Finite Group Databasebeta

← #11904786

Subgroups — #11904786

Order 1152.

3209 conjugacy classes of subgroups.

The subgroup lattice has 1023 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64309C211yesmaximal, characteristic, complemented
2C22×#3798C211yesmaximal, characteristic, complemented
3#10596077C211yesmaximal, characteristic, complemented
4C3×#5606C212yesmaximal, complemented
5D4×#627C212yesmaximal, complemented
6#10595240C211yesmaximal, characteristic, complemented
7#10595232C212yesmaximal, complemented
8#10595225C212yesmaximal, complemented
9#10595135C214yesmaximal, complemented
10#10594925C211yesmaximal, characteristic, complemented
11D3×#924C212yesmaximal, complemented
12#10594529C211yesmaximal, characteristic, complemented
13#10594511C211yesmaximal, characteristic, complemented
14#10594380C212yesmaximal, complemented
15#10594189C212yesmaximal, complemented
16#10594188C214yesmaximal, complemented
17#10594185C212yesmaximal, complemented
18#86042—32nomaximal
19C2×#3830C2211yescharacteristic, complemented
20C22×C4×C3⋊D3C2211yescharacteristic
21C2×C3×#237C2212yescomplemented
22C22×C3×C4×D3C2212yes—
23C22×#627C2211yescharacteristic
24C22×#627C2212yescomplemented
25C22×#626C2212yes—
26C22×#625C2211yescharacteristic
27C2×#3805C2212yescomplemented
28C2×#3804C2214yescomplemented
29#64309—28no—
30C2×#3798—28no—
31C2×#3798C2212yes—
32C2×#3798C2211yescharacteristic
33C2×#3798C2212yes—
34C2×#3798C2211yescharacteristic
35C2×#3798C2211yescharacteristic
36C2×#3798C2211yescharacteristic
37C2×#3797C2211yescharacteristic, complemented
38C2×D3×Dic6C2212yescomplemented
39C32×#121C2211yescharacteristic
40#64147C2211yescharacteristic, complemented
41#64146C2212yes—
42D4×C3⋊Dic3C2212yes—
43#64133C2211yescharacteristic
44#64106C2211yescharacteristic, complemented
45#64101C2211yescharacteristic, complemented
46#64092C2212yescomplemented
47#64090C2212yescomplemented
48C3×#938C2212yescomplemented
49C3×#937C2214yes—
50C3×D4×Dic3C2214yes—
51C3×#924C2212yes—
52C3×#897C2212yescomplemented
53C3×#892C2212yescomplemented
54C3×#883C2214yescomplemented
55C3×#67⋊C4C2214yescomplemented
56#63982C2212yes—
57#63982C2212yescomplemented
58#63980C2212yescomplemented
59#63978C2214yescomplemented
60#63974C2212yes—
61#63971C2214yescomplemented
62#63970C2214yescomplemented
63D3×#217C2214yes—
64#63964C2214yes—
65#63964C2214yescomplemented
66#63958C2214yescomplemented
67#63919C2212yescomplemented
68#63918C2214yescomplemented
69C4×#627C2212yescomplemented
70#63915C2212yescomplemented
71#63902C2212yescomplemented
72#63900C2211yescharacteristic, complemented
73#63891C2214yescomplemented
74#63890C2214yescomplemented
75D3×C4⋊Dic3C2212yescomplemented
76#63883C2212yescomplemented
