Finite Group Databasebeta

← #11904548

Subgroups — #11904548

Order 1152.

3237 conjugacy classes of subgroups.

The subgroup lattice has 1005 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64316C211yesmaximal, characteristic, complemented
2C2×#64306C211yesmaximal, characteristic, complemented
3#10596098C211yesmaximal, characteristic, complemented
4C3×#5633C212yesmaximal, complemented
5#10595433C211yesmaximal, characteristic, complemented
6#10595401C212yesmaximal, complemented
7#10595016C211yesmaximal, characteristic, complemented
8#10595007C212yesmaximal, complemented
9#10594634C211yesmaximal, characteristic, complemented
10#10594623C214yesmaximal, complemented
11#10594524C212yesmaximal, complemented
12#10594521C212yesmaximal, complemented
13#10594520C212yesmaximal, complemented
14#10594347C211yesmaximal, characteristic, complemented
15#10594287C214yesmaximal, complemented
16#10594191C212yesmaximal, complemented
17#10594190C212yesmaximal, complemented
18#86736—32nomaximal
19C2×#3832C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C2×C3×D3×Q8C2212yescomplemented
22C2×C3×#235C2212yes—
23C2×#3811C2212yes—
24C2×#3805C2212yes—
25#64316—28no—
26#64306—28no—
27C2×#3802C2211yescharacteristic
28C2×C4×D32C2212yes—
29C2×#3799C2214yes—
30C2×#3799C2212yescomplemented
31C2×#3798C2212yes—
32C2×#3798C2211yescharacteristic
33C2×#3798C2212yescomplemented
34C2×#3797C2211yescharacteristic
35C2×#3797C2212yescomplemented
36C2×#3796C2212yes—
37C32×C22⋊Q8C2211yescharacteristic, complemented
38#64155C2211yescharacteristic, complemented
39#64139C2211yescharacteristic, complemented
40#64104C2211yescharacteristic, complemented
41#64103C2212yes—
42#64102C2212yescomplemented
43#64101C2211yescharacteristic
44#64091C2212yes—
45#64090C2212yescomplemented
46C3×#947C2212yescomplemented
47C3×C4×#67C2212yescomplemented
48C3×#896C2214yescomplemented
49C3×#895C2212yescomplemented
50C3×#893C2214yescomplemented
51C3×#887C2212yescomplemented
52C3×#885C2214yescomplemented
53C3×#884C2214yescomplemented
54#63982C2211yescharacteristic, complemented
55#63981C2212yes—
56#63980C2211yescharacteristic, complemented
57#63979C2214yescomplemented
58#63958C2214yescomplemented
59#63923C2214yes—
60#63922C2214yes—
61C4×#627C2212yescomplemented
62#63915C2212yescomplemented
63#63914C2212yescomplemented
64#63912C2212yescomplemented
65#63912C2212yescomplemented
66#63912C2211yescharacteristic, complemented
67#63911C2212yescomplemented
68#63911C2214yescomplemented
69#63910C2214yescomplemented
70#63908C2212yescomplemented
71#63907C2214yescomplemented
72#63906C2214yescomplemented
73#63906C2214yescomplemented
74#63904C2214yescomplemented
75C4×#626C2212yescomplemented
