Finite Group Databasebeta

← #11910815

Subgroups — #11910815

Order 1152.

2287 conjugacy classes of subgroups.

The subgroup lattice has 1199 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595996C211yesmaximal, characteristic, complemented
2C3×#5531C212yesmaximal, complemented
3#10595080C211yesmaximal, characteristic, complemented
4C2×#63897C211yesmaximal, characteristic, complemented
5#10594917C212yesmaximal, complemented
6#10594652C212yesmaximal, complemented
7#10594593C212yesmaximal, complemented
8#10594483C212yesmaximal, complemented
9#10594468C212yesmaximal, complemented
10#10594293C212yesmaximal, complemented
11#10594243C212yesmaximal, complemented
12#10594166C212yesmaximal, complemented
13#10594079C212yesmaximal, complemented
14#10594023C211yesmaximal, characteristic, complemented
15#10594014C211yesmaximal, characteristic, complemented
16#10593989C212yesmaximal, complemented
17#10593963C211yesmaximal, characteristic, complemented
18#10593936C212yesmaximal, complemented
19#10593857C211yesmaximal, characteristic, complemented
20#86864—32nomaximal
21C2×#3828C2211yescharacteristic, complemented
22C22×C4⋊(C3⋊D3)C2211yescharacteristic
23C2×#3811C2211yescharacteristic
24C22×#624C2211yescharacteristic, complemented
25C2×#3804C2212yes—
26C32×#117C2211yescharacteristic, complemented
27#64104C2212yes—
28#64104C2212yescomplemented
29#64091C2212yes—
30#64091C2212yescomplemented
31#64084C2211yescharacteristic
32#64084C2211yescharacteristic, complemented
33#64083C2211yescharacteristic
34#64083C2211yescharacteristic, complemented
35C3×#929C2212yes—
36C2×C3×Dic3⋊C4C2212yescomplemented
37C3×#898C2212yescomplemented
38C3×#896C2212yescomplemented
39C3×#889C2212yescomplemented
40C3×#889C2212yescomplemented
41C3×#886C2212yes—
42C3×#67⋊C4C2212yes—
43C3×#878C2212yescomplemented
44C3×#877C2212yescomplemented
45C3×#876C2212yescomplemented
46C3×#872C2212yescomplemented
47C3×#870C2212yescomplemented
48C3×C4×Dic6C2212yescomplemented
49#63981C2212yes—
50#63978C2212yes—
51#63974C2211yescharacteristic
52#63966C2212yescomplemented
53C2×#3722C2212yes—
54C2×#3722C2211yescharacteristic, complemented
55#63952C2212yescomplemented
56#63923C2211yescharacteristic
57#63923C2211yescharacteristic
58#63923C2212yescomplemented
59D3×(C2×D3)⋊C4C2212yescomplemented
60#63910C2212yes—
61#63910C2212yes—
62#63910C2212yescomplemented
63#63910C2212yescomplemented
64#63910C2212yescomplemented
65#63910C2212yescomplemented
66#63910C2212yescomplemented
67#63909C2212yescomplemented
68#63909C2212yescomplemented
69#63907C2212yescomplemented
70#63897C2211yescharacteristic
71#63897C2211yescharacteristic
72#63897C2211yescharacteristic
73#63897C2212yes—
74#63897C2211yescharacteristic
75#63897C2211yescharacteristic, complemented
76#63897C2212yescomplemented
77#63897C2212yescomplemented
78#63897C2212yescomplemented
79#63897C2211yescharacteristic, complemented
80#63897C2212yescomplemented
81#63897C2212yescomplemented
82#63896C2212yescomplemented
83#63895C2212yescomplemented
84#63895C2212yescomplemented
85#63895C2212yescomplemented
86#63894C2212yescomplemented
87#63894C2212yescomplemented
88#63894C2212yescomplemented
89#63894C2212yescomplemented
90#63890C2212yescomplemented
91#63888C2212yescomplemented
