Finite Group Databasebeta

← #11903788

Subgroups — #11903788

Order 1152.

2247 conjugacy classes of subgroups.

The subgroup lattice has 1076 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596093C211yesmaximal, characteristic, complemented
2C3×#5636C212yesmaximal, complemented
3#10595421C211yesmaximal, characteristic, complemented
4#10595370C211yesmaximal, characteristic, complemented
5#10595368C212yesmaximal, complemented
6#10594951C212yesmaximal, complemented
7C4×#3805C211yesmaximal, characteristic
8C2×#63838C211yesmaximal, characteristic, complemented
9#10594596C212yesmaximal, complemented
10#10594533C212yesmaximal, complemented
11#10594388C212yesmaximal, complemented
12#10594388C212yesmaximal, complemented
13#10594377C211yesmaximal, characteristic, complemented
14D3×#887C212yesmaximal, complemented
15#10594315C211yesmaximal, characteristic, complemented
16#10594156C212yesmaximal, complemented
17#10594071C212yesmaximal, complemented
18#10594050C212yesmaximal
19#10594030C212yesmaximal, complemented
20#86923—32nomaximal
21C22×#627C2211yescharacteristic
22C2×#3805C2211yescharacteristic
23C2×D3×Dic6C2212yes—
24C32×C22⋊Q8C2211yescharacteristic
25Q8×C3⋊Dic3C2211yescharacteristic
26#64153C2211yescharacteristic
27#64133C2211yescharacteristic
28C2×C4×C3⋊Dic3C2211yescharacteristic
29#64098C2212yes—
30#64097C2211yescharacteristic
31#64096C2212yes—
32#64096C2211yescharacteristic
33#64087C2212yes—
34#64086C2212yes—
35C3×#946C2212yes—
36C3×#944C2212yes—
37C3×C4×#67C2212yes—
38C2×C3×Dic3⋊C4C2212yes—
39C3×#896C2212yes—
40C3×#896C2212yes—
41C3×D3×C4⋊C4C2212yes—
42C3×#889C2212yes—
43C3×#889C2212yes—
44C3×#887C2212yes—
45C3×#67⋊C4C2212yes—
46C3×#67⋊C4C2212yes—
47C3×#878C2212yes—
48C3×#878C2212yes—
49#67⋊Dic3C2212yes—
50Dic3×#67C2212yes—
51Dic3×#67C2212yes—
52C2×#3724C2211yescharacteristic
53#63964C2212yes—
54#63964C2212yes—
55#63957C2211yescharacteristic
56C2×Dic32C2212yes—
57#63918C2212yes—
58C4×#627C2211yescharacteristic
59#63902C2211yescharacteristic
60C4×#625C2211yescharacteristic
61#63899C2212yes—
62#63899C2212yes—
63#63896C2212yes—
64#63896C2212yes—
65#63893C2212yes—
66#63893C2212yes—
67#63879C2212yes—
68#63879C2212yes—
69#63878C2212yes—
70#63878C2212yes—
71#63878C2212yes—
72D3×Dic3⋊C4C2212yes—
73D3×Dic3⋊C4C2212yes—
74C4×D3×Dic3C2212yes—
75C4×D3×Dic3C2212yes—
76C4×D3×Dic3C2212yes—
77#63867C2212yes—
78#63867C2212yes—
79#63856C2212yes—
80#63851C2212yes—
81#63851C2212yes—
82#63847C2212yes—
83#63847C2212yes—
84#63845C2212yes—
85#63845C2212yes—
86#63844C2212yes—
87#63843C2212yes—
88#63843C2212yes—
89#63840C2212yes—
90#63840C2212yes—
91#63839C2212yes—
92#63839C2212yes—
93#63839C2212yes—
94#63839C2212yes—
95#63838C2211yescharacteristic
