Finite Group Databasebeta

← #11904552

Subgroups — #11904552

Order 1152.

3205 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64319C211yesmaximal, characteristic, complemented
2C2×#64315C211yesmaximal, characteristic, complemented
3#10596043C211yesmaximal, characteristic, complemented
4C3×#5577C211yesmaximal, characteristic, complemented
5C3×#5576C211yesmaximal, characteristic, complemented
6#10595412C211yesmaximal, characteristic, complemented
7#10595409C211yesmaximal, characteristic, complemented
8#10594634C213yesmaximal, complemented
9#10594632C213yesmaximal, complemented
10#10594527C213yesmaximal, complemented
11#10594525C213yesmaximal, complemented
12#10594010C213yesmaximal, complemented
13#10594006C213yesmaximal, complemented
14#10593906C213yesmaximal, complemented
15#10593905C213yesmaximal, complemented
16#86783—31nomaximal
17#86736—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×#239C2211yescharacteristic
21C2×C3×#239C2211yescharacteristic, complemented
22C2×C3×D3×Q8C2211yescharacteristic, complemented
23#64319—28no—
24#64315—28no—
25C2×#3802C2213yes—
26C2×C4×D32C2213yes—
27C2×#3798C2213yes—
28C2×#3796C2213yes—
29C2×#3795C2213yes—
30C2×#3795C2213yes—
31C2×#3795C2213yescomplemented
32C2×D3×Dic6C2213yescomplemented
33C32×C4×Q8C2211yescharacteristic, complemented
34Q8×C3⋊Dic3C2211yescharacteristic, complemented
35#64101C2213yes—
36#64096C2213yescomplemented
37#64081C2213yes—
38C4×#634C2213yescomplemented
39C3×#897C2213yescomplemented
40C3×#895C2213yescomplemented
41C3×#895C2213yescomplemented
42C3×#895C2213yescomplemented
43C3×#875C2213yescomplemented
44C3×#874C2213yescomplemented
45C3×C4×D12C2213yescomplemented
46C3×C4×D12C2213yescomplemented
47#63922C2216yes—
48#63922C2213yes—
49#63922C2213yes—
50#63915C2216yescomplemented
51#63914C2216yescomplemented
52#63914C2213yescomplemented
53#63908C2213yescomplemented
54#63908C2213yescomplemented
55#63908C2213yescomplemented
56#63902C2216yescomplemented
57C4×#625C2213yescomplemented
58C4×#625C2213yescomplemented
59#63899C2213yescomplemented
60#63899C2213yescomplemented
61#63898C2216yescomplemented
62#63885C2216yescomplemented
63#63885C2213yescomplemented
64#63885C2213yescomplemented
65#63885C2216yescomplemented
66#63863C2213yescomplemented
67#63856C2213yescomplemented
68#63854C2213yes—
69#63854C2211yescharacteristic
70C2×#1010—31no—
71C2×D3×#41—31no—
72C2×D3×#41—31no—
73C2×#1007—31no—
74C3×#550—31no—
75C3×#548—31no—
76#5834—31no—
77#5834—31no—
78#5831—31no—
79#5817—31no—
80#5718—33no—
81#5715—33no—
82#5677—33no—
83#5674—33no—
84#5633—33no—
85#5627—33no—
86#5607—33no—
87#5607—33no—
88#5606—33no—
89#5599—33no—
90#5599—33no—
91#5598—33no—
92#5577D311yescharacteristic, complemented
93#5576D311yescharacteristic, complemented
