Finite Group Databasebeta

← #11904764

Subgroups — #11904764

Order 1152.

3205 conjugacy classes of subgroups.

The subgroup lattice has 1300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64306C211yesmaximal, characteristic, complemented
2C2×#64298C211yesmaximal, characteristic, complemented
3C2×#64105C211yesmaximal, characteristic, complemented
4C3×#5507C212yesmaximal, complemented
5#10595075C212yesmaximal, complemented
6#10595068C212yesmaximal, complemented
7#10594930C211yesmaximal, characteristic, complemented
8#10594921C211yesmaximal, characteristic, complemented
9#10594920C211yesmaximal, characteristic, complemented
10#10594888C212yesmaximal, complemented
11#10594876C211yesmaximal, characteristic, complemented
12#10594617C212yesmaximal, complemented
13#10594614C212yesmaximal, complemented
14D3×#896C212yesmaximal, complemented
15#10594513C212yesmaximal, complemented
16#10594378C212yesmaximal, complemented
17#10594375C212yesmaximal, complemented
18#10594368C212yesmaximal, complemented
19#10594366C212yesmaximal, complemented
20#86677—32nomaximal
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×#634C2211yescharacteristic, complemented
23C2×C3×#235C2212yes—
24C2×C3×#235C2212yescomplemented
25C2×#3811C2212yes—
26C2×#3805C2211yescharacteristic
27C2×#3805C2211yescharacteristic
28C2×#3805C2212yescomplemented
29C2×#3805C2211yescharacteristic, complemented
30#64306—28no—
31C2×#3802C2211yescharacteristic
32C2×C4×D32C2212yes—
33C2×#3798C2211yescharacteristic
34C2×#3798C2211yescharacteristic
35C2×#3797C2211yescharacteristic
36#64298—28no—
37C2×#3796C2212yes—
38C2×#3795C2212yescomplemented
39C2×#3795C2212yescomplemented
40C2×D3×Dic6C2212yescomplemented
41C2×D3×Dic6C2212yescomplemented
42C2×C32×C4⋊C4C2211yescharacteristic, complemented
43C2×#3752C2211yescharacteristic
44C2×#3752C2211yescharacteristic
45C2×#3750C2211yescharacteristic, complemented
46C2×#3750C2211yescharacteristic, complemented
47#64105C2212yes—
48#64105C2212yes—
49#64105C2212yescomplemented
50#64105C2212yescomplemented
51C3×#930C2212yescomplemented
52C3×#929C2212yescomplemented
53C3×#929C2212yescomplemented
54C3×C4×#67C2212yescomplemented
55C3×#896C2212yescomplemented
56C3×#896C2212yescomplemented
57C3×#895C2212yescomplemented
58C3×#894C2212yescomplemented
59C3×#894C2212yescomplemented
60C3×#893C2212yescomplemented
61C3×D3×C4⋊C4C2212yescomplemented
62C3×#888C2212yescomplemented
63#63981C2212yes—
64#63980C2212yescomplemented
65#67⋊Dic3C2212yescomplemented
66#63962C2212yescomplemented
67#63957C2211yescharacteristic, complemented
68#63922C2212yes—
69#63922C2212yes—
70D3×(C2×D3)⋊C4C2212yes—
71D3×(C2×D3)⋊C4C2212yes—
72#63913C2212yescomplemented
73#63912C2211yescharacteristic
74#63912C2211yescharacteristic, complemented
75#63907C2212yescomplemented
76#63906C2212yescomplemented
77#63906C2212yescomplemented
78#63905C2212yescomplemented
79#63904C2212yes—
80#63899C2212yescomplemented
81#63899C2212yescomplemented
82#63896C2212yescomplemented
83#63896C2212yescomplemented
84#63895C2212yes—
85#63890C2212yescomplemented
86#63888C2212yes—
87#63887C2212yescomplemented
88#63886C2212yescomplemented
89#63886C2212yescomplemented
90#63885C2212yescomplemented
91#63885C2212yescomplemented
92#63885C2212yescomplemented
93#63884C2212yescomplemented
94#63881C2212yes—
95#63881C2212yescomplemented
96#63880C2212yes—
97#63879C2212yescomplemented
98#63879C2212yescomplemented
99#63877C2212yescomplemented
100D3×Dic3⋊C4C2212yescomplemented
101D3×Dic3⋊C4C2212yescomplemented
