Finite Group Databasebeta

← #11904487

Subgroups — #11904487

Order 1152.

3129 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×#1010C211yesmaximal, characteristic, complemented
2C2×D32×Q8C211yesmaximal, characteristic, complemented
3#10596302C211yesmaximal, characteristic, complemented
4C3×#5831C211yesmaximal, characteristic, complemented
5Q8×#626C211yesmaximal, characteristic, complemented
6Q8×#625C211yesmaximal, characteristic, complemented
7#10595347C211yesmaximal, characteristic, complemented
8#10595301C213yesmaximal, complemented
9#10595237C213yesmaximal, complemented
10#10595157C213yesmaximal, complemented
11#10595147C213yesmaximal, complemented
12#10595060C213yesmaximal, complemented
13Dic6×#67C213yesmaximal, complemented
14#10594884C213yesmaximal, complemented
15#10594803C213yesmaximal, complemented
16#87294—31nomaximal
17#86735—31nomaximal
18C2×C32×#41C2211yescharacteristic, complemented
19C2×Q8×C3⋊D3C2211yescharacteristic
20C3×#1010—28no—
21C2×C3×D3×Q8C2211yescharacteristic
22C2×C3×D3×Q8C2211yescharacteristic
23C2×C3×D3×Q8C2211yescharacteristic, complemented
24C2×C3×#237C2213yes—
25C2×C3×#237C2213yescomplemented
26C2×C3×#235C2213yes—
27C22×C3×Dic6C2213yescomplemented
28D32×Q8—28no—
29C2×C4×D32C2213yes—
30C2×#3797C2213yes—
31C2×D3×Dic6C2213yes—
32C2×D3×Dic6C2213yes—
33Q8×C3⋊Dic3C2211yescharacteristic, complemented
34#64147C2213yes—
35#64145C2213yescomplemented
36C4×#638C2213yes—
37#64133C2213yescomplemented
38C3×Q8×Dic3C2211yescharacteristic, complemented
39C3×#938C2213yes—
40C3×#936C2213yescomplemented
41C3×C4×#67C2213yes—
42C3×#924C2213yescomplemented
43#63983C2213yes—
44Dic3×#67C2216yes—
45#63970C2213yes—
46#63969C2216yes—
47#63969C2213yes—
48#63964C2216yescomplemented
49#63964C2216yescomplemented
50#63959C2216yescomplemented
51#63958C2213yes—
52#63952C2216yes—
53#63922C2211yescharacteristic
54C4×#626C2213yes—
55C4×#625C2213yes—
56#63888C2213yes—
57#63887C2213yes—
58#63884C2213yes—
59#63873C2213yescomplemented
60#63871C2213yes—
61#63866C2213yescomplemented
62#63857C2213yescomplemented
63#63856C2213yes—
64#63856C2213yescomplemented
65#63855C2213yes—
66#63843C2213yescomplemented
67Dic3×Dic6C2213yescomplemented
68#63841C2213yes—
69#63839C2216yescomplemented
70C2×C3×2−1+4—31no—
71C2×#1010D311yescharacteristic, complemented
72C22×D3×Q8—31no—
73C22×D3×Q8—31no—
74C3×#548—31no—
75#5831—31no—
76#5831—31no—
77#5831—33no—
78#5831—33no—
79#5831—61no—
80#5831D311yescharacteristic, complemented
81#5828—33no—
82#5828—33no—
83#5825—33no—
84#5825—33no—
85Q8×#67—31no—
86Q8×#67—31no—
