Finite Group Databasebeta

← #11909884

Subgroups — #11909884

Order 1152.

2101 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596120C211yesmaximal, characteristic
2C3×#5650C212yesmaximal, complemented
3D4×#627C211yesmaximal, characteristic, complemented
4#10595120C211yesmaximal, characteristic, complemented
5#10595116C212yesmaximal
6#10595050C211yesmaximal, characteristic, complemented
7#10594807C212yesmaximal, complemented
8C2×#63838C211yesmaximal, characteristic, complemented
9#10594599C211yesmaximal, characteristic, complemented
10#10594597C211yesmaximal, characteristic, complemented
11#10594596C212yesmaximal, complemented
12#10594347C211yesmaximal, characteristic, complemented
13#10594324C211yesmaximal, characteristic, complemented
14#10594320C212yesmaximal, complemented
15#10594250C211yesmaximal, characteristic, complemented
16#10594249C211yesmaximal, characteristic, complemented
17#10594245C211yesmaximal, characteristic, complemented
18#10594110C212yesmaximal, complemented
19#10594072C211yesmaximal, characteristic, complemented
20#10594072C211yesmaximal, characteristic, complemented
21#10594046C211yesmaximal, characteristic, complemented
22#10594029C212yesmaximal, complemented
23#10594028C212yesmaximal, complemented
24#86842—32nomaximal
25C22×#627C2211yescharacteristic
26C22×#627C2211yescharacteristic
27C2×#3797C2211yescharacteristic
28C32×#123C2211yescharacteristic
29#64148C2211yescharacteristic
30D4×C3⋊Dic3C2211yescharacteristic
31#64138C2211yescharacteristic
32C2×C4×C3⋊Dic3C2211yescharacteristic
33#64107C2211yescharacteristic
34#64101C2211yescharacteristic
35#64098C2211yescharacteristic
36#64096C2211yescharacteristic
37#64094C2211yescharacteristic
38#64090C2211yescharacteristic
39#64090C2211yescharacteristic
40#64088C2211yescharacteristic
41#64087C2211yescharacteristic
42#64086C2211yescharacteristic
43C3×#935C2212yes—
44C3×D4×Dic3C2212yes—
45C3×#926C2212yes—
46C2×C3×Dic3⋊C4C2212yes—
47C3×#890C2212yes—
48C3×#889C2212yes—
49C3×#889C2212yes—
50C3×#887C2212yes—
51C3×#879C2212yes—
52C3×#879C2212yes—
53C3×#878C2212yes—
54C3×#878C2212yes—
55C3×#877C2212yes—
56C3×#877C2212yes—
57#63982C2211yescharacteristic
58#63982C2211yescharacteristic
59#63982C2212yes—
60#63982C2211yescharacteristic
61#63982C2211yescharacteristic
62C2×#3724C2211yescharacteristic
63#63966C2212yes—
64#63964C2212yes—
65#63964C2212yes—
66#63957C2211yescharacteristic
67#63956C2212yes—
68#63956C2212yes—
69#63955C2212yes—
70#63955C2212yes—
71C2×Dic32C2212yes—
72#63953C2212yes—
73#63952C2212yes—
74#63952C2212yes—
75#63919C2211yescharacteristic
76#63919C2211yescharacteristic
77#63919C2211yescharacteristic
78#63919C2211yescharacteristic
79#63918C2212yes—
80C4×#627C2211yescharacteristic
81C4×#627C2212yes—
82C4×#627C2211yescharacteristic
83C4×#627C2211yescharacteristic
84C4×#627C2211yescharacteristic
85#63895C2212yes—
86#63895C2212yes—
87#63874C2211yescharacteristic
88#63872C2212yes—
89#63870C2211yescharacteristic
