Finite Group Databasebeta

← #11889782

Subgroups — #11889782

Order 1152.

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

normal subgroups only

This group has 691 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#10594183C211yesmaximal, characteristic
2#10594168C211yesmaximal, characteristic, complemented
3#10593740C211yesmaximal, characteristic, complemented
4#10593527C211yesmaximal, characteristic, complemented
5#10593523C211yesmaximal, characteristic, complemented
6#10593500C211yesmaximal, characteristic, complemented
7C2×#63739C211yesmaximal, characteristic, complemented
8#10593441C211yesmaximal, characteristic, complemented
9#10593440C211yesmaximal, characteristic, complemented
10#10593434C211yesmaximal, characteristic, complemented
11#10593431C211yesmaximal, characteristic, complemented
12#10593368C211yesmaximal, characteristic, complemented
13#10593360C211yesmaximal, characteristic, complemented
14#10593358C211yesmaximal, characteristic, complemented
15#10593347C211yesmaximal, characteristic, complemented
16C22×#625C2211yescharacteristic
17C2×#3798C2211yescharacteristic
18C22×#622C2211yescharacteristic
19C2×#3788C2211yescharacteristic, complemented
20C2×#3776C2211yescharacteristic, complemented
21C2×#3775C2211yescharacteristic
22C2×#3775C2211yescharacteristic
23#64090C2211yescharacteristic
24C3×D3×C22⋊C4—21no—
25C3×#878—21no—
26#63982C2211yescharacteristic
27#63982C2211yescharacteristic
28#63977—21no—
29C2×#3724C2211yescharacteristic
30#63952—21no—
31#63915C2211yescharacteristic
32#63912C2211yescharacteristic
33#63906—21no—
34#63905—21no—
35C4×#625C2211yescharacteristic
36#63900C2211yescharacteristic, complemented
37#63888—21no—
38#63873C2211yescharacteristic, complemented
39#63865C2211yescharacteristic, complemented
40#63847—21no—
41#63838C2211yescharacteristic, complemented
42C22⋊#622C2211yescharacteristic
43#63778C2211yescharacteristic, complemented
44#63777C2211yescharacteristic, complemented
45C4⋊#622C2211yescharacteristic, complemented
46#63743C2211yescharacteristic, complemented
47#63743C2211yescharacteristic, complemented
48#63743C2211yescharacteristic, 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#5636—61no—
60#5490—61no—
61C23×C3×D3—21no—
62C2×#638D411yescharacteristic
63C22×C3⋊Dic3C2311yescharacteristic
64C2×C4×C3⋊D3C2311yescharacteristic
65C22×C3×Dic3—21no—
66C2×C3×C4×D3—21no—
67C2×C3×C4×D3—21no—
68C2×C3×Dic6—21no—
69C2×#627C2311yescharacteristic
70C2×#627C2311yescharacteristic
71C2×#626—21no—
72C2×#626—21no—
73C2×#625—22no—
74C2×#625—21no—
