Subgroups — Q₈×D₄₁₂ #20268458

Order 6592.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×D₁₀₃	C₂	1	2	yes	maximal, complemented
2	#15693021	C₂	1	3	yes	maximal, complemented
3	#15693001	C₂	1	6	yes	maximal, complemented
4	C₄×D₄₁₂	C₂	1	3	yes	maximal
5	C₄×Q₈×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₂₀₆	C₂²	1	6	yes	—
7	Q₈×D₁₀₃	—	2	8	no	—
8	C₂×D₄₁₂	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₁₀₃	C₂²	1	6	yes	—
10	C₄⋊Dic₁₀₃	C₂²	1	3	yes	—
11	C₄⋊Dic₁₀₃	C₂²	1	6	yes	—
12	(C₂×D₁₀₃)⋊C₄	C₂²	1	6	yes	—
13	C₂×Q₈×C₁₀₃	C₂²	1	1	yes	characteristic
14	C₄⋊C₄×C₁₀₃	C₂²	1	3	yes	—
15	C₄²×C₁₀₃	C₂²	1	3	yes	—
16	C₂²×D₁₀₃	C₂³	1	2	yes	—
17	Q₈×C₁₀₃	D₄	1	4	yes	complemented
18	C₂×C₄×C₁₀₃	C₂³	1	3	yes	—
19	C₂×C₄×C₁₀₃	C₂³	1	3	yes	—
20	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
21	C₂×Dic₁₀₃	C₂³	1	6	yes	—
22	D₄₁₂	Q₈	1	4	yes	direct product factor
23	C₄×D₁₀₃	—	2	12	no	—
24	Dic₂₀₆	—	2	12	no	—
25	C₂²×C₁₀₃	C₂⁴	1	1	yes	characteristic
26	C₂×D₁₀₃	—	2	2	no	—
27	C₂×D₁₀₃	—	2	2	no	—
28	C₂×D₁₀₃	C₂×Q₈	1	4	yes	complemented
29	C₄×C₁₀₃	—	2	3	no	—
30	C₄×C₁₀₃	C₂×D₄	1	6	yes	—
31	C₄×C₁₀₃	C₂×Q₈	1	2	yes	complemented
32	Dic₁₀₃	—	2	6	no	—
33	C₂×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
34	C₂×C₁₀₃	C₂²×Q₈	1	1	yes	characteristic
35	C₂×C₁₀₃	2₋¹⁺⁴	1	1	yes	characteristic
36	D₁₀₃	—	2	4	no	—
37	C₁₀₃	D₄×Q₈	1	1	yes	characteristic, complemented, Sylow
38	D₄×Q₈	—	103	1	no	maximal, Sylow
39	C₂²×Q₈	—	103	2	no	—
40	C₄⋊Q₈	—	103	3	no	—
41	C₂²⋊Q₈	—	103	6	no	—
42	C₄×Q₈	D₁₀₃	1	1	yes	characteristic, complemented
43	C₄×D₄	—	103	3	no	—
44	C₂×Q₈	—	103	6	no	—
45	C₂×Q₈	—	206	8	no	—
46	C₂×Q₈	C₂×D₁₀₃	1	1	yes	characteristic
47	C₂×D₄	—	103	1	no	—
48	C₂²×C₄	—	103	6	no	—
49	C₄⋊C₄	—	103	3	no	—
50	C₄⋊C₄	—	103	6	no	—
51	C₄⋊C₄	C₂×D₁₀₃	1	3	yes	—
52	C₂²⋊C₄	—	103	6	no	—
53	C₄²	C₂×D₁₀₃	1	3	yes	—
54	C₂³	—	103	2	no	—
55	Q₈	—	206	12	no	—
56	Q₈	D₄₁₂	1	4	yes	direct product factor
57	D₄	—	103	4	no	—
58	C₂×C₄	—	103	6	no	—
59	C₂×C₄	—	206	12	no	—
60	C₂×C₄	C₂²×D₁₀₃	1	3	yes	—
61	C₂×C₄	C₂²×D₁₀₃	1	3	yes	—
62	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
63	C₂²	—	103	4	no	—
64	C₂²	—	206	2	no	—
65	C₂²	—	206	2	no	—
66	C₂²	C₂³×D₁₀₃	1	1	yes	characteristic
67	C₄	—	2	3	no	—
68	C₄	—	206	6	no	—
69	C₄	C₂×D₄₁₂	1	6	yes	—
70	C₄	Q₈×D₁₀₃	1	2	yes	complemented
71	C₂	—	206	4	no	—
72	C₂	C₂²×D₄₁₂	1	1	yes	characteristic
73	C₂	C₂×Q₈×D₁₀₃	1	1	yes	characteristic
74	C₂	#15693068	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₁₀₃
commutator, socle	C₂²×C₁₀₃	C₂⁴
Fitting	C₄×Q₈×C₁₀₃	C₂
hypercenter	C₄×Q₈	D₁₀₃
hypocenter	C₁₀₃	D₄×Q₈
LCS	G ▷ C₂²×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈×D₁₀₃	C₂	semidirect
2. #15693021	C₂	semidirect
3. #15693001	C₂	semidirect
5. C₄×Q₈×C₁₀₃	C₂	semidirect
17. Q₈×C₁₀₃	D₄	semidirect
22. D₄₁₂	Q₈	direct (N × H)
28. C₂×D₁₀₃	C₂×Q₈	semidirect
31. C₄×C₁₀₃	C₂×Q₈	semidirect
37. C₁₀₃	D₄×Q₈	semidirect
42. C₄×Q₈	D₁₀₃	semidirect
56. Q₈	D₄₁₂	direct (N × H)
70. C₄	Q₈×D₁₀₃	semidirect

Subgroups — Q8×D412 #20268458

Conjugacy classes of subgroups

Complements

Subgroups — Q₈×D₄₁₂ #20268458