Subgroups — Q₈×D₅₂ #11719280

Order 832.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×D₁₃	C₂	1	2	yes	maximal, complemented
2	C₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#88151	C₂	1	6	yes	maximal, complemented
4	C₄×D₅₂	C₂	1	3	yes	maximal
5	#88123	C₂	1	3	yes	maximal, complemented
6	C₂×Q₈×C₁₃	C₂²	1	1	yes	characteristic
7	Q₈×D₁₃	—	2	8	no	—
8	C₂×D₅₂	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₁₃	C₂²	1	6	yes	—
10	C₂×Dic₂₆	C₂²	1	6	yes	—
11	C₁₃×C₄⋊C₄	C₂²	1	3	yes	—
12	C₄²×C₁₃	C₂²	1	3	yes	—
13	#6103	C₂²	1	6	yes	—
14	C₄⋊Dic₁₃	C₂²	1	3	yes	—
15	C₄⋊Dic₁₃	C₂²	1	6	yes	—
16	C₂²×D₁₃	C₂³	1	2	yes	—
17	Q₈×C₁₃	D₄	1	4	yes	complemented
18	C₂×C₄×C₁₃	C₂³	1	3	yes	—
19	C₂×C₄×C₁₃	C₂³	1	3	yes	—
20	C₂×C₄×C₁₃	C₂³	1	1	yes	characteristic
21	C₂×Dic₁₃	C₂³	1	6	yes	—
22	D₅₂	Q₈	1	4	yes	direct product factor
23	C₄×D₁₃	—	2	12	no	—
24	Dic₂₆	—	2	12	no	—
25	D₄×Q₈	—	13	1	no	maximal, Sylow
26	C₂²×C₁₃	C₂⁴	1	1	yes	characteristic
27	C₂×D₁₃	—	2	2	no	—
28	C₂×D₁₃	—	2	2	no	—
29	C₂×D₁₃	C₂×Q₈	1	4	yes	complemented
30	C₄×C₁₃	—	2	3	no	—
31	C₄×C₁₃	C₂×D₄	1	6	yes	—
32	C₄×C₁₃	C₂×Q₈	1	2	yes	complemented
33	Dic₁₃	—	2	6	no	—
34	C₂²×Q₈	—	13	2	no	—
35	C₄⋊Q₈	—	13	3	no	—
36	C₂²⋊Q₈	—	13	6	no	—
37	C₄×Q₈	D₁₃	1	1	yes	characteristic, complemented
38	C₄×D₄	—	13	3	no	—
39	C₂×C₁₃	C₂²×D₄	1	1	yes	characteristic
40	C₂×C₁₃	C₂²×Q₈	1	1	yes	characteristic
41	C₂×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
42	D₁₃	—	2	4	no	—
43	C₂×Q₈	—	13	6	no	—
44	C₂×Q₈	—	26	8	no	—
45	C₂×Q₈	C₂×D₁₃	1	1	yes	characteristic
46	C₂×D₄	—	13	1	no	—
47	C₂²×C₄	—	13	6	no	—
48	C₄⋊C₄	—	13	3	no	—
49	C₄⋊C₄	—	13	6	no	—
50	C₄⋊C₄	C₂×D₁₃	1	3	yes	—
51	C₂²⋊C₄	—	13	6	no	—
52	C₄²	C₂×D₁₃	1	3	yes	—
53	C₁₃	D₄×Q₈	1	1	yes	characteristic, complemented, Sylow
54	C₂³	—	13	2	no	—
55	Q₈	—	26	12	no	—
56	Q₈	D₅₂	1	4	yes	direct product factor
57	D₄	—	13	4	no	—
58	C₂×C₄	—	13	6	no	—
59	C₂×C₄	—	26	12	no	—
60	C₂×C₄	C₂²×D₁₃	1	3	yes	—
61	C₂×C₄	C₂²×D₁₃	1	3	yes	—
62	C₂×C₄	C₂²×D₁₃	1	1	yes	characteristic
63	C₂²	—	13	4	no	—
64	C₂²	—	26	2	no	—
65	C₂²	—	26	2	no	—
66	C₂²	C₂³×D₁₃	1	1	yes	characteristic
67	C₄	—	2	3	no	—
68	C₄	—	26	6	no	—
69	C₄	C₂×D₅₂	1	6	yes	—
70	C₄	Q₈×D₁₃	1	2	yes	complemented
71	C₂	—	26	4	no	—
72	C₂	C₂²×D₅₂	1	1	yes	characteristic
73	C₂	C₂×Q₈×D₁₃	1	1	yes	characteristic
74	C₂	#88257	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁴
Fitting	C₄×Q₈×C₁₃	C₂
prime radical	C₂×D₅₂	C₂²
hypercenter	C₄×Q₈	D₁₃
hypocenter	C₁₃	D₄×Q₈
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈×D₁₃	C₂	semidirect
2. C₄×Q₈×C₁₃	C₂	semidirect
3. #88151	C₂	semidirect
5. #88123	C₂	semidirect
17. Q₈×C₁₃	D₄	semidirect
22. D₅₂	Q₈	direct (N × H)
29. C₂×D₁₃	C₂×Q₈	semidirect
32. C₄×C₁₃	C₂×Q₈	semidirect
37. C₄×Q₈	D₁₃	semidirect
53. C₁₃	D₄×Q₈	semidirect
56. Q₈	D₅₂	direct (N × H)
70. C₄	Q₈×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈×D₁₃	2
C₄×Q₈×C₁₃	2
#88151	2
C₄×D₅₂	2
#88123	2
D₄×Q₈	13

Subgroups — Q8×D52 #11719280

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×D₅₂ #11719280