3)⋊Dic3C2312yes—
176(C2×D3)⋊Dic3C2314yes—
177(C2×D3)⋊Dic3C2312yes—
178#3520—91noSylow
179C2×#239—32no—
180C2×D3×Q8—32no—
181C2×D3×D4—32no—
182C2×#235—34no—
183C2×#235—32no—
184C22×C4×D3—32no—
185C22×C4×D3—32no—
186C22×Dic6—32no—
187C3×#126—34no—
188C3×#125—21no—
189C3×#125—34no—
190C3×#125C2×D312yescomplemented
191C3×#123—34no—
192C3×C22⋊Q8—32no—
193C3×C22⋊Q8—32no—
194C3×C4×Q8—32no—
195C3×C4×D4—32no—
196C3×#117—34no—
197C3×#117—32no—
198C2×C3×C4⋊C4—32no—
199#946—32no—
200#944—32no—
201#939—34no—
202D4×Dic3—32no—
203#930—32no—
204#929—34no—
205C4×#67—32no—
206C4×#67—32no—
207C2×(C2×D3)⋊C4—34no—
208C2×C4⋊Dic3—34no—
209#924—32no—
210#898—34no—
211#898—62no—
212#898C2×D314yescomplemented
213#897—32no—
214#897—32no—
215#897—32no—
216#897—34no—
217#897—34no—
218#897—34no—
219#897—61no—
220#897C2×D312yescomplemented
221#897C2×D312yescomplemented
222#896—34no—
223#896—34no—
224#896—34no—
225#896—34no—
226#896—34no—
227#895—34no—
228#895—32no—
229#895—32no—
230#895—61no—
231#894—34no—
232#894—34no—
233#894—34no—
234#894—34no—
235#894—62no—
236#894C2×D314yes—
237#893—32no—
238#893—34no—
239#893—32no—
240#893—34no—
241#893—62no—
242#893—61no—
243#892—34no—
244#892—62no—
245#892C2×D314yescomplemented
246#892C2×D312yescomplemented
247D3×C4⋊C4—34no—
248D3×C4⋊C4—32no—
249D3×C4⋊C4—34no—
250D3×C4⋊C4C2×D312yescomplemented
251#890C2×D314yescomplemented
252#889—34no—
253#888—34no—
254#888—32no—
255#887—32no—
256#887—61no—
257#886—34no—
258#885—34no—
259#885—34no—
260#884—34no—
261#883—34no—
262#882—34no—
263#882—34no—
264#67⋊C4—34no—
265#67⋊C4—32no—
266#67⋊C4—32no—
267#67⋊C4—34no—
268#67⋊C4—34no—
269D3×C22⋊C4—34no—
270D3×C22⋊C4—32no—
271D3×C22⋊C4—32no—
272#879—34no—
273#878—34no—
274#878—34no—
275#876—34no—
276#875—32no—
277#875—34no—
278#875—61no—
279C4×D12—34no—
280C4×D12—34no—
281C4×D12—34no—
282C4×D12C2×D312yes—
283#872—34no—
284C42×D3—32no—
285C42×D3—61no—
286C4×Dic6—34no—
287C4×Dic6—34no—
288C4×Dic6C2×D312yescomplemented
289C22×C3⋊D3C2412yes—
290C22×C3⋊D3C2411yescharacteristic
291C22×C3×D3C2412yes—
292C22×C3×D3C2412yes—
293C2×D32—24no—
294C2×D32—24no—
295C2×D32—42no—
296C2×C32×C4C2411yescharacteristic
297C2×C32×C4C2412yes—
298C2×C32×C4C2411yescharacteristic
299C2×C32×C4C2412yes—
300C2×C32×C4C2411yescharacteristic
301C2×C3⋊Dic3C2411yescharacteristic
302C2×C3⋊Dic3C2412yes—
303C2×C3⋊Dic3C2411yescharacteristic
304C2×C3⋊Dic3C2411yescharacteristic
305C4⋊(C3⋊D3)—24no—