102#63865C2211yescharacteristic
103#63865C2211yescharacteristic, complemented
104#63852C2212yescomplemented
105#63851C2212yescomplemented
106#63850C2212yescomplemented
107#63840C2212yescomplemented
108#63839C2212yescomplemented
109#63837C2212yescomplemented
110C2×#1010—32no—
111C2×D3×#41—32no—
112C3×#547—32no—
113#5829—32no—
114#5824—32no—
115#5727—32no—
116#5724—32no—
117#5656—32no—
118#5656—32no—
119#5655—32no—
120#5655—32no—
121#5654—32no—
122#5654—32no—
123#5648—32no—
124#5648—32no—
125#5633—32no—
126#5632—32no—
127#5629—32no—
128D3×C22⋊Q8—32no—
129#5610—32no—
130#5610—32no—
131#5597—32no—
132#5597—32no—
133#5554—32no—
134#5552—32no—
135#5547—32no—
136#5546—32no—
137C2×#896—32no—
138C2×#896—32no—
139C2×#896—61no—
140#5507—32no—
141#5507D312yescomplemented
142C23×C3⋊D3C2311yescharacteristic
143C22×D32C2312yes—
144C22×C32×C4C2311yescharacteristic
145C22×C32×C4C2311yescharacteristic
146C22×C32×C4C2311yescharacteristic
147C22×C3⋊Dic3C2311yescharacteristic
148C22×C3⋊Dic3C2311yescharacteristic
149C22×C3⋊Dic3C2311yescharacteristic
150C2×C4×C3⋊D3—24no—
151C2×C4×C3⋊D3C2311yescharacteristic
152C2×C4×C3⋊D3C2311yescharacteristic
153C2×C4×C3⋊D3C2311yescharacteristic
154C2×C4×C3⋊D3C2311yescharacteristic
155C2×#634—24no—
156C2×#634C2312yes—
157C2×#634C2312yes—
158C2×C3×#67C2312yes—
159C2×C3×#67C2312yes—
160C2×C3×#67C2312yes—
161C3×#235—28no—
162C3×#235—28no—
163C2×C3×D12C2312yes—
164C2×C3×D12C2312yes—
165C2×C3×D12C2312yes—
166C2×C3×C4×D3C2312yes—
167C2×C3×C4×D3C2312yes—
168C2×C3×C4×D3C2312yes—
169C2×C3×C4×D3C2312yes—
170C2×C3×C4×D3C2312yes—
171C2×C3×Dic6C2312yes—
172C2×C3×Dic6C2312yes—
173#3811—28no—
174C2×#627C2312yes—
175C2×#627C2311yescharacteristic
176C2×#627C2311yescharacteristic
177C2×#627C2311yescharacteristic
178C2×#626C2312yes—
179C2×#626C2312yes—
180C2×#626C2312yes—
181C2×#626C2312yes—
182C2×#625C2311yescharacteristic
183C2×#625C2312yes—
184C2×#625C2311yescharacteristic
185C2×#625C2312yes—
186C2×#625C2311yescharacteristic
187C2×#624C2312yes—
188#3805—24no—
189#3805—24no—
190#3805—28no—
191#3805D418yescomplemented
192C2×D3×Dic3C2312yes—
193C2×D3×Dic3C2312yes—
194C2×D3×Dic3C2312yes—
195C2×D3×Dic3C2312yes—
196C2×D3×Dic3C2312yes—
197C2×D3×Dic3C2312yes—
198#3802—24no—
199C4×D32—28no—
200#3798—24no—
201#3798—24no—
202#3797—24no—
203#3796—28no—
204#3795—28no—
205#3795—28no—
206D3×Dic6—28no—
207D3×Dic6—28no—
208C32×C4⋊C4C2312yes—
209C32×C4⋊C4C2312yes—
210#3752C2312yes—
211#3752C2312yes—
212#3752C2312yes—
213#3752C2312yes—
214#3750C2312yes—
215#3750C2312yes—
216#3750C2312yes—
217#3750C2312yes—
218C3×#217C2312yes—
219C3×(C2×D3)⋊C4C2312yes—
220C3×(C2×D3)⋊C4C2312yes—
221C3×(C2×D3)⋊C4C2312yes—
222C3×(C2×D3)⋊C4C2312yes—
223C3×(C2×D3)⋊C4C2312yes—
224C3×(C2×D3)⋊C4C2312yes—
225C3×(C2×D3)⋊C4C2312yes—
226C3×C4⋊Dic3C2312yes—
227C3×Dic3⋊C4C2312yes—
228C3×Dic3⋊C4C2312yes—
229C3×Dic3⋊C4C2312yes—
230C3×Dic3⋊C4C2312yes—
231C3×Dic3⋊C4C2312yes—
232C3×C4×Dic3C2312yes—
233#3724C2312yes—
234#3724C2311yescharacteristic
235#3724C2311yescharacteristic
236Dic3⋊Dic3C2312yes—
237Dic3⋊Dic3C2312yes—
238Dic3⋊Dic3C2312yes—
239#3722C2312yes—
240#3722C2312yes—
241(C2×D3)⋊Dic3C2312yes—
242(C2×D3)⋊Dic3C2312yes—
243(C2×D3)⋊Dic3C2312yes—
244(C2×D3)⋊Dic3C2312yes—
245(C2×D3)⋊Dic3C2312yes—
246Dic32C2312yes—
247Dic32C2312yes—
248#3489—91noSylow
249C2×C3×#41—32no—
250C2×C3×#41—32no—
251#1010—616no—
252D3×#41—616no—
253C2×#239—32no—
254C2×D3×Q8—32no—
255C2×D3×Q8—32no—
256C2×D3×Q8—32no—
257C2×#237—32no—
258C2×#237—32no—
259C2×#237—32no—
260C2×#237—32no—
261C2×#237—32no—
262C2×#237—32no—