87Q8×#67—31no—
88Q8×#67—33no—
89Q8×#67—33no—
90#5812—31no—
91#5677—33no—
92#5675—33no—
93#5632—33no—
94#5628—33no—
95#5606—33no—
96#5598—33no—
97Q8×D12—31no—
98#5572—31no—
99#5547—33no—
100D4×Dic6—33no—
101C22×D32C2311yescharacteristic
102C32×#41—24no—
103C2×C32×Q8C2311yescharacteristic
104C2×C32×D4C2313yes—
105C22×C32×C4C2313yes—
106C2×#638C2313yes—
107Q8×C3⋊D3—24no—
108C2×C4×C3⋊D3C2313yes—
109C2×#634C2313yes—
110C2×C3×#67C2313yes—
111C2×C3×#67C2313yes—
112C2×C3×#67C2313yes—
113C22×C3×Dic3C2316yes—
114C3×D3×Q8—24no—
115C3×D3×Q8—24no—
116C3×D3×Q8D418yescomplemented
117C3×#237—212no—
118C3×#237—212no—
119C3×#235—212no—
120C2×C3×D12C2311yescharacteristic
121C2×C3×C4×D3C2313yes—
122C2×C3×C4×D3C2313yes—
123C2×C3×C4×D3C2313yes—
124C2×C3×Dic6—212no—
125C2×C3×Dic6C2313yes—
126C2×C3×Dic6C2313yes—
127C2×C3×Dic6C2313yes—
128C2×C3×Dic6C2313yes—
129C2×#627C2316yes—
130C2×#626C2311yescharacteristic
131C2×#625C2311yescharacteristic
132C2×#624C2313yes—
133C2×D3×Dic3C2313yes—
134C2×D3×Dic3C2313yes—
135C4×D32—212no—
136#3797—212no—
137D3×Dic6—212no—
138D3×Dic6—212no—
139#3757C2316yes—
140#3757C2313yes—
141#3752C2311yescharacteristic
142C4⋊(C3⋊Dic3)C2313yes—
143#3750C2313yes—
144C4×C3⋊Dic3C2313yes—
145C3×#217C2316yes—
146C3×#217C2313yes—
147C3×(C2×D3)⋊C4C2311yescharacteristic
148C3×C4⋊Dic3C2313yes—
149C3×Dic3⋊C4C2313yes—
150C3×C4×Dic3C2313yes—
151#3724C2316yes—
152#3724C2313yes—
153Dic3⋊Dic3C2316yes—
154Dic3⋊Dic3C2313yes—
155Dic3⋊Dic3C2313yes—
156Dic3⋊Dic3C2313yes—
157#3722C2313yes—
158(C2×D3)⋊Dic3C2313yes—
159(C2×D3)⋊Dic3C2311yescharacteristic
160(C2×D3)⋊Dic3C2313yes—
161(C2×D3)⋊Dic3C2313yes—
162(C2×D3)⋊Dic3C2313yes—
163Dic32C2316yes—
164#3486—91noSylow
165C3×2−1+4—68no—
166C2×C3×#41—21no—
167C2×C3×#41—33no—
168C2×C3×#41—33no—
169C2×C3×#41—33no—
170C2×C3×#41C2×D311yescharacteristic, complemented
171C2×C3×#41C2×D311yescharacteristic, complemented
172C22×C3×Q8—31no—
173C22×C3×Q8—31no—
174C22×C3×Q8—31no—
175C22×C3×Q8—33no—
176#1010—28no—
177C2×D3×Q8—31no—
178C2×D3×Q8—31no—
179C2×D3×Q8—33no—
180C2×D3×Q8—33no—
181C2×D3×Q8—33no—
182C2×D3×Q8—33no—
183C2×D3×Q8—61no—
184C2×D3×Q8—68no—
185C2×D3×Q8—68no—
186C2×D3×Q8C2×D311yescharacteristic
187C2×D3×Q8C2×D311yescharacteristic
188C2×D3×Q8C2×D311yescharacteristic, complemented
189C2×#237C2×D313yes—
190C2×#237C2×D313yescomplemented
191C2×#235C2×D313yes—
192C22×C4×D3—33no—
193C22×C4×D3—33no—
194C22×Dic6—33no—
195C22×Dic6—33no—
196C22×Dic6C2×D313yescomplemented
197C3×#124—33no—
198C3×C22⋊Q8—33no—
199C3×#121—33no—
200C3×C4×Q8—31no—
201C3×C4×D4—33no—
202#946—33no—
203#946—33no—