76#63887C2214yescomplemented
77#63886C2214yescomplemented
78#63880C2214yescomplemented
79#63879C2214yescomplemented
80#63874C2211yescharacteristic
81#63865C2211yescharacteristic, complemented
82#63853C2212yes—
83Dic3×Dic6C2212yescomplemented
84#63838C2212yescomplemented
85#63836C2214yes—
86C2×D3×#41—32no—
87C2×#1007—32no—
88C3×#548—32no—
89#5834—32no—
90#5817—32no—
91#5677—32no—
92#5677—34no—
93#5674—32no—
94#5674—34no—
95#5633—34no—
96#5633D312yescomplemented
97#5627—32no—
98#5627—34no—
99#5627—61no—
100#5607—32no—
101#5607—34no—
102#5599—32no—
103#5599—34no—
104#5577—32no—
105#5572—32no—
106#5553—32no—
107#5553—34no—
108#5547—32no—
109#5547—34no—
110C23×C3⋊D3C2311yescharacteristic
111C22×D32C2312yes—
112C2×C32×Q8C2311yescharacteristic
113C22×C32×C4C2311yescharacteristic
114C2×#638C2312yes—
115C22×C3⋊Dic3C2311yescharacteristic
116#3832—24no—
117C2×C4⋊(C3⋊D3)C2312yes—
118C2×C4⋊(C3⋊D3)C2311yescharacteristic
119C2×C4⋊(C3⋊D3)C2312yes—
120C2×C4×C3⋊D3—24no—
121C2×C4×C3⋊D3C2311yescharacteristic
122C2×C4×C3⋊D3C2312yes—
123C2×C4×C3⋊D3C2311yescharacteristic
124C2×C4×C3⋊D3C2311yescharacteristic
125C2×C4×C3⋊D3C2311yescharacteristic
126C2×C3×#67C2314yes—
127C2×C3×#67C2312yes—
128C3×D3×Q8—28no—
129C3×#235—28no—
130C2×C3×D12C2312yes—
131C2×C3×D12C2314yes—
132C2×C3×C4×D3C2314yes—
133C2×C3×C4×D3C2314yes—
134C2×C3×C4×D3C2312yes—
135C2×C3×Dic6C2314yes—
136C2×C3×Dic6C2312yes—
137#3811—28no—
138C2×#627C2311yescharacteristic
139C2×#627C2312yes—
140C2×#626C2314yes—
141C2×#626C2312yes—
142C2×#626C2314yes—
143C2×#626C2314yes—
144C2×#626C2314yes—
145C2×#626C2312yes—
146C2×#625C2311yescharacteristic
147C2×#625C2312yes—
148C2×#625C2314yes—
149C2×#624C2314yes—
150C2×#624C2312yes—
151#3805—28no—
152C2×D3×Dic3C2314yes—
153#3802—24no—
154C4×D32—28no—
155#3799—28no—
156#3799—216no—
157#3798—24no—
158#3798—28no—
159#3798—28no—
160#3797—28no—
161#3797D418yescomplemented
162#3796—28no—
163C32×C4⋊C4C2311yescharacteristic
164C32×C4⋊C4C2312yes—
165C32×C22⋊C4C2312yes—
166#3752C2312yes—
167#3752C2312yes—
168#3752C2312yes—
169#3752C2312yes—
170C4⋊(C3⋊Dic3)C2311yescharacteristic
171#3750C2312yes—
172C4×C3⋊Dic3C2312yes—
173C3×#217C2312yes—
174C3×(C2×D3)⋊C4C2314yes—
175C3×(C2×D3)⋊C4C2314yes—
176C3×(C2×D3)⋊C4C2314yes—
177C3×(C2×D3)⋊C4C2312yes—
178C3×Dic3⋊C4C2314yes—
179C3×Dic3⋊C4C2312yes—
180C3×C4×Dic3C2314yes—
181C3×C4×Dic3C2312yes—
182#3724C2311yescharacteristic
183#3724C2311yescharacteristic
184Dic3⋊Dic3C2314yes—
185Dic3⋊Dic3C2312yes—
186#3722C2312yes—
187#3722C2312yes—
188(C2×D3)⋊Dic3C2312yes—
189(C2×D3)⋊Dic3C2314yes—
190Dic32C2314yes—
191#3487—91noSylow
192C2×C3×#41—32no—
193C22×C3×Q8—32no—
194D3×#41—616no—
195#1007—616no—
