Finite Group Databasebeta

← #11910477

Subgroups — #11910477

Order 1152.

1977 conjugacy classes of subgroups.

The subgroup lattice has 1143 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595950C211yesmaximal, characteristic, complemented
2C3×#5479C211yesmaximal, characteristic, complemented
3C3×#5470C211yesmaximal, characteristic, complemented
4#10594978C212yesmaximal, complemented
5#10594976C212yesmaximal, complemented
6#10594972C212yesmaximal, complemented
7#10594933C212yesmaximal, complemented
8#10594836C212yesmaximal, complemented
9#10594811C212yesmaximal, complemented
10#10593957C212yesmaximal, complemented
11#10593957C212yesmaximal, complemented
12#10593953C211yesmaximal, characteristic, complemented
13#10593952C211yesmaximal, characteristic, complemented
14#10593935C212yesmaximal, complemented
15#10593934C212yesmaximal, complemented
16#10593926C212yesmaximal, complemented
17#10593911C212yesmaximal, complemented
18#10593868C211yesmaximal, characteristic, complemented
19#10593857C211yesmaximal, characteristic, complemented
20#86286—31nomaximal
21#86132—31nomaximal
22C2×C32×C42C2211yescharacteristic
23#64139C2211yescharacteristic
24#64138C2212yes—
25C4×#638C2212yes—
26#64133C2211yescharacteristic
27#64085C2212yes—
28#64084C2211yescharacteristic
29C4×C4⋊(C3⋊D3)C2211yescharacteristic
30#64081C2212yes—
31#64079C2211yescharacteristic
32C4×#634C2211yescharacteristic
33C3×#930C2211yescharacteristic
34C3×#929C2212yes—
35C3×C4×#67C2212yes—
36C3×#926C2211yescharacteristic
37C3×#926C2211yescharacteristic
38C3×#924C2212yes—
39C3×#924C2212yes—
40C3×#924C2211yescharacteristic
41C3×#876C2212yes—
42C3×#875C2211yescharacteristic
43C3×C4×D12C2211yescharacteristic
44C3×#872C2212yes—
45C3×#870C2211yescharacteristic
46C3×#870C2211yescharacteristic
47C3×#870C2211yescharacteristic
48C3×#869C2211yescharacteristic
49C3×#869C2211yescharacteristic
50C3×C4×Dic6C2212yes—
51C3×C4×Dic6C2212yes—
52C3×C4×Dic6C2211yescharacteristic
53#63975C2212yes—
54#63971C2212yes—
55#63969C2212yes—
56#63959C2212yes—
57#63958C2212yes—
58#63956C2212yes—
59#63956C2212yes—
60#63953C2212yes—
61C4×#627C2212yes—
62C4×#627C2212yes—
63#63910C2212yes—
64#63907C2212yes—
65#63907C2212yes—
66C4×#626C2212yes—
67C4×#626C2212yes—
68#63899C2212yes—
69#63899C2212yes—
70#63897C2212yes—
71#63896C2212yes—
72#63895C2212yes—
73#63895C2212yes—
74#63895C2212yes—
75#63893C2212yes—
76#63890C2212yes—
77#63890C2212yes—
78#63888C2212yes—
79#63888C2212yes—
80#63888C2212yes—
81#63887C2212yes—
82#63887C2212yes—
83#63886C2212yes—
84#63884C2212yes—
85C4×#624C2212yes—
86C4×D3×Dic3C2212yes—
87#63874C2212yes—
88#63861C2212yes—
89#63858C2212yes—
90#63858C2212yes—
91#63855C2212yes—
92#63854C2212yes—
93#63854C2212yes—
94#63848C2212yes—
95#63848C2212yes—
96#63848C2212yes—
97#63847C2212yes—
98#63847C2212yes—
99#63847C2212yes—
100#63846C2212yes—
101#63846C2212yes—
102#63846C2212yes—
