Subgroups — #20268027

Order 6592.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₈₂₄	C₂	1	1	yes	maximal, characteristic, complemented
2	#15692995	C₂	1	2	yes	maximal, complemented
3	#15692955	C₂	1	1	yes	maximal, characteristic, complemented
4	#15692943	C₂	1	2	yes	maximal, complemented
5	C₂²×C₈×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄₁₂	C₂²	1	2	yes	—
7	C₂×C₂²⋊D₁₀₃	—	2	2	no	—
8	D₈₂₄	—	2	2	no	—
9	C₄⋊Dic₁₀₃	C₂²	1	2	yes	—
10	(C₂×D₁₀₃)⋊C₄	—	2	2	no	—
11	C₂²×C₄×C₁₀₃	C₂²	1	1	yes	characteristic
12	C₂×C₈×C₁₀₃	—	2	2	no	—
13	C₂×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
14	C₂×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
15	C₂³×C₁₀₃	D₄	1	1	yes	characteristic
16	C₂²×D₁₀₃	—	2	2	no	—
17	C₂×C₄×C₁₀₃	—	2	1	no	—
18	C₂×C₄×C₁₀₃	—	2	1	no	—
19	C₂×C₄×C₁₀₃	D₄	1	1	yes	characteristic
20	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
21	C₂²⋊D₁₀₃	—	4	4	no	—
22	C₂×Dic₁₀₃	—	2	2	no	—
23	D₄₁₂	—	2	2	no	—
24	D₄₁₂	—	2	2	no	—
25	C₈×C₁₀₃	—	2	1	no	—
26	C₈×C₁₀₃	D₄	1	2	yes	complemented
27	C₂²×C₁₀₃	—	2	1	no	—
28	C₂²×C₁₀₃	—	2	1	no	—
29	C₂²×C₁₀₃	D₈	1	2	yes	complemented
30	C₂²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
31	C₂×D₁₀₃	—	4	2	no	—
32	C₂×D₁₀₃	—	4	2	no	—
33	C₂×D₁₀₃	—	4	2	no	—
34	C₄×C₁₀₃	—	2	1	no	—
35	C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
36	C₄×C₁₀₃	#41	1	1	yes	characteristic
37	Dic₁₀₃	—	4	2	no	—
38	C₂×C₁₀₃	—	2	2	no	—
39	C₂×C₁₀₃	#121	1	1	yes	characteristic
40	C₂×C₁₀₃	C₂×D₈	1	1	yes	characteristic
41	C₂×C₁₀₃	#135	1	1	yes	characteristic
42	D₁₀₃	—	8	2	no	—
43	C₁₀₃	#466	1	1	yes	characteristic, complemented, Sylow
44	#466	—	103	1	no	maximal, Sylow
45	C₂×D₈	—	103	1	no	—
46	C₂²×C₈	D₁₀₃	1	1	yes	characteristic, complemented
47	#121	—	103	2	no	—
48	#107	—	103	1	no	—
49	#102	—	103	2	no	—
50	C₂×D₄	—	103	2	no	—
51	C₂×D₄	—	206	2	no	—
52	C₂²×C₄	C₂×D₁₀₃	1	1	yes	characteristic
53	D₈	—	206	2	no	—
54	C₂×C₈	—	2	2	no	—
55	C₂×C₈	C₂×D₁₀₃	1	1	yes	characteristic
56	C₂×C₈	C₂×D₁₀₃	1	1	yes	characteristic
57	C₄⋊C₄	—	103	2	no	—
58	C₂²⋊C₄	—	206	2	no	—
59	C₂³	—	206	2	no	—
60	C₂³	D₄₁₂	1	1	yes	characteristic
61	D₄	—	412	4	no	—
62	D₄	—	206	2	no	—
63	D₄	—	206	2	no	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	206	2	no	—
67	C₂×C₄	D₄₁₂	1	1	yes	characteristic
68	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	C₂²⋊D₁₀₃	1	2	yes	complemented
71	C₂²	—	2	1	no	—
72	C₂²	—	2	1	no	—
73	C₂²	—	412	2	no	—
74	C₂²	—	412	2	no	—
75	C₂²	—	412	2	no	—
76	C₂²	D₈₂₄	1	2	yes	complemented
77	C₂²	C₂×D₄₁₂	1	1	yes	characteristic
78	C₄	—	2	1	no	—
79	C₄	—	412	2	no	—
80	C₄	C₂×C₂²⋊D₁₀₃	1	1	yes	characteristic
81	C₄	#13110105	1	1	yes	characteristic
82	C₂	—	2	2	no	—
83	C₂	—	824	2	no	—
84	C₂	#15692995	1	1	yes	characteristic
85	C₂	C₂×D₈₂₄	1	1	yes	characteristic
86	C₂	#15693043	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄₁₂
commutator	C₂×C₄×C₁₀₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₃
Fitting	C₂²×C₈×C₁₀₃	C₂
socle	C₂²×C₁₀₃	C₂×D₄
hypercenter	C₂²×C₈	D₁₀₃
hypocenter	C₁₀₃	#466
LCS	G ▷ C₂×C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×D₈₂₄	C₂	semidirect
2. #15692995	C₂	semidirect
3. #15692955	C₂	semidirect
4. #15692943	C₂	semidirect
5. C₂²×C₈×C₁₀₃	C₂	semidirect
26. C₈×C₁₀₃	D₄	semidirect
29. C₂²×C₁₀₃	D₈	semidirect
43. C₁₀₃	#466	semidirect
46. C₂²×C₈	D₁₀₃	semidirect
70. C₈	C₂²⋊D₁₀₃	semidirect
76. C₂²	D₈₂₄	semidirect