96#63838C2211yescharacteristic
97#63838C2212yes—
98#63838C2212yes—
99#63838C2212yes—
100#63838C2211yescharacteristic
101#63838C2211yescharacteristic
102#63838C2212yes—
103#63838C2211yescharacteristic
104#63837C2212yes—
105#63837C2212yes—
106#63837C2212yes—
107#63837C2212yes—
108C3×#554—32no—
109#5728—32no—
110#5722—32no—
111#5688—32no—
112#5688—32no—
113#5685—32no—
114#5685—32no—
115#5636—32no—
116#5636—32no—
117#5636—32no—
118#5636D312yescomplemented
119#5632—32no—
120#5632—32no—
121#5622—32no—
122#5622—32no—
123#5622—32no—
124#5622—32no—
125#5622—32no—
126#5622—32no—
127#5622—61no—
128C4×D3×Q8—32no—
129#5567—32no—
130#5539—32no—
131#5539—32no—
132D4×Dic6—32no—
133C4×#237—32no—
134C4×#237—32no—
135C4×#237—32no—
136#5511—32no—
137#5511—32no—
138C2×#887—32no—
139C2×#887—32no—
140C2×C32×Q8C2311yescharacteristic
141C22×C32×C4C2311yescharacteristic
142C22×C3⋊Dic3C2311yescharacteristic
143C22×C3⋊Dic3C2311yescharacteristic
144C2×#634C2312yes—
145C2×#634C2311yescharacteristic
146C2×C3×#67C2312yes—
147C22×C3×Dic3C2312yes—
148C22×C3×Dic3C2312yes—
149C2×C3×C4×D3C2312yes—
150C2×C3×C4×D3C2312yes—
151C2×C3×C4×D3C2312yes—
152C2×C3×Dic6C2312yes—
153C2×C3×Dic6C2312yes—
154C2×#627—24no—
155C2×#627C2312yes—
156C2×#627C2312yes—
157C2×#627C2311yescharacteristic
158C2×#627C2312yes—
159C2×#627C2311yescharacteristic
160C2×#627C2311yescharacteristic
161C2×#625C2311yescharacteristic
162#3805Q818yescomplemented
163C2×D3×Dic3C2312yes—
164C2×D3×Dic3C2312yes—
165C2×D3×Dic3C2312yes—
166C2×D3×Dic3C2312yes—
167D3×Dic6—28no—
168C32×C4⋊C4C2312yes—
169C32×C4⋊C4C2311yescharacteristic
170C32×C22⋊C4C2312yes—
171#3757C2312yes—
172C4⋊(C3⋊Dic3)C2312yes—
173C4⋊(C3⋊Dic3)C2311yescharacteristic
174#3750C2312yes—
175#3750C2312yes—
176#3750C2312yes—
177#3750C2312yes—
178#3750C2312yes—
179C4×C3⋊Dic3C2312yes—
180C4×C3⋊Dic3C2312yes—
181C4×C3⋊Dic3C2311yescharacteristic
182C4×C3⋊Dic3C2311yescharacteristic
183C4×C3⋊Dic3C2311yescharacteristic
184C4×C3⋊Dic3C2311yescharacteristic
185C3×#217C2312yes—
186C3×(C2×D3)⋊C4C2312yes—
187C3×(C2×D3)⋊C4C2312yes—
188C3×(C2×D3)⋊C4C2312yes—
189C3×C4⋊Dic3C2312yes—
190C3×C4⋊Dic3C2312yes—
191C3×Dic3⋊C4C2312yes—
192C3×Dic3⋊C4C2312yes—
193C3×Dic3⋊C4C2312yes—
194C3×Dic3⋊C4C2312yes—
195C3×Dic3⋊C4C2312yes—
196C3×Dic3⋊C4C2312yes—
197C3×Dic3⋊C4C2312yes—
198C3×Dic3⋊C4C2312yes—
199C3×Dic3⋊C4C2312yes—
200C3×Dic3⋊C4C2312yes—
201C3×Dic3⋊C4C2312yes—
202C3×C4×Dic3C2312yes—
203C3×C4×Dic3C2312yes—
204C3×C4×Dic3C2312yes—
205#3724C2311yescharacteristic
206#3724C2311yescharacteristic
207#3724C2312yes—
208#3724C2311yescharacteristic
209#3724C2312yes—
210#3724C2312yes—
211#3724C2311yescharacteristic
212Dic3⋊Dic3C2312yes—
213Dic3⋊Dic3C2312yes—
214Dic3⋊Dic3C2312yes—