90#63870C2211yescharacteristic
91#63868C2212yes—
92#63868C2212yes—
93#63867C2212yes—
94#63867C2212yes—
95#63865C2211yescharacteristic
96#63865C2211yescharacteristic
97#63848C2212yes—
98#63848C2212yes—
99#63847C2212yes—
100#63847C2212yes—
101#63846C2212yes—
102#63846C2212yes—
103#63845C2212yes—
104#63845C2212yes—
105#63844C2212yes—
106Dic3×Dic6C2212yes—
107#63840C2212yes—
108#63839C2212yes—
109#63839C2212yes—
110#63838C2212yes—
111#63838C2211yescharacteristic
112#63838C2211yescharacteristic
113#63838C2211yescharacteristic
114#63838C2211yescharacteristic
115#63838C2212yes—
116#63838C2211yescharacteristic
117#63838C2211yescharacteristic
118#63837C2212yes—
119#63837C2212yes—
120#63837C2212yes—
121#63837C2212yes—
122#63836C2212yes—
123#63836C2212yes—
124C3×#552—32no—
125#5702—32no—
126#5702—32no—
127#5701—32no—
128#5701—32no—
129#5698—32no—
130#5696—32no—
131#5696—32no—
132#5685—32no—
133#5685—32no—
134#5685—32no—
135#5650—32no—
136#5650D312yescomplemented
137#5649—32no—
138#5649—32no—
139#5649—61no—
140#5632—32no—
141#5632—32no—
142#5625—32no—
143#5622—32no—
144#5572—32no—
145#5567—32no—
146#5538—32no—
147D4×Dic6—32no—
148#5533—32no—
149#5531—32no—
150#5531—32no—
151#5517—32no—
152#5517—32no—
153#5516—32no—
154#5513—32no—
155C2×#887—32no—
156C2×C32×D4C2311yescharacteristic
157C22×C32×C4C2311yescharacteristic
158C2×#638C2311yescharacteristic
159C2×#638C2311yescharacteristic
160C22×C3⋊Dic3C2311yescharacteristic
161C22×C3⋊Dic3C2311yescharacteristic
162C22×C3⋊Dic3C2311yescharacteristic
163C2×C4×C3⋊D3C2311yescharacteristic
164C2×#634C2311yescharacteristic
165C22×C3×Dic3C2312yes—
166C22×C3×Dic3C2312yes—
167C22×C3×Dic3C2312yes—
168C2×C3×Dic6C2312yes—
169C2×#627—24no—
170C2×#627—24no—
171C2×#627C2311yescharacteristic
172C2×#627C2312yes—
173C2×#627C2312yes—
174C2×#627C2311yescharacteristic
175C2×#627C2311yescharacteristic
176C2×#627C2312yes—
177C2×#627C2311yescharacteristic
178C2×#624C2312yes—
179#3797—24no—
180C32×C4⋊C4C2311yescharacteristic
181C32×C4⋊C4C2311yescharacteristic
182C32×C22⋊C4C2311yescharacteristic
183C32×C22⋊C4C2311yescharacteristic
184C32×C22⋊C4C2311yescharacteristic
185#3757C2311yescharacteristic
186#3757C2311yescharacteristic
187#3757C2311yescharacteristic
188#3752C2311yescharacteristic
189#3752C2311yescharacteristic
190#3752C2311yescharacteristic
191#3752C2311yescharacteristic
192C4⋊(C3⋊Dic3)C2311yescharacteristic
193C4⋊(C3⋊Dic3)C2311yescharacteristic
194#3750C2311yescharacteristic
195#3750C2311yescharacteristic
196#3750C2311yescharacteristic
197#3750C2311yescharacteristic
198#3750C2311yescharacteristic
199#3750C2311yescharacteristic
200C4×C3⋊Dic3C2311yescharacteristic
201C4×C3⋊Dic3C2311yescharacteristic
202C4×C3⋊Dic3C2311yescharacteristic
203C4×C3⋊Dic3C2311yescharacteristic
204C4×C3⋊Dic3C2311yescharacteristic
205C4×C3⋊Dic3C2311yescharacteristic
206C3×#217C2312yes—
207C3×#217C2312yes—
208C3×#217C2312yes—
209C3×#217C2312yes—
210C3×#217C2312yes—
211C3×C4⋊Dic3C2312yes—
212C3×C4⋊Dic3C2312yes—