196C2×#239—32no—
197C2×#239—32no—
198C2×#239—34no—
199C2×#239—32no—
200C2×#239—61no—
201C2×D3×Q8—32no—
202C2×D3×Q8—34no—
203C2×D3×Q8C2×D312yescomplemented
204C2×#237—34no—
205C2×#237—32no—
206C2×D3×D4—34no—
207C2×D3×D4—32no—
208C2×#235—34no—
209C2×#235—32no—
210C2×#235—34no—
211C2×#235—34no—
212C2×#235—32no—
213C2×#235C2×D312yes—
214C22×C4×D3—32no—
215C22×C4×D3—34no—
216C22×C4×D3—61no—
217C3×#124—32no—
218C3×#124—34no—
219C3×C22⋊Q8—21no—
220C3×C22⋊Q8—34no—
221C3×C22⋊Q8C2×D312yescomplemented
222C3×#121—32no—
223C3×#121—34no—
224C3×C4×Q8—32no—
225C3×C4×D4—32no—
226C3×C4×D4—34no—
227#947—34no—
228#947C2×D312yescomplemented
229#946—32no—
230#946—34no—
231#946—61no—
232Q8×Dic3—32no—
233#940—34no—
234#940—34no—
235#940—34no—
236#940—32no—
237#940—34no—
238#939—32no—
239#939—34no—
240#938—32no—
241#938—34no—
242#937—32no—
243#937—34no—
244#930—32no—
245#930—32no—
246#930—34no—
247#930—34no—
248#930—61no—
249C4×#67—34no—
250C4×#67—34no—
251C4×#67—32no—
252C4×#67C2×D312yescomplemented
253#896—32no—
254#896C2×D314yescomplemented
255#895—34no—
256#895—32no—
257#895—34no—
258#895—61no—
259#895C2×D312yescomplemented
260#894—34no—
261#894—32no—
262#894—62no—
263#893—34no—
264#893—34no—
265#893—62no—
266#893C2×D314yescomplemented
267#892—32no—
268#892—34no—
269#892—61no—
270#887—34no—
271#887C2×D312yescomplemented
272#885—34no—
273#885—34no—
274#885C2×D314yescomplemented
275#884—34no—
276#884—34no—
277#884—34no—
278#884—34no—
279#884—34no—
280#884—32no—
281#884—34no—
282#884C2×D314yescomplemented
283#883—32no—
284#882—32no—
285#882—34no—
286#882—34no—
287#882—34no—
288#882—34no—
289#882—62no—
290#67⋊C4—34no—
291#67⋊C4—34no—
292#67⋊C4—34no—
293#67⋊C4—62no—
294#878—34no—
295#878—32no—
296#874—34no—
297#874—32no—
298C4×D12—32no—
299C4×D12—34no—
300#872—34no—
301#872—32no—
302C4×Dic6—32no—
303C4×Dic6—34no—
304C23×C32C2411yescharacteristic
305C22×C3⋊D3—22no—
306C22×C3⋊D3—41no—
307C22×C3⋊D3—41no—
308C22×C3⋊D3C2411yescharacteristic
309C22×C3⋊D3C2412yes—
310C22×C3⋊D3C2411yescharacteristic
311C22×C3×D3C2414yes—
312C22×C3×D3C2412yes—
313C2×D32—24no—
314C2×D32—42no—
315C2×D32—42no—
316C32×Q8—22no—
317C2×C32×C4—22no—
318C2×C32×C4C2412yes—
319C2×C32×C4C2411yescharacteristic
320C2×C32×C4C2412yes—
321C2×C32×C4C2411yescharacteristic
322#638—42no—
323C2×C3⋊Dic3—22no—
324C2×C3⋊Dic3C2412yes—
325C2×C3⋊Dic3C2411yescharacteristic
326C2×C3⋊Dic3C2411yescharacteristic
327C4⋊(C3⋊D3)—24no—
328C4⋊(C3⋊D3)—22no—
329C4⋊(C3⋊D3)—42no—
330C4×C3⋊D3—22no—
331C4×C3⋊D3—22no—
332C4×C3⋊D3—24no—
333C4×C3⋊D3—22no—
334C4×C3⋊D3C2×D414yes—
335C3×#67—28no—
336C3×#67—42no—
337C2×C3×Dic3C2412yes—
338C2×C3×Dic3C2412yes—
339C2×C3×Dic3C2412yes—
340C2×C3×Dic3C2414yes—
341C3×D12—24no—
