Subgroups — #20268185

Order 6592.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₄₁₂	C₂	1	2	yes	maximal, complemented
2	C₂×#13110094	C₂	1	2	yes	maximal
3	#15693021	C₂	1	1	yes	maximal, characteristic, complemented
4	#15693009	C₂	1	1	yes	maximal, characteristic
5	#97×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₂₀₆	C₂²	1	1	yes	characteristic
7	C₂×Dic₂₀₆	C₂²	1	2	yes	—
8	C₂×D₄₁₂	C₂²	1	1	yes	characteristic
9	Dic₄₁₂	—	2	4	no	—
10	#13110094	—	2	4	no	—
11	C₄⋊Dic₁₀₃	—	2	2	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	C₂×C₄×C₁₀₃	D₄	1	2	yes	—
17	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
18	C₂×Dic₁₀₃	—	2	1	no	—
19	C₂×Dic₁₀₃	—	2	2	no	—
20	D₄₁₂	—	2	2	no	—
21	Dic₂₀₆	—	2	2	no	—
22	Dic₂₀₆	—	2	2	no	—
23	Dic₂₀₆	—	2	2	no	—
24	C₈×C₁₀₃	D₄	1	4	yes	—
25	C₂²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
26	C₂×D₁₀₃	—	4	1	no	—
27	C₂×D₁₀₃	—	4	2	no	—
28	C₄×C₁₀₃	—	2	2	no	—
29	C₄×C₁₀₃	C₂×D₄	1	2	yes	—
30	Dic₁₀₃	—	4	2	no	—
31	Dic₁₀₃	—	4	1	no	—
32	C₂×C₁₀₃	#127	1	1	yes	characteristic
33	C₂×C₁₀₃	#137	1	2	yes	—
34	D₁₀₃	—	8	1	no	—
35	C₁₀₃	#497	1	1	yes	characteristic, complemented, Sylow
36	#497	—	103	1	no	maximal, Sylow
37	C₂×Q₁₆	—	103	2	no	—
38	C₂×SD₁₆	—	103	2	no	—
39	C₄⋊Q₈	—	103	1	no	—
40	#124	—	103	1	no	—
41	#97	D₁₀₃	1	1	yes	characteristic, complemented
42	C₂×Q₈	—	103	1	no	—
43	C₂×Q₈	—	103	2	no	—
44	C₂×D₄	—	103	1	no	—
45	Q₁₆	—	206	4	no	—
46	SD₁₆	—	206	4	no	—
47	C₂×C₈	C₂×D₁₀₃	1	2	yes	—
48	C₄⋊C₄	—	206	2	no	—
49	C₂²⋊C₄	—	206	2	no	—
50	C₄²	C₂×D₁₀₃	1	1	yes	characteristic
51	C₂³	—	206	1	no	—
52	Q₈	—	206	2	no	—
53	Q₈	—	206	2	no	—
54	Q₈	—	206	2	no	—
55	D₄	—	206	2	no	—
56	C₂×C₄	—	206	1	no	—
57	C₂×C₄	—	206	2	no	—
58	C₂×C₄	D₄₁₂	1	2	yes	—
59	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
60	C₈	D₄₁₂	1	4	yes	—
61	C₂²	—	412	1	no	—
62	C₂²	—	412	2	no	—
63	C₂²	C₂×D₄₁₂	1	1	yes	characteristic
64	C₄	—	2	2	no	—
65	C₄	—	412	1	no	—
66	C₄	—	412	2	no	—
67	C₄	C₂×D₄₁₂	1	2	yes	—
68	C₂	—	824	1	no	—
69	C₂	#15693018	1	1	yes	characteristic
70	C₂	#15693054	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	#497
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×Dic₄₁₂	C₂	semidirect
3. #15693021	C₂	semidirect
5. #97×C₁₀₃	C₂	semidirect
35. C₁₀₃	#497	semidirect
41. #97	D₁₀₃	semidirect