213C3×C4⋊Dic3C2312yes—
214C3×C4⋊Dic3C2312yes—
215C3×Dic3⋊C4C2312yes—
216C3×Dic3⋊C4C2312yes—
217C3×Dic3⋊C4C2312yes—
218C3×Dic3⋊C4C2312yes—
219C3×Dic3⋊C4C2312yes—
220C3×Dic3⋊C4C2312yes—
221C3×Dic3⋊C4C2312yes—
222C3×Dic3⋊C4C2312yes—
223C3×Dic3⋊C4C2312yes—
224C3×Dic3⋊C4C2312yes—
225C3×C4×Dic3C2312yes—
226C3×C4×Dic3C2312yes—
227C3×C4×Dic3C2312yes—
228C3×C4×Dic3C2312yes—
229C3×C4×Dic3C2312yes—
230#3724C2311yescharacteristic
231#3724C2312yes—
232#3724C2311yescharacteristic
233#3724C2311yescharacteristic
234#3724C2312yes—
235#3724C2312yes—
236#3724C2312yes—
237#3724C2311yescharacteristic
238Dic3⋊Dic3C2312yes—
239Dic3⋊Dic3C2312yes—
240Dic3⋊Dic3C2312yes—
241Dic3⋊Dic3C2312yes—
242Dic3⋊Dic3C2312yes—
243Dic3⋊Dic3C2312yes—
244Dic3⋊Dic3C2312yes—
245Dic3⋊Dic3C2312yes—
246Dic3⋊Dic3C2312yes—
247Dic3⋊Dic3C2312yes—
248#3722C2312yes—
249#3722C2312yes—
250#3722C2312yes—
251Dic32C2312yes—
252Dic32C2312yes—
253Dic32C2312yes—
254Dic32C2312yes—
255Dic32C2312yes—
256Dic32C2312yes—
257Dic32C2312yes—
258#3523—91noSylow
259C2×D3×Q8—32no—
260C22×Dic6—32no—
261C22×Dic6—32no—
262C3×#126—32no—
263C3×#126—32no—
264C3×#125—32no—
265C3×#125—32no—
266C3×#125—32no—
267C3×#123—21no—
268C3×#123—32no—
269C3×#123C2×D312yes—
270C3×C22⋊Q8—32no—
271C3×C22⋊Q8—32no—
272C3×C4×Q8—32no—
273C3×C4×D4—32no—
274C3×#117—32no—
275C3×#117—32no—
276C3×#117—32no—
277C2×C3×C4⋊C4—32no—
278Q8×Dic3—32no—
279#944—32no—
280#944—32no—
281#939—32no—
282#939—61no—
283#935C2×D312yes—
284D4×Dic3—32no—
285D4×Dic3—61no—
286D4×Dic3C2×D312yes—
287#929—32no—
288#929—32no—
289#929—61no—
290C4×#67—32no—
291C4×#67—32no—
292#926—32no—
293#926—32no—
294#926C2×D312yes—
295#924—32no—
296#924—32no—
297C2×Dic3⋊C4—32no—
298C2×Dic3⋊C4C2×D312yes—
299C2×C4×Dic3—32no—
300C2×C4×Dic3—32no—
301C2×C4×Dic3—32no—
302C2×C4×Dic3—61no—
303#898—32no—
304#898—32no—
305#898—32no—
306#898—32no—
307#898—32no—
308#898—32no—
309#898—32no—
310#898—61no—
311#897—32no—
312#897—32no—
313#896—32no—
314#896—32no—
315#896—32no—
316#896—32no—
317#892—32no—
318#892—32no—
319#892—32no—
320#892—61no—
321#890—32no—
322#890—32no—
323#890—32no—
324#890—32no—
325#890—32no—
326#890—32no—
327#890C2×D312yes—
328#889—32no—
329#889—32no—
330#889—32no—
331#889—32no—
332#889—32no—
333#889—32no—
334#889—32no—
335#889—32no—
336#889—32no—
337#889—32no—
338#889—32no—
339#889—32no—
340#889—32no—
341#889—61no—
342#889C2×D312yes—
343#889C2×D312yes—
344#888—32no—
345#888—32no—
346#888—32no—
347#888—32no—
348#888—32no—
349#888—32no—
350#888—32no—
351#888—32no—
352#888—32no—
353#887—32no—
354#887—32no—
355#887—32no—
356#887—32no—
357#887—32no—
358#887—32no—
359#887—32no—
360#887—32no—
361#887—32no—
362#887—32no—
363#887—32no—
364#887—32no—
365#887—32no—
366#887—32no—
367#887—32no—
368#887—32no—
369#887—61no—
370#887C2×D312yes—
371#886—32no—
372#885—32no—
373#885—32no—
374#885—32no—
375#885—61no—
376#67⋊C4—32no—
377#67⋊C4—32no—
378#67⋊C4—32no—
379#67⋊C4—32no—
380#67⋊C4—61no—
381#67⋊C4—61no—
382#879—32no—
383#879—32no—
384#879—32no—
