Finite Group Databasebeta

← #11904781

Subgroups — #11904781

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×#64316C211yesmaximal, characteristic, complemented
2C22×#3798C211yesmaximal, characteristic, complemented
3#10596098C211yesmaximal, characteristic, complemented
4C3×D3×C22⋊Q8C212yesmaximal, complemented
5#10595404C211yesmaximal, characteristic, complemented
6#10595397C212yesmaximal, complemented
7#10595005C212yesmaximal, complemented
8#10594925C211yesmaximal, characteristic, complemented
9#10594529C211yesmaximal, characteristic, complemented
10#10594523C212yesmaximal, complemented
11#10594521C212yesmaximal, complemented
12#10594516C214yesmaximal, complemented
13#10594512C212yesmaximal, complemented
14#10594509C211yesmaximal, characteristic, complemented
15#10594187C214yesmaximal, complemented
16#10594183C212yesmaximal, complemented
17#10594072C212yesmaximal, complemented
18#85985—32nomaximal
19C2×#3832C2211yescharacteristic, complemented
20C22×C4×C3⋊D3C2211yescharacteristic
21C2×C3×D3×Q8C2212yescomplemented
22C22×C3×C4×D3C2212yes—
23C22×#627C2211yescharacteristic
24C22×#626C2212yes—
25C22×#625C2211yescharacteristic
26#64316—28no—
27C2×#3799C2214yescomplemented
28C2×#3799C2212yescomplemented
29C2×#3798—28no—
30C2×#3798C2212yes—
31C2×#3798C2211yescharacteristic
32C2×#3798C2211yescharacteristic
33C2×#3798C2212yes—
34C2×#3798C2211yescharacteristic
35C2×#3798C2211yescharacteristic
36C2×#3798C2212yescomplemented
37C2×#3797C2212yescomplemented
38C2×#3797C2211yescharacteristic, complemented
39C32×C22⋊Q8C2211yescharacteristic
40#64155C2211yescharacteristic, complemented
41#64139C2211yescharacteristic
42#64104C2211yescharacteristic, complemented
43#64103C2212yescomplemented
44#64102C2212yescomplemented
45#64101C2211yescharacteristic, complemented
46#64091C2212yes—
47#64090C2212yes—
48C3×#946C2212yescomplemented
49C3×#924C2212yes—
50C3×#897C2212yescomplemented
51C3×#896C2214yescomplemented
52C3×D3×C4⋊C4C2212yescomplemented
53C3×D3×C4⋊C4C2214yescomplemented
54C3×D3×C22⋊C4C2214yes—
55C3×#878C2214yes—
56#63982C2212yes—
57#63977C2214yes—
58#63974C2212yes—
59#63952C2214yes—
60#63919C2212yescomplemented
61#63915C2212yescomplemented
62#63912C2212yescomplemented
63#63910C2214yescomplemented
64#63910C2214yescomplemented
65#63909C2212yescomplemented
66#63909C2214yescomplemented
67#63907C2214yescomplemented
68#63906C2214yescomplemented
69#63905C2214yescomplemented
70#63904C2214yescomplemented
71#63904C2214yescomplemented
72C4×#625C2212yescomplemented
73#63900C2211yescharacteristic, complemented
74#63895C2214yescomplemented