215Dic3⋊Dic3C2312yes—
216Dic3⋊Dic3C2312yes—
217Dic3⋊Dic3C2312yes—
218Dic3⋊Dic3C2312yes—
219(C2×D3)⋊Dic3C2312yes—
220(C2×D3)⋊Dic3C2312yes—
221(C2×D3)⋊Dic3C2312yes—
222Dic32C2312yes—
223Dic32C2312yes—
224Dic32C2312yes—
225Dic32C2312yes—
226Dic32C2312yes—
227Dic32C2312yes—
228Dic32C2312yes—
229Dic32C2312yes—
230Q8×#41—91noSylow
231C2×D3×Q8—32no—
232C2×#237—32no—
233C22×Dic6—32no—
234C22×Dic6—32no—
235C3×C4⋊Q8—32no—
236C3×#125—32no—
237C3×#125—32no—
238C3×C22⋊Q8—21no—
239C3×C22⋊Q8—32no—
240C3×C22⋊Q8—32no—
241C3×C22⋊Q8—32no—
242C3×C22⋊Q8—32no—
243C3×C22⋊Q8—32no—
244C3×C22⋊Q8C2×D312yes—
245C3×C4×Q8—32no—
246C3×C4×D4—32no—
247C3×C4×D4—32no—
248C3×C4×D4—32no—
249C2×C3×C4⋊C4—32no—
250C2×C3×C4⋊C4—32no—
251#946—32no—
252#946C2×D312yes—
253Q8×Dic3—32no—
254Q8×Dic3—32no—
255Q8×Dic3—32no—
256Q8×Dic3—61no—
257#944—32no—
258#944—32no—
259#944—32no—
260#944—32no—
261#944—32no—
262#944—61no—
263#944C2×D312yes—
264D4×Dic3—32no—
265D4×Dic3—32no—
266D4×Dic3—32no—
267C4×#67—32no—
268C4×#67—32no—
269C4×#67—32no—
270C4×#67—32no—
271C4×#67—32no—
272C4×#67C2×D312yes—
273#924—32no—
274#924—32no—
275#924—32no—
276#924—32no—
277#924—32no—
278#924—32no—
279#924—61no—
280C2×Dic3⋊C4—32no—
281C2×Dic3⋊C4—32no—
282C2×Dic3⋊C4—32no—
283C2×Dic3⋊C4C2×D312yes—
284C2×C4×Dic3—32no—
285C2×C4×Dic3—32no—
286C2×C4×Dic3—32no—
287C2×C4×Dic3—32no—
288C2×C4×Dic3—32no—
289C2×C4×Dic3—32no—
290C2×C4×Dic3—61no—
291#897—32no—
292#897—32no—
293#896—32no—
294#896—32no—
295#896—32no—
296#896—32no—
297#896—32no—
298#896—32no—
299#896C2×D312yes—
300#896C2×D312yes—
301#892—32no—
302#892—32no—
303#892—32no—
304D3×C4⋊C4—32no—
305D3×C4⋊C4—32no—
306D3×C4⋊C4C2×D312yes—
307#890—32no—
308#890—32no—
309#889—32no—
310#889—32no—
311#889—32no—
312#889—32no—
313#889—32no—
314#889—32no—
315#889—32no—
316#889—32no—
317#889—32no—
318#889—32no—
319#889—62no—
320#889C2×D312yes—
321#889C2×D312yes—
322#888—32no—
323#888—32no—
324#888—32no—
325#888—32no—
326#888—32no—
327#888—32no—
328#888—32no—
329#888—32no—
330#888—32no—
331#888—32no—
332#888—61no—
333#887—32no—
334#887—32no—
335#887—32no—
336#887—32no—
337#887—32no—
338#887—32no—
339#887—32no—
340#887—32no—
341#887—32no—
342#887—32no—
343#887—32no—
344#887—32no—
345#887—32no—
346#887—32no—
347#887—32no—
348#887—32no—
349#887—32no—
350#887—32no—
351#887—32no—
352#887—32no—
353#887—32no—
354#887—32no—
355#887—32no—
356#887—62no—
357#887—61no—
358#887C2×D312yes—
359#67⋊C4—32no—
360#67⋊C4—32no—
361#67⋊C4—32no—
362#67⋊C4—32no—
363#67⋊C4C2×D312yes—
364#67⋊C4C2×D312yes—
365#878—32no—
366#878—32no—
367#878—32no—
368#878—32no—
369#878—32no—
370#878—32no—
371#878—32no—
372#878—32no—
373#878—32no—
374#878—32no—
375#878—62no—
376#878C2×D312yes—
377#878C2×D312yes—