385#879—32no—
386#879—32no—
387#879—61no—
388#879C2×D312yes—
389#879C2×D312yes—
390#878—32no—
391#878—32no—
392#878—32no—
393#878—32no—
394#878—32no—
395#878—32no—
396#878—32no—
397#878—32no—
398#878—32no—
399#878—61no—
400#878C2×D312yes—
401#878C2×D312yes—
402#877—32no—
403#877—32no—
404#877—32no—
405#877—32no—
406#877—61no—
407#877C2×D312yes—
408#877C2×D312yes—
409#876—32no—
410#876—32no—
411#872—32no—
412#872—32no—
413#872—32no—
414#870—32no—
415#870—32no—
416#869—32no—
417C4×Dic6—32no—
418C4×Dic6—32no—
419C4×Dic6—32no—
420C4×Dic6—32no—
421C4×Dic6—32no—
422C4×Dic6—32no—
423C4×Dic6—32no—
424C4×Dic6—32no—
425C4×Dic6—32no—
426C4×Dic6—32no—
427C4×Dic6—32no—
428C4×Dic6—32no—
429C23×C32C2411yescharacteristic
430C23×C32C2411yescharacteristic
431C22×C3⋊D3C2411yescharacteristic
432C32×D4—22no—
433C2×C32×C4—22no—
434C2×C32×C4C2411yescharacteristic
435C2×C32×C4C2411yescharacteristic
436C2×C32×C4C2411yescharacteristic
437C2×C32×C4C2411yescharacteristic
438C2×C32×C4C2411yescharacteristic
439#638—22no—
440#638—22no—
441C2×C3⋊Dic3—22no—
442C2×C3⋊Dic3—22no—
443C2×C3⋊Dic3—22no—
444C2×C3⋊Dic3C2411yescharacteristic
445C2×C3⋊Dic3C2411yescharacteristic
446C2×C3⋊Dic3C2411yescharacteristic
447C2×C3⋊Dic3C2411yescharacteristic
448C2×C3⋊Dic3C2411yescharacteristic
449C2×C3⋊Dic3C2411yescharacteristic
450C2×C3⋊Dic3C2411yescharacteristic
451C4×C3⋊D3—22no—
452#634—22no—
453C2×C3×Dic3—24no—
454C2×C3×Dic3—24no—
455C2×C3×Dic3—24no—
456C2×C3×Dic3C2412yes—
457C2×C3×Dic3C2412yes—
458C2×C3×Dic3C2412yes—
459C2×C3×Dic3C2412yes—
460C2×C3×Dic3C2412yes—
461C2×C3×Dic3C2412yes—
462C2×C3×Dic3C2412yes—
463C2×C3×Dic3C2412yes—
464C3×Dic6—24no—
465#627—22no—
466#627—22no—
467#627—22no—
468#627—24no—
469#627—24no—
470#627—24no—
471#627#4114yes—
472#624—24no—
473#557—92no—
474#557—91no—
475#557—91no—
476#556—92no—
477#556—91no—
478#552—32no—
479#552—92no—
480#552—91no—
481#552—91no—
482D4×Q8—91no—
483D4×Q8—91no—
484D4×Q8—91no—
485#541—92no—
486#541—91no—
487#541—92no—
488#541—91no—
489#533—91no—
490#533—92no—
491#529—92no—
492#529—91no—
493#519—91no—
494#519—91no—
495C2×C4×Q8—91no—
496C2×C3×Q8—32no—
497C2×C3×D4—21no—
498C2×C3×D4C22×D312yes—
499C22×C3×C4—21no—
500C22×C3×C4—32no—
501C22×C3×C4—32no—
502C22×C3×C4—32no—
503C22×C3×C4C22×D312yes—
504C2×#67—32no—
505C2×#67—32no—
506C2×#67—61no—
507C2×#67—61no—
508C22×Dic3—32no—
509C22×Dic3—32no—
510C22×Dic3—32no—
511C22×Dic3—61no—
512C22×Dic3—61no—
513C22×Dic3—61no—
514C22×Dic3C22×D312yes—
515C22×Dic3C22×D312yes—
516C22×Dic3C22×D312yes—
517D3×Q8—68no—
518C2×C4×D3—32no—
519C2×C4×D3—32no—
520C2×C4×D3—32no—
521C2×C4×D3—61no—
522C2×Dic6—32no—
523C2×Dic6—32no—
524C2×Dic6—32no—
525C2×Dic6—32no—
526C2×Dic6—32no—
527C2×Dic6—32no—
528C2×Dic6—32no—
529C2×Dic6—32no—
530C2×Dic6—32no—
531C2×Dic6—32no—
532C2×Dic6—32no—
533C2×Dic6—61no—
534C2×Dic6—68no—
535C2×Dic6—68no—
536C2×Dic6C22×D312yes—
537C3×C4⋊C4—21no—
538C3×C4⋊C4—21no—
539C3×C4⋊C4—32no—
540C3×C4⋊C4—32no—
541C3×C4⋊C4—32no—
542C3×C4⋊C4—32no—
543C3×C4⋊C4—32no—