103#63845C2212yes—
104#63845C2212yes—
105#63840C2212yes—
106#63839C2212yes—
107#63839C2212yes—
108#63839C2212yes—
109C3×#533—31no—
110C3×#529—31no—
111#5735—32no—
112#5735—32no—
113#5712—32no—
114#5712—32no—
115#5700—31no—
116#5699—31no—
117#5699—31no—
118#5699—31no—
119C3⋊#564—31no—
120C3⋊#564—31no—
121#5684—31no—
122#5672—31no—
123#5667—32no—
124#5651—32no—
125#5647—32no—
126#5647—32no—
127#5646—32no—
128#5646—32no—
129#5646—32no—
130#5621—32no—
131#5580—32no—
132#5580—32no—
133#5578—32no—
134#5578—32no—
135#5578—32no—
136#5557—32no—
137#5538—32no—
138#5538—32no—
139#5528—32no—
140#5528—32no—
141#5528—32no—
142#5517—32no—
143#5479—31no—
144#5479—31no—
145#5479—61no—
146#5479D311yescharacteristic, complemented
147#5470D311yescharacteristic, complemented
148C22×C32×C4C2311yescharacteristic
149C22×C32×C4C2311yescharacteristic
150C22×C32×C4C2311yescharacteristic
151C2×#638C2312yes—
152C2×C4⋊(C3⋊D3)C2311yescharacteristic
153C2×C4×C3⋊D3C2312yes—
154C2×#634C2311yescharacteristic
155C2×C3×#67C2312yes—
156C2×C3×D12C2311yescharacteristic
157C2×C3×C4×D3C2312yes—
158C2×C3×Dic6C2311yescharacteristic
159C2×C3×Dic6C2312yes—
160C2×C3×Dic6C2312yes—
161C2×#627C2312yes—
162C2×#627C2312yes—
163C2×#626C2312yes—
164C2×#626C2312yes—
165C2×#624C2312yes—
166C2×#624C2312yes—
167C2×D3×Dic3C2312yes—
168C2×D3×Dic3C2312yes—
169C32×C42C2311yescharacteristic
170C32×C42C2311yescharacteristic
171C32×C42C2311yescharacteristic
172C32×C42C2311yescharacteristic
173#3757C2312yes—
174#3752C2312yes—
175#3752C2312yes—
176#3752C2312yes—
177#3752C2312yes—
178C4⋊(C3⋊Dic3)C2311yescharacteristic
179C4⋊(C3⋊Dic3)C2311yescharacteristic
180#3750C2312yes—
181#3750C2312yes—
182#3750C2312yes—
183#3750C2312yes—
184C4×C3⋊Dic3C2312yes—
185C3×#217C2312yes—
186C3×#217C2312yes—
187C3×#217C2312yes—
188C3×(C2×D3)⋊C4C2312yes—
189C3×(C2×D3)⋊C4C2312yes—
190C3×(C2×D3)⋊C4C2312yes—
191C3×(C2×D3)⋊C4C2312yes—
192C3×C4⋊Dic3C2311yescharacteristic
193C3×C4⋊Dic3C2312yes—
194C3×C4⋊Dic3C2312yes—
195C3×C4⋊Dic3C2311yescharacteristic
196C3×C4⋊Dic3C2311yescharacteristic
197C3×C4⋊Dic3C2311yescharacteristic
198C3×C4⋊Dic3C2311yescharacteristic
199C3×C4⋊Dic3C2311yescharacteristic
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—
212#3724C2312yes—
213#3724C2312yes—
214#3724C2312yes—
215Dic3⋊Dic3C2312yes—
216Dic3⋊Dic3C2312yes—
217Dic3⋊Dic3C2312yes—
218Dic3⋊Dic3C2312yes—
219Dic3⋊Dic3C2312yes—
220Dic3⋊Dic3C2312yes—
221Dic3⋊Dic3C2312yes—
222Dic3⋊Dic3C2312yes—
223#3722C2312yes—
224#3722C2312yes—
225#3722C2312yes—
226#3722C2312yes—
227(C2×D3)⋊Dic3C2312yes—
228(C2×D3)⋊Dic3C2312yes—
229(C2×D3)⋊Dic3C2312yes—
230(C2×D3)⋊Dic3C2312yes—
231Dic32C2312yes—
232Dic32C2312yes—
233Dic32C2312yes—
234Dic32C2312yes—
235#3531—91noSylow
236C3×C4⋊Q8—31no—
237C3×C4⋊Q8—31no—
238C3×#126—32no—
239C3×#125—31no—
240C3×#125—31no—
241C3×#125—31no—
242C3×#124—31no—
243C3×#123—32no—
244C3×C22⋊Q8—31no—
245C3×C22⋊Q8—32no—