378#877—32no—
379#877—32no—
380#877—32no—
381#877—32no—
382#877—32no—
383#877—32no—
384#877—62no—
385C42×D3—32no—
386C42×D3—32no—
387C42×D3—32no—
388#870—32no—
389#870—32no—
390#869—32no—
391C4×Dic6—32no—
392C4×Dic6—32no—
393C4×Dic6—32no—
394C4×Dic6—32no—
395C4×Dic6—32no—
396C4×Dic6—32no—
397C23×C32C2411yescharacteristic
398C22×C3×D3C2412yes—
399C32×Q8—41no—
400C2×C32×C4—41no—
401C2×C32×C4C2411yescharacteristic
402C2×C32×C4C2412yes—
403C2×C32×C4C2412yes—
404C2×C32×C4C2411yescharacteristic
405C2×C3⋊Dic3—22no—
406C2×C3⋊Dic3C2×Q814yescomplemented
407C2×C3⋊Dic3C2412yes—
408C2×C3⋊Dic3C2412yes—
409C2×C3⋊Dic3C2411yescharacteristic
410C2×C3⋊Dic3C2411yescharacteristic
411C2×C3⋊Dic3C2411yescharacteristic
412C2×C3⋊Dic3C2411yescharacteristic
413#634—24no—
414#634—41no—
415C3×#67C2×Q818yescomplemented
416C2×C3×Dic3—24no—
417C2×C3×Dic3—42no—
418C2×C3×Dic3C2412yes—
419C2×C3×Dic3C2412yes—
420C2×C3×Dic3C2412yes—
421C2×C3×Dic3C2412yes—
422C2×C3×Dic3C2412yes—
423C2×C3×Dic3C2412yes—
424C2×C3×Dic3C2412yes—
425C3×C4×D3—24no—
426C3×C4×D3—42no—
427C3×C4×D3—42no—
428C3×Dic6—24no—
429C3×Dic6—42no—
430#627—22no—
431#627—24no—
432#627—24no—
433#627—42no—
434#627C2×Q814yescomplemented
435#627#4114yescomplemented
436#625C2×Q814yescomplemented
437D3×Dic3—24no—
438D3×Dic3—24no—
439D3×Dic3—42no—
440D3×Dic3C2×Q818yescomplemented
441Q82—91no—
442#557—92no—
443#557—91no—
444#554—32no—
445#554—92no—
446#554—92no—
447#554—92no—
448#554—91no—
449D4×Q8—92no—
450D4×Q8—91no—
451#533—92no—
452#533—92no—
453#533—92no—
454#533—92no—
455#533—91no—
456C4×#41—92no—
457C4×#41—91no—
458C2×C4×Q8—91no—
459C2×C4×Q8—92no—
460C2×C3×Q8—21no—
461C2×C3×Q8—32no—
462C2×C3×Q8—32no—
463C2×C3×Q8C22×D312yes—
464C2×C3×D4—32no—
465C22×C3×C4—21no—
466C22×C3×C4—32no—
467C22×C3×C4—32no—
468C22×C3×C4—32no—
469C22×C3×C4—32no—
470C22×C3×C4—32no—
471C22×C3×C4C22×D312yes—
472C2×#67—32no—
473C2×#67C22×D312yes—
474C22×Dic3—32no—
475C22×Dic3—32no—
476C22×Dic3—32no—
477C22×Dic3—32no—
478C22×Dic3—32no—
479C22×Dic3—32no—
480C22×Dic3—61no—
481C22×Dic3—61no—
482C22×Dic3C22×D312yes—
483C22×Dic3C22×D312yes—
484D3×Q8—68no—
485#237—316no—
486C2×C4×D3—32no—
487C2×C4×D3—32no—
488C2×C4×D3—32no—
489C2×C4×D3—32no—
490C2×C4×D3C22×D312yes—
491C2×C4×D3C22×D312yes—
492C2×C4×D3C22×D312yes—
493C2×Dic6—32no—
494C2×Dic6—32no—
495C2×Dic6—32no—
496C2×Dic6—32no—
497C2×Dic6—32no—
498C2×Dic6—32no—
499C2×Dic6—32no—
500C2×Dic6—32no—
501C2×Dic6—32no—
502C2×Dic6—32no—
503C2×Dic6—32no—
504C2×Dic6—32no—
505C2×Dic6—62no—
506C2×Dic6—61no—
507C2×Dic6—68no—
508C2×Dic6—68no—
509C2×Dic6C22×D312yes—
510C2×Dic6C22×D312yes—
511C3×C4⋊C4—21no—
512C3×C4⋊C4—22no—
513C3×C4⋊C4—32no—
514C3×C4⋊C4—32no—
515C3×C4⋊C4—32no—
516C3×C4⋊C4—32no—