544C3×C4⋊C4—32no—
545C3×C4⋊C4—32no—
546C3×C4⋊C4—32no—
547C3×C4⋊C4—32no—
548C3×C4⋊C4—32no—
549C3×C4⋊C4—32no—
550C3×C4⋊C4—32no—
551C3×C4⋊C4—32no—
552C3×C4⋊C4—32no—
553C3×C4⋊C4C22×D312yes—
554C3×C4⋊C4C22×D312yes—
555C3×C22⋊C4—21no—
556C3×C22⋊C4—21no—
557C3×C22⋊C4—21no—
558C3×C22⋊C4—32no—
559C3×C22⋊C4—32no—
560C3×C22⋊C4—32no—
561C3×C22⋊C4—32no—
562C3×C22⋊C4—32no—
563C3×C22⋊C4C22×D312yes—
564C3×C22⋊C4C22×D312yes—
565C3×C22⋊C4C22×D312yes—
566C3×C42—32no—
567C3×C42—32no—
568C3×C42—32no—
569C3×C42—32no—
570C3×C42—32no—
571#217—32no—
572#217—32no—
573#217—32no—
574#217—61no—
575#217—61no—
576#217—61no—
577#217C22×D312yes—
578#217C22×D312yes—
579#217C22×D312yes—
580#217C22×D312yes—
581#217C22×D312yes—
582(C2×D3)⋊C4—32no—
583(C2×D3)⋊C4—32no—
584(C2×D3)⋊C4—32no—
585(C2×D3)⋊C4—32no—
586(C2×D3)⋊C4—32no—
587(C2×D3)⋊C4—32no—
588(C2×D3)⋊C4—32no—
589(C2×D3)⋊C4—32no—
590(C2×D3)⋊C4—32no—
591(C2×D3)⋊C4—32no—
592(C2×D3)⋊C4—61no—
593(C2×D3)⋊C4—61no—
594(C2×D3)⋊C4—61no—
595(C2×D3)⋊C4—61no—
596C4⋊Dic3—32no—
597C4⋊Dic3—32no—
598C4⋊Dic3—32no—
599C4⋊Dic3—32no—
600C4⋊Dic3—32no—
601C4⋊Dic3—32no—
602C4⋊Dic3—32no—
603C4⋊Dic3—32no—
604C4⋊Dic3—32no—
605C4⋊Dic3—32no—
606C4⋊Dic3—32no—
607C4⋊Dic3—32no—
608C4⋊Dic3—61no—
609C4⋊Dic3—61no—
610C4⋊Dic3C22×D312yes—
611C4⋊Dic3C22×D312yes—
612C4⋊Dic3C22×D312yes—
613C4⋊Dic3C22×D312yes—
614Dic3⋊C4—32no—
615Dic3⋊C4—32no—
616Dic3⋊C4—32no—
617Dic3⋊C4—32no—
618Dic3⋊C4—32no—
619Dic3⋊C4—32no—
620Dic3⋊C4—32no—
621Dic3⋊C4—32no—
622Dic3⋊C4—32no—
623Dic3⋊C4—32no—
624Dic3⋊C4—32no—
625Dic3⋊C4—32no—
626Dic3⋊C4—32no—
627Dic3⋊C4—32no—
628Dic3⋊C4—32no—
629Dic3⋊C4—32no—
630Dic3⋊C4—32no—
631Dic3⋊C4—32no—
632Dic3⋊C4—32no—
633Dic3⋊C4—32no—
634Dic3⋊C4—32no—
635Dic3⋊C4—32no—
636Dic3⋊C4—32no—
637Dic3⋊C4—32no—
638Dic3⋊C4—32no—
639Dic3⋊C4—32no—
640Dic3⋊C4—32no—
641Dic3⋊C4—32no—
642Dic3⋊C4—61no—
643Dic3⋊C4—61no—
644Dic3⋊C4—61no—
645Dic3⋊C4—61no—
646Dic3⋊C4—61no—
647Dic3⋊C4—61no—
648Dic3⋊C4C22×D312yes—
649Dic3⋊C4C22×D312yes—
650Dic3⋊C4C22×D312yes—
651Dic3⋊C4C22×D312yes—
652Dic3⋊C4C22×D312yes—
653Dic3⋊C4C22×D312yes—
654Dic3⋊C4C22×D312yes—
655Dic3⋊C4C22×D312yes—
656Dic3⋊C4C22×D312yes—
657Dic3⋊C4C22×D312yes—
658C4×Dic3—32no—
659C4×Dic3—32no—
660C4×Dic3—32no—
661C4×Dic3—32no—
662C4×Dic3—32no—
663C4×Dic3—32no—
664C4×Dic3—32no—
665C4×Dic3—32no—
666C4×Dic3—32no—
667C4×Dic3—32no—
668C4×Dic3—32no—
669C4×Dic3—32no—
670C4×Dic3—32no—
671C4×Dic3—32no—
672C4×Dic3—32no—
673C4×Dic3—32no—
674C4×Dic3—32no—
675C4×Dic3—32no—
676C4×Dic3—32no—
677C4×Dic3—32no—
678C4×Dic3—61no—
679C4×Dic3—61no—
680C4×Dic3—61no—
681C4×Dic3—61no—
682C4×Dic3—61no—
683C4×Dic3—61no—
684C4×Dic3C22×D312yes—
685C4×Dic3C22×D312yes—
686C4×Dic3C22×D312yes—
687C4×Dic3C22×D312yes—
688C4×Dic3C22×D312yes—
689C22×C32—21no—
690C22×C32—21no—
691C22×C32—21no—
692C22×C32—21no—
693C22×C32—21no—
694C22×C322−1+412yes—
695C22×C32C2511yescharacteristic
696C2×C3⋊D3—21no—
697C2×C3⋊D3—21no—
698C2×C3⋊D3—21no—
699C32×C4—21no—
700C32×C4—21no—
701C32×C4—21no—
702C32×C4—21no—
703C32×C4—21no—
