Finite Group Databasebeta

← #11904249

Subgroups — #11904249

Order 1152.

2522 conjugacy classes of subgroups.

The subgroup lattice has 1451 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596003C211yesmaximal, characteristic, complemented
2C3×#5532C211yesmaximal, characteristic, complemented
3C3×#5522C211yesmaximal, characteristic, complemented
4#10595007C211yesmaximal, characteristic, complemented
5#10595006C211yesmaximal, characteristic, complemented
6#10594910C211yesmaximal, characteristic, complemented
7C4×#3804C211yesmaximal, characteristic, complemented
8#10594555C211yesmaximal, characteristic, complemented
9#10594524C211yesmaximal, characteristic, complemented
10#10594520C211yesmaximal, characteristic, complemented
11#10594518C211yesmaximal, characteristic, complemented
12#10594367C211yesmaximal, characteristic, complemented
13#10594362C211yesmaximal, characteristic, complemented
14#10594360C211yesmaximal, characteristic, complemented
15#10594312C211yesmaximal, characteristic, complemented
16#10594246C212yesmaximal, complemented
17#10594201C212yesmaximal, complemented
18#10594068C212yesmaximal, complemented
19#10594058C212yesmaximal, complemented
20#10593977C212yesmaximal, complemented
21#10593969C212yesmaximal, complemented
22#10593965C212yesmaximal, complemented
23#10593930C212yesmaximal, complemented
24#86959—31nomaximal
25#85845—31nomaximal
26C2×C3×#235C2211yescharacteristic
27C2×#3804C2211yescharacteristic
28C2×#3804C2212yes—
29C2×#3799C2211yescharacteristic
30C2×#3799C2212yes—
31C2×#3798C2212yes—
32C2×#3796C2211yescharacteristic
33C2×#3795C2212yes—
34C32×#117C2211yescharacteristic
35#64139C2211yescharacteristic
36C4×#638C2211yescharacteristic
37#64104C2211yescharacteristic
38#64102C2211yescharacteristic
39#64101C2211yescharacteristic
40#64097C2211yescharacteristic
41#64094C2212yes—
42#64093C2212yes—
43#64084C2212yes—
44#64081C2212yes—
45C3×#930C2211yescharacteristic
46C3×C4×#67C2211yescharacteristic
47C2×C3×C4×Dic3C2211yescharacteristic
48C3×#895C2211yescharacteristic
49C3×#893C2211yescharacteristic
50C3×#893C2211yescharacteristic
51C3×#893C2211yescharacteristic
52C3×#892C2211yescharacteristic
53C3×#888C2211yescharacteristic
54C3×#887C2211yescharacteristic
55C3×#887C2211yescharacteristic
56C3×#885C2212yes—
57C3×#884C2212yes—
58C3×#67⋊C4C2212yes—
59C3×#67⋊C4C2212yes—
60C3×#875C2212yes—
61C3×#872C2212yes—
62C3×#872C2212yes—
63C3×C42×D3C2212yes—
64#63979C2212yes—
65#63979C2212yes—
66#63978C2212yes—
67Dic3×#67C2211yescharacteristic
68#63970C2212yes—
69#63958C2212yes—
70#63955C2211yescharacteristic
71#63952C2211yescharacteristic
72#63918C2211yescharacteristic
73C4×#627C2211yescharacteristic
74#63916C2211yescharacteristic
75#63915C2212yes—
76#63914C2211yescharacteristic
77#63913C2212yes—
78#63912C2212yes—
79#63911C2211yescharacteristic
80#63911C2212yes—
81#63911C2211yescharacteristic
82#63910C2212yes—
83#63910C2212yes—
84#63908C2211yescharacteristic
85#63907C2212yes—
86#63906C2212yes—
87#63906C2212yes—
88#63906C2212yes—
89#63906C2212yes—
90#63906C2212yes—
91#63904C2212yes—
92#63904C2212yes—
93#63904C2212yes—
94C4×#626C2211yescharacteristic
95#63894C2211yescharacteristic
96Dic3×D12C2211yescharacteristic
97#63886C2212yes—
98#63885C2212yes—
99C4×#624C2212yes—
100C4×#624C2211yescharacteristic
101#63881C2212yes—
102#63880C2212yes—
103#63880C2212yes—
104#63880C2211yescharacteristic
105#63880C2212yes—
106#63880C2212yes—
107#63879C2212yes—
108#63879C2212yes—
109#63878C2212yes—
110#63877C2211yescharacteristic
111C4×D3×Dic3C2212yes—
112C4×D3×Dic3C2211yescharacteristic
113#63866C2212yes—
114#63855C2212yes—
115#63852C2212yes—
116#63852C2212yes—
117#63843C2211yescharacteristic
118Dic3×Dic6C2211yescharacteristic