77#63880C2214yescomplemented
78D3×Dic3⋊C4C2214yescomplemented
79#63871C2212yescomplemented
80#63865C2212yescomplemented
81#63857C2212yescomplemented
82#63856C2212yescomplemented
83#63854C2214yescomplemented
84#63852C2214yescomplemented
85#63851C2214yescomplemented
86C2×#1010—32no—
87C22×#235—32no—
88C3×#525—32no—
89#5833—32no—
90C2×#924—32no—
91#5655—34no—
92#5655—34no—
93#5628—32no—
94#5628—32no—
95D3×C22⋊Q8—32no—
96D3×C22⋊Q8—32no—
97#5608—32no—
98#5608—32no—
99#5606—32no—
100#5606—61no—
101#5606D312yescomplemented
102#5591—34no—
103#5591—34no—
104#5552—34no—
105#5551—34no—
106#5550—34no—
107D4×Dic6—34no—
108#5526—32no—
109#5523—32no—
110C23×C3⋊D3C2311yescharacteristic
111C23×C3×D3C2312yes—
112C2×C32×D4C2312yes—
113C2×C32×D4C2311yescharacteristic
114C22×C32×C4C2311yescharacteristic
115C2×#638C2312yes—
116C2×#638C2312yes—
117C22×C3⋊Dic3C2312yes—
118C22×C3⋊Dic3C2311yescharacteristic
119#3830—24no—
120C2×C4×C3⋊D3—24no—
121C2×C4×C3⋊D3C2311yescharacteristic
122C2×C4×C3⋊D3C2311yescharacteristic
123C2×C4×C3⋊D3C2311yescharacteristic
124C2×C4×C3⋊D3C2311yescharacteristic
125C2×#634C2311yescharacteristic
126C2×C3×#67C2314yes—
127C2×C3×#67C2314yes—
128C22×C3×Dic3C2314yes—
129C22×C3×Dic3C2312yes—
130C3×#237—28no—
131C2×C3×C4×D3—28no—
132C2×C3×C4×D3C2312yes—
133C2×C3×C4×D3C2312yes—
134C2×C3×C4×D3C2312yes—
135C2×C3×C4×D3C2312yes—
136C2×C3×Dic6C2312yes—
137C2×#627—24no—
138C2×#627—28no—
139C2×#627C2314yes—
140C2×#627C2312yes—
141C2×#627C2312yes—
142C2×#627C2311yescharacteristic
143C2×#627C2311yescharacteristic
144C2×#626—28no—
145C2×#626C2312yes—
146C2×#626C2312yes—
147C2×#626C2312yes—
148C2×#626C2312yes—
149C2×#625—24no—
150C2×#625C2312yes—
151C2×#625C2311yescharacteristic
152C2×#625C2311yescharacteristic
153C2×#624C2312yes—
154C2×#624C2312yes—
155#3805—28no—
156#3804—216no—
157C2×D3×Dic3C2314yes—
158C2×D3×Dic3C2314yes—
159#3798—24no—
160#3798—28no—
161#3798—24no—
162#3798—28no—
163#3798—24no—
164#3798D418yescomplemented
165#3797—24no—
166D3×Dic6—28no—
167C32×C4⋊C4C2311yescharacteristic
168C32×C22⋊C4C2312yes—
169#3757C2312yes—
170#3757C2312yes—
171#3752C2312yes—
172#3752C2312yes—
173C4⋊(C3⋊Dic3)C2312yes—
174C4⋊(C3⋊Dic3)C2311yescharacteristic
175#3750C2312yes—
176C4×C3⋊Dic3C2312yes—
177C3×#217C2314yes—
178C3×#217C2314yes—
179C3×(C2×D3)⋊C4C2314yes—
180C3×(C2×D3)⋊C4C2314yes—
181C3×C4⋊Dic3C2314yes—
182C3×C4⋊Dic3C2312yes—
183C3×Dic3⋊C4C2314yes—
184C3×C4×Dic3C2314yes—
185#3724C2314yes—
186#3724C2312yes—
187Dic3⋊Dic3C2314yes—
188Dic3⋊Dic3C2314yes—
189Dic3⋊Dic3C2314yes—
190#3722C2314yes—
191(C2×D3)⋊Dic3C2314yes—
192(C2×D3)⋊Dic3C2314yes—
193#3489—91noSylow
194C2×C3×#41—32no—
195C23×C3×C4—32no—
196C22×#67—32no—
197C22×#67—32no—
198#1010—616no—
199C2×D3×Q8—32no—
200C2×D3×Q8—32no—
