Finite Group Databasebeta

← #11887327

Subgroups — #11887327

Order 1152.

682 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 682 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595225C211yesmaximal, characteristic
2#10595120C211yesmaximal, characteristic, complemented
3D4×#622C211yesmaximal, characteristic, complemented
4#10593527C211yesmaximal, characteristic, complemented
5#10593526C211yesmaximal, characteristic, complemented
6#10593524C211yesmaximal, characteristic, complemented
7#10593523C211yesmaximal, characteristic, complemented
8#10593504C211yesmaximal, characteristic, complemented
9#10593498C211yesmaximal, characteristic, complemented
10#10593494C211yesmaximal, characteristic, complemented
11C2×#63739C211yesmaximal, characteristic, complemented
12#10593440C211yesmaximal, characteristic, complemented
13#10593433C211yesmaximal, characteristic, complemented
14#10593364C211yesmaximal, characteristic, complemented
15#10593353C211yesmaximal, characteristic, complemented
16C22×#625C2211yescharacteristic
17C2×#3805C2211yescharacteristic
18C22×#622C2211yescharacteristic
19C22×#622C2211yescharacteristic, complemented
20C2×#3776C2211yescharacteristic, complemented
21C2×#3775C2211yescharacteristic
22C2×#3775C2211yescharacteristic
23D4×C3⋊Dic3C2211yescharacteristic
24C3×#937—21no—
25C3×#935—21no—
26#63982C2211yescharacteristic
27#63982C2211yescharacteristic
28#63982C2211yescharacteristic, complemented
29#63980C2211yescharacteristic
30#63970—21no—
31D3×#217—21no—
32C2×#3724C2211yescharacteristic
33#63957C2211yescharacteristic, complemented
34#63956—21no—
35#63955—21no—
36#63915C2211yescharacteristic
37#63902C2211yescharacteristic
38#63891—21no—
39#63870C2211yescharacteristic, complemented
40#63845—21no—
41#63838C2211yescharacteristic, complemented
42C22⋊#622C2211yescharacteristic
43C22⋊#622C2211yescharacteristic, complemented
44C4⋊#622C2211yescharacteristic, complemented
45C4×#622C2211yescharacteristic, complemented
46#63743C2211yescharacteristic, complemented
47#63742C2211yescharacteristic, complemented
48#63742C2211yescharacteristic, complemented
49#63740C2211yescharacteristic, complemented
50#63740C2211yescharacteristic, complemented
51#63740C2211yescharacteristic, complemented
52#63740C2211yescharacteristic, complemented
53#63739C2211yescharacteristic
54#63739C2211yescharacteristic
55#63739C2211yescharacteristic
56#63739C2211yescharacteristic
57#63739C2211yescharacteristic
58#63739C2211yescharacteristic
59#5650—61no—
60#5591—61no—
61C23×C3×D3—21no—
62C2×C32×D4D411yescharacteristic
63C22×C3⋊Dic3C2311yescharacteristic
64C22×C3⋊Dic3C2311yescharacteristic
65C2×C3×#67—21no—