246C3×C22⋊Q8—32no—
247C3×#121—31no—
248C3×C4×Q8—31no—
249C3×C4×Q8—32no—
250C3×C4×Q8—32no—
251C3×C4×D4—32no—
252C3×C4×D4—31no—
253C3×#117—31no—
254C3×#117—31no—
255C3×#117—32no—
256C2×C3×C42—21no—
257C2×C3×C42C2×D311yescharacteristic
258C2×C3×C42C2×D311yescharacteristic
259#947—32no—
260#947—32no—
261#946—32no—
262#946—32no—
263#946—32no—
264#946—32no—
265#946—32no—
266#944—32no—
267#944—32no—
268#944—32no—
269#939—32no—
270#939—32no—
271#938—32no—
272#936—32no—
273#935—32no—
274#935—32no—
275#930—31no—
276#930—31no—
277#930—61no—
278#930C2×D311yescharacteristic
279#929—32no—
280#929—32no—
281#929—62no—
282#929C2×D312yes—
283C4×#67—32no—
284C4×#67—32no—
285C4×#67—32no—
286C4×#67—32no—
287C4×#67—62no—
288C4×#67C2×D312yes—
289#926—32no—
290#926C2×D311yescharacteristic
291#926C2×D311yescharacteristic
292#924—31no—
293#924—31no—
294#924—61no—
295#924C2×D311yescharacteristic
296#924C2×D312yes—
297#924C2×D312yes—
298C2×C4×Dic3—32no—
299#898—32no—
300#898—32no—
301#898—32no—
302#898—32no—
303#898—32no—
304#898—32no—
305#898—32no—
306#898—32no—
307#898—32no—
308#897—32no—
309#897—32no—
310#897—32no—
311#897—32no—
312#896—32no—
313#896—32no—
314#896—32no—
315#896—32no—
316#896—32no—
317#896—32no—
318#896—32no—
319#896—32no—
320#896—32no—
321#895—32no—
322#895—32no—
323#894—32no—
324#894—32no—
325#894—32no—
326#894—32no—
327#894—32no—
328#894—32no—
329#894—32no—
330#890—32no—
331#890—32no—
332#890—32no—
333#890—32no—
334#890—32no—
335#889—32no—
336#889—32no—
337#889—32no—
338#889—32no—
339#889—32no—
340#889—32no—
341#889—32no—
342#889—32no—
343#889—32no—
344#889—32no—
345#889—32no—
346#888—32no—
347#888—32no—
348#888—32no—
349#888—32no—
350#888—32no—
351#886—32no—
352#886—32no—
353#885—32no—
354#885—32no—
355#885—32no—
356#885—32no—
357#885—32no—
358#884—32no—
359#884—32no—
360#884—32no—
361#883—32no—
362#883—32no—
363#883—32no—
364#883—32no—
365#883—32no—
366#879—32no—
367#879—32no—
368#879—32no—
369#879—32no—
370#879—32no—
371#879—32no—
372#879—32no—
373#878—32no—
374#878—32no—
375#878—32no—
376#878—32no—
377#878—32no—
378#878—32no—
379#876—32no—
380#876—32no—
381#876—62no—
382#876C2×D312yes—
383#875—31no—
384#875—31no—
385#875—61no—
386#875C2×D311yescharacteristic
387C4×D12—32no—
388C4×D12—32no—
389C4×D12—31no—
390C4×D12—31no—
391C4×D12—61no—
392C4×D12C2×D311yescharacteristic
393#872—32no—
394#872—32no—
395#872—32no—
396#872—32no—
397#872—32no—
398#872—62no—
399#872C2×D312yes—
400C42×D3—32no—
401C42×D3—32no—
402C42×D3—32no—
403#870—31no—
404#870—31no—
405#870—61no—
406#870C2×D311yescharacteristic
407#870C2×D311yescharacteristic
408#870C2×D311yescharacteristic
409#869C2×D311yescharacteristic
410#869C2×D311yescharacteristic
411C4×Dic6—31no—
412C4×Dic6—31no—
413C4×Dic6—32no—
414C4×Dic6—32no—
415C4×Dic6—32no—
416C4×Dic6—32no—
417C4×Dic6—61no—
418C4×Dic6C2×D312yes—
419C4×Dic6C2×D312yes—
420C4×Dic6C2×D311yescharacteristic