201C2×#237—32no—
202C2×#237—34no—
203C2×#237—34no—
204C2×#237—61no—
205C2×#237C2×D312yescomplemented
206C2×#235—34no—
207C2×#235—32no—
208C2×#235—32no—
209C2×#235—32no—
210C2×#235—32no—
211C2×#235—32no—
212C2×#235—32no—
213C2×#235—32no—
214C2×#235—32no—
215C2×#235—616no—
216C22×D12—32no—
217C22×C4×D3—32no—
218C22×C4×D3—61no—
219C22×C4×D3C2×D312yes—
220C22×Dic6—32no—
221C22×Dic6—34no—
222C22×Dic6—32no—
223C3×#123—34no—
224C3×C22⋊Q8—32no—
225C3×C22⋊Q8—32no—
226C3×#121—21no—
227C3×#121—32no—
228C3×#121C2×D312yes—
229C3×#120—34no—
230C3×C4×D4—34no—
231C3×C4×D4—34no—
232C3×#117—32no—
233C2×#217—34no—
234#946—32no—
235#946—32no—
236#939—34no—
237#939—34no—
238#939—34no—
239#939—34no—
240#938—32no—
241#938—34no—
242#938—34no—
243#938—61no—
244#938C2×D312yescomplemented
245#937—34no—
246#937—62no—
247#937C2×D314yes—
248D4×Dic3—34no—
249D4×Dic3—62no—
250D4×Dic3C2×D314yes—
251#930—34no—
252C2×C4⋊Dic3—32no—
253#924—32no—
254#924—32no—
255#924—34no—
256#924—34no—
257#924—32no—
258#924—34no—
259#924—61no—
260#924C2×D312yes—
261C2×Dic3⋊C4—34no—
262#897—32no—
263#897—32no—
264#897—32no—
265#897—61no—
266#897C2×D312yescomplemented
267#896—34no—
268#896—34no—
269#894—34no—
270#894—34no—
271#892—32no—
272#892—61no—
273#892C2×D312yescomplemented
274D3×C4⋊C4—34no—
275D3×C4⋊C4—32no—
276D3×C4⋊C4—32no—
277D3×C4⋊C4—34no—
278#888—34no—
279#888—34no—
280#886—34no—
281#886—34no—
282#885—34no—
283#885—34no—
284#884—34no—
285#884—34no—
286#883—34no—
287#883—34no—
288#883—34no—
289#883—62no—
290#883C2×D314yescomplemented
291#67⋊C4—34no—
292#67⋊C4—34no—
293#67⋊C4—34no—
294#67⋊C4—62no—
295#67⋊C4C2×D314yescomplemented
296D3×C22⋊C4—34no—
297D3×C22⋊C4—34no—
298#878—34no—
299#878—34no—
300#878—34no—
301#878—34no—
302#875—34no—
303C4×D12—34no—
304#869—34no—
305C4×Dic6—34no—
306C23×C32C2412yes—
307C23×C32C2411yescharacteristic
308C22×C3⋊D3—22no—
309C22×C3⋊D3—22no—
310C22×C3⋊D3—41no—
311C22×C3⋊D3C2411yescharacteristic
312C22×C3⋊D3C2411yescharacteristic
313C22×C3×D3—24no—
314C22×C3×D3—24no—
315C22×C3×D3—42no—
316C22×C3×D3C2412yes—
317C22×C3×D3C2412yes—
318C32×D4—24no—
319C32×D4—22no—
320C2×C32×C4—22no—
321C2×C32×C4C2412yes—
322C2×C32×C4C2411yescharacteristic
323C2×C32×C4C2411yescharacteristic
324#638—24no—
325#638—42no—
326C2×C3⋊Dic3—24no—
327C2×C3⋊Dic3—22no—
328C2×C3⋊Dic3C2412yes—
329C2×C3⋊Dic3C2412yes—
330C2×C3⋊Dic3C2411yescharacteristic
331C2×C3⋊Dic3C2411yescharacteristic
332C4×C3⋊D3—22no—
333C4×C3⋊D3—22no—
334C4×C3⋊D3—22no—
335C4×C3⋊D3C2×D414yes—
336#634—22no—
337C3×#67—28no—
338C3×#67—44no—
339C2×C3×Dic3—28no—
340C2×C3×Dic3—24no—
341C2×C3×Dic3C2414yes—
342C2×C3×Dic3C2414yes—
343C2×C3×Dic3C2412yes—
344C2×C3×Dic3C2412yes—
345C3×C4×D3—24no—
346C3×C4×D3—24no—
347C3×C4×D3—24no—