75C2×#625—41no—
76C2×#625C2311yescharacteristic
77C2×#625C2311yescharacteristic
78C2×#624—21no—
79#3798—22no—
80#3798—41no—
81C2×#622—41no—
82C2×#622C2311yescharacteristic
83C2×#622C2311yescharacteristic
84C2×#622C2311yescharacteristic
85C2×#622C2311yescharacteristic
86#3788—41no—
87#3776—41no—
88#3775—22no—
89#3775—41no—
90C32×C22⋊C4D411yescharacteristic
91#3752D411yescharacteristic
92#3750D411yescharacteristic
93C4×C3⋊Dic3C2311yescharacteristic
94C3×#217—21no—
95C3×#217—21no—
96C3×(C2×D3)⋊C4—21no—
97C3×(C2×D3)⋊C4—21no—
98C3×C4⋊Dic3—21no—
99C3×Dic3⋊C4—21no—
100C3×Dic3⋊C4—21no—
101#3724—21no—
102#3724—21no—
103#3724C2311yescharacteristic
104#3724C2311yescharacteristic
105#3724C2311yescharacteristic
106#3724C2311yescharacteristic
107Dic3⋊Dic3—21no—
108Dic3⋊Dic3—21no—
109#3722—21no—
110(C2×D3)⋊Dic3—21no—
111(C2×D3)⋊Dic3—21no—
112Dic32—21no—
113#3314—91nomaximal, Sylow
114C22×#67—61no—
115C2×#235—61no—
116C3×C22⋊Q8—61no—
117C2×C3×C22⋊C4—61no—
118#953—61no—
119#946—61no—
120#944—61no—
121#930—61no—
122#929—61no—
123C4×#67—61no—
124C4×#67—61no—
125C2×Dic3⋊C4—61no—
126#896—61no—
127#896—61no—
128D3×C4⋊C4—61no—
129#889—61no—
130#889—61no—
131#887—61no—
132#885—61no—
133#884—61no—
134#884—61no—
135#883—61no—
136#882—61no—
137#67⋊C4—61no—
138#67⋊C4—61no—
139#67⋊C4—61no—
140D3×C22⋊C4—21no—
141#878—21no—
142#878—61no—
143#878—61no—
144C23×C32C2×D411yescharacteristic
145C22×C3⋊D3C2×D411yescharacteristic
146C22×C3×D3—21no—
147C22×C3×D3—21no—
148C22×C3×D3—42no—
149C22×C3×D3—42no—
150C22×C3×D3—81no—
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D411yescharacteristic
153#638—22no—
154C2×C3⋊Dic3—21no—
155C2×C3⋊Dic3—21no—
156C2×C3⋊Dic3C2×D411yescharacteristic
157C2×C3⋊Dic3C2×D411yescharacteristic
158C2×C3⋊Dic3C2411yescharacteristic
159C4×C3⋊D3—21no—
160C4×C3⋊D3—21no—
161C2×C3×Dic3—21no—
162C2×C3×Dic3—21no—
163C2×C3×Dic3—21no—
164C2×C3×Dic3—21no—
165C2×C3×Dic3—21no—
166C2×C3×Dic3—21no—
167C2×C3×Dic3—81no—
168C3×C4×D3—42no—
169C3×C4×D3—81no—
170C3×Dic6—81no—
171#627—21no—
172#627—21no—
173#627—21no—
174#627—21no—
175#626—42no—
176#626—81no—
177#625—21no—
178#625—21no—
179#625—21no—
180#625—42no—
181#625#4112yes—
182#624—81no—
183#622—21no—
184#622—21no—
185#622—21no—
186#622—21no—
187#554—91no—
188#546—91no—
189#489—91no—
190#484—91no—
191#480—91no—
192#474—91no—
193#468—91no—
194#467—91no—
195#464—91no—
196#452—91no—
197#450—91no—
198#440—91no—
199#435—91no—
200#417—91no—
201C2×#102—91no—
202C24×C3—61no—
203C23×D3—21no—
204C2×C3×Q8—61no—
205C22×C3×C4—61no—
206C22×C3×C4—61no—