421C23×C32C2411yescharacteristic
422C22×C3⋊D3C2412yes—
423C22×C3×D3C2412yes—
424C2×C32×C4—22no—
425C2×C32×C4—41no—
426C2×C32×C4—41no—
427C2×C32×C4C2411yescharacteristic
428C2×C32×C4C2411yescharacteristic
429C2×C32×C4C2411yescharacteristic
430C2×C32×C4C2411yescharacteristic
431C2×C32×C4C2411yescharacteristic
432C2×C32×C4C2411yescharacteristic
433#638—42no—
434C2×C3⋊Dic3C2412yes—
435C2×C3⋊Dic3C2412yes—
436C2×C3⋊Dic3C2412yes—
437C4⋊(C3⋊D3)—41no—
438C4×C3⋊D3—24no—
439#634—41no—
440C3×#67—42no—
441C2×C3×Dic3C2412yes—
442C2×C3×Dic3C2412yes—
443C2×C3×Dic3C2412yes—
444C2×C3×Dic3C2412yes—
445C2×C3×Dic3C2412yes—
446C2×C3×Dic3C2412yes—
447C2×C3×Dic3C2412yes—
448C3×D12—41no—
449C3×C4×D3—24no—
450C3×Dic6—42no—
451C3×Dic6—42no—
452C3×Dic6—41no—
453#627—42no—
454#627—42no—
455#626—42no—
456#626—42no—
457#624—42no—
458#624—42no—
459D3×Dic3—42no—
460D3×Dic3—42no—
461#564—91no—
462#563—92no—
463#563—92no—
464#563—91no—
465#563—91no—
466#563—92no—
467#563—92no—
468#562—92no—
469#562—92no—
470#562—91no—
471#533—31no—
472#533—92no—
473#533—92no—
474#529—31no—
475#529—92no—
476#529—92no—
477#529—92no—
478#529—92no—
479#529—91no—
480C2×C3×Q8—31no—
481C2×C3×Q8—32no—
482C2×C3×Q8—32no—
483C2×C3×D4—32no—
484C2×C3×D4—31no—
485C22×C3×C4—21no—
486C22×C3×C4—21no—
487C22×C3×C4—21no—
488C22×C3×C4—32no—
489C22×C3×C4C22×D311yescharacteristic
490C22×C3×C4C22×D311yescharacteristic
491C22×C3×C4C22×D311yescharacteristic
492C22×C3×C4C22×D311yescharacteristic
493C22×C3×C4C22×D311yescharacteristic
494C22×C3×C4C22×D311yescharacteristic
495C2×#67—32no—
496C2×#67—32no—
497C2×#67—32no—
498C2×#67—32no—
499C2×#67—62no—
500C2×#67C22×D312yes—
501C22×Dic3—32no—
502C22×Dic3—32no—
503C2×D12—32no—
504C2×D12—32no—
505C2×D12—31no—
506C2×D12—31no—
507C2×D12—61no—
508C2×D12C22×D311yescharacteristic
509C2×C4×D3—32no—
510C2×C4×D3—32no—
511C2×C4×D3—32no—
512C2×C4×D3—32no—
513C2×C4×D3—32no—
514C2×C4×D3—32no—
515C2×C4×D3—32no—
516C2×C4×D3—32no—
517C2×C4×D3—62no—
518C2×C4×D3C22×D312yes—
519C2×Dic6—31no—
520C2×Dic6—31no—
521C2×Dic6—32no—
522C2×Dic6—32no—
523C2×Dic6—32no—
524C2×Dic6—32no—
525C2×Dic6—61no—
526C2×Dic6C22×D312yes—
527C2×Dic6C22×D312yes—
528C2×Dic6C22×D311yescharacteristic
529C3×C4⋊C4—32no—
530C3×C4⋊C4—32no—
531C3×C4⋊C4—32no—
532C3×C4⋊C4—32no—
533C3×C4⋊C4—32no—
534C3×C4⋊C4—31no—
535C3×C4⋊C4—31no—
536C3×C4⋊C4—31no—
537C3×C4⋊C4—31no—
538C3×C4⋊C4—32no—
539C3×C4⋊C4—32no—
540C3×C4⋊C4—32no—
541C3×C4⋊C4—32no—
542C3×C4⋊C4—32no—
543C3×C4⋊C4—31no—
544C3×C4⋊C4—31no—
545C3×C22⋊C4—32no—
546C3×C22⋊C4—32no—
547C3×C22⋊C4—32no—
548C3×C22⋊C4—32no—
549C3×C22⋊C4—32no—
550C3×C22⋊C4—32no—
551C3×C22⋊C4—32no—
552C3×C42—21no—
553C3×C42—21no—
554C3×C42—21no—
555C3×C42—21no—
556C3×C42—32no—
557C3×C42—32no—
558C3×C42—32no—
559C3×C42C22×D311yescharacteristic
560C3×C42C22×D311yescharacteristic
561C3×C42C22×D311yescharacteristic
562C3×C42C22×D311yescharacteristic
563C3×C42C22×D311yescharacteristic
