Finite Group Databasebeta

← #11910053

Subgroups — #11910053

Order 1152.

2168 conjugacy classes of subgroups.

The subgroup lattice has 1362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596153C211yesmaximal, characteristic, complemented
2C3×#5681C211yesmaximal, characteristic, complemented
3C3×#5677C211yesmaximal, characteristic, complemented
4#10595401C211yesmaximal, characteristic, complemented
5#10595377C211yesmaximal, characteristic, complemented
6#10595347C211yesmaximal, characteristic, complemented
7#10595344C211yesmaximal, characteristic, complemented
8#10595217C211yesmaximal, characteristic, complemented
9Dic3×#237C211yesmaximal, characteristic, complemented
10#10595158C211yesmaximal, characteristic, complemented
11#10595122C211yesmaximal, characteristic, complemented
12#10594220C212yesmaximal, complemented
13#10594216C212yesmaximal, complemented
14#10594201C212yesmaximal, complemented
15#10594198C212yesmaximal, complemented
16#10594143C212yesmaximal, complemented
17#10594132C212yesmaximal, complemented
18#10594131C212yesmaximal, complemented
19#10594118C212yesmaximal, complemented
20#10593988C211yesmaximal, characteristic, complemented
21#10593911C211yesmaximal, characteristic, complemented
22#10593889C211yesmaximal, characteristic, complemented
23#10593860C211yesmaximal, characteristic, complemented
24#87056—31nomaximal
25#86723—31nomaximal
26C2×C3×D3×Q8C2211yescharacteristic
27C2×C3×#237C2211yescharacteristic
28C2×#3796C2211yescharacteristic
29C32×#124C2211yescharacteristic
30#64155C2211yescharacteristic
31Q8×C3⋊Dic3C2211yescharacteristic
32#64147C2211yescharacteristic
33D4×C3⋊Dic3C2211yescharacteristic
34#64095C2212yes—
35#64094C2212yes—
36#64088C2212yes—
37#64087C2212yes—
38#64081C2211yescharacteristic
39#64078C2211yescharacteristic
40C3×#947C2211yescharacteristic
41C3×#946C2211yescharacteristic
42C3×Q8×Dic3C2211yescharacteristic
43C3×#940C2211yescharacteristic
44C3×#938C2211yescharacteristic
45C3×D4×Dic3C2211yescharacteristic
46C3×#886C2212yes—
47C3×#885C2212yes—
48C3×#885C2212yes—
49C3×#884C2212yes—
50C3×#883C2212yes—
51C3×#67⋊C4C2212yes—
52C3×#67⋊C4C2212yes—
53C3×#878C2212yes—
54C3×C4×D12C2211yescharacteristic
55C3×C4×D12C2211yescharacteristic
56C3×C4×Dic6C2211yescharacteristic
57C3×C4×Dic6C2211yescharacteristic
58#63980C2212yes—
59#63979C2212yes—
60#63978C2212yes—
61#67⋊Dic3C2212yes—
62Dic3×#67C2212yes—
63Dic3×#67C2212yes—
64#63970C2212yes—
65#63970C2212yes—
66#63969C2212yes—
67#63962C2212yes—
68#63961C2212yes—
69#63958C2212yes—
70#63956C2212yes—
71#63955C2212yes—
72C2×Dic32C2212yes—
73#63952C2212yes—
74#63913C2212yes—
75#63913C2212yes—
76#63908C2211yescharacteristic
77#63908C2211yescharacteristic
78#63908C2212yes—
79#63907C2212yes—
80#63907C2211yescharacteristic
81#63906C2212yes—
82#63904C2212yes—
83C4×#626C2211yescharacteristic
84C4×#626C2211yescharacteristic
85#63902C2212yes—
86#63900C2211yescharacteristic
87#63898C2211yescharacteristic
88#63891C2212yes—
89#63890C2211yescharacteristic
90#63887C2212yes—
91#63887C2211yescharacteristic
92#63886C2211yescharacteristic
93#63884C2211yescharacteristic
94#63880C2212yes—
95#63879C2212yes—
96#63878C2212yes—
97#63877C2212yes—
98D3×Dic3⋊C4C2212yes—
99C4×D3×Dic3C2211yescharacteristic
100#63869C2211yescharacteristic
101#63869C2211yescharacteristic
102#63866C2212yes—
103#63861C2212yes—
104#63859C2212yes—
105#63858C2211yescharacteristic
106#63855C2211yescharacteristic
107#63855C2212yes—
108#63854C2212yes—
109#63848C2211yescharacteristic
110#63847C2212yes—
111#63846C2211yescharacteristic