263C2×#237—32no—
264C2×#237—32no—
265C2×D3×D4—32no—
266C2×D3×D4—32no—
267C2×D3×D4—32no—
268C2×#235—32no—
269C2×#235—32no—
270C2×#235—32no—
271C2×#235—32no—
272C2×#235C2×D312yes—
273C2×#235C2×D312yescomplemented
274C22×C4×D3—32no—
275C22×C4×D3—32no—
276C22×C4×D3—32no—
277C22×C4×D3—61no—
278C22×Dic6—32no—
279C22×Dic6—32no—
280C22×Dic6—32no—
281C22×Dic6—61no—
282C3×C4⋊Q8—32no—
283C3×#123—32no—
284C3×#123—32no—
285C3×#123—32no—
286C3×#123—32no—
287C3×C22⋊Q8—32no—
288C3×C22⋊Q8—32no—
289C3×#121—32no—
290C3×#121—32no—
291C3×C4×D4—32no—
292C3×C4×D4—32no—
293C2×C3×C4⋊C4—21no—
294C2×C3×C4⋊C4—32no—
295C2×C3×C4⋊C4C2×D312yescomplemented
296#947—32no—
297#946—32no—
298#946—32no—
299#944—32no—
300#939—32no—
301#939—32no—
302#939—32no—
303#939—32no—
304#939—32no—
305#939—32no—
306#939—32no—
307#937—32no—
308#937—32no—
309#937—32no—
310#935—32no—
311#935—32no—
312D4×Dic3—32no—
313#930—32no—
314#930—32no—
315#930C2×D312yescomplemented
316#929—32no—
317#929—32no—
318#929C2×D312yescomplemented
319#929C2×D312yescomplemented
320C4×#67—32no—
321C4×#67—32no—
322C4×#67—32no—
323C4×#67C2×D312yescomplemented
324C2×(C2×D3)⋊C4—32no—
325C2×(C2×D3)⋊C4—32no—
326C2×(C2×D3)⋊C4—32no—
327C2×(C2×D3)⋊C4—32no—
328C2×(C2×D3)⋊C4—61no—
329C2×(C2×D3)⋊C4—61no—
330#924—32no—
331C2×Dic3⋊C4—32no—
332C2×Dic3⋊C4—32no—
333C2×Dic3⋊C4—32no—
334C2×Dic3⋊C4—32no—
335C2×Dic3⋊C4—61no—
336C2×Dic3⋊C4—61no—
337#897—32no—
338#896—32no—
339#896—32no—
340#896—32no—
341#896—32no—
342#896—32no—
343#896—32no—
344#896—32no—
345#896—32no—
346#896—32no—
347#896—32no—
348#896—32no—
349#896—32no—
350#896—32no—
351#896—32no—
352#896—32no—
353#896—32no—
354#896—32no—
355#896—62no—
356#896—62no—
357#896—62no—
358#896—62no—
359#896C2×D312yescomplemented
360#896C2×D312yescomplemented
361#895—32no—
362#895—32no—
363#895C2×D312yescomplemented
364#894—32no—
365#894—32no—
366#894—32no—
367#894C2×D312yescomplemented
368#894C2×D312yescomplemented
369#893—32no—
370#893—32no—
371#893—32no—
372#893C2×D312yescomplemented
373D3×C4⋊C4—32no—
374D3×C4⋊C4—32no—
375D3×C4⋊C4C2×D312yescomplemented
376#888—32no—
377#888—32no—
378#888—32no—
379#888C2×D312yescomplemented
380#887—32no—
381#886—32no—
382#886—32no—
383#885—32no—
384#885—32no—
385#885—32no—
386#885—32no—
387#884—32no—
388#884—32no—
389#884—32no—
390#884—32no—
391#884—32no—
392#884—32no—
393#884—32no—
394#883—32no—
395#882—32no—
396#882—32no—
397#882—32no—
398#67⋊C4—32no—
399#67⋊C4—32no—
400#67⋊C4—32no—
401#67⋊C4—32no—
402#67⋊C4—32no—
403#67⋊C4—32no—
404D3×C22⋊C4—32no—
405D3×C22⋊C4—32no—
406#878—32no—
407#878—32no—
408#878—32no—
409#878—32no—
410#878—32no—
411#877—32no—
412#877—32no—
413#875—32no—
414C4×D12—32no—
415#872—32no—
416C4×Dic6—32no—
417C23×C32C2411yescharacteristic
418C22×C3⋊D3—22no—
419C22×C3⋊D3—22no—
420C22×C3⋊D3—41no—
421C22×C3⋊D3C2411yescharacteristic
422C22×C3⋊D3C2411yescharacteristic
423C22×C3×D3C2412yes—
424C22×C3×D3C2412yes—
425C22×C3×D3C2412yes—
426C2×D32—24no—
427C2×D32—24no—
428C2×D32—42no—
429C2×C32×C4—22no—
430C2×C32×C4—22no—
431C2×C32×C4—41no—
432C2×C32×C4C2412yes—
433C2×C32×C4C2411yescharacteristic
434C2×C32×C4C2411yescharacteristic
435C2×C32×C4C2412yes—
436C2×C3⋊Dic3—22no—
437C2×C3⋊Dic3—41no—
438C2×C3⋊Dic3C2×D414yes—
439C2×C3⋊Dic3C2412yes—
440C2×C3⋊Dic3C2412yes—
441C2×C3⋊Dic3C2411yescharacteristic
442C2×C3⋊Dic3C2411yescharacteristic
443C4×C3⋊D3—22no—
444C4×C3⋊D3—22no—
445C4×C3⋊D3—22no—
446C4×C3⋊D3—22no—
447#634—24no—
448#634—24no—
449C3×#67—24no—
450C3×#67—24no—
451C3×#67C2×D418yes—
452C2×C3×Dic3C2412yes—