75#63883C2212yescomplemented
76#63871C2212yescomplemented
77#63865C2212yescomplemented
78#63865C2212yescomplemented
79#63856C2212yescomplemented
80#63854C2214yescomplemented
81#63850C2214yescomplemented
82#63850C2214yescomplemented
83#63841C2212yescomplemented
84#63839C2214yescomplemented
85#63838C2212yescomplemented
86C2×#1007—32no—
87C22×#235—32no—
88C2×C3×C22⋊Q8—32no—
89#5816—32no—
90#5791—32no—
91#5633—34no—
92#5632—34no—
93#5631—34no—
94#5630—34no—
95#5629—32no—
96#5629—32no—
97#5628—32no—
98#5628—32no—
99#5627—32no—
100#5627—32no—
101#5627—61no—
102D3×C22⋊Q8—32no—
103D3×C22⋊Q8D312yescomplemented
104#5510—32no—
105#5507—34no—
106#5507—34no—
107#5504—32no—
108#5490—34no—
109#5490—34no—
110C23×C3⋊D3C2311yescharacteristic
111C23×C3×D3C2312yes—
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⋊D3C2312yes—
122C2×C4×C3⋊D3C2311yescharacteristic
123C2×C4×C3⋊D3C2311yescharacteristic
124C2×C4×C3⋊D3C2311yescharacteristic
125C2×C4×C3⋊D3C2311yescharacteristic
126C22×C3×Dic3C2312yes—
127C3×D3×Q8—28no—
128C2×C3×C4×D3—28no—
129C2×C3×C4×D3C2314yes—
130C2×C3×C4×D3C2312yes—
131C2×C3×C4×D3C2312yes—
132C2×C3×C4×D3C2312yes—
133C2×C3×C4×D3C2314yes—
134C2×C3×C4×D3C2312yes—
135C2×C3×Dic6C2314yes—
136C2×C3×Dic6C2312yes—
137C2×#627—24no—
138C2×#627C2312yes—
139C2×#627C2312yes—
140C2×#627C2311yescharacteristic
141C2×#627C2311yescharacteristic
142C2×#626—28no—
143C2×#626C2312yes—
144C2×#626C2312yes—
145C2×#626C2312yes—
146C2×#626C2314yes—
147C2×#626C2314yes—
148C2×#626C2312yes—
149C2×#625—24no—
150C2×#625C2312yes—
151C2×#625C2311yescharacteristic
152C2×#625C2311yescharacteristic
153C2×#624C2312yes—
154C2×#624C2314yes—
155C2×#624C2312yes—
156#3799—28no—
157#3799—216no—
158#3798—24no—
159#3798—28no—
160#3798—24no—
161#3798—28no—
162#3798—24no—
163#3798—28no—
164#3798D418yescomplemented
165#3797—24no—
166#3797—28no—
167C32×C4⋊C4C2312yes—
168C32×C4⋊C4C2311yescharacteristic
169C32×C22⋊C4C2312yes—
170#3752C2312yes—
171#3752C2312yes—
172#3752C2312yes—
173#3752C2312yes—
174C4⋊(C3⋊Dic3)C2311yescharacteristic
175#3750C2312yes—
176C4×C3⋊Dic3C2312yes—
177C3×#217C2314yes—
178C3×(C2×D3)⋊C4C2314yes—
179C3×(C2×D3)⋊C4C2314yes—
180C3×C4⋊Dic3C2314yes—
181C3×C4⋊Dic3C2312yes—
182C3×Dic3⋊C4C2314yes—
183C3×Dic3⋊C4C2314yes—
184C3×Dic3⋊C4C2314yes—
185#3724C2312yes—
186#3724C2314yes—
187Dic3⋊Dic3C2314yes—
188#3722C2314yes—
189#3722C2314yes—
190(C2×D3)⋊Dic3C2314yes—
191(C2×D3)⋊Dic3C2314yes—
192Dic32C2314yes—
193#3489—91noSylow
194C22×C3×Q8—32no—
195C23×C3×C4—32no—
196C22×#67—32no—
197C22×#67—32no—
198#1007—616no—
199C2×#239—32no—
200C2×#239—32no—
201C2×#239—34no—
202C2×#239—61no—