564C3×C42C22×D311yescharacteristic
565C3×C42C22×D311yescharacteristic
566C3×C42C22×D311yescharacteristic
567#217—32no—
568#217—32no—
569#217—32no—
570#217—32no—
571#217—32no—
572#217—32no—
573#217—62no—
574#217C22×D312yes—
575#217C22×D312yes—
576#217C22×D312yes—
577(C2×D3)⋊C4—32no—
578(C2×D3)⋊C4—32no—
579(C2×D3)⋊C4—32no—
580(C2×D3)⋊C4—32no—
581(C2×D3)⋊C4—32no—
582(C2×D3)⋊C4—32no—
583(C2×D3)⋊C4—32no—
584(C2×D3)⋊C4—32no—
585(C2×D3)⋊C4—32no—
586(C2×D3)⋊C4—32no—
587(C2×D3)⋊C4—32no—
588(C2×D3)⋊C4—32no—
589(C2×D3)⋊C4—32no—
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—62no—
598(C2×D3)⋊C4—62no—
599(C2×D3)⋊C4—62no—
600(C2×D3)⋊C4—62no—
601(C2×D3)⋊C4C22×D312yes—
602(C2×D3)⋊C4C22×D312yes—
603(C2×D3)⋊C4C22×D312yes—
604(C2×D3)⋊C4C22×D312yes—
605C4⋊Dic3—31no—
606C4⋊Dic3—31no—
607C4⋊Dic3—31no—
608C4⋊Dic3—31no—
609C4⋊Dic3—32no—
610C4⋊Dic3—32no—
611C4⋊Dic3—32no—
612C4⋊Dic3—32no—
613C4⋊Dic3—32no—
614C4⋊Dic3—32no—
615C4⋊Dic3—32no—
616C4⋊Dic3—32no—
617C4⋊Dic3—61no—
618C4⋊Dic3—61no—
619C4⋊Dic3C22×D312yes—
620C4⋊Dic3C22×D312yes—
621C4⋊Dic3C22×D311yescharacteristic
622C4⋊Dic3C22×D311yescharacteristic
623C4⋊Dic3C22×D311yescharacteristic
624C4⋊Dic3C22×D311yescharacteristic
625C4⋊Dic3C22×D311yescharacteristic
626C4⋊Dic3C22×D311yescharacteristic
627Dic3⋊C4—32no—
628Dic3⋊C4—32no—
629Dic3⋊C4—32no—
630Dic3⋊C4—32no—
631Dic3⋊C4—32no—
632Dic3⋊C4—32no—
633Dic3⋊C4—32no—
634Dic3⋊C4—32no—
635Dic3⋊C4—32no—
636Dic3⋊C4—32no—
637Dic3⋊C4—32no—
638Dic3⋊C4—32no—
639Dic3⋊C4—32no—
640Dic3⋊C4—32no—
641Dic3⋊C4—32no—
642Dic3⋊C4—32no—
643Dic3⋊C4—32no—
644Dic3⋊C4—32no—
645Dic3⋊C4—32no—
646Dic3⋊C4—32no—
647Dic3⋊C4—32no—
648Dic3⋊C4—32no—
649Dic3⋊C4—32no—
650Dic3⋊C4—32no—
651Dic3⋊C4—62no—
652Dic3⋊C4—62no—
653Dic3⋊C4—62no—
654Dic3⋊C4—62no—
655Dic3⋊C4C22×D312yes—
656Dic3⋊C4C22×D312yes—
657Dic3⋊C4C22×D312yes—
658Dic3⋊C4C22×D312yes—
659Dic3⋊C4C22×D312yes—
660Dic3⋊C4C22×D312yes—
661Dic3⋊C4C22×D312yes—
662Dic3⋊C4C22×D312yes—
663C4×Dic3—32no—
664C4×Dic3—32no—
665C4×Dic3—32no—
666C4×Dic3—32no—
667C4×Dic3—32no—
668C4×Dic3—32no—
669C4×Dic3—32no—
670C4×Dic3—32no—
671C4×Dic3—32no—
672C4×Dic3—32no—
673C4×Dic3—62no—
674C4×Dic3C22×D312yes—
675C4×Dic3C22×D312yes—
676C4×Dic3C22×D312yes—
677C22×C32—21no—
678C22×C32—21no—
679C22×C32—21no—
680C22×C32C2511yescharacteristic
681C2×C3⋊D3—22no—
682C2×C3⋊D3—22no—
683C2×C3⋊D3—22no—
684C2×C3×D3—22no—
685C2×C3×D3—22no—
686C2×C3×D3—22no—
687C32×C4—21no—
688C32×C4—21no—
689C32×C4—21no—
690C32×C4—21no—
691C32×C4—21no—
692C32×C42−1+412yes—
693C3⋊Dic3—22no—
694C3⋊Dic3—22no—
695C3⋊Dic3—22no—
696C3×Dic3—22no—
697C3×Dic3—22no—
698C3×Dic3—22no—
699C3×Dic3—22no—
700C3×Dic3—22no—
701C3×Dic3—22no—
702C3×Dic3—22no—
703C4⋊Q8—31no—
704C4⋊Q8—31no—
705C4⋊Q8—92no—
706C4⋊Q8—92no—
707C4⋊Q8—92no—
708C4⋊Q8—92no—
709#126—32no—
710#126—92no—
711#126—92no—
712#126—92no—
713#126—92no—
714#126—92no—
715#126—92no—
716#126—92no—
717#126—92no—
718#126—92no—