348C3×C4×D3C2×D418yes—
349C3×Dic6—24no—
350#627—24no—
351#627—22no—
352#627—28no—
353#627—24no—
354#627C2×D414yes—
355#626—24no—
356#626—24no—
357#626—24no—
358#626C2×D418yes—
359#625—24no—
360#625—22no—
361#625C2×D414yes—
362#624—24no—
363#624—42no—
364D3×Dic3—28no—
365D3×Dic3—44no—
366C2×2−1+4—91no—
367C22×#41—91no—
368D4×Q8—92no—
369#548—92no—
370#547—94no—
371#547—92no—
372#546—94no—
373#546—92no—
374#537—91no—
375#537—92no—
376#536—92no—
377#536—91no—
378#525—32no—
379#525—91no—
380C2×C22⋊Q8—91no—
381C2×C22⋊Q8—92no—
382#520—91no—
383C24×C3—32no—
384C23×D3—32no—
385C23×D3—61no—
386C23×D3C22×D312yes—
387C3×#41—68no—
388C2×C3×Q8—32no—
389C2×C3×D4—22no—
390C2×C3×D4—21no—
391C2×C3×D4—34no—
392C2×C3×D4—34no—
393C2×C3×D4C22×D314yes—
394C2×C3×D4C22×D312yes—
395C22×C3×C4—21no—
396C22×C3×C4—32no—
397C22×C3×C4—32no—
398C22×C3×C4—34no—
399C22×C3×C4—32no—
400C22×C3×C4—32no—
401C22×C3×C4—32no—
402C22×C3×C4—68no—
403C22×C3×C4C22×D312yes—
404C2×#67—32no—
405C2×#67—34no—
406C2×#67—32no—
407C2×#67—32no—
408C2×#67—32no—
409C2×#67—34no—
410C2×#67—32no—
411C2×#67—32no—
412C2×#67—32no—
413C2×#67—32no—
414C2×#67—62no—
415C2×#67—62no—
416C2×#67—68no—
417C2×#67—68no—
418C2×#67C22×D314yes—
419C2×#67C22×D314yes—
420C22×Dic3—32no—
421C22×Dic3—34no—
422C22×Dic3—34no—
423C22×Dic3—34no—
424C22×Dic3—62no—
425C22×Dic3—61no—
426C22×Dic3C22×D312yes—
427C22×Dic3C22×D314yes—
428D3×Q8—68no—
429D3×Q8—68no—
430#237—28no—
431#237—68no—
432#237—616no—
433#237—616no—
434#237—124no—
435#235—316no—
436#235—68no—
437#235—68no—
438#235—68no—
439#235—68no—
440#235—68no—
441#235—68no—
442#235—616no—
443#235—68no—
444C2×D12—32no—
445C2×D12—32no—
446C2×D12—32no—
447C2×D12—32no—
448C2×D12—68no—
449C2×C4×D3—28no—
450C2×C4×D3—32no—
451C2×C4×D3—34no—
452C2×C4×D3—32no—
453C2×C4×D3—32no—
454C2×C4×D3—32no—
455C2×C4×D3—34no—
456C2×C4×D3—34no—
457C2×C4×D3—34no—
458C2×C4×D3—61no—
459C2×C4×D3—61no—
460C2×C4×D3—61no—
461C2×C4×D3—61no—
462C2×C4×D3—68no—
463C2×C4×D3—124no—
464C2×C4×D3C22×D312yes—
465C2×C4×D3C22×D312yes—
466C2×C4×D3C22×D312yes—
467C2×C4×D3C22×D312yes—
468C2×Dic6—32no—
469C2×Dic6—32no—
470C2×Dic6—32no—
471C2×Dic6—34no—
472C2×Dic6—32no—
473C2×Dic6—32no—
474C2×Dic6—34no—
475C2×Dic6—34no—
476C2×Dic6—61no—
477C2×Dic6—68no—
478C2×Dic6—68no—
479C2×Dic6—616no—
480C2×Dic6C22×D312yes—
481C3×C4⋊C4—21no—
482C3×C4⋊C4—34no—
483C3×C4⋊C4—34no—
484C3×C4⋊C4—32no—
485C3×C4⋊C4C22×D312yes—
486C3×C22⋊C4—22no—
487C3×C22⋊C4—34no—
488C3×C22⋊C4—34no—
489C3×C22⋊C4—34no—
490C3×C22⋊C4—34no—
491C3×C22⋊C4C22×D314yes—
492C3×C42—34no—
493#217—34no—
494#217—34no—
495#217—34no—
496#217—34no—
497#217—62no—
498#217—62no—
499#217C22×D314yes—
500#217C22×D314yes—
501(C2×D3)⋊C4—34no—
502(C2×D3)⋊C4—34no—
503(C2×D3)⋊C4—34no—
504(C2×D3)⋊C4—34no—
