Finite Group Databasebeta

← #11903556

Subgroups — #11903556

Order 1152.

2419 conjugacy classes of subgroups.

The subgroup lattice has 875 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595993C211yesmaximal, characteristic, complemented
2C3×D3×#117C212yesmaximal, complemented
3#10595050C211yesmaximal, characteristic, complemented
4#10595023C212yesmaximal, complemented
5C2×C4×#625C211yesmaximal, characteristic, complemented
6#10594581C211yesmaximal, characteristic, complemented
7#10594575C211yesmaximal, characteristic, complemented
8#10594559C212yesmaximal, complemented
9#10594550C212yesmaximal, complemented
10#10594531C211yesmaximal, characteristic, complemented
11#10594512C211yesmaximal, characteristic, complemented
12#10594183C212yesmaximal, complemented
13#10594046C212yesmaximal, complemented
14#10594037C214yesmaximal, complemented
15#10593980C212yesmaximal, complemented
16#10593973C214yesmaximal, complemented
17C4×#3798C212yesmaximal, complemented
18#85744—32nomaximal
19C2×#3828C2211yescharacteristic
20C22×C3×C4×D3C2212yes—
21C22×#625C2211yescharacteristic
22C2×#3798C2212yes—
23C32×#117C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25#64102C2211yescharacteristic, complemented
26#64102C2211yescharacteristic, complemented
27#64096C2211yescharacteristic, complemented
28#64096C2211yescharacteristic, complemented
29#64090C2212yes—
30#64090C2212yes—
31#64081C2212yescomplemented
32C42×C3⋊D3C2212yescomplemented
33C3×#926C2212yes—
34C3×#892C2212yescomplemented
35C3×#892C2212yescomplemented
36C3×D3×C4⋊C4C2212yescomplemented
37C3×D3×C4⋊C4C2212yescomplemented
38C3×D3×C22⋊C4C2214yes—
39C3×#877C2214yes—
40C3×#872C2214yescomplemented
41C3×C42×D3C2214yescomplemented
42#63982C2212yes—
43#63982C2212yes—
44#63977C2214yes—
45C2×#3724C2211yescharacteristic
46#63966C2214yes—
47C2×(C2×D3)⋊Dic3C2212yes—
48#63919C2211yescharacteristic, complemented
49#63919C2211yescharacteristic, complemented
50C4×#627C2212yescomplemented
51C4×#627C2212yescomplemented
52C4×#627C2212yescomplemented
53#63915C2212yes—
54#63912C2212yes—
55#63909C2212yescomplemented
56#63909C2212yescomplemented
57#63906C2214yes—
58#63905C2214yes—
59C4×#626C2214yescomplemented
60C4×#626C2214yescomplemented
61C4×#626C2214yescomplemented
62C4×#625C2211yescharacteristic
63C4×#625C2212yes—
64C4×#625C2211yescharacteristic
65C4×#625C2212yes—
66C4×#625C2211yescharacteristic
67C4×#625C2211yescharacteristic