119#63840C2212yes—
120#63839C2212yes—
121#63837C2212yes—
122#63837C2211yescharacteristic
123#63836C2211yescharacteristic
124#63836C2212yes—
125C3×#555—31no—
126C3×C4×#41—31no—
127#5834—31no—
128#5834—31no—
129#5725—31no—
130#5722—31no—
131#5670—32no—
132#5670—32no—
133#5668—32no—
134#5668—32no—
135#5599—31no—
136#5599—31no—
137#5599—32no—
138#5596—31no—
139#5596—31no—
140#5596—32no—
141#5577—31no—
142C4×#239—31no—
143C4×#239—31no—
144Q8×Dic6—31no—
145#5563—31no—
146#5563—32no—
147#5553—31no—
148#5553—31no—
149#5553—31no—
150#5553—32no—
151#5548—31no—
152#5548—31no—
153#5548—32no—
154#5548—32no—
155C4×#237—31no—
156C4×#237—31no—
157#5532—31no—
158#5532—31no—
159#5532—31no—
160#5532—32no—
161#5532—32no—
162#5532—32no—
163#5532—61no—
164#5532D311yescharacteristic, complemented
165#5522—31no—
166#5522—32no—
167#5522D311yescharacteristic, complemented
168#5477—31no—
169#5477—32no—
170C4×#235—31no—
171C4×#235—32no—
172C22×C32×C4C2311yescharacteristic
173C2×#638C2311yescharacteristic
174C2×#638C2312yes—
175C2×C4⋊(C3⋊D3)C2311yescharacteristic
176C2×C4⋊(C3⋊D3)C2312yes—
177C2×C4×C3⋊D3C2311yescharacteristic
178C2×C4×C3⋊D3C2312yes—
179C2×#634C2312yes—
180C2×C3×#67C2312yes—
181C2×C3×#67C2311yescharacteristic
182C2×C3×#67C2312yes—
183C22×C3×Dic3C2311yescharacteristic
184C22×C3×Dic3C2311yescharacteristic
185C3×#235—24no—
186C2×C3×D12C2311yescharacteristic
187C2×C3×D12C2311yescharacteristic
188C2×C3×D12C2312yes—
189C2×C3×C4×D3C2312yes—
190C2×C3×C4×D3C2312yes—
191C2×C3×C4×D3C2312yes—
192C2×C3×C4×D3C2311yescharacteristic
193C2×C3×C4×D3C2312yes—
194C2×C3×Dic6C2312yes—
195C2×C3×Dic6C2311yescharacteristic
196C2×#627C2312yes—
197C2×#627C2311yescharacteristic
198C2×#626C2312yes—
199C2×#626C2312yes—
200C2×#626C2312yes—
201C2×#626C2312yes—
202C2×#626C2311yescharacteristic
203C2×#626C2312yes—
204C2×#626C2312yes—
205C2×#626C2312yes—
206C2×#625C2312yes—
207C2×#625C2312yes—
208C2×#625C2312yes—
209C2×#624C2311yescharacteristic
210C2×#624C2312yes—
211C2×#624C2312yes—
212C2×#624C2311yescharacteristic
213#3804—24no—
214#3804—44no—
215C2×D3×Dic3C2311yescharacteristic
216C2×D3×Dic3C2312yes—
217C2×D3×Dic3C2312yes—
218C2×D3×Dic3C2311yescharacteristic
219#3799—24no—
220#3799—44no—
221#3798—28no—
222#3796—24no—
223#3795—44no—
224C32×C4⋊C4C2311yescharacteristic
225C32×C4⋊C4C2311yescharacteristic
226C32×C22⋊C4C2312yes—
227C32×C42C2312yes—
228#3757C2311yescharacteristic
229#3752C2312yes—
230#3752C2312yes—
231#3752C2311yescharacteristic
232#3752C2312yes—
233#3752C2312yes—
234C4⋊(C3⋊Dic3)C2311yescharacteristic
235#3750C2311yescharacteristic
236#3750C2312yes—
237C4×C3⋊Dic3C2312yes—
238C4×C3⋊Dic3C2311yescharacteristic
239C3×#217C2311yescharacteristic
240C3×(C2×D3)⋊C4C2312yes—
241C3×(C2×D3)⋊C4C2312yes—
242C3×(C2×D3)⋊C4C2312yes—
243C3×(C2×D3)⋊C4C2312yes—
244C3×(C2×D3)⋊C4C2312yes—
245C3×(C2×D3)⋊C4C2311yescharacteristic
246C3×(C2×D3)⋊C4C2312yes—
247C3×C4⋊Dic3C2311yescharacteristic
248C3×Dic3⋊C4C2312yes—
249C3×Dic3⋊C4C2312yes—
250C3×Dic3⋊C4C2312yes—
251C3×Dic3⋊C4C2311yescharacteristic
252C3×C4×Dic3C2312yes—
253C3×C4×Dic3C2312yes—
254C3×C4×Dic3C2312yes—
255C3×C4×Dic3C2311yescharacteristic
256C3×C4×Dic3C2311yescharacteristic
257C3×C4×Dic3C2311yescharacteristic
258C3×C4×Dic3C2311yescharacteristic
259C3×C4×Dic3C2311yescharacteristic
260#3724C2311yescharacteristic
261Dic3⋊Dic3C2311yescharacteristic
262Dic3⋊Dic3C2312yes—
263Dic3⋊Dic3C2311yescharacteristic
264Dic3⋊Dic3C2312yes—
265Dic3⋊Dic3C2312yes—
266Dic3⋊Dic3C2311yescharacteristic
267#3722C2311yescharacteristic
268#3722C2312yes—
269(C2×D3)⋊Dic3C2312yes—
270(C2×D3)⋊Dic3C2312yes—
271(C2×D3)⋊Dic3C2312yes—
272(C2×D3)⋊Dic3C2311yescharacteristic
273Dic32C2311yescharacteristic
274Dic32C2312yes—
275Dic32C2312yes—
276Dic32C2311yescharacteristic