112#63845C2212yes—
113#63845C2212yes—
114#63844C2212yes—
115#63843C2212yes—
116#63843C2211yescharacteristic
117Dic3×Dic6C2211yescharacteristic
118Dic3×Dic6C2212yes—
119Dic3×Dic6C2211yescharacteristic
120#63841C2211yescharacteristic
121#63841C2211yescharacteristic
122#63841C2212yes—
123#63841C2212yes—
124#63836C2212yes—
125C3×#559—31no—
126C3×#548—31no—
127#5834—31no—
128Dic3×#41—31no—
129#5817—31no—
130#5812—31no—
131#5719—31no—
132#5718—31no—
133#5682—31no—
134#5682—31no—
135#5682—32no—
136#5682—61no—
137#5681—32no—
138#5681D311yescharacteristic, complemented
139#5680—31no—
140#5677—31no—
141#5677D311yescharacteristic, complemented
142#5670—32no—
143#5669—32no—
144#5664—32no—
145#5663—32no—
146#5650—32no—
147#5649—32no—
148#5639—31no—
149#5639—32no—
150#5624—31no—
151#5624—32no—
152#5619—31no—
153#5619—32no—
154#5614—31no—
155#5614—32no—
156#5581—31no—
157#5580—31no—
158#5574—31no—
159#5572—31no—
160#5570—31no—
161#5567—31no—
162#5563—32no—
163#5563—31no—
164#5563—31no—
165#5558—31no—
166#5546—31no—
167#5540—32no—
168#5538—32no—
169#5538—32no—
170#5538—31no—
171C4×#237—31no—
172C2×C32×Q8C2311yescharacteristic
173C2×C32×D4C2311yescharacteristic
174C2×#638C2312yes—
175C22×C3⋊Dic3C2312yes—
176C2×C4×C3⋊D3C2311yescharacteristic
177C2×#634C2312yes—
178C2×C3×#67C2312yes—
179C2×C3×#67C2312yes—
180C2×C3×#67C2312yes—
181C2×C3×#67C2312yes—
182C22×C3×Dic3C2312yes—
183C22×C3×Dic3C2312yes—
184C3×D3×Q8—24no—
185C3×#237—24no—
186C2×C3×D12C2311yescharacteristic
187C2×C3×D12C2311yescharacteristic
188C2×C3×C4×D3C2312yes—
189C2×C3×C4×D3C2311yescharacteristic
190C2×C3×C4×D3C2311yescharacteristic
191C2×C3×C4×D3C2312yes—
192C2×C3×Dic6C2312yes—
193C2×C3×Dic6C2311yescharacteristic
194C2×C3×Dic6C2311yescharacteristic
195C2×#626C2312yes—
196C2×#626C2311yescharacteristic
197C2×#626C2311yescharacteristic
198C2×#625C2312yes—
199C2×#625C2312yes—
200C2×#624C2312yes—
201C2×D3×Dic3C2312yes—
202C2×D3×Dic3C2311yescharacteristic
203C2×D3×Dic3C2311yescharacteristic
204C2×D3×Dic3C2312yes—
205#3796—24no—
206C32×C22⋊C4C2312yes—
207C32×C22⋊C4C2312yes—
208C32×C42C2311yescharacteristic
209#3757C2312yes—
210#3757C2312yes—
211#3752C2311yescharacteristic
212#3752C2311yescharacteristic
213#3752C2312yes—
214C4⋊(C3⋊Dic3)C2312yes—
215C4⋊(C3⋊Dic3)C2311yescharacteristic
216C4⋊(C3⋊Dic3)C2311yescharacteristic
217C4⋊(C3⋊Dic3)C2312yes—
218#3750C2311yescharacteristic
219#3750C2311yescharacteristic
220#3750C2312yes—
221C4×C3⋊Dic3C2311yescharacteristic
222C4×C3⋊Dic3C2312yes—
223C3×#217C2312yes—
224C3×#217C2312yes—
225C3×(C2×D3)⋊C4C2311yescharacteristic
226C3×(C2×D3)⋊C4C2312yes—
227C3×(C2×D3)⋊C4C2312yes—
228C3×(C2×D3)⋊C4C2312yes—
229C3×(C2×D3)⋊C4C2311yescharacteristic
230C3×(C2×D3)⋊C4C2312yes—
231C3×C4⋊Dic3C2311yescharacteristic
232C3×C4⋊Dic3C2312yes—
233C3×C4⋊Dic3C2311yescharacteristic
234C3×C4⋊Dic3C2311yescharacteristic
235C3×C4⋊Dic3C2311yescharacteristic
236C3×Dic3⋊C4C2312yes—
237C3×Dic3⋊C4C2312yes—
238C3×Dic3⋊C4C2311yescharacteristic
239C3×Dic3⋊C4C2311yescharacteristic
240C3×C4×Dic3C2312yes—
241C3×C4×Dic3C2312yes—
242C3×C4×Dic3C2311yescharacteristic
243C3×C4×Dic3C2311yescharacteristic
244#3724C2312yes—
245#3724C2312yes—
246#3724C2312yes—
247Dic3⋊Dic3C2312yes—
248Dic3⋊Dic3C2312yes—
249Dic3⋊Dic3C2311yescharacteristic
250Dic3⋊Dic3C2312yes—
251Dic3⋊Dic3C2311yescharacteristic
252Dic3⋊Dic3C2312yes—
253Dic3⋊Dic3C2312yes—
254Dic3⋊Dic3C2311yescharacteristic
255Dic3⋊Dic3C2311yescharacteristic
256#3722C2311yescharacteristic
257#3722C2311yescharacteristic
258(C2×D3)⋊Dic3C2311yescharacteristic
