Finite Group Databasebeta

← #11904490

Subgroups — #11904490

Order 1152.

3117 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D32×Q8C211yesmaximal, characteristic, complemented
2C2×#64315C211yesmaximal, characteristic, complemented
3#10596043C211yesmaximal, characteristic, complemented
4C3×#5576C211yesmaximal, characteristic, complemented
5C3×Q8×D12C211yesmaximal, characteristic, complemented
6#10595409C211yesmaximal, characteristic, complemented
7Q8×#625C211yesmaximal, characteristic, complemented
8#10594632C213yesmaximal, complemented
9#10594529C213yesmaximal, complemented
10#10594526C213yesmaximal, complemented
11#10594525C213yesmaximal, complemented
12#10594006C213yesmaximal, complemented
13#10593908C213yesmaximal, complemented
14#10593905C213yesmaximal, complemented
15#10593904C213yesmaximal, complemented
16#86759—31nomaximal
17#86735—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic, complemented
20C2×C3×D3×Q8C2211yescharacteristic
21C2×C3×D3×Q8C2211yescharacteristic
22C2×C3×D3×Q8C2211yescharacteristic, complemented
23D32×Q8—28no—
24#64315—28no—
25C2×C4×D32C2213yes—
26C2×#3798C2213yes—
27C2×#3797C2213yes—
28C2×#3796C2213yes—
29C2×#3795C2213yescomplemented
30C2×D3×Dic6C2213yes—
31C2×D3×Dic6C2213yes—
32C2×D3×Dic6C2213yescomplemented
33C32×C4×Q8C2211yescharacteristic, complemented
34Q8×C3⋊Dic3C2211yescharacteristic, complemented
35#64101C2213yes—
36#64096C2213yescomplemented
37#64081C2213yes—
38C4×#634C2213yescomplemented
39C3×#897C2213yes—
40C3×#897C2213yescomplemented
41C3×#897C2213yescomplemented
42C3×#895C2213yes—
43C3×#875C2213yescomplemented
44C3×C4×D12C2213yes—
45C3×C4×D12C2213yes—
46C3×#869C2213yescomplemented
47#63922C2213yes—
48#63922C2211yescharacteristic
49#63919C2216yescomplemented
50#63915C2216yescomplemented
51#63908C2213yes—
52#63902C2216yes—
53C4×#625C2213yes—
54C4×#625C2213yes—
55#63899C2213yes—
56#63899C2213yes—
57#63899C2216yescomplemented
58#63899C2216yescomplemented
59#63898C2216yes—
60#63885C2213yes—
61#63885C2213yes—
62#63873C2213yescomplemented
63#63863C2213yescomplemented
64#63856C2213yes—
65#63856C2213yescomplemented
66#63856C2213yescomplemented
67#63854C2216yes—
68#63854C2213yes—
69#63854C2213yes—
70C2×#1010—31no—
71C2×#1007—31no—
72C22×D3×Q8—31no—
73C22×D3×Q8—31no—
74C3×D4×Q8—31no—
75C3×#548—31no—
76#5831—31no—
77#5817—31no—
78Q8×#67—31no—
79Q8×#67—31no—
80#5727—33no—
81#5724—33no—
82#5677—33no—
83#5675—33no—
84#5633—33no—
85#5632—33no—
86#5632—33no—
87#5628—33no—
88#5628—33no—
89#5627—33no—
90#5606—33no—
91#5598—33no—
92#5576D311yescharacteristic, complemented
93Q8×D12D311yescharacteristic, complemented
94#5572—31no—