453C2×C3×Dic3C2412yes—
454C2×C3×Dic3C2412yes—
455C2×C3×Dic3C2412yes—
456C2×C3×Dic3C2412yes—
457C3×D12—24no—
458C3×D12—24no—
459C3×D12—42no—
460C3×C4×D3—24no—
461C3×C4×D3—24no—
462C3×C4×D3—24no—
463C3×C4×D3—24no—
464C3×C4×D3—42no—
465C3×Dic6—24no—
466C3×Dic6—24no—
467#627—22no—
468#627—22no—
469#627—24no—
470#627C2×D414yes—
471#626—24no—
472#626—24no—
473#626—24no—
474#626—42no—
475#625—24no—
476#625—22no—
477#625—22no—
478#625—42no—
479#625C2×D414yes—
480#624—24no—
481D3×Dic3—24no—
482D3×Dic3—24no—
483D3×Dic3—24no—
484D3×Dic3—24no—
485D3×Dic3—42no—
486D3×Dic3C2×D418yes—
487C2×2−1+4—91no—
488C22×#41—91no—
489D4×Q8—92no—
490#548—92no—
491#547—32no—
492#547—92no—
493#547—92no—
494#546—92no—
495#546—92no—
496#546—92no—
497#537—91no—
498#537—92no—
499#536—91no—
500#536—92no—
501#525—92no—
502#525—91no—
503C2×C22⋊Q8—92no—
504C2×C22⋊Q8—91no—
505#520—91no—
506C23×D3—32no—
507C23×D3—32no—
508C23×D3—32no—
509C23×D3—61no—
510C3×#41—68no—
511C3×#41—68no—
512C2×C3×Q8—32no—
513C2×C3×Q8—32no—
514C2×C3×D4—32no—
515C2×C3×D4—32no—
516C2×C3×D4—32no—
517C2×C3×D4—32no—
518C2×C3×D4—32no—
519C2×C3×D4—32no—
520C22×C3×C4—21no—
521C22×C3×C4—21no—
522C22×C3×C4—21no—
523C22×C3×C4—32no—
524C22×C3×C4—32no—
525C22×C3×C4—32no—
526C22×C3×C4—32no—
527C22×C3×C4—32no—
528C22×C3×C4C22×D312yes—
529C22×C3×C4C22×D312yes—
530C22×C3×C4C22×D312yes—
531C2×#67—32no—
532C2×#67—32no—
533C2×#67—32no—
534C2×#67—32no—
535C2×#67—32no—
536C2×#67—32no—
537C2×#67—32no—
538C2×#67—32no—
539C2×#67—32no—
540C2×#67—32no—
541C2×#67—32no—
542C2×#67C22×D312yes—
543C2×#67C22×D312yes—
544C2×#67C22×D312yes—
545C22×Dic3—32no—
546C22×Dic3—32no—
547C22×Dic3—32no—
548C22×Dic3—32no—
549C22×Dic3—32no—
550C22×Dic3—32no—
551C22×Dic3—32no—
552C22×Dic3—32no—
553C22×Dic3—32no—
554C22×Dic3—61no—
555C22×Dic3—61no—
556C22×Dic3—61no—
557#239—68no—
558D3×Q8—68no—
559D3×Q8—68no—
560D3×Q8—68no—
561#237—316no—
562#237—68no—
563#237—68no—
564#237—68no—
565#237—68no—
566#237—68no—
567#237—68no—
568#237—68no—
569D3×D4—68no—
570D3×D4—68no—
571D3×D4—68no—
572#235—28no—
573#235—28no—
574#235—68no—
575#235—68no—
576#235—68no—
577#235—68no—
578C2×D12—32no—
579C2×D12—32no—
580C2×D12—32no—
581C2×D12—32no—
582C2×D12C22×D312yes—
583C2×D12C22×D312yes—
584C2×D12C22×D312yes—
585C2×C4×D3—32no—
586C2×C4×D3—32no—
587C2×C4×D3—32no—
588C2×C4×D3—32no—
589C2×C4×D3—32no—
590C2×C4×D3—32no—
591C2×C4×D3—32no—
592C2×C4×D3—32no—
593C2×C4×D3—32no—
594C2×C4×D3—32no—
595C2×C4×D3—32no—
596C2×C4×D3—32no—
597C2×C4×D3—61no—
598C2×C4×D3—61no—
599C2×C4×D3—61no—
600C2×C4×D3—61no—
601C2×C4×D3—68no—
602C2×C4×D3—68no—
603C2×C4×D3—68no—
604C2×C4×D3—124no—
605C2×C4×D3C22×D312yes—
606C2×C4×D3C22×D312yes—
607C2×C4×D3C22×D312yes—
608C2×C4×D3C22×D312yes—
609C2×C4×D3C22×D312yes—
610C2×Dic6—32no—
611C2×Dic6—32no—
612C2×Dic6—32no—
613C2×Dic6—32no—
614C2×Dic6—32no—
615C2×Dic6—32no—
616C2×Dic6—32no—
617C2×Dic6—32no—
618C2×Dic6—32no—
619C2×Dic6—62no—
620C2×Dic6—62no—
621C2×Dic6—68no—
622C2×Dic6—68no—
623C2×Dic6—68no—
624C2×Dic6—124no—
625C2×Dic6C22×D312yes—
626C2×Dic6C22×D312yes—
627C3×C4⋊C4—22no—
628C3×C4⋊C4—22no—
629C3×C4⋊C4—32no—
630C3×C4⋊C4—32no—
631C3×C4⋊C4—32no—
632C3×C4⋊C4—32no—
633C3×C4⋊C4—32no—
634C3×C4⋊C4—32no—
635C3×C4⋊C4C22×D312yes—
636C3×C4⋊C4C22×D312yes—
637C3×C4⋊C4C22×D312yes—
638C3×C4⋊C4C22×D312yes—
639C3×C22⋊C4—32no—
640C3×C22⋊C4—32no—
641C3×C22⋊C4—32no—
642C3×C22⋊C4—32no—
643C3×C22⋊C4—32no—
644C3×C22⋊C4—32no—
645C3×C22⋊C4—32no—
646C3×C22⋊C4—32no—
647C3×C42—32no—
648#217—32no—
649#217—32no—
650#217—32no—
651#217—32no—
652#217—32no—
653#217C22×D312yes—