203C2×D3×Q8—34no—
204C2×D3×Q8—32no—
205C2×D3×Q8C2×D312yescomplemented
206C2×#235—32no—
207C2×#235—32no—
208C2×#235—32no—
209C2×#235—32no—
210C2×#235—32no—
211C2×#235—32no—
212C2×#235—32no—
213C2×#235—32no—
214C2×#235—34no—
215C2×#235—34no—
216C2×#235—32no—
217C2×#235—616no—
218C22×D12—32no—
219C22×C4×D3—32no—
220C22×C4×D3—61no—
221C22×C4×D3C2×D312yes—
222C22×Dic6—32no—
223C3×C22⋊Q8—21no—
224C3×C22⋊Q8—32no—
225C3×C22⋊Q8—32no—
226C3×C22⋊Q8—34no—
227C3×C22⋊Q8—32no—
228C3×C22⋊Q8—34no—
229C3×C22⋊Q8C2×D312yes—
230C2×C3×C4⋊C4—32no—
231C2×C3×C4⋊C4—34no—
232C2×C3×C22⋊C4—34no—
233#953—34no—
234#947—34no—
235#946—32no—
236#946—32no—
237#946—32no—
238#946—61no—
239#946C2×D312yescomplemented
240#944—34no—
241#930—32no—
242#930—34no—
243#930—34no—
244#930—32no—
245#930—61no—
246#929—34no—
247#929—34no—
248#929—34no—
249C4×#67—34no—
250C4×#67—34no—
251C4×#67—34no—
252C4×#67—34no—
253#926—32no—
254#924—32no—
255#924C2×D312yes—
256#897—32no—
257#897—34no—
258#897C2×D312yescomplemented
259#896—34no—
260#896—34no—
261#896—34no—
262#896C2×D314yescomplemented
263#895—34no—
264#895—32no—
265#895—32no—
266#895—34no—
267#895—34no—
268#895—61no—
269#894—34no—
270#894—34no—
271#894—34no—
272#894—34no—
273#894—62no—
274#893—34no—
275#893—34no—
276#893—34no—
277#893—62no—
278#892—32no—
279#892—32no—
280#892—61no—
281D3×C4⋊C4—32no—
282D3×C4⋊C4—34no—
283D3×C4⋊C4C2×D312yescomplemented
284D3×C4⋊C4C2×D314yescomplemented
285#888—34no—
286#888—34no—
287#887—34no—
288#885—34no—
289#885—34no—
290#884—34no—
291#884—34no—
292#884—34no—
293#884—34no—
294#883—34no—
295#883—34no—
296#882—34no—
297#882—34no—
298#882—62no—
299#67⋊C4—34no—
300#67⋊C4—34no—
301#67⋊C4—62no—
302D3×C22⋊C4—34no—
303D3×C22⋊C4C2×D314yes—
304#878—34no—
305#878C2×D314yes—
306C23×C32C2411yescharacteristic
307C22×C3⋊D3—22no—
308C22×C3⋊D3—22no—
309C22×C3⋊D3—41no—
310C22×C3⋊D3C2411yescharacteristic
311C22×C3⋊D3C2412yes—
312C22×C3⋊D3C2411yescharacteristic
313C22×C3×D3—24no—
314C22×C3×D3—24no—
315C22×C3×D3—42no—
316C22×C3×D3C2412yes—
317C22×C3×D3C2412yes—
318C32×Q8—22no—
319C2×C32×C4—22no—
320C2×C32×C4C2411yescharacteristic
321C2×C32×C4C2412yes—
322C2×C32×C4C2412yes—
323C2×C32×C4C2411yescharacteristic
324#638—24no—
325C2×C3⋊Dic3—22no—
326C2×C3⋊Dic3C2412yes—
327C2×C3⋊Dic3C2411yescharacteristic
328C2×C3⋊Dic3C2411yescharacteristic
329C4⋊(C3⋊D3)—24no—
330C4⋊(C3⋊D3)—22no—
331C4⋊(C3⋊D3)—42no—
332C4×C3⋊D3—22no—
333C4×C3⋊D3—22no—
334C4×C3⋊D3—24no—
335C4×C3⋊D3—22no—
336C4×C3⋊D3C2×D414yes—
337C2×C3×Dic3—24no—
338C2×C3×Dic3C2414yes—
339C2×C3×Dic3C2414yes—
340C2×C3×Dic3C2412yes—
341C2×C3×Dic3C2412yes—
342C3×C4×D3—24no—