95#5572—31no—
96#5572—61no—
97#5552—33no—
98#5547—33no—
99#5547—33no—
100D4×Dic6—33no—
101C22×D32C2311yescharacteristic
102C2×C32×Q8C2311yescharacteristic
103Q8×C3⋊D3D418yescomplemented
104C2×C4×C3⋊D3C2313yes—
105C2×#634C2313yes—
106C3×#239—24no—
107C3×D3×Q8—24no—
108C3×D3×Q8—24no—
109C3×D3×Q8—24no—
110C2×C3×D12C2313yes—
111C2×C3×D12C2313yes—
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3C2313yes—
114C2×C3×C4×D3C2313yes—
115C2×C3×C4×D3C2313yes—
116C2×C3×C4×D3C2313yes—
117C2×C3×Dic6C2313yes—
118C2×C3×Dic6C2313yes—
119C2×C3×Dic6C2313yes—
120C2×#627C2316yes—
121C2×#627C2313yes—
122C2×#626C2313yes—
123C2×#626C2311yescharacteristic
124C2×#625C2313yes—
125C2×#625C2311yescharacteristic
126C2×#625C2313yes—
127C2×#624C2313yes—
128C2×D3×Dic3C2313yes—
129C2×D3×Dic3C2313yes—
130C2×D3×Dic3C2316yes—
131C4×D32—212no—
132#3798—212no—
133#3797—212no—
134#3796—212no—
135#3795—212no—
136D3×Dic6—212no—
137D3×Dic6—212no—
138D3×Dic6—212no—
139C32×C4⋊C4C2313yes—
140C32×C42C2313yes—
141#3752C2311yescharacteristic
142#3752C2313yes—
143C4⋊(C3⋊Dic3)C2313yes—
144#3750C2313yes—
145#3750C2313yes—
146C4×C3⋊Dic3C2316yes—
147C4×C3⋊Dic3C2313yes—
148C3×(C2×D3)⋊C4C2316yes—
149C3×(C2×D3)⋊C4C2313yes—
150C3×(C2×D3)⋊C4C2313yes—
151C3×(C2×D3)⋊C4C2313yes—
152C3×(C2×D3)⋊C4C2311yescharacteristic
153C3×C4⋊Dic3C2316yes—
154C3×C4⋊Dic3C2313yes—
155C3×C4⋊Dic3C2313yes—
156#3724C2316yes—
157#3724C2313yes—
158#3724C2313yes—
159(C2×D3)⋊Dic3C2313yes—
160(C2×D3)⋊Dic3C2316yes—
161(C2×D3)⋊Dic3C2313yes—
162(C2×D3)⋊Dic3C2313yes—
163(C2×D3)⋊Dic3C2311yescharacteristic
164#3486—91noSylow
165C2×C3×#41—31no—
166C22×C3×Q8—31no—
167C22×C3×Q8—31no—
168C22×C3×Q8—31no—
169#1010—68no—
170#1007—68no—
171C2×#239—33no—
172C2×#239C2×D311yescharacteristic, complemented
173C2×D3×Q8—31no—
174C2×D3×Q8—31no—
175C2×D3×Q8—33no—
176C2×D3×Q8—33no—
177C2×D3×Q8—33no—
178C2×D3×Q8—33no—
179C2×D3×Q8—33no—
180C2×D3×Q8—61no—
181C2×D3×Q8—68no—
182C2×D3×Q8—68no—
183C2×D3×Q8C2×D311yescharacteristic
184C2×D3×Q8C2×D311yescharacteristic
185C2×D3×Q8C2×D311yescharacteristic, complemented
186C2×#237—33no—
187C2×#237—33no—
188C2×#235—33no—
189C2×#235—33no—
190C2×#235—33no—
191C22×C4×D3—33no—
192C22×C4×D3—33no—
193C22×Dic6—33no—
194C22×Dic6—33no—
195C22×Dic6—33no—
196C3×C4⋊Q8—33no—
197C3×#124—33no—
198C3×C22⋊Q8—33no—
199C3×C22⋊Q8—33no—
200C3×C22⋊Q8—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—
209#946—33no—
210#946—33no—
211Q8×Dic3—31no—
212Q8×Dic3—31no—
213Q8×Dic3—61no—
214#944—33no—
215#944—33no—
216#939—33no—
217#939—33no—
218#938—33no—
219#937—31no—
220#937—33no—
221#936—33no—
222D4×Dic3—36no—
223#930—33no—
224C4×#67—33no—
225C4×#67—33no—