719#125—31no—
720#125—31no—
721#125—31no—
722#125—92no—
723#125—92no—
724#125—92no—
725#125—92no—
726#125—92no—
727#125—92no—
728#125—92no—
729#125—92no—
730#125—91no—
731#124—31no—
732#124—92no—
733#124—92no—
734#124—92no—
735#124—92no—
736#124—91no—
737#123—32no—
738#123—92no—
739#123—92no—
740#123—92no—
741#123—92no—
742#123—92no—
743#123—92no—
744#123—92no—
745#123—92no—
746#123—92no—
747C22⋊Q8—31no—
748C22⋊Q8—32no—
749C22⋊Q8—32no—
750C22⋊Q8—92no—
751C22⋊Q8—92no—
752C22⋊Q8—92no—
753C22⋊Q8—92no—
754C22⋊Q8—92no—
755C22⋊Q8—92no—
756C22⋊Q8—92no—
757C22⋊Q8—92no—
758C22⋊Q8—92no—
759C22⋊Q8—92no—
760C22⋊Q8—92no—
761C22⋊Q8—92no—
762C22⋊Q8—91no—
763#121—31no—
764#121—92no—
765#121—92no—
766#121—92no—
767#121—92no—
768#121—91no—
769C4×Q8—31no—
770C4×Q8—32no—
771C4×Q8—32no—
772C4×Q8—92no—
773C4×Q8—92no—
774C4×Q8—91no—
775C4×D4—32no—
776C4×D4—31no—
777C4×D4—92no—
778C4×D4—92no—
779C4×D4—92no—
780C4×D4—91no—
781#117—31no—
782#117—31no—
783#117—32no—
784#117—92no—
785#117—92no—
786#117—92no—
787C2×C42—92no—
788C2×C42—92no—
789C2×C42D3211yescharacteristic
790C23×C3—21no—
791C23×C3—32no—
792C23×C3C23×D311yescharacteristic
793C23×C3C23×D311yescharacteristic
794C22×D3—32no—
795C22×D3—32no—
796C22×D3—62no—
797C22×D3C23×D312yes—
798C3×Q8—121no—
799C3×Q8—122no—
800C3×Q8—122no—
801C3×D4—121no—
802C3×D4—122no—
803C2×C3×C4—22no—
804C2×C3×C4—22no—
805C2×C3×C4—21no—
806C2×C3×C4—21no—
807C2×C3×C4—21no—
808C2×C3×C4—21no—
809C2×C3×C4—21no—
810C2×C3×C4—21no—
811C2×C3×C4—32no—
812C2×C3×C4—32no—
813C2×C3×C4—32no—
814C2×C3×C4—32no—
815C2×C3×C4—32no—
816C2×C3×C4—32no—
817C2×C3×C4—32no—
818C2×C3×C4—42no—
819C2×C3×C4—41no—
820C2×C3×C4—41no—
821C2×C3×C4—41no—
822C2×C3×C4—41no—
823C2×C3×C4—42no—
824C2×C3×C4—42no—
825C2×C3×C4—64no—
826C2×C3×C4C23×D311yescharacteristic
827C2×C3×C4C23×D311yescharacteristic
828C2×C3×C4C23×D311yescharacteristic
829C2×C3×C4C23×D311yescharacteristic
830C2×C3×C4C23×D311yescharacteristic
831C2×C3×C4C23×D311yescharacteristic
832C2×C3×C4C23×D311yescharacteristic
833C2×C3×C4C23×D311yescharacteristic
834C2×C3×C4C23×D311yescharacteristic
835C2×C3×C4C23×D311yescharacteristic
836C2×C3×C4C23×D311yescharacteristic
837C2×C3×C4C23×D311yescharacteristic
838#67—42no—
839#67—122no—
840#67—122no—
841#67—122no—
842#67—122no—
843#67—124no—
844C2×Dic3—32no—
845C2×Dic3—32no—
846C2×Dic3—32no—
847C2×Dic3—32no—
848C2×Dic3—32no—
849C2×Dic3—32no—
850C2×Dic3—62no—
851C2×Dic3—62no—
852C2×Dic3—62no—
853C2×Dic3—122no—
854C2×Dic3—122no—
855C2×Dic3C23×D312yes—
856C2×Dic3C23×D312yes—
857C2×Dic3C23×D312yes—
858C2×Dic3C23×D312yes—
859C2×Dic3C23×D312yes—
860C2×Dic3C23×D312yes—
861C2×Dic3C23×D312yes—
862D12—41no—
863D12—121no—
864D12—121no—
865D12—122no—
866D12—122no—
867D12—122no—
868C4×D3—24no—
869C4×D3—64no—
870C4×D3—64no—
871C4×D3—124no—
872C4×D3—122no—
873C4×D3—122no—
874C4×D3—122no—
875C4×D3—122no—
876C4×D3—122no—
877C4×D3—122no—
878Dic6—41no—