277Dic32C2311yescharacteristic
278Dic32C2311yescharacteristic
279#3483—91noSylow
280C2×C3×#41—31no—
281C2×#239—31no—
282C2×#239—31no—
283C2×#239—32no—
284C2×#237—31no—
285C2×#237—32no—
286C2×#237—32no—
287C2×#237—31no—
288C2×#235—31no—
289C2×#235—32no—
290C2×#235—32no—
291C2×#235—32no—
292C2×#235—32no—
293C2×#235—31no—
294C2×#235—32no—
295C2×#235C2×D311yescharacteristic
296C3×C4⋊Q8—31no—
297C3×#124—32no—
298C3×#124—32no—
299C3×#121—31no—
300C3×#121—31no—
301C3×#121—32no—
302C3×C4×Q8—31no—
303C3×C4×Q8—31no—
304C3×C4×D4—31no—
305C3×C4×D4—31no—
306C3×C4×D4—31no—
307C3×C4×D4—31no—
308C3×C4×D4—32no—
309C3×C4×D4—32no—
310C3×#117—21no—
311C3×#117—31no—
312C3×#117—32no—
313C3×#117—32no—
314C3×#117C2×D311yescharacteristic
315C3×#117C2×D311yescharacteristic
316C2×C3×C42—31no—
317C2×C3×C42—32no—
318#947—32no—
319Q8×Dic3—31no—
320Q8×Dic3—31no—
321#944—32no—
322#944—32no—
323#940—32no—
324#940—32no—
325#940—32no—
326#940—32no—
327#940—31no—
328#940—31no—
329#940—32no—
330#940—31no—
331#940—31no—
332#939—32no—
333#939—32no—
334#939—32no—
335#939—32no—
336#938—32no—
337#938—31no—
338#938—32no—
339#938—31no—
340D4×Dic3—31no—
341D4×Dic3—31no—
342#930—31no—
343#930—31no—
344#930—32no—
345#930—31no—
346#930—32no—
347#930—32no—
348#930—32no—
349#930—32no—
350#930—32no—
351#930—61no—
352#930C2×D311yescharacteristic
353C4×#67—31no—
354C4×#67—31no—
355C4×#67—31no—
356C4×#67—31no—
357C4×#67—32no—
358C4×#67—32no—
359C4×#67—32no—
360C4×#67—32no—
361C4×#67—32no—
362C4×#67—31no—
363C4×#67—61no—
364C4×#67C2×D311yescharacteristic
365#926—31no—
366#926—32no—
367C2×C4×Dic3—31no—
368C2×C4×Dic3—32no—
369C2×C4×Dic3C2×D311yescharacteristic
370#895—31no—
371#895—32no—
372#895—31no—
373#895—31no—
374#895—32no—
375#895—32no—
376#895—61no—
377#895C2×D311yescharacteristic
378#893—32no—
379#893—32no—
380#893—32no—
381#893—31no—
382#893—31no—
383#893—32no—
384#893—31no—
385#893—61no—
386#893C2×D311yescharacteristic
387#893C2×D311yescharacteristic
388#893C2×D311yescharacteristic
389#892—31no—
390#892—31no—
391#892—32no—
392#892—31no—
393#892—32no—
394#892—61no—
395#892C2×D311yescharacteristic
396#888—32no—
397#888—31no—
398#888—31no—
399#888—32no—
400#888—32no—
401#888—31no—
402#888—61no—
403#888C2×D311yescharacteristic
404#887—31no—
405#887—32no—
406#887—31no—
407#887C2×D311yescharacteristic
408#887C2×D311yescharacteristic
409#885—32no—
410#885—32no—
411#885—32no—
412#885—32no—
413#885—32no—
414#885—32no—
415#885—32no—
416#885—32no—
417#885—32no—
418#885—62no—
419#885C2×D312yes—
420#884—32no—
421#884—32no—
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—32no—
432#884—32no—
433#884—62no—
434#884C2×D312yes—
435#67⋊C4—31no—
436#67⋊C4—32no—
437#67⋊C4—32no—
438#67⋊C4—32no—
439#67⋊C4—32no—
440#67⋊C4—31no—
441#67⋊C4—32no—
442#67⋊C4—32no—
443#67⋊C4—32no—
444#67⋊C4C2×D312yes—
445#67⋊C4C2×D312yes—
446#877—31no—
447#877—32no—
448#877—31no—
449#875—32no—
450#875—32no—
451#875—32no—
452#875—32no—
453#875—62no—
454#875C2×D312yes—
455#874—31no—
456#874—32no—
457#874—31no—
458C4×D12—31no—
459C4×D12—31no—
460C4×D12—31no—
461C4×D12—32no—
462C4×D12—32no—
463C4×D12—32no—
464C4×D12—32no—
465C4×D12—31no—
466#872—32no—
467#872—32no—
468#872—32no—
469#872—31no—
470#872—32no—
471#872—31no—
472#872—62no—
473#872C2×D312yes—
474#872C2×D312yes—
475C42×D3—31no—
476C42×D3—32no—
477C42×D3—32no—
478C42×D3—31no—
479C42×D3—32no—
480C42×D3—31no—
481C42×D3C2×D312yes—
482#869—32no—
483#869—31no—
484C4×Dic6—31no—
485C4×Dic6—31no—
486C4×Dic6—32no—
487C4×Dic6—31no—
488C4×Dic6—31no—
489C23×C32C2411yescharacteristic
490C22×C3⋊D3C2412yes—
491C22×C3⋊D3C2411yescharacteristic
492C22×C3×D3C2412yes—
493C22×C3×D3C2412yes—
494C22×C3×D3C2411yescharacteristic
495C2×C32×C4—22no—
496C2×C32×C4C2412yes—