704C3⋊Dic3—21no—
705C3⋊Dic3—21no—
706C3⋊Dic3—21no—
707C3⋊Dic3—21no—
708C3⋊Dic3—21no—
709C3⋊Dic3C2×#4112yes—
710C3⋊Dic32−1+412yes—
711C3×Dic3—22no—
712C3×Dic3—22no—
713C3×Dic3—22no—
714C3×Dic3—22no—
715C3×Dic3—22no—
716C3×Dic3—22no—
717C3×Dic3—22no—
718C3×Dic3C2×#4114yes—
719C22×Q8—91no—
720C22×Q8—91no—
721C22×Q8—91no—
722C4⋊Q8—92no—
723C4⋊Q8—91no—
724C4⋊Q8—92no—
725C4⋊Q8—91no—
726C4⋊Q8—91no—
727C4⋊Q8—91no—
728C4⋊Q8—92no—
729C4⋊Q8—92no—
730#126—32no—
731#126—32no—
732#126—92no—
733#126—92no—
734#126—92no—
735#126—92no—
736#126—92no—
737#126—92no—
738#126—91no—
739#126—91no—
740#125—32no—
741#125—32no—
742#125—32no—
743#125—92no—
744#125—92no—
745#125—92no—
746#125—92no—
747#125—92no—
748#125—92no—
749#125—92no—
750#125—91no—
751#125—91no—
752#125—92no—
753#125—92no—
754#125—91no—
755#124—92no—
756#124—91no—
757#123—32no—
758#123—92no—
759#123—91no—
760#123D3211yescharacteristic
761C22⋊Q8—32no—
762C22⋊Q8—32no—
763C22⋊Q8—92no—
764C22⋊Q8—91no—
765C22⋊Q8—91no—
766C22⋊Q8—91no—
767C22⋊Q8—91no—
768C22⋊Q8—92no—
769C22⋊Q8—92no—
770C22⋊Q8—91no—
771C22⋊Q8—92no—
772C22⋊Q8—91no—
773C22⋊Q8—92no—
774C22⋊Q8—91no—
775#121—91no—
776C4×Q8—32no—
777C4×Q8—91no—
778C4×Q8—91no—
779C4×Q8—91no—
780C4×Q8—91no—
781C4×Q8—92no—
782C4×Q8—92no—
783C4×Q8—92no—
784C4×Q8—92no—
785C4×Q8—92no—
786C4×Q8—92no—
787C4×Q8—92no—
788C4×Q8—91no—
789C4×Q8—92no—
790C4×Q8—91no—
791C4×Q8—91no—
792C4×Q8—92no—
793C4×Q8—91no—
794C4×Q8—91no—
795C4×Q8—91no—
796C4×Q8—91no—
797C4×D4—32no—
798C4×D4—92no—
799C4×D4—92no—
800C4×D4—91no—
801C4×D4—91no—
802C4×D4—91no—
803#117—32no—
804#117—32no—
805#117—32no—
806#117—91no—
807#117—92no—
808#117—92no—
809#117—91no—
810#117—92no—
811#117—92no—
812#117—91no—
813#117—91no—
814C2×C4⋊C4—32no—
815C2×C4⋊C4—91no—
816C2×C42—92no—
817C2×C42—91no—
818C23×C3—21no—
819C23×C3—21no—
820C23×C3C23×D312yes—
821C23×C3C23×D312yes—
822C22×D3—32no—
823C22×D3—61no—
824C3×Q8—64no—
825C3×D4—24no—
826C3×D4—42no—
827C2×C3×C4—24no—
828C2×C3×C4—21no—
829C2×C3×C4—21no—
830C2×C3×C4—21no—
831C2×C3×C4—21no—
832C2×C3×C4—21no—
833C2×C3×C4—32no—
834C2×C3×C4—32no—
835C2×C3×C4—32no—
836C2×C3×C4—32no—
837C2×C3×C4—32no—
838C2×C3×C4—32no—
839C2×C3×C4—32no—
840C2×C3×C4—32no—
841C2×C3×C4—42no—
842C2×C3×C4—64no—
843C2×C3×C4—64no—
844C2×C3×C4—64no—
845C2×C3×C4C23×D312yes—
846C2×C3×C4C23×D312yes—
847C2×C3×C4C23×D312yes—
848C2×C3×C4C23×D312yes—
849C2×C3×C4C23×D312yes—
850#67—64no—
851#67—64no—
852#67—122no—
853#67—122no—
854C2×Dic3—24no—
855C2×Dic3—24no—
856C2×Dic3—24no—
857C2×Dic3—32no—
858C2×Dic3—32no—
859C2×Dic3—32no—
860C2×Dic3—32no—
861C2×Dic3—32no—
862C2×Dic3—32no—
863C2×Dic3—32no—
864C2×Dic3—61no—
865C2×Dic3—61no—
866C2×Dic3—61no—
867C2×Dic3—61no—
868C2×Dic3—61no—
869C2×Dic3—61no—
870C2×Dic3—61no—
871C2×Dic3—64no—
872C2×Dic3—64no—
873C2×Dic3—64no—
874C2×Dic3—122no—
875C2×Dic3—122no—
876C2×Dic3—122no—
877C2×Dic3C23×D312yes—
878C2×Dic3C23×D312yes—
879C2×Dic3C23×D312yes—
880C2×Dic3C23×D312yes—
881C2×Dic3C23×D312yes—
882C2×Dic3C23×D312yes—