342C3×D12—44no—
343C3×C4×D3—24no—
344C3×C4×D3—28no—
345C3×C4×D3—28no—
346C3×Dic6—28no—
347C3×Dic6C2×D418yes—
348#627—22no—
349#627C2×D418yes—
350#626—24no—
351#626—28no—
352#626—28no—
353#626—42no—
354#626—44no—
355#626—44no—
356#625—22no—
357#625—24no—
358#625—44no—
359#624—28no—
360#624C2×D418yes—
361D3×Dic3—28no—
362C2×2−1+4—91no—
363C22×#41—91no—
364#550—92no—
365#550—92no—
366#550—92no—
367#550—92no—
368#548—32no—
369#548—92no—
370#548—92no—
371#548—92no—
372#535—91no—
373#535—94no—
374#535—91no—
375#525—91no—
376#525—94no—
377#525—91no—
378#519—91no—
379C23×D3—32no—
380C23×D3—34no—
381C23×D3—61no—
382C3×#41—68no—
383C2×C3×Q8—21no—
384C2×C3×Q8—32no—
385C2×C3×Q8—34no—
386C2×C3×Q8—68no—
387C2×C3×Q8C22×D312yes—
388C2×C3×D4—34no—
389C2×C3×D4—32no—
390C2×C3×D4—32no—
391C2×C3×D4—34no—
392C22×C3×C4—21no—
393C22×C3×C4—34no—
394C22×C3×C4—32no—
395C22×C3×C4—34no—
396C22×C3×C4C22×D312yes—
397C2×#67—34no—
398C2×#67—32no—
399C2×#67—34no—
400C2×#67—34no—
401C2×#67—34no—
402C2×#67—32no—
403C2×#67—34no—
404C2×#67—34no—
405C2×#67—34no—
406C2×#67—34no—
407C2×#67—32no—
408C2×#67—62no—
409C2×#67C22×D314yes—
410C2×#67C22×D312yes—
411C22×Dic3—32no—
412C22×Dic3—34no—
413C22×Dic3—61no—
414#239—616no—
415#239—68no—
416#239—68no—
417#239—68no—
418#239—124no—
419D3×Q8—28no—
420D3×Q8—316no—
421D3×Q8—616no—
422#237—616no—
423#237—68no—
424D3×D4—68no—
425D3×D4—616no—
426#235—28no—
427#235—616no—
428#235—616no—
429#235—616no—
430#235—68no—
431#235—68no—
432C2×D12—34no—
433C2×D12—34no—
434C2×D12—32no—
435C2×D12—32no—
436C2×D12—34no—
437C2×D12—32no—
438C2×D12—34no—
439C2×D12—34no—
440C2×D12—34no—
441C2×D12—62no—
442C2×D12—62no—
443C2×D12—61no—
444C2×D12C22×D312yes—
445C2×D12C22×D314yes—
446C2×C4×D3—32no—
447C2×C4×D3—34no—
448C2×C4×D3—34no—
449C2×C4×D3—32no—
450C2×C4×D3—34no—
451C2×C4×D3—32no—
452C2×C4×D3—32no—
453C2×C4×D3—34no—
454C2×C4×D3—34no—
455C2×C4×D3—61no—
456C2×C4×D3—62no—
457C2×C4×D3—61no—
458C2×C4×D3—61no—
459C2×C4×D3—61no—
460C2×C4×D3—616no—
461C2×C4×D3—68no—
462C2×C4×D3—124no—
463C2×C4×D3C22×D312yes—
464C2×C4×D3C22×D314yes—
465C2×C4×D3C22×D314yes—
466C2×Dic6—34no—
467C2×Dic6—32no—
468C2×Dic6C22×D314yes—
469C2×Dic6C22×D312yes—
470C3×C4⋊C4—21no—
471C3×C4⋊C4—22no—
472C3×C4⋊C4—34no—
473C3×C4⋊C4—32no—
474C3×C4⋊C4C22×D312yes—
475C3×C4⋊C4C22×D314yes—
476C3×C22⋊C4—22no—
477C3×C22⋊C4—32no—
478C3×C22⋊C4—34no—
479C3×C22⋊C4—34no—
480C3×C22⋊C4—34no—
481C3×C22⋊C4—32no—
482C3×C22⋊C4C22×D314yes—
483C3×C42—34no—
484C3×C42—32no—
485#217—34no—
486#217—32no—
487#217C22×D312yes—
488(C2×D3)⋊C4—32no—
489(C2×D3)⋊C4—34no—
490(C2×D3)⋊C4—34no—
491(C2×D3)⋊C4—34no—
492(C2×D3)⋊C4—34no—
493(C2×D3)⋊C4—34no—
494(C2×D3)⋊C4—32no—
495(C2×D3)⋊C4—32no—