68C4×#625C2212yes—
69#63874C2212yescomplemented
70#63872C2212yescomplemented
71#63870C2212yescomplemented
72#63868C2214yescomplemented
73#63867C2214yescomplemented
74#63865C2212yescomplemented
75#63862C2214yescomplemented
76#63859C2214yescomplemented
77#63857C2212yescomplemented
78#63857C2212yescomplemented
79#63855C2214yescomplemented
80#63853C2214yescomplemented
81#63852C2214yescomplemented
82#63851C2214yescomplemented
83#63850C2214yescomplemented
84C2×C3×#117—32no—
85#5791—32no—
86C2×C4×#67—32no—
87#5533—32no—
88#5532—32no—
89#5531—34no—
90#5530—32no—
91#5529—32no—
92#5528—34no—
93#5528—34no—
94#5527—34no—
95#5524—32no—
96#5522—32no—
97#5522—61no—
98D3×#117D312yescomplemented
99#5517—32no—
100#5514—32no—
101#5513—32no—
102#5511—32no—
103#5507—32no—
104#5495—34no—
105#5490—34no—
106#5479—34no—
107C4×#235—34no—
108C23×C3×D3C2312yes—
109C22×C32×C4C2311yescharacteristic
110C2×#638C2312yes—
111C22×C3⋊Dic3C2311yescharacteristic
112C22×C3⋊Dic3C2311yescharacteristic
113#3828—24no—
114C2×C4⋊(C3⋊D3)C2311yescharacteristic
115C2×C4×C3⋊D3C2312yes—
116C2×C4×C3⋊D3C2312yes—
117C2×C4×C3⋊D3C2312yes—
118C2×#634C2311yescharacteristic
119C22×C3×Dic3C2312yes—
120C2×C3×C4×D3—28no—
121C2×C3×C4×D3C2314yes—
122C2×C3×C4×D3C2312yes—
123C2×C3×C4×D3C2312yes—
124C2×C3×C4×D3C2312yes—
125C2×C3×C4×D3C2312yes—
126C2×C3×C4×D3C2314yes—
127C2×#627C2312yes—
128C2×#627C2312yes—
129C2×#626C2314yes—
130C2×#626C2314yes—
131C2×#625—24no—
132C2×#625C2312yes—
133C2×#625C2311yescharacteristic
134C2×#625C2311yescharacteristic
135#3798—28no—
136C32×C4⋊C4C2311yescharacteristic
137C32×C4⋊C4C2311yescharacteristic
138C32×C22⋊C4C2312yes—
139C32×C42C2312yes—
140#3752C2312yes—
141#3752C2312yes—
142#3750C2312yes—
143#3750C2312yes—
144C4×C3⋊Dic3C2311yescharacteristic
145C4×C3⋊Dic3C2312yes—
146C4×C3⋊Dic3C2312yes—
147C4×C3⋊Dic3C2311yescharacteristic
148C4×C3⋊Dic3C2311yescharacteristic
149C4×C3⋊Dic3C2311yescharacteristic
150C3×#217C2314yes—
151C3×(C2×D3)⋊C4C2314yes—
152C3×(C2×D3)⋊C4C2314yes—
153C3×C4⋊Dic3C2312yes—
154C3×C4⋊Dic3C2312yes—
155C3×Dic3⋊C4C2314yes—
156C3×Dic3⋊C4C2314yes—
157C3×C4×Dic3C2314yes—
158C3×C4×Dic3C2314yes—
159C3×C4×Dic3C2314yes—
160#3724C2312yes—
161#3724C2311yescharacteristic
162#3724C2312yes—
163#3724C2312yes—
164#3724C2311yescharacteristic
165Dic3⋊Dic3C2314yes—
166Dic3⋊Dic3C2314yes—
167Dic3⋊Dic3C2314yes—
168Dic3⋊Dic3C2314yes—
169#3722C2314yes—
170#3722C2314yes—
