Subgroups — #20268158

Order 6592.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15693019	C₂	1	1	yes	maximal, characteristic
2	#15693012	C₂	1	1	yes	maximal, characteristic
3	#15692946	C₂	1	1	yes	maximal, characteristic
4	#15692945	C₂	1	1	yes	maximal, characteristic
5	#15692944	C₂	1	1	yes	maximal, characteristic
6	#15692931	C₂	1	1	yes	maximal, characteristic
7	#103×C₁₀₃	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₂₀₆	C₂²	1	1	yes	characteristic
9	C₂×C₁₀₃⋊C₈	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₁₀₃	—	2	1	no	—
11	C₄⋊Dic₁₀₃	C₂²	1	1	yes	characteristic
12	Dic₁₀₃⋊C₄	—	2	1	no	—
13	Dic₁₀₃⋊C₄	—	2	1	no	—
14	Dic₁₀₃⋊C₄	—	2	1	no	—
15	C₄×Dic₁₀₃	C₂²	1	1	yes	characteristic
16	C₂×Q₈×C₁₀₃	C₂²	1	1	yes	characteristic
17	C₂×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₁₀₃	C₂²	1	1	yes	characteristic
19	Q₈×C₁₀₃	—	2	1	no	—
20	Q₈×C₁₀₃	—	2	1	no	—
21	C₂×C₄×C₁₀₃	—	2	1	no	—
22	C₂×C₄×C₁₀₃	—	2	1	no	—
23	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
24	C₂×Dic₁₀₃	—	2	1	no	—
25	C₂×Dic₁₀₃	—	2	1	no	—
26	C₂×Dic₁₀₃	D₄	1	1	yes	characteristic
27	C₂×Dic₁₀₃	D₄	1	1	yes	characteristic
28	Dic₂₀₆	—	2	1	no	—
29	Dic₂₀₆	—	2	1	no	—
30	C₈×C₁₀₃	—	2	1	no	—
31	C₁₀₃⋊C₈	—	2	1	no	—
32	C₂²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
33	C₄×C₁₀₃	—	4	1	no	—
34	C₄×C₁₀₃	—	4	1	no	—
35	C₄×C₁₀₃	#41	1	1	yes	characteristic
36	C₄×C₁₀₃	#41	1	1	yes	characteristic
37	Dic₁₀₃	—	2	1	no	—
38	Dic₁₀₃	—	2	1	no	—
39	Dic₁₀₃	—	4	1	no	—
40	Dic₁₀₃	—	4	1	no	—
41	C₂×C₁₀₃	#124	1	1	yes	characteristic
42	C₂×C₁₀₃	#137	1	1	yes	characteristic
43	C₂×C₁₀₃	#137	1	1	yes	characteristic
44	C₁₀₃	#491	1	1	yes	characteristic, complemented, Sylow
45	#491	—	103	1	no	maximal, Sylow
46	C₄⋊Q₈	—	103	1	no	—
47	#125	—	103	1	no	—
48	#103	—	103	1	no	—
49	#103	—	103	1	no	—
50	#103	—	103	1	no	—
51	#103	D₁₀₃	1	1	yes	characteristic
52	#97	—	103	1	no	—
53	C₂×Q₈	—	103	1	no	—
54	C₂×Q₈	C₂×D₁₀₃	1	1	yes	characteristic
55	C₂×C₈	—	103	1	no	—
56	C₂×C₈	C₂×D₁₀₃	1	1	yes	characteristic
57	C₄⋊C₄	—	103	1	no	—
58	C₄⋊C₄	—	206	1	no	—
59	C₄⋊C₄	—	206	1	no	—
60	C₄⋊C₄	—	206	1	no	—
61	C₄⋊C₄	—	206	1	no	—
62	C₄⋊C₄	C₂×D₁₀₃	1	1	yes	characteristic
63	C₄²	—	103	1	no	—
64	Q₈	—	2	1	no	—
65	Q₈	—	2	1	no	—
66	Q₈	—	206	1	no	—
67	Q₈	—	206	1	no	—
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	103	1	no	—
71	C₂×C₄	—	103	1	no	—
72	C₂×C₄	—	206	1	no	—
73	C₂×C₄	—	206	1	no	—
74	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
75	C₈	—	2	1	no	—
76	C₈	—	206	1	no	—
77	C₂²	D₄×D₁₀₃	1	1	yes	characteristic
78	C₄	—	4	1	no	—
79	C₄	—	4	1	no	—
80	C₄	—	412	1	no	—
81	C₄	—	412	1	no	—
82	C₄	—	206	1	no	—
83	C₄	—	206	1	no	—
84	C₄	#13110104	1	1	yes	characteristic
85	C₄	#13110105	1	1	yes	characteristic
86	C₂	#15693007	1	1	yes	characteristic
87	C₂	#15693050	1	1	yes	characteristic
88	C₂	#15693053	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₀₃
commutator	C₂×C₄×C₁₀₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₃
Fitting	#103×C₁₀₃	C₂
socle	C₂²×C₁₀₃	C₂×D₄
hypercenter	#103	D₁₀₃
hypocenter	C₁₀₃	#491
LCS	G ▷ C₂×C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
44. C₁₀₃	#491	semidirect