343C3×C4×D3—28no—
344C3×C4×D3—24no—
345C3×C4×D3—24no—
346C3×C4×D3—44no—
347C3×C4×D3C2×D418yes—
348C3×Dic6—24no—
349C3×Dic6—28no—
350#627—24no—
351#627—22no—
352#627—24no—
353#627C2×D414yes—
354#626—24no—
355#626—24no—
356#626—28no—
357#626—24no—
358#626—44no—
359#626C2×D418yes—
360#625—24no—
361#625—22no—
362#625C2×D414yes—
363#624—24no—
364#624—28no—
365#624—42no—
366C2×2−1+4—91no—
367C22×#41—91no—
368D4×Q8—92no—
369#548—92no—
370#547—92no—
371#547—94no—
372#546—92no—
373#546—94no—
374#537—92no—
375#537—91no—
376#536—91no—
377#536—92no—
378#525—92no—
379#525—91no—
380C2×C22⋊Q8—32no—
381C2×C22⋊Q8—91no—
382#520—91no—
383C24×C3—32no—
384C23×D3—32no—
385C23×D3—61no—
386C23×D3C22×D312yes—
387C2×C3×Q8—21no—
388C2×C3×Q8—34no—
389C2×C3×Q8—32no—
390C2×C3×Q8—68no—
391C2×C3×Q8C22×D312yes—
392C22×C3×C4—21no—
393C22×C3×C4—32no—
394C22×C3×C4—32no—
395C22×C3×C4—32no—
396C22×C3×C4—32no—
397C22×C3×C4—34no—
398C22×C3×C4—32no—
399C22×C3×C4—34no—
400C22×C3×C4—68no—
401C22×C3×C4C22×D312yes—
402C2×#67—32no—
403C2×#67—34no—
404C2×#67—32no—
405C2×#67—32no—
406C2×#67—32no—
407C2×#67—32no—
408C2×#67—32no—
409C2×#67—32no—
410C2×#67—32no—
411C2×#67—34no—
412C2×#67—34no—
413C2×#67—62no—
414C2×#67—68no—
415C2×#67—68no—
416C22×Dic3—32no—
417C22×Dic3—61no—
418C22×Dic3C22×D312yes—
419#239—616no—
420#239—68no—
421#239—68no—
422#239—124no—
423D3×Q8—28no—
424D3×Q8—616no—
425D3×Q8—68no—
426#235—316no—
427#235—616no—
428#235—68no—
429#235—68no—
430#235—68no—
431#235—68no—
432#235—68no—
433#235—68no—
434#235—616no—
435#235—68no—
436#235—68no—
437C2×D12—32no—
438C2×D12—34no—
439C2×D12—32no—
440C2×D12—32no—
441C2×D12—32no—
442C2×D12—34no—
443C2×D12—32no—
444C2×D12—34no—
445C2×D12—34no—
446C2×D12—62no—
447C2×D12—62no—
448C2×D12—61no—
449C2×D12—68no—
450C2×C4×D3—28no—
451C2×C4×D3—32no—
452C2×C4×D3—34no—
453C2×C4×D3—32no—
454C2×C4×D3—32no—
455C2×C4×D3—32no—
456C2×C4×D3—34no—
457C2×C4×D3—34no—
458C2×C4×D3—34no—
459C2×C4×D3—34no—
460C2×C4×D3—61no—
461C2×C4×D3—62no—
462C2×C4×D3—61no—
463C2×C4×D3—61no—
464C2×C4×D3—61no—
465C2×C4×D3—68no—
466C2×C4×D3—124no—
467C2×C4×D3C22×D314yes—
468C2×C4×D3C22×D312yes—
469C2×C4×D3C22×D312yes—
470C2×C4×D3C22×D312yes—
471C2×C4×D3C22×D314yes—
472C2×C4×D3C22×D312yes—
473C2×Dic6—32no—
474C2×Dic6—34no—
475C2×Dic6—32no—
476C2×Dic6—32no—
477C2×Dic6—32no—
478C2×Dic6—68no—
479C2×Dic6C22×D314yes—
480C2×Dic6C22×D312yes—
481C3×C4⋊C4—21no—
482C3×C4⋊C4—22no—
483C3×C4⋊C4—34no—
484C3×C4⋊C4—34no—
485C3×C4⋊C4—34no—
486C3×C4⋊C4—32no—
487C3×C4⋊C4—34no—
488C3×C4⋊C4C22×D312yes—
489C3×C4⋊C4C22×D314yes—
490C3×C22⋊C4—22no—
491C3×C22⋊C4—34no—
492C3×C22⋊C4—34no—
493C3×C22⋊C4—34no—