171(C2×D3)⋊Dic3C2312yes—
172(C2×D3)⋊Dic3C2314yes—
173(C2×D3)⋊Dic3C2312yes—
174(C2×D3)⋊Dic3C2312yes—
175(C2×D3)⋊Dic3C2312yes—
176(C2×D3)⋊Dic3C2314yes—
177#3475—91noSylow
178C23×C3×C4—32no—
179C22×#67—32no—
180C2×#235—32no—
181C2×#235—34no—
182C2×#235—61no—
183C22×C4×D3C2×D312yes—
184C3×#117—21no—
185C3×#117—32no—
186C3×#117—32no—
187C3×#117—32no—
188C3×#117—34no—
189C3×#117—34no—
190C3×#117C2×D312yes—
191C2×C3×C4⋊C4—32no—
192C2×C3×C4⋊C4—32no—
193C2×C3×C22⋊C4—34no—
194C2×C3×C42—34no—
195#953—34no—
196C2×#217—32no—
197#930—34no—
198#930—32no—
199#930—32no—
200#929—34no—
201#929—34no—
202#929—34no—
203C4×#67—32no—
204C4×#67—34no—
205C4×#67—32no—
206C4×#67—32no—
207C4×#67—32no—
208C4×#67—32no—
209C4×#67—32no—
210C4×#67—32no—
211C4×#67—32no—
212C4×#67—34no—
213C4×#67—34no—
214C4×#67—34no—
215C2×(C2×D3)⋊C4—32no—
216#926—34no—
217#926C2×D312yes—
218#924—32no—
219#924—32no—
220#924—34no—
221C2×Dic3⋊C4—32no—
222C2×C4×Dic3—32no—
223C2×C4×Dic3—61no—
224#898—34no—
225#898—34no—
226#897—32no—
227#897—32no—
228#896—34no—
229#896—34no—
230#895—32no—
231#895—32no—
232#894—34no—
233#894—34no—
234#893—32no—
235#893—32no—
236#893—61no—
237#893—61no—
238#892C2×D312yescomplemented
239#892C2×D312yescomplemented
240D3×C4⋊C4C2×D312yescomplemented
241D3×C4⋊C4C2×D312yescomplemented
242#890—32no—
243#890—32no—
244#889—34no—
245#889—34no—
246#888—32no—
247#888—32no—
248#887—32no—
249#887—32no—
250#887—61no—
251#887—61no—
252#886—34no—
253#885—34no—
254#885—34no—
255#884—34no—
256#884—34no—
257#883—34no—
258#883—34no—
259#882—34no—
260#67⋊C4—34no—
261#67⋊C4—34no—
262#67⋊C4—62no—
263#67⋊C4—62no—
264D3×C22⋊C4C2×D314yes—
265#879—34no—
266#879—34no—
267#878—34no—
268#878—34no—
269#877C2×D314yes—
270#876—34no—
271#876—34no—
272#875—34no—
273C4×D12—34no—
274C4×D12—34no—
275C4×D12—34no—
276#872—34no—
277#872—34no—
278#872—34no—
279#872—62no—
280#872C2×D314yescomplemented
281C42×D3—34no—
282C42×D3—62no—
283C42×D3C2×D314yescomplemented
284#870—34no—
285C4×Dic6—34no—
286C4×Dic6—34no—
287C4×Dic6—34no—
288C23×C32C2411yescharacteristic
289C22×C3⋊D3C2412yes—
290C22×C3×D3—24no—
291C22×C3×D3—24no—
292C22×C3×D3—42no—
293C22×C3×D3C2412yes—
294C22×C3×D3C2412yes—
295C2×C32×C4#4114yescomplemented
296C2×C32×C4C2412yes—
297C2×C32×C4C2412yes—
298C2×C32×C4C2411yescharacteristic
299C2×C32×C4C2411yescharacteristic
300#638—24no—
301C2×C3⋊Dic3—22no—
302C2×C3⋊Dic3—41no—
303C2×C3⋊Dic3C2411yescharacteristic