497C2×C32×C4C2411yescharacteristic
498C2×C32×C4C2412yes—
499C2×C32×C4C2411yescharacteristic
500#638—22no—
501#638—42no—
502C2×C3⋊Dic3C2411yescharacteristic
503C2×C3⋊Dic3C2412yes—
504C2×C3⋊Dic3C2411yescharacteristic
505C2×C3⋊Dic3C2411yescharacteristic
506C4⋊(C3⋊D3)—22no—
507C4⋊(C3⋊D3)—42no—
508C4×C3⋊D3—22no—
509C4×C3⋊D3—24no—
510#634—42no—
511C3×#67—22no—
512C3×#67—24no—
513C3×#67—42no—
514C2×C3×Dic3—22no—
515C2×C3×Dic3—22no—
516C2×C3×Dic3C2411yescharacteristic
517C2×C3×Dic3C2411yescharacteristic
518C2×C3×Dic3C2412yes—
519C2×C3×Dic3C2411yescharacteristic
520C2×C3×Dic3C2411yescharacteristic
521C2×C3×Dic3C2411yescharacteristic
522C2×C3×Dic3C2412yes—
523C2×C3×Dic3C2411yescharacteristic
524C2×C3×Dic3C2411yescharacteristic
525C3×D12—22no—
526C3×D12—22no—
527C3×D12—42no—
528C3×C4×D3—22no—
529C3×C4×D3—24no—
530C3×C4×D3—24no—
531C3×C4×D3—24no—
532C3×C4×D3—24no—
533C3×Dic6—42no—
534C3×Dic6#4114yescomplemented
535#627—42no—
536#627#4114yescomplemented
537#626—24no—
538#626—24no—
539#626—24no—
540#626—24no—
541#626—22no—
542#626—42no—
543#626—42no—
544#626—42no—
545#625—24no—
546#625—42no—
547#625—42no—
548#624—24no—
549#624—22no—
550#624—22no—
551#624—24no—
552D3×Dic3—22no—
553D3×Dic3—24no—
554D3×Dic3—22no—
555D3×Dic3—24no—
556Q82—91no—
557#555—31no—
558#555—92no—
559#555—91no—
560#555—92no—
561#555—92no—
562#555—91no—
563#550—91no—
564#550—92no—
565#550—91no—
566#550—91no—
567#550—91no—
568#532—91no—
569#532—92no—
570#532—91no—
571#532—92no—
572#532—92no—
573#532—91no—
574C4×#41—31no—
575C4×#41—92no—
576C4×#41—91no—
577C4×#41—91no—
578C4×#41—91no—
579C3×#41—64no—
580C2×C3×Q8—31no—
581C2×C3×Q8—32no—
582C2×C3×D4—31no—
583C2×C3×D4—32no—
584C2×C3×D4—32no—
585C2×C3×D4—31no—
586C2×C3×D4—31no—
587C2×C3×D4—32no—
588C22×C3×C4—21no—
589C22×C3×C4—31no—
590C22×C3×C4—31no—
591C22×C3×C4—32no—
592C22×C3×C4—31no—
593C22×C3×C4—32no—
594C22×C3×C4—32no—
595C22×C3×C4—32no—
596C22×C3×C4C22×D311yescharacteristic
597C22×C3×C4C22×D311yescharacteristic
598C2×#67—31no—
599C2×#67—31no—
600C2×#67—32no—
601C2×#67—32no—
602C2×#67—32no—
603C2×#67—32no—
604C2×#67—32no—
605C2×#67—32no—
606C2×#67—32no—
607C2×#67—32no—
608C2×#67—32no—
609C2×#67—32no—
610C2×#67—32no—
611C2×#67—31no—
612C2×#67—32no—
613C2×#67—32no—
614C2×#67—32no—
615C2×#67—32no—
616C2×#67—61no—
617C2×#67—62no—
618C2×#67C22×D312yes—
619C2×#67C22×D311yescharacteristic
620C2×#67C22×D312yes—
621C22×Dic3—31no—
622C22×Dic3—32no—
623C22×Dic3—32no—
624C22×Dic3—31no—
625C22×Dic3C22×D311yescharacteristic
626C22×Dic3C22×D311yescharacteristic
627#239—64no—
628#239—64no—
629#239—124no—
630#237—64no—
631#237—64no—
632#237—124no—
633#237—124no—
634#235—24no—
635#235—68no—
636#235—68no—
637#235—64no—
638#235—64no—
639#235—124no—
640#235—124no—
641#235—124no—
642C2×D12—31no—
643C2×D12—32no—
644C2×D12—32no—
645C2×D12—32no—
646C2×D12—32no—
647C2×D12—31no—
648C2×D12—31no—
649C2×D12—32no—
650C2×D12—32no—
651C2×D12—32no—
652C2×D12—32no—
653C2×D12—32no—
654C2×D12—61no—
655C2×D12—62no—
656C2×D12C22×D311yescharacteristic
657C2×D12C22×D311yescharacteristic
658C2×D12C22×D312yes—
659C2×C4×D3—31no—
660C2×C4×D3—32no—
661C2×C4×D3—31no—
662C2×C4×D3—32no—
663C2×C4×D3—32no—
664C2×C4×D3—32no—
665C2×C4×D3—31no—
666C2×C4×D3—31no—
667C2×C4×D3—32no—
668C2×C4×D3—31no—
669C2×C4×D3—31no—
670C2×C4×D3—32no—
671C2×C4×D3—32no—
672C2×C4×D3—31no—
673C2×C4×D3—32no—
674C2×C4×D3—31no—
675C2×C4×D3—62no—
676C2×C4×D3—61no—
677C2×C4×D3C22×D312yes—
678C2×C4×D3C22×D311yescharacteristic
679C2×C4×D3C22×D312yes—
680C2×C4×D3C22×D312yes—
681C2×C4×D3C22×D312yes—
682C2×Dic6—31no—
683C2×Dic6—31no—
684C2×Dic6—32no—
685C2×Dic6—32no—
686C2×Dic6—32no—
687C2×Dic6—32no—
688C2×Dic6—62no—
689C2×Dic6C22×D312yes—
690C2×Dic6C22×D311yescharacteristic
691C3×C4⋊C4—21no—