66C2×C3×#67—21no—
67C22×C3×Dic3—21no—
68C2×#627C2311yescharacteristic
69C2×#627C2311yescharacteristic
70C2×#625—22no—
71C2×#625—21no—
72C2×#625—41no—
73C2×#625C2311yescharacteristic
74C2×#625C2311yescharacteristic
75#3805—22no—
76#3805—41no—
77C2×D3×Dic3—21no—
78C2×D3×Dic3—21no—
79C2×#622—41no—
80C2×#622—41no—
81C2×#622C2311yescharacteristic
82C2×#622C2311yescharacteristic
83C2×#622C2311yescharacteristic
84C2×#622C2311yescharacteristic
85#3776—41no—
86#3775—22no—
87#3775—41no—
88#3757D411yescharacteristic
89#3757D411yescharacteristic
90C4⋊(C3⋊Dic3)D411yescharacteristic
91C4×C3⋊Dic3C2311yescharacteristic
92C3×#217—21no—
93C3×#217—21no—
94C3×#217—21no—
95C3×#217—21no—
96C3×(C2×D3)⋊C4—21no—
97C3×(C2×D3)⋊C4—21no—
98C3×Dic3⋊C4—21no—
99C3×Dic3⋊C4—21no—
100#3724—21no—
101#3724C2311yescharacteristic
102#3724C2311yescharacteristic
103#3724C2311yescharacteristic
104#3724C2311yescharacteristic
105Dic3⋊Dic3—21no—
106Dic3⋊Dic3—21no—
107Dic3⋊Dic3—21no—
108Dic3⋊Dic3—21no—
109(C2×D3)⋊Dic3—21no—
110(C2×D3)⋊Dic3—21no—
111Dic32—21no—
112Dic32—21no—
113#3296—91nomaximal, Sylow
114C22×#67—61no—
115C2×#237—61no—
116C3×#123—61no—
117C3×#120—61no—
118C2×#217—61no—
119#939—61no—
120#939—61no—
121#938—61no—
122#937—21no—
123#935—21no—
124D4×Dic3—61no—
125D4×Dic3—61no—
126#926—61no—
127C2×Dic3⋊C4—61no—
128#890—61no—
129#889—61no—
130#889—61no—
131#887—61no—
132#886—61no—
133#885—61no—
134#883—61no—
135#67⋊C4—61no—
136D3×C22⋊C4—61no—
137#879—61no—
138#879—61no—
139#878—61no—
140#878—61no—
141#878—61no—
142#877—61no—
143#877—61no—
144C23×C32C2×D411yescharacteristic
145C23×C32C2×D411yescharacteristic
146C22×C3×D3—21no—
147C22×C3×D3—21no—
148C22×C3×D3—42no—
149C22×C3×D3—42no—
150C22×C3×D3—81no—
151C32×D4—22no—
152C2×C32×C4C2×D411yescharacteristic
153C2×C3⋊Dic3—21no—
154C2×C3⋊Dic3—21no—
155C2×C3⋊Dic3—21no—
156C2×C3⋊Dic3—21no—
157C2×C3⋊Dic3C2×D411yescharacteristic
158C2×C3⋊Dic3C2×D411yescharacteristic
159C2×C3⋊Dic3C2×D411yescharacteristic
160C2×C3⋊Dic3C2411yescharacteristic
161C3×#67—42no—
162C3×#67—81no—
163C2×C3×Dic3—21no—
164C2×C3×Dic3—21no—
165C2×C3×Dic3—21no—
166C2×C3×Dic3—21no—
167C2×C3×Dic3—21no—
168C2×C3×Dic3—21no—
169C2×C3×Dic3—42no—
170#627—21no—
171#627—21no—
172#627—21no—
173#627—21no—
174#625—21no—
175#625—21no—
176#625—21no—
177#625—42no—
178#625#4112yes—
179D3×Dic3—42no—
180D3×Dic3—81no—
181#622—21no—
182#622—21no—
183#622—21no—
184#622—21no—
185#552—91no—
186#546—91no—
187#488—91no—
188#483—91no—
189#482—91no—
190#478—91no—
191#467—91no—
192#465—91no—
193#464—91no—
194#452—91no—
195#450—91no—
196C4×SD16—91no—
197C8×D4—91no—
198#416—91no—
199C2×#102—91no—
200C24×C3—61no—
201C23×D3—21no—