494C3×C22⋊C4C22×D314yes—
495#217—34no—
496#217—34no—
497#217C22×D314yes—
498(C2×D3)⋊C4—34no—
499(C2×D3)⋊C4—34no—
500(C2×D3)⋊C4—34no—
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—34no—
508(C2×D3)⋊C4—62no—
509(C2×D3)⋊C4—62no—
510(C2×D3)⋊C4—62no—
511(C2×D3)⋊C4—62no—
512(C2×D3)⋊C4C22×D314yes—
513(C2×D3)⋊C4C22×D314yes—
514C4⋊Dic3—32no—
515C4⋊Dic3—34no—
516C4⋊Dic3—61no—
517C4⋊Dic3C22×D314yes—
518C4⋊Dic3C22×D312yes—
519Dic3⋊C4—34no—
520Dic3⋊C4—34no—
521Dic3⋊C4—34no—
522Dic3⋊C4—34no—
523Dic3⋊C4—34no—
524Dic3⋊C4—62no—
525Dic3⋊C4C22×D314yes—
526Dic3⋊C4C22×D314yes—
527Dic3⋊C4C22×D314yes—
528C4×Dic3—34no—
529C4×Dic3—34no—
530C4×Dic3—34no—
531C4×Dic3—62no—
532C22×C32—21no—
533C22×C32—21no—
534C22×C322−1+412yescomplemented
535C22×C32C2511yescharacteristic
536C2×C3⋊D3—21no—
537C2×C3⋊D3—21no—
538C2×C3⋊D3—21no—
539C2×C3⋊D3—22no—
540C2×C3⋊D3—21no—
541C2×C3⋊D3—22no—
542C2×C3⋊D3—21no—
543C2×C3⋊D3—22no—
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—22no—
554C32×C4—21no—
555C32×C4—22no—
556C32×C4C22×D412yes—
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—91no—
566C2×#41—92no—
567C2×#41—91no—
568C2×#41—92no—
569C2×#41—91no—
570C2×#41—92no—
571C2×#41—91no—
572C2×#41—92no—
573C2×#41—94no—
574C2×#41—91no—
575C2×#41—188no—
576C22×Q8—32no—
577C22×Q8—91no—
578C22×Q8—91no—
579C22×Q8—92no—
580C22×D4—92no—
581C22×D4—91no—
582C23×C4—32no—
583C23×C4—91no—
584C4⋊Q8—92no—
585C4⋊Q8—94no—
586#124—92no—
587#124—94no—
588#123—94no—
589#123—94no—
590#123—94no—
591#123—94no—
592#123—92no—
593C22⋊Q8—32no—
594C22⋊Q8—32no—
595C22⋊Q8—32no—
596C22⋊Q8—34no—
597C22⋊Q8—34no—
598C22⋊Q8—92no—
599C22⋊Q8—92no—
600C22⋊Q8—92no—
601C22⋊Q8—94no—
602C22⋊Q8—92no—
603C22⋊Q8—92no—
604C22⋊Q8—91no—
605C22⋊Q8D3211yescharacteristic
606#121—92no—
607#121—94no—
608#121—94no—
609#121—94no—
610#121—92no—
611#121—94no—
612#121—91no—
613#121—91no—
614#120—94no—
615#120—92no—
616C4×Q8—92no—
617C4×D4—94no—
618C4×D4—94no—
619C4×D4—94no—
620C4×D4—92no—
621C4×D4—92no—
622C4×D4—92no—
623#117—92no—
624#117—91no—
625C2×C4⋊C4—32no—
626C2×C4⋊C4—34no—
627C2×C4⋊C4—91no—
628C2×C4⋊C4—92no—
629C2×C22⋊C4—34no—
630C2×C22⋊C4—92no—
631C23×C3—21no—
632C23×C3—32no—
633C23×C3—32no—
634C23×C3—64no—
635C23×C3—64no—
636C23×C3—122no—
637C23×C3C23×D312yes—
638C22×D3—24no—
639C22×D3—24no—
640C22×D3—32no—
641C22×D3—32no—
642C22×D3—34no—
643C22×D3—42no—
644C22×D3—61no—
645C22×D3—61no—
646C22×D3—62no—
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—24no—
656C3×Q8—42no—
657C3×Q8—68no—
658C3×Q8—64no—
659C2×C3×C4—24no—
660C2×C3×C4—21no—
661C2×C3×C4—22no—
662C2×C3×C4—22no—
663C2×C3×C4—21no—
664C2×C3×C4—32no—