517C3×C4⋊C4—32no—
518C3×C4⋊C4—32no—
519C3×C4⋊C4—32no—
520C3×C4⋊C4—32no—
521C3×C4⋊C4—32no—
522C3×C4⋊C4—32no—
523C3×C4⋊C4—32no—
524C3×C4⋊C4—32no—
525C3×C4⋊C4—32no—
526C3×C4⋊C4C22×D312yes—
527C3×C4⋊C4C22×D312yes—
528C3×C4⋊C4C22×D312yes—
529C3×C22⋊C4—22no—
530C3×C22⋊C4—32no—
531C3×C22⋊C4—32no—
532C3×C22⋊C4—32no—
533C3×C22⋊C4—32no—
534C3×C22⋊C4C22×D312yes—
535C3×C22⋊C4C22×D312yes—
536C3×C42—32no—
537C3×C42—32no—
538C3×C42—32no—
539#217—32no—
540#217—32no—
541#217—32no—
542#217—32no—
543#217—32no—
544#217—62no—
545#217C22×D312yes—
546(C2×D3)⋊C4—32no—
547(C2×D3)⋊C4—32no—
548(C2×D3)⋊C4—32no—
549(C2×D3)⋊C4C22×D312yes—
550(C2×D3)⋊C4C22×D312yes—
551(C2×D3)⋊C4C22×D312yes—
552C4⋊Dic3—32no—
553C4⋊Dic3—32no—
554C4⋊Dic3—32no—
555C4⋊Dic3—32no—
556C4⋊Dic3—32no—
557C4⋊Dic3—32no—
558C4⋊Dic3—32no—
559C4⋊Dic3—32no—
560C4⋊Dic3—32no—
561C4⋊Dic3—32no—
562C4⋊Dic3—62no—
563C4⋊Dic3—61no—
564C4⋊Dic3C22×D312yes—
565C4⋊Dic3C22×D312yes—
566Dic3⋊C4—32no—
567Dic3⋊C4—32no—
568Dic3⋊C4—32no—
569Dic3⋊C4—32no—
570Dic3⋊C4—32no—
571Dic3⋊C4—32no—
572Dic3⋊C4—32no—
573Dic3⋊C4—32no—
574Dic3⋊C4—32no—
575Dic3⋊C4—32no—
576Dic3⋊C4—32no—
577Dic3⋊C4—32no—
578Dic3⋊C4—32no—
579Dic3⋊C4—32no—
580Dic3⋊C4—32no—
581Dic3⋊C4—32no—
582Dic3⋊C4—32no—
583Dic3⋊C4—32no—
584Dic3⋊C4—32no—
585Dic3⋊C4—32no—
586Dic3⋊C4—32no—
587Dic3⋊C4—32no—
588Dic3⋊C4—32no—
589Dic3⋊C4—32no—
590Dic3⋊C4—32no—
591Dic3⋊C4—32no—
592Dic3⋊C4—32no—
593Dic3⋊C4—62no—
594Dic3⋊C4—62no—
595Dic3⋊C4—62no—
596Dic3⋊C4—62no—
597Dic3⋊C4—62no—
598Dic3⋊C4C22×D312yes—
599Dic3⋊C4C22×D312yes—
600Dic3⋊C4C22×D312yes—
601Dic3⋊C4C22×D312yes—
602Dic3⋊C4C22×D312yes—
603Dic3⋊C4C22×D312yes—
604Dic3⋊C4C22×D312yes—
605Dic3⋊C4C22×D312yes—
606Dic3⋊C4C22×D312yes—
607Dic3⋊C4C22×D312yes—
608Dic3⋊C4C22×D312yes—
609C4×Dic3—32no—
610C4×Dic3—32no—
611C4×Dic3—32no—
612C4×Dic3—32no—
613C4×Dic3—32no—
614C4×Dic3—32no—
615C4×Dic3—32no—
616C4×Dic3—32no—
617C4×Dic3—32no—
618C4×Dic3—32no—
619C4×Dic3—32no—
620C4×Dic3—32no—
621C4×Dic3—32no—
622C4×Dic3—32no—
623C4×Dic3—32no—
624C4×Dic3—32no—
625C4×Dic3—32no—
626C4×Dic3—32no—
627C4×Dic3—32no—
628C4×Dic3—32no—
629C4×Dic3—32no—
630C4×Dic3—32no—
631C4×Dic3—32no—
632C4×Dic3—32no—
633C4×Dic3—62no—
634C4×Dic3—62no—
635C4×Dic3—61no—
636C4×Dic3—61no—
637C4×Dic3—61no—
638C4×Dic3—61no—
639C4×Dic3C22×D312yes—
640C4×Dic3C22×D312yes—
641C4×Dic3C22×D312yes—
642C22×C32—21no—
643C22×C32—21no—
644C22×C32C22×Q812yes—
645C22×C32C2511yescharacteristic
646C2×C3×D3—22no—
647C2×C3×D3—22no—
648C2×C3×D3C22×Q814yes—
649C32×C4—21no—
650C32×C4—22no—
651C32×C4—22no—
652C32×C4—21no—
653C3⋊Dic3—22no—
654C3⋊Dic3—21no—
655C3⋊Dic3—22no—
656C3⋊Dic3C22×Q812yes—
657C3⋊Dic3C22×Q812yes—
658C3⋊Dic3C2×#4112yes—
659C3×Dic3—22no—
660C3×Dic3—22no—