496(C2×D3)⋊C4—32no—
497(C2×D3)⋊C4—32no—
498(C2×D3)⋊C4—62no—
499(C2×D3)⋊C4—62no—
500(C2×D3)⋊C4—62no—
501(C2×D3)⋊C4—62no—
502(C2×D3)⋊C4C22×D314yes—
503(C2×D3)⋊C4C22×D314yes—
504(C2×D3)⋊C4C22×D314yes—
505(C2×D3)⋊C4C22×D312yes—
506C4⋊Dic3—32no—
507C4⋊Dic3—34no—
508C4⋊Dic3—32no—
509C4⋊Dic3—61no—
510Dic3⋊C4—34no—
511Dic3⋊C4—34no—
512Dic3⋊C4—32no—
513Dic3⋊C4—32no—
514Dic3⋊C4—32no—
515Dic3⋊C4—62no—
516Dic3⋊C4C22×D314yes—
517Dic3⋊C4C22×D312yes—
518C4×Dic3—34no—
519C4×Dic3—34no—
520C4×Dic3—34no—
521C4×Dic3—62no—
522C4×Dic3C22×D314yes—
523C4×Dic3C22×D312yes—
524C22×C32—21no—
525C22×C32—21no—
526C22×C32—21no—
527C22×C32C2511yescharacteristic
528C2×C3⋊D3—21no—
529C2×C3⋊D3—21no—
530C2×C3⋊D3—21no—
531C2×C3⋊D3—22no—
532C2×C3⋊D3—21no—
533C2×C3⋊D3—22no—
534C2×C3⋊D3—22no—
535C2×C3⋊D3—21no—
536C2×C3⋊D3—44no—
537C2×C3⋊D3C22×D412yes—
538C2×C3×D3—24no—
539C2×C3×D3—22no—
540C2×C3×D3—22no—
541C2×C3×D3—24no—
542C2×C3×D3—24no—
543C2×C3×D3—22no—
544D32—48no—
545C32×C4—22no—
546C32×C4—21no—
547C32×C4—22no—
548C32×C4C22×D412yes—
549C3⋊Dic3—21no—
550C3⋊Dic3—22no—
551C3⋊Dic3C22×D412yes—
552C3×Dic3—22no—
553C3×Dic3—22no—
554C3×Dic3—22no—
555C3×Dic3C22×D418yes—
5562−1+4—188no—
557C2×#41—32no—
558C2×#41—91no—
559C2×#41—92no—
560C2×#41—92no—
561C2×#41—94no—
562C2×#41—92no—
563C2×#41—92no—
564C2×#41—92no—
565C2×#41—91no—
566C2×#41—188no—
567C22×Q8—32no—
568C22×Q8—91no—
569C22×Q8—92no—
570C22×D4—92no—
571C22×D4—91no—
572C23×C4—92no—
573C23×C4—91no—
574#127—92no—
575#127—94no—
576#127—94no—
577#127—92no—
578#124—32no—
579#124—34no—
580#124—92no—
581#124—94no—
582#123—92no—
583#123—92no—
584C22⋊Q8—34no—
585C22⋊Q8—91no—
586C22⋊Q8—94no—
587C22⋊Q8—91no—
588C22⋊Q8—91no—
589C22⋊Q8D3211yescharacteristic, complemented
590#121—32no—
591#121—34no—
592#121—91no—
593#121—92no—
594#121—92no—
595#121—94no—
596#121—94no—
597#121—94no—
598#121—94no—
599#121—94no—
600#121—92no—
601#121—91no—
602#121—91no—
603#121—91no—
604#120—94no—
605#120—92no—
606#120—94no—
607#120—92no—
608C4×Q8—32no—
609C4×Q8—92no—
610C4×Q8—92no—
611C4×Q8—92no—
612C4×D4—32no—
613C4×D4—34no—
614C4×D4—94no—
615C4×D4—92no—
616C4×D4—94no—
617C4×D4—94no—
618C4×D4—92no—
619C4×D4—92no—
620#117—91no—
621#117—94no—
622#117—91no—
623C23×C3—21no—
624C23×C3—34no—
625C23×C3—32no—
626C23×C3C23×D312yes—
627C22×D3—32no—
628C22×D3—32no—
629C22×D3—34no—
630C22×D3—61no—
631C22×D3—61no—
632C22×D3—62no—
633C22×D3—68no—
634C22×D3—64no—
635C22×D3—122no—
636C22×D3—124no—
637C22×D3—124no—
638C22×D3—122no—
639C22×D3—122no—
640C22×D3—122no—
641C22×D3—122no—
642C22×D3C23×D314yes—
643C22×D3C23×D312yes—
644C3×Q8—24no—
645C3×Q8—38no—
646C3×Q8—42no—
647C3×Q8—68no—
648C3×D4—68no—
649C3×D4—64no—
650C3×D4—124no—