92#63883C2212yescomplemented
93#63881C2212yescomplemented
94#63880C2212yescomplemented
95#63880C2212yescomplemented
96#63868C2212yescomplemented
97#63868C2212yescomplemented
98#63865C2212yescomplemented
99#63864C2212yescomplemented
100#63864C2212yescomplemented
101#63853C2212yescomplemented
102#63852C2212yescomplemented
103#63850C2212yescomplemented
104#63848C2212yescomplemented
105#63848C2212yescomplemented
106#63840C2212yescomplemented
107#63836C2212yescomplemented
108C3×#552—32no—
109#5711—32no—
110#5710—32no—
111#5709—32no—
112#5704—32no—
113#5700—32no—
114#5699—32no—
115#5697—32no—
116#5695—32no—
117#5692—32no—
118#5692—32no—
119#5656—32no—
120#5655—32no—
121#5654—32no—
122#5653—32no—
123#5647—32no—
124#5644—32no—
125#5644—32no—
126#5637—32no—
127#5585—32no—
128#5582—32no—
129#5560—32no—
130#5554—32no—
131#5535—32no—
132#5531D312yescomplemented
133#5527—32no—
134#5527—32no—
135#5525—32no—
136#5525—61no—
137#5524—32no—
138#5507—32no—
139C2×#894—32no—
140C23×C3⋊D3C2311yescharacteristic
141C23×C3⋊D3C2311yescharacteristic
142C22×D32C2311yescharacteristic
143C22×C32×C4C2311yescharacteristic
144C2×#638C2312yes—
145#3828—42no—
146C2×C4⋊(C3⋊D3)—42no—
147C2×C4⋊(C3⋊D3)C2311yescharacteristic
148C2×C4⋊(C3⋊D3)C2311yescharacteristic
149C2×C4⋊(C3⋊D3)C2312yes—
150C2×C4⋊(C3⋊D3)C2312yes—
151C2×C4⋊(C3⋊D3)C2311yescharacteristic
152C2×C4⋊(C3⋊D3)C2312yes—
153C2×C4⋊(C3⋊D3)C2312yes—
154C2×C4⋊(C3⋊D3)C2311yescharacteristic
155C2×C4⋊(C3⋊D3)C2311yescharacteristic
156C2×C4×C3⋊D3C2312yes—
157C2×#634C2311yescharacteristic
158C2×C3×#67C2312yes—
159C22×C3×Dic3C2312yes—
160C22×C3×Dic3C2312yes—
161C2×C3×C4×D3C2312yes—
162C2×C3×Dic6C2312yes—
163#3811—42no—
164C2×#627C2312yes—
165C2×#626C2312yes—
166C2×#626C2312yes—
167C2×#626C2312yes—
168C2×#626C2312yes—
169C2×#626C2312yes—
170C2×#624—42no—
171C2×#624C2312yes—
172C2×#624C2311yescharacteristic
173C2×#624C2312yes—
174C2×#624C2311yescharacteristic
175C2×#624C2311yescharacteristic
176C2×#624C2312yes—
177C2×#624C2312yes—
178#3804—44no—
179C2×D3×Dic3C2312yes—
180C32×C4⋊C4C2312yes—
181C32×C22⋊C4C2312yes—
182C32×C42C2311yescharacteristic
183C32×C42C2311yescharacteristic
184#3752C2312yes—
185#3752C2312yes—
186#3752C2312yes—
187#3752C2312yes—
188C3×#217C2312yes—
189C3×(C2×D3)⋊C4C2312yes—
190C3×(C2×D3)⋊C4C2312yes—
191C3×(C2×D3)⋊C4C2312yes—
192C3×(C2×D3)⋊C4C2312yes—
193C3×(C2×D3)⋊C4C2312yes—
194C3×C4⋊Dic3C2312yes—
195C3×C4⋊Dic3C2312yes—
196C3×C4⋊Dic3C2312yes—
197C3×Dic3⋊C4C2312yes—
198C3×Dic3⋊C4C2312yes—
199C3×Dic3⋊C4C2312yes—
200C3×Dic3⋊C4C2312yes—
201C3×Dic3⋊C4C2312yes—
202C3×Dic3⋊C4C2312yes—
203C3×Dic3⋊C4C2312yes—
204C3×Dic3⋊C4C2312yes—
205C3×Dic3⋊C4C2312yes—
206C3×Dic3⋊C4C2312yes—
207C3×Dic3⋊C4C2312yes—
208C3×C4×Dic3C2312yes—
209C3×C4×Dic3C2312yes—
210C3×C4×Dic3C2312yes—
211#3724C2312yes—
212Dic3⋊Dic3C2312yes—
213Dic3⋊Dic3C2312yes—
214Dic3⋊Dic3C2312yes—
215#3722C2312yes—
216#3722C2311yescharacteristic
217#3722C2311yescharacteristic
218#3722C2312yes—
219#3722C2312yes—
220#3722C2311yescharacteristic
221#3722C2312yes—
222#3722C2312yes—
223#3722C2312yes—
224#3722C2312yes—
225#3722C2312yes—
226#3722C2312yes—
227#3722C2311yescharacteristic
228#3722C2312yes—
229#3722C2312yes—
230(C2×D3)⋊Dic3C2312yes—
231Dic32C2312yes—
232#3533—91noSylow
233C2×#237—32no—