654(C2×D3)⋊C4—32no—
655(C2×D3)⋊C4—32no—
656(C2×D3)⋊C4—32no—
657(C2×D3)⋊C4—32no—
658(C2×D3)⋊C4—32no—
659(C2×D3)⋊C4—32no—
660(C2×D3)⋊C4—32no—
661(C2×D3)⋊C4—32no—
662(C2×D3)⋊C4—32no—
663(C2×D3)⋊C4—32no—
664(C2×D3)⋊C4—32no—
665(C2×D3)⋊C4—32no—
666(C2×D3)⋊C4—32no—
667(C2×D3)⋊C4—32no—
668(C2×D3)⋊C4—32no—
669(C2×D3)⋊C4—32no—
670(C2×D3)⋊C4—32no—
671(C2×D3)⋊C4—62no—
672(C2×D3)⋊C4—62no—
673(C2×D3)⋊C4—62no—
674(C2×D3)⋊C4—62no—
675(C2×D3)⋊C4C22×D312yes—
676(C2×D3)⋊C4C22×D312yes—
677(C2×D3)⋊C4C22×D312yes—
678(C2×D3)⋊C4C22×D312yes—
679(C2×D3)⋊C4C22×D312yes—
680(C2×D3)⋊C4C22×D312yes—
681(C2×D3)⋊C4C22×D312yes—
682C4⋊Dic3—32no—
683C4⋊Dic3—32no—
684C4⋊Dic3—32no—
685C4⋊Dic3C22×D312yes—
686Dic3⋊C4—32no—
687Dic3⋊C4—32no—
688Dic3⋊C4—32no—
689Dic3⋊C4—32no—
690Dic3⋊C4—32no—
691Dic3⋊C4—32no—
692Dic3⋊C4—32no—
693Dic3⋊C4—32no—
694Dic3⋊C4—32no—
695Dic3⋊C4—32no—
696Dic3⋊C4—32no—
697Dic3⋊C4—32no—
698Dic3⋊C4—32no—
699Dic3⋊C4—32no—
700Dic3⋊C4—32no—
701Dic3⋊C4—62no—
702Dic3⋊C4—62no—
703Dic3⋊C4—62no—
704Dic3⋊C4—62no—
705Dic3⋊C4C22×D312yes—
706Dic3⋊C4C22×D312yes—
707Dic3⋊C4C22×D312yes—
708Dic3⋊C4C22×D312yes—
709Dic3⋊C4C22×D312yes—
710C4×Dic3—32no—
711C4×Dic3—32no—
712C4×Dic3—32no—
713C4×Dic3—32no—
714C4×Dic3C22×D312yes—
715C22×C32—21no—
716C22×C32—21no—
717C22×C32C22×D412yes—
718C22×C32C2511yescharacteristic
719C2×C3⋊D3—21no—
720C2×C3⋊D3—21no—
721C2×C3⋊D3—21no—
722C2×C3⋊D3—21no—
723C2×C3⋊D3—21no—
724C2×C3⋊D3—44no—
725C2×C3⋊D32−1+412yescomplemented
726C2×C3×D3—22no—
727C2×C3×D3—22no—
728C2×C3×D3—22no—
729C2×C3×D3—22no—
730C2×C3×D3—22no—
731C2×C3×D3—22no—
732C2×C3×D3—22no—
733C2×C3×D3—22no—
734C2×C3×D3C22×D414yes—
735D32—48no—
736C32×C4—21no—
737C32×C4—22no—
738C32×C4—21no—
739C32×C4—22no—
740C3⋊Dic3—22no—
741C3⋊Dic3—22no—
742C3⋊Dic3C22×D412yes—
743C3⋊Dic3C22×D412yes—
744C3×Dic3—22no—
745C3×Dic3—22no—
746C3×Dic3—22no—
747C3×Dic3—22no—
748C3×Dic3C22×D414yes—
7492−1+4—188no—
750C2×#41—32no—
751C2×#41—32no—
752C2×#41—91no—
753C2×#41—91no—
754C2×#41—92no—
755C2×#41—92no—
756C2×#41—91no—
757C2×#41—91no—
758C2×#41—91no—
759C2×#41—92no—
760C2×#41—92no—
761C2×#41—188no—
762C22×Q8—92no—
763C22×Q8—92no—
764C22×Q8—91no—
765C22×Q8—91no—
766C22×D4—92no—
767C22×D4—91no—
768C23×C4—92no—
769C23×C4—91no—
770C4⋊Q8—32no—
771C4⋊Q8—92no—
772C4⋊Q8—92no—
773#124—92no—
774#124—92no—
775#124—92no—
776#123—32no—
777#123—32no—
778#123—32no—
779#123—32no—
780#123—92no—
781#123—92no—
782#123—92no—
783#123—92no—
784#123—92no—
785C22⋊Q8—32no—
786C22⋊Q8—32no—
787C22⋊Q8—92no—
788C22⋊Q8—92no—
789C22⋊Q8—92no—
790C22⋊Q8—92no—
791C22⋊Q8—92no—
792C22⋊Q8—91no—
793C22⋊Q8—92no—
794C22⋊Q8—91no—
795C22⋊Q8—92no—
796C22⋊Q8—92no—
797C22⋊Q8—92no—
798C22⋊Q8—92no—
799C22⋊Q8—92no—
800C22⋊Q8—92no—
801#121—32no—
802#121—32no—
803#121—91no—
804#121—91no—
805#121—92no—
806#121—92no—
807#121—92no—
808#121—92no—
809#121—92no—
810#121—92no—
811#121—92no—
812#121—92no—
813#120—92no—
814#120—92no—
815#120—92no—
816C4×Q8—92no—
817C4×D4—32no—
818C4×D4—32no—
819C4×D4—92no—
820C4×D4—92no—
821C4×D4—92no—
822C4×D4—92no—
823C4×D4—92no—
824C4×D4—92no—
825C4×D4—92no—
826#117—92no—
827#117—91no—
828C2×C4⋊C4—32no—
829C2×C4⋊C4—92no—
830C2×C4⋊C4—92no—
831C2×C4⋊C4—91no—
832C2×C4⋊C4—91no—
833C2×C4⋊C4D3211yescharacteristic, complemented
834C2×C22⋊C4—92no—
835C2×C22⋊C4—92no—
836C2×C22⋊C4—91no—
837C2×C22⋊C4—91no—
838C23×C3—21no—
839C23×C3—32no—
840C23×C3—32no—
841C23×C3—32no—
842C23×C3C23×D312yes—
843C22×D3—32no—
844C22×D3—32no—
845C22×D3—61no—
846C22×D3—61no—
847C22×D3—64no—
848C22×D3—64no—
849C22×D3—64no—
850C22×D3—64no—