259(C2×D3)⋊Dic3C2312yes—
260(C2×D3)⋊Dic3C2312yes—
261(C2×D3)⋊Dic3C2312yes—
262(C2×D3)⋊Dic3C2312yes—
263(C2×D3)⋊Dic3C2311yescharacteristic
264(C2×D3)⋊Dic3C2311yescharacteristic
265(C2×D3)⋊Dic3C2311yescharacteristic
266(C2×D3)⋊Dic3C2312yes—
267Dic32C2312yes—
268Dic32C2312yes—
269Dic32C2312yes—
270Dic32C2312yes—
271Dic32C2312yes—
272Dic32C2311yescharacteristic
273Dic32C2311yescharacteristic
274#3524—91noSylow
275C2×C3×#41—31no—
276C22×C3×Q8—31no—
277C2×#239—31no—
278C2×D3×Q8C2×D311yescharacteristic
279C2×#237—31no—
280C2×#237C2×D311yescharacteristic
281C3×#127—31no—
282C3×#124—21no—
283C3×#124—31no—
284C3×#124—32no—
285C3×#124—32no—
286C3×#124C2×D311yescharacteristic
287C3×#124C2×D311yescharacteristic
288C3×#123—32no—
289C3×#123—32no—
290C3×C22⋊Q8—31no—
291C3×C22⋊Q8—32no—
292C3×#121—31no—
293C3×#121—32no—
294C3×C4×Q8—31no—
295C3×C4×Q8—31no—
296C3×C4×Q8—31no—
297C3×C4×D4—31no—
298C3×C4×D4—32no—
299C3×C4×D4—32no—
300C3×C4×D4—31no—
301C3×C4×D4—31no—
302#947—31no—
303#947—32no—
304#947C2×D311yescharacteristic
305#946—31no—
306#946—31no—
307#946—32no—
308#946—31no—
309#946—61no—
310#946C2×D311yescharacteristic
311Q8×Dic3—31no—
312Q8×Dic3—31no—
313Q8×Dic3—32no—
314Q8×Dic3—31no—
315Q8×Dic3—32no—
316Q8×Dic3—31no—
317Q8×Dic3—31no—
318Q8×Dic3—61no—
319Q8×Dic3C2×D311yescharacteristic
320#944—32no—
321#940—32no—
322#940—32no—
323#940C2×D311yescharacteristic
324#939—32no—
325#939—32no—
326#939—32no—
327#939—32no—
328#939—32no—
329#939—31no—
330#938—31no—
331#938—31no—
332#938—32no—
333#938—32no—
334#938—31no—
335#938—31no—
336#938—32no—
337#938—32no—
338#938—61no—
339#938C2×D311yescharacteristic
340#935—32no—
341#935—32no—
342#935—32no—
343#935—31no—
344D4×Dic3—31no—
345D4×Dic3—31no—
346D4×Dic3—32no—
347D4×Dic3—32no—
348D4×Dic3—32no—
349D4×Dic3—31no—
350D4×Dic3—61no—
351D4×Dic3C2×D311yescharacteristic
352#930—32no—
353#930—32no—
354#930—31no—
355#930—31no—
356#930—32no—
357#929—32no—
358C4×#67—32no—
359C4×#67—32no—
360C4×#67—32no—
361C4×#67—32no—
362C4×#67—32no—
363C4×#67—31no—
364C4×#67—31no—
365#926—32no—
366#926—31no—
367#926—32no—
368#926—32no—
369#926—31no—
370#926—31no—
371#926—32no—
372C2×Dic3⋊C4—32no—
373C2×C4×Dic3—32no—
374C2×C4×Dic3—32no—
375C2×C4×Dic3—31no—
376#898—31no—
377#898—32no—
378#898—31no—
379#898—31no—
380#895—31no—
381#894—31no—
382#894—32no—
383#894—31no—
384#893—31no—
385#893—32no—
386#892—32no—
387#892—32no—
388#892—31no—
389#892—31no—
390#892—32no—
391#892—32no—
392D3×C4⋊C4—32no—
393D3×C4⋊C4—31no—
394D3×C4⋊C4—31no—
395#890—31no—
396#890—32no—
397#890—32no—
398#890—31no—
399#890—31no—
400#889—32no—
401#889—31no—
402#889—32no—
403#889—32no—
404#889—32no—
405#887—32no—
406#887—31no—
407#887—32no—
408#886—32no—
409#886—32no—
410#886—32no—
411#886—32no—
412#886—31no—
413#886—62no—
414#886C2×D312yes—
415#885—32no—
416#885—31no—
417#885—32no—
418#885—32no—
419#885—32no—
420#885—32no—
421#885—32no—
422#885—32no—
423#885—62no—
424#885C2×D312yes—
425#885C2×D312yes—
426#884—32no—
427#884—32no—
428#884C2×D312yes—
429#883—32no—
430#883—32no—
431#883—32no—
432#883C2×D312yes—
433#67⋊C4—32no—
434#67⋊C4—32no—
435#67⋊C4—32no—
436#67⋊C4—32no—
437#67⋊C4—32no—
438#67⋊C4—32no—
439#67⋊C4C2×D312yes—
440#67⋊C4C2×D312yes—
441#879—32no—
442#879—32no—
443#879—32no—
444#879—32no—
445#879—31no—
446#879—32no—
447#879—32no—
448#879—62no—
449#878—32no—
450#878—31no—
451#878—32no—
452#878—32no—
453#878—62no—
454#878C2×D312yes—
455#877—32no—
456#877—32no—
457#877—32no—
458#876—32no—
459C4×D12—31no—
460C4×D12—31no—
461C4×D12—32no—
462C4×D12C2×D311yescharacteristic