692C3×C4⋊C4—21no—
693C3×C4⋊C4—32no—
694C3×C4⋊C4—31no—
695C3×C4⋊C4—31no—
696C3×C4⋊C4—32no—
697C3×C4⋊C4—32no—
698C3×C4⋊C4C22×D311yescharacteristic
699C3×C4⋊C4C22×D311yescharacteristic
700C3×C4⋊C4C22×D311yescharacteristic
701C3×C4⋊C4C22×D311yescharacteristic
702C3×C22⋊C4—22no—
703C3×C22⋊C4—31no—
704C3×C22⋊C4—32no—
705C3×C22⋊C4—31no—
706C3×C22⋊C4—32no—
707C3×C22⋊C4—32no—
708C3×C22⋊C4—32no—
709C3×C22⋊C4—32no—
710C3×C22⋊C4—32no—
711C3×C22⋊C4C22×D312yes—
712C3×C22⋊C4C22×D312yes—
713C3×C42—22no—
714C3×C42—31no—
715C3×C42—32no—
716C3×C42—31no—
717C3×C42—31no—
718C3×C42—32no—
719C3×C42—31no—
720C3×C42—32no—
721C3×C42—31no—
722C3×C42C22×D312yes—
723C3×C42C22×D312yes—
724#217—31no—
725#217—31no—
726#217—31no—
727#217—32no—
728#217—32no—
729#217—32no—
730#217—61no—
731#217C22×D311yescharacteristic
732(C2×D3)⋊C4—31no—
733(C2×D3)⋊C4—32no—
734(C2×D3)⋊C4—32no—
735(C2×D3)⋊C4—32no—
736(C2×D3)⋊C4—32no—
737(C2×D3)⋊C4—31no—
738(C2×D3)⋊C4—32no—
739(C2×D3)⋊C4—32no—
740(C2×D3)⋊C4—32no—
741(C2×D3)⋊C4—32no—
742(C2×D3)⋊C4—32no—
743(C2×D3)⋊C4—32no—
744(C2×D3)⋊C4—32no—
745(C2×D3)⋊C4—31no—
746(C2×D3)⋊C4—31no—
747(C2×D3)⋊C4—32no—
748(C2×D3)⋊C4—32no—
749(C2×D3)⋊C4—31no—
750(C2×D3)⋊C4—62no—
751(C2×D3)⋊C4—62no—
752(C2×D3)⋊C4—61no—
753(C2×D3)⋊C4—62no—
754(C2×D3)⋊C4—62no—
755(C2×D3)⋊C4C22×D311yescharacteristic
756(C2×D3)⋊C4C22×D312yes—
757(C2×D3)⋊C4C22×D312yes—
758(C2×D3)⋊C4C22×D312yes—
759(C2×D3)⋊C4C22×D312yes—
760(C2×D3)⋊C4C22×D312yes—
761(C2×D3)⋊C4C22×D312yes—
762C4⋊Dic3—31no—
763C4⋊Dic3—31no—
764C4⋊Dic3—31no—
765C4⋊Dic3—32no—
766C4⋊Dic3—31no—
767C4⋊Dic3—31no—
768C4⋊Dic3—32no—
769C4⋊Dic3—32no—
770C4⋊Dic3—61no—
771C4⋊Dic3C22×D311yescharacteristic
772Dic3⋊C4—31no—
773Dic3⋊C4—32no—
774Dic3⋊C4—31no—
775Dic3⋊C4—32no—
776Dic3⋊C4—31no—
777Dic3⋊C4—31no—
778Dic3⋊C4—32no—
779Dic3⋊C4—31no—
780Dic3⋊C4—31no—
781Dic3⋊C4—31no—
782Dic3⋊C4—32no—
783Dic3⋊C4—32no—
784Dic3⋊C4—61no—
785Dic3⋊C4—62no—
786Dic3⋊C4C22×D311yescharacteristic
787Dic3⋊C4C22×D312yes—
788Dic3⋊C4C22×D312yes—
789Dic3⋊C4C22×D312yes—
790C4×Dic3—31no—
791C4×Dic3—31no—
792C4×Dic3—32no—
793C4×Dic3—32no—
794C4×Dic3—31no—
795C4×Dic3—31no—
796C4×Dic3—32no—
797C4×Dic3—32no—
798C4×Dic3—32no—
799C4×Dic3—31no—
800C4×Dic3—31no—
801C4×Dic3—31no—
802C4×Dic3—31no—
803C4×Dic3—32no—
804C4×Dic3—31no—
805C4×Dic3—31no—
806C4×Dic3—62no—
807C4×Dic3—61no—
808C4×Dic3C22×D311yescharacteristic
809C4×Dic3C22×D311yescharacteristic
810C4×Dic3C22×D312yes—
811C4×Dic3C22×D312yes—
812C4×Dic3C22×D311yescharacteristic
813C4×Dic3C22×D311yescharacteristic
814C4×Dic3C22×D312yes—
815C4×Dic3C22×D311yescharacteristic
816C22×C32—21no—
817C22×C32—21no—
818C22×C32—21no—
819C22×C32C2511yescharacteristic
820C2×C3⋊D3—22no—
821C2×C3⋊D3—21no—
822C2×C3⋊D3—21no—
823C2×C3⋊D3—22no—
824C2×C3⋊D3—21no—
825C2×C3⋊D3—22no—
826C2×C3×D3—22no—
827C2×C3×D3—21no—
828C2×C3×D3—22no—
829C2×C3×D3—22no—
830C2×C3×D3—21no—
831C2×C3×D3—22no—
832C2×C3×D3—21no—
833C2×C3×D3—22no—
834C2×C3×D3—22no—
835C32×C4—22no—
836C32×C4—21no—
837C32×C4—22no—
838C32×C4C2×#4112yes—
839C3⋊Dic3—21no—
840C3⋊Dic3—21no—
841C3⋊Dic3—22no—
842C3⋊Dic3C2×#4112yes—
843C3×Dic3—21no—
844C3×Dic3—21no—
845C3×Dic3—21no—
846C3×Dic3—22no—
847C3×Dic3—21no—
848C3×Dic3C2×#4114yes—
849C3×Dic3C2×#4112yes—
850C3×Dic3C2×#4112yes—
851C3×Dic3H(5,𝔽2)12yes—
852C2×#41—31no—
853C2×#41—92no—
854C2×#41—91no—
855C2×#41—92no—
856C2×#41—92no—
857C2×#41—91no—
858C2×#41—92no—
859C2×#41—91no—
860C4⋊Q8—31no—
861C4⋊Q8—91no—
862C4⋊Q8—92no—
863C4⋊Q8—92no—
864C4⋊Q8—92no—
865C4⋊Q8—91no—
866#127—91no—
867#127—92no—
868#127—91no—
869#127—92no—
870#127—92no—
871#127—91no—
872#124—32no—
873#124—32no—
874#124—92no—
875#124—92no—
876#124—92no—
877#124—92no—
878#124—92no—
879#124—92no—
880#124—92no—
881#121—31no—
882#121—31no—
883#121—32no—