234C2×D3×D4—32no—
235C2×#235—32no—
236C2×#235—32no—
237C2×#235—61no—
238C22×D12—32no—
239C22×D12—61no—
240C22×C4×D3—32no—
241C3×#126—32no—
242C3×#126—32no—
243C3×#125—32no—
244C3×#125—32no—
245C3×#125—32no—
246C3×#123—32no—
247C3×#123—32no—
248C3×C22⋊Q8—32no—
249C3×C22⋊Q8—32no—
250C3×C4×Q8—32no—
251C3×C4×D4—32no—
252C3×#117—21no—
253C3×#117—32no—
254C3×#117—32no—
255C3×#117C2×D312yescomplemented
256C2×C3×C4⋊C4—32no—
257#947—32no—
258#947—32no—
259#947—32no—
260#946—32no—
261#939—32no—
262#937—32no—
263#930—32no—
264#930—32no—
265#930—32no—
266#929—32no—
267#929—32no—
268#929C2×D312yes—
269C4×#67—32no—
270C2×(C2×D3)⋊C4—32no—
271C2×(C2×D3)⋊C4—32no—
272C2×(C2×D3)⋊C4—32no—
273C2×(C2×D3)⋊C4—32no—
274C2×Dic3⋊C4C2×D312yescomplemented
275#898—32no—
276#898—32no—
277#898—32no—
278#898—32no—
279#898—32no—
280#898—32no—
281#898C2×D312yescomplemented
282#897—32no—
283#897—32no—
284#897—32no—
285#896—32no—
286#896—32no—
287#896—32no—
288#896—32no—
289#896—32no—
290#896—32no—
291#896—32no—
292#896C2×D312yescomplemented
293#895—32no—
294#895—32no—
295#895—32no—
296#895—32no—
297#895—32no—
298#895—32no—
299#895—32no—
300#895—32no—
301#895—32no—
302#895—32no—
303#895—32no—
304#895—32no—
305#895—32no—
306#895—62no—
307#895—62no—
308#894—32no—
309#894—32no—
310#894—32no—
311#894—32no—
312#894—32no—
313#894—32no—
314#894—32no—
315#894—32no—
316#894—32no—
317#894—32no—
318#894—32no—
319#894—32no—
320#894—32no—
321#894—32no—
322#894—32no—
323#894—32no—
324#894—32no—
325#894—32no—
326#894—32no—
327#894—32no—
328#894—32no—
329#893—32no—
330#893—32no—
331#893—32no—
332#893—32no—
333#893—32no—
334#892—32no—
335D3×C4⋊C4—32no—
336D3×C4⋊C4—32no—
337#889C2×D312yescomplemented
338#889C2×D312yescomplemented
339#888—32no—
340#888—32no—
341#886—32no—
342#886—32no—
343#886C2×D312yes—
344#885—32no—
345#885—32no—
346#884—32no—
347#884—32no—
348#884—32no—
349#884—32no—
350#884—32no—
351#884—32no—
352#884—32no—
353#883—32no—
354#882—32no—
355#882—32no—
356#882—32no—
357#882—32no—
358#882—32no—
359#882—32no—
360#882—32no—
361#882—32no—
362#882—32no—
363#882—62no—
364#882—62no—
365#67⋊C4—32no—
366#67⋊C4—32no—
367#67⋊C4—32no—
368#67⋊C4—32no—
369#67⋊C4C2×D312yes—
370D3×C22⋊C4—32no—
371D3×C22⋊C4—32no—
372#878—32no—
373#878C2×D312yescomplemented
374#877C2×D312yescomplemented
375#876—32no—
376#876—32no—
377#876C2×D312yescomplemented
378#875—32no—
379#875—32no—
380#875—32no—
381#875—32no—
382#875—32no—
383#875—61no—
384#875—61no—
385#874—32no—
386#874—32no—
387#874—61no—
388#874—61no—
389C4×D12—32no—
390C4×D12—32no—
391C4×D12—32no—
392C4×D12—32no—
393C4×D12—32no—
394C4×D12—32no—
395#872—32no—
396#872C2×D312yescomplemented
397#870C2×D312yescomplemented
398C4×Dic6C2×D312yescomplemented
399C23×C32C2411yescharacteristic
400C22×C3⋊D3—22no—
401C22×C3⋊D3—22no—
402C22×C3⋊D3—42no—
403C22×C3⋊D3—42no—
404C22×C3⋊D3C2411yescharacteristic
405C22×C3⋊D3C2411yescharacteristic
406C22×C3⋊D3C2411yescharacteristic
407C22×C3⋊D3C2411yescharacteristic
408C22×C3⋊D3C2412yes—
409C22×C3×D3C2412yes—
410C2×D32—42no—
411C2×D32—41no—
412C2×C32×C4—22no—
413C2×C32×C4C2412yes—
414C2×C32×C4C2412yes—
415C2×C32×C4C2411yescharacteristic
416C2×C32×C4C2411yescharacteristic
417#638—24no—
418C2×C3⋊Dic3C2412yes—
419C4⋊(C3⋊D3)—41no—
420C4⋊(C3⋊D3)—41no—
