Finite Group Databasebeta

← #11904492

Subgroups — #11904492

Order 1152.

3124 conjugacy classes of subgroups.

The subgroup lattice has 889 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1007C211yesmaximal, characteristic, complemented
2C2×D32×Q8C211yesmaximal, characteristic, complemented
3Q8×#638C211yesmaximal, characteristic, complemented
4C3×Q8×#67C211yesmaximal, characteristic, complemented
5#10595424C213yesmaximal, complemented
6#10595414C211yesmaximal, characteristic, complemented
7#10595409C211yesmaximal, characteristic, complemented
8#10595403C213yesmaximal, complemented
9#10595400C213yesmaximal, complemented
10#10595356C213yesmaximal, complemented
11#10595347C211yesmaximal, characteristic, complemented
12#10595060C213yesmaximal, complemented
13#10594899C213yesmaximal, complemented
14#10594884C213yesmaximal, complemented
15#10594830C213yesmaximal, complemented
16#87294—31nomaximal
17#86759—31nomaximal
18C22×C32×Q8C2211yescharacteristic, complemented
19C2×Q8×C3⋊D3C2211yescharacteristic
20C3×#1007—28no—
21C2×C3×#239C2213yes—
22C2×C3×#239C2211yescharacteristic, complemented
23C2×C3×D3×Q8C2211yescharacteristic
24C2×C3×D3×Q8C2211yescharacteristic
25C2×C3×D3×Q8C2213yescomplemented
26C2×C3×#235C2213yes—
27C2×C3×#235C2213yescomplemented
28D32×Q8—28no—
29C2×C4×D32C2213yes—
30C2×#3797C2213yes—
31C2×D3×Dic6C2213yes—
32C2×D3×Dic6C2213yes—
33#64155C2213yes—
34Q8×C3⋊Dic3C2211yescharacteristic, complemented
35#64153C2213yescomplemented
36C4×#638C2213yes—
37#64133C2213yescomplemented
38C3×#946C2213yes—
39C3×Q8×Dic3C2211yescharacteristic, complemented
40C3×#944C2213yescomplemented
41C3×C4×#67C2213yes—
42C3×#924C2213yescomplemented
43#63983C2211yescharacteristic
44#63970C2213yes—
45#63969C2213yes—
46#63959C2216yescomplemented
47#63958C2213yes—
48#63922C2213yes—
49#63916C2213yes—
50#63908C2213yes—
51#63904C2216yes—
52C4×#626C2213yes—
53C4×#625C2213yes—
54#63888C2213yes—
55#63887C2213yes—
56#63884C2213yes—
57#63884C2216yes—
58#63879C2216yes—
59#63863C2213yescomplemented
60#63860C2213yescomplemented
61#63857C2213yescomplemented
62#63856C2213yescomplemented
63#63855C2213yes—
64#63851C2216yescomplemented
65#63851C2216yescomplemented
66#63843C2213yescomplemented
67Dic3×Dic6C2213yescomplemented
68#63841C2213yes—
69#63839C2216yescomplemented
70C2×C3×2−1+4—31no—
71C2×#1007D311yescharacteristic, complemented