94#5572—31no—
95#5572—31no—
96#5572—61no—
97#5553—33no—
98#5552—33no—
99#5547—33no—
100#5547—33no—
101C22×D32C2313yes—
102C2×C32×Q8C2311yescharacteristic
103Q8×C3⋊D3D418yescomplemented
104C2×C4×C3⋊D3C2313yes—
105C2×#634C2313yes—
106C3×#239—24no—
107C3×#239—24no—
108C3×#239—24no—
109C3×D3×Q8—24no—
110C2×C3×D12C2313yes—
111C2×C3×D12C2313yes—
112C2×C3×D12C2313yes—
113C2×C3×D12C2316yes—
114C2×C3×D12C2313yes—
115C2×C3×D12C2313yes—
116C2×C3×C4×D3C2313yes—
117C2×C3×C4×D3C2313yes—
118C2×C3×C4×D3C2313yes—
119C2×C3×C4×D3C2313yes—
120C2×C3×Dic6C2313yes—
121C2×#627C2313yes—
122C2×#626C2313yes—
123C2×#626C2311yescharacteristic
124C2×#625C2316yes—
125C2×#625C2313yes—
126C2×#625C2313yes—
127C2×#625C2313yes—
128C2×#625C2316yes—
129C2×#624C2311yescharacteristic
130C2×D3×Dic3C2316yes—
131C2×D3×Dic3C2313yes—
132C2×D3×Dic3C2313yes—
133#3802—212no—
134C4×D32—212no—
135#3798—212no—
136#3796—212no—
137#3795—212no—
138#3795—212no—
139#3795—212no—
140D3×Dic6—212no—
141C32×C4⋊C4C2313yes—
142C32×C42C2313yes—
143#3752C2311yescharacteristic
144#3752C2313yes—
145C4⋊(C3⋊Dic3)C2313yes—
146#3750C2313yes—
147#3750C2313yes—
148C4×C3⋊Dic3C2316yes—
149C4×C3⋊Dic3C2313yes—
150C3×(C2×D3)⋊C4C2313yes—
151C3×(C2×D3)⋊C4C2313yes—
152C3×(C2×D3)⋊C4C2316yes—
153C3×(C2×D3)⋊C4C2311yescharacteristic
154C3×(C2×D3)⋊C4C2313yes—
155C3×C4⋊Dic3C2313yes—
156C3×C4⋊Dic3C2311yescharacteristic
157#3724C2313yes—
158#3724C2311yescharacteristic
159(C2×D3)⋊Dic3C2311yescharacteristic
160(C2×D3)⋊Dic3C2313yes—
161(C2×D3)⋊Dic3C2316yes—
162(C2×D3)⋊Dic3C2313yes—
163(C2×D3)⋊Dic3C2313yes—
164#3487—91noSylow
165C2×C3×#41—31no—
166C2×C3×#41—31no—
167C2×C3×#41—31no—
168C22×C3×Q8—31no—
169#1010—68no—
170D3×#41—68no—
171D3×#41—68no—
172#1007—68no—
173C2×#239—33no—
174C2×#239C2×D311yescharacteristic
175C2×#239C2×D311yescharacteristic
176C2×#239C2×D311yescharacteristic, complemented
177C2×D3×Q8—31no—
178C2×D3×Q8—31no—
179C2×D3×Q8—33no—
180C2×D3×Q8—61no—
181C2×D3×Q8C2×D311yescharacteristic, complemented
182C2×#237—33no—
183C2×#237—33no—
184C2×#237—33no—
185C2×#237—33no—
186C2×D3×D4—33no—
187C2×D3×D4—33no—
188C2×#235—33no—
189C2×#235—33no—
190C2×#235—33no—
191C2×#235—33no—
192C2×#235—33no—
193C22×C4×D3—33no—
194C22×C4×D3—33no—
195C22×Dic6—33no—
196C3×#127—33no—
197C3×#124—33no—
198C3×C22⋊Q8—33no—
199C3×#121—33no—
200C3×#121—33no—
201C3×#121—33no—
202C3×C4×Q8—21no—
203C3×C4×Q8C2×D311yescharacteristic, complemented
204C3×C4×Q8C2×D311yescharacteristic, complemented
205C3×C4×D4—33no—
206C3×C4×D4—33no—
207#947—33no—
208#946—33no—
209Q8×Dic3—31no—
210Q8×Dic3—31no—
211Q8×Dic3—61no—
212#940—33no—
213#940—33no—
214#940—36no—
215#940—36no—
216#939—36no—
217#939—36no—
218#939—33no—
219#939—33no—
220#938—33no—
221#938—33no—
222#938—33no—
223#937—33no—
224#937—36no—