421C4⋊(C3⋊D3)—41no—
422C4⋊(C3⋊D3)—41no—
423C4⋊(C3⋊D3)—41no—
424C4⋊(C3⋊D3)—42no—
425C4⋊(C3⋊D3)—42no—
426C4⋊(C3⋊D3)—42no—
427C4⋊(C3⋊D3)—42no—
428C4×C3⋊D3—42no—
429#634—41no—
430C3×#67—24no—
431C2×C3×Dic3—24no—
432C2×C3×Dic3—42no—
433C2×C3×Dic3C2412yes—
434C2×C3×Dic3C2412yes—
435C2×C3×Dic3C2412yes—
436C2×C3×Dic3C2412yes—
437C2×C3×Dic3C2412yes—
438C2×C3×Dic3C2412yes—
439C2×C3×Dic3C2412yes—
440C3×C4×D3—42no—
441C3×Dic6—42no—
442#627—42no—
443#626—42no—
444#626—42no—
445#626—42no—
446#626—42no—
447#626—42no—
448#624—42no—
449#624—41no—
450#624—42no—
451#624—41no—
452#624—42no—
453#624—42no—
454#624—41no—
455D3×Dic3—42no—
456#563—91no—
457#562—92no—
458#560—91no—
459#559—91no—
460#553—92no—
461#552—32no—
462#551—91no—
463#551—92no—
464#547—92no—
465#546—92no—
466#542—92no—
467#540—92no—
468#539—92no—
469#538—92no—
470#538—92no—
471#535—91no—
472#534—91no—
473#525—92no—
474C2×#123—91no—
475C23×D3—32no—
476C23×D3—32no—
477C23×D3—32no—
478C23×D3—61no—
479C23×D3—61no—
480C2×C3×Q8—32no—
481C2×C3×D4—32no—
482C22×C3×C4—21no—
483C22×C3×C4—32no—
484C22×C3×C4—32no—
485C22×C3×C4—32no—
486C22×C3×C4C22×D312yes—
487C2×#67—32no—
488C2×#67—32no—
489C2×#67—32no—
490C2×#67—32no—
491C2×#67—32no—
492C2×#67—32no—
493C2×#67—32no—
494C2×#67—62no—
495C2×#67C22×D312yes—
496C22×Dic3—32no—
497C22×Dic3C22×D312yes—
498C22×Dic3C22×D312yes—
499#237—124no—
500D3×D4—124no—
501#235—124no—
502#235—124no—
503#235—124no—
504C2×D12—32no—
505C2×D12—32no—
506C2×D12—32no—
507C2×D12—32no—
508C2×D12—32no—
509C2×D12—32no—
510C2×D12—32no—
511C2×D12—32no—
512C2×D12—32no—
513C2×D12—32no—
514C2×D12—32no—
515C2×D12—32no—
516C2×D12—32no—
517C2×D12—32no—
518C2×D12—32no—
519C2×D12—32no—
520C2×D12—32no—
521C2×D12—32no—
522C2×D12—61no—
523C2×D12—61no—
524C2×D12—61no—
525C2×D12—61no—
526C2×D12—61no—
527C2×D12—62no—
528C2×D12—62no—
529C2×D12—62no—
530C2×D12—62no—
531C2×D12—124no—
532C2×D12—124no—
533C2×C4×D3—32no—
534C2×C4×D3—32no—
535C2×C4×D3—32no—
536C2×C4×D3—32no—
537C2×C4×D3—32no—
538C2×C4×D3—32no—
539C2×C4×D3—32no—
540C2×C4×D3—32no—
541C2×C4×D3—32no—
542C2×C4×D3—32no—
543C2×C4×D3—32no—
544C2×C4×D3—32no—
545C2×C4×D3—32no—
546C2×C4×D3—32no—
547C2×C4×D3—62no—
548C2×C4×D3—124no—
549C2×C4×D3C22×D312yes—
550C2×Dic6—32no—
551C2×Dic6—32no—
552C2×Dic6—32no—
553C2×Dic6—61no—
554C2×Dic6C22×D312yes—
555C3×C4⋊C4—22no—
556C3×C4⋊C4—32no—
557C3×C4⋊C4—32no—
558C3×C4⋊C4—32no—
559C3×C4⋊C4—32no—
560C3×C4⋊C4—32no—
561C3×C4⋊C4—32no—
562C3×C4⋊C4—32no—
563C3×C4⋊C4—32no—
564C3×C4⋊C4—32no—
565C3×C4⋊C4—32no—
566C3×C4⋊C4—32no—
567C3×C4⋊C4—32no—
568C3×C4⋊C4—32no—
569C3×C4⋊C4—32no—
570C3×C4⋊C4C22×D312yes—
571C3×C4⋊C4C22×D312yes—
572C3×C22⋊C4—22no—
573C3×C22⋊C4—32no—
574C3×C22⋊C4—32no—
575C3×C22⋊C4—32no—
576C3×C22⋊C4—32no—
577C3×C22⋊C4—32no—
578C3×C22⋊C4—32no—
579C3×C22⋊C4C22×D312yes—
580C3×C22⋊C4C22×D312yes—
581C3×C42—21no—
582C3×C42—21no—
583C3×C42—32no—
584C3×C42—32no—
585C3×C42—32no—
586C3×C42C22×D312yes—
587C3×C42C22×D312yes—
588#217—32no—
589#217C22×D312yes—
590(C2×D3)⋊C4—32no—
591(C2×D3)⋊C4—32no—
592(C2×D3)⋊C4—32no—
593(C2×D3)⋊C4—32no—
594(C2×D3)⋊C4—32no—
595(C2×D3)⋊C4—32no—
596(C2×D3)⋊C4—32no—
597(C2×D3)⋊C4—32no—
598(C2×D3)⋊C4—32no—
599(C2×D3)⋊C4—32no—
600(C2×D3)⋊C4—32no—
601(C2×D3)⋊C4—32no—
602(C2×D3)⋊C4—32no—
603(C2×D3)⋊C4—32no—