226C4×#67—33no—
227C4×#67—33no—
228#924—33no—
229#924—33no—
230#924—33no—
231#897C2×D313yes—
232#897C2×D313yescomplemented
233#897C2×D313yescomplemented
234#896—33no—
235#896—36no—
236#896—36no—
237#896—33no—
238#895C2×D313yes—
239#894—33no—
240#894—36no—
241#894—33no—
242#893—36no—
243#892—33no—
244#892—33no—
245#892—63no—
246#888—36no—
247#888—36no—
248#887—33no—
249#887—33no—
250#887—63no—
251#885—36no—
252#885—36no—
253#884—33no—
254#884—33no—
255#883—33no—
256#883—36no—
257#883—33no—
258#882—31no—
259#882—33no—
260#67⋊C4—36no—
261#67⋊C4—36no—
262#878—33no—
263#878—36no—
264#878—36no—
265#878—33no—
266#875C2×D313yescomplemented
267C4×D12C2×D313yes—
268C4×D12C2×D313yes—
269#872—33no—
270#872—33no—
271#872—63no—
272#869C2×D313yescomplemented
273C4×Dic6—33no—
274C4×Dic6—33no—
275C4×Dic6—63no—
276C22×C3⋊D3C2411yescharacteristic
277C22×C3×D3C2413yes—
278C22×C3×D3C2411yescharacteristic
279C22×C3×D3C2411yescharacteristic
280C22×C3×D3C2411yescharacteristic
281C2×D32—22no—
282C2×D32—22no—
283C2×D32—22no—
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×Dic3C2413yes—
294C2×C3×Dic3C2413yes—
295C2×C3×Dic3C2411yescharacteristic
296C2×C3×Dic3C2413yes—
297C3×D12—22no—
298C3×D12—26no—
299C3×D12—26no—
300C3×C4×D3—26no—
301C3×C4×D3—26no—
302C3×C4×D3—26no—
303C3×C4×D3—26no—
304C3×Dic6—26no—
305C3×Dic6—26no—
306C3×Dic6—26no—
307#627—212no—
308#627—26no—
309#626—26no—
310#626—22no—
311#625—26no—
312#625—22no—
313#625—26no—
314#624—26no—
315D3×Dic3—26no—
316D3×Dic3—26no—
317D3×Dic3—212no—
318C2×2−1+4—91no—
319C23×Q8—91no—
320D4×Q8—31no—
321D4×Q8—93no—
322D4×Q8—93no—
323D4×Q8—91no—
324#548—31no—
325#548—93no—
326#548—93no—
327#548—91no—
328#536—93no—
329#536—93no—
330#525—93no—
331#525—93no—
332#519—91no—
333C23×D3—31no—
334C23×D3—31no—
335C3×#41—64no—
336C2×C3×Q8—21no—
337C2×C3×Q8—33no—
338C2×C3×Q8—33no—
339C2×C3×Q8—33no—
340C2×C3×Q8—64no—
341C2×C3×Q8—64no—
342C2×C3×Q8—64no—
343C2×C3×Q8C22×D311yescharacteristic
344C2×C3×Q8C22×D311yescharacteristic
345C2×C3×D4—33no—
346C2×C3×D4—33no—
347C2×C3×D4—31no—
348C22×C3×C4—33no—
349C22×C3×C4—33no—
350C22×C3×C4—33no—
351C22×C3×C4—33no—
352C2×#67—33no—
353C2×#67—33no—
354C2×#67—31no—
355C2×#67—31no—
356C2×#67—33no—
357C2×#67—33no—
358C2×#67—31no—
359C2×#67—33no—
360C22×Dic3—36no—
361C22×Dic3—33no—
362C22×Dic3—33no—
363#239—24no—
364#239—612no—
365D3×Q8—24no—
366D3×Q8—24no—
367D3×Q8—24no—
368D3×Q8—38no—
369D3×Q8—38no—
370D3×Q8—68no—
371D3×Q8—612no—
372D3×Q8—612no—
373D3×Q8—612no—
374D3×Q8—612no—
375D3×Q8—612no—
376#237—612no—
377#237—612no—
378#235—612no—
379#235—612no—
380#235—612no—
381C2×D12—31no—
382C2×D12—33no—
383C2×D12C22×D311yescharacteristic