72C22×D3×Q8—31no—
73C22×D3×Q8—31no—
74C3×D4×Q8—31no—
75#5831—31no—
76#5831—31no—
77#5831—33no—
78#5831—33no—
79#5828—33no—
80#5828—33no—
81#5825—33no—
82#5825—33no—
83#5817—31no—
84Q8×#67—31no—
85Q8×#67—31no—
86Q8×#67—33no—
87Q8×#67—33no—
88Q8×#67—61no—
89Q8×#67D311yescharacteristic, complemented
90#5812—31no—
91#5727—33no—
92#5724—33no—
93#5633—33no—
94#5632—33no—
95#5628—33no—
96#5627—33no—
97#5576—31no—
98#5572—31no—
99#5552—33no—
100#5547—33no—
101C22×D32C2311yescharacteristic
102C2×C32×Q8—24no—
103C2×C32×Q8C2313yes—
104C2×C32×Q8C2311yescharacteristic
105C22×C32×C4C2313yes—
106C2×#638C2311yescharacteristic
107Q8×C3⋊D3—24no—
108C2×C4×C3⋊D3C2313yes—
109C2×#634C2313yes—
110C2×C3×#67C2311yescharacteristic
111C2×C3×#67C2311yescharacteristic
112C2×C3×#67C2313yes—
113C3×#239—24no—
114C3×#239—212no—
115C3×D3×Q8—24no—
116C3×D3×Q8—212no—
117C3×D3×Q8D418yescomplemented
118C3×#235—212no—
119C3×#235—212no—
120C2×C3×D12C2313yes—
121C2×C3×D12C2313yes—
122C2×C3×C4×D3C2313yes—
123C2×C3×C4×D3C2313yes—
124C2×C3×C4×D3C2316yes—
125C2×C3×C4×D3C2313yes—
126C2×C3×Dic6C2313yes—
127C2×C3×Dic6C2313yes—
128C2×C3×Dic6C2313yes—
129C2×#627C2316yes—
130C2×#626C2313yes—
131C2×#625C2313yes—
132C2×#624C2313yes—
133C2×D3×Dic3C2313yes—
134C2×D3×Dic3C2313yes—
135C4×D32—212no—
136#3797—212no—
137D3×Dic6—212no—
138D3×Dic6—212no—
139#3757C2313yes—
140#3752C2313yes—
141C4⋊(C3⋊Dic3)C2313yes—
142#3750C2316yes—
143#3750C2313yes—
144C4×C3⋊Dic3C2313yes—
145C3×#217C2313yes—
146C3×(C2×D3)⋊C4C2313yes—
147C3×C4⋊Dic3C2313yes—
148C3×Dic3⋊C4C2316yes—
149C3×Dic3⋊C4C2313yes—
150C3×C4×Dic3C2313yes—
151#3724C2313yes—
152Dic3⋊Dic3C2313yes—
153Dic3⋊Dic3C2313yes—
154Dic3⋊Dic3C2313yes—
155#3722C2311yescharacteristic
156(C2×D3)⋊Dic3C2313yes—
157(C2×D3)⋊Dic3C2313yes—
158(C2×D3)⋊Dic3C2313yes—
159(C2×D3)⋊Dic3C2316yes—
160(C2×D3)⋊Dic3C2316yes—
161(C2×D3)⋊Dic3C2311yescharacteristic
162(C2×D3)⋊Dic3C2311yescharacteristic
163Dic32C2316yes—
164#3486—91noSylow
165C3×2−1+4—68no—
166C2×C3×#41—33no—
167C2×C3×#41—31no—
168C2×C3×#41—33no—
169C2×C3×#41—33no—
170C22×C3×Q8—21no—
171C22×C3×Q8—31no—
172C22×C3×Q8—31no—
173C22×C3×Q8—33no—
174C22×C3×Q8C2×D311yescharacteristic, complemented
175C22×C3×Q8C2×D311yescharacteristic, complemented
176#1007—28no—
177C2×#239C2×D313yes—
178C2×#239C2×D311yescharacteristic, complemented
179C2×D3×Q8—31no—
180C2×D3×Q8—31no—
181C2×D3×Q8—33no—