604(C2×D3)⋊C4—32no—
605(C2×D3)⋊C4—32no—
606(C2×D3)⋊C4—32no—
607(C2×D3)⋊C4—32no—
608(C2×D3)⋊C4—32no—
609(C2×D3)⋊C4—32no—
610(C2×D3)⋊C4—32no—
611(C2×D3)⋊C4—32no—
612(C2×D3)⋊C4—32no—
613(C2×D3)⋊C4—32no—
614(C2×D3)⋊C4—32no—
615(C2×D3)⋊C4—32no—
616(C2×D3)⋊C4—32no—
617(C2×D3)⋊C4—32no—
618(C2×D3)⋊C4—32no—
619(C2×D3)⋊C4—32no—
620(C2×D3)⋊C4—32no—
621(C2×D3)⋊C4—32no—
622(C2×D3)⋊C4—32no—
623(C2×D3)⋊C4—32no—
624(C2×D3)⋊C4—32no—
625(C2×D3)⋊C4—62no—
626(C2×D3)⋊C4—62no—
627(C2×D3)⋊C4—62no—
628(C2×D3)⋊C4—62no—
629(C2×D3)⋊C4C22×D312yes—
630(C2×D3)⋊C4C22×D312yes—
631(C2×D3)⋊C4C22×D312yes—
632(C2×D3)⋊C4C22×D312yes—
633(C2×D3)⋊C4C22×D312yes—
634C4⋊Dic3—32no—
635C4⋊Dic3—32no—
636C4⋊Dic3—32no—
637C4⋊Dic3C22×D312yes—
638C4⋊Dic3C22×D312yes—
639C4⋊Dic3C22×D312yes—
640Dic3⋊C4—32no—
641Dic3⋊C4—32no—
642Dic3⋊C4—32no—
643Dic3⋊C4—32no—
644Dic3⋊C4—32no—
645Dic3⋊C4C22×D312yes—
646Dic3⋊C4C22×D312yes—
647Dic3⋊C4C22×D312yes—
648Dic3⋊C4C22×D312yes—
649Dic3⋊C4C22×D312yes—
650Dic3⋊C4C22×D312yes—
651Dic3⋊C4C22×D312yes—
652Dic3⋊C4C22×D312yes—
653Dic3⋊C4C22×D312yes—
654Dic3⋊C4C22×D312yes—
655Dic3⋊C4C22×D312yes—
656C4×Dic3—32no—
657C4×Dic3—32no—
658C4×Dic3C22×D312yes—
659C4×Dic3C22×D312yes—
660C4×Dic3C22×D312yes—
661C22×C32—22no—
662C22×C32H(5,𝔽2)12yes—
663C22×C32C2511yescharacteristic
664C2×C3⋊D3—21no—
665C2×C3⋊D3—21no—
666C2×C3⋊D3—22no—
667C2×C3⋊D3—21no—
668C2×C3⋊D3—21no—
669C2×C3⋊D3—22no—
670C2×C3⋊D3—22no—
671C2×C3⋊D3—22no—
672C2×C3⋊D3—22no—
673C2×C3⋊D3—22no—
674C2×C3⋊D3—22no—
675C2×C3⋊D3—44no—
676C2×C3⋊D3—82no—
677C2×C3×D3—22no—
678C2×C3×D3—22no—
679C2×C3×D3—22no—
680D32—82no—
681C32×C4—21no—
682C32×C4—21no—
683C32×C4—22no—
684C32×C4—22no—
685C3⋊Dic3—22no—
686C3×Dic3—22no—
687C3×Dic3—22no—
688C3×Dic3—22no—
689C3×Dic3—22no—
690C3×Dic3—22no—
691C3×Dic3—22no—
692C3×Dic3—22no—
693C2×#41—92no—
694C2×#41—91no—
695C22×D4—91no—
696C22×D4—91no—
697C23×C4—91no—
698C4⋊Q8—92no—
699#127—91no—
700#127—91no—
701#126—32no—
702#126—32no—
703#126—92no—
704#126—92no—
705#126—92no—
706#126—92no—
707#125—32no—
708#125—32no—
709#125—32no—
710#124—92no—
711#124—92no—
712#124—92no—
713#124—92no—
714#124—91no—
715#124—91no—
716#123—32no—
717#123—32no—
718#123—92no—
719#123—92no—
720#123—92no—
721#123—92no—
722#123—92no—
723#123—91no—
724#123—91no—
725#123—91no—
726#123—91no—
727#123—91no—
728#123—91no—
729#123—92no—
730#123—92no—
731#123—92no—
732#123—92no—
733#123—92no—
734C22⋊Q8—32no—
735C22⋊Q8—32no—
736C22⋊Q8—92no—
737C22⋊Q8—92no—
738C22⋊Q8—92no—
739C22⋊Q8—92no—
740C22⋊Q8—92no—
741C22⋊Q8—92no—
742#121—92no—
743#121—92no—
744#121—92no—
745#121—92no—
746#121—92no—
747#121—92no—
748#121—92no—
749#121—92no—
750#121—92no—
751#121—92no—
752#121—92no—
753#121—92no—
754#120—91no—
755#120—91no—
756#120—92no—
757#120—92no—
758#120—92no—
759#120—92no—
760C4×Q8—32no—
761C4×D4—32no—
762C4×D4—92no—
763C4×D4—92no—
764C4×D4—92no—
765C4×D4—92no—
766C4×D4—92no—
767C4×D4—92no—
768C4×D4—92no—
769C4×D4—92no—
770#117—32no—
771#117—32no—
772#117—92no—
773#117D3211yescharacteristic, complemented
774C2×C4⋊C4—32no—
775C2×C4⋊C4—92no—
776C2×C22⋊C4—91no—
777C2×C22⋊C4—92no—
778C2×C22⋊C4—91no—
779C2×C22⋊C4—92no—
780C23×C3—21no—
781C23×C3—32no—
782C23×C3C23×D312yes—
783C22×D3—32no—
784C22×D3—32no—
785C22×D3—32no—
786C22×D3—32no—
787C22×D3—32no—