384C2×D12C22×D313yes—
385C2×D12C22×D313yes—
386C2×C4×D3—33no—
387C2×C4×D3—33no—
388C2×C4×D3—33no—
389C2×C4×D3—36no—
390C2×C4×D3—33no—
391C2×C4×D3—33no—
392C2×C4×D3—33no—
393C2×C4×D3—63no—
394C2×C4×D3—612no—
395C2×C4×D3—612no—
396C2×C4×D3C22×D313yes—
397C2×C4×D3C22×D313yes—
398C2×C4×D3C22×D313yes—
399C2×C4×D3C22×D313yes—
400C2×Dic6—33no—
401C2×Dic6—33no—
402C2×Dic6—36no—
403C2×Dic6—33no—
404C2×Dic6—33no—
405C2×Dic6—36no—
406C2×Dic6—63no—
407C2×Dic6—612no—
408C2×Dic6—612no—
409C2×Dic6—612no—
410C2×Dic6C22×D313yes—
411C2×Dic6C22×D313yes—
412C2×Dic6C22×D313yes—
413C3×C4⋊C4—23no—
414C3×C4⋊C4—33no—
415C3×C4⋊C4—36no—
416C3×C4⋊C4—33no—
417C3×C4⋊C4C22×D313yes—
418C3×C4⋊C4C22×D313yes—
419C3×C22⋊C4—31no—
420C3×C22⋊C4—33no—
421C3×C22⋊C4—33no—
422C3×C22⋊C4—36no—
423C3×C22⋊C4—33no—
424C3×C42—23no—
425C3×C42C22×D313yes—
426C3×C42C22×D313yes—
427#217—31no—
428#217—33no—
429#217—36no—
430#217—33no—
431#217—33no—
432(C2×D3)⋊C4—33no—
433(C2×D3)⋊C4—31no—
434(C2×D3)⋊C4—33no—
435(C2×D3)⋊C4—33no—
436(C2×D3)⋊C4—36no—
437(C2×D3)⋊C4—31no—
438(C2×D3)⋊C4—31no—
439(C2×D3)⋊C4—33no—
440(C2×D3)⋊C4—33no—
441(C2×D3)⋊C4—61no—
442(C2×D3)⋊C4—63no—
443(C2×D3)⋊C4C22×D311yescharacteristic
444(C2×D3)⋊C4C22×D313yes—
445(C2×D3)⋊C4C22×D313yes—
446(C2×D3)⋊C4C22×D313yes—
447(C2×D3)⋊C4C22×D316yes—
448C4⋊Dic3—33no—
449C4⋊Dic3—33no—
450C4⋊Dic3—63no—
451C4⋊Dic3C22×D313yes—
452C4⋊Dic3C22×D316yes—
453C4⋊Dic3C22×D313yes—
454Dic3⋊C4—33no—
455Dic3⋊C4—33no—
456Dic3⋊C4—33no—
457Dic3⋊C4—33no—
458Dic3⋊C4—33no—
459Dic3⋊C4—36no—
460Dic3⋊C4—33no—
461Dic3⋊C4—33no—
462Dic3⋊C4—36no—
463Dic3⋊C4—33no—
464Dic3⋊C4—63no—
465Dic3⋊C4—63no—
466C4×Dic3—36no—
467C4×Dic3—36no—
468C4×Dic3—33no—
469C4×Dic3—33no—
470C4×Dic3—66no—
471C4×Dic3—63no—
472C22×C32C2511yescharacteristic
473C2×C3⋊D3—21no—
474C2×C3⋊D3—21no—
475C2×C3⋊D3C22×D412yes—
476C2×C3×D3—21no—
477C2×C3×D3—21no—
478C2×C3×D3—21no—
479C2×C3×D3—21no—
480C2×C3×D3—23no—
481C2×C3×D3—21no—
482C2×C3×D3—23no—
483C2×C3×D3—21no—
484C2×C3×D3—21no—
485C2×C3×D3—23no—
486C2×C3×D32−1+412yescomplemented
487C2×C3×D32−1+412yescomplemented
488D32—28no—
489C32×C4—21no—
490C32×C4—23no—
491C32×C4C22×D416yes—
492C3⋊Dic3—23no—
493C3⋊Dic3—21no—
494C3⋊Dic3C22×D416yes—
495C3×Dic3—23no—
496C3×Dic3—23no—
497C3×Dic3—23no—
498C3×Dic3—21no—
4992−1+4—188no—
500C2×#41—31no—
501C2×#41—93no—
502C2×#41—93no—
503C2×#41—93no—
504C22×Q8—31no—
505C22×Q8—31no—
506C22×Q8—31no—
507C22×Q8—93no—
508C22×Q8—93no—
509C22×Q8—93no—
510C22×Q8—93no—
511C22×Q8—91no—
512C22×Q8—188no—
513C23×C4—93no—
514C4⋊Q8—33no—
515C4⋊Q8—96no—
516C4⋊Q8—93no—
517#124—33no—
518#124—96no—
519#124—93no—
520#123—93no—
521#123—93no—
522#123—96no—
