Subgroups — #20268153

Order 6592.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15693009	C₂	1	1	yes	maximal, characteristic
2	#15692944	C₂	1	2	yes	maximal, complemented
3	#15692941	C₂	1	2	yes	maximal
4	#15692932	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄⋊Q₈×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₂₀₆	C₂²	1	1	yes	characteristic
7	C₂×D₄₁₂	C₂²	1	1	yes	characteristic
8	C₂×C₁₀₃⋊C₈	C₂²	1	2	yes	—
9	(C₂×D₁₀₃)⋊C₄	—	2	1	no	—
10	(C₂×D₁₀₃)⋊C₄	—	2	1	no	—
11	C₂×Q₈×C₁₀₃	—	2	1	no	—
12	C₄⋊C₄×C₁₀₃	—	2	1	no	—
13	C₄⋊C₄×C₁₀₃	C₂²	1	2	yes	—
14	C₄²×C₁₀₃	C₂²	1	1	yes	characteristic
15	C₂²×D₁₀₃	—	2	1	no	—
16	Q₈×C₁₀₃	—	4	2	no	—
17	C₂×C₄×C₁₀₃	—	2	2	no	—
18	C₂×C₄×C₁₀₃	D₄	1	1	yes	characteristic
19	C₂×C₄×C₁₀₃	D₄	1	1	yes	characteristic
20	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
21	C₂×Dic₁₀₃	—	2	1	no	—
22	D₄₁₂	—	2	2	no	—
23	Dic₂₀₆	—	2	2	no	—
24	C₁₀₃⋊C₈	—	2	2	no	—
25	C₂²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
26	C₂×D₁₀₃	—	4	1	no	—
27	C₂×D₁₀₃	—	4	1	no	—
28	C₂×D₁₀₃	—	4	1	no	—
29	C₄×C₁₀₃	—	2	1	no	—
30	C₄×C₁₀₃	—	2	1	no	—
31	C₄×C₁₀₃	—	4	2	no	—
32	C₄×C₁₀₃	#41	1	2	yes	—
33	Dic₁₀₃	—	4	1	no	—
34	C₂×C₁₀₃	#124	1	1	yes	characteristic
35	C₂×C₁₀₃	AGL(1,ℤ/8)	1	1	yes	characteristic
36	C₂×C₁₀₃	#137	1	1	yes	characteristic
37	D₁₀₃	—	8	1	no	—
38	C₁₀₃	#489	1	1	yes	characteristic, complemented, Sylow
39	#489	—	103	1	no	maximal, Sylow
40	C₄⋊Q₈	D₁₀₃	1	1	yes	characteristic, complemented
41	#124	—	103	1	no	—
42	#103	—	103	2	no	—
43	#102	—	103	2	no	—
44	#97	—	103	1	no	—
45	C₂×Q₈	—	2	1	no	—
46	C₂×Q₈	—	103	1	no	—
47	C₂×D₄	—	103	1	no	—
48	C₂×C₈	—	103	2	no	—
49	C₄⋊C₄	—	2	1	no	—
50	C₄⋊C₄	C₂×D₁₀₃	1	2	yes	—
51	C₂²⋊C₄	—	206	1	no	—
52	C₂²⋊C₄	—	206	1	no	—
53	C₄²	C₂×D₁₀₃	1	1	yes	characteristic
54	C₂³	—	206	1	no	—
55	Q₈	—	4	2	no	—
56	Q₈	—	206	2	no	—
57	D₄	—	206	2	no	—
58	C₂×C₄	—	2	2	no	—
59	C₂×C₄	—	206	1	no	—
60	C₂×C₄	C₂²⋊D₁₀₃	1	1	yes	characteristic
61	C₂×C₄	C₂²⋊D₁₀₃	1	1	yes	characteristic
62	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
63	C₈	—	206	2	no	—
64	C₂²	—	412	1	no	—
65	C₂²	—	412	1	no	—
66	C₂²	—	412	1	no	—
67	C₂²	C₂×C₂²⋊D₁₀₃	1	1	yes	characteristic
68	C₄	—	2	1	no	—
69	C₄	—	2	1	no	—
70	C₄	—	4	2	no	—
71	C₄	—	412	1	no	—
72	C₄	#13110106	1	2	yes	—
73	C₂	—	824	1	no	—
74	C₂	#15693010	1	1	yes	characteristic
75	C₂	#15693047	1	1	yes	characteristic
76	C₂	#15693052	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₁₀₃
commutator	C₂×C₄×C₁₀₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₃
Fitting	C₄⋊Q₈×C₁₀₃	C₂
socle	C₂²×C₁₀₃	C₂×D₄
hypercenter	C₄⋊Q₈	D₁₀₃
hypocenter	C₁₀₃	#489
LCS	G ▷ C₂×C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
2. #15692944	C₂	semidirect
4. #15692932	C₂	semidirect
5. C₄⋊Q₈×C₁₀₃	C₂	semidirect
38. C₁₀₃	#489	semidirect
40. C₄⋊Q₈	D₁₀₃	semidirect