Subgroups — #20267973

Order 6592.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15693069	C₂	1	1	yes	maximal, characteristic
2	#15693052	C₂	1	2	yes	maximal, complemented
3	#15692949	C₂	1	2	yes	maximal, complemented
4	#15692940	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄⋊Q₈×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#13110106	—	2	2	no	—
7	#13110105	—	2	2	no	—
8	#13110105	C₂²	1	2	yes	—
9	Q₈×D₁₀₃	—	2	2	no	—
10	#13110095	—	2	2	no	—
11	#13110092	—	2	2	no	—
12	#13110089	C₂²	1	2	yes	—
13	C₂×Q₈×C₁₀₃	C₂²	1	1	yes	characteristic
14	C₂×Q₈×C₁₀₃	C₂²	1	1	yes	characteristic
15	C₄⋊C₄×C₁₀₃	—	2	2	no	—
16	C₄²×C₁₀₃	C₂²	1	1	yes	characteristic
17	Q₈×C₁₀₃	—	2	2	no	—
18	Q₈×C₁₀₃	—	2	2	no	—
19	C₂×C₄×C₁₀₃	—	2	1	no	—
20	C₂×C₄×C₁₀₃	—	2	1	no	—
21	C₂×C₄×C₁₀₃	D₄	1	2	yes	—
22	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
23	C₂²⋊D₁₀₃	—	2	2	no	—
24	D₄₁₂	—	2	2	no	—
25	D₄₁₂	D₄	1	2	yes	—
26	C₄×D₁₀₃	—	2	4	no	—
27	C₄×D₁₀₃	—	2	2	no	—
28	Dic₂₀₆	—	2	2	no	—
29	Dic₂₀₆	D₄	1	2	yes	—
30	C₁₀₃⋊C₈	—	2	2	no	—
31	C₂²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
32	C₂×D₁₀₃	—	2	2	no	—
33	C₄×C₁₀₃	—	2	2	no	—
34	C₄×C₁₀₃	—	2	2	no	—
35	C₄×C₁₀₃	—	4	1	no	—
36	C₄×C₁₀₃	C₂×D₄	1	2	yes	—
37	Dic₁₀₃	—	2	2	no	—
38	C₂×C₁₀₃	—	2	1	no	—
39	C₂×C₁₀₃	#120	1	1	yes	characteristic
40	D₁₀₃	—	4	2	no	—
41	C₁₀₃	#456	1	1	yes	characteristic, complemented, Sylow
42	#456	—	103	1	no	maximal, Sylow
43	2₋¹⁺⁴	—	103	1	no	—
44	#137	—	103	2	no	—
45	C₄⋊Q₈	D₁₀₃	1	1	yes	characteristic, complemented
46	#104	—	103	2	no	—
47	#101	—	103	1	no	—
48	#41	—	103	2	no	—
49	#41	—	206	2	no	—
50	#41	—	206	2	no	—
51	C₂×Q₈	—	206	2	no	—
52	C₂×Q₈	C₂×D₁₀₃	1	1	yes	characteristic
53	C₂×Q₈	C₂×D₁₀₃	1	1	yes	characteristic
54	Q₁₆	—	206	2	no	—
55	SD₁₆	—	206	2	no	—
56	M₁₆	—	103	2	no	—
57	C₄⋊C₄	—	2	2	no	—
58	C₄²	C₂×D₁₀₃	1	1	yes	characteristic
59	Q₈	—	2	2	no	—
60	Q₈	—	2	2	no	—
61	Q₈	—	103	2	no	—
62	Q₈	—	206	2	no	—
63	D₄	—	103	2	no	—
64	D₄	—	206	2	no	—
65	D₄	—	206	2	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	2	1	no	—
68	C₂×C₄	—	206	4	no	—
69	C₂×C₄	—	206	2	no	—
70	C₂×C₄	C₂²⋊D₁₀₃	1	2	yes	—
71	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
72	C₈	—	206	2	no	—
73	C₂²	—	206	2	no	—
74	C₂²	C₂×C₂²⋊D₁₀₃	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	—	2	2	no	—
77	C₄	—	4	1	no	—
78	C₄	—	206	2	no	—
79	C₄	D₄×D₁₀₃	1	2	yes	—
80	C₂	—	2	1	no	—
81	C₂	—	412	2	no	—
82	C₂	#15692989	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#15692989
commutator	C₂×C₄×C₁₀₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₃
Fitting	C₄⋊Q₈×C₁₀₃	C₂
socle	C₂×C₁₀₃	#120
hypercenter	C₄⋊Q₈	D₁₀₃
hypocenter	C₁₀₃	#456
LCS	G ▷ C₂×C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
2. #15693052	C₂	semidirect
3. #15692949	C₂	semidirect
4. #15692940	C₂	semidirect
5. C₄⋊Q₈×C₁₀₃	C₂	semidirect
41. C₁₀₃	#456	semidirect
45. C₄⋊Q₈	D₁₀₃	semidirect