523C22⋊Q8—33no—
524C22⋊Q8—33no—
525C22⋊Q8—33no—
526C22⋊Q8—93no—
527C22⋊Q8—93no—
528C22⋊Q8—96no—
529C22⋊Q8—96no—
530C22⋊Q8—93no—
531C22⋊Q8—93no—
532C22⋊Q8—93no—
533#121—33no—
534#121—93no—
535#121—93no—
536#121—93no—
537#120—91no—
538#120—93no—
539C4×Q8—91no—
540C4×Q8—93no—
541C4×Q8—93no—
542C4×Q8D3211yescharacteristic, complemented
543C4×D4—33no—
544C4×D4—33no—
545C4×D4—96no—
546C4×D4—96no—
547C4×D4—93no—
548C4×D4—93no—
549#117—93no—
550#117—93no—
551C23×C3—31no—
552C23×C3—31no—
553C23×C3—33no—
554C23×C3—31no—
555C22×D3—31no—
556C22×D3—31no—
557C22×D3—61no—
558C22×D3—62no—
559C22×D3—62no—
560C22×D3—62no—
561C22×D3—62no—
562C22×D3—62no—
563C22×D3—62no—
564C22×D3C23×D313yes—
565C22×D3C23×D311yescharacteristic
566C22×D3C23×D311yescharacteristic
567C22×D3C23×D311yescharacteristic
568C3×Q8—24no—
569C3×Q8—66no—
570C3×Q8—66no—
571C3×Q8—66no—
572C3×Q8D3×D414yes—
573C3×Q8D3×D414yes—
574C3×D4—62no—
575C3×D4—66no—
576C3×D4—66no—
577C2×C3×C4—23no—
578C2×C3×C4—23no—
579C2×C3×C4—21no—
580C2×C3×C4—33no—
581C2×C3×C4—31no—
582C2×C3×C4—33no—
583C2×C3×C4—33no—
584C2×C3×C4—66no—
585C2×C3×C4—66no—
586C2×C3×C4—66no—
587C2×C3×C4—66no—
588C2×C3×C4C23×D313yes—
589C2×C3×C4C23×D313yes—
590C2×C3×C4C23×D311yescharacteristic
591C2×C3×C4C23×D311yescharacteristic
592C2×C3×C4C23×D313yes—
593C2×C3×C4C23×D313yes—
594#67—62no—
595#67—66no—
596#67—66no—
597#67—66no—
598#67—66no—
599#67—62no—
600#67—66no—
601#67—62no—
602C2×Dic3—33no—
603C2×Dic3—33no—
604C2×Dic3—31no—
605C2×Dic3—31no—
606C2×Dic3—33no—
607C2×Dic3—33no—
608C2×Dic3—63no—
609C2×Dic3—61no—
610C2×Dic3—63no—
611C2×Dic3—66no—
612C2×Dic3—66no—
613C2×Dic3—612no—
614C2×Dic3C23×D311yescharacteristic
615C2×Dic3C23×D313yes—
616C2×Dic3C23×D313yes—
617C2×Dic3C23×D313yes—
618D12—22no—
619D12—26no—
620D12—26no—
621D12—62no—
622D12—66no—
623C4×D3—26no—
624C4×D3—26no—
625C4×D3—26no—
626C4×D3—26no—
627C4×D3—312no—
628C4×D3—312no—
629C4×D3—612no—
630C4×D3—66no—
631C4×D3—66no—
632C4×D3—66no—
633C4×D3—66no—
634C4×D3—612no—
635Dic6—26no—
636Dic6—26no—
637Dic6—26no—
638Dic6—312no—
639Dic6—312no—
640Dic6—612no—
641Dic6—66no—
642Dic6—612no—
643Dic6—612no—
644Dic6—66no—
645C2×C32C23×D411yescharacteristic
646C2×C32C2×2−1+411yescharacteristic
647C2×C32C2×2−1+411yescharacteristic
648C3⋊D3—22no—
649C3×D3—22no—
650C3×D3—22no—
651C3×D3—43no—
652C3×D3—41no—
653C24—91no—
654#41—64no—
655#41—1812no—
656#41—1812no—
657#41—1812no—
658C2×Q8—33no—
659C2×Q8—33no—
660C2×Q8—33no—
661C2×Q8—64no—
662C2×Q8—64no—
663C2×Q8—64no—
664C2×Q8—96no—
665C2×Q8—93no—
666C2×Q8—98no—
667C2×Q8—93no—
668C2×Q8—1812no—
669C2×Q8—1812no—
670C2×Q8—1812no—
671C2×Q8—1812no—
672C2×Q8C2×D3211yescharacteristic