182C2×D3×Q8—33no—
183C2×D3×Q8—33no—
184C2×D3×Q8—33no—
185C2×D3×Q8—61no—
186C2×D3×Q8—68no—
187C2×D3×Q8—68no—
188C2×D3×Q8C2×D311yescharacteristic
189C2×D3×Q8C2×D311yescharacteristic
190C2×D3×Q8C2×D313yescomplemented
191C2×#235C2×D313yes—
192C2×#235C2×D313yescomplemented
193C22×C4×D3—33no—
194C22×C4×D3—33no—
195C22×Dic6—33no—
196C22×Dic6—33no—
197C3×C4⋊Q8—33no—
198C3×C22⋊Q8—33no—
199C3×C22⋊Q8—33no—
200C3×C4×Q8—31no—
201C3×C4×D4—33no—
202#947—33no—
203#946—33no—
204#946—33no—
205#946—33no—
206#946—33no—
207#946—33no—
208#946—63no—
209#946C2×D313yes—
210Q8×Dic3—31no—
211Q8×Dic3—31no—
212Q8×Dic3—33no—
213Q8×Dic3—33no—
214Q8×Dic3—61no—
215Q8×Dic3C2×D311yescharacteristic, complemented
216#944—33no—
217#944—33no—
218#944—36no—
219#944—63no—
220#944C2×D313yescomplemented
221#939—33no—
222#938—33no—
223#938—33no—
224#938—33no—
225#938—33no—
226#937—31no—
227#937—31no—
228#937—33no—
229#936—33no—
230#936—36no—
231#936—33no—
232#935—33no—
233#935—33no—
234#935—36no—
235#930—33no—
236C4×#67—33no—
237C4×#67—33no—
238C4×#67—33no—
239C4×#67—33no—
240C4×#67—36no—
241C4×#67—36no—
242C4×#67—33no—
243C4×#67—63no—
244C4×#67C2×D313yes—
245#926—33no—
246#926—33no—
247#924—33no—
248#924—33no—
249#924—33no—
250#924—33no—
251#924—36no—
252#924—36no—
253#924—63no—
254#924C2×D313yescomplemented
255#897—33no—
256#896—36no—
257#896—36no—
258#896—33no—
259#895—33no—
260#894—33no—
261#894—36no—
262#893—36no—
263#892—33no—
264#888—36no—
265#887—33no—
266#885—36no—
267#884—33no—
268#883—33no—
269#882—33no—
270#67⋊C4—36no—
271#878—33no—
272#875—33no—
273C4×D12—33no—
274#872—33no—
275C4×Dic6—33no—
276C23×C32C2411yescharacteristic
277C22×C3⋊D3C2411yescharacteristic
278C22×C3×D3C2413yes—
279C22×C3×D3C2411yescharacteristic
280C22×C3×D3C2411yescharacteristic
281C2×D32—22no—
282C2×D32—22no—
283C2×D32—22no—
284C32×Q8—26no—
285C32×Q8C2×D414yes—
286C2×C32×C4—26no—
287C2×C32×C4C2413yes—
288C2×C32×C4C2413yes—
289#638—22no—
290C2×C3⋊Dic3C2413yes—
291C2×C3⋊Dic3C2411yescharacteristic
292C2×C3⋊Dic3C2413yes—
293C4×C3⋊D3—26no—
294#634—26no—
295C3×#67—22no—
296C3×#67—22no—
297C3×#67—26no—
298C2×C3×Dic3C2413yes—
299C2×C3×Dic3C2411yescharacteristic
300C2×C3×Dic3C2413yes—
301C2×C3×Dic3C2411yescharacteristic
302C2×C3×Dic3C2413yes—
303C3×D12—26no—
304C3×D12—26no—
305C3×C4×D3—26no—
306C3×C4×D3—26no—
307C3×C4×D3—212no—
308C3×C4×D3C2×D4112yes—
309C3×Dic6—26no—