304C2×C3⋊Dic3C2412yes—
305C2×C3⋊Dic3C2411yescharacteristic
306C2×C3⋊Dic3C2411yescharacteristic
307C2×C3⋊Dic3C2411yescharacteristic
308C4⋊(C3⋊D3)—22no—
309C4×C3⋊D3—24no—
310C4×C3⋊D3—24no—
311C4×C3⋊D3—42no—
312#634—22no—
313C2×C3×Dic3—24no—
314C2×C3×Dic3C2412yes—
315C2×C3×Dic3C2412yes—
316C2×C3×Dic3C2414yes—
317C2×C3×Dic3C2414yes—
318C3×C4×D3—28no—
319C3×C4×D3—24no—
320C3×C4×D3—24no—
321C3×C4×D3—24no—
322C3×C4×D3—24no—
323C3×C4×D3—44no—
324#627—24no—
325#627—42no—
326#626—28no—
327#626—44no—
328#625—24no—
329#625—22no—
330#625#4114yescomplemented
331#556—91no—
332#555—91no—
333#554—91no—
334#553—92no—
335#552—92no—
336#552—92no—
337#551—94no—
338#547—91no—
339#546—92no—
340#533—91no—
341#529—94no—
342#529—92no—
343#525—92no—
344C4×#41—92no—
345C4×#41—91no—
346C2×C4×D4—91no—
347C2×#117—32no—
348C24×C3—32no—
349C23×D3C22×D312yes—
350C22×C3×C4—21no—
351C22×C3×C4—32no—
352C22×C3×C4—32no—
353C22×C3×C4—32no—
354C22×C3×C4—34no—
355C22×C3×C4—32no—
356C22×C3×C4—32no—
357C22×C3×C4—34no—
358C22×C3×C4—68no—
359C22×C3×C4C22×D312yes—
360C2×#67—32no—
361C2×#67—34no—
362C2×#67—32no—
363C2×#67—32no—
364C2×#67—32no—
365C2×#67—34no—
366C2×#67—34no—
367C2×#67—62no—
368C2×#67—68no—
369C22×Dic3—32no—
370C22×Dic3—32no—
371C22×Dic3—61no—
372C22×Dic3—61no—
373C22×Dic3C22×D312yes—
374#235—616no—
375#235—68no—
376#235—68no—
377C2×D12—34no—
378C2×D12—32no—
379C2×D12—34no—
380C2×D12—61no—
381C2×C4×D3—28no—
382C2×C4×D3—34no—
383C2×C4×D3—34no—
384C2×C4×D3—34no—
385C2×C4×D3—62no—
386C2×C4×D3—62no—
387C2×C4×D3—62no—
388C2×C4×D3C22×D312yes—
389C2×C4×D3C22×D314yes—
390C2×C4×D3C22×D312yes—
391C2×C4×D3C22×D312yes—
392C2×C4×D3C22×D312yes—
393C2×C4×D3C22×D314yes—
394C2×Dic6—32no—
395C2×Dic6—34no—
396C2×Dic6—34no—
397C2×Dic6—61no—
398C3×C4⋊C4—21no—
399C3×C4⋊C4—21no—
400C3×C4⋊C4—32no—
401C3×C4⋊C4—32no—
402C3×C4⋊C4—34no—
403C3×C4⋊C4—34no—
404C3×C4⋊C4C22×D312yes—
405C3×C4⋊C4C22×D312yes—
406C3×C22⋊C4—22no—
407C3×C22⋊C4—34no—
408C3×C22⋊C4—34no—
409C3×C22⋊C4—34no—
410C3×C22⋊C4C22×D314yes—
411C3×C42—22no—
412C3×C42—34no—
413C3×C42—34no—
414C3×C42—34no—
415C3×C42C22×D314yes—
416#217—32no—
417#217—34no—
418#217—32no—
419#217—34no—
420#217—32no—
421#217—32no—
422#217C22×D314yes—
423(C2×D3)⋊C4—32no—
424(C2×D3)⋊C4—34no—
425(C2×D3)⋊C4—34no—
426(C2×D3)⋊C4—32no—
427(C2×D3)⋊C4—32no—
428(C2×D3)⋊C4—32no—
429(C2×D3)⋊C4—34no—
430(C2×D3)⋊C4—34no—
431(C2×D3)⋊C4—34no—
432(C2×D3)⋊C4—34no—
433(C2×D3)⋊C4—34no—