651C3×D4—122no—
652C2×C3×C4—24no—
653C2×C3×C4—21no—
654C2×C3×C4—22no—
655C2×C3×C4—22no—
656C2×C3×C4—21no—
657C2×C3×C4—34no—
658C2×C3×C4—32no—
659C2×C3×C4—32no—
660C2×C3×C4—32no—
661C2×C3×C4—42no—
662C2×C3×C4—68no—
663C2×C3×C4—68no—
664C2×C3×C4—64no—
665C2×C3×C4C23×D314yes—
666C2×C3×C4C23×D314yes—
667C2×C3×C4C23×D312yes—
668C2×C3×C4C23×D312yes—
669#67—28no—
670#67—42no—
671#67—64no—
672#67—64no—
673#67—68no—
674#67—68no—
675#67—68no—
676#67—124no—
677#67—124no—
678#67—122no—
679#67—124no—
680#67—124no—
681#67—124no—
682#67—124no—
683C2×Dic3—32no—
684C2×Dic3—34no—
685C2×Dic3—32no—
686C2×Dic3—61no—
687C2×Dic3—62no—
688C2×Dic3—61no—
689C2×Dic3—64no—
690C2×Dic3—68no—
691C2×Dic3—122no—
692C2×Dic3C23×D312yes—
693C2×Dic3C23×D312yes—
694C2×Dic3C23×D312yes—
695C2×Dic3C23×D314yes—
696D12—24no—
697D12—44no—
698D12—68no—
699D12—68no—
700D12—68no—
701D12—64no—
702D12—64no—
703D12—122no—
704D12—124no—
705D12—124no—
706D12—124no—
707D12—124no—
708D12—122no—
709D12—124no—
710C4×D3—24no—
711C4×D3—28no—
712C4×D3—28no—
713C4×D3—38no—
714C4×D3—316no—
715C4×D3—64no—
716C4×D3—68no—
717C4×D3—64no—
718C4×D3—68no—
719C4×D3—64no—
720C4×D3—68no—
721C4×D3—64no—
722C4×D3—68no—
723C4×D3—122no—
724C4×D3—124no—
725C4×D3—122no—
726C4×D3—122no—
727Dic6—28no—
728Dic6—316no—
729Dic6—64no—
730Dic6D3×D418yes—
731C2×C32—41no—
732C2×C32C23×D411yescharacteristic
733C2×C32#58511yescharacteristic
734C2×C32#58511yescharacteristic
735C3⋊D3—22no—
736C3⋊D3—41no—
737C3⋊D3—42no—
738C3×D3—44no—
739C3×D3—42no—
740C24—92no—
741C24—91no—
742#41—68no—
743#41—184no—
744#41—188no—
745#41—188no—
746#41—1816no—
747#41—188no—
748#41—184no—
749#41—188no—
750#41—188no—
751C2×Q8—32no—
752C2×Q8—34no—
753C2×Q8—68no—
754C2×Q8—92no—
755C2×Q8—91no—
756C2×Q8—98no—
757C2×Q8—188no—
758C2×Q8C2×D3211yescharacteristic
759C2×D4—34no—
760C2×D4—32no—
761C2×D4—32no—
762C2×D4—34no—
763C2×D4—92no—
764C2×D4—94no—
765C2×D4—94no—
766C2×D4—94no—
767C2×D4—92no—
768C2×D4—94no—
769C2×D4—92no—
770C2×D4—91no—
771C2×D4—94no—
772C2×D4—92no—
773C2×D4—92no—
774C2×D4—91no—
775C2×D4—92no—
776C2×D4—188no—
777C2×D4—184no—
778C22×C4—34no—
779C22×C4—32no—
780C22×C4—34no—
781C22×C4—92no—
782C22×C4—94no—
783C22×C4—94no—
784C22×C4—91no—
785C22×C4—91no—
786C22×C4—92no—
787C22×C4—91no—
788C22×C4—91no—
789C22×C4—91no—
790C22×C4—184no—
791C22×C4—188no—
792C22×C4C2×D3211yescharacteristic
793C4⋊C4—34no—
794C4⋊C4—32no—
795C4⋊C4—91no—
796C4⋊C4—91no—
797C4⋊C4—94no—
798C4⋊C4—92no—
799C4⋊C4—91no—
800C4⋊C4—92no—
801C4⋊C4C2×D3211yescharacteristic
802C4⋊C4C2×D3212yes—
803C22⋊C4—32no—
804C22⋊C4—32no—
805C22⋊C4—34no—
806C22⋊C4—34no—
807C22⋊C4—34no—
808C22⋊C4—92no—
809C22⋊C4—92no—
810C22⋊C4—92no—
811C22⋊C4—94no—
812C22⋊C4—92no—