851C22×D3—64no—
852C22×D3—64no—
853C22×D3—64no—
854C22×D3—122no—
855C22×D3—122no—
856C22×D3—122no—
857C22×D3—122no—
858C22×D3—122no—
859C22×D3C23×D312yes—
860C22×D3C23×D312yes—
861C22×D3C23×D312yes—
862C3×Q8—64no—
863C3×Q8—64no—
864C3×D4—38no—
865C3×D4—64no—
866C3×D4—64no—
867C3×D4—64no—
868C3×D4—64no—
869C3×D4—122no—
870C2×C3×C4—24no—
871C2×C3×C4—24no—
872C2×C3×C4—22no—
873C2×C3×C4—21no—
874C2×C3×C4—21no—
875C2×C3×C4—22no—
876C2×C3×C4—32no—
877C2×C3×C4—32no—
878C2×C3×C4—32no—
879C2×C3×C4—32no—
880C2×C3×C4—32no—
881C2×C3×C4—42no—
882C2×C3×C4—42no—
883C2×C3×C4—42no—
884C2×C3×C4—42no—
885C2×C3×C4—64no—
886C2×C3×C4—64no—
887C2×C3×C4—64no—
888C2×C3×C4—64no—
889C2×C3×C4—122no—
890C2×C3×C4C23×D312yes—
891C2×C3×C4C23×D312yes—
892C2×C3×C4C23×D312yes—
893C2×C3×C4C23×D312yes—
894C2×C3×C4C23×D312yes—
895C2×C3×C4C23×D312yes—
896#67—24no—
897#67—24no—
898#67—38no—
899#67—64no—
900#67—64no—
901#67—64no—
902#67—64no—
903#67—64no—
904#67—64no—
905#67—64no—
906#67—122no—
907#67—122no—
908#67—122no—
909#67D3×D418yes—
910C2×Dic3—38no—
911C2×Dic3—32no—
912C2×Dic3—32no—
913C2×Dic3—38no—
914C2×Dic3—32no—
915C2×Dic3—32no—
916C2×Dic3—32no—
917C2×Dic3—32no—
918C2×Dic3—64no—
919C2×Dic3—61no—
920C2×Dic3—61no—
921C2×Dic3—62no—
922C2×Dic3—62no—
923C2×Dic3—64no—
924C2×Dic3—64no—
925C2×Dic3—64no—
926C2×Dic3—64no—
927C2×Dic3—64no—
928C2×Dic3—122no—
929C2×Dic3—122no—
930C2×Dic3—122no—
931C2×Dic3—122no—
932C2×Dic3C23×D312yes—
933C2×Dic3C23×D312yes—
934C2×Dic3C23×D312yes—
935C2×Dic3C23×D312yes—
936C2×Dic3C23×D312yes—
937D12—24no—
938D12—24no—
939D12—42no—
940D12—64no—
941D12—64no—
942D12—64no—
943D12—122no—
944C4×D3—24no—
945C4×D3—24no—
946C4×D3—24no—
947C4×D3—24no—
948C4×D3—38no—
949C4×D3—42no—
950C4×D3—64no—
951C4×D3—64no—
952C4×D3—64no—
953C4×D3—64no—
954C4×D3—64no—
955C4×D3—64no—
956C4×D3—64no—
957C4×D3—64no—
958C4×D3—64no—
959C4×D3—64no—
960C4×D3—122no—
961C4×D3—122no—
962C4×D3—122no—
963C4×D3—122no—
964C4×D3—122no—
965Dic6—24no—
966Dic6—24no—
967Dic6—38no—
968Dic6—64no—
969Dic6—64no—
970Dic6—64no—
971Dic6—64no—
972Dic6—64no—
973Dic6—64no—
974Dic6—64no—
975Dic6—64no—
976Dic6—124no—
977Dic6—124no—
978C2×C32—22no—
979C2×C32C23×D411yescharacteristic
980C2×C32C2×2−1+411yescharacteristic
981C2×C32#58511yescharacteristic
982C3⋊D3—22no—
983C3⋊D3—41no—
984C3×D3—24no—
985C3×D3—42no—
986C3×D3—42no—
987C24—92no—
988C24—91no—
989#41—68no—
990#41—68no—
991#41—98no—
992#41—184no—
993#41—184no—
994#41—188no—
995#41—188no—
996#41—184no—
997#41—184no—
998#41—188no—
999#41—188no—
1000C2×Q8—32no—
1001C2×Q8—32no—
1002C2×Q8—91no—
1003C2×Q8—91no—
1004C2×Q8—92no—
1005C2×Q8—91no—
1006C2×Q8—92no—
1007C2×Q8—92no—
1008C2×Q8—184no—
1009C2×Q8—188no—
1010C2×Q8—188no—
1011C2×Q8—184no—
1012C2×D4—32no—
1013C2×D4—32no—
1014C2×D4—32no—
1015C2×D4—32no—
1016C2×D4—32no—
1017C2×D4—32no—
1018C2×D4—92no—
1019C2×D4—92no—
1020C2×D4—92no—
1021C2×D4—92no—
1022C2×D4—91no—
1023C2×D4—92no—
1024C2×D4—91no—
1025C2×D4—91no—
1026C2×D4—92no—
1027C2×D4—188no—
1028C2×D4—184no—
1029C22×C4—32no—
1030C22×C4—32no—
1031C22×C4—32no—
1032C22×C4—32no—
1033C22×C4—32no—
1034C22×C4—92no—
1035C22×C4—92no—
1036C22×C4—92no—
1037C22×C4—92no—
1038C22×C4—92no—
1039C22×C4—92no—
1040C22×C4—92no—
1041C22×C4—91no—
1042C22×C4—91no—
1043C22×C4—91no—
1044C22×C4—91no—
1045C22×C4—91no—
1046C22×C4—91no—
1047C22×C4—91no—
1048C22×C4—184no—
1049C22×C4—188no—
1050C22×C4C2×D3211yescharacteristic
1051C22×C4C2×D3211yescharacteristic
1052C22×C4C2×D3211yescharacteristic
1053C4⋊C4—32no—
1054C4⋊C4—32no—
1055C4⋊C4—32no—
1056C4⋊C4—32no—