434(C2×D3)⋊C4—34no—
435(C2×D3)⋊C4—62no—
436(C2×D3)⋊C4—62no—
437(C2×D3)⋊C4C22×D314yes—
438(C2×D3)⋊C4C22×D314yes—
439C4⋊Dic3—34no—
440C4⋊Dic3—34no—
441C4⋊Dic3—34no—
442C4⋊Dic3—34no—
443C4⋊Dic3C22×D312yes—
444C4⋊Dic3C22×D312yes—
445Dic3⋊C4—34no—
446Dic3⋊C4—34no—
447Dic3⋊C4—32no—
448Dic3⋊C4—34no—
449Dic3⋊C4—34no—
450Dic3⋊C4—34no—
451Dic3⋊C4—34no—
452Dic3⋊C4—34no—
453Dic3⋊C4—32no—
454Dic3⋊C4—32no—
455Dic3⋊C4—34no—
456Dic3⋊C4—32no—
457Dic3⋊C4—62no—
458Dic3⋊C4—62no—
459Dic3⋊C4C22×D314yes—
460Dic3⋊C4C22×D314yes—
461C4×Dic3—32no—
462C4×Dic3—32no—
463C4×Dic3—34no—
464C4×Dic3—34no—
465C4×Dic3—32no—
466C4×Dic3—32no—
467C4×Dic3—61no—
468C4×Dic3—62no—
469C4×Dic3—62no—
470C4×Dic3—61no—
471C4×Dic3—61no—
472C4×Dic3—61no—
473C4×Dic3C22×D314yes—
474C4×Dic3C22×D314yes—
475C4×Dic3C22×D314yes—
476C22×C32—21no—
477C22×C32—21no—
478C22×C32C2×#4112yes—
479C22×C32C2511yescharacteristic
480C2×C3⋊D3—22no—
481C2×C3⋊D3—22no—
482C2×C3⋊D3—22no—
483C2×C3×D3—22no—
484C2×C3×D3—22no—
485C2×C3×D3—22no—
486C2×C3×D3—22no—
487C2×C3×D3—22no—
488C2×C3×D3—48no—
489C2×C3×D3C2×#4114yes—
490C32×C4—22no—
491C32×C4—22no—
492C32×C4C2×#4112yes—
493C32×C4C2×#4112yes—
494C3⋊Dic3—22no—
495C3⋊Dic3—21no—
496C3⋊Dic3—21no—
497C3⋊Dic3—21no—
498C3⋊Dic3C2×#4112yes—
499C3×Dic3—24no—
500C3×Dic3—22no—
501C3×Dic3—22no—
502C3×Dic3—24no—
503C2×#41—92no—
504C2×#41—91no—
505C22×D4—91no—
506C23×C4—32no—
507C4⋊Q8—91no—
508C4⋊Q8—91no—
509#126—94no—
510#126—94no—
511#126—94no—
512#125—94no—
513#125—92no—
514#125—92no—
515#124—94no—
516#124—92no—
517#123—94no—
518#123—94no—
519#123—94no—
520#123—94no—
521C22⋊Q8—92no—
522C22⋊Q8—92no—
523C22⋊Q8—92no—
524C22⋊Q8—92no—
525C22⋊Q8—92no—
526C22⋊Q8—94no—
527#121—92no—
528#121—94no—
529#121—92no—
530#121—92no—
531#120—94no—
532C4×Q8—92no—
533C4×Q8—92no—
534C4×Q8—92no—
535C4×Q8—91no—
536C4×Q8—91no—
537C4×D4—94no—
538C4×D4—94no—
539C4×D4—94no—
540C4×D4—91no—
541C4×D4—91no—
542C4×D4—92no—
543C4×D4—91no—
544C4×D4—92no—
545C4×D4—91no—
546C4×D4—92no—
547C4×D4—91no—
548C4×D4—91no—
549C4×D4—92no—
550C4×D4—92no—
551#117—32no—
552#117—32no—
553#117—32no—
554#117—34no—
555#117—34no—
556#117—92no—
557#117—94no—
558#117—92no—
559#117D3211yescharacteristic
560C2×C4⋊C4—32no—
561C2×C4⋊C4—32no—
562C2×C4⋊C4—91no—
563C2×C22⋊C4—34no—
564C2×C22⋊C4—92no—
565C2×C42—34no—
566C2×C42—91no—
567C2×C42—92no—
568C23×C3—21no—
569C23×C3—32no—
570C23×C3—32no—
571C23×C3—64no—
572C23×C3—64no—
573C23×C3—122no—