665C2×C3×C4—38no—
666C2×C3×C4—34no—
667C2×C3×C4—34no—
668C2×C3×C4—32no—
669C2×C3×C4—42no—
670C2×C3×C4—64no—
671C2×C3×C4—64no—
672C2×C3×C4—68no—
673C2×C3×C4—64no—
674C2×C3×C4—64no—
675C2×C3×C4—124no—
676C2×C3×C4C23×D314yes—
677C2×C3×C4C23×D314yes—
678C2×C3×C4C23×D312yes—
679C2×C3×C4C23×D312yes—
680#67—38no—
681#67—38no—
682#67—64no—
683#67—68no—
684#67—64no—
685#67—64no—
686#67—64no—
687#67—68no—
688#67—64no—
689#67—64no—
690#67—124no—
691#67—124no—
692C2×Dic3—24no—
693C2×Dic3—32no—
694C2×Dic3—34no—
695C2×Dic3—32no—
696C2×Dic3—61no—
697C2×Dic3—62no—
698C2×Dic3—61no—
699C2×Dic3—64no—
700C2×Dic3—122no—
701C2×Dic3C23×D314yes—
702C2×Dic3C23×D312yes—
703C2×Dic3C23×D314yes—
704C2×Dic3C23×D312yes—
705D12—38no—
706D12—68no—
707D12—64no—
708D12—64no—
709D12—64no—
710D12—68no—
711D12—64no—
712D12—122no—
713D12—124no—
714D12—124no—
715D12—124no—
716D12—124no—
717C4×D3—24no—
718C4×D3—28no—
719C4×D3—24no—
720C4×D3—24no—
721C4×D3—38no—
722C4×D3—44no—
723C4×D3—64no—
724C4×D3—68no—
725C4×D3—68no—
726C4×D3—64no—
727C4×D3—68no—
728C4×D3—64no—
729C4×D3—64no—
730C4×D3—68no—
731C4×D3—122no—
732C4×D3—124no—
733C4×D3—122no—
734C4×D3—122no—
735C4×D3—124no—
736C4×D3D3×D418yes—
737Dic6—24no—
738Dic6—28no—
739Dic6—38no—
740Dic6—64no—
741Dic6—68no—
742Dic6—64no—
743Dic6—64no—
744C2×C32—22no—
745C2×C32C23×D411yescharacteristic
746C2×C32C2×2−1+411yescharacteristic
747C2×C32#58511yescharacteristic
748C3⋊D3—22no—
749C3⋊D3—41no—
750C3⋊D3—42no—
751C3×D3—24no—
752C3×D3—42no—
753C24—32no—
754C24—91no—
755#41—98no—
756#41—188no—
757#41—188no—
758#41—184no—
759#41—188no—
760#41—184no—
761#41—188no—
762#41—184no—
763#41—1816no—
764#41—184no—
765C2×Q8—32no—
766C2×Q8—34no—
767C2×Q8—68no—
768C2×Q8—91no—
769C2×Q8—92no—
770C2×Q8—92no—
771C2×Q8—91no—
772C2×Q8—184no—
773C2×Q8—184no—
774C2×Q8—188no—
775C2×Q8C2×D3211yescharacteristic
776C2×D4—92no—
777C2×D4—94no—
778C2×D4—92no—
779C2×D4—92no—
780C2×D4—92no—
781C2×D4—94no—
782C2×D4—91no—
783C2×D4—92no—
784C2×D4—91no—
785C2×D4—92no—
786C2×D4—92no—
787C2×D4—91no—
788C2×D4—92no—
789C2×D4—188no—
790C2×D4—184no—
791C22×C4—32no—
792C22×C4—32no—
793C22×C4—34no—
794C22×C4—32no—
795C22×C4—32no—
796C22×C4—32no—
797C22×C4—34no—
798C22×C4—68no—
799C22×C4—92no—
800C22×C4—94no—
801C22×C4—92no—
802C22×C4—91no—
803C22×C4—91no—
804C22×C4—91no—
805C22×C4—92no—
806C22×C4—91no—
807C22×C4—91no—
808C22×C4—184no—
809C22×C4C2×D3211yescharacteristic
810C4⋊C4—32no—
811C4⋊C4—34no—
812C4⋊C4—34no—
813C4⋊C4—34no—
814C4⋊C4—34no—
815C4⋊C4—92no—
816C4⋊C4—94no—
817C4⋊C4—94no—
818C4⋊C4—91no—
819C4⋊C4—92no—
820C4⋊C4C2×D3211yescharacteristic
821C4⋊C4C2×D3212yes—