505(C2×D3)⋊C4—34no—
506(C2×D3)⋊C4—34no—
507(C2×D3)⋊C4—62no—
508(C2×D3)⋊C4—62no—
509(C2×D3)⋊C4C22×D314yes—
510(C2×D3)⋊C4C22×D314yes—
511C4⋊Dic3—34no—
512C4⋊Dic3—32no—
513C4⋊Dic3—34no—
514C4⋊Dic3—34no—
515C4⋊Dic3—34no—
516C4⋊Dic3—62no—
517C4⋊Dic3—61no—
518C4⋊Dic3C22×D314yes—
519C4⋊Dic3C22×D312yes—
520Dic3⋊C4—34no—
521Dic3⋊C4—34no—
522Dic3⋊C4—34no—
523Dic3⋊C4—34no—
524Dic3⋊C4—34no—
525Dic3⋊C4—34no—
526Dic3⋊C4—34no—
527Dic3⋊C4—62no—
528Dic3⋊C4C22×D314yes—
529C4×Dic3—34no—
530C4×Dic3—62no—
531C4×Dic3C22×D314yes—
532C22×C32—21no—
533C22×C32—21no—
534C22×C32—22no—
535C22×C32—22no—
536C22×C32—22no—
537C22×C322−1+412yescomplemented
538C22×C32C2511yescharacteristic
539C2×C3⋊D3—21no—
540C2×C3⋊D3—21no—
541C2×C3⋊D3—21no—
542C2×C3⋊D3—21no—
543C2×C3⋊D3—21no—
544C2×C3⋊D3—44no—
545C2×C3⋊D3C22×D412yes—
546C2×C3×D3—22no—
547C2×C3×D3—22no—
548C2×C3×D3—22no—
549C2×C3×D3—22no—
550C2×C3×D3—22no—
551C2×C3×D3—48no—
552C2×C3×D3C22×D414yes—
553C32×C4—21no—
554C32×C4—22no—
555C32×C4C22×D412yes—
556C3⋊Dic3—22no—
557C3⋊Dic3—21no—
558C3⋊Dic3—22no—
559C3⋊Dic3C22×D412yes—
560C3×Dic3—24no—
561C3×Dic3—22no—
562C3×Dic3—24no—
563C3×Dic3C22×D414yes—
5642−1+4—188no—
565C2×#41—32no—
566C2×#41—91no—
567C2×#41—92no—
568C2×#41—91no—
569C2×#41—91no—
570C2×#41—92no—
571C2×#41—91no—
572C2×#41—94no—
573C2×#41—92no—
574C2×#41—91no—
575C2×#41—188no—
576C22×Q8—92no—
577C22×Q8—91no—
578C22×Q8—92no—
579C22×Q8—91no—
580C22×D4—92no—
581C22×D4—91no—
582C23×C4—32no—
583C23×C4—91no—
584C4⋊Q8—94no—
585C4⋊Q8—92no—
586#124—94no—
587#124—92no—
588#123—34no—
589#123—94no—
590#123—94no—
591#123—94no—
592#123—92no—
593C22⋊Q8—32no—
594C22⋊Q8—32no—
595C22⋊Q8—92no—
596C22⋊Q8—92no—
597C22⋊Q8—94no—
598C22⋊Q8—94no—
599C22⋊Q8—92no—
600C22⋊Q8—92no—
601C22⋊Q8—94no—
602C22⋊Q8—92no—
603C22⋊Q8—92no—
604C22⋊Q8—91no—
605C22⋊Q8—91no—
606#121—32no—
607#121—94no—
608#121—94no—
609#121—94no—
610#121—94no—
611#121—92no—
612#121—91no—
613#121D3211yescharacteristic
614#120—34no—
615#120—92no—
616C4×Q8—92no—
617C4×D4—34no—
618C4×D4—34no—
619C4×D4—94no—
620C4×D4—92no—
621C4×D4—92no—
622C4×D4—92no—
623#117—32no—
624#117—91no—
625C2×C4⋊C4—91no—
626C2×C4⋊C4—92no—
627C2×C4⋊C4—92no—
628C2×C4⋊C4—94no—
629C2×C22⋊C4—92no—
630C2×C22⋊C4—94no—
631C23×C3—21no—
632C23×C3—22no—
633C23×C3—32no—
634C23×C3—32no—
635C23×C3—64no—
636C23×C3—64no—
637C23×C3—122no—
638C23×C3C23×D314yes—
639C23×C3C23×D312yes—
640C22×D3—24no—
641C22×D3—24no—
642C22×D3—32no—
643C22×D3—32no—
644C22×D3—42no—
645C22×D3—61no—
646C22×D3—61no—
647C22×D3—64no—
648C22×D3—64no—
649C22×D3—122no—
650C22×D3—122no—
651C22×D3—122no—
652C22×D3—122no—
653C22×D3C23×D312yes—
654C22×D3C23×D312yes—
655C3×Q8—64no—
656C3×D4—28no—
657C3×D4—24no—
658C3×D4—42no—
659C3×D4—44no—
660C3×D4—68no—