879Dic6—42no—
880Dic6—42no—
881Dic6—122no—
882Dic6—122no—
883Dic6—122no—
884Dic6—122no—
885Dic6—121no—
886Dic6—121no—
887Dic6—122no—
888C2×C32—41no—
889C2×C32C2×2−1+411yescharacteristic
890C2×C32#58511yescharacteristic
891C2×C32#58511yescharacteristic
892C3⋊D3—42no—
893C3×D3—42no—
894C2×Q8—31no—
895C2×Q8—32no—
896C2×Q8—32no—
897C2×Q8—92no—
898C2×Q8—92no—
899C2×Q8—91no—
900C2×D4—32no—
901C2×D4—31no—
902C2×D4—92no—
903C2×D4—92no—
904C2×D4—92no—
905C2×D4—91no—
906C22×C4—32no—
907C22×C4—92no—
908C22×C4—92no—
909C22×C4—92no—
910C22×C4—92no—
911C22×C4—92no—
912C22×C4C2×D3211yescharacteristic
913C22×C4C2×D3211yescharacteristic
914C22×C4C2×D3211yescharacteristic
915C4⋊C4—32no—
916C4⋊C4—31no—
917C4⋊C4—31no—
918C4⋊C4—32no—
919C4⋊C4—31no—
920C4⋊C4—31no—
921C4⋊C4—31no—
922C4⋊C4—32no—
923C4⋊C4—31no—
924C4⋊C4—32no—
925C4⋊C4—32no—
926C4⋊C4—32no—
927C4⋊C4—32no—
928C4⋊C4—32no—
929C4⋊C4—32no—
930C4⋊C4—32no—
931C4⋊C4—92no—
932C4⋊C4—92no—
933C4⋊C4—92no—
934C4⋊C4—92no—
935C4⋊C4—92no—
936C4⋊C4—92no—
937C4⋊C4—92no—
938C4⋊C4—92no—
939C4⋊C4—92no—
940C4⋊C4—92no—
941C4⋊C4—92no—
942C4⋊C4—92no—
943C4⋊C4—92no—
944C4⋊C4—92no—
945C4⋊C4—92no—
946C4⋊C4—91no—
947C4⋊C4—91no—
948C4⋊C4—92no—
949C22⋊C4—32no—
950C22⋊C4—32no—
951C22⋊C4—32no—
952C22⋊C4—32no—
953C22⋊C4—32no—
954C22⋊C4—32no—
955C22⋊C4—32no—
956C22⋊C4—92no—
957C22⋊C4—92no—
958C22⋊C4—92no—
959C22⋊C4—92no—
960C22⋊C4—92no—
961C22⋊C4—92no—
962C22⋊C4—92no—
963C22⋊C4—92no—
964C22⋊C4—92no—
965C22⋊C4—92no—
966C22⋊C4—92no—
967C22⋊C4—92no—
968C22⋊C4—92no—
969C42—32no—
970C42—32no—
971C42—32no—
972C42—92no—
973C42—92no—
974C42—92no—
975C42—92no—
976C42—92no—
977C42C2×D3211yescharacteristic
978C42C2×D3211yescharacteristic
979C42C2×D3211yescharacteristic
980C42C2×D3211yescharacteristic
981C22×C3—22no—
982C22×C3—21no—
983C22×C3—21no—
984C22×C3—21no—
985C22×C3—21no—
986C22×C3—21no—
987C22×C3—21no—
988C22×C3—21no—
989C22×C3—41no—
990C22×C3—41no—
991C22×C3—62no—
992C22×C3—62no—
993C22×C3—62no—
994C22×C3C24×D311yescharacteristic
995C22×C3C24×D311yescharacteristic
996C2×D3—22no—
997C2×D3—22no—
998C2×D3—22no—
999C2×D3—62no—
1000C2×D3—62no—
1001C2×D3—62no—
1002C2×D3—62no—
1003C2×D3—62no—
1004C2×D3—62no—
1005C2×D3—122no—
1006C2×D3—122no—
1007C2×D3—122no—
1008C3×C4—22no—
1009C3×C4—21no—
1010C3×C4—21no—
1011C3×C4—21no—
1012C3×C4—21no—
1013C3×C4—21no—
1014C3×C4—21no—
1015C3×C4—21no—
1016C3×C4—21no—
1017C3×C4—21no—
1018C3×C4—21no—
1019C3×C4—22no—
1020C3×C4—41no—
1021C3×C4—41no—
1022C3×C4—41no—
1023C3×C4—41no—
1024C3×C4—62no—
1025C3×C4—62no—
1026C3×C4—62no—
1027C3×C4—62no—
1028C3×C4—62no—
1029C3×C4—62no—
1030C3×C4—62no—
1031C3×C4#100712yes—
1032C3×C4#101012yes—
1033Dic3—22no—
1034Dic3—22no—
1035Dic3—22no—
1036Dic3—22no—
1037Dic3—22no—
1038Dic3—22no—
1039Dic3—22no—
1040Dic3—62no—
1041Dic3—62no—
1042Dic3—62no—
1043Dic3—62no—
1044Dic3—62no—
1045Dic3—62no—
1046Dic3—122no—
1047Dic3—122no—
1048Dic3—122no—