813C22⋊C4—92no—
814C22⋊C4—92no—
815C22⋊C4—92no—
816C22⋊C4C2×D3212yes—
817C42—34no—
818C42—32no—
819C42—94no—
820C42—92no—
821C22×C3—22no—
822C22×C3—22no—
823C22×C3—22no—
824C22×C3—22no—
825C22×C3—21no—
826C22×C3—41no—
827C22×C3—41no—
828C22×C3—64no—
829C22×C3—62no—
830C22×C3—64no—
831C22×C3—62no—
832C22×C3—62no—
833C22×C3—64no—
834C22×C3C24×D312yes—
835C2×D3—22no—
836C2×D3—24no—
837C2×D3—22no—
838C2×D3—24no—
839C2×D3—22no—
840C2×D3—24no—
841C2×D3—34no—
842C2×D3—62no—
843C2×D3—62no—
844C2×D3—62no—
845C2×D3—62no—
846C2×D3—64no—
847C2×D3—62no—
848C2×D3—64no—
849C2×D3—62no—
850C2×D3—64no—
851C2×D3—62no—
852C2×D3—121no—
853C2×D3—121no—
854C2×D3—121no—
855C2×D3—121no—
856C2×D3—122no—
857C2×D3—122no—
858C2×D3—122no—
859C2×D3—1216no—
860C2×D3—128no—
861C2×D3—128no—
862C3×C4—24no—
863C3×C4—22no—
864C3×C4—24no—
865C3×C4—22no—
866C3×C4—38no—
867C3×C4—41no—
868C3×C4—42no—
869C3×C4—42no—
870C3×C4—62no—
871C3×C4—62no—
872C3×C4—62no—
873C3×C4C2×D3×D414yes—
874Dic3—22no—
875Dic3—22no—
876Dic3—22no—
877Dic3—34no—
878Dic3—62no—
879Dic3—62no—
880Dic3—64no—
881Dic3—121no—
882Dic3—122no—
883Dic3C2×D3×D418yes—
884C32#348711yescharacteristic, complemented, Sylow
885C23—34no—
886C23—32no—
887C23—91no—
888C23—91no—
889C23—92no—
890C23—182no—
891C23—184no—
892C23—361no—
893C23—361no—
894C23—362no—
895C23—362no—
896C23C22×D3211yescharacteristic
897Q8—22no—
898Q8—38no—
899Q8—68no—
900Q8—98no—
901Q8—182no—
902D4—68no—
903D4—64no—
904D4—124no—
905D4—122no—
906D4—184no—
907D4—188no—
908D4—188no—
909D4—184no—
910D4—184no—
911D4—182no—
912D4—182no—
913D4—362no—
914D4—362no—
915D4—364no—
916D4—364no—
917D4—362no—
918D4—364no—
919C2×C4—22no—
920C2×C4—34no—
921C2×C4—32no—
922C2×C4—32no—
923C2×C4—32no—
924C2×C4—68no—
925C2×C4—68no—
926C2×C4—64no—
927C2×C4—98no—
928C2×C4—91no—
929C2×C4—94no—
930C2×C4—92no—
931C2×C4—91no—
932C2×C4—182no—
933C2×C4—184no—
934C2×C4—182no—
935C2×C4—188no—
936C2×C4—188no—
937C2×C4—182no—
938C2×C4—182no—
939C2×C4C22×D3212yes—
940C2×C4C22×D3212yes—
941C2×C4C22×D3211yescharacteristic
942C2×C4C22×D3211yescharacteristic
943C2×C3—21no—
944C2×C3—21no—
945C2×C3—21no—
946C2×C3—42no—
947C2×C3—42no—
948C2×C3—124no—
949C2×C3—122no—
950C2×C3C22×D3×D412yes—
951C2×C3#596412yes—
952C2×C3#596812yes—
953D3—44no—
954D3—42no—
955D3—64no—
956D3—122no—
957D3—122no—
958D3—122no—
959D3—124no—
960D3—242no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—62no—
965C22—64no—
966C22—62no—
967C22—64no—
968C22—62no—
969C22—64no—
970C22—92no—
971C22—181no—
972C22—181no—
973C22—182no—
974C22—181no—
975C22—182no—
976C22—181no—
977C22—182no—
978C22—181no—
979C22—364no—
980C22—368no—
981C22C23×D3211yescharacteristic
982C4—21no—
983C4—22no—