306C4⋊(C3⋊D3)—22no—
307C4×C3⋊D3—22no—
308C4×C3⋊D3—22no—
309C4×C3⋊D3—24no—
310C4×C3⋊D3—22no—
311#634—22no—
312C2×C3×Dic3C2414yes—
313C2×C3×Dic3C2412yes—
314C2×C3×Dic3C2412yes—
315C2×C3×Dic3C2414yes—
316C3×D12—24no—
317C3×C4×D3—28no—
318C3×C4×D3—24no—
319C3×C4×D3—24no—
320C3×Dic6—24no—
321#627—24no—
322#627—44no—
323#626—28no—
324#626—44no—
325#625—22no—
326#625#4114yescomplemented
327#624—44no—
328#624—42no—
329D3×Dic3—44no—
330D3×Dic3—42no—
331D3×Dic3—42no—
332#556—91no—
333#554—92no—
334#552—32no—
335#551—94no—
336D4×Q8—91no—
337#548—92no—
338#547—91no—
339#547—91no—
340#546—92no—
341#542—92no—
342#539—94no—
343#533—91no—
344#529—91no—
345#525—92no—
346C2×C22⋊Q8—92no—
347#520—92no—
348C2×C4×D4—91no—
349C23×D3—32no—
350C23×D3—32no—
351C2×C3×Q8—32no—
352C2×C3×D4—32no—
353C22×C3×C4—32no—
354C22×C3×C4—34no—
355C22×C3×C4—32no—
356C2×#67—32no—
357C2×#67—32no—
358C2×#67—34no—
359C2×#67—34no—
360C22×Dic3—32no—
361C22×Dic3—34no—
362C22×Dic3—32no—
363#239—124no—
364D3×Q8—124no—
365D3×D4—68no—
366#235—616no—
367#235—124no—
368C2×D12—34no—
369C2×D12—34no—
370C2×D12—32no—
371C2×D12—34no—
372C2×D12—61no—
373C2×D12—62no—
374C2×D12C22×D312yes—
375C2×C4×D3—32no—
376C2×C4×D3—32no—
377C2×C4×D3—32no—
378C2×C4×D3—34no—
379C2×C4×D3—32no—
380C2×C4×D3—34no—
381C2×C4×D3—32no—
382C2×C4×D3—32no—
383C2×C4×D3—34no—
384C2×C4×D3—34no—
385C2×C4×D3—32no—
386C2×C4×D3—61no—
387C2×C4×D3—61no—
388C2×C4×D3—61no—
389C2×C4×D3—62no—
390C2×C4×D3—124no—
391C2×C4×D3—124no—
392C2×C4×D3C22×D312yes—
393C2×C4×D3C22×D312yes—
394C2×C4×D3C22×D314yes—
395C2×Dic6—32no—
396C2×Dic6—34no—
397C2×Dic6—34no—
398C2×Dic6—34no—
399C2×Dic6—61no—
400C2×Dic6—124no—
401C2×Dic6C22×D312yes—
402C3×C4⋊C4—21no—
403C3×C4⋊C4—22no—
404C3×C4⋊C4—21no—
405C3×C4⋊C4—22no—
406C3×C4⋊C4—34no—
407C3×C4⋊C4—32no—
408C3×C4⋊C4—34no—
409C3×C4⋊C4—34no—
410C3×C4⋊C4—32no—
411C3×C4⋊C4—34no—
412C3×C4⋊C4C22×D312yes—
413C3×C4⋊C4C22×D314yes—
414C3×C4⋊C4C22×D312yes—
415C3×C4⋊C4C22×D314yes—
416C3×C22⋊C4—34no—
417C3×C22⋊C4—34no—
418C3×C22⋊C4—34no—
419C3×C22⋊C4—32no—
420C3×C22⋊C4—32no—
421C3×C42—21no—
422C3×C42—34no—
423C3×C42—34no—
424C3×C42C22×D312yes—
425#217—32no—
426#217—34no—
427#217—32no—
428(C2×D3)⋊C4—34no—
429(C2×D3)⋊C4—32no—
430(C2×D3)⋊C4—32no—
431(C2×D3)⋊C4—34no—
432(C2×D3)⋊C4—34no—
433(C2×D3)⋊C4—34no—
434(C2×D3)⋊C4—34no—
435(C2×D3)⋊C4—34no—
436(C2×D3)⋊C4—34no—
437(C2×D3)⋊C4—34no—
438(C2×D3)⋊C4—34no—
439(C2×D3)⋊C4—34no—