1057C4⋊C4—32no—
1058C4⋊C4—32no—
1059C4⋊C4—91no—
1060C4⋊C4—92no—
1061C4⋊C4—92no—
1062C4⋊C4—92no—
1063C4⋊C4—91no—
1064C4⋊C4—92no—
1065C4⋊C4—92no—
1066C4⋊C4—92no—
1067C4⋊C4—92no—
1068C4⋊C4—92no—
1069C4⋊C4C2×D3212yes—
1070C4⋊C4C2×D3212yes—
1071C22⋊C4—32no—
1072C22⋊C4—32no—
1073C22⋊C4—32no—
1074C22⋊C4—32no—
1075C22⋊C4—32no—
1076C22⋊C4—32no—
1077C22⋊C4—32no—
1078C22⋊C4—32no—
1079C22⋊C4—92no—
1080C22⋊C4—92no—
1081C22⋊C4—92no—
1082C22⋊C4—92no—
1083C22⋊C4—92no—
1084C22⋊C4—92no—
1085C22⋊C4—92no—
1086C22⋊C4—92no—
1087C22⋊C4—92no—
1088C22⋊C4—92no—
1089C22⋊C4—92no—
1090C42—32no—
1091C42—92no—
1092C42—92no—
1093C22×C3—22no—
1094C22×C3—22no—
1095C22×C3—22no—
1096C22×C3—22no—
1097C22×C3—22no—
1098C22×C3—21no—
1099C22×C3—34no—
1100C22×C3—62no—
1101C22×C3—62no—
1102C22×C3—62no—
1103C22×C3—62no—
1104C22×C3—62no—
1105C22×C3—62no—
1106C22×C3—62no—
1107C22×C3—62no—
1108C22×C3C2×D3×D414yes—
1109C22×C3C24×D312yes—
1110C2×D3—22no—
1111C2×D3—22no—
1112C2×D3—22no—
1113C2×D3—22no—
1114C2×D3—22no—
1115C2×D3—22no—
1116C2×D3—22no—
1117C2×D3—22no—
1118C2×D3—34no—
1119C2×D3—62no—
1120C2×D3—62no—
1121C2×D3—62no—
1122C2×D3—62no—
1123C2×D3—62no—
1124C2×D3—62no—
1125C2×D3—62no—
1126C2×D3—121no—
1127C2×D3—121no—
1128C2×D3—121no—
1129C2×D3—121no—
1130C2×D3—128no—
1131C2×D3—128no—
1132C2×D3—128no—
1133C2×D3—128no—
1134C2×D3C2×D3×D414yes—
1135C3×C4—22no—
1136C3×C4—22no—
1137C3×C4—22no—
1138C3×C4—22no—
1139C3×C4—22no—
1140C3×C4—22no—
1141C3×C4—34no—
1142C3×C4—42no—
1143C3×C4—41no—
1144C3×C4—41no—
1145C3×C4—42no—
1146C3×C4—62no—
1147C3×C4—62no—
1148C3×C4—62no—
1149C3×C4—62no—
1150Dic3—22no—
1151Dic3—22no—
1152Dic3—22no—
1153Dic3—22no—
1154Dic3—34no—
1155Dic3—34no—
1156Dic3—62no—
1157Dic3—62no—
1158Dic3—62no—
1159Dic3—62no—
1160Dic3—62no—
1161Dic3—62no—
1162Dic3—122no—
1163Dic3—122no—
1164Dic3C2×D3×D414yes—
1165C32#348911yescharacteristic, complemented, Sylow
1166C23—32no—
1167C23—32no—
1168C23—32no—
1169C23—91no—
1170C23—91no—
1171C23—182no—
1172C23—184no—
1173C23—184no—
1174C23—182no—
1175C23—361no—
1176C23—362no—
1177C23C22×D3211yescharacteristic
1178Q8—64no—
1179Q8—64no—
1180Q8—94no—
1181Q8—184no—
1182Q8—184no—
1183Q8—184no—
1184Q8—182no—
1185Q8—182no—
1186D4—38no—
1187D4—64no—
1188D4—64no—
1189D4—64no—
1190D4—64no—
1191D4—94no—
1192D4—122no—
1193D4—184no—
1194D4—184no—
1195D4—184no—
1196D4—182no—
1197D4—182no—
1198D4—184no—
1199D4—362no—
1200D4—362no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—32no—
1204C2×C4—32no—
1205C2×C4—32no—
1206C2×C4—32no—
1207C2×C4—32no—
1208C2×C4—41no—
1209C2×C4—64no—
1210C2×C4—64no—
1211C2×C4—64no—
1212C2×C4—64no—
1213C2×C4—98no—
1214C2×C4—94no—
1215C2×C4—91no—
1216C2×C4—91no—
1217C2×C4—92no—
1218C2×C4—92no—
1219C2×C4—122no—
1220C2×C4—182no—
1221C2×C4—182no—
1222C2×C4—182no—
1223C2×C4—182no—
1224C2×C4—184no—
1225C2×C4—184no—
1226C2×C4—184no—
1227C2×C4—184no—
1228C2×C4—184no—
1229C2×C4—182no—
1230C2×C4—362no—
1231C2×C4—361no—
1232C2×C4C22×D3212yes—
1233C2×C4C22×D3212yes—
1234C2×C4C22×D3211yescharacteristic
1235C2×C4C22×D3211yescharacteristic
1236C2×C3—24no—
1237C2×C3—24no—
1238C2×C3—21no—
1239C2×C3—21no—
1240C2×C3—21no—
1241C2×C3—64no—
1242C2×C3—122no—
1243C2×C3—122no—
1244C2×C3C22×D3×D412yes—
1245C2×C3#596412yes—
1246C2×C3D3×2−1+412yes—
1247D3—24no—
1248D3—42no—
1249D3—42no—
1250D3—64no—
1251D3—122no—
1252D3—122no—
1253D3—122no—
1254C22—21no—
1255C22—21no—
1256C22—34no—
1257C22—62no—
1258C22—62no—
1259C22—62no—
1260C22—62no—
1261C22—62no—
1262C22—62no—
1263C22—62no—
1264C22—62no—
1265C22—92no—
1266C22—181no—
1267C22—181no—