225#937—33no—
226#936—33no—
227D4×Dic3—36no—
228#930—33no—
229#930—33no—
230#930—33no—
231C4×#67—33no—
232C4×#67—33no—
233C4×#67—33no—
234C4×#67—33no—
235#924—33no—
236#897C2×D313yescomplemented
237#896—33no—
238#896—33no—
239#895C2×D313yescomplemented
240#895C2×D313yescomplemented
241#895C2×D313yescomplemented
242#894—31no—
243#894—33no—
244#893—36no—
245#892—33no—
246#892—33no—
247#892—63no—
248#887—33no—
249#887—33no—
250#887—63no—
251#885—36no—
252#885—36no—
253#884—36no—
254#884—36no—
255#884—33no—
256#884—33no—
257#883—31no—
258#883—33no—
259#882—33no—
260#882—36no—
261#882—33no—
262#67⋊C4—36no—
263#67⋊C4—36no—
264#878—33no—
265#878—33no—
266#875C2×D313yescomplemented
267#874C2×D313yescomplemented
268C4×D12C2×D313yescomplemented
269C4×D12C2×D313yescomplemented
270#872—33no—
271#872—33no—
272#872—63no—
273C4×Dic6—33no—
274C4×Dic6—33no—
275C4×Dic6—63no—
276C22×C3⋊D3C2411yescharacteristic
277C22×C3×D3C2413yes—
278C22×C3×D3C2413yes—
279C22×C3×D3C2413yes—
280C22×C3×D3C2411yescharacteristic
281C2×D32—26no—
282C2×D32—43no—
283C2×D32—43no—
284C32×Q8C2×D414yes—
285C2×C32×C4C2413yes—
286C2×C32×C4C2411yescharacteristic
287C2×C32×C4C2413yes—
288C2×C3⋊Dic3C2411yescharacteristic
289C2×C3⋊Dic3C2413yes—
290C2×C3⋊Dic3C2413yes—
291C4×C3⋊D3C2×D4112yes—
292#634C2×D4112yes—
293C2×C3×Dic3C2411yescharacteristic
294C2×C3×Dic3C2413yes—
295C2×C3×Dic3C2411yescharacteristic
296C2×C3×Dic3C2411yescharacteristic
297C3×D12—26no—
298C3×D12—26no—
299C3×D12—26no—
300C3×D12—43no—
301C3×D12—46no—
302C3×D12—43no—
303C3×C4×D3—26no—
304C3×C4×D3—26no—
305C3×C4×D3—26no—
306C3×C4×D3—26no—
307C3×Dic6—26no—
308#627—26no—
309#626—26no—
310#626—22no—
311#625—26no—
312#625—212no—
313#625—43no—
314#625—46no—
315#625—43no—
316#624—22no—
317D3×Dic3—212no—
318D3×Dic3—26no—
319D3×Dic3—26no—
320C2×2−1+4—91no—
321C22×#41—91no—
322#550—31no—
323#550—93no—
324#550—93no—
325#550—91no—
326#548—31no—
327#548—93no—
328#548—93no—
329#548—91no—
330#535—93no—
331#535—93no—
332#525—93no—
333#525—93no—
334#519—91no—
335C23×D3—33no—
336C23×D3—33no—
337C3×#41—64no—
338C3×#41—64no—
339C3×#41—64no—
340C2×C3×Q8—21no—
341C2×C3×Q8—33no—
342C2×C3×Q8—64no—
343C2×C3×Q8C22×D311yescharacteristic
344C2×C3×Q8C22×D311yescharacteristic
345C2×C3×D4—33no—
346C2×C3×D4—33no—
347C2×C3×D4—33no—
348C2×C3×D4—36no—
349C2×C3×D4—33no—
350C2×C3×D4—33no—
351C22×C3×C4—33no—
352C22×C3×C4—33no—
353C22×C3×C4—33no—
354C22×C3×C4—33no—
355C2×#67—36no—
356C2×#67—33no—
357C2×#67—33no—
358C2×#67—36no—
359C2×#67—36no—
360C2×#67—36no—
361C2×#67—33no—
362C2×#67—33no—
363C2×#67—33no—
364C2×#67—33no—
365C2×#67—31no—
366C2×#67—33no—
367C22×Dic3—33no—
368C22×Dic3—33no—
369C22×Dic3—36no—
370#239—24no—
371#239—24no—
372#239—24no—
373#239—612no—
374D3×Q8—24no—
375D3×Q8—38no—
376D3×Q8—38no—