673C2×D4—31no—
674C2×D4—33no—
675C2×D4—33no—
676C2×D4—91no—
677C2×D4—93no—
678C2×D4—93no—
679C2×D4—91no—
680C2×D4—93no—
681C22×C4—33no—
682C22×C4—33no—
683C22×C4—33no—
684C22×C4—33no—
685C22×C4—93no—
686C22×C4—93no—
687C22×C4—93no—
688C22×C4—96no—
689C22×C4—93no—
690C22×C4—1812no—
691C4⋊C4—33no—
692C4⋊C4—33no—
693C4⋊C4—36no—
694C4⋊C4—96no—
695C4⋊C4—93no—
696C4⋊C4—93no—
697C4⋊C4—93no—
698C4⋊C4—93no—
699C4⋊C4—93no—
700C4⋊C4C2×D3213yes—
701C22⋊C4—31no—
702C22⋊C4—33no—
703C22⋊C4—33no—
704C22⋊C4—33no—
705C22⋊C4—36no—
706C22⋊C4—91no—
707C22⋊C4—93no—
708C22⋊C4—93no—
709C22⋊C4—96no—
710C22⋊C4—93no—
711C22⋊C4—93no—
712C22⋊C4—91no—
713C42—96no—
714C42—93no—
715C42C2×D3213yes—
716C22×C3—21no—
717C22×C3—32no—
718C22×C3—32no—
719C22×C3—61no—
720C22×C3—61no—
721C22×C3—61no—
722C22×C3—61no—
723C22×C3—63no—
724C22×C3—61no—
725C22×C3—63no—
726C22×C3—61no—
727C22×C3—61no—
728C22×C3—63no—
729C22×C3C24×D311yescharacteristic
730C22×C3C24×D311yescharacteristic
731C2×D3—21no—
732C2×D3—21no—
733C2×D3—21no—
734C2×D3—21no—
735C2×D3—21no—
736C2×D3—23no—
737C2×D3—21no—
738C2×D3—23no—
739C2×D3—23no—
740C2×D3—21no—
741C2×D3—32no—
742C2×D3—32no—
743C2×D3—62no—
744C2×D3—68no—
745C2×D3—68no—
746C2×D3—61no—
747C2×D3—61no—
748C2×D3—61no—
749C2×D3—61no—
750C2×D3—121no—
751C2×D3—121no—
752C2×D3#100712yescomplemented
753C2×D3#101012yescomplemented
754C3×C4—21no—
755C3×C4—23no—
756C3×C4—21no—
757C3×C4—23no—
758C3×C4—26no—
759C3×C4—41no—
760C3×C4—43no—
761C3×C4—61no—
762C3×C4—63no—
763C3×C4—63no—
764C3×C4—63no—
765C3×C4C2×D3×D416yes—
766C3×C4C2×D3×D416yes—
767Dic3—23no—
768Dic3—23no—
769Dic3—23no—
770Dic3—21no—
771Dic3—36no—
772Dic3—36no—
773Dic3—66no—
774Dic3—63no—
775Dic3—61no—
776Dic3—63no—
777Dic3—61no—
778Dic3—123no—
779Dic3—121no—
780C32#348611yescharacteristic, complemented, Sylow
781C23—31no—
782C23—31no—
783C23—31no—
784C23—33no—
785C23—91no—
786C23—182no—
787C23—182no—
788C23—182no—
789Q8—66no—
790Q8—66no—
791Q8—66no—
792Q8—912no—
793Q8—1812no—
794Q8—186no—
795Q8#380214yes—
796D4—62no—
797D4—66no—
798D4—66no—
799D4—182no—
800D4—186no—
801D4—186no—
802D4—186no—
803D4—182no—
804C2×C4—33no—
805C2×C4—33no—
806C2×C4—31no—
807C2×C4—33no—
808C2×C4—66no—
809C2×C4—66no—
810C2×C4—66no—
811C2×C4—66no—
812C2×C4—93no—
813C2×C4—912no—
814C2×C4—93no—
815C2×C4—91no—
816C2×C4—186no—
817C2×C4—186no—
818C2×C4—186no—
819C2×C4—1812no—
820C2×C4C22×D3213yes—
821C2×C4C22×D3211yescharacteristic
822C2×C4C22×D3213yes—
823C2×C3—21no—
824C2×C3—21no—
825C2×C3—21no—
826C2×C3—62no—
827C2×C3—62no—
828C2×C3—121no—
829C2×C3—123no—
830C2×C3C22×D3×D411yescharacteristic
831C2×C3C22×D3×D411yescharacteristic
832C2×C3C2×#100711yescharacteristic