661C3×D4—124no—
662C2×C3×C4—24no—
663C2×C3×C4—21no—
664C2×C3×C4—22no—
665C2×C3×C4—21no—
666C2×C3×C4—32no—
667C2×C3×C4—38no—
668C2×C3×C4—32no—
669C2×C3×C4—34no—
670C2×C3×C4—34no—
671C2×C3×C4—42no—
672C2×C3×C4—64no—
673C2×C3×C4—64no—
674C2×C3×C4—64no—
675C2×C3×C4—68no—
676C2×C3×C4—64no—
677C2×C3×C4C23×D314yes—
678C2×C3×C4C23×D312yes—
679C2×C3×C4C23×D312yes—
680#67—28no—
681#67—38no—
682#67—38no—
683#67—44no—
684#67—64no—
685#67—64no—
686#67—64no—
687#67—64no—
688#67—68no—
689#67—64no—
690#67—64no—
691#67—124no—
692#67—124no—
693#67—124no—
694C2×Dic3—24no—
695C2×Dic3—28no—
696C2×Dic3—32no—
697C2×Dic3—34no—
698C2×Dic3—32no—
699C2×Dic3—34no—
700C2×Dic3—61no—
701C2×Dic3—62no—
702C2×Dic3—62no—
703C2×Dic3—61no—
704C2×Dic3—68no—
705C2×Dic3—64no—
706C2×Dic3—68no—
707C2×Dic3—122no—
708C2×Dic3—124no—
709C2×Dic3—124no—
710C2×Dic3C23×D314yes—
711C2×Dic3C23×D312yes—
712C2×Dic3C23×D314yes—
713C2×Dic3C23×D312yes—
714D12—38no—
715D12—64no—
716D12—64no—
717D12—64no—
718C4×D3—24no—
719C4×D3—24no—
720C4×D3—24no—
721C4×D3—38no—
722C4×D3—64no—
723C4×D3—68no—
724C4×D3—64no—
725C4×D3—64no—
726C4×D3—68no—
727C4×D3—64no—
728C4×D3—122no—
729C4×D3—122no—
730C4×D3—122no—
731C4×D3—124no—
732C4×D3—124no—
733C4×D3D3×D418yes—
734Dic6—24no—
735Dic6—38no—
736Dic6—64no—
737Dic6—68no—
738Dic6—68no—
739Dic6—64no—
740Dic6—64no—
741Dic6—64no—
742Dic6—68no—
743Dic6—122no—
744C2×C32—22no—
745C2×C32—42no—
746C2×C32C23×D411yescharacteristic
747C2×C32C2×2−1+411yescharacteristic
748C2×C32#58511yescharacteristic
749C3⋊D3—22no—
750C3⋊D3—41no—
751C3×D3—24no—
752C3×D3—42no—
753C24—32no—
754C24—91no—
755#41—68no—
756#41—98no—
757#41—188no—
758#41—184no—
759#41—188no—
760#41—184no—
761#41—184no—
762#41—1816no—
763#41—184no—
764#41—188no—
765C2×Q8—32no—
766C2×Q8—91no—
767C2×Q8—94no—
768C2×Q8—92no—
769C2×Q8—92no—
770C2×Q8—91no—
771C2×Q8—91no—
772C2×Q8—188no—
773C2×Q8—184no—
774C2×Q8—188no—
775C2×Q8—184no—
776C2×D4—34no—
777C2×D4—34no—
778C2×D4—92no—
779C2×D4—92no—
780C2×D4—92no—
781C2×D4—92no—
782C2×D4—91no—
783C2×D4—92no—
784C2×D4—91no—
785C2×D4—92no—
786C2×D4—92no—
787C2×D4—188no—
788C2×D4—184no—
789C2×D4C2×D3212yes—
790C2×D4C2×D3211yescharacteristic
791C22×C4—32no—
792C22×C4—34no—
793C22×C4—32no—
794C22×C4—32no—
795C22×C4—32no—
796C22×C4—32no—
797C22×C4—68no—
798C22×C4—92no—
799C22×C4—92no—
800C22×C4—94no—
801C22×C4—94no—
802C22×C4—91no—
803C22×C4—92no—
804C22×C4—91no—
805C22×C4—91no—
806C22×C4—91no—
807C22×C4—91no—
808C22×C4—184no—
809C22×C4C2×D3211yescharacteristic
810C4⋊C4—32no—
811C4⋊C4—34no—
812C4⋊C4—34no—
813C4⋊C4—92no—
814C4⋊C4—94no—
815C4⋊C4—94no—
816C4⋊C4—94no—
817C4⋊C4—94no—
818C4⋊C4—91no—
819C4⋊C4—92no—
820C4⋊C4—92no—
821C4⋊C4C2×D3211yescharacteristic
822C22⋊C4—34no—
823C22⋊C4—34no—