310C3×Dic6—26no—
311C3×Dic6C2×D4112yes—
312#627—212no—
313#626—26no—
314#625—26no—
315#624—26no—
316D3×Dic3—26no—
317D3×Dic3—26no—
318C2×2−1+4—31no—
319C23×Q8—91no—
320D4×Q8—31no—
321D4×Q8—93no—
322D4×Q8—93no—
323D4×Q8—91no—
324#548—93no—
325#548—91no—
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—612no—
336C3×#41—612no—
337C3×#41—612no—
338C3×#41—64no—
339C2×C3×Q8—24no—
340C2×C3×Q8—24no—
341C2×C3×Q8—21no—
342C2×C3×Q8—23no—
343C2×C3×Q8—38no—
344C2×C3×Q8—33no—
345C2×C3×Q8—33no—
346C2×C3×Q8—33no—
347C2×C3×Q8—44no—
348C2×C3×Q8—612no—
349C2×C3×Q8—64no—
350C2×C3×Q8C22×D313yes—
351C2×C3×Q8C22×D313yes—
352C2×C3×Q8C22×D311yescharacteristic
353C2×C3×Q8C22×D311yescharacteristic
354C2×C3×D4—31no—
355C2×C3×D4—33no—
356C2×C3×D4—31no—
357C2×C3×D4—33no—
358C2×C3×D4—33no—
359C22×C3×C4—23no—
360C22×C3×C4—33no—
361C22×C3×C4—36no—
362C22×C3×C4—33no—
363C22×C3×C4—33no—
364C22×C3×C4C22×D313yes—
365C22×C3×C4C22×D313yes—
366C2×#67—31no—
367C2×#67—31no—
368C2×#67—33no—
369C2×#67—33no—
370C2×#67—33no—
371C2×#67—61no—
372C2×#67C22×D311yescharacteristic
373C2×#67C22×D313yes—
374C2×#67C22×D311yescharacteristic
375C22×Dic3—33no—
376C22×Dic3—33no—
377#239—24no—
378#239—212no—
379D3×Q8—24no—
380D3×Q8—212no—
381D3×Q8—612no—
382D3×Q8—612no—
383D3×Q8—64no—
384D3×Q8—64no—
385D3×Q8—612no—
386D3×Q8—612no—
387D3×Q8—124no—
388D3×Q8#6718yescomplemented
389#235—212no—
390#235—212no—
391C2×D12—33no—
392C2×D12C22×D313yes—
393C2×D12C22×D313yes—
394C2×C4×D3—33no—
395C2×C4×D3—33no—
396C2×C4×D3—33no—
397C2×C4×D3—33no—
398C2×C4×D3—33no—
399C2×C4×D3—33no—
400C2×C4×D3—63no—
401C2×C4×D3—612no—
402C2×C4×D3—612no—
403C2×C4×D3C22×D313yes—
404C2×C4×D3C22×D316yes—
405C2×C4×D3C22×D313yes—
406C2×C4×D3C22×D313yes—
407C2×Dic6—33no—
408C2×Dic6—33no—
409C2×Dic6—36no—
410C2×Dic6—36no—
411C2×Dic6—63no—
412C2×Dic6—612no—
413C2×Dic6—612no—
414C2×Dic6C22×D313yes—
415C2×Dic6C22×D313yes—
416C2×Dic6C22×D313yes—
417C3×C4⋊C4—33no—
418C3×C4⋊C4—36no—
419C3×C4⋊C4—33no—
420C3×C22⋊C4—33no—
421C3×C22⋊C4—33no—
422C3×C42—33no—
423#217—33no—
424#217—33no—
425#217—31no—
426#217—33no—
427#217—36no—
428#217—36no—
429#217—33no—
430#217—33no—
431#217—31no—
432#217—63no—
433#217C22×D313yes—
434(C2×D3)⋊C4—31no—
435(C2×D3)⋊C4—33no—
436(C2×D3)⋊C4—33no—
437(C2×D3)⋊C4—36no—
438(C2×D3)⋊C4—33no—
439(C2×D3)⋊C4—36no—
440(C2×D3)⋊C4—31no—
441(C2×D3)⋊C4—33no—
442(C2×D3)⋊C4—33no—
443(C2×D3)⋊C4—31no—