883C2×Dic3C23×D312yes—
884C2×Dic3C23×D312yes—
885C4×D3—64no—
886C4×D3—64no—
887C4×D3—64no—
888C4×D3—122no—
889Dic6—24no—
890Dic6—38no—
891Dic6—64no—
892Dic6—64no—
893Dic6—64no—
894Dic6—64no—
895Dic6—64no—
896Dic6—64no—
897Dic6—64no—
898Dic6—64no—
899Dic6—64no—
900Dic6—64no—
901Dic6—122no—
902C2×C32—22no—
903C2×C32—41no—
904C2×C32C22×#4111yescharacteristic
905C2×C32C2×2−1+411yescharacteristic
906C2×C32C2×2−1+411yescharacteristic
907C3⋊D3—41no—
908C2×Q8—32no—
909C2×Q8—91no—
910C2×Q8—92no—
911C2×Q8—92no—
912C2×Q8—92no—
913C2×Q8—91no—
914C2×Q8—91no—
915C2×Q8—91no—
916C2×Q8—91no—
917C2×Q8—184no—
918C2×Q8—184no—
919C2×Q8—184no—
920C2×D4—91no—
921C2×D4—91no—
922C2×D4C2×D3211yescharacteristic
923C22×C4—32no—
924C22×C4—32no—
925C22×C4—32no—
926C22×C4—92no—
927C22×C4—91no—
928C22×C4—91no—
929C22×C4—91no—
930C22×C4—91no—
931C22×C4C2×D3211yescharacteristic
932C4⋊C4—32no—
933C4⋊C4—32no—
934C4⋊C4—32no—
935C4⋊C4—32no—
936C4⋊C4—32no—
937C4⋊C4—32no—
938C4⋊C4—32no—
939C4⋊C4—32no—
940C4⋊C4—32no—
941C4⋊C4—32no—
942C4⋊C4—32no—
943C4⋊C4—32no—
944C4⋊C4—32no—
945C4⋊C4—32no—
946C4⋊C4—91no—
947C4⋊C4—91no—
948C4⋊C4—92no—
949C4⋊C4—91no—
950C4⋊C4—91no—
951C4⋊C4—92no—
952C4⋊C4—92no—
953C4⋊C4—92no—
954C4⋊C4—92no—
955C4⋊C4—92no—
956C4⋊C4—92no—
957C4⋊C4—92no—
958C4⋊C4—92no—
959C4⋊C4—92no—
960C4⋊C4—92no—
961C4⋊C4—92no—
962C4⋊C4—92no—
963C4⋊C4—92no—
964C4⋊C4—91no—
965C4⋊C4—91no—
966C4⋊C4—91no—
967C4⋊C4—91no—
968C4⋊C4—91no—
969C4⋊C4—91no—
970C4⋊C4—91no—
971C4⋊C4—91no—
972C4⋊C4C2×D3211yescharacteristic
973C4⋊C4C2×D3211yescharacteristic
974C22⋊C4—32no—
975C22⋊C4—32no—
976C22⋊C4—32no—
977C22⋊C4—32no—
978C22⋊C4—32no—
979C22⋊C4—92no—
980C22⋊C4—92no—
981C22⋊C4—92no—
982C22⋊C4—91no—
983C22⋊C4—91no—
984C22⋊C4—91no—
985C22⋊C4—91no—
986C22⋊C4—91no—
987C22⋊C4—91no—
988C22⋊C4—91no—
989C22⋊C4C2×D3211yescharacteristic
990C22⋊C4C2×D3211yescharacteristic
991C22⋊C4C2×D3211yescharacteristic
992C42—32no—
993C42—32no—
994C42—32no—
995C42—32no—
996C42—32no—
997C42—92no—
998C42—92no—
999C42—92no—
1000C42—92no—
1001C42—92no—
1002C42—92no—
1003C42—92no—
1004C42—91no—
1005C42—91no—
1006C42—91no—
1007C42—91no—
1008C42—91no—
1009C42—91no—
1010C22×C3—22no—
1011C22×C3—22no—
1012C22×C3—22no—
1013C22×C3—22no—
1014C22×C3—22no—
1015C22×C3—22no—
1016C22×C3—21no—
1017C22×C3—41no—
1018C22×C3—41no—
1019C22×C3—41no—
1020C22×C3—41no—
1021C22×C3—41no—
1022C22×C3#101014yes—
1023C22×C3C24×D312yes—
1024C2×D3—62no—
1025C2×D3—62no—
1026C2×D3—62no—
1027C2×D3—121no—
1028C2×D3—121no—
1029C2×D3—121no—
1030C3×C4—22no—
1031C3×C4—22no—
1032C3×C4—22no—
1033C3×C4—22no—
1034C3×C4—22no—
1035C3×C4—34no—
1036C3×C4—41no—
1037C3×C4—41no—
1038C3×C4—41no—
1039C3×C4—41no—
1040C3×C4—41no—
1041C3×C4—62no—
1042C3×C4—62no—
1043C3×C4—62no—
1044C3×C4—62no—
1045C3×C4—62no—
1046C3×C4—62no—
1047C3×C4—62no—
1048Dic3—22no—
1049Dic3—22no—
1050Dic3—22no—
1051Dic3—22no—
1052Dic3—22no—
1053Dic3—22no—
1054Dic3—22no—
1055Dic3—34no—
1056Dic3—34no—
1057Dic3—62no—
1058Dic3—62no—
1059Dic3—62no—
1060Dic3—62no—