440(C2×D3)⋊C4—62no—
441(C2×D3)⋊C4—62no—
442(C2×D3)⋊C4—62no—
443(C2×D3)⋊C4—62no—
444(C2×D3)⋊C4—62no—
445(C2×D3)⋊C4C22×D312yes—
446(C2×D3)⋊C4C22×D314yes—
447(C2×D3)⋊C4C22×D312yes—
448(C2×D3)⋊C4C22×D314yes—
449(C2×D3)⋊C4C22×D314yes—
450C4⋊Dic3—34no—
451C4⋊Dic3—34no—
452C4⋊Dic3—34no—
453C4⋊Dic3—62no—
454C4⋊Dic3C22×D312yes—
455C4⋊Dic3C22×D314yes—
456C4⋊Dic3C22×D312yes—
457C4⋊Dic3C22×D314yes—
458Dic3⋊C4—34no—
459Dic3⋊C4—32no—
460Dic3⋊C4—34no—
461Dic3⋊C4—34no—
462Dic3⋊C4—34no—
463Dic3⋊C4—34no—
464Dic3⋊C4—34no—
465Dic3⋊C4—32no—
466Dic3⋊C4—62no—
467Dic3⋊C4C22×D314yes—
468Dic3⋊C4C22×D314yes—
469C4×Dic3—32no—
470C4×Dic3—34no—
471C4×Dic3—32no—
472C4×Dic3—32no—
473C4×Dic3—61no—
474C4×Dic3—61no—
475C4×Dic3—61no—
476C4×Dic3—62no—
477C4×Dic3C22×D314yes—
478C4×Dic3C22×D314yes—
479C22×C32C2511yescharacteristic
480C2×C3⋊D3—21no—
481C2×C3⋊D3—21no—
482C2×C3⋊D3—22no—
483C2×C3⋊D3—22no—
484C2×C3⋊D3—22no—
485C2×C3⋊D32−1+412yes—
486C2×C3×D3—22no—
487C2×C3×D3—22no—
488C2×C3×D3—22no—
489C2×C3×D3—22no—
490C2×C3×D3—22no—
491C2×C3×D3C2×#4114yes—
492D32—48no—
493C32×C4—22no—
494C32×C4—21no—
495C32×C4—21no—
496C32×C4—22no—
497C32×C4H(5,𝔽2)12yes—
498C3⋊Dic3—21no—
499C3⋊Dic3—22no—
500C3⋊Dic3—21no—
501C3⋊Dic3C2×#4112yes—
502C3×Dic3—24no—
503C3×Dic3—22no—
504C3×Dic3—24no—
505C3×Dic3—22no—
506C2×#41—92no—
507C2×#41—92no—
508C22×Q8—92no—
509C22×D4—91no—
510C23×C4—92no—
511C4⋊Q8—91no—
512C4⋊Q8—92no—
513C4⋊Q8—91no—
514#126—34no—
515#126—94no—
516#126—92no—
517#125—34no—
518#125—92no—
519#125D3211yescharacteristic, complemented
520#124—94no—
521#124—92no—
522#124—91no—
523#123—34no—
524#123—94no—
525#123—94no—
526#123—94no—
527#123—92no—
528C22⋊Q8—32no—
529C22⋊Q8—32no—
530C22⋊Q8—94no—
531C22⋊Q8—94no—
532C22⋊Q8—94no—
533C22⋊Q8—92no—
534C22⋊Q8—94no—
535C22⋊Q8—92no—
536C22⋊Q8—92no—
537C22⋊Q8—92no—
538C22⋊Q8—91no—
539#121—92no—
540#121—92no—
541#121—94no—
542#121—91no—
543#120—94no—
544C4×Q8—32no—
545C4×Q8—92no—
546C4×Q8—92no—
547C4×Q8—91no—
548C4×D4—32no—
549C4×D4—94no—
550C4×D4—94no—
551C4×D4—94no—
552C4×D4—91no—
553C4×D4—91no—
554C4×D4—92no—
555C4×D4—92no—
556C4×D4—91no—
557C4×D4—91no—
558C4×D4—92no—
559C4×D4—91no—
560#117—34no—
561#117—32no—
562#117—92no—
563#117—92no—
564C2×C4⋊C4—32no—
565C2×C4⋊C4—91no—
566C2×C4⋊C4—92no—
567C2×C4⋊C4—94no—
568C2×C22⋊C4—92no—
569C2×C22⋊C4—94no—
570C2×C42—91no—
571C23×C3—32no—
572C23×C3—32no—
573C22×D3—32no—
574C22×D3—34no—
575C22×D3—61no—
576C22×D3—62no—