463C4×D12C2×D311yescharacteristic
464#872—32no—
465#872—31no—
466#872—31no—
467#872—31no—
468#872—32no—
469#872—32no—
470#872—61no—
471C42×D3—31no—
472#870—31no—
473#870—31no—
474#869—32no—
475#869—31no—
476#869—31no—
477#869—61no—
478C4×Dic6—32no—
479C4×Dic6—31no—
480C4×Dic6—31no—
481C4×Dic6—32no—
482C4×Dic6C2×D311yescharacteristic
483C4×Dic6C2×D311yescharacteristic
484C23×C32C2412yes—
485C22×C3⋊D3C2411yescharacteristic
486C22×C3×D3C2411yescharacteristic
487C22×C3×D3C2412yes—
488C22×C3×D3C2411yescharacteristic
489C32×Q8—22no—
490C32×D4—22no—
491C2×C32×C4C2411yescharacteristic
492C2×C32×C4C2412yes—
493C2×C32×C4C2411yescharacteristic
494C2×C32×C4C2411yescharacteristic
495#638—42no—
496C2×C3⋊Dic3—42no—
497C2×C3⋊Dic3C2411yescharacteristic
498C2×C3⋊Dic3C2412yes—
499C2×C3⋊Dic3C2412yes—
500C2×C3⋊Dic3C2411yescharacteristic
501C2×C3⋊Dic3C2411yescharacteristic
502C4×C3⋊D3—22no—
503#634—42no—
504C3×#67—24no—
505C3×#67—42no—
506C3×#67—42no—
507C3×#67—42no—
508C2×C3×Dic3—24no—
509C2×C3×Dic3—42no—
510C2×C3×Dic3C2411yescharacteristic
511C2×C3×Dic3C2412yes—
512C2×C3×Dic3C2411yescharacteristic
513C2×C3×Dic3C2411yescharacteristic
514C2×C3×Dic3C2411yescharacteristic
515C2×C3×Dic3C2411yescharacteristic
516C2×C3×Dic3C2411yescharacteristic
517C2×C3×Dic3C2412yes—
518C2×C3×Dic3C2412yes—
519C3×D12—22no—
520C3×D12—41no—
521C3×C4×D3—22no—
522C3×C4×D3—22no—
523C3×C4×D3—24no—
524C3×C4×D3—42no—
525C3×Dic6—24no—
526C3×Dic6—41no—
527C3×Dic6#4114yes—
528#626—24no—
529#626—41no—
530#626—41no—
531#625—42no—
532#625—42no—
533#624—42no—
534D3×Dic3—24no—
535D3×Dic3—42no—
536D3×Dic3—41no—
537D3×Dic3—41no—
538#559—31no—
539#559—92no—
540#557—91no—
541#555—91no—
542#555—92no—
543#553—92no—
544#553—91no—
545#552—91no—
546#552—92no—
547#550—91no—
548#548—31no—
549#548—91no—
550#542—92no—
551#542—91no—
552#540—92no—
553#540—91no—
554#529—91no—
555#529—92no—
556#529—92no—
557#529—91no—
558#520—91no—
559#519—91no—
560C4×#41—91no—
561C3×#41—64no—
562C2×C3×Q8—21no—
563C2×C3×Q8—31no—
564C2×C3×Q8—32no—
565C2×C3×Q8—31no—
566C2×C3×Q8—64no—
567C2×C3×Q8C22×D311yescharacteristic
568C2×C3×Q8C22×D311yescharacteristic
569C2×C3×D4—21no—
570C2×C3×D4—32no—
571C2×C3×D4—32no—
572C2×C3×D4—32no—
573C2×C3×D4—32no—
574C2×C3×D4—31no—
575C2×C3×D4—31no—
576C2×C3×D4C22×D311yescharacteristic
577C2×C3×D4C22×D311yescharacteristic
578C22×C3×C4—32no—
579C22×C3×C4—32no—
580C22×C3×C4—31no—
581C22×C3×C4—32no—
582C22×C3×C4—31no—
583C22×C3×C4—32no—
584C2×#67—32no—
585C2×#67—32no—
586C2×#67—32no—
587C2×#67—32no—
588C2×#67—32no—
589C2×#67—32no—
590C2×#67—32no—
591C2×#67—31no—
592C2×#67—31no—
593C2×#67—62no—
594C2×#67C22×D312yes—
595C2×#67C22×D312yes—
596C2×#67C22×D312yes—
597C2×#67C22×D312yes—
598C22×Dic3—32no—
599C22×Dic3—32no—
600C22×Dic3—32no—
601C22×Dic3—32no—
602C22×Dic3—31no—
603C22×Dic3—31no—
604C22×Dic3—62no—
605C22×Dic3C22×D312yes—
606C22×Dic3C22×D312yes—
607#239—64no—
608D3×Q8—24no—
609#237—24no—
610#237—64no—
611C2×D12—32no—
612C2×D12—31no—
613C2×D12—31no—
614C2×D12C22×D311yescharacteristic
615C2×D12C22×D311yescharacteristic
616C2×C4×D3—32no—
617C2×C4×D3—31no—
618C2×C4×D3—31no—
619C2×C4×D3—31no—
620C2×C4×D3—31no—
621C2×C4×D3—32no—
622C2×C4×D3—32no—
623C2×C4×D3—32no—
624C2×C4×D3—61no—
625C2×C4×D3C22×D311yescharacteristic
626C2×C4×D3C22×D311yescharacteristic
627C2×C4×D3C22×D312yes—
628C2×C4×D3C22×D312yes—
629C2×Dic6—32no—
630C2×Dic6—32no—
631C2×Dic6—62no—
632C2×Dic6C22×D312yes—
633C2×Dic6C22×D311yescharacteristic
634C2×Dic6C22×D311yescharacteristic
635C3×C4⋊C4—31no—
636C3×C4⋊C4—32no—
637C3×C4⋊C4—31no—
638C3×C4⋊C4—31no—