661C3×Dic3—22no—
662C3×Dic3—22no—
663C3×Dic3—22no—
664C3×Dic3C22×Q814yes—
665C3×Dic3C2×#4114yes—
666C2×#41—91no—
667C22×Q8—91no—
668C22×Q8—92no—
669C4⋊Q8—32no—
670C4⋊Q8—92no—
671C4⋊Q8—92no—
672C4⋊Q8—92no—
673C4⋊Q8—92no—
674C4⋊Q8—92no—
675C4⋊Q8—92no—
676C4⋊Q8—92no—
677C4⋊Q8—91no—
678C4⋊Q8—91no—
679#125—32no—
680#125—32no—
681#125—92no—
682#125—92no—
683#125—92no—
684#125—92no—
685#125—92no—
686#125—92no—
687#125—92no—
688C22⋊Q8—32no—
689C22⋊Q8—32no—
690C22⋊Q8—32no—
691C22⋊Q8—32no—
692C22⋊Q8—32no—
693C22⋊Q8—92no—
694C22⋊Q8—92no—
695C22⋊Q8—92no—
696C22⋊Q8—92no—
697C22⋊Q8—92no—
698C22⋊Q8—92no—
699C22⋊Q8—92no—
700C22⋊Q8—92no—
701C22⋊Q8—92no—
702C22⋊Q8—92no—
703C22⋊Q8—92no—
704C22⋊Q8—91no—
705C22⋊Q8—92no—
706C22⋊Q8D3211yescharacteristic
707C4×Q8—32no—
708C4×Q8—91no—
709C4×Q8—92no—
710C4×Q8—92no—
711C4×Q8—92no—
712C4×Q8—92no—
713C4×Q8—92no—
714C4×Q8—91no—
715C4×Q8—92no—
716C4×Q8—92no—
717C4×Q8—91no—
718C4×Q8—91no—
719C4×Q8—91no—
720C4×Q8—92no—
721C4×Q8—91no—
722C4×Q8—92no—
723C4×Q8—92no—
724C4×Q8—92no—
725C4×Q8—91no—
726C4×Q8—92no—
727C4×Q8—91no—
728C4×D4—32no—
729C4×D4—32no—
730C4×D4—32no—
731C4×D4—91no—
732C4×D4—92no—
733C4×D4—92no—
734C4×D4—92no—
735C4×D4—91no—
736C4×D4—92no—
737C4×D4—92no—
738#117—91no—
739#117—92no—
740#117—92no—
741#117—92no—
742#117—92no—
743C2×C4⋊C4—32no—
744C2×C4⋊C4—32no—
745C2×C4⋊C4—92no—
746C2×C4⋊C4—92no—
747C2×C4⋊C4—91no—
748C2×C42—92no—
749C2×C42—92no—
750C2×C42—92no—
751C2×C42—92no—
752C2×C42—91no—
753C23×C3—21no—
754C23×C3—32no—
755C23×C3C23×D312yes—
756C22×D3C23×D312yes—
757C3×Q8—42no—
758C3×Q8—42no—
759C3×Q8—64no—
760C3×Q8—122no—
761C3×D4—38no—
762C2×C3×C4—21no—
763C2×C3×C4—21no—
764C2×C3×C4—22no—
765C2×C3×C4—22no—
766C2×C3×C4—32no—
767C2×C3×C4—32no—
768C2×C3×C4—32no—
769C2×C3×C4—32no—
770C2×C3×C4—32no—
771C2×C3×C4—32no—
772C2×C3×C4—32no—
773C2×C3×C4—42no—
774C2×C3×C4—42no—
775C2×C3×C4—64no—
776C2×C3×C4—64no—
777C2×C3×C4—122no—
778C2×C3×C4—122no—
779C2×C3×C4—122no—
780C2×C3×C4C23×D312yes—
781C2×C3×C4C23×D312yes—
782C2×C3×C4C23×D312yes—
783C2×C3×C4C23×D312yes—
784C2×C3×C4C23×D312yes—
785C2×C3×C4C23×D312yes—
786#67—38no—
787#67D3×Q818yescomplemented
788C2×Dic3—24no—
789C2×Dic3—38no—
790C2×Dic3—32no—
791C2×Dic3—32no—
792C2×Dic3—32no—
793C2×Dic3—38no—
794C2×Dic3—32no—
795C2×Dic3—32no—
796C2×Dic3—32no—
797C2×Dic3—32no—
798C2×Dic3—32no—
799C2×Dic3—42no—
800C2×Dic3—64no—
801C2×Dic3—61no—
802C2×Dic3—61no—
803C2×Dic3—61no—
804C2×Dic3—61no—
805C2×Dic3—62no—
806C2×Dic3—62no—
807C2×Dic3—64no—
808C2×Dic3—64no—
809C2×Dic3—64no—
810C2×Dic3—122no—
811C2×Dic3—122no—
812C2×Dic3C23×D312yes—
813C2×Dic3C23×D312yes—
814C2×Dic3C23×D312yes—
815C2×Dic3C23×D312yes—
816C2×Dic3C23×D312yes—
817C2×Dic3C23×D312yes—
818C2×Dic3C23×D312yes—