822C22⋊C4—34no—
823C22⋊C4—34no—
824C22⋊C4—34no—
825C22⋊C4—94no—
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—94no—
835C42—92no—
836C22×C3—22no—
837C22×C3—22no—
838C22×C3—22no—
839C22×C3—21no—
840C22×C3—34no—
841C22×C3—41no—
842C22×C3—41no—
843C22×C3—62no—
844C22×C3—62no—
845C22×C3—62no—
846C22×C3—62no—
847C22×C3—62no—
848C22×C3—128no—
849C22×C3#100714yescomplemented
850C22×C3C24×D312yes—
851C2×D3—22no—
852C2×D3—22no—
853C2×D3—22no—
854C2×D3—22no—
855C2×D3—22no—
856C2×D3—34no—
857C2×D3—48no—
858C2×D3—62no—
859C2×D3—62no—
860C2×D3—62no—
861C2×D3—62no—
862C2×D3—64no—
863C2×D3—62no—
864C2×D3—64no—
865C2×D3—62no—
866C2×D3—64no—
867C2×D3—62no—
868C2×D3—121no—
869C2×D3—121no—
870C2×D3—121no—
871C2×D3—121no—
872C2×D3—122no—
873C2×D3—122no—
874C2×D3—122no—
875C2×D3—128no—
876C2×D3—128no—
877C2×D3C2×D3×D414yes—
878C3×C4—24no—
879C3×C4—22no—
880C3×C4—24no—
881C3×C4—22no—
882C3×C4—34no—
883C3×C4—41no—
884C3×C4—42no—
885C3×C4—42no—
886C3×C4—62no—
887C3×C4—64no—
888C3×C4—64no—
889C3×C4C2×D3×D414yes—
890Dic3—24no—
891Dic3—22no—
892Dic3—24no—
893Dic3—34no—
894Dic3—62no—
895Dic3—62no—
896Dic3—64no—
897Dic3—121no—
898Dic3—122no—
899Dic3C2×D3×D414yes—
900C32#348911yescharacteristic, complemented, Sylow
901C23—32no—
902C23—32no—
903C23—64no—
904C23—64no—
905C23—91no—
906C23—91no—
907C23—92no—
908C23—122no—
909C23—182no—
910C23—182no—
911C23—361no—
912C23C22×D3211yescharacteristic
913Q8—22no—
914Q8—68no—
915Q8—64no—
916Q8—94no—
917Q8—184no—
918Q8—184no—
919Q8—182no—
920D4—98no—
921D4—94no—
922D4—184no—
923D4—184no—
924D4—184no—
925D4—188no—
926D4—184no—
927D4—182no—
928D4—184no—
929D4—184no—
930D4—182no—
931D4—362no—
932D4—364no—
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—68no—
942C2×C4—64no—
943C2×C4—64no—
944C2×C4—91no—
945C2×C4—94no—
946C2×C4—92no—
947C2×C4—91no—
948C2×C4—124no—
949C2×C4—182no—
950C2×C4—184no—
951C2×C4—182no—
952C2×C4—188no—
953C2×C4—184no—
954C2×C4—182no—
955C2×C4—182no—
956C2×C4—362no—
957C2×C4C22×D3212yes—
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—64no—
967C2×C3—122no—
968C2×C3C22×D3×D412yes—
969C2×C3C2×#100712yes—
970C2×C3#596412yes—
971D3—24no—
972D3—42no—
973D3—64no—
974D3—122no—
975D3—122no—
976D3—122no—
977D3—124no—
978D3—242no—
979C22—21no—
980C22—21no—
981C22—34no—
982C22—62no—
983C22—62no—
984C22—62no—
985C22—62no—
986C22—62no—
987C22—92no—
988C22—128no—
989C22—181no—
990C22—181no—
991C22—182no—
992C22—181no—
993C22—182no—
994C22—181no—
995C22—182no—
996C22—181no—
997C22—364no—
998C22#6431612yescomplemented
999C22C23×D3211yescharacteristic
1000C4—21no—
1001C4—22no—
1002C4—22no—