204#946—33no—
205#946—33no—
206#946—33no—
207Q8×Dic3—31no—
208Q8×Dic3—31no—
209Q8×Dic3—33no—
210Q8×Dic3—33no—
211Q8×Dic3—61no—
212Q8×Dic3C2×D311yescharacteristic, complemented
213#944—33no—
214#944—33no—
215#944—36no—
216#944—33no—
217#939—33no—
218#938—33no—
219#938—33no—
220#938—33no—
221#938—33no—
222#938—63no—
223#938C2×D313yes—
224#937—33no—
225#937—33no—
226#937—31no—
227#936—33no—
228#936—33no—
229#936—36no—
230#936—63no—
231#936C2×D313yescomplemented
232#935—33no—
233#935—36no—
234#935—33no—
235D4×Dic3—36no—
236C4×#67—33no—
237C4×#67—33no—
238C4×#67—36no—
239C4×#67—33no—
240C4×#67—33no—
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—33no—
254#924—63no—
255#924C2×D313yescomplemented
256#897—33no—
257#897—33no—
258#896—33no—
259#894—33no—
260#892—33no—
261#888—36no—
262#887—33no—
263#885—36no—
264#884—33no—
265#883—33no—
266#883—36no—
267#882—31no—
268#67⋊C4—36no—
269#878—36no—
270#878—36no—
271#878—33no—
272C4×D12—33no—
273#872—33no—
274#869—33no—
275C4×Dic6—33no—
276C23×C32C2413yes—
277C22×C3⋊D3C2411yescharacteristic
278C22×C3×D3C2411yescharacteristic
279C22×C3×D3C2411yescharacteristic
280C22×C3×D3C2411yescharacteristic
281C2×D32—22no—
282C2×D32—22no—
283C2×D32—22no—
284C32×Q8C2×D414yes—
285C32×D4—26no—
286C2×C32×C4—26no—
287C2×C32×C4C2411yescharacteristic
288C2×C32×C4C2413yes—
289#638—26no—
290C2×C3⋊Dic3C2413yes—
291C2×C3⋊Dic3C2411yescharacteristic
292C2×C3⋊Dic3C2413yes—
293C4×C3⋊D3—26no—
294#634—26no—
295C3×#67—26no—
296C3×#67—26no—
297C3×#67—26no—
298C2×C3×Dic3—212no—
299C2×C3×Dic3C2413yes—
300C2×C3×Dic3C2413yes—
301C2×C3×Dic3C2411yescharacteristic
302C2×C3×Dic3C2413yes—
303C2×C3×Dic3C2413yes—
304C3×D12—22no—
305C3×C4×D3—26no—
306C3×C4×D3—26no—
307C3×C4×D3C2×D4112yes—
308C3×Dic6—26no—
309C3×Dic6—26no—
310C3×Dic6—26no—
311C3×Dic6C2×D4112yes—
312#627—212no—
313#626—22no—
314#625—22no—
315#624—26no—
316D3×Dic3—26no—
317D3×Dic3—26no—
318C2×2−1+4—31no—
319C23×Q8—91no—
320D4×Q8—93no—
321D4×Q8—91no—
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—24no—
336C3×#41—24no—
337C3×#41—44no—
338C3×#41—612no—
339C3×#41—612no—
340C3×#41—612no—
341C2×C3×Q8—21no—
342C2×C3×Q8—38no—
343C2×C3×Q8—33no—
344C2×C3×Q8—33no—
345C2×C3×Q8—33no—
346C2×C3×Q8—33no—
347C2×C3×Q8—612no—
348C2×C3×Q8—64no—
349C2×C3×Q8—64no—
350C2×C3×Q8C22×D311yescharacteristic
351C2×C3×Q8C22×D311yescharacteristic
352C2×C3×D4—23no—
353C2×C3×D4—33no—
354C2×C3×D4—33no—
355C2×C3×D4—33no—
356C2×C3×D4—31no—
357C2×C3×D4C22×D313yes—
358C2×C3×D4C22×D313yes—
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—33no—
367C2×#67—33no—