833C2×C3C2×#101011yescharacteristic
834C2×C3D3×2−1+411yescharacteristic
835C2×C3D3×2−1+411yescharacteristic
836D3—22no—
837D3—22no—
838D3—43no—
839D3—41no—
840D3—62no—
841D3—62no—
842D3—122no—
843C22—32no—
844C22—32no—
845C22—61no—
846C22—61no—
847C22—61no—
848C22—61no—
849C22—61no—
850C22—63no—
851C22—61no—
852C22—63no—
853C22—63no—
854C22—61no—
855C22—92no—
856C22—188no—
857C22—181no—
858C22—181no—
859C22C23×D3211yescharacteristic
860C4—21no—
861C4—23no—
862C4—61no—
863C4—63no—
864C4—63no—
865C4—63no—
866C4—96no—
867C4—183no—
868C4—181no—
869C4C2×#380216yes—
870C3—21no—
871C3#8673511yescharacteristic, complemented
872C3#8675911yescharacteristic, complemented
873C2—62no—
874C2—62no—
875C2—121no—
876C2—123no—
877C2—182no—
878C2C22×#380211yescharacteristic
879C2D3×#100711yescharacteristic
880C2D3×#101011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
hypercenterC4×Q8D32
hypocenterC32#3486
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×D32×Q8C2semidirect
2. C2×#64315C2semidirect
3. #10596043C2semidirect
4. C3×#5576C2semidirect
5. C3×Q8×D12C2semidirect
6. #10595409C2semidirect
7. Q8×#625C2semidirect
8. #10594632C2semidirect
9. #10594529C2semidirect
10. #10594526C2semidirect
11. #10594525C2semidirect
12. #10594006C2semidirect
13. #10593908C2semidirect
14. #10593905C2semidirect
15. #10593904C2semidirect
19. C2×C3×#239C22semidirect
22. C2×C3×D3×Q8C22semidirect
29. C2×#3795C22semidirect
32. C2×D3×Dic6C22semidirect
33. C32×C4×Q8C22semidirect
34. Q8×C3⋊Dic3C22semidirect
36. #64096C22semidirect
38. C4×#634C22semidirect
40. C3×#897C22semidirect
41. C3×#897C22semidirect
43. C3×#875C22semidirect
46. C3×#869C22semidirect
49. #63919C22semidirect
50. #63915C22semidirect
57. #63899C22semidirect
58. #63899C22semidirect
62. #63873C22semidirect
63. #63863C22semidirect
65. #63856C22semidirect
66. #63856C22semidirect
92. #5576D3semidirect
93. Q8×D12D3semidirect
103. Q8×C3⋊D3D4semidirect
172. C2×#239C2×D3semidirect
185. C2×D3×Q8C2×D3semidirect
203. C3×C4×Q8C2×D3semidirect
204. C3×C4×Q8C2×D3semidirect
232. #897C2×D3semidirect
233. #897C2×D3semidirect
266. #875C2×D3semidirect
272. #869C2×D3semidirect
486. C2×C3×D32−1+4semidirect
487. C2×C3×D32−1+4semidirect
542. C4×Q8D32semidirect
752. C2×D3#1007semidirect
753. C2×D3#1010semidirect
780. C32#3486semidirect
871. C3#86735semidirect
872. C3#86759semidirect

Maximal subgroups

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

subgroupindex
C2×D32×Q82
C2×#643152
#105960432
C3×#55762
C3×Q8×D122
#105954092
Q8×#6252
#105946322
#105945292
#105945262
#105945252
#105940062
#105939082
#105939052
#105939042
#867593
#867353