1061Dic3—62no—
1062Dic3—62no—
1063Dic3—62no—
1064Dic3—121no—
1065Dic3—121no—
1066Dic3—121no—
1067Dic3—121no—
1068Dic3—121no—
1069Dic3D3×#4114yes—
1070C32#352311yescharacteristic, complemented, Sylow
1071C23—91no—
1072C23C22×D3211yescharacteristic
1073C23C22×D3211yescharacteristic
1074Q8—64no—
1075Q8—94no—
1076Q8—182no—
1077Q8—184no—
1078Q8—184no—
1079Q8—182no—
1080Q8—182no—
1081Q8—182no—
1082Q8—184no—
1083D4—22no—
1084D4—182no—
1085D4—182no—
1086C2×C4—22no—
1087C2×C4—32no—
1088C2×C4—32no—
1089C2×C4—32no—
1090C2×C4—32no—
1091C2×C4—32no—
1092C2×C4—32no—
1093C2×C4—32no—
1094C2×C4—32no—
1095C2×C4—64no—
1096C2×C4—64no—
1097C2×C4—64no—
1098C2×C4—91no—
1099C2×C4—91no—
1100C2×C4—91no—
1101C2×C4—91no—
1102C2×C4—91no—
1103C2×C4—91no—
1104C2×C4—91no—
1105C2×C4—182no—
1106C2×C4—184no—
1107C2×C4—182no—
1108C2×C4—182no—
1109C2×C4—182no—
1110C2×C4C22×D3211yescharacteristic
1111C2×C4C22×D3211yescharacteristic
1112C2×C4C22×D3211yescharacteristic
1113C2×C4C22×D3211yescharacteristic
1114C2×C4C22×D3211yescharacteristic
1115C2×C3—24no—
1116C2×C3—21no—
1117C2×C3—21no—
1118C2×C3—21no—
1119C2×C3—42no—
1120C2×C3—42no—
1121C2×C3—81no—
1122C2×C3C2×D3×#4112yes—
1123C2×C3C2×#101012yes—
1124C2×C3D3×2−1+412yes—
1125D3—122no—
1126D3—241no—
1127C22—21no—
1128C22—21no—
1129C22—21no—
1130C22—21no—
1131C22—21no—
1132C22—181no—
1133C22—181no—
1134C22—181no—
1135C22#6430912yes—
1136C22C23×D3211yescharacteristic
1137C4—21no—
1138C4—21no—
1139C4—21no—
1140C4—21no—
1141C4—21no—
1142C4—34no—
1143C4—62no—
1144C4—62no—
1145C4—62no—
1146C4—62no—
1147C4—62no—
1148C4—62no—
1149C4—62no—
1150C4—92no—
1151C4—92no—
1152C4—181no—
1153C4—181no—
1154C4—181no—
1155C4—181no—
1156C4—181no—
1157C3—21no—
1158C3#8684212yescomplemented
1159C2—22no—
1160C2—41no—
1161C2—361no—
1162C2C2×#6430911yescharacteristic
1163C2D32×#4111yescharacteristic
1164C2#1059669411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#123C22
prime radical#64148C22
hypercenter#123D32
hypocenterC32#3523
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
2. C3×#5650C2semidirect
3. D4×#627C2semidirect
4. #10595120C2semidirect
6. #10595050C2semidirect
7. #10594807C2semidirect
8. C2×#63838C2semidirect
9. #10594599C2semidirect
10. #10594597C2semidirect
11. #10594596C2semidirect
12. #10594347C2semidirect
13. #10594324C2semidirect
14. #10594320C2semidirect
15. #10594250C2semidirect
16. #10594249C2semidirect
17. #10594245C2semidirect
18. #10594110C2semidirect
19. #10594072C2semidirect
20. #10594072C2semidirect
21. #10594046C2semidirect
22. #10594029C2semidirect
23. #10594028C2semidirect
136. #5650D3semidirect
1070. C32#3523semidirect
1158. C3#86842semidirect

Maximal subgroups

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

subgroupindex
#105961202
C3×#56502
D4×#6272
#105951202
#105951162
#105950502
#105948072
C2×#638382
#105945992
#105945972
#105945962
#105943472
#105943242
#105943202
#105942502
#105942492
#105942452
#105941102
#105940722
#105940462
#105940292
#105940282
#868423