1049C32#353111yescharacteristic, complemented, Sylow
1050C23—32no—
1051C23—92no—
1052C23C22×D3211yescharacteristic
1053Q8—121no—
1054Q8—122no—
1055Q8—122no—
1056Q8—361no—
1057Q8—362no—
1058Q8—362no—
1059D4—121no—
1060D4—122no—
1061D4—361no—
1062D4—362no—
1063D4—362no—
1064D4—362no—
1065C2×C4—22no—
1066C2×C4—32no—
1067C2×C4—32no—
1068C2×C4—32no—
1069C2×C4—32no—
1070C2×C4—32no—
1071C2×C4—32no—
1072C2×C4—32no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—64no—
1076C2×C4—92no—
1077C2×C4—92no—
1078C2×C4—92no—
1079C2×C4—184no—
1080C2×C4—362no—
1081C2×C4—362no—
1082C2×C4—362no—
1083C2×C4—362no—
1084C2×C4C22×D3211yescharacteristic
1085C2×C4C22×D3211yescharacteristic
1086C2×C4C22×D3211yescharacteristic
1087C2×C4C22×D3211yescharacteristic
1088C2×C4C22×D3211yescharacteristic
1089C2×C4C22×D3211yescharacteristic
1090C2×C3—21no—
1091C2×C3—21no—
1092C2×C3—21no—
1093C2×C3—42no—
1094C2×C3—41no—
1095C2×C3—41no—
1096C2×C3—122no—
1097C2×C3C2×#100711yescharacteristic
1098C2×C3C2×#101011yescharacteristic
1099C2×C3#596411yescharacteristic
1100C2×C3#596411yescharacteristic
1101C2×C3#596411yescharacteristic
1102C2×C3#596411yescharacteristic
1103D3—42no—
1104D3—122no—
1105D3—122no—
1106D3—242no—
1107C22—21no—
1108C22—21no—
1109C22—21no—
1110C22—62no—
1111C22—62no—
1112C22—62no—
1113C22—182no—
1114C22—182no—
1115C22—182no—
1116C22C23×D3211yescharacteristic
1117C4—21no—
1118C4—21no—
1119C4—21no—
1120C4—21no—
1121C4—21no—
1122C4—62no—
1123C4—62no—
1124C4—62no—
1125C4—62no—
1126C4—62no—
1127C4—62no—
1128C4—62no—
1129C4—182no—
1130C4—182no—
1131C4—182no—
1132C4#6429712yes—
1133C3—21no—
1134C3#8613211yescharacteristic, complemented
1135C3#8628611yescharacteristic, complemented
1136C2—41no—
1137C2—122no—
1138C2—362no—
1139C2C2×#6429711yescharacteristic
1140C2#1059666911yescharacteristic
1141C2#1059666911yescharacteristic
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
hypercenterC2×C42D32
hypocenterC32#3531
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #10595950C2semidirect
2. C3×#5479C2semidirect
3. C3×#5470C2semidirect
4. #10594978C2semidirect
5. #10594976C2semidirect
6. #10594972C2semidirect
7. #10594933C2semidirect
8. #10594836C2semidirect
9. #10594811C2semidirect
10. #10593957C2semidirect
11. #10593957C2semidirect
12. #10593953C2semidirect
13. #10593952C2semidirect
14. #10593935C2semidirect
15. #10593934C2semidirect
16. #10593926C2semidirect
17. #10593911C2semidirect
18. #10593868C2semidirect
19. #10593857C2semidirect
146. #5479D3semidirect
147. #5470D3semidirect
1049. C32#3531semidirect
1134. C3#86132semidirect
1135. C3#86286semidirect

Maximal subgroups

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

subgroupindex
#105959502
C3×#54792
C3×#54702
#105949782
#105949762
#105949722
#105949332
#105948362
#105948112
#105939572
#105939532
#105939522
#105939352
#105939342
#105939262
#105939112
#105938682
#105938572
#862863
#861323