444(C2×D3)⋊C4—31no—
445(C2×D3)⋊C4—63no—
446(C2×D3)⋊C4C22×D313yes—
447C4⋊Dic3—33no—
448C4⋊Dic3—33no—
449C4⋊Dic3—33no—
450C4⋊Dic3—33no—
451C4⋊Dic3—33no—
452C4⋊Dic3—63no—
453C4⋊Dic3C22×D313yes—
454Dic3⋊C4—33no—
455Dic3⋊C4—36no—
456Dic3⋊C4—36no—
457Dic3⋊C4—33no—
458Dic3⋊C4—33no—
459Dic3⋊C4—33no—
460Dic3⋊C4—33no—
461Dic3⋊C4—33no—
462Dic3⋊C4—33no—
463Dic3⋊C4—66no—
464Dic3⋊C4—63no—
465Dic3⋊C4C22×D313yes—
466Dic3⋊C4C22×D316yes—
467C4×Dic3—33no—
468C4×Dic3—33no—
469C4×Dic3—36no—
470C4×Dic3—36no—
471C4×Dic3—63no—
472C4×Dic3C22×D313yes—
473C22×C32—21no—
474C22×C32—21no—
475C22×C32—21no—
476C22×C32C2511yescharacteristic
477C2×C3⋊D3—21no—
478C2×C3⋊D3—21no—
479C2×C3⋊D32−1+412yescomplemented
480C2×C3×D3—21no—
481C2×C3×D3—21no—
482C2×C3×D3—21no—
483C2×C3×D3—21no—
484C2×C3×D3—23no—
485C2×C3×D3—23no—
486C2×C3×D3—23no—
487C2×C3×D3C22×D412yes—
488C2×C3×D32−1+412yescomplemented
489D32—28no—
490C32×C4—23no—
491C32×C4C22×D416yes—
492C3⋊Dic3—21no—
493C3⋊Dic3—23no—
494C3⋊Dic3—23no—
495C3×Dic3—23no—
496C3×Dic3—21no—
497C3×Dic3—23no—
498C3×Dic3—21no—
499C3×Dic3C22×D416yes—
5002−1+4—68no—
501C2×#41—33no—
502C2×#41—31no—
503C2×#41—33no—
504C2×#41—33no—
505C22×Q8—31no—
506C22×Q8—31no—
507C22×Q8—33no—
508C22×Q8—93no—
509C22×Q8—93no—
510C22×Q8—93no—
511C22×Q8—91no—
512C22×Q8—188no—
513C22×Q8D3211yescharacteristic, complemented
514C23×C4—93no—
515C4⋊Q8—33no—
516C4⋊Q8—96no—
517C4⋊Q8—93no—
518#124—93no—
519#124—96no—
520#124—93no—
521#123—93no—
522#123—93no—
523#123—96no—
524C22⋊Q8—33no—
525C22⋊Q8—33no—
526C22⋊Q8—93no—
527C22⋊Q8—96no—
528C22⋊Q8—96no—
529C22⋊Q8—93no—
530C22⋊Q8—93no—
531C22⋊Q8—93no—
532C22⋊Q8—93no—
533C22⋊Q8—93no—
534#121—93no—
535#121—93no—
536#121—93no—
537#121—93no—
538#120—93no—
539#120—91no—
540C4×Q8—31no—
541C4×Q8—93no—
542C4×Q8—93no—
543C4×Q8—91no—
544C4×D4—33no—
545C4×D4—93no—
546C4×D4—96no—
547C4×D4—96no—
548C4×D4—93no—
549C4×D4—93no—
550#117—93no—
551#117—93no—
552C23×C3—21no—
553C23×C3—31no—
554C23×C3—31no—
555C23×C3—33no—
556C23×C3C23×D311yescharacteristic
557C23×C3C23×D311yescharacteristic
558C22×D3—31no—
559C22×D3—31no—
560C22×D3—61no—
561C22×D3—62no—
562C22×D3—62no—
563C22×D3—62no—
564C22×D3—62no—
565C22×D3—62no—
566C22×D3—62no—
567C22×D3C23×D313yes—
568C22×D3C23×D311yescharacteristic
569C22×D3C23×D311yescharacteristic
570C3×Q8—26no—
571C3×Q8—26no—
572C3×Q8—24no—
573C3×Q8—312no—
574C3×Q8—46no—