884#121—92no—
885#121—92no—
886#121—92no—
887#121—92no—
888#121—92no—
889#121—92no—
890#121—92no—
891#121—92no—
892#121—92no—
893#121—92no—
894#121—91no—
895#121—92no—
896#121—91no—
897#121—92no—
898#121—92no—
899#121—91no—
900#121—91no—
901#121—92no—
902C4×Q8—31no—
903C4×Q8—31no—
904C4×Q8—91no—
905C4×Q8—91no—
906C4×Q8—92no—
907C4×Q8—91no—
908C4×Q8—91no—
909C4×D4—31no—
910C4×D4—31no—
911C4×D4—31no—
912C4×D4—31no—
913C4×D4—32no—
914C4×D4—32no—
915C4×D4—92no—
916C4×D4—91no—
917C4×D4—92no—
918C4×D4—92no—
919C4×D4—92no—
920C4×D4—91no—
921C4×D4—91no—
922C4×D4—91no—
923C4×D4—92no—
924C4×D4—91no—
925C4×D4—92no—
926C4×D4—92no—
927C4×D4—92no—
928C4×D4—92no—
929C4×D4—92no—
930C4×D4—91no—
931C4×D4—91no—
932C4×D4—91no—
933#117—31no—
934#117—32no—
935#117—32no—
936#117—91no—
937#117—91no—
938#117—92no—
939#117—92no—
940#117—92no—
941#117—91no—
942#117—91no—
943#117—92no—
944#117D3211yescharacteristic
945C2×C42—31no—
946C2×C42—32no—
947C2×C42—92no—
948C2×C42—91no—
949C2×C42—91no—
950C2×C42—92no—
951C23×C3—21no—
952C23×C3—32no—
953C23×C3—32no—
954C23×C3—31no—
955C23×C3C23×D311yescharacteristic
956C23×C3C23×D311yescharacteristic
957C22×D3—32no—
958C22×D3—31no—
959C22×D3—32no—
960C22×D3—31no—
961C22×D3—62no—
962C22×D3—61no—
963C22×D3C23×D312yes—
964C22×D3C23×D311yescharacteristic
965C22×D3C23×D312yes—
966C3×Q8—34no—
967C3×Q8—122no—
968C3×D4—62no—
969C3×D4—64no—
970C3×D4—62no—
971C3×D4—62no—
972C3×D4—122no—
973C3×D4—122no—
974C2×C3×C4—22no—
975C2×C3×C4—22no—
976C2×C3×C4—21no—
977C2×C3×C4—22no—
978C2×C3×C4—21no—
979C2×C3×C4—22no—
980C2×C3×C4—31no—
981C2×C3×C4—32no—
982C2×C3×C4—31no—
983C2×C3×C4—31no—
984C2×C3×C4—31no—
985C2×C3×C4—31no—
986C2×C3×C4—31no—
987C2×C3×C4—32no—
988C2×C3×C4—31no—
989C2×C3×C4—42no—
990C2×C3×C4—64no—
991C2×C3×C4—64no—
992C2×C3×C4—64no—
993C2×C3×C4—64no—
994C2×C3×C4—62no—
995C2×C3×C4—62no—
996C2×C3×C4—62no—
997C2×C3×C4C23×D312yes—
998C2×C3×C4C23×D312yes—
999C2×C3×C4C23×D311yescharacteristic
1000C2×C3×C4C23×D312yes—
1001C2×C3×C4C23×D311yescharacteristic
1002C2×C3×C4C23×D312yes—
1003C2×C3×C4C23×D311yescharacteristic
1004C2×C3×C4C23×D311yescharacteristic
1005#67—24no—
1006#67—22no—
1007#67—42no—
1008#67—64no—
1009#67—64no—
1010#67—62no—
1011#67—62no—
1012#67—64no—
1013#67—64no—
1014#67—64no—
1015#67—64no—
1016#67—62no—
1017#67—122no—
1018#67—122no—
1019#67—122no—
1020#67—122no—
1021#67—122no—
1022#67—122no—
1023#67—122no—
1024#67—122no—
1025#67—122no—
1026#67—122no—
1027#67—242no—
1028C2×Dic3—22no—
1029C2×Dic3—22no—
1030C2×Dic3—31no—
1031C2×Dic3—31no—
1032C2×Dic3—31no—
1033C2×Dic3—31no—
1034C2×Dic3—32no—
1035C2×Dic3—31no—
1036C2×Dic3—32no—
1037C2×Dic3—31no—
1038C2×Dic3—61no—
1039C2×Dic3—61no—
1040C2×Dic3—62no—
1041C2×Dic3—61no—
1042C2×Dic3—62no—
1043C2×Dic3—64no—
1044C2×Dic3—62no—
1045C2×Dic3—64no—
1046C2×Dic3C23×D311yescharacteristic
1047C2×Dic3C23×D311yescharacteristic
1048C2×Dic3C23×D311yescharacteristic
1049C2×Dic3C23×D312yes—
1050C2×Dic3C23×D311yescharacteristic
1051C2×Dic3C23×D312yes—
1052C2×Dic3C23×D311yescharacteristic
1053C2×Dic3C23×D311yescharacteristic
1054C2×Dic3C23×D311yescharacteristic
1055D12—22no—
1056D12—22no—
1057D12—42no—
1058D12—64no—
1059D12—64no—
1060D12—62no—
1061D12—64no—
1062D12—64no—
1063D12—62no—
1064D12—62no—
1065D12—122no—
1066D12—122no—
1067D12—122no—
1068D12—122no—
1069D12—122no—
1070D12—122no—
1071D12—242no—
1072C4×D3—22no—
1073C4×D3—24no—
1074C4×D3—24no—
1075C4×D3—24no—
1076C4×D3—24no—
1077C4×D3—62no—
1078C4×D3—64no—
1079C4×D3—62no—
1080C4×D3—64no—
1081C4×D3—64no—
1082C4×D3—64no—
1083C4×D3—62no—
1084C4×D3—62no—
1085C4×D3—64no—
1086C4×D3—64no—
1087C4×D3—62no—
1088C4×D3—62no—
1089C4×D3—64no—
1090C4×D3—62no—
1091C4×D3—64no—
1092C4×D3—62no—
1093C4×D3—124no—
1094C4×D3—122no—
1095Dic6—34no—