577C22×D3—64no—
578C22×D3—64no—
579C22×D3—64no—
580C22×D3—64no—
581C22×D3—122no—
582C22×D3—122no—
583C22×D3C23×D312yes—
584C22×D3C23×D312yes—
585C3×Q8—64no—
586C3×D4—64no—
587C2×C3×C4—21no—
588C2×C3×C4—22no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—22no—
592C2×C3×C4—32no—
593C2×C3×C4—34no—
594C2×C3×C4—34no—
595C2×C3×C4—32no—
596C2×C3×C4—68no—
597C2×C3×C4—64no—
598C2×C3×C4—64no—
599C2×C3×C4C23×D312yes—
600C2×C3×C4C23×D314yes—
601C2×C3×C4C23×D312yes—
602C2×C3×C4C23×D314yes—
603C2×C3×C4C23×D312yes—
604#67—38no—
605#67—68no—
606#67—64no—
607#67—124no—
608C2×Dic3—32no—
609C2×Dic3—32no—
610C2×Dic3—32no—
611C2×Dic3—34no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—62no—
616C2×Dic3—124no—
617C2×Dic3—122no—
618C2×Dic3—122no—
619C2×Dic3C23×D314yes—
620C2×Dic3C23×D312yes—
621C2×Dic3C23×D314yes—
622C2×Dic3C23×D312yes—
623D12—24no—
624D12—68no—
625D12—68no—
626D12—64no—
627D12—122no—
628D12—124no—
629D12—124no—
630C4×D3—28no—
631C4×D3—24no—
632C4×D3—24no—
633C4×D3—68no—
634C4×D3—64no—
635C4×D3—64no—
636C4×D3—64no—
637C4×D3—122no—
638C4×D3—124no—
639C4×D3—122no—
640C4×D3—122no—
641C4×D3—122no—
642C4×D3—122no—
643C4×D3—124no—
644C4×D3—124no—
645C4×D3—122no—
646C4×D3—122no—
647C4×D3—124no—
648Dic6—24no—
649Dic6—68no—
650Dic6—64no—
651Dic6—122no—
652Dic6—124no—
653Dic6—124no—
654C2×C32C22×#4111yescharacteristic
655C2×C32C2×H(5,𝔽2)11yescharacteristic
656C2×C32C2×2−1+411yescharacteristic
657C3⋊D3—22no—
658C3⋊D3—42no—
659C3×D3—24no—
660C3×D3—42no—
661C24—92no—
662#41—188no—
663#41—364no—
664C2×Q8—32no—
665C2×Q8—92no—
666C2×Q8—94no—
667C2×Q8—91no—
668C2×Q8—364no—
669C2×D4—32no—
670C2×D4—94no—
671C2×D4—94no—
672C2×D4—91no—
673C2×D4—91no—
674C2×D4—92no—
675C2×D4—91no—
676C2×D4—184no—
677C22×C4—34no—
678C22×C4—32no—
679C22×C4—32no—
680C22×C4—92no—
681C22×C4—94no—
682C22×C4—94no—
683C22×C4—92no—
684C22×C4—92no—
685C22×C4—91no—
686C22×C4—91no—
687C22×C4—91no—
688C22×C4—92no—
689C22×C4—364no—
690C4⋊C4—32no—
691C4⋊C4—34no—
692C4⋊C4—34no—
693C4⋊C4—32no—
694C4⋊C4—34no—
695C4⋊C4—34no—
696C4⋊C4—91no—
697C4⋊C4—91no—
698C4⋊C4—92no—
699C4⋊C4—94no—
700C4⋊C4—94no—
701C4⋊C4—92no—
702C4⋊C4—92no—
703C4⋊C4—92no—
704C4⋊C4—92no—
705C4⋊C4C2×D3211yescharacteristic
706C4⋊C4C2×D3212yes—
707C4⋊C4C2×D3211yescharacteristic
708C4⋊C4C2×D3212yes—
709C22⋊C4—32no—
710C22⋊C4—32no—
711C22⋊C4—34no—
712C22⋊C4—34no—
713C22⋊C4—34no—
714C22⋊C4—94no—
715C22⋊C4—94no—
716C22⋊C4—92no—
717C22⋊C4—92no—
