Subgroups — #20268180

Order 6592.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13110094	C₂	1	2	yes	maximal, complemented
2	C₂×D₈₂₄	C₂	1	2	yes	maximal, complemented
3	#15693018	C₂	1	1	yes	maximal, characteristic, complemented
4	#15693009	C₂	1	1	yes	maximal, characteristic, complemented
5	#97×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₂₀₆	C₂²	1	1	yes	characteristic
7	C₂×D₄₁₂	—	2	2	no	—
8	C₂×D₄₁₂	C₂²	1	1	yes	characteristic
9	C₂×D₄₁₂	C₂²	1	2	yes	—
10	#13110094	—	2	4	no	—
11	D₈₂₄	—	2	4	no	—
12	(C₂×D₁₀₃)⋊C₄	—	2	2	no	—
13	C₂×C₈×C₁₀₃	C₂²	1	2	yes	—
14	C₄²×C₁₀₃	C₂²	1	1	yes	characteristic
15	C₂²×D₁₀₃	—	2	1	no	—
16	C₂²×D₁₀₃	—	2	2	no	—
17	C₂×C₄×C₁₀₃	D₄	1	2	yes	—
18	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
19	C₂×Dic₁₀₃	—	2	1	no	—
20	D₄₁₂	—	2	2	no	—
21	D₄₁₂	—	2	2	no	—
22	D₄₁₂	—	2	2	no	—
23	D₄₁₂	—	4	4	no	—
24	Dic₂₀₆	—	2	2	no	—
25	C₈×C₁₀₃	D₄	1	4	yes	complemented
26	C₂²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
27	C₂×D₁₀₃	—	4	1	no	—
28	C₂×D₁₀₃	—	4	2	no	—
29	C₂×D₁₀₃	—	4	4	no	—
30	C₂×D₁₀₃	—	4	2	no	—
31	C₄×C₁₀₃	—	2	2	no	—
32	C₄×C₁₀₃	C₂×D₄	1	2	yes	—
33	Dic₁₀₃	—	4	1	no	—
34	C₂×C₁₀₃	#127	1	1	yes	characteristic
35	C₂×C₁₀₃	AGL(1,ℤ/8)	1	2	yes	—
36	D₁₀₃	—	8	2	no	—
37	D₁₀₃	—	8	1	no	—
38	C₁₀₃	#496	1	1	yes	characteristic, complemented, Sylow
39	#496	—	103	1	no	maximal, Sylow
40	C₂×SD₁₆	—	103	2	no	—
41	C₂×D₈	—	103	2	no	—
42	#127	—	103	1	no	—
43	#124	—	103	1	no	—
44	#97	D₁₀₃	1	1	yes	characteristic, complemented
45	C₂×Q₈	—	103	1	no	—
46	C₂×D₄	—	103	1	no	—
47	C₂×D₄	—	103	2	no	—
48	C₂×D₄	—	206	2	no	—
49	SD₁₆	—	206	4	no	—
50	D₈	—	206	4	no	—
51	C₂×C₈	C₂×D₁₀₃	1	2	yes	—
52	C₂²⋊C₄	—	206	2	no	—
53	C₄²	C₂×D₁₀₃	1	1	yes	characteristic
54	C₂³	—	206	1	no	—
55	C₂³	—	206	2	no	—
56	Q₈	—	206	2	no	—
57	D₄	—	412	4	no	—
58	D₄	—	206	2	no	—
59	D₄	—	206	2	no	—
60	D₄	—	206	2	no	—
61	C₂×C₄	—	206	1	no	—
62	C₂×C₄	D₄₁₂	1	2	yes	—
63	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
64	C₈	D₄₁₂	1	4	yes	complemented
65	C₂²	—	412	1	no	—
66	C₂²	—	412	2	no	—
67	C₂²	—	412	4	no	—
68	C₂²	—	412	2	no	—
69	C₂²	C₂×D₄₁₂	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	—	412	1	no	—
72	C₄	C₂×D₄₁₂	1	2	yes	—
73	C₂	—	824	2	no	—
74	C₂	—	824	1	no	—
75	C₂	#15693018	1	1	yes	characteristic
76	C₂	#15693049	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₄₁₂
commutator	C₂×C₄×C₁₀₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₃
Fitting	#97×C₁₀₃	C₂
socle	C₂²×C₁₀₃	C₂×D₄
hypercenter	#97	D₁₀₃
hypocenter	C₁₀₃	#496
LCS	G ▷ C₂×C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
1. C₂×#13110094	C₂	semidirect
2. C₂×D₈₂₄	C₂	semidirect
3. #15693018	C₂	semidirect
4. #15693009	C₂	semidirect
5. #97×C₁₀₃	C₂	semidirect
25. C₈×C₁₀₃	D₄	semidirect
38. C₁₀₃	#496	semidirect
44. #97	D₁₀₃	semidirect
64. C₈	D₄₁₂	semidirect