575C3×Q8—66no—
576C3×Q8—66no—
577C3×Q8D3×D414yes—
578C3×Q8C2×#6714yes—
579C3×D4—66no—
580C3×D4—66no—
581C3×D4—62no—
582C3×D4—62no—
583C3×D4—66no—
584C2×C3×C4—26no—
585C2×C3×C4—26no—
586C2×C3×C4—23no—
587C2×C3×C4—23no—
588C2×C3×C4—33no—
589C2×C3×C4—312no—
590C2×C3×C4—33no—
591C2×C3×C4—31no—
592C2×C3×C4—31no—
593C2×C3×C4—33no—
594C2×C3×C4—46no—
595C2×C3×C4—612no—
596C2×C3×C4—66no—
597C2×C3×C4—66no—
598C2×C3×C4C23×D313yes—
599C2×C3×C4C23×D313yes—
600C2×C3×C4C23×D313yes—
601C2×C3×C4C23×D313yes—
602#67—22no—
603#67—22no—
604#67—26no—
605#67—66no—
606#67—66no—
607#67—62no—
608#67—62no—
609#67—64no—
610#67—66no—
611C2×Dic3—31no—
612C2×Dic3—33no—
613C2×Dic3—33no—
614C2×Dic3—31no—
615C2×Dic3—33no—
616C2×Dic3—33no—
617C2×Dic3—61no—
618C2×Dic3—63no—
619C2×Dic3—63no—
620C2×Dic3—66no—
621C2×Dic3—66no—
622C2×Dic3C23×D313yes—
623C2×Dic3C23×D311yescharacteristic
624C2×Dic3C23×D311yescharacteristic
625C2×Dic3C23×D313yes—
626C2×Dic3C23×D313yes—
627D12—26no—
628D12—26no—
629D12—66no—
630C4×D3—26no—
631C4×D3—26no—
632C4×D3—212no—
633C4×D3—66no—
634C4×D3—66no—
635C4×D3—66no—
636C4×D3—66no—
637C4×D3—66no—
638C4×D3—66no—
639C4×D3—126no—
640C4×D3C2×#67112yes—
641Dic6—26no—
642Dic6—26no—
643Dic6—612no—
644Dic6—66no—
645Dic6—66no—
646Dic6—612no—
647Dic6—126no—
648Dic6C2×#67112yes—
649C2×C32—41no—
650C2×C32C23×D411yescharacteristic
651C2×C32C2×2−1+411yescharacteristic
652C2×C32C2×2−1+411yescharacteristic
653C3⋊D3—22no—
654C3×D3—22no—
655C3×D3—22no—
656C3×D3—43no—
657C24—91no—
658#41—612no—
659#41—612no—
660#41—612no—
661#41—64no—
662C2×Q8—24no—
663C2×Q8—38no—
664C2×Q8—33no—
665C2×Q8—33no—
666C2×Q8—33no—
667C2×Q8—612no—
668C2×Q8—64no—
669C2×Q8—96no—
670C2×Q8—93no—
671C2×Q8—1812no—
672C2×Q8—1812no—
673C2×Q8—1812no—
674C2×Q8—184no—
675C2×Q8C2×D3213yes—
676C2×Q8C2×D3211yescharacteristic
677C2×D4—31no—
678C2×D4—31no—
679C2×D4—33no—
680C2×D4—33no—
681C2×D4—33no—
682C2×D4—93no—
683C2×D4—93no—
684C2×D4—91no—
685C22×C4—33no—
686C22×C4—33no—
687C22×C4—36no—
688C22×C4—33no—
689C22×C4—93no—
690C22×C4—93no—
691C22×C4—93no—
692C22×C4—93no—
693C22×C4—1812no—
694C22×C4C2×D3213yes—
695C4⋊C4—33no—
696C4⋊C4—33no—
697C4⋊C4—36no—
698C4⋊C4—93no—
699C4⋊C4—93no—
700C4⋊C4—93no—
701C4⋊C4—93no—
702C4⋊C4—93no—
703C4⋊C4—96no—
704C4⋊C4—93no—
705C22⋊C4—33no—
706C22⋊C4—33no—
707C22⋊C4—91no—
708C22⋊C4—91no—
709C22⋊C4—93no—
710C22⋊C4—91no—
711C22⋊C4—93no—
712C22⋊C4—96no—