824C22⋊C4—34no—
825C22⋊C4—34no—
826C22⋊C4—94no—
827C22⋊C4—94no—
828C22⋊C4—94no—
829C22⋊C4—92no—
830C22⋊C4—92no—
831C22⋊C4—92no—
832C22⋊C4—92no—
833C22⋊C4C2×D3212yes—
834C42—34no—
835C42—92no—
836C22×C3—22no—
837C22×C3—22no—
838C22×C3—24no—
839C22×C3—24no—
840C22×C3—24no—
841C22×C3—22no—
842C22×C3—21no—
843C22×C3—34no—
844C22×C3—41no—
845C22×C3—41no—
846C22×C3—42no—
847C22×C3—42no—
848C22×C3—42no—
849C22×C3—62no—
850C22×C3—62no—
851C22×C3—62no—
852C22×C3—62no—
853C22×C3—62no—
854C22×C3—128no—
855C22×C3#101014yescomplemented
856C22×C3C24×D312yes—
857C2×D3—22no—
858C2×D3—22no—
859C2×D3—22no—
860C2×D3—22no—
861C2×D3—22no—
862C2×D3—34no—
863C2×D3—48no—
864C2×D3—62no—
865C2×D3—62no—
866C2×D3—62no—
867C2×D3—62no—
868C2×D3—62no—
869C2×D3—62no—
870C2×D3—62no—
871C2×D3—121no—
872C2×D3—121no—
873C2×D3—121no—
874C2×D3—121no—
875C2×D3—128no—
876C2×D3—128no—
877C2×D3C2×D3×D414yes—
878C3×C4—22no—
879C3×C4—24no—
880C3×C4—22no—
881C3×C4—34no—
882C3×C4—41no—
883C3×C4—42no—
884C3×C4—64no—
885C3×C4—62no—
886C3×C4—64no—
887C3×C4C2×D3×D414yes—
888Dic3—24no—
889Dic3—22no—
890Dic3—24no—
891Dic3—34no—
892Dic3—62no—
893Dic3—64no—
894Dic3—62no—
895Dic3—64no—
896Dic3—122no—
897Dic3—121no—
898Dic3—122no—
899Dic3C2×D3×D414yes—
900C32#348911yescharacteristic, complemented, Sylow
901C23—32no—
902C23—32no—
903C23—64no—
904C23—64no—
905C23—91no—
906C23—91no—
907C23—122no—
908C23—182no—
909C23—182no—
910C23—361no—
911C23C22×D3212yes—
912C23C22×D3211yescharacteristic
913Q8—64no—
914Q8—94no—
915Q8—188no—
916Q8—184no—
917Q8—184no—
918Q8—182no—
919Q8—182no—
920D4—24no—
921D4—22no—
922D4—68no—
923D4—98no—
924D4—94no—
925D4—124no—
926D4—184no—
927D4—184no—
928D4—184no—
929D4—182no—
930D4—184no—
931D4—184no—
932D4—362no—
933C2×C4—22no—
934C2×C4—32no—
935C2×C4—38no—
936C2×C4—34no—
937C2×C4—34no—
938C2×C4—32no—
939C2×C4—64no—
940C2×C4—64no—
941C2×C4—64no—
942C2×C4—68no—
943C2×C4—64no—
944C2×C4—91no—
945C2×C4—94no—
946C2×C4—92no—
947C2×C4—92no—
948C2×C4—91no—
949C2×C4—182no—
950C2×C4—182no—
951C2×C4—184no—
952C2×C4—188no—
953C2×C4—182no—
954C2×C4—184no—
955C2×C4—182no—
956C2×C4—362no—
957C2×C4—364no—
958C2×C4C22×D3212yes—
959C2×C4C22×D3211yescharacteristic
960C2×C4C22×D3211yescharacteristic
961C2×C3—24no—
962C2×C3—21no—
963C2×C3—21no—
964C2×C3—21no—
965C2×C3—42no—
966C2×C3—44no—
967C2×C3—64no—
968C2×C3—82no—
969C2×C3—122no—
970C2×C3C22×D3×D412yes—
971C2×C3C2×#101012yes—
972C2×C3#596412yes—
973D3—24no—
974D3—42no—
975D3—64no—
976D3—122no—
977D3—122no—
978D3—122no—
979C22—21no—
980C22—21no—
981C22—22no—
982C22—22no—
983C22—22no—
984C22—34no—
985C22—62no—
986C22—62no—
987C22—62no—
988C22—62no—
989C22—62no—
990C22—92no—
991C22—128no—
992C22—181no—
993C22—181no—
994C22—181no—
995C22—181no—