718C22⋊C4—94no—
719C22⋊C4—92no—
720C22⋊C4—92no—
721C22⋊C4—92no—
722C22⋊C4—92no—
723C22⋊C4—92no—
724C42—34no—
725C42—34no—
726C42—91no—
727C42—91no—
728C42—91no—
729C42—92no—
730C42C2×D3211yescharacteristic
731C22×C3—21no—
732C22×C3—34no—
733C22×C3—62no—
734C22×C3—62no—
735C22×C3—62no—
736C22×C3—62no—
737C22×C3—62no—
738C22×C3C24×D312yes—
739C2×D3—22no—
740C2×D3—22no—
741C2×D3—22no—
742C2×D3—22no—
743C2×D3—22no—
744C2×D3—34no—
745C2×D3—62no—
746C2×D3—62no—
747C2×D3—62no—
748C2×D3—64no—
749C2×D3—64no—
750C2×D3—64no—
751C2×D3—121no—
752C2×D3—121no—
753C2×D3—122no—
754C2×D3—122no—
755C2×D3—122no—
756C2×D3—128no—
757C2×D3—128no—
758C2×D3D3×#4114yes—
759C3×C4—24no—
760C3×C4—22no—
761C3×C4—22no—
762C3×C4—24no—
763C3×C4—22no—
764C3×C4—42no—
765C3×C4—41no—
766C3×C4—41no—
767C3×C4—42no—
768C3×C4—64no—
769C3×C4—62no—
770C3×C4—64no—
771C3×C4—62no—
772C3×C4#100914yes—
773Dic3—24no—
774Dic3—24no—
775Dic3—22no—
776Dic3—22no—
777Dic3—34no—
778Dic3—62no—
779Dic3—64no—
780Dic3—62no—
781Dic3—62no—
782Dic3—122no—
783Dic3—121no—
784Dic3—121no—
785C32#352011yescharacteristic, complemented, Sylow
786C23—32no—
787C23—32no—
788C23—91no—
789C23—92no—
790C23—184no—
791C23—184no—
792C23—362no—
793Q8—64no—
794Q8—184no—
795Q8—182no—
796Q8—364no—
797D4—64no—
798D4—94no—
799D4—184no—
800D4—188no—
801D4—182no—
802D4—182no—
803D4—364no—
804C2×C4—34no—
805C2×C4—32no—
806C2×C4—34no—
807C2×C4—32no—
808C2×C4—68no—
809C2×C4—64no—
810C2×C4—64no—
811C2×C4—91no—
812C2×C4—91no—
813C2×C4—91no—
814C2×C4—92no—
815C2×C4—182no—
816C2×C4—184no—
817C2×C4—182no—
818C2×C4—182no—
819C2×C4—362no—
820C2×C4—364no—
821C2×C4—362no—
822C2×C4—362no—
823C2×C4—364no—
824C2×C4C22×D3211yescharacteristic
825C2×C4C22×D3212yes—
826C2×C4C22×D3211yescharacteristic
827C2×C4C22×D3212yes—
828C2×C4C22×D3211yescharacteristic
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—64no—
833C2×C3—122no—
834C2×C3C2×D3×#4112yes—
835C2×C3C2×#100912yes—
836C2×C3D3×2−1+412yes—
837D3—24no—
838D3—42no—
839D3—64no—
840D3—122no—
841D3—124no—
842D3—242no—
843C22—34no—
844C22—62no—
845C22—62no—
846C22—62no—
847C22—62no—
848C22—62no—
849C22—92no—
850C22—181no—
851C22—181no—
852C22—182no—
853C22—182no—
854C22—182no—
855C22—368no—
856C22C23×D3211yescharacteristic
857C4—22no—
858C4—21no—
859C4—21no—
860C4—22no—
861C4—62no—
862C4—62no—
863C4—64no—
864C4—64no—
865C4—92no—
866C4—181no—
867C4—182no—
868C4—181no—
869C4#6432012yes—