713C22⋊C4—96no—
714C22⋊C4—93no—
715C22⋊C4—93no—
716C22⋊C4—93no—
717C42—33no—
718C42—96no—
719C42—93no—
720C22×C3—22no—
721C22×C3—21no—
722C22×C3—21no—
723C22×C3—21no—
724C22×C3—21no—
725C22×C3—21no—
726C22×C3—21no—
727C22×C3—21no—
728C22×C3—32no—
729C22×C3—32no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—61no—
733C22×C3—61no—
734C22×C3—61no—
735C22×C3—61no—
736C22×C3—63no—
737C22×C3—63no—
738C22×C3—63no—
739C22×C3C24×D311yescharacteristic
740C22×C3C24×D311yescharacteristic
741C2×D3—21no—
742C2×D3—21no—
743C2×D3—21no—
744C2×D3—21no—
745C2×D3—23no—
746C2×D3—23no—
747C2×D3—23no—
748C2×D3—32no—
749C2×D3—32no—
750C2×D3—62no—
751C2×D3—68no—
752C2×D3—68no—
753C2×D3—61no—
754C2×D3—61no—
755C2×D3—61no—
756C2×D3—61no—
757C2×D3—121no—
758C2×D3—121no—
759C2×D3#100712yescomplemented
760C2×D3C22×#6712yes—
761C3×C4—23no—
762C3×C4—23no—
763C3×C4—26no—
764C3×C4—36no—
765C3×C4—43no—
766C3×C4—61no—
767C3×C4—63no—
768C3×C4—61no—
769C3×C4—63no—
770C3×C4C2×D3×D416yes—
771C3×C4C22×#6716yes—
772Dic3—23no—
773Dic3—21no—
774Dic3—23no—
775Dic3—21no—
776Dic3—62no—
777Dic3—63no—
778Dic3—63no—
779Dic3—63no—
780Dic3—61no—
781Dic3—61no—
782Dic3—63no—
783Dic3—123no—
784Dic3—123no—
785Dic3C22×#6716yes—
786C32#348611yescharacteristic, complemented, Sylow
787C23—31no—
788C23—31no—
789C23—33no—
790C23—91no—
791C23—182no—
792C23—182no—
793C23—182no—
794C23C22×D3211yescharacteristic
795Q8—26no—
796Q8—312no—
797Q8—66no—
798Q8—66no—
799Q8—1812no—
800Q8—186no—
801Q8D3×#6714yes—
802D4—66no—
803D4—66no—
804D4—62no—
805D4—62no—
806D4—66no—
807D4—186no—
808D4—182no—
809D4—186no—
810C2×C4—26no—
811C2×C4—33no—
812C2×C4—312no—
813C2×C4—31no—
814C2×C4—33no—
815C2×C4—33no—
816C2×C4—31no—
817C2×C4—612no—
818C2×C4—66no—
819C2×C4—66no—
820C2×C4—93no—
821C2×C4—91no—
822C2×C4—93no—
823C2×C4—186no—
824C2×C4—186no—
825C2×C4—186no—
826C2×C4—186no—
827C2×C4C22×D3213yes—
828C2×C4C22×D3213yes—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—42no—
833C2×C3—41no—
834C2×C3—41no—
835C2×C3—62no—
836C2×C3—62no—
837C2×C3—123no—
838C2×C3C22×D3×D411yescharacteristic
839C2×C3C2×#100711yescharacteristic
840C2×C3D3×2−1+411yescharacteristic
841C2×C3D3×2−1+411yescharacteristic
842C2×C3D3×2−1+411yescharacteristic
843C2×C3C23×#6711yescharacteristic
844D3—22no—
845D3—22no—
846D3—43no—
847D3—62no—
848D3—62no—
849D3—122no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—32no—