368C2×#67—31no—
369C2×#67—31no—
370C2×#67—31no—
371C2×#67—63no—
372C2×#67C22×D313yes—
373C2×#67C22×D313yes—
374C2×#67C22×D313yes—
375C22×Dic3—33no—
376C22×Dic3—33no—
377C22×Dic3C22×D316yes—
378D3×Q8—24no—
379D3×Q8—24no—
380D3×Q8—612no—
381D3×Q8—612no—
382D3×Q8—64no—
383D3×Q8—64no—
384D3×Q8—612no—
385D3×Q8—612no—
386D3×Q8—124no—
387D3×Q8#6718yescomplemented
388#237—212no—
389#237—212no—
390#235—212no—
391C2×D12—31no—
392C2×D12C22×D311yescharacteristic
393C2×C4×D3—33no—
394C2×C4×D3—33no—
395C2×C4×D3—33no—
396C2×C4×D3—33no—
397C2×C4×D3—33no—
398C2×C4×D3—33no—
399C2×C4×D3—63no—
400C2×C4×D3—612no—
401C2×C4×D3—612no—
402C2×C4×D3C22×D313yes—
403C2×C4×D3C22×D313yes—
404C2×C4×D3C22×D313yes—
405C2×Dic6—212no—
406C2×Dic6—33no—
407C2×Dic6—33no—
408C2×Dic6—36no—
409C2×Dic6—36no—
410C2×Dic6—63no—
411C2×Dic6—612no—
412C2×Dic6—612no—
413C2×Dic6C22×D313yes—
414C2×Dic6C22×D313yes—
415C2×Dic6C22×D313yes—
416C2×Dic6C22×D313yes—
417C3×C4⋊C4—33no—
418C3×C4⋊C4—33no—
419C3×C22⋊C4—33no—
420C3×C22⋊C4—36no—
421C3×C22⋊C4—31no—
422C3×C42—33no—
423#217—33no—
424#217—36no—
425#217—36no—
426#217—33no—
427#217—33no—
428#217—33no—
429#217—33no—
430#217—33no—
431#217—31no—
432#217—66no—
433#217—63no—
434#217C22×D313yes—
435#217C22×D316yes—
436(C2×D3)⋊C4—31no—
437(C2×D3)⋊C4—33no—
438(C2×D3)⋊C4—33no—
439(C2×D3)⋊C4—33no—
440(C2×D3)⋊C4—33no—
441(C2×D3)⋊C4—31no—
442(C2×D3)⋊C4—31no—
443(C2×D3)⋊C4—33no—
444(C2×D3)⋊C4—33no—
445(C2×D3)⋊C4—61no—
446(C2×D3)⋊C4C22×D311yescharacteristic
447C4⋊Dic3—33no—
448C4⋊Dic3—33no—
449C4⋊Dic3—33no—
450C4⋊Dic3—36no—
451C4⋊Dic3—33no—
452C4⋊Dic3—33no—
453C4⋊Dic3—63no—
454C4⋊Dic3C22×D313yes—
455Dic3⋊C4—33no—
456Dic3⋊C4—33no—
457Dic3⋊C4—33no—
458Dic3⋊C4—33no—
459Dic3⋊C4—33no—
460Dic3⋊C4—36no—
461Dic3⋊C4—36no—
462Dic3⋊C4—33no—
463Dic3⋊C4—36no—
464Dic3⋊C4—33no—
465Dic3⋊C4—63no—
466Dic3⋊C4C22×D313yes—
467C4×Dic3—33no—
468C4×Dic3—33no—
469C4×Dic3—36no—
470C4×Dic3—36no—
471C4×Dic3—63no—
472C4×Dic3C22×D313yes—
473C22×C32—23no—
474C22×C32—23no—
475C22×C32—23no—
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—21no—
485C2×C3×D3—21no—
486C2×C3×D3—21no—
487C2×C3×D3C22×D412yes—
488C2×C3×D32−1+412yescomplemented
489D32—28no—
490C32×C4—21no—
491C32×C4C22×D416yes—
492C3⋊Dic3—23no—
493C3⋊Dic3—21no—
494C3⋊Dic3—23no—
495C3×Dic3—23no—
496C3×Dic3—23no—
497C3×Dic3—21no—
498C3×Dic3—23no—
499C3×Dic3C22×D416yes—
5002−1+4—68no—
501C2×#41—33no—
502C2×#41—33no—
503C2×#41—33no—
504C2×#41D3211yescharacteristic, complemented
505C22×Q8—31no—
506C22×Q8—31no—
507C22×Q8—31no—
508C22×Q8—33no—
509C22×Q8—93no—
510C22×Q8—93no—
511C22×Q8—93no—