377D3×Q8—68no—
378D3×Q8—612no—
379#237—612no—
380#237—612no—
381#237—612no—
382#237—612no—
383D3×D4—612no—
384D3×D4—612no—
385#235—612no—
386#235—612no—
387#235—612no—
388#235—612no—
389#235—612no—
390C2×D12—31no—
391C2×D12—33no—
392C2×D12C22×D313yes—
393C2×D12C22×D313yes—
394C2×D12C22×D313yes—
395C2×D12C22×D313yes—
396C2×D12C22×D313yes—
397C2×D12C22×D316yes—
398C2×C4×D3—33no—
399C2×C4×D3—33no—
400C2×C4×D3—33no—
401C2×C4×D3—36no—
402C2×C4×D3—33no—
403C2×C4×D3—31no—
404C2×C4×D3—31no—
405C2×C4×D3—63no—
406C2×C4×D3—612no—
407C2×C4×D3—612no—
408C2×C4×D3C22×D313yes—
409C2×C4×D3C22×D313yes—
410C2×C4×D3C22×D313yes—
411C2×C4×D3C22×D313yes—
412C2×Dic6—33no—
413C2×Dic6—33no—
414C2×Dic6—33no—
415C2×Dic6—33no—
416C2×Dic6—63no—
417C2×Dic6—612no—
418C2×Dic6C22×D313yes—
419C3×C4⋊C4—23no—
420C3×C4⋊C4—33no—
421C3×C4⋊C4—31no—
422C3×C4⋊C4C22×D313yes—
423C3×C4⋊C4C22×D313yes—
424C3×C22⋊C4—33no—
425C3×C22⋊C4—33no—
426C3×C22⋊C4—33no—
427C3×C22⋊C4—36no—
428C3×C22⋊C4—31no—
429C3×C42—23no—
430C3×C42C22×D313yes—
431C3×C42C22×D313yes—
432#217—33no—
433#217—33no—
434#217—31no—
435#217—33no—
436#217—36no—
437(C2×D3)⋊C4—33no—
438(C2×D3)⋊C4—36no—
439(C2×D3)⋊C4—33no—
440(C2×D3)⋊C4—31no—
441(C2×D3)⋊C4—33no—
442(C2×D3)⋊C4—31no—
443(C2×D3)⋊C4—31no—
444(C2×D3)⋊C4—33no—
445(C2×D3)⋊C4—33no—
446(C2×D3)⋊C4—61no—
447(C2×D3)⋊C4—63no—
448(C2×D3)⋊C4C22×D311yescharacteristic
449(C2×D3)⋊C4C22×D313yes—
450(C2×D3)⋊C4C22×D313yes—
451(C2×D3)⋊C4C22×D313yes—
452(C2×D3)⋊C4C22×D316yes—
453C4⋊Dic3—33no—
454C4⋊Dic3—33no—
455C4⋊Dic3—63no—
456C4⋊Dic3C22×D311yescharacteristic
457C4⋊Dic3C22×D313yes—
458Dic3⋊C4—33no—
459Dic3⋊C4—33no—
460Dic3⋊C4—33no—
461Dic3⋊C4—33no—
462Dic3⋊C4—31no—
463Dic3⋊C4—33no—
464Dic3⋊C4—33no—
465Dic3⋊C4—31no—
466Dic3⋊C4—63no—
467Dic3⋊C4—63no—
468C4×Dic3—36no—
469C4×Dic3—36no—
470C4×Dic3—33no—
471C4×Dic3—33no—
472C4×Dic3—66no—
473C4×Dic3—63no—
474C22×C32C2511yescharacteristic
475C2×C3⋊D3—21no—
476C2×C3⋊D3—21no—
477C2×C3⋊D3C22×D412yes—
478C2×C3×D3—23no—
479C2×C3×D3—23no—
480C2×C3×D3—23no—
481C2×C3×D3—21no—
482C2×C3×D3—21no—
483C2×C3×D3—23no—
484C2×C3×D3—23no—
485C2×C3×D3—23no—
486C2×C3×D3—23no—
487C2×C3×D3—23no—
488C2×C3×D3—21no—
489C2×C3×D3—23no—
490D32—412no—
491C32×C4—21no—
492C32×C4—23no—
493C32×C4C22×D416yes—
494C3⋊Dic3—21no—
495C3⋊Dic3—23no—
496C3⋊Dic3C22×D416yes—
497C3×Dic3—21no—
498C3×Dic3—21no—
499C3×Dic3—23no—
500C3×Dic3—21no—
5012−1+4—188no—
502C2×#41—31no—
503C2×#41—31no—
504C2×#41—31no—
505C2×#41—93no—
506C2×#41—93no—
507C2×#41—93no—
508C2×#41—93no—
509C2×#41—93no—
510C2×#41—188no—
511C22×Q8—31no—
512C22×Q8—93no—
513C22×Q8—91no—
514C22×D4—93no—
515C23×C4—93no—
516#127—33no—
517#127—93no—
518#127—96no—
519#124—33no—
520#124—96no—
521#124—93no—
522#123—91no—
523#123—93no—
524C22⋊Q8—33no—
525C22⋊Q8—93no—