207C22×C3×C4—61no—
208C2×#67—61no—
209C2×#67—61no—
210C2×#67—61no—
211C2×#67—61no—
212C2×#67—61no—
213C2×#67—61no—
214C2×#67—61no—
215C2×#67—61no—
216C2×#67—122no—
217C2×#67—122no—
218C22×Dic3—21no—
219C22×Dic3—61no—
220C22×Dic3—61no—
221#235—122no—
222#235—122no—
223C2×D12—61no—
224C2×D12—61no—
225C2×C4×D3—21no—
226C2×C4×D3—21no—
227C2×C4×D3—61no—
228C2×C4×D3—61no—
229C2×C4×D3—61no—
230C2×C4×D3—61no—
231C2×Dic6—21no—
232C2×Dic6—61no—
233C2×Dic6—61no—
234C3×C4⋊C4—61no—
235C3×C4⋊C4—61no—
236C3×C4⋊C4—61no—
237C3×C22⋊C4—21no—
238C3×C22⋊C4—21no—
239C3×C22⋊C4—61no—
240C3×C22⋊C4—61no—
241C3×C22⋊C4—61no—
242C3×C22⋊C4—61no—
243#217—21no—
244#217—21no—
245#217—61no—
246#217—61no—
247(C2×D3)⋊C4—21no—
248(C2×D3)⋊C4—21no—
249(C2×D3)⋊C4—61no—
250(C2×D3)⋊C4—61no—
251(C2×D3)⋊C4—61no—
252(C2×D3)⋊C4—61no—
253(C2×D3)⋊C4—61no—
254(C2×D3)⋊C4—61no—
255C4⋊Dic3—21no—
256C4⋊Dic3—61no—
257C4⋊Dic3—61no—
258Dic3⋊C4—21no—
259Dic3⋊C4—21no—
260Dic3⋊C4—61no—
261Dic3⋊C4—61no—
262Dic3⋊C4—61no—
263Dic3⋊C4—61no—
264Dic3⋊C4—61no—
265Dic3⋊C4—61no—
266Dic3⋊C4—61no—
267Dic3⋊C4—61no—
268Dic3⋊C4—61no—
269Dic3⋊C4—61no—
270Dic3⋊C4—61no—
271Dic3⋊C4—61no—
272C4×Dic3—61no—
273C4×Dic3—61no—
274C4×Dic3—61no—
275C4×Dic3—61no—
276C22×C32—21no—
277C22×C32—21no—
278C22×C32#13712yes—
279C22×C32C22×D411yescharacteristic
280C2×C3⋊D3—21no—
281C2×C3⋊D3—21no—
282C2×C3⋊D3—21no—
283C2×C3×D3—22no—
284C2×C3×D3—41no—
285C2×C3×D3—41no—
286C2×C3×D3—41no—
287C2×C3×D3—41no—
288C2×C3×D3—41no—
289C2×C3×D3—84no—
290C32×C4—21no—
291C32×C4—21no—
292C3⋊Dic3—21no—
293C3⋊Dic3—21no—
294C3⋊Dic3C2×#4111yescharacteristic
295C3⋊Dic3H(5,𝔽2)11yescharacteristic
296C3×Dic3—41no—
297C3×Dic3—41no—
298C3×Dic3—41no—
299C3×Dic3—41no—
300C3×Dic3—41no—
301C3×Dic3—41no—
302C2×#41—91no—
303C22×D4—91no—
304C2×Q16—91no—
305C2×SD16—91no—
306C2×SD16—91no—
307C2×M16—91no—
308C22×C8—91no—
309C4⋊Q8—91no—
310#125—181no—
311#124—91no—
312#123—181no—
313C22⋊Q8—61no—
314C22⋊Q8—91no—
315C22⋊Q8—91no—
316C22⋊Q8—91no—
317C22⋊Q8—181no—
318#121—91no—
319#121—181no—
320#120—181no—
321C4×Q8—91no—
322C4×D4—91no—
323C4×D4—91no—
324C4×D4—181no—
325C2×C4⋊C4—91no—
326C2×C4⋊C4—91no—
327C2×C22⋊C4—61no—
328#107—91no—
329#107—91no—
330#107—91no—
331C4⋊C8—91no—
332#103—91no—
333#103—91no—
334#103—91no—
335#103—91no—
336#102—91no—
337#102—91no—
338#102—91no—
339#102—91no—
340#102—91no—
341#102—91no—
342C22⋊C8—91no—
343C22⋊C8—91no—
344#97—91no—
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—61no—
357C22×D3—61no—
358C22×D3—81no—
359C3×Q8—241no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—61no—