639C3×C4⋊C4—31no—
640C3×C4⋊C4—32no—
641C3×C4⋊C4—31no—
642C3×C4⋊C4—32no—
643C3×C4⋊C4—31no—
644C3×C22⋊C4—22no—
645C3×C22⋊C4—22no—
646C3×C22⋊C4—32no—
647C3×C22⋊C4—32no—
648C3×C22⋊C4—32no—
649C3×C22⋊C4—32no—
650C3×C22⋊C4—31no—
651C3×C22⋊C4—32no—
652C3×C22⋊C4—32no—
653C3×C22⋊C4—31no—
654C3×C22⋊C4C22×D312yes—
655C3×C22⋊C4C22×D312yes—
656C3×C22⋊C4C22×D312yes—
657C3×C22⋊C4C22×D312yes—
658C3×C42—21no—
659C3×C42—32no—
660C3×C42—31no—
661C3×C42—31no—
662C3×C42—32no—
663C3×C42C22×D311yescharacteristic
664C3×C42C22×D311yescharacteristic
665#217—32no—
666#217—32no—
667#217—32no—
668#217—32no—
669#217—32no—
670#217—32no—
671#217—31no—
672#217—32no—
673#217—32no—
674#217—31no—
675#217—31no—
676#217—31no—
677#217—32no—
678#217—62no—
679#217—62no—
680#217C22×D312yes—
681#217C22×D312yes—
682(C2×D3)⋊C4—31no—
683(C2×D3)⋊C4—32no—
684(C2×D3)⋊C4—32no—
685(C2×D3)⋊C4—31no—
686(C2×D3)⋊C4—31no—
687(C2×D3)⋊C4—31no—
688(C2×D3)⋊C4—32no—
689(C2×D3)⋊C4—32no—
690(C2×D3)⋊C4—32no—
691(C2×D3)⋊C4—31no—
692(C2×D3)⋊C4—31no—
693(C2×D3)⋊C4—32no—
694(C2×D3)⋊C4—31no—
695(C2×D3)⋊C4—31no—
696(C2×D3)⋊C4—32no—
697(C2×D3)⋊C4—31no—
698(C2×D3)⋊C4—31no—
699(C2×D3)⋊C4—31no—
700(C2×D3)⋊C4—31no—
701(C2×D3)⋊C4—61no—
702(C2×D3)⋊C4—61no—
703(C2×D3)⋊C4—62no—
704(C2×D3)⋊C4C22×D312yes—
705(C2×D3)⋊C4C22×D311yescharacteristic
706(C2×D3)⋊C4C22×D311yescharacteristic
707(C2×D3)⋊C4C22×D312yes—
708(C2×D3)⋊C4C22×D312yes—
709(C2×D3)⋊C4C22×D312yes—
710C4⋊Dic3—31no—
711C4⋊Dic3—31no—
712C4⋊Dic3—32no—
713C4⋊Dic3—32no—
714C4⋊Dic3—32no—
715C4⋊Dic3—31no—
716C4⋊Dic3—31no—
717C4⋊Dic3—32no—
718C4⋊Dic3—32no—
719C4⋊Dic3—32no—
720C4⋊Dic3—32no—
721C4⋊Dic3—32no—
722C4⋊Dic3—31no—
723C4⋊Dic3—31no—
724C4⋊Dic3—32no—
725C4⋊Dic3—31no—
726C4⋊Dic3—31no—
727C4⋊Dic3—62no—
728C4⋊Dic3—61no—
729C4⋊Dic3—61no—
730C4⋊Dic3—62no—
731C4⋊Dic3C22×D311yescharacteristic
732C4⋊Dic3C22×D311yescharacteristic
733C4⋊Dic3C22×D311yescharacteristic
734C4⋊Dic3C22×D311yescharacteristic
735C4⋊Dic3C22×D312yes—
736Dic3⋊C4—31no—
737Dic3⋊C4—31no—
738Dic3⋊C4—31no—
739Dic3⋊C4—31no—
740Dic3⋊C4—32no—
741Dic3⋊C4—32no—
742Dic3⋊C4—32no—
743Dic3⋊C4—31no—
744Dic3⋊C4—32no—
745Dic3⋊C4—32no—
746Dic3⋊C4—32no—
747Dic3⋊C4—32no—
748Dic3⋊C4—32no—
749Dic3⋊C4—32no—
750Dic3⋊C4—32no—
751Dic3⋊C4—32no—
752Dic3⋊C4—32no—
753Dic3⋊C4—31no—
754Dic3⋊C4—32no—
755Dic3⋊C4—31no—
756Dic3⋊C4—31no—
757Dic3⋊C4—61no—
758Dic3⋊C4—61no—
759Dic3⋊C4—62no—
760Dic3⋊C4C22×D312yes—
761Dic3⋊C4C22×D311yescharacteristic
762Dic3⋊C4C22×D311yescharacteristic
763Dic3⋊C4C22×D312yes—
764C4×Dic3—31no—
765C4×Dic3—32no—
766C4×Dic3—31no—
767C4×Dic3—32no—
768C4×Dic3—32no—
769C4×Dic3—32no—
770C4×Dic3—32no—
771C4×Dic3—32no—
772C4×Dic3—32no—
773C4×Dic3—32no—
774C4×Dic3—31no—
775C4×Dic3—31no—
776C4×Dic3—32no—
777C4×Dic3—32no—
778C4×Dic3—32no—
779C4×Dic3—31no—
780C4×Dic3—31no—
781C4×Dic3—32no—
782C4×Dic3—61no—
783C4×Dic3—62no—
784C4×Dic3C22×D312yes—
785C4×Dic3C22×D311yescharacteristic
786C4×Dic3C22×D311yescharacteristic
787C4×Dic3C22×D312yes—
788C22×C32—22no—
789C22×C32—22no—
790C22×C32—22no—
791C22×C32C2511yescharacteristic
792C2×C3⋊D3—21no—
793C2×C3⋊D3—21no—
794C2×C3⋊D3—21no—
795C2×C3×D3—22no—
796C2×C3×D3—21no—
797C2×C3×D3—21no—
798C2×C3×D3—21no—
799C2×C3×D3—21no—
800C2×C3×D3—22no—
801C2×C3×D3—21no—
802C2×C3×D3—22no—
803C2×C3×D3—21no—
804C32×C4—22no—
805C32×C4—21no—
806C32×C4—21no—
807C32×C4C2×#4112yes—
808C3⋊Dic3—21no—
809C3⋊Dic3—21no—
810C3⋊Dic3—21no—
811C3⋊Dic3—22no—
812C3⋊Dic3—22no—
813C3×Dic3—21no—
814C3×Dic3—21no—
815C3×Dic3—22no—
816C3×Dic3—21no—
817C3×Dic3—21no—
818C3×Dic3—22no—
819C3×Dic3—21no—
820C3×Dic3—21no—