202C2×C3×D4—21no—
203C2×C3×D4—21no—
204C2×C3×D4—61no—
205C2×C3×D4—61no—
206C22×C3×C4—61no—
207C2×#67—21no—
208C2×#67—21no—
209C2×#67—61no—
210C2×#67—61no—
211C2×#67—61no—
212C2×#67—61no—
213C2×#67—122no—
214C2×#67—122no—
215C22×Dic3—21no—
216C22×Dic3—61no—
217C22×Dic3—61no—
218C22×Dic3—61no—
219C22×Dic3—61no—
220C22×Dic3—61no—
221C22×Dic3—61no—
222#237—122no—
223#237—122no—
224C2×C4×D3—61no—
225C2×C4×D3—61no—
226C2×Dic6—61no—
227C2×Dic6—61no—
228C3×C4⋊C4—61no—
229C3×C4⋊C4—61no—
230C3×C22⋊C4—61no—
231C3×C22⋊C4—61no—
232C3×C22⋊C4—61no—
233C3×C22⋊C4—61no—
234C3×C22⋊C4—61no—
235C3×C22⋊C4—61no—
236#217—21no—
237#217—21no—
238#217—21no—
239#217—21no—
240#217—61no—
241#217—61no—
242#217—61no—
243#217—61no—
244#217—61no—
245#217—61no—
246(C2×D3)⋊C4—21no—
247(C2×D3)⋊C4—21no—
248(C2×D3)⋊C4—61no—
249(C2×D3)⋊C4—61no—
250C4⋊Dic3—61no—
251C4⋊Dic3—61no—
252C4⋊Dic3—61no—
253C4⋊Dic3—61no—
254C4⋊Dic3—61no—
255C4⋊Dic3—61no—
256Dic3⋊C4—21no—
257Dic3⋊C4—21no—
258Dic3⋊C4—61no—
259Dic3⋊C4—61no—
260Dic3⋊C4—61no—
261Dic3⋊C4—61no—
262Dic3⋊C4—61no—
263Dic3⋊C4—61no—
264Dic3⋊C4—61no—
265Dic3⋊C4—61no—
266Dic3⋊C4—61no—
267Dic3⋊C4—61no—
268C4×Dic3—61no—
269C4×Dic3—61no—
270C4×Dic3—61no—
271C4×Dic3—61no—
272C4×Dic3—61no—
273C4×Dic3—61no—
274C22×C32—21no—
275C22×C32—21no—
276C22×C32—21no—
277C22×C32—21no—
278C22×C32—21no—
279C22×C32#13512yes—
280C22×C32C22×D411yescharacteristic
281C2×C3×D3—22no—
282C2×C3×D3—41no—
283C2×C3×D3—41no—
284C2×C3×D3—41no—
285C2×C3×D3—41no—
286C2×C3×D3—41no—
287C2×C3×D3—84no—
288C32×C4—21no—
289C3⋊Dic3—21no—
290C3⋊Dic3—21no—
291C3⋊Dic3—21no—
292C3⋊Dic3C2×#4111yescharacteristic
293C3⋊Dic3H(5,𝔽2)11yescharacteristic
294C3×Dic3—41no—
295C3×Dic3—41no—
296C3×Dic3—41no—
297C3×Dic3—41no—
298C3×Dic3—41no—
299C3×Dic3—41no—
300C2×#41—91no—
301C22×D4—91no—
302C2×Q16—91no—
303C2×SD16—91no—
304C2×SD16—91no—
305C22×C8—91no—
306C22×C8—91no—
307#126—181no—
308#125—91no—
309#125—181no—
310#124—91no—
311#123—61no—
312#123—181no—
313C22⋊Q8—91no—
314C22⋊Q8—91no—
315C22⋊Q8—91no—
316#121—91no—
317#121—181no—
318#120—61no—
319C4×Q8—91no—
320C4×D4—91no—
321C4×D4—91no—
322#117—91no—
323#117—181no—
324C2×C4⋊C4—91no—
325C2×C22⋊C4—181no—
326#107—91no—
327#106—91no—
328#106—91no—
329C4⋊C8—91no—
330#103—91no—
331#103—91no—
332#103—91no—
333#103—91no—
334#102—91no—
335#102—91no—
336#102—91no—
337#102—91no—
338#102—91no—
339#102—91no—
340C22⋊C8—91no—
341C22⋊C8—91no—
342C4×C8—91no—
343C23×C3—21no—
344C23×C3—21no—
345C23×C3—21no—
346C23×C3—21no—
347C23×C3—61no—
348C23×C3—61no—
349C23×C3—122no—
350C23×C3—122no—
351C23×C3—241no—
352C22×D3—21no—
353C22×D3—21no—
354C22×D3—42no—
355C22×D3—42no—
356C22×D3—81no—
357C3×D4—42no—