512C22×Q8—91no—
513C22×Q8—188no—
514C23×C4—93no—
515C4⋊Q8—93no—
516C4⋊Q8—96no—
517C4⋊Q8—93no—
518#124—33no—
519#124—96no—
520#124—93no—
521#123—93no—
522#123—96no—
523#123—93no—
524C22⋊Q8—33no—
525C22⋊Q8—96no—
526C22⋊Q8—96no—
527C22⋊Q8—93no—
528C22⋊Q8—93no—
529C22⋊Q8—93no—
530C22⋊Q8—93no—
531C22⋊Q8—93no—
532C22⋊Q8—93no—
533C22⋊Q8—93no—
534#121—33no—
535#121—93no—
536#121—93no—
537#121—93no—
538#120—91no—
539#120—93no—
540C4×Q8—31no—
541C4×Q8—93no—
542C4×Q8—93no—
543C4×Q8—91no—
544C4×D4—33no—
545C4×D4—93no—
546C4×D4—96no—
547C4×D4—93no—
548C4×D4—96no—
549C4×D4—93no—
550#117—93no—
551#117—93no—
552C23×C3—23no—
553C23×C3—31no—
554C23×C3—31no—
555C23×C3—31no—
556C23×C3C23×D313yes—
557C23×C3C23×D313yes—
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×D311yescharacteristic
568C22×D3C23×D311yescharacteristic
569C22×D3C23×D311yescharacteristic
570C3×Q8—24no—
571C3×Q8—312no—
572C3×Q8—66no—
573C3×Q8—66no—
574C3×Q8—66no—
575C3×Q8D3×D414yes—
576C3×Q8C2×#6714yes—
577C3×D4—26no—
578C3×D4—26no—
579C3×D4—46no—
580C3×D4—62no—
581C3×D4—66no—
582C3×D4—66no—
583C3×D4—66no—
584C2×C3×C4—26no—
585C2×C3×C4—26no—
586C2×C3×C4—23no—
587C2×C3×C4—21no—
588C2×C3×C4—33no—
589C2×C3×C4—312no—
590C2×C3×C4—33no—
591C2×C3×C4—33no—
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×D311yescharacteristic
599C2×C3×C4C23×D311yescharacteristic
600C2×C3×C4C23×D313yes—
601C2×C3×C4C23×D313yes—
602#67—26no—
603#67—26no—
604#67—26no—
605#67—62no—
606#67—62no—
607#67—66no—
608#67—66no—
609#67—62no—
610#67—126no—
611C2×Dic3—212no—
612C2×Dic3—31no—
613C2×Dic3—33no—
614C2×Dic3—31no—
615C2×Dic3—33no—
616C2×Dic3—33no—
617C2×Dic3—33no—
618C2×Dic3—61no—
619C2×Dic3—63no—
620C2×Dic3—63no—
621C2×Dic3—66no—
622C2×Dic3—66no—
623C2×Dic3C23×D313yes—
624C2×Dic3C23×D311yescharacteristic
625C2×Dic3C23×D313yes—
626C2×Dic3C23×D313yes—
627C2×Dic3C23×D313yes—
628D12—22no—
629D12—62no—
630C4×D3—26no—
631C4×D3—26no—
632C4×D3—66no—
633C4×D3—66no—
634C4×D3—66no—
635C4×D3—66no—
636C4×D3—66no—
637C4×D3—66no—
638C4×D3—126no—
639C4×D3C2×#67112yes—
640Dic6—26no—
641Dic6—26no—
642Dic6—26no—
643Dic6—612no—
644Dic6—66no—
645Dic6—66no—
646Dic6—612no—
647Dic6—126no—
648Dic6C2×#67112yes—
649C2×C32—43no—
650C2×C32C23×D411yescharacteristic
651C2×C32C2×2−1+411yescharacteristic
652C2×C32C2×2−1+411yescharacteristic
653C3⋊D3—22no—
654C3×D3—22no—
655C3×D3—22no—
656C3×D3—41no—
657C24—91no—
658#41—24no—
659#41—612no—
660#41—612no—
661#41—612no—
662C2×Q8—38no—
663C2×Q8—33no—
664C2×Q8—33no—
665C2×Q8—33no—
666C2×Q8—33no—
667C2×Q8—612no—
668C2×Q8—64no—
669C2×Q8—64no—