821C3×Dic3C2×#4114yes—
822C2×#41—31no—
823C2×#41—91no—
824C22×Q8—31no—
825C4⋊Q8—92no—
826C4⋊Q8—91no—
827#127—31no—
828#127—92no—
829#126—92no—
830#126—92no—
831#126—91no—
832#126—92no—
833#126—91no—
834#126—92no—
835#125—91no—
836#125—91no—
837#125—92no—
838#125—91no—
839#125—92no—
840#125—92no—
841#124—31no—
842#124—32no—
843#124—32no—
844#124—92no—
845#124—92no—
846#124—92no—
847#124—91no—
848#124—92no—
849#124D3211yescharacteristic
850#123—32no—
851#123—32no—
852#123—92no—
853#123—91no—
854#123—92no—
855#123—92no—
856#123—92no—
857#123—91no—
858#123—92no—
859#123—92no—
860C22⋊Q8—31no—
861C22⋊Q8—32no—
862C22⋊Q8—91no—
863C22⋊Q8—92no—
864C22⋊Q8—91no—
865C22⋊Q8—92no—
866#121—31no—
867#121—32no—
868#121—92no—
869#121—92no—
870#121—91no—
871#121—91no—
872#121—92no—
873#121—91no—
874#121—92no—
875#121—92no—
876#121—92no—
877#121—92no—
878#121—91no—
879C4×Q8—31no—
880C4×Q8—31no—
881C4×Q8—31no—
882C4×Q8—92no—
883C4×Q8—91no—
884C4×Q8—92no—
885C4×Q8—91no—
886C4×Q8—91no—
887C4×Q8—92no—
888C4×Q8—91no—
889C4×D4—31no—
890C4×D4—32no—
891C4×D4—32no—
892C4×D4—31no—
893C4×D4—31no—
894C4×D4—92no—
895C4×D4—91no—
896C4×D4—91no—
897C4×D4—92no—
898C4×D4—92no—
899C4×D4—92no—
900C4×D4—92no—
901C4×D4—92no—
902C4×D4—91no—
903C4×D4—92no—
904C4×D4—92no—
905C4×D4—91no—
906#117—92no—
907#117—92no—
908#117—91no—
909#117—92no—
910#117—92no—
911#117—92no—
912#117—91no—
913#117—92no—
914#117—91no—
915#117—92no—
916#117—91no—
917C2×C4⋊C4—91no—
918C2×C4⋊C4—92no—
919C2×C42—91no—
920C2×C42—92no—
921C23×C3—22no—
922C23×C3—31no—
923C23×C3—32no—
924C23×C3—31no—
925C23×C3C23×D312yes—
926C23×C3C23×D312yes—
927C22×D3—31no—
928C22×D3—31no—
929C22×D3—61no—
930C22×D3C23×D311yescharacteristic
931C22×D3C23×D311yescharacteristic
932C22×D3C23×D312yes—
933C3×Q8—22no—
934C3×Q8—22no—
935C3×Q8—34no—
936C3×Q8—42no—
937C3×Q8—64no—
938C3×Q8—121no—
939C3×D4—22no—
940C3×D4—22no—
941C3×D4—42no—
942C3×D4—64no—
943C3×D4—62no—
944C3×D4—121no—
945C3×D4—122no—
946C3×D4—122no—
947C3×D4—122no—
948C2×C3×C4—21no—
949C2×C3×C4—22no—
950C2×C3×C4—21no—
951C2×C3×C4—21no—
952C2×C3×C4—32no—
953C2×C3×C4—31no—
954C2×C3×C4—32no—
955C2×C3×C4—31no—
956C2×C3×C4—31no—
957C2×C3×C4—31no—
958C2×C3×C4—31no—
959C2×C3×C4—31no—
960C2×C3×C4—32no—
961C2×C3×C4—64no—
962C2×C3×C4—64no—
963C2×C3×C4—62no—
964C2×C3×C4—62no—
965C2×C3×C4—122no—
966C2×C3×C4—122no—
967C2×C3×C4C23×D312yes—
968C2×C3×C4C23×D312yes—
969C2×C3×C4C23×D311yescharacteristic
970C2×C3×C4C23×D311yescharacteristic
971C2×C3×C4C23×D311yescharacteristic
972C2×C3×C4C23×D311yescharacteristic
973C2×C3×C4C23×D311yescharacteristic
974C2×C3×C4C23×D311yescharacteristic
975#67—24no—
976#67—42no—
977#67—42no—
978#67—42no—
979#67—64no—
980#67—121no—
981#67—121no—
982#67—122no—
983#67—122no—
984#67—122no—
985#67—122no—
986#67—122no—
987#67—122no—
988#67—242no—
989C2×Dic3—24no—
990C2×Dic3—31no—
991C2×Dic3—31no—
992C2×Dic3—31no—
993C2×Dic3—31no—
994C2×Dic3—32no—
995C2×Dic3—32no—
996C2×Dic3—32no—
997C2×Dic3—32no—
998C2×Dic3—31no—
999C2×Dic3—31no—
1000C2×Dic3—42no—
1001C2×Dic3—61no—
1002C2×Dic3—61no—
1003C2×Dic3—62no—
1004C2×Dic3—61no—
1005C2×Dic3—62no—
1006C2×Dic3—64no—
1007C2×Dic3—121no—
1008C2×Dic3—122no—
1009C2×Dic3—121no—
1010C2×Dic3—122no—
1011C2×Dic3—122no—
1012C2×Dic3—242no—
1013C2×Dic3C23×D311yescharacteristic
1014C2×Dic3C23×D311yescharacteristic
1015C2×Dic3C23×D312yes—
1016C2×Dic3C23×D311yescharacteristic
1017C2×Dic3C23×D311yescharacteristic
1018C2×Dic3C23×D311yescharacteristic
1019C2×Dic3C23×D311yescharacteristic
1020C2×Dic3C23×D312yes—
1021C2×Dic3C23×D312yes—
1022D12—22no—
1023D12—41no—