365C2×C3×C4—61no—
366C2×C3×C4—61no—
367C2×C3×C4—61no—
368C2×C3×C4—61no—
369C2×C3×C4—61no—
370C2×C3×C4—122no—
371C2×C3×C4—241no—
372C2×C3×C4—241no—
373#67—62no—
374#67—62no—
375#67—64no—
376#67—121no—
377#67—121no—
378#67—122no—
379#67—122no—
380#67—122no—
381#67—122no—
382#67—241no—
383C2×Dic3—21no—
384C2×Dic3—21no—
385C2×Dic3—21no—
386C2×Dic3—21no—
387C2×Dic3—21no—
388C2×Dic3—21no—
389C2×Dic3—61no—
390C2×Dic3—61no—
391C2×Dic3—61no—
392C2×Dic3—61no—
393C2×Dic3—61no—
394C2×Dic3—61no—
395C2×Dic3—81no—
396C2×Dic3—121no—
397C2×Dic3—121no—
398C2×Dic3—121no—
399C2×Dic3—121no—
400D12—122no—
401D12—241no—
402C4×D3—42no—
403C4×D3—81no—
404C4×D3—121no—
405C4×D3—121no—
406C4×D3—121no—
407C4×D3—121no—
408C4×D3—241no—
409C4×D3—241no—
410Dic6—81no—
411Dic6—121no—
412Dic6—121no—
413Dic6—121no—
414Dic6—121no—
415C2×C32—22no—
416C2×C32#54611yescharacteristic
417C2×C32C2×#13711yescharacteristic
418C2×C32#57611yescharacteristic
419C3⋊D3—41no—
420C3×D3—42no—
421C3×D3—81no—
422C24—61no—
423#41—182no—
424#41—361no—
425C2×Q8—61no—
426C2×Q8—91no—
427C2×Q8—91no—
428C2×D4—91no—
429C2×D4—91no—
430C2×D4—91no—
431C2×D4—181no—
432C2×D4—181no—
433C2×D4—181no—
434C2×D4—182no—
435C2×D4—361no—
436C22×C4—61no—
437C22×C4—61no—
438C22×C4—61no—
439C22×C4—91no—
440C22×C4—91no—
441C22×C4—181no—
442Q16—361no—
443SD16—182no—
444SD16—361no—
445M16—361no—
446C2×C8—91no—
447C2×C8—91no—
448C2×C8—91no—
449C2×C8—91no—
450C2×C8—361no—
451C4⋊C4—61no—
452C4⋊C4—61no—
453C4⋊C4—61no—
454C4⋊C4—91no—
455C4⋊C4—91no—
456C4⋊C4—91no—
457C4⋊C4—91no—
458C4⋊C4—91no—
459C4⋊C4—181no—
460C4⋊C4—181no—
461C4⋊C4—181no—
462C4⋊C4—181no—
463C22⋊C4—61no—
464C22⋊C4—61no—
465C22⋊C4—61no—
466C22⋊C4—61no—
467C22⋊C4—91no—
468C22⋊C4—181no—
469C22⋊C4—181no—
470C22⋊C4—181no—
471C22⋊C4GO+(4,𝔽2)11yescharacteristic
472C42—91no—
473C42—181no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—22no—
477C22×C3—22no—
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—62no—
496C2×D3—84no—
497C2×D3—121no—
498C2×D3—121no—
499C2×D3—121no—
500C2×D3—121no—
501C2×D3—121no—
502C3×C4—41no—
503C3×C4—41no—
504C3×C4—41no—
505C3×C4—41no—
506C3×C4—121no—
507C3×C4—121no—
508C3×C4—121no—
509C3×C4—121no—
510C3×C4—121no—
511C3×C4—121no—
512Dic3—41no—
513Dic3—41no—
514Dic3—41no—
515Dic3—41no—
516Dic3—41no—
517Dic3—41no—
518Dic3—61no—
519Dic3—61no—
520Dic3—61no—
521Dic3—61no—
522Dic3—62no—
523Dic3—121no—
524Dic3—121no—
525Dic3—121no—
526C32#331411yescharacteristic, complemented, Sylow
527C23—61no—
528C23—61no—
529C23—91no—
530C23—122no—
531C23—122no—
532C23—241no—