358C3×D4—42no—
359C3×D4—122no—
360C3×D4—241no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—61no—
364C2×C3×C4—61no—
365C2×C3×C4—61no—
366C2×C3×C4—61no—
367C2×C3×C4—61no—
368C2×C3×C4—61no—
369C2×C3×C4—122no—
370#67—42no—
371#67—62no—
372#67—62no—
373#67—81no—
374#67—121no—
375#67—121no—
376#67—122no—
377#67—122no—
378C2×Dic3—21no—
379C2×Dic3—21no—
380C2×Dic3—21no—
381C2×Dic3—21no—
382C2×Dic3—21no—
383C2×Dic3—21no—
384C2×Dic3—42no—
385C2×Dic3—61no—
386C2×Dic3—61no—
387C2×Dic3—61no—
388C2×Dic3—61no—
389C2×Dic3—61no—
390C2×Dic3—61no—
391C2×Dic3—61no—
392C2×Dic3—61no—
393C2×Dic3—121no—
394C2×Dic3—121no—
395C2×Dic3—121no—
396C2×Dic3—121no—
397C2×Dic3—121no—
398C2×Dic3—121no—
399C2×Dic3—121no—
400C2×Dic3—121no—
401C2×Dic3—122no—
402C2×Dic3—241no—
403C4×D3—122no—
404C4×D3—241no—
405Dic6—121no—
406Dic6—121no—
407Dic6—121no—
408Dic6—121no—
409C2×C32—22no—
410C2×C32—41no—
411C2×C32#54611yescharacteristic
412C2×C32C2×#13511yescharacteristic
413C2×C32#57711yescharacteristic
414C3×D3—42no—
415C3×D3—81no—
416C24—61no—
417#41—182no—
418#41—361no—
419C2×Q8—91no—
420C2×Q8—91no—
421C2×D4—61no—
422C2×D4—61no—
423C2×D4—91no—
424C2×D4—91no—
425C2×D4—181no—
426C2×D4—182no—
427C2×D4—361no—
428C2×D4GO+(4,𝔽2)11yescharacteristic
429C22×C4—61no—
430C22×C4—91no—
431C22×C4—91no—
432C22×C4—181no—
433C22×C4—181no—
434Q16—361no—
435SD16—182no—
436SD16—361no—
437C2×C8—91no—
438C2×C8—91no—
439C2×C8—91no—
440C2×C8—91no—
441C2×C8—361no—
442C2×C8—361no—
443C4⋊C4—61no—
444C4⋊C4—61no—
445C4⋊C4—91no—
446C4⋊C4—91no—
447C4⋊C4—91no—
448C4⋊C4—91no—
449C4⋊C4—91no—
450C4⋊C4—181no—
451C4⋊C4—181no—
452C4⋊C4—181no—
453C4⋊C4—181no—
454C4⋊C4—181no—
455C22⋊C4—61no—
456C22⋊C4—61no—
457C22⋊C4—61no—
458C22⋊C4—61no—
459C22⋊C4—61no—
460C22⋊C4—61no—
461C22⋊C4—91no—
462C22⋊C4—91no—
463C22⋊C4—181no—
464C22⋊C4—181no—
465C42—91no—
466C42—181no—
467C42—181no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—22no—
471C22×C3—22no—
472C22×C3—41no—
473C22×C3—41no—
474C22×C3—41no—
475C22×C3—41no—
476C22×C3—41no—
477C22×C3—41no—
478C22×C3—41no—
479C22×C3—41no—
480C22×C3—41no—
481C22×C3—41no—
482C22×C3—62no—
483C22×C3—121no—
484C22×C3—121no—
485C22×C3—121no—
486C22×C3—121no—
487C22×C3—121no—
488C22×C3—244no—
489C2×D3—22no—
490C2×D3—41no—
491C2×D3—41no—
492C2×D3—41no—
493C2×D3—41no—
494C2×D3—41no—
495C2×D3—84no—
496C3×C4—41no—
497C3×C4—41no—
498C3×C4—121no—
499C3×C4—121no—
500C3×C4—121no—
501C3×C4—121no—
502C3×C4—121no—
503C3×C4—121no—
504Dic3—41no—
505Dic3—41no—
506Dic3—41no—
507Dic3—41no—
508Dic3—41no—
509Dic3—41no—
510Dic3—61no—
511Dic3—61no—
512Dic3—61no—
513Dic3—61no—
514Dic3—121no—
515Dic3—121no—
516Dic3—121no—
517Dic3—121no—
518Dic3—121no—