854C22—32no—
855C22—61no—
856C22—61no—
857C22—61no—
858C22—61no—
859C22—63no—
860C22—63no—
861C22—63no—
862C22—92no—
863C22—188no—
864C22—181no—
865C22—181no—
866C22C23×D3211yescharacteristic
867C4—23no—
868C4—36no—
869C4—61no—
870C4—63no—
871C4—61no—
872C4—63no—
873C4—183no—
874C4—181no—
875C4—183no—
876C4C2×D3×#6716yes—
877C3—21no—
878C3#8675911yescharacteristic, complemented
879C3#8729411yescharacteristic, complemented
880C2—41no—
881C2—62no—
882C2—62no—
883C2—123no—
884C2—182no—
885C2D3×#100711yescharacteristic
886C2#1059668711yescharacteristic
887C2C22×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×Q8C22
hypercenterC22×Q8D32
hypocenterC32#3486
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1007C2semidirect
2. C2×D32×Q8C2semidirect
3. Q8×#638C2semidirect
4. C3×Q8×#67C2semidirect
5. #10595424C2semidirect
6. #10595414C2semidirect
7. #10595409C2semidirect
8. #10595403C2semidirect
9. #10595400C2semidirect
10. #10595356C2semidirect
11. #10595347C2semidirect
12. #10595060C2semidirect
13. #10594899C2semidirect
14. #10594884C2semidirect
15. #10594830C2semidirect
18. C22×C32×Q8C22semidirect
22. C2×C3×#239C22semidirect
25. C2×C3×D3×Q8C22semidirect
27. C2×C3×#235C22semidirect
34. Q8×C3⋊Dic3C22semidirect
35. #64153C22semidirect
37. #64133C22semidirect
39. C3×Q8×Dic3C22semidirect
40. C3×#944C22semidirect
42. C3×#924C22semidirect
46. #63959C22semidirect
59. #63863C22semidirect
60. #63860C22semidirect
61. #63857C22semidirect
62. #63856C22semidirect
64. #63851C22semidirect
65. #63851C22semidirect
66. #63843C22semidirect
67. Dic3×Dic6C22semidirect
69. #63839C22semidirect
71. C2×#1007D3semidirect
89. Q8×#67D3semidirect
117. C3×D3×Q8D4semidirect
174. C22×C3×Q8C2×D3semidirect
175. C22×C3×Q8C2×D3semidirect
178. C2×#239C2×D3semidirect
190. C2×D3×Q8C2×D3semidirect
192. C2×#235C2×D3semidirect
215. Q8×Dic3C2×D3semidirect
220. #944C2×D3semidirect
254. #924C2×D3semidirect
388. D3×Q8#67semidirect
479. C2×C3⋊D32−1+4semidirect
488. C2×C3×D32−1+4semidirect
513. C22×Q8D32semidirect
759. C2×D3#1007semidirect
786. C32#3486semidirect
878. C3#86759semidirect
879. C3#87294semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10072
C2×D32×Q82
Q8×#6382
C3×Q8×#672
#105954242
#105954142
#105954092
#105954032
#105954002
#105953562
#105953472
#105950602
#105948992
#105948842
#105948302
#872943
#867593