1024D12—64no—
1025D12—121no—
1026D12—121no—
1027C4×D3—22no—
1028C4×D3—22no—
1029C4×D3—24no—
1030C4×D3—42no—
1031C4×D3—64no—
1032C4×D3—62no—
1033C4×D3—62no—
1034C4×D3—122no—
1035C4×D3—122no—
1036C4×D3—122no—
1037C4×D3—121no—
1038C4×D3—122no—
1039C4×D3—121no—
1040Dic6—24no—
1041Dic6—41no—
1042Dic6—122no—
1043Dic6—122no—
1044Dic6—242no—
1045Dic6#23714yes—
1046C2×C32—42no—
1047C2×C32C22×#4111yescharacteristic
1048C2×C32#58511yescharacteristic
1049C2×C32#58511yescharacteristic
1050C3⋊D3—41no—
1051C3×D3—42no—
1052C3×D3—41no—
1053C3×D3—41no—
1054#41—64no—
1055#41—184no—
1056C2×Q8—31no—
1057C2×Q8—32no—
1058C2×Q8—31no—
1059C2×Q8—64no—
1060C2×Q8—92no—
1061C2×Q8C2×D3211yescharacteristic
1062C2×D4—32no—
1063C2×D4—32no—
1064C2×D4—32no—
1065C2×D4—32no—
1066C2×D4—31no—
1067C2×D4—31no—
1068C2×D4—92no—
1069C2×D4—91no—
1070C2×D4—91no—
1071C2×D4—92no—
1072C2×D4—92no—
1073C2×D4—92no—
1074C2×D4C2×D3211yescharacteristic
1075C22×C4—32no—
1076C22×C4—32no—
1077C22×C4—31no—
1078C22×C4—32no—
1079C22×C4—31no—
1080C22×C4—32no—
1081C22×C4—92no—
1082C22×C4—92no—
1083C22×C4—91no—
1084C22×C4—91no—
1085C22×C4—92no—
1086C22×C4—92no—
1087C22×C4—91no—
1088C4⋊C4—31no—
1089C4⋊C4—32no—
1090C4⋊C4—31no—
1091C4⋊C4—32no—
1092C4⋊C4—31no—
1093C4⋊C4—32no—
1094C4⋊C4—31no—
1095C4⋊C4—31no—
1096C4⋊C4—31no—
1097C4⋊C4—92no—
1098C4⋊C4—92no—
1099C4⋊C4—92no—
1100C4⋊C4—92no—
1101C4⋊C4—91no—
1102C4⋊C4—91no—
1103C4⋊C4—92no—
1104C4⋊C4—92no—
1105C4⋊C4—91no—
1106C4⋊C4—92no—
1107C4⋊C4—91no—
1108C4⋊C4—92no—
1109C4⋊C4—91no—
1110C4⋊C4—91no—
1111C4⋊C4—91no—
1112C4⋊C4—91no—
1113C4⋊C4—92no—
1114C4⋊C4—92no—
1115C4⋊C4—92no—
1116C22⋊C4—32no—
1117C22⋊C4—32no—
1118C22⋊C4—32no—
1119C22⋊C4—32no—
1120C22⋊C4—31no—
1121C22⋊C4—32no—
1122C22⋊C4—31no—
1123C22⋊C4—32no—
1124C22⋊C4—91no—
1125C22⋊C4—91no—
1126C22⋊C4—91no—
1127C22⋊C4—91no—
1128C22⋊C4—92no—
1129C22⋊C4—92no—
1130C22⋊C4—92no—
1131C22⋊C4—92no—
1132C22⋊C4—92no—
1133C22⋊C4—91no—
1134C22⋊C4—91no—
1135C22⋊C4—92no—
1136C22⋊C4—92no—
1137C22⋊C4—91no—
1138C22⋊C4—91no—
1139C22⋊C4—92no—
1140C22⋊C4C2×D3212yes—
1141C22⋊C4C2×D3212yes—
1142C42—31no—
1143C42—32no—
1144C42—32no—
1145C42—31no—
1146C42—91no—
1147C42—92no—
1148C42—91no—
1149C42—92no—
1150C42—92no—
1151C42—92no—
1152C42—92no—
1153C42—91no—
1154C42—92no—
1155C42C2×D3211yescharacteristic
1156C22×C3—22no—
1157C22×C3—22no—
1158C22×C3—22no—
1159C22×C3—22no—
1160C22×C3—22no—
1161C22×C3—22no—
1162C22×C3—21no—
1163C22×C3—42no—
1164C22×C3—42no—
1165C22×C3—42no—
1166C22×C3—62no—
1167C22×C3—61no—
1168C22×C3—61no—
1169C22×C3—61no—
1170C22×C3—62no—
1171C22×C3—61no—
1172C22×C3—61no—
1173C22×C3—61no—
1174C22×C3—62no—
1175C22×C3C24×D311yescharacteristic
1176C22×C3C24×D311yescharacteristic
1177C2×D3—21no—
1178C2×D3—21no—
1179C2×D3—22no—
1180C2×D3—21no—
1181C2×D3—21no—
1182C2×D3—22no—
1183C2×D3—22no—
1184C2×D3—21no—
1185C2×D3—21no—
1186C2×D3—61no—
1187C2×D3—61no—
1188C2×D3—61no—
1189C2×D3—61no—
1190C2×D3—61no—
1191C2×D3—61no—
1192C2×D3—121no—
1193C2×D3—121no—
1194C2×D3—121no—
1195C3×C4—22no—
1196C3×C4—22no—
1197C3×C4—21no—
1198C3×C4—21no—
1199C3×C4—21no—
1200C3×C4—21no—
1201C3×C4—22no—
1202C3×C4—34no—
1203C3×C4—41no—
1204C3×C4—42no—
1205C3×C4—41no—
1206C3×C4—61no—
1207C3×C4—61no—
1208C3×C4—62no—
1209C3×C4—61no—
1210C3×C4—61no—
1211C3×C4—62no—
1212C3×C4—61no—
1213C3×C4—61no—
1214C3×C4C2×#23712yes—
1215C3×C4D3×#4112yes—
1216Dic3—21no—
1217Dic3—21no—
1218Dic3—21no—
1219Dic3—21no—
1220Dic3—22no—
1221Dic3—22no—
1222Dic3—21no—
1223Dic3—21no—
1224Dic3—61no—
1225Dic3—61no—
1226Dic3—62no—
1227Dic3—62no—
1228Dic3—61no—
1229Dic3—61no—
1230Dic3—61no—