670C2×Q8—96no—
671C2×Q8—93no—
672C2×Q8—1812no—
673C2×Q8—1812no—
674C2×Q8—1812no—
675C2×Q8—184no—
676C2×Q8C2×D3211yescharacteristic
677C2×D4—33no—
678C2×D4—33no—
679C2×D4—33no—
680C2×D4—31no—
681C2×D4—91no—
682C2×D4—91no—
683C2×D4—93no—
684C2×D4C2×D3213yes—
685C22×C4—33no—
686C22×C4—36no—
687C22×C4—33no—
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—93no—
698C4⋊C4—93no—
699C4⋊C4—96no—
700C4⋊C4—93no—
701C4⋊C4—93no—
702C4⋊C4—96no—
703C4⋊C4—93no—
704C4⋊C4—93no—
705C22⋊C4—33no—
706C22⋊C4—36no—
707C22⋊C4—31no—
708C22⋊C4—93no—
709C22⋊C4—91no—
710C22⋊C4—93no—
711C22⋊C4—93no—
712C22⋊C4—93no—
713C22⋊C4—93no—
714C22⋊C4—96no—
715C22⋊C4—93no—
716C22⋊C4—91no—
717C42—33no—
718C42—96no—
719C42—93no—
720C22×C3—23no—
721C22×C3—23no—
722C22×C3—23no—
723C22×C3—23no—
724C22×C3—23no—
725C22×C3—23no—
726C22×C3—21no—
727C22×C3—32no—
728C22×C3—32no—
729C22×C3—43no—
730C22×C3—43no—
731C22×C3—43no—
732C22×C3—61no—
733C22×C3—61no—
734C22×C3—61no—
735C22×C3—61no—
736C22×C3—61no—
737C22×C3—61no—
738C22×C3—61no—
739C22×C3C24×D311yescharacteristic
740C22×C3C24×D311yescharacteristic
741C2×D3—21no—
742C2×D3—21no—
743C2×D3—21no—
744C2×D3—21no—
745C2×D3—21no—
746C2×D3—21no—
747C2×D3—21no—
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#101012yescomplemented
760C2×D3C22×#6712yes—
761C3×C4—21no—
762C3×C4—21no—
763C3×C4—26no—
764C3×C4—36no—
765C3×C4—41no—
766C3×C4—63no—
767C3×C4—61no—
768C3×C4—63no—
769C3×C4—63no—
770C3×C4C2×D3×D416yes—
771C3×C4C22×#6716yes—
772Dic3—23no—
773Dic3—23no—
774Dic3—21no—
775Dic3—23no—
776Dic3—63no—
777Dic3—61no—
778Dic3—61no—
779Dic3—63no—
780Dic3—63no—
781Dic3—63no—
782Dic3—123no—
783Dic3—123no—
784Dic3—121no—
785Dic3C22×#6716yes—
786C32#348611yescharacteristic, complemented, Sylow
787C23—31no—
788C23—31no—
789C23—31no—
790C23—91no—
791C23—182no—
792C23—182no—
793C23—182no—
794C23C22×D3213yes—
795Q8—312no—
796Q8—66no—
797Q8—66no—
798Q8—66no—
799Q8—1812no—
800Q8—186no—
801Q8D3×#6714yes—
802D4—26no—
803D4—62no—
804D4—66no—
805D4—66no—
806D4—66no—
807D4—182no—
808D4—186no—
809D4—182no—
810C2×C4—26no—
811C2×C4—33no—
812C2×C4—312no—
813C2×C4—31no—
814C2×C4—33no—
815C2×C4—33no—
816C2×C4—33no—
817C2×C4—612no—
818C2×C4—66no—
819C2×C4—66no—
820C2×C4—91no—
821C2×C4—93no—
822C2×C4—93no—
823C2×C4—186no—
824C2×C4—186no—
825C2×C4—186no—
826C2×C4—186no—
827C2×C4C22×D3211yescharacteristic
828C2×C4C22×D3213yes—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—43no—
833C2×C3—43no—
834C2×C3—62no—
835C2×C3—62no—
836C2×C3—83no—
837C2×C3—121no—
838C2×C3C22×D3×D411yescharacteristic
839C2×C3C2×#101011yescharacteristic