1268C22—181no—
1269C22—181no—
1270C22—181no—
1271C22—364no—
1272C22—368no—
1273C22D32×D412yes—
1274C22C23×D3211yescharacteristic
1275C4—22no—
1276C4—21no—
1277C4—22no—
1278C4—21no—
1279C4—34no—
1280C4—62no—
1281C4—62no—
1282C4—62no—
1283C4—62no—
1284C4—92no—
1285C4—92no—
1286C4—182no—
1287C4—182no—
1288C3—21no—
1289C3#8667712yescomplemented
1290C2—22no—
1291C2—64no—
1292C2—122no—
1293C2—122no—
1294C2—182no—
1295C2—361no—
1296C2#1059666911yescharacteristic
1297C2C2×D32×D411yescharacteristic
1298C2#1059668711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C4⋊C4C22
hypercenterC2×C4⋊C4D32
hypocenterC32#3489
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64306C2semidirect
2. C2×#64298C2semidirect
3. C2×#64105C2semidirect
4. C3×#5507C2semidirect
5. #10595075C2semidirect
6. #10595068C2semidirect
7. #10594930C2semidirect
8. #10594921C2semidirect
9. #10594920C2semidirect
10. #10594888C2semidirect
11. #10594876C2semidirect
12. #10594617C2semidirect
13. #10594614C2semidirect
14. D3×#896C2semidirect
15. #10594513C2semidirect
16. #10594378C2semidirect
17. #10594375C2semidirect
18. #10594368C2semidirect
19. #10594366C2semidirect
22. C22×#634C22semidirect
24. C2×C3×#235C22semidirect
28. C2×#3805C22semidirect
29. C2×#3805C22semidirect
38. C2×#3795C22semidirect
39. C2×#3795C22semidirect
40. C2×D3×Dic6C22semidirect
41. C2×D3×Dic6C22semidirect
42. C2×C32×C4⋊C4C22semidirect
45. C2×#3750C22semidirect
46. C2×#3750C22semidirect
49. #64105C22semidirect
50. #64105C22semidirect
51. C3×#930C22semidirect
52. C3×#929C22semidirect
53. C3×#929C22semidirect
54. C3×C4×#67C22semidirect
55. C3×#896C22semidirect
56. C3×#896C22semidirect
57. C3×#895C22semidirect
58. C3×#894C22semidirect
59. C3×#894C22semidirect
60. C3×#893C22semidirect
61. C3×D3×C4⋊C4C22semidirect
62. C3×#888C22semidirect
64. #63980C22semidirect
65. #67⋊Dic3C22semidirect
66. #63962C22semidirect
67. #63957C22semidirect
72. #63913C22semidirect
74. #63912C22semidirect
75. #63907C22semidirect
76. #63906C22semidirect
77. #63906C22semidirect
78. #63905C22semidirect
80. #63899C22semidirect
81. #63899C22semidirect
82. #63896C22semidirect
83. #63896C22semidirect
85. #63890C22semidirect
87. #63887C22semidirect
88. #63886C22semidirect
89. #63886C22semidirect
90. #63885C22semidirect
91. #63885C22semidirect
92. #63885C22semidirect
93. #63884C22semidirect
95. #63881C22semidirect
97. #63879C22semidirect
98. #63879C22semidirect
99. #63877C22semidirect
100. D3×Dic3⋊C4C22semidirect
101. D3×Dic3⋊C4C22semidirect
103. #63865C22semidirect
104. #63852C22semidirect
105. #63851C22semidirect
106. #63850C22semidirect
107. #63840C22semidirect
108. #63839C22semidirect
109. #63837C22semidirect
141. #5507D3semidirect
191. #3805D4semidirect
273. C2×#235C2×D3semidirect
295. C2×C3×C4⋊C4C2×D3semidirect
315. #930C2×D3semidirect
318. #929C2×D3semidirect
319. #929C2×D3semidirect
323. C4×#67C2×D3semidirect
359. #896C2×D3semidirect
360. #896C2×D3semidirect
363. #895C2×D3semidirect
367. #894C2×D3semidirect
368. #894C2×D3semidirect
372. #893C2×D3semidirect
375. D3×C4⋊C4C2×D3semidirect
379. #888C2×D3semidirect
725. C2×C3⋊D32−1+4semidirect
833. C2×C4⋊C4D32semidirect
1165. C32#3489semidirect
1289. C3#86677semidirect

Maximal subgroups

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

subgroupindex
C2×#643062
C2×#642982
C2×#641052
C3×#55072
#105950752
#105950682
#105949302
#105949212
#105949202
#105948882
#105948762
#105946172
#105946142
D3×#8962
#105945132
#105943782
#105943752
#105943682
#105943662
#866773