526C22⋊Q8—93no—
527C22⋊Q8—93no—
528#121—33no—
529#121—33no—
530#121—33no—
531#121—93no—
532#121—93no—
533#121—96no—
534#121—96no—
535#121—93no—
536#121—93no—
537#121—93no—
538#120—93no—
539#120—93no—
540#120—96no—
541C4×Q8—91no—
542C4×Q8—93no—
543C4×Q8—93no—
544C4×Q8D3211yescharacteristic, complemented
545C4×D4—33no—
546C4×D4—33no—
547C4×D4—96no—
548C4×D4—96no—
549C4×D4—93no—
550C4×D4—93no—
551#117—93no—
552#117—93no—
553C23×C3—33no—
554C23×C3—33no—
555C23×C3—33no—
556C23×C3—31no—
557C22×D3—31no—
558C22×D3—31no—
559C22×D3—61no—
560C22×D3—66no—
561C22×D3—66no—
562C22×D3—123no—
563C22×D3—123no—
564C22×D3—123no—
565C22×D3—123no—
566C22×D3C23×D313yes—
567C22×D3C23×D313yes—
568C22×D3C23×D313yes—
569C22×D3C23×D311yescharacteristic
570C3×Q8—24no—
571C3×Q8—66no—
572C3×Q8D3×D414yes—
573C3×Q8D3×D414yes—
574C3×D4—66no—
575C3×D4—66no—
576C3×D4—66no—
577C3×D4—126no—
578C3×D4—123no—
579C3×D4—123no—
580C2×C3×C4—23no—
581C2×C3×C4—23no—
582C2×C3×C4—21no—
583C2×C3×C4—31no—
584C2×C3×C4—31no—
585C2×C3×C4—33no—
586C2×C3×C4—31no—
587C2×C3×C4—66no—
588C2×C3×C4—66no—
589C2×C3×C4—66no—
590C2×C3×C4—66no—
591C2×C3×C4C23×D313yes—
592C2×C3×C4C23×D313yes—
593C2×C3×C4C23×D311yescharacteristic
594C2×C3×C4C23×D311yescharacteristic
595C2×C3×C4C23×D313yes—
596C2×C3×C4C23×D313yes—
597#67—62no—
598#67—66no—
599#67—66no—
600#67—612no—
601#67—612no—
602#67—66no—
603#67—126no—
604#67—123no—
605#67—123no—
606#67—123no—
607#67—123no—
608#67—126no—
609C2×Dic3—33no—
610C2×Dic3—33no—
611C2×Dic3—31no—
612C2×Dic3—31no—
613C2×Dic3—33no—
614C2×Dic3—33no—
615C2×Dic3—63no—
616C2×Dic3—61no—
617C2×Dic3—63no—
618C2×Dic3—612no—
619C2×Dic3—66no—
620C2×Dic3—66no—
621C2×Dic3C23×D311yescharacteristic
622C2×Dic3C23×D311yescharacteristic
623C2×Dic3C23×D311yescharacteristic
624C2×Dic3C23×D313yes—
625D12—26no—
626D12—26no—
627D12—26no—
628D12—43no—
629D12—43no—
630D12—46no—
631D12—62no—
632D12—66no—
633C4×D3—26no—
634C4×D3—26no—
635C4×D3—26no—
636C4×D3—26no—
637C4×D3—312no—
638C4×D3—312no—
639C4×D3—612no—
640C4×D3—62no—
641C4×D3—62no—
642C4×D3—66no—
643C4×D3—66no—
644C4×D3—612no—
645Dic6—26no—
646Dic6—312no—
647Dic6—312no—
648Dic6—612no—
649Dic6—66no—
650Dic6—66no—
651C2×C32C23×D411yescharacteristic
652C2×C32#58511yescharacteristic
653C2×C32#58511yescharacteristic
654C3⋊D3—22no—
655C3×D3—43no—
656C3×D3—43no—
657C3×D3—41no—
658C3×D3—43no—
659C24—93no—
660#41—64no—
661#41—64no—
662#41—64no—
663#41—1812no—
664#41—1812no—
665#41—1812no—
666#41—1812no—
667#41—1812no—
668C2×Q8—33no—
669C2×Q8—64no—
670C2×Q8—93no—
671C2×Q8—98no—
672C2×Q8—93no—
673C2×Q8—1812no—
674C2×Q8C2×D3211yescharacteristic
675C2×D4—33no—
676C2×D4—33no—
677C2×D4—33no—
678C2×D4—33no—
679C2×D4—33no—
680C2×D4—36no—
681C2×D4—91no—
682C2×D4—93no—
683C2×D4—96no—
684C2×D4—93no—
685C2×D4—96no—