788C22×D3—32no—
789C22×D3—61no—
790C22×D3—61no—
791C22×D3—61no—
792C22×D3—61no—
793C22×D3—62no—
794C22×D3—64no—
795C22×D3—64no—
796C22×D3—122no—
797C22×D3—122no—
798C22×D3—122no—
799C22×D3—122no—
800C22×D3—122no—
801C22×D3—122no—
802C22×D3—122no—
803C22×D3—122no—
804C22×D3—122no—
805C22×D3—242no—
806C22×D3—242no—
807C22×D3C23×D312yes—
808C3×Q8—122no—
809C3×D4—64no—
810C2×C3×C4—24no—
811C2×C3×C4—24no—
812C2×C3×C4—21no—
813C2×C3×C4—21no—
814C2×C3×C4—22no—
815C2×C3×C4—22no—
816C2×C3×C4—32no—
817C2×C3×C4—32no—
818C2×C3×C4—32no—
819C2×C3×C4—32no—
820C2×C3×C4—32no—
821C2×C3×C4—32no—
822C2×C3×C4—32no—
823C2×C3×C4—64no—
824C2×C3×C4—122no—
825C2×C3×C4—122no—
826C2×C3×C4C23×D312yes—
827C2×C3×C4C23×D312yes—
828C2×C3×C4C23×D312yes—
829C2×C3×C4C23×D312yes—
830C2×C3×C4C23×D312yes—
831C2×C3×C4C23×D312yes—
832#67—24no—
833#67—64no—
834#67—64no—
835#67—124no—
836#67—122no—
837#67—122no—
838#67—122no—
839#67—122no—
840#67—122no—
841C2×Dic3—24no—
842C2×Dic3—32no—
843C2×Dic3—32no—
844C2×Dic3—42no—
845C2×Dic3—62no—
846C2×Dic3—122no—
847C2×Dic3C23×D312yes—
848C2×Dic3C23×D312yes—
849C2×Dic3C23×D312yes—
850C2×Dic3C23×D312yes—
851C2×Dic3C23×D312yes—
852C2×Dic3C23×D312yes—
853C2×Dic3C23×D312yes—
854D12—122no—
855D12—122no—
856D12—122no—
857D12—122no—
858D12—122no—
859D12—122no—
860D12—122no—
861D12—122no—
862D12—122no—
863D12—122no—
864D12—122no—
865D12—122no—
866D12—122no—
867D12—122no—
868D12—122no—
869D12—122no—
870D12—122no—
871D12—122no—
872D12—122no—
873D12—122no—
874D12—122no—
875D12—122no—
876D12—122no—
877D12—242no—
878D12—242no—
879D12—242no—
880D12—242no—
881C4×D3—42no—
882C4×D3—122no—
883C4×D3—122no—
884C4×D3—122no—
885C4×D3—122no—
886C4×D3—122no—
887C4×D3—122no—
888C4×D3—122no—
889C4×D3—122no—
890C4×D3—122no—
891C4×D3—122no—
892C4×D3—122no—
893C4×D3—122no—
894C4×D3—122no—
895C4×D3—122no—
896C4×D3—124no—
897Dic6—42no—
898Dic6—122no—
899Dic6—122no—
900Dic6—122no—
901Dic6—122no—
902C2×C32—22no—
903C2×C32C2×H(5,𝔽2)11yescharacteristic
904C2×C32#58512yes—
905C3⋊D3—41no—
906C3⋊D3—42no—
907C3⋊D3—41no—
908C3⋊D3—41no—
909C3⋊D3—41no—
910C3×D3—42no—
911C24—91no—
912C24—91no—
913C24—91no—
914#41—362no—
915#41—364no—
916C2×Q8—32no—
917C2×Q8—92no—
918C2×Q8—91no—
919C2×D4—32no—
920C2×D4—92no—
921C2×D4—92no—
922C2×D4—92no—
923C2×D4—92no—
924C2×D4—92no—
925C2×D4—92no—
926C2×D4—92no—
927C2×D4—92no—
928C2×D4—92no—
929C2×D4—92no—
930C2×D4—91no—
931C2×D4—91no—
932C2×D4—91no—
933C2×D4—91no—
934C2×D4—91no—
935C2×D4—362no—
936C2×D4—362no—
937C22×C4—32no—
938C22×C4—32no—
939C22×C4—32no—
940C22×C4—92no—
941C22×C4—92no—
942C22×C4—92no—
943C22×C4—91no—
944C22×C4—92no—
945C22×C4—91no—
946C22×C4—91no—
947C22×C4—92no—
948C22×C4—92no—
949C22×C4—362no—
950C22×C4C2×D3211yescharacteristic
951C4⋊C4—32no—
952C4⋊C4—32no—
953C4⋊C4—32no—
954C4⋊C4—32no—
955C4⋊C4—32no—
956C4⋊C4—32no—
957C4⋊C4—32no—
958C4⋊C4—32no—
959C4⋊C4—32no—
960C4⋊C4—32no—
961C4⋊C4—32no—
962C4⋊C4—32no—
963C4⋊C4—32no—
964C4⋊C4—32no—
965C4⋊C4—92no—
966C4⋊C4—92no—
967C4⋊C4—92no—
968C4⋊C4—92no—
969C4⋊C4C2×D3212yes—
970C22⋊C4—32no—
971C22⋊C4—32no—
972C22⋊C4—32no—
973C22⋊C4—32no—
974C22⋊C4—32no—
975C22⋊C4—32no—
976C22⋊C4—92no—
977C22⋊C4—92no—
978C22⋊C4—92no—
979C22⋊C4—91no—
980C22⋊C4—91no—
981C22⋊C4—91no—
982C22⋊C4—92no—
983C22⋊C4—92no—
984C22⋊C4—91no—