1096Dic6—34no—
1097Dic6—42no—
1098Dic6—122no—
1099Dic6—122no—
1100Dic6—122no—
1101Dic6—122no—
1102Dic6—242no—
1103Dic6#23514yescomplemented
1104C2×C32—41no—
1105C2×C32C22×#4111yescharacteristic
1106C2×C32C22×#4111yescharacteristic
1107C2×C32C2×H(5,𝔽2)11yescharacteristic
1108C3⋊D3—42no—
1109C3⋊D3—41no—
1110C3×D3—42no—
1111C3×D3—42no—
1112C3×D3—41no—
1113#41—64no—
1114#41—188no—
1115#41—184no—
1116#41—184no—
1117#41—184no—
1118#41—364no—
1119#41—364no—
1120#41—364no—
1121C2×Q8—31no—
1122C2×Q8—32no—
1123C2×Q8—91no—
1124C2×Q8—92no—
1125C2×Q8—92no—
1126C2×D4—32no—
1127C2×D4—31no—
1128C2×D4—32no—
1129C2×D4—31no—
1130C2×D4—31no—
1131C2×D4—32no—
1132C2×D4—92no—
1133C2×D4—91no—
1134C2×D4—92no—
1135C2×D4—92no—
1136C2×D4—92no—
1137C2×D4—92no—
1138C2×D4—92no—
1139C2×D4—92no—
1140C2×D4—92no—
1141C2×D4—91no—
1142C2×D4—92no—
1143C2×D4—92no—
1144C2×D4—92no—
1145C2×D4—91no—
1146C2×D4—92no—
1147C22×C4—31no—
1148C22×C4—31no—
1149C22×C4—32no—
1150C22×C4—32no—
1151C22×C4—32no—
1152C22×C4—32no—
1153C22×C4—31no—
1154C22×C4—92no—
1155C22×C4—91no—
1156C22×C4—91no—
1157C22×C4—92no—
1158C22×C4—92no—
1159C22×C4—91no—
1160C22×C4—91no—
1161C22×C4—92no—
1162C22×C4—92no—
1163C22×C4—91no—
1164C22×C4C2×D3211yescharacteristic
1165C4⋊C4—31no—
1166C4⋊C4—32no—
1167C4⋊C4—32no—
1168C4⋊C4—32no—
1169C4⋊C4—31no—
1170C4⋊C4—91no—
1171C4⋊C4—91no—
1172C4⋊C4—91no—
1173C4⋊C4—92no—
1174C4⋊C4—92no—
1175C4⋊C4—92no—
1176C4⋊C4—91no—
1177C4⋊C4—91no—
1178C4⋊C4—92no—
1179C4⋊C4—91no—
1180C4⋊C4C2×D3211yescharacteristic
1181C4⋊C4C2×D3211yescharacteristic
1182C22⋊C4—31no—
1183C22⋊C4—32no—
1184C22⋊C4—32no—
1185C22⋊C4—32no—
1186C22⋊C4—32no—
1187C22⋊C4—32no—
1188C22⋊C4—32no—
1189C22⋊C4—31no—
1190C22⋊C4—91no—
1191C22⋊C4—92no—
1192C22⋊C4—92no—
1193C22⋊C4—92no—
1194C22⋊C4—91no—
1195C22⋊C4—92no—
1196C22⋊C4—91no—
1197C22⋊C4—92no—
1198C22⋊C4—92no—
1199C22⋊C4—92no—
1200C22⋊C4—91no—
1201C22⋊C4—92no—
1202C22⋊C4C2×D3212yes—
1203C42—31no—
1204C42—32no—
1205C42—31no—
1206C42—31no—
1207C42—32no—
1208C42—31no—
1209C42—32no—
1210C42—31no—
1211C42—91no—
1212C42—91no—
1213C42—91no—
1214C42—91no—
1215C42—92no—
1216C42—92no—
1217C42—92no—
1218C42—91no—
1219C42C2×D3212yes—
1220C22×C3—21no—
1221C22×C3—21no—
1222C22×C3—21no—
1223C22×C3—21no—
1224C22×C3—21no—
1225C22×C3—21no—
1226C22×C3—21no—
1227C22×C3—41no—
1228C22×C3—41no—
1229C22×C3—41no—
1230C22×C3—62no—
1231C22×C3—61no—
1232C22×C3—61no—
1233C22×C3—62no—
1234C22×C3—62no—
1235C22×C3—62no—
1236C22×C3—62no—
1237C22×C3—61no—
1238C22×C3—62no—
1239C22×C3C24×D311yescharacteristic
1240C22×C3C24×D311yescharacteristic
1241C2×D3—22no—
1242C2×D3—21no—
1243C2×D3—22no—
1244C2×D3—22no—
1245C2×D3—22no—
1246C2×D3—21no—
1247C2×D3—22no—
1248C2×D3—21no—
1249C2×D3—22no—
1250C2×D3—62no—
1251C2×D3—61no—
1252C2×D3—62no—
1253C2×D3—61no—
1254C2×D3—62no—
1255C2×D3—62no—
1256C2×D3—61no—
1257C2×D3—61no—
1258C2×D3—61no—
1259C2×D3—62no—
1260C2×D3—61no—
1261C2×D3—62no—
1262C2×D3—121no—
1263C2×D3—122no—
1264C2×D3—122no—
1265C2×D3—121no—
1266C2×D3—122no—
1267C2×D3—121no—
1268C3×C4—21no—
1269C3×C4—22no—
1270C3×C4—22no—
1271C3×C4—21no—
1272C3×C4—22no—
1273C3×C4—22no—
1274C3×C4—22no—
1275C3×C4—32no—
1276C3×C4—32no—
1277C3×C4—34no—
1278C3×C4—32no—
1279C3×C4—42no—
1280C3×C4—42no—
1281C3×C4—41no—
1282C3×C4—61no—
1283C3×C4—61no—
1284C3×C4—62no—
1285C3×C4—61no—
1286C3×C4—61no—
1287C3×C4C2×#23512yes—
1288C3×C4D3×#4112yes—
1289Dic3—21no—
1290Dic3—21no—
1291Dic3—21no—
1292Dic3—21no—
1293Dic3—22no—
1294Dic3—32no—
1295Dic3—32no—
1296Dic3—62no—
1297Dic3—61no—
1298Dic3—61no—
1299Dic3—62no—
1300Dic3—61no—
1301Dic3—62no—
1302Dic3—61no—
1303Dic3—121no—
1304Dic3—122no—
1305Dic3—121no—
1306Dic3C2×#23514yes—
1307Dic3D3×#4112yes—
1308Dic3D3×#4112yes—
1309Dic3#100912yes—
1310C32#348311yescharacteristic, complemented, Sylow