819C4×D3—24no—
820C4×D3—38no—
821C4×D3—42no—
822C4×D3—42no—
823C4×D3—64no—
824C4×D3—64no—
825C4×D3—122no—
826Dic6—24no—
827Dic6—38no—
828Dic6—38no—
829Dic6—42no—
830Dic6—64no—
831Dic6—64no—
832Dic6—64no—
833Dic6—64no—
834Dic6—64no—
835Dic6—64no—
836Dic6—64no—
837Dic6—124no—
838Dic6—122no—
839Dic6—122no—
840Dic6—122no—
841Dic6—122no—
842C2×C32—22no—
843C2×C32C23×Q811yescharacteristic
844C2×C32C22×#4111yescharacteristic
845C2×C32#58511yescharacteristic
846C3×D3—24no—
847#41—98no—
848C2×Q8—32no—
849C2×Q8—32no—
850C2×Q8—91no—
851C2×Q8—91no—
852C2×Q8—92no—
853C2×Q8—92no—
854C2×Q8—91no—
855C2×Q8—92no—
856C2×Q8—92no—
857C2×Q8—91no—
858C2×Q8—184no—
859C2×Q8—188no—
860C2×Q8C2×D3211yescharacteristic
861C2×D4—32no—
862C2×D4—91no—
863C22×C4—32no—
864C22×C4—32no—
865C22×C4—32no—
866C22×C4—32no—
867C22×C4—32no—
868C22×C4—92no—
869C22×C4—92no—
870C22×C4—92no—
871C22×C4—92no—
872C22×C4—91no—
873C22×C4—91no—
874C22×C4C2×D3211yescharacteristic
875C4⋊C4—32no—
876C4⋊C4—32no—
877C4⋊C4—32no—
878C4⋊C4—32no—
879C4⋊C4—32no—
880C4⋊C4—32no—
881C4⋊C4—32no—
882C4⋊C4—32no—
883C4⋊C4—32no—
884C4⋊C4—32no—
885C4⋊C4—32no—
886C4⋊C4—32no—
887C4⋊C4—32no—
888C4⋊C4—91no—
889C4⋊C4—92no—
890C4⋊C4—92no—
891C4⋊C4—92no—
892C4⋊C4—91no—
893C4⋊C4—92no—
894C4⋊C4—91no—
895C4⋊C4—91no—
896C4⋊C4—92no—
897C4⋊C4—92no—
898C4⋊C4—92no—
899C4⋊C4—92no—
900C4⋊C4—92no—
901C4⋊C4—92no—
902C4⋊C4—92no—
903C4⋊C4—92no—
904C4⋊C4—92no—
905C4⋊C4—92no—
906C4⋊C4—92no—
907C4⋊C4—92no—
908C4⋊C4—91no—
909C4⋊C4C2×D3212yes—
910C4⋊C4C2×D3211yescharacteristic
911C22⋊C4—32no—
912C22⋊C4—32no—
913C22⋊C4—32no—
914C22⋊C4—32no—
915C22⋊C4—92no—
916C22⋊C4—92no—
917C22⋊C4—92no—
918C22⋊C4—92no—
919C22⋊C4C2×D3212yes—
920C42—32no—
921C42—32no—
922C42—32no—
923C42—92no—
924C42—92no—
925C42—92no—
926C42—92no—
927C42—92no—
928C42—92no—
929C42—92no—
930C42—92no—
931C42—91no—
932C42—92no—
933C42—92no—
934C42—91no—
935C42—91no—
936C42—91no—
937C22×C3—22no—
938C22×C3—22no—
939C22×C3—22no—
940C22×C3—21no—
941C22×C3—34no—
942C22×C3—41no—
943C22×C3—41no—
944C22×C3—62no—
945C22×C3—62no—
946C22×C3C2×D3×Q814yes—
947C22×C3C24×D312yes—
948C2×D3—22no—
949C2×D3—22no—
950C2×D3C2×D3×Q814yes—
951C3×C4—22no—
952C3×C4—22no—
953C3×C4—22no—
954C3×C4—22no—
955C3×C4—22no—
956C3×C4—22no—
957C3×C4—22no—
958C3×C4—34no—
959C3×C4—34no—
960C3×C4—42no—
961C3×C4—41no—
962C3×C4—42no—
963C3×C4—62no—
964C3×C4—62no—
965C3×C4—62no—
966C3×C4—62no—
967C3×C4—62no—
968Dic3—22no—
969Dic3—22no—
970Dic3—22no—
971Dic3—22no—
972Dic3—22no—
973Dic3—34no—
974Dic3—34no—
975Dic3—34no—
976Dic3—62no—
977Dic3—62no—
978Dic3—62no—
979Dic3—62no—
980Dic3—62no—
981Dic3—62no—
982Dic3—62no—
983Dic3—62no—
984Dic3—122no—
985Dic3—122no—
986Dic3—121no—
987Dic3C2×D3×Q814yes—