519Dic3—121no—
520C32#329611yescharacteristic, complemented, Sylow
521C23—61no—
522C23—61no—
523C23—122no—
524C23—122no—
525C23—241no—
526C23C2×GO+(4,𝔽2)11yescharacteristic
527C23C2×GO+(4,𝔽2)11yescharacteristic
528Q8—181no—
529Q8—181no—
530Q8—181no—
531Q8—181no—
532D4—22no—
533D4—92no—
534D4—122no—
535D4—181no—
536D4—181no—
537D4—181no—
538D4—241no—
539D4—362no—
540C2×C4—61no—
541C2×C4—61no—
542C2×C4—61no—
543C2×C4—61no—
544C2×C4—61no—
545C2×C4—61no—
546C2×C4—91no—
547C2×C4—91no—
548C2×C4—91no—
549C2×C4—91no—
550C2×C4—122no—
551C2×C4—181no—
552C2×C4—181no—
553C2×C4—181no—
554C2×C4—181no—
555C2×C4—362no—
556C2×C4—721no—
557C2×C4C2×GO+(4,𝔽2)11yescharacteristic
558C8—181no—
559C8—181no—
560C8—181no—
561C8—181no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—42no—
569C2×C3—42no—
570C2×C3—81no—
571C2×C3—81no—
572C2×C3—122no—
573C2×C3—241no—
574D3—42no—
575D3—81no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—62no—
582C22—121no—
583C22—121no—
584C22—121no—
585C22—121no—
586C22—121no—
587C22—244no—
588C22#6423712yes—
589C22C22×GO+(4,𝔽2)11yescharacteristic
590C4—21no—
591C4—91no—
592C4—91no—
593C4—121no—
594C4—121no—
595C4—121no—
596C4—121no—
597C4—121no—
598C4—121no—
599C4—181no—
600C4—181no—
601C4—181no—
602C3—21no—
603C3—21no—
604C2—22no—
605C2—41no—
606C2—122no—
607C2—241no—
608C2#1059651511yescharacteristic
609C2#1059651811yescharacteristic
610C2C2×#6423711yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC2×C32×D4D4
socleC22×C32C22×D4
prime radical#10595225C2
hypercenterC2×D4GO+(4,𝔽2)
hypocenterC32#3296
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. #10595120C2semidirect
3. D4×#622C2semidirect
4. #10593527C2semidirect
5. #10593526C2semidirect
6. #10593524C2semidirect
7. #10593523C2semidirect
8. #10593504C2semidirect
9. #10593498C2semidirect
10. #10593494C2semidirect
11. C2×#63739C2semidirect
12. #10593440C2semidirect
13. #10593433C2semidirect
14. #10593364C2semidirect
15. #10593353C2semidirect
19. C22×#622C22semidirect
20. C2×#3776C22semidirect
28. #63982C22semidirect
33. #63957C22semidirect
39. #63870C22semidirect
41. #63838C22semidirect
43. C22⋊#622C22semidirect
44. C4⋊#622C22semidirect
45. C4×#622C22semidirect
46. #63743C22semidirect
47. #63742C22semidirect
48. #63742C22semidirect
49. #63740C22semidirect
50. #63740C22semidirect
51. #63740C22semidirect
52. #63740C22semidirect
520. C32#3296semidirect

Maximal subgroups

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

subgroupindex
#105952252
#105951202
D4×#6222
#105935272
#105935262
#105935242
#105935232
#105935042
#105934982
#105934942
C2×#637392
#105934402
#105934332
#105933642
#105933532
#32969