985C22⋊C4—92no—
986C22⋊C4—92no—
987C22⋊C4—92no—
988C22⋊C4—92no—
989C22⋊C4—92no—
990C22⋊C4—92no—
991C22⋊C4—92no—
992C22⋊C4—92no—
993C22⋊C4—92no—
994C22⋊C4—92no—
995C22⋊C4—92no—
996C22⋊C4C2×D3212yes—
997C42—32no—
998C42—32no—
999C42—32no—
1000C42—92no—
1001C42C2×D3211yescharacteristic
1002C42C2×D3211yescharacteristic
1003C22×C3—22no—
1004C22×C3—22no—
1005C22×C3—22no—
1006C22×C3—21no—
1007C22×C3—42no—
1008C22×C3—62no—
1009C22×C3—62no—
1010C22×C3—62no—
1011C22×C3#100914yes—
1012C22×C3C24×D312yes—
1013C2×D3—22no—
1014C2×D3—22no—
1015C2×D3—22no—
1016C2×D3—62no—
1017C2×D3—62no—
1018C2×D3—62no—
1019C2×D3—62no—
1020C2×D3—62no—
1021C2×D3—62no—
1022C2×D3—62no—
1023C2×D3—62no—
1024C2×D3—62no—
1025C2×D3—62no—
1026C2×D3—62no—
1027C2×D3—62no—
1028C2×D3—62no—
1029C2×D3—62no—
1030C2×D3—62no—
1031C2×D3—62no—
1032C2×D3—62no—
1033C2×D3—62no—
1034C2×D3—122no—
1035C2×D3—121no—
1036C2×D3—121no—
1037C2×D3—121no—
1038C2×D3—121no—
1039C2×D3—122no—
1040C2×D3—122no—
1041C2×D3—122no—
1042C2×D3—122no—
1043C2×D3—122no—
1044C2×D3—122no—
1045C2×D3—128no—
1046C2×D3—244no—
1047C2×D3—244no—
1048C2×D3—244no—
1049C2×D3—244no—
1050C3×C4—22no—
1051C3×C4—22no—
1052C3×C4—22no—
1053C3×C4—22no—
1054C3×C4—22no—
1055C3×C4—22no—
1056C3×C4—22no—
1057C3×C4—22no—
1058C3×C4—42no—
1059C3×C4—42no—
1060C3×C4—62no—
1061C3×C4—62no—
1062C3×C4—62no—
1063C3×C4—62no—
1064C3×C4—62no—
1065C3×C4—62no—
1066C3×C4—62no—
1067Dic3—22no—
1068Dic3—22no—
1069Dic3—22no—
1070Dic3—22no—
1071Dic3—22no—
1072Dic3—22no—
1073Dic3—22no—
1074Dic3—62no—
1075Dic3—62no—
1076Dic3—122no—
1077C32#353311yescharacteristic, complemented, Sylow
1078C23—32no—
1079C23—91no—
1080C23—91no—
1081C23—91no—
1082C23—91no—
1083C23—92no—
1084C23—182no—
1085C23—182no—
1086C23—362no—
1087C23—362no—
1088C23—361no—
1089C23—362no—
1090C23C22×D3211yescharacteristic
1091Q8—122no—
1092Q8—361no—
1093Q8—362no—
1094D4—64no—
1095D4—184no—
1096D4—361no—
1097D4—361no—
1098D4—361no—
1099D4—361no—
1100D4—361no—
1101D4—362no—
1102D4—362no—
1103D4—362no—
1104D4—362no—
1105D4—362no—
1106D4—362no—
1107D4—362no—
1108D4—362no—
1109D4—362no—
1110C2×C4—22no—
1111C2×C4—32no—
1112C2×C4—32no—
1113C2×C4—32no—
1114C2×C4—32no—
1115C2×C4—32no—
1116C2×C4—32no—
1117C2×C4—32no—
1118C2×C4—64no—
1119C2×C4—92no—
1120C2×C4—122no—
1121C2×C4—122no—
1122C2×C4—362no—
1123C2×C4—361no—
1124C2×C4—362no—
1125C2×C4—361no—
1126C2×C4—361no—
1127C2×C4—362no—
1128C2×C4—362no—
1129C2×C4—362no—
1130C2×C4—362no—
1131C2×C4C22×D3212yes—
1132C2×C4C22×D3212yes—
1133C2×C4C22×D3211yescharacteristic
1134C2×C4C22×D3211yescharacteristic
1135C2×C3—24no—
1136C2×C3—21no—
1137C2×C3—22no—
1138C2×C3—42no—
1139C2×C3—122no—
1140C2×C3C2×#100912yes—
1141C2×C3#596412yes—
1142C2×C3#596812yes—
1143D3—42no—
1144D3—122no—
1145D3—122no—
1146D3—122no—
1147D3—122no—
1148D3—122no—
1149D3—122no—
1150D3—241no—
1151D3—241no—
1152D3—241no—
1153D3—241no—
1154D3—242no—
1155C22—22no—
1156C22—62no—
1157C22—62no—
1158C22—62no—
1159C22—182no—
1160C22—181no—
1161C22—181no—
1162C22—181no—
1163C22—181no—
1164C22—182no—
1165C22—182no—
1166C22—182no—
1167C22—182no—
1168C22—182no—
1169C22—182no—
1170C22—364no—
1171C22—722no—
1172C22—722no—
1173C22#6430812yes—
1174C22C23×D3211yescharacteristic
1175C4—21no—
1176C4—21no—
1177C4—22no—
1178C4—22no—