574C23×C3C23×D312yes—
575C22×D3—24no—
576C22×D3—24no—
577C22×D3—34no—
578C22×D3—42no—
579C22×D3—62no—
580C22×D3C23×D312yes—
581C22×D3C23×D312yes—
582C2×C3×C4—21no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—21no—
586C2×C3×C4—24no—
587C2×C3×C4—32no—
588C2×C3×C4—32no—
589C2×C3×C4—34no—
590C2×C3×C4—34no—
591C2×C3×C4—68no—
592C2×C3×C4—64no—
593C2×C3×C4—64no—
594C2×C3×C4—64no—
595C2×C3×C4—64no—
596C2×C3×C4—64no—
597C2×C3×C4—124no—
598C2×C3×C4#23518yescomplemented
599C2×C3×C4C23×D314yes—
600C2×C3×C4C23×D314yes—
601C2×C3×C4C23×D312yes—
602C2×C3×C4C23×D312yes—
603#67—38no—
604#67—68no—
605#67—64no—
606#67—64no—
607#67—68no—
608#67—68no—
609#67—64no—
610#67—124no—
611C2×Dic3—24no—
612C2×Dic3—32no—
613C2×Dic3—32no—
614C2×Dic3—32no—
615C2×Dic3—34no—
616C2×Dic3—32no—
617C2×Dic3—61no—
618C2×Dic3—61no—
619C2×Dic3—62no—
620C2×Dic3—61no—
621C2×Dic3—61no—
622C2×Dic3—64no—
623C2×Dic3—122no—
624C2×Dic3—122no—
625C2×Dic3—122no—
626C2×Dic3C23×D312yes—
627C2×Dic3C23×D314yes—
628C2×Dic3C23×D314yes—
629C2×Dic3C23×D312yes—
630D12—64no—
631D12—68no—
632D12—64no—
633D12—124no—
634C4×D3—28no—
635C4×D3—24no—
636C4×D3—24no—
637C4×D3—24no—
638C4×D3—24no—
639C4×D3—44no—
640C4×D3—68no—
641C4×D3—68no—
642C4×D3—68no—
643C4×D3—124no—
644C4×D3—124no—
645C4×D3—124no—
646Dic6—68no—
647Dic6—64no—
648Dic6—64no—
649Dic6—124no—
650C2×C32—22no—
651C2×C32C22×#4111yescharacteristic
652C2×C32C22×#4111yescharacteristic
653C2×C32#58511yescharacteristic
654C3⋊D3—42no—
655C3×D3—24no—
656C3×D3—42no—
657C24—32no—
658#41—188no—
659#41—184no—
660C2×Q8—92no—
661C2×Q8—92no—
662C2×Q8—91no—
663C2×D4—94no—
664C2×D4—94no—
665C2×D4—91no—
666C2×D4—92no—
667C2×D4—91no—
668C2×D4—92no—
669C2×D4—91no—
670C2×D4—184no—
671C22×C4—32no—
672C22×C4—34no—
673C22×C4—32no—
674C22×C4—32no—
675C22×C4—32no—
676C22×C4—32no—
677C22×C4—34no—
678C22×C4—68no—
679C22×C4—91no—
680C22×C4—91no—
681C22×C4—92no—
682C22×C4—92no—
683C22×C4—92no—
684C22×C4C2×D3211yescharacteristic
685C4⋊C4—32no—
686C4⋊C4—32no—
687C4⋊C4—34no—
688C4⋊C4—34no—
689C4⋊C4—91no—
690C4⋊C4—91no—
691C4⋊C4—92no—
692C4⋊C4—92no—
693C4⋊C4—94no—
694C4⋊C4—94no—
695C4⋊C4—94no—
696C4⋊C4—94no—
697C4⋊C4—92no—
698C4⋊C4—92no—
699C4⋊C4—92no—
700C4⋊C4C2×D3211yescharacteristic
701C4⋊C4C2×D3211yescharacteristic
702C22⋊C4—34no—
703C22⋊C4—34no—
704C22⋊C4—34no—
705C22⋊C4—94no—
706C22⋊C4—94no—
707C22⋊C4—92no—
708C22⋊C4—92no—
709C22⋊C4—92no—
710C22⋊C4—92no—