1003C4—34no—
1004C4—62no—
1005C4—64no—
1006C4—64no—
1007C4—92no—
1008C4—181no—
1009C4—182no—
1010C4D32×D412yes—
1011C3—21no—
1012C3#8598512yescomplemented
1013C2—22no—
1014C2—64no—
1015C2—122no—
1016C2—182no—
1017C2—361no—
1018C2—362no—
1019C2C2×D32×D411yescharacteristic
1020C2C2×#6431611yescharacteristic
1021C2#1059669511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C22⋊Q8C22
hypercenterC22⋊Q8D32
hypocenterC32#3489
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. C22×#3798C2semidirect
3. #10596098C2semidirect
4. C3×D3×C22⋊Q8C2semidirect
5. #10595404C2semidirect
6. #10595397C2semidirect
7. #10595005C2semidirect
8. #10594925C2semidirect
9. #10594529C2semidirect
10. #10594523C2semidirect
11. #10594521C2semidirect
12. #10594516C2semidirect
13. #10594512C2semidirect
14. #10594509C2semidirect
15. #10594187C2semidirect
16. #10594183C2semidirect
17. #10594072C2semidirect
19. C2×#3832C22semidirect
21. C2×C3×D3×Q8C22semidirect
27. C2×#3799C22semidirect
28. C2×#3799C22semidirect
36. C2×#3798C22semidirect
37. C2×#3797C22semidirect
38. C2×#3797C22semidirect
40. #64155C22semidirect
42. #64104C22semidirect
43. #64103C22semidirect
44. #64102C22semidirect
45. #64101C22semidirect
48. C3×#946C22semidirect
50. C3×#897C22semidirect
51. C3×#896C22semidirect
52. C3×D3×C4⋊C4C22semidirect
53. C3×D3×C4⋊C4C22semidirect
60. #63919C22semidirect
61. #63915C22semidirect
62. #63912C22semidirect
63. #63910C22semidirect
64. #63910C22semidirect
65. #63909C22semidirect
66. #63909C22semidirect
67. #63907C22semidirect
68. #63906C22semidirect
69. #63905C22semidirect
70. #63904C22semidirect
71. #63904C22semidirect
72. C4×#625C22semidirect
73. #63900C22semidirect
74. #63895C22semidirect
75. #63883C22semidirect
76. #63871C22semidirect
77. #63865C22semidirect
78. #63865C22semidirect
79. #63856C22semidirect
80. #63854C22semidirect
81. #63850C22semidirect
82. #63850C22semidirect
83. #63841C22semidirect
84. #63839C22semidirect
85. #63838C22semidirect
103. D3×C22⋊Q8D3semidirect
164. #3798D4semidirect
205. C2×D3×Q8C2×D3semidirect
239. #946C2×D3semidirect
258. #897C2×D3semidirect
262. #896C2×D3semidirect
283. D3×C4⋊C4C2×D3semidirect
284. D3×C4⋊C4C2×D3semidirect
534. C22×C322−1+4semidirect
849. C22×C3#1007semidirect
900. C32#3489semidirect
998. C22#64316semidirect
1012. C3#85985semidirect

Maximal subgroups

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

subgroupindex
C2×#643162
C22×#37982
#105960982
C3×D3×C22⋊Q82
#105954042
#105953972
#105950052
#105949252
#105945292
#105945232
#105945212
#105945162
#105945122
#105945092
#105941872
#105941832
#105940722
#859853