988Dic3D3×#4114yes—
989C32Q8×#4111yescharacteristic, complemented, Sylow
990C23—32no—
991C23C22×D3211yescharacteristic
992Q8—41no—
993Q8—64no—
994Q8—94no—
995Q8—94no—
996Q8—122no—
997Q8—184no—
998Q8—184no—
999Q8—184no—
1000Q8—182no—
1001Q8—361no—
1002Q8—362no—
1003D4—38no—
1004D4—94no—
1005C2×C4—32no—
1006C2×C4—32no—
1007C2×C4—32no—
1008C2×C4—32no—
1009C2×C4—32no—
1010C2×C4—32no—
1011C2×C4—32no—
1012C2×C4—41no—
1013C2×C4—64no—
1014C2×C4—64no—
1015C2×C4—98no—
1016C2×C4—94no—
1017C2×C4—91no—
1018C2×C4—91no—
1019C2×C4—91no—
1020C2×C4—92no—
1021C2×C4—92no—
1022C2×C4—91no—
1023C2×C4—122no—
1024C2×C4—122no—
1025C2×C4—122no—
1026C2×C4—184no—
1027C2×C4—184no—
1028C2×C4—182no—
1029C2×C4—362no—
1030C2×C4C22×D3211yescharacteristic
1031C2×C4C22×D3212yes—
1032C2×C4C22×D3212yes—
1033C2×C4C22×D3211yescharacteristic
1034C2×C3—24no—
1035C2×C3—21no—
1036C2×C3—21no—
1037C2×C3—21no—
1038C2×C3—42no—
1039C2×C3—64no—
1040C2×C3C22×D3×Q812yes—
1041C2×C3C2×D3×#4112yes—
1042C2×C3#596612yes—
1043D3—24no—
1044C22—21no—
1045C22—21no—
1046C22—34no—
1047C22—62no—
1048C22—62no—
1049C22D32×Q812yes—
1050C22C23×D3211yescharacteristic
1051C4—21no—
1052C4—21no—
1053C4—22no—
1054C4—22no—
1055C4—34no—
1056C4—34no—
1057C4—62no—
1058C4—62no—
1059C4—62no—
1060C4—62no—
1061C4—62no—
1062C4—92no—
1063C4—92no—
1064C4—92no—
1065C4—182no—
1066C4—182no—
1067C4—181no—
1068C3—21no—
1069C3#8692312yescomplemented
1070C2—22no—
1071C2—64no—
1072C2#1059667911yescharacteristic
1073C2C2×D32×Q811yescharacteristic
1074C2D32×#4111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C22⋊Q8C22
prime radicalC2×#3805C22
hypercenterC22⋊Q8D32
hypocenterC32Q8×#41
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596093C2semidirect
2. C3×#5636C2semidirect
3. #10595421C2semidirect
4. #10595370C2semidirect
5. #10595368C2semidirect
6. #10594951C2semidirect
8. C2×#63838C2semidirect
9. #10594596C2semidirect
10. #10594533C2semidirect
11. #10594388C2semidirect
12. #10594388C2semidirect
13. #10594377C2semidirect
14. D3×#887C2semidirect
15. #10594315C2semidirect
16. #10594156C2semidirect
17. #10594071C2semidirect
19. #10594030C2semidirect
118. #5636D3semidirect
162. #3805Q8semidirect
406. C2×C3⋊Dic3C2×Q8semidirect
415. C3×#67C2×Q8semidirect
434. #627C2×Q8semidirect
435. #627#41semidirect
436. #625C2×Q8semidirect
440. D3×Dic3C2×Q8semidirect
787. #67D3×Q8semidirect
989. C32Q8×#41semidirect
1069. C3#86923semidirect

Maximal subgroups

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

subgroupindex
#105960932
C3×#56362
#105954212
#105953702
#105953682
#105949512
C4×#38052
C2×#638382
#105945962
#105945332
#105943882
#105943772
D3×#8872
#105943152
#105941562
#105940712
#105940502
#105940302
#869233