1311C23—31no—
1312C23—32no—
1313C23—32no—
1314C23—91no—
1315C23—92no—
1316C23C22×D3211yescharacteristic
1317Q8—34no—
1318Q8—94no—
1319Q8—122no—
1320Q8—362no—
1321Q8—362no—
1322D4—64no—
1323D4—62no—
1324D4—62no—
1325D4—62no—
1326D4—122no—
1327D4—122no—
1328D4—184no—
1329D4—184no—
1330D4—184no—
1331D4—182no—
1332D4—184no—
1333D4—182no—
1334D4—184no—
1335D4—182no—
1336D4—362no—
1337D4—362no—
1338D4—362no—
1339D4—362no—
1340D4—362no—
1341D4—362no—
1342D4—362no—
1343C2×C4—22no—
1344C2×C4—31no—
1345C2×C4—31no—
1346C2×C4—32no—
1347C2×C4—31no—
1348C2×C4—31no—
1349C2×C4—31no—
1350C2×C4—31no—
1351C2×C4—31no—
1352C2×C4—32no—
1353C2×C4—64no—
1354C2×C4—64no—
1355C2×C4—64no—
1356C2×C4—64no—
1357C2×C4—62no—
1358C2×C4—62no—
1359C2×C4—62no—
1360C2×C4—91no—
1361C2×C4—91no—
1362C2×C4—91no—
1363C2×C4—92no—
1364C2×C4—184no—
1365C2×C4—184no—
1366C2×C4—182no—
1367C2×C4—184no—
1368C2×C4—182no—
1369C2×C4—184no—
1370C2×C4—184no—
1371C2×C4—182no—
1372C2×C4—182no—
1373C2×C4—182no—
1374C2×C4C22×D3212yes—
1375C2×C4C22×D3211yescharacteristic
1376C2×C4C22×D3212yes—
1377C2×C4C22×D3211yescharacteristic
1378C2×C3—21no—
1379C2×C3—21no—
1380C2×C3—21no—
1381C2×C3—41no—
1382C2×C3—41no—
1383C2×C3—81no—
1384C2×C3—122no—
1385C2×C3—121no—
1386C2×C3—122no—
1387C2×C3C22×#23511yescharacteristic
1388C2×C3C2×D3×#4111yescharacteristic
1389C2×C3C2×D3×#4111yescharacteristic
1390C2×C3C2×D3×#4111yescharacteristic
1391C2×C3C2×#100911yescharacteristic
1392C2×C3D3×H(5,𝔽2)11yescharacteristic
1393D3—42no—
1394D3—41no—
1395D3—42no—
1396D3—122no—
1397D3—121no—
1398D3—122no—
1399D3—121no—
1400D3—242no—
1401D3—241no—
1402C22—21no—
1403C22—21no—
1404C22—21no—
1405C22—62no—
1406C22—61no—
1407C22—62no—
1408C22—62no—
1409C22—62no—
1410C22—61no—
1411C22—62no—
1412C22—61no—
1413C22—62no—
1414C22—182no—
1415C22—181no—
1416C22—182no—
1417C22—181no—
1418C22—181no—
1419C22—182no—
1420C22C23×D3211yescharacteristic
1421C4—21no—
1422C4—22no—
1423C4—22no—
1424C4—34no—
1425C4—32no—
1426C4—32no—
1427C4—32no—
1428C4—61no—
1429C4—61no—
1430C4—61no—
1431C4—62no—
1432C4—61no—
1433C4—92no—
1434C4—181no—
1435C4—182no—
1436C4—181no—
1437C4D3×#23512yes—
1438C3—21no—
1439C3#8584511yescharacteristic, complemented
1440C3#8695911yescharacteristic, complemented
1441C2—41no—
1442C2—122no—
1443C2—121no—
1444C2—122no—
1445C2—362no—
1446C2—361no—
1447C2C2×D3×#23511yescharacteristic
1448C2D32×#4111yescharacteristic
1449C2D3×#100911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#117C22
hypercenter#117D32
hypocenterC32#3483
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10596003C2semidirect
2. C3×#5532C2semidirect
3. C3×#5522C2semidirect
4. #10595007C2semidirect
5. #10595006C2semidirect
6. #10594910C2semidirect
7. C4×#3804C2semidirect
8. #10594555C2semidirect
9. #10594524C2semidirect
10. #10594520C2semidirect
11. #10594518C2semidirect
12. #10594367C2semidirect
13. #10594362C2semidirect
14. #10594360C2semidirect
15. #10594312C2semidirect
16. #10594246C2semidirect
17. #10594201C2semidirect
18. #10594068C2semidirect
19. #10594058C2semidirect
20. #10593977C2semidirect
21. #10593969C2semidirect
22. #10593965C2semidirect
23. #10593930C2semidirect
164. #5532D3semidirect
167. #5522D3semidirect
534. C3×Dic6#41semidirect
536. #627#41semidirect
1103. Dic6#235semidirect
1310. C32#3483semidirect
1439. C3#85845semidirect
1440. C3#86959semidirect

Maximal subgroups

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

subgroupindex
#105960032
C3×#55322
C3×#55222
#105950072
#105950062
#105949102
C4×#38042
#105945552
#105945242
#105945202
#105945182
#105943672
#105943622
#105943602
#105943122
#105942462
#105942012
#105940682
#105940582
#105939772
#105939692
#105939652
#105939302
#869593
#858453