711C22⋊C4—94no—
712C22⋊C4—94no—
713C22⋊C4—92no—
714C22⋊C4—92no—
715C22⋊C4C2×D3212yes—
716C42—34no—
717C42—34no—
718C42—34no—
719C42—92no—
720C42—91no—
721C42—91no—
722C42—92no—
723C42—91no—
724C42—91no—
725C42C2×D3212yes—
726C22×C3—22no—
727C22×C3—22no—
728C22×C3—22no—
729C22×C3—21no—
730C22×C3—34no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—62no—
734C22×C3—62no—
735C22×C3—62no—
736C22×C3—62no—
737C22×C3—62no—
738C22×C3—128no—
739C22×C3C2×#23514yes—
740C22×C3C24×D312yes—
741C2×D3—22no—
742C2×D3—22no—
743C2×D3—22no—
744C2×D3—22no—
745C2×D3—22no—
746C2×D3—48no—
747C2×D3—64no—
748C2×D3—64no—
749C2×D3—64no—
750C2×D3—64no—
751C2×D3—122no—
752C2×D3—122no—
753C2×D3D3×#4114yes—
754C3×C4—24no—
755C3×C4—24no—
756C3×C4—22no—
757C3×C4—22no—
758C3×C4—42no—
759C3×C4—42no—
760C3×C4—62no—
761C3×C4—62no—
762C3×C4—64no—
763C3×C4—64no—
764C3×C4C2×#23514yes—
765C3×C4C2×#23514yes—
766Dic3—22no—
767Dic3—22no—
768Dic3—24no—
769Dic3—24no—
770Dic3—34no—
771Dic3—62no—
772Dic3—64no—
773Dic3—62no—
774Dic3—64no—
775Dic3—62no—
776Dic3—62no—
777Dic3—62no—
778Dic3—121no—
779Dic3—121no—
780C32#347511yescharacteristic, complemented, Sylow
781C23—32no—
782C23—32no—
783C23—64no—
784C23—64no—
785C23—92no—
786C23—122no—
787C23C22×D3211yescharacteristic
788Q8—184no—
789Q8—182no—
790Q8—362no—
791D4—94no—
792D4—188no—
793D4—182no—
794D4—184no—
795D4—184no—
796D4—182no—
797D4—364no—
798C2×C4—32no—
799C2×C4—34no—
800C2×C4—34no—
801C2×C4—32no—
802C2×C4—68no—
803C2×C4—64no—
804C2×C4—64no—
805C2×C4—64no—
806C2×C4—64no—
807C2×C4—64no—
808C2×C4—91no—
809C2×C4—91no—
810C2×C4—91no—
811C2×C4—92no—
812C2×C4—91no—
813C2×C4—124no—
814C2×C4—184no—
815C2×C4—182no—
816C2×C4—184no—
817C2×C4—362no—
818C2×C4—361no—
819C2×C4#379814yescomplemented
820C2×C4C22×D3212yes—
821C2×C4C22×D3212yes—
822C2×C4C22×D3211yescharacteristic
823C2×C4C22×D3211yescharacteristic
824C2×C3—24no—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—21no—
828C2×C3—42no—
829C2×C3—64no—
830C2×C3—122no—
831C2×C3C22×#23512yes—
832C2×C3C2×D3×#4112yes—
833C2×C3#596412yes—
834D3—24no—
835D3—42no—
836D3—124no—
837D3—124no—
838C22—21no—
839C22—21no—
840C22—34no—
841C22—62no—
842C22—62no—
843C22—62no—
844C22—62no—
845C22—62no—
846C22—128no—
847C22—182no—
848C22—182no—
849C22—182no—
850C22C2×#379812yes—
851C22C23×D3211yescharacteristic
852C4—22no—
853C4—22no—
854C4—62no—
855C4—62no—
856C4—64no—
857C4—64no—
858C4—92no—
859C4—182no—