1179C4—62no—
1180C4—62no—
1181C4—62no—
1182C4—62no—
1183C4—62no—
1184C4—62no—
1185C4—62no—
1186C4—182no—
1187C3—21no—
1188C3#8686412yescomplemented
1189C2—22no—
1190C2—122no—
1191C2—361no—
1192C2—361no—
1193C2—361no—
1194C2—361no—
1195C2—362no—
1196C2C2×#6430811yescharacteristic
1197C2#1059669712yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#117C22
hypercenter#117D32
hypocenterC32#3533
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595996C2semidirect
2. C3×#5531C2semidirect
3. #10595080C2semidirect
4. C2×#63897C2semidirect
5. #10594917C2semidirect
6. #10594652C2semidirect
7. #10594593C2semidirect
8. #10594483C2semidirect
9. #10594468C2semidirect
10. #10594293C2semidirect
11. #10594243C2semidirect
12. #10594166C2semidirect
13. #10594079C2semidirect
14. #10594023C2semidirect
15. #10594014C2semidirect
16. #10593989C2semidirect
17. #10593963C2semidirect
18. #10593936C2semidirect
19. #10593857C2semidirect
21. C2×#3828C22semidirect
24. C22×#624C22semidirect
26. C32×#117C22semidirect
28. #64104C22semidirect
30. #64091C22semidirect
32. #64084C22semidirect
34. #64083C22semidirect
36. C2×C3×Dic3⋊C4C22semidirect
37. C3×#898C22semidirect
38. C3×#896C22semidirect
39. C3×#889C22semidirect
40. C3×#889C22semidirect
43. C3×#878C22semidirect
44. C3×#877C22semidirect
45. C3×#876C22semidirect
46. C3×#872C22semidirect
47. C3×#870C22semidirect
48. C3×C4×Dic6C22semidirect
52. #63966C22semidirect
54. C2×#3722C22semidirect
55. #63952C22semidirect
58. #63923C22semidirect
59. D3×(C2×D3)⋊C4C22semidirect
62. #63910C22semidirect
63. #63910C22semidirect
64. #63910C22semidirect
65. #63910C22semidirect
66. #63910C22semidirect
67. #63909C22semidirect
68. #63909C22semidirect
69. #63907C22semidirect
75. #63897C22semidirect
76. #63897C22semidirect
77. #63897C22semidirect
78. #63897C22semidirect
79. #63897C22semidirect
80. #63897C22semidirect
81. #63897C22semidirect
82. #63896C22semidirect
83. #63895C22semidirect
84. #63895C22semidirect
85. #63895C22semidirect
86. #63894C22semidirect
87. #63894C22semidirect
88. #63894C22semidirect
89. #63894C22semidirect
90. #63890C22semidirect
91. #63888C22semidirect
92. #63883C22semidirect
93. #63881C22semidirect
94. #63880C22semidirect
95. #63880C22semidirect
96. #63868C22semidirect
97. #63868C22semidirect
98. #63865C22semidirect
99. #63864C22semidirect
100. #63864C22semidirect
101. #63853C22semidirect
102. #63852C22semidirect
103. #63850C22semidirect
104. #63848C22semidirect
105. #63848C22semidirect
106. #63840C22semidirect
107. #63836C22semidirect
132. #5531D3semidirect
255. C3×#117C2×D3semidirect
274. C2×Dic3⋊C4C2×D3semidirect
281. #898C2×D3semidirect
292. #896C2×D3semidirect
337. #889C2×D3semidirect
338. #889C2×D3semidirect
373. #878C2×D3semidirect
374. #877C2×D3semidirect
377. #876C2×D3semidirect
396. #872C2×D3semidirect
397. #870C2×D3semidirect
398. C4×Dic6C2×D3semidirect
773. #117D32semidirect
1077. C32#3533semidirect
1188. C3#86864semidirect

Maximal subgroups

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

subgroupindex
#105959962
C3×#55312
#105950802
C2×#638972
#105949172
#105946522
#105945932
#105944832
#105944682
#105942932
#105942432
#105941662
#105940792
#105940232
#105940142
#105939892
#105939632
#105939362
#105938572
#868643