984C4—22no—
985C4—38no—
986C4—62no—
987C4—62no—
988C4—62no—
989C4—92no—
990C4—181no—
991C4—182no—
992C4D32×D412yes—
993C3—21no—
994C3#8673612yescomplemented
995C2—41no—
996C2—124no—
997C2—122no—
998C2—182no—
999C2—361no—
1000C2—362no—
1001C2C2×D32×D411yescharacteristic
1002C2#1059668911yescharacteristic
1003C2#1059669511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C22⋊Q8C22
hypercenterC22⋊Q8D32
hypocenterC32#3487
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64316C2semidirect
2. C2×#64306C2semidirect
3. #10596098C2semidirect
4. C3×#5633C2semidirect
5. #10595433C2semidirect
6. #10595401C2semidirect
7. #10595016C2semidirect
8. #10595007C2semidirect
9. #10594634C2semidirect
10. #10594623C2semidirect
11. #10594524C2semidirect
12. #10594521C2semidirect
13. #10594520C2semidirect
14. #10594347C2semidirect
15. #10594287C2semidirect
16. #10594191C2semidirect
17. #10594190C2semidirect
21. C2×C3×D3×Q8C22semidirect
30. C2×#3799C22semidirect
33. C2×#3798C22semidirect
35. C2×#3797C22semidirect
37. C32×C22⋊Q8C22semidirect
38. #64155C22semidirect
39. #64139C22semidirect
40. #64104C22semidirect
42. #64102C22semidirect
45. #64090C22semidirect
46. C3×#947C22semidirect
47. C3×C4×#67C22semidirect
48. C3×#896C22semidirect
49. C3×#895C22semidirect
50. C3×#893C22semidirect
51. C3×#887C22semidirect
52. C3×#885C22semidirect
53. C3×#884C22semidirect
54. #63982C22semidirect
56. #63980C22semidirect
57. #63979C22semidirect
58. #63958C22semidirect
61. C4×#627C22semidirect
62. #63915C22semidirect
63. #63914C22semidirect
64. #63912C22semidirect
65. #63912C22semidirect
66. #63912C22semidirect
67. #63911C22semidirect
68. #63911C22semidirect
69. #63910C22semidirect
70. #63908C22semidirect
71. #63907C22semidirect
72. #63906C22semidirect
73. #63906C22semidirect
74. #63904C22semidirect
75. C4×#626C22semidirect
76. #63887C22semidirect
77. #63886C22semidirect
78. #63880C22semidirect
79. #63879C22semidirect
81. #63865C22semidirect
83. Dic3×Dic6C22semidirect
84. #63838C22semidirect
96. #5633D3semidirect
161. #3797D4semidirect
203. C2×D3×Q8C2×D3semidirect
221. C3×C22⋊Q8C2×D3semidirect
228. #947C2×D3semidirect
252. C4×#67C2×D3semidirect
254. #896C2×D3semidirect
259. #895C2×D3semidirect
266. #893C2×D3semidirect
271. #887C2×D3semidirect
274. #885C2×D3semidirect
282. #884C2×D3semidirect
589. C22⋊Q8D32semidirect
884. C32#3487semidirect
994. C3#86736semidirect

Maximal subgroups

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

subgroupindex
C2×#643162
C2×#643062
#105960982
C3×#56332
#105954332
#105954012
#105950162
#105950072
#105946342
#105946232
#105945242
#105945212
#105945202
#105943472
#105942872
#105941912
#105941902
#867363