860C4—181no—
861C4—181no—
862C4—181no—
863C4C2×#379812yes—
864C4C2×#379812yes—
865C3—21no—
866C3#8574412yescomplemented
867C2—22no—
868C2—64no—
869C2—122no—
870C2—362no—
871C2C22×#379811yescharacteristic
872C2D32×#4111yescharacteristic
873C2#1059669511yescharacteristic
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC32×#117C22
hypercenter#117D32
hypocenterC32#3475
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595993C2semidirect
2. C3×D3×#117C2semidirect
3. #10595050C2semidirect
4. #10595023C2semidirect
5. C2×C4×#625C2semidirect
6. #10594581C2semidirect
7. #10594575C2semidirect
8. #10594559C2semidirect
9. #10594550C2semidirect
10. #10594531C2semidirect
11. #10594512C2semidirect
12. #10594183C2semidirect
13. #10594046C2semidirect
14. #10594037C2semidirect
15. #10593980C2semidirect
16. #10593973C2semidirect
17. C4×#3798C2semidirect
25. #64102C22semidirect
26. #64102C22semidirect
27. #64096C22semidirect
28. #64096C22semidirect
31. #64081C22semidirect
32. C42×C3⋊D3C22semidirect
34. C3×#892C22semidirect
35. C3×#892C22semidirect
36. C3×D3×C4⋊C4C22semidirect
37. C3×D3×C4⋊C4C22semidirect
40. C3×#872C22semidirect
41. C3×C42×D3C22semidirect
48. #63919C22semidirect
49. #63919C22semidirect
50. C4×#627C22semidirect
51. C4×#627C22semidirect
52. C4×#627C22semidirect
55. #63909C22semidirect
56. #63909C22semidirect
59. C4×#626C22semidirect
60. C4×#626C22semidirect
61. C4×#626C22semidirect
69. #63874C22semidirect
70. #63872C22semidirect
71. #63870C22semidirect
72. #63868C22semidirect
73. #63867C22semidirect
74. #63865C22semidirect
75. #63862C22semidirect
76. #63859C22semidirect
77. #63857C22semidirect
78. #63857C22semidirect
79. #63855C22semidirect
80. #63853C22semidirect
81. #63852C22semidirect
82. #63851C22semidirect
83. #63850C22semidirect
98. D3×#117D3semidirect
238. #892C2×D3semidirect
239. #892C2×D3semidirect
240. D3×C4⋊C4C2×D3semidirect
241. D3×C4⋊C4C2×D3semidirect
280. #872C2×D3semidirect
283. C42×D3C2×D3semidirect
295. C2×C32×C4#41semidirect
330. #625#41semidirect
598. C2×C3×C4#235semidirect
780. C32#3475semidirect
819. C2×C4#3798semidirect
866. C3#85744semidirect

Maximal subgroups

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

subgroupindex
#105959932
C3×D3×#1172
#105950502
#105950232
C2×C4×#6252
#105945812
#105945752
#105945592
#105945502
#105945312
#105945122
#105941832
#105940462
#105940372
#105939802
#105939732
C4×#37982
#857443