686C2×D4—93no—
687C2×D4—93no—
688C2×D4—1812no—
689C22×C4—33no—
690C22×C4—33no—
691C22×C4—33no—
692C22×C4—33no—
693C22×C4—91no—
694C22×C4—96no—
695C22×C4—93no—
696C22×C4—93no—
697C22×C4—93no—
698C22×C4—1812no—
699C4⋊C4—31no—
700C4⋊C4—33no—
701C4⋊C4—91no—
702C4⋊C4—93no—
703C4⋊C4—93no—
704C4⋊C4—93no—
705C4⋊C4—93no—
706C4⋊C4C2×D3213yes—
707C22⋊C4—31no—
708C22⋊C4—33no—
709C22⋊C4—33no—
710C22⋊C4—33no—
711C22⋊C4—36no—
712C22⋊C4—91no—
713C22⋊C4—93no—
714C22⋊C4—93no—
715C22⋊C4—96no—
716C22⋊C4—93no—
717C22⋊C4—93no—
718C22⋊C4—91no—
719C42—96no—
720C42—93no—
721C42C2×D3213yes—
722C22×C3—21no—
723C22×C3—63no—
724C22×C3—63no—
725C22×C3—63no—
726C22×C3—61no—
727C22×C3—61no—
728C22×C3—63no—
729C22×C3—63no—
730C22×C3—63no—
731C22×C3—63no—
732C22×C3—61no—
733C22×C3—63no—
734C22×C3—63no—
735C22×C3C24×D311yescharacteristic
736C22×C3C24×D311yescharacteristic
737C2×D3—21no—
738C2×D3—23no—
739C2×D3—23no—
740C2×D3—23no—
741C2×D3—21no—
742C2×D3—23no—
743C2×D3—23no—
744C2×D3—23no—
745C2×D3—23no—
746C2×D3—23no—
747C2×D3—21no—
748C2×D3—23no—
749C2×D3—32no—
750C2×D3—32no—
751C2×D3—62no—
752C2×D3—61no—
753C2×D3—61no—
754C2×D3—61no—
755C2×D3—61no—
756C2×D3—121no—
757C2×D3—121no—
758C2×D3—1212no—
759C2×D3—1212no—
760C3×C4—21no—
761C3×C4—23no—
762C3×C4—23no—
763C3×C4—21no—
764C3×C4—26no—
765C3×C4—41no—
766C3×C4—43no—
767C3×C4—61no—
768C3×C4—63no—
769C3×C4—61no—
770C3×C4—61no—
771C3×C4C2×D3×D416yes—
772C3×C4C2×D3×D416yes—
773Dic3—23no—
774Dic3—21no—
775Dic3—21no—
776Dic3—21no—
777Dic3—36no—
778Dic3—36no—
779Dic3—66no—
780Dic3—63no—
781Dic3—61no—
782Dic3—61no—
783Dic3—63no—
784Dic3—123no—
785Dic3—121no—
786C32#348711yescharacteristic, complemented, Sylow
787C23—33no—
788C23—33no—
789C23—31no—
790C23—33no—
791C23—91no—
792C23—186no—
793C23—363no—
794C23—363no—
795Q8—66no—
796Q8—912no—
797Q8—186no—
798Q8#380214yes—
799D4—66no—
800D4—66no—
801D4—66no—
802D4—123no—
803D4—123no—
804D4—126no—
805D4—182no—
806D4—186no—
807D4—1812no—
808D4—186no—
809D4—366no—
810D4—363no—
811D4—363no—
812C2×C4—31no—
813C2×C4—33no—
814C2×C4—31no—
815C2×C4—31no—
816C2×C4—66no—
817C2×C4—66no—
818C2×C4—66no—
819C2×C4—66no—
820C2×C4—93no—
821C2×C4—912no—
822C2×C4—93no—
823C2×C4—91no—
824C2×C4—182no—
825C2×C4—186no—
826C2×C4—186no—
827C2×C4—1812no—
828C2×C4C22×D3213yes—
829C2×C4C22×D3211yescharacteristic
830C2×C4C22×D3213yes—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—123no—
835C2×C3—123no—
836C2×C3—123no—
837C2×C3—121no—
838C2×C3C22×D3×D411yescharacteristic
839C2×C3C22×D3×D411yescharacteristic
840C2×C3#596411yescharacteristic
841C2×C3#596411yescharacteristic
842C2×C3#596611yescharacteristic
843C2×C3#596811yescharacteristic
844D3—43no—
845D3—41no—
846D3—43no—
847D3—43no—
848D3—62no—
849D3—62no—
850D3—122no—
851C22—61no—
852C22—63no—