996C22—181no—
997C22—364no—
998C22#6430912yescomplemented
999C22C23×D3211yescharacteristic
1000C4—22no—
1001C4—21no—
1002C4—34no—
1003C4—62no—
1004C4—64no—
1005C4—64no—
1006C4—92no—
1007C4—181no—
1008C4—182no—
1009C4—182no—
1010C4D32×D412yes—
1011C3—21no—
1012C3#8604212yescomplemented
1013C2—22no—
1014C2—42no—
1015C2—64no—
1016C2—122no—
1017C2—182no—
1018C2—361no—
1019C2C2×#6430911yescharacteristic
1020C2C2×D32×D411yescharacteristic
1021C2#1059669511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#121C22
hypercenter#121D32
hypocenterC32#3489
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#64309C2semidirect
2. C22×#3798C2semidirect
3. #10596077C2semidirect
4. C3×#5606C2semidirect
5. D4×#627C2semidirect
6. #10595240C2semidirect
7. #10595232C2semidirect
8. #10595225C2semidirect
9. #10595135C2semidirect
10. #10594925C2semidirect
11. D3×#924C2semidirect
12. #10594529C2semidirect
13. #10594511C2semidirect
14. #10594380C2semidirect
15. #10594189C2semidirect
16. #10594188C2semidirect
17. #10594185C2semidirect
19. C2×#3830C22semidirect
21. C2×C3×#237C22semidirect
24. C22×#627C22semidirect
27. C2×#3805C22semidirect
28. C2×#3804C22semidirect
37. C2×#3797C22semidirect
38. C2×D3×Dic6C22semidirect
40. #64147C22semidirect
44. #64106C22semidirect
45. #64101C22semidirect
46. #64092C22semidirect
47. #64090C22semidirect
48. C3×#938C22semidirect
52. C3×#897C22semidirect
53. C3×#892C22semidirect
54. C3×#883C22semidirect
55. C3×#67⋊C4C22semidirect
57. #63982C22semidirect
58. #63980C22semidirect
59. #63978C22semidirect
61. #63971C22semidirect
62. #63970C22semidirect
65. #63964C22semidirect
66. #63958C22semidirect
67. #63919C22semidirect
68. #63918C22semidirect
69. C4×#627C22semidirect
70. #63915C22semidirect
71. #63902C22semidirect
72. #63900C22semidirect
73. #63891C22semidirect
74. #63890C22semidirect
75. D3×C4⋊Dic3C22semidirect
76. #63883C22semidirect
77. #63880C22semidirect
78. D3×Dic3⋊C4C22semidirect
79. #63871C22semidirect
80. #63865C22semidirect
81. #63857C22semidirect
82. #63856C22semidirect
83. #63854C22semidirect
84. #63852C22semidirect
85. #63851C22semidirect
101. #5606D3semidirect
164. #3798D4semidirect
205. C2×#237C2×D3semidirect
244. #938C2×D3semidirect
266. #897C2×D3semidirect
273. #892C2×D3semidirect
290. #883C2×D3semidirect
295. #67⋊C4C2×D3semidirect
537. C22×C322−1+4semidirect
855. C22×C3#1010semidirect
900. C32#3489semidirect
998. C22#64309semidirect
1012. C3#86042semidirect

Maximal subgroups

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

subgroupindex
C2×#643092
C22×#37982
#105960772
C3×#56062
D4×#6272
#105952402
#105952322
#105952252
#105951352
#105949252
D3×#9242
#105945292
#105945112
#105943802
#105941892
#105941882
#105941852
#860423