870C3—21no—
871C3#8683912yescomplemented
872C2—64no—
873C2—122no—
874C2—182no—
875C2—362no—
876C2C2×#6432011yescharacteristic
877C2D32×#4111yescharacteristic
878C2#1059669411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#125C22
hypercenter#125D32
hypocenterC32#3520
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #125

Complements

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

NH ≅ G/Ntype
1. #10596162C2semidirect
2. C3×#5694C2semidirect
3. #10594643C2semidirect
4. #10594627C2semidirect
5. D3×#897C2semidirect
6. #10594616C2semidirect
7. #10594581C2semidirect
8. #10594571C2semidirect
9. #10594530C2semidirect
10. #10594526C2semidirect
11. #10594512C2semidirect
12. #10594511C2semidirect
13. #10594484C2semidirect
14. #10594440C2semidirect
15. C4×#3802C2semidirect
16. #10593899C2semidirect
17. #10593882C2semidirect
21. C2×#3799C22semidirect
23. C2×D3×Dic6C22semidirect
24. C32×#125C22semidirect
25. #64107C22semidirect
30. #64102C22semidirect
31. #64101C22semidirect
32. #64096C22semidirect
33. #64084C22semidirect
35. C3×#898C22semidirect
36. C3×#897C22semidirect
37. C3×#897C22semidirect
39. C3×#892C22semidirect
40. C3×#892C22semidirect
41. C3×D3×C4⋊C4C22semidirect
42. C3×#890C22semidirect
44. C3×C4×Dic6C22semidirect
48. #63919C22semidirect
49. #63919C22semidirect
50. C4×#627C22semidirect
51. C4×#627C22semidirect
54. #63909C22semidirect
61. #63900C22semidirect
62. #63899C22semidirect
65. #63895C22semidirect
67. #63893C22semidirect
68. #63890C22semidirect
69. D3×C4⋊Dic3C22semidirect
71. #63880C22semidirect
72. #63880C22semidirect
74. #63873C22semidirect
76. #63870C22semidirect
78. #63865C22semidirect
79. #63859C22semidirect
80. #63857C22semidirect
81. #63854C22semidirect
82. #63852C22semidirect
83. #63850C22semidirect
87. #5694D3semidirect
190. C3×#125C2×D3semidirect
212. #898C2×D3semidirect
220. #897C2×D3semidirect
221. #897C2×D3semidirect
245. #892C2×D3semidirect
246. #892C2×D3semidirect
250. D3×C4⋊C4C2×D3semidirect
251. #890C2×D3semidirect
288. C4×Dic6C2×D3semidirect
326. #625#41semidirect
519. #125D32semidirect
785. C32#3520semidirect
871. C3#86839semidirect

Maximal subgroups

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

subgroupindex
#105961622
C3×#56942
#105946432
#105946272
D3×#8972
#105946162
#105945812
#105945712
#105945302
#105945262
#105945122
#105945112
#105944842
#105944402
C4×#38022
#105938992
#105938822
#868393