840C2×C3D3×2−1+411yescharacteristic
841C2×C3D3×2−1+411yescharacteristic
842C2×C3D3×2−1+411yescharacteristic
843C2×C3C23×#6711yescharacteristic
844D3—22no—
845D3—22no—
846D3—41no—
847D3—62no—
848D3—62no—
849D3—122no—
850C22—23no—
851C22—23no—
852C22—23no—
853C22—32no—
854C22—32no—
855C22—61no—
856C22—61no—
857C22—61no—
858C22—61no—
859C22—61no—
860C22—61no—
861C22—61no—
862C22—92no—
863C22—188no—
864C22—181no—
865C22—181no—
866C22C23×D3211yescharacteristic
867C4—21no—
868C4—36no—
869C4—63no—
870C4—61no—
871C4—63no—
872C4—63no—
873C4—181no—
874C4—183no—
875C4—183no—
876C4C2×D3×#6716yes—
877C3—21no—
878C3#8673511yescharacteristic, complemented
879C3#8729411yescharacteristic, complemented
880C2—43no—
881C2—62no—
882C2—62no—
883C2—121no—
884C2—182no—
885C2D3×#101011yescharacteristic
886C2#1059669411yescharacteristic
887C2C22×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32#3486
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1010C2semidirect
2. C2×D32×Q8C2semidirect
3. #10596302C2semidirect
4. C3×#5831C2semidirect
5. Q8×#626C2semidirect
6. Q8×#625C2semidirect
7. #10595347C2semidirect
8. #10595301C2semidirect
9. #10595237C2semidirect
10. #10595157C2semidirect
11. #10595147C2semidirect
12. #10595060C2semidirect
13. Dic6×#67C2semidirect
14. #10594884C2semidirect
15. #10594803C2semidirect
18. C2×C32×#41C22semidirect
23. C2×C3×D3×Q8C22semidirect
25. C2×C3×#237C22semidirect
27. C22×C3×Dic6C22semidirect
33. Q8×C3⋊Dic3C22semidirect
35. #64145C22semidirect
37. #64133C22semidirect
38. C3×Q8×Dic3C22semidirect
40. C3×#936C22semidirect
42. C3×#924C22semidirect
48. #63964C22semidirect
49. #63964C22semidirect
50. #63959C22semidirect
59. #63873C22semidirect
61. #63866C22semidirect
62. #63857C22semidirect
64. #63856C22semidirect
66. #63843C22semidirect
67. Dic3×Dic6C22semidirect
69. #63839C22semidirect
71. C2×#1010D3semidirect
80. #5831D3semidirect
116. C3×D3×Q8D4semidirect
170. C2×C3×#41C2×D3semidirect
171. C2×C3×#41C2×D3semidirect
188. C2×D3×Q8C2×D3semidirect
190. C2×#237C2×D3semidirect
196. C22×Dic6C2×D3semidirect
212. Q8×Dic3C2×D3semidirect
231. #936C2×D3semidirect
255. #924C2×D3semidirect
387. D3×Q8#67semidirect
479. C2×C3⋊D32−1+4semidirect
488. C2×C3×D32−1+4semidirect
504. C2×#41D32semidirect
759. C2×D3#1010semidirect
786. C32#3486semidirect
878. C3#86735semidirect
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×#10102
C2×D32×Q82
#105963022
C3×#58312
Q8×#6262
Q8×#6252
#105953472
#105953012
#105952372
#105951572
#105951472
#105950602
Dic6×#672
#105948842
#105948032
#872943
#867353