853C22—63no—
854C22—63no—
855C22—63no—
856C22—63no—
857C22—61no—
858C22—63no—
859C22—61no—
860C22—63no—
861C22—63no—
862C22—63no—
863C22—92no—
864C22—181no—
865C22—181no—
866C22—3612no—
867C22C23×D3211yescharacteristic
868C4—21no—
869C4—23no—
870C4—61no—
871C4—61no—
872C4—61no—
873C4—63no—
874C4—96no—
875C4—183no—
876C4—181no—
877C4C2×#380216yes—
878C3—21no—
879C3#8673611yescharacteristic, complemented
880C3#8678311yescharacteristic, complemented
881C2—123no—
882C2—123no—
883C2—121no—
884C2—123no—
885C2—182no—
886C2C22×#380211yescharacteristic
887C2#1059668811yescharacteristic
888C2#1059669611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
hypercenterC4×Q8D32
hypocenterC32#3487
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64319C2semidirect
2. C2×#64315C2semidirect
3. #10596043C2semidirect
4. C3×#5577C2semidirect
5. C3×#5576C2semidirect
6. #10595412C2semidirect
7. #10595409C2semidirect
8. #10594634C2semidirect
9. #10594632C2semidirect
10. #10594527C2semidirect
11. #10594525C2semidirect
12. #10594010C2semidirect
13. #10594006C2semidirect
14. #10593906C2semidirect
15. #10593905C2semidirect
21. C2×C3×#239C22semidirect
22. C2×C3×D3×Q8C22semidirect
31. C2×#3795C22semidirect
32. C2×D3×Dic6C22semidirect
33. C32×C4×Q8C22semidirect
34. Q8×C3⋊Dic3C22semidirect
36. #64096C22semidirect
38. C4×#634C22semidirect
39. C3×#897C22semidirect
40. C3×#895C22semidirect
41. C3×#895C22semidirect
42. C3×#895C22semidirect
43. C3×#875C22semidirect
44. C3×#874C22semidirect
45. C3×C4×D12C22semidirect
46. C3×C4×D12C22semidirect
50. #63915C22semidirect
51. #63914C22semidirect
52. #63914C22semidirect
53. #63908C22semidirect
54. #63908C22semidirect
55. #63908C22semidirect
56. #63902C22semidirect
57. C4×#625C22semidirect
58. C4×#625C22semidirect
59. #63899C22semidirect
60. #63899C22semidirect
61. #63898C22semidirect
62. #63885C22semidirect
63. #63885C22semidirect
64. #63885C22semidirect
65. #63885C22semidirect
66. #63863C22semidirect
67. #63856C22semidirect
92. #5577D3semidirect
93. #5576D3semidirect
103. Q8×C3⋊D3D4semidirect
176. C2×#239C2×D3semidirect
181. C2×D3×Q8C2×D3semidirect
203. C3×C4×Q8C2×D3semidirect
204. C3×C4×Q8C2×D3semidirect
236. #897C2×D3semidirect
239. #895C2×D3semidirect
240. #895C2×D3semidirect
241. #895C2×D3semidirect
266. #875C2×D3semidirect
267. #874C2×D3semidirect
268. C4×D12C2×D3semidirect
269. C4×D12C2×D3semidirect
544. C4×Q8D32semidirect
786. C32#3487semidirect
879. C3#86736semidirect
880. C3#86783semidirect

Maximal subgroups

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

subgroupindex
C2×#643192
C2×#643152
#105960432
C3×#55772
C3×#55762
#105954122
#105954092
#105946342
#105946322
#105945272
#105945252
#105940102
#105940062
#105939062
#105939052
#867833
#867363