533C23C2×GO+(4,𝔽2)11yescharacteristic
534Q8—181no—
535Q8—181no—
536Q8—181no—
537Q8—181no—
538Q8—241no—
539D4—92no—
540D4—181no—
541D4—181no—
542D4—181no—
543D4—182no—
544D4—362no—
545D4—362no—
546D4—721no—
547C2×C4—61no—
548C2×C4—61no—
549C2×C4—61no—
550C2×C4—61no—
551C2×C4—61no—
552C2×C4—61no—
553C2×C4—91no—
554C2×C4—91no—
555C2×C4—91no—
556C2×C4—122no—
557C2×C4—181no—
558C2×C4—181no—
559C2×C4—181no—
560C2×C4—181no—
561C2×C4—241no—
562C2×C4—241no—
563C2×C4—721no—
564C2×C4C2×GO+(4,𝔽2)11yescharacteristic
565C2×C4C2×GO+(4,𝔽2)11yescharacteristic
566C8—181no—
567C8—181no—
568C8—181no—
569C8—181no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—42no—
577C2×C3—42no—
578C2×C3—122no—
579C2×C3—241no—
580D3—42no—
581D3—81no—
582D3—122no—
583D3—241no—
584C22—21no—
585C22—21no—
586C22—62no—
587C22—121no—
588C22—121no—
589C22—121no—
590C22—121no—
591C22—121no—
592C22—181no—
593C22—181no—
594C22—181no—
595C22—244no—
596C22#6422612yes—
597C22C22×GO+(4,𝔽2)11yescharacteristic
598C4—21no—
599C4—21no—
600C4—91no—
601C4—91no—
602C4—121no—
603C4—121no—
604C4—121no—
605C4—121no—
606C4—121no—
607C4—121no—
608C4—181no—
609C4—181no—
610C3—21no—
611C3—21no—
612C2—22no—
613C2—122no—
614C2—241no—
615C2—361no—
616C2C2×#6422611yescharacteristic
617C2#1059651411yescharacteristic
618C2#1059651811yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC32×C22⋊C4D4
socleC22×C32C22×D4
prime radical#10594183C2
hypercenterC22⋊C4GO+(4,𝔽2)
hypocenterC32#3314
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #10594168C2semidirect
3. #10593740C2semidirect
4. #10593527C2semidirect
5. #10593523C2semidirect
6. #10593500C2semidirect
7. C2×#63739C2semidirect
8. #10593441C2semidirect
9. #10593440C2semidirect
10. #10593434C2semidirect
11. #10593431C2semidirect
12. #10593368C2semidirect
13. #10593360C2semidirect
14. #10593358C2semidirect
15. #10593347C2semidirect
19. C2×#3788C22semidirect
20. C2×#3776C22semidirect
36. #63900C22semidirect
38. #63873C22semidirect
39. #63865C22semidirect
41. #63838C22semidirect
43. #63778C22semidirect
44. #63777C22semidirect
45. C4⋊#622C22semidirect
46. #63743C22semidirect
47. #63743C22semidirect
48. #63743C22semidirect
49. #63740C22semidirect
50. #63740C22semidirect
51. #63740C22semidirect
52. #63740C22semidirect
526. C32#3314semidirect

Maximal subgroups

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

subgroupindex
#105941832
#105941682
#105937402
#105935272
#105935232
#105935002
C2×#637392
#105934412
#105934402
#105934342
#105934312
#105933682
#105933602
#105933582
#105933472
#33149