1231Dic3—62no—
1232Dic3—62no—
1233Dic3—61no—
1234Dic3—122no—
1235Dic3—122no—
1236Dic3—121no—
1237Dic3—121no—
1238Dic3—121no—
1239Dic3C2×#23714yes—
1240C32#352411yescharacteristic, complemented, Sylow
1241C23—31no—
1242C23—32no—
1243C23—31no—
1244C23—91no—
1245C23C22×D3212yes—
1246Q8—22no—
1247Q8—34no—
1248Q8—64no—
1249Q8—121no—
1250Q8—362no—
1251D4—22no—
1252D4—64no—
1253D4—62no—
1254D4—121no—
1255D4—122no—
1256D4—122no—
1257D4—122no—
1258D4—184no—
1259D4—361no—
1260D4—361no—
1261D4—362no—
1262D4—362no—
1263D4—362no—
1264C2×C4—32no—
1265C2×C4—31no—
1266C2×C4—31no—
1267C2×C4—32no—
1268C2×C4—31no—
1269C2×C4—31no—
1270C2×C4—32no—
1271C2×C4—31no—
1272C2×C4—31no—
1273C2×C4—64no—
1274C2×C4—64no—
1275C2×C4—62no—
1276C2×C4—62no—
1277C2×C4—91no—
1278C2×C4—91no—
1279C2×C4—92no—
1280C2×C4—92no—
1281C2×C4—91no—
1282C2×C4—122no—
1283C2×C4—122no—
1284C2×C4—184no—
1285C2×C4—182no—
1286C2×C4—362no—
1287C2×C4—361no—
1288C2×C4—362no—
1289C2×C4—361no—
1290C2×C4—362no—
1291C2×C4C22×D3211yescharacteristic
1292C2×C4C22×D3212yes—
1293C2×C4C22×D3211yescharacteristic
1294C2×C4C22×D3211yescharacteristic
1295C2×C3—21no—
1296C2×C3—21no—
1297C2×C3—21no—
1298C2×C3—42no—
1299C2×C3—42no—
1300C2×C3—82no—
1301C2×C3—121no—
1302C2×C3—121no—
1303C2×C3—122no—
1304C2×C3C22×#23711yescharacteristic
1305C2×C3C2×D3×#4111yescharacteristic
1306C2×C3#596411yescharacteristic
1307C2×C3#596411yescharacteristic
1308C2×C3#596611yescharacteristic
1309C2×C3#596811yescharacteristic
1310D3—42no—
1311D3—41no—
1312D3—41no—
1313D3—121no—
1314D3—121no—
1315D3—241no—
1316C22—22no—
1317C22—22no—
1318C22—22no—
1319C22—61no—
1320C22—61no—
1321C22—62no—
1322C22—62no—
1323C22—61no—
1324C22—61no—
1325C22—61no—
1326C22—62no—
1327C22—61no—
1328C22—181no—
1329C22—181no—
1330C22—181no—
1331C22C23×D3211yescharacteristic
1332C4—22no—
1333C4—21no—
1334C4—21no—
1335C4—34no—
1336C4—61no—
1337C4—61no—
1338C4—62no—
1339C4—61no—
1340C4—62no—
1341C4—61no—
1342C4—61no—
1343C4—61no—
1344C4—181no—
1345C4—181no—
1346C4—181no—
1347C4—182no—
1348C4—182no—
1349C4D3×#23712yes—
1350C3—21no—
1351C3#8672311yescharacteristic, complemented
1352C3#8705611yescharacteristic, complemented
1353C2—42no—
1354C2—121no—
1355C2—121no—
1356C2—122no—
1357C2—361no—
1358C2C2×D3×#23711yescharacteristic
1359C2#1059669611yescharacteristic
1360C2#1059669711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#124C22
hypercenter#124D32
hypocenterC32#3524
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #10596153C2semidirect
2. C3×#5681C2semidirect
3. C3×#5677C2semidirect
4. #10595401C2semidirect
5. #10595377C2semidirect
6. #10595347C2semidirect
7. #10595344C2semidirect
8. #10595217C2semidirect
9. Dic3×#237C2semidirect
10. #10595158C2semidirect
11. #10595122C2semidirect
12. #10594220C2semidirect
13. #10594216C2semidirect
14. #10594201C2semidirect
15. #10594198C2semidirect
16. #10594143C2semidirect
17. #10594132C2semidirect
18. #10594131C2semidirect
19. #10594118C2semidirect
20. #10593988C2semidirect
21. #10593911C2semidirect
22. #10593889C2semidirect
23. #10593860C2semidirect
138. #5681D3semidirect
141. #5677D3semidirect
1240. C32#3524semidirect
1351. C3#86723semidirect
1352. C3#87056semidirect

Maximal subgroups

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

subgroupindex
#105961532
C3×#56812
C3×#56772
#105954012
#105953772
#105953472
#105953442
#105952172
Dic3×#2372
#105951582
#105951222
#105942202
#105942162
#105942012
#105941982
#105941432
#105941322
#105941312
#105941182
#105939882
#105939112
#105938892
#105938602
#870563
#867233