Subgroups — #20268181

Order 6592.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13110092	C₂	1	2	yes	maximal, complemented
2	C₂×#13110090	C₂	1	2	yes	maximal, complemented
3	#15693018	C₂	1	1	yes	maximal, characteristic, complemented
4	#15692932	C₂	1	1	yes	maximal, characteristic, complemented
5	#124×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄₁₂	—	2	2	no	—
7	C₂×D₄₁₂	C₂²	1	2	yes	—
8	#13110092	—	2	4	no	—
9	#13110090	—	2	4	no	—
10	C₂×C₁₀₃⋊C₈	C₂²	1	2	yes	—
11	C₂×Q₈×C₁₀₃	C₂²	1	1	yes	characteristic
12	C₂×D₄×C₁₀₃	C₂²	1	1	yes	characteristic
13	C₂²⋊C₄×C₁₀₃	—	2	2	no	—
14	C₄²×C₁₀₃	C₂²	1	1	yes	characteristic
15	C₂³×C₁₀₃	—	2	1	no	—
16	C₂²×D₁₀₃	—	2	2	no	—
17	Q₈×C₁₀₃	—	2	2	no	—
18	D₄×C₁₀₃	—	2	2	no	—
19	C₂×C₄×C₁₀₃	—	2	1	no	—
20	C₂×C₄×C₁₀₃	D₄	1	2	yes	—
21	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
22	D₄₁₂	—	2	2	no	—
23	D₄₁₂	—	2	2	no	—
24	D₄₁₂	—	4	4	no	—
25	C₁₀₃⋊C₈	D₄	1	4	yes	complemented
26	C₂²×C₁₀₃	—	4	1	no	—
27	C₂²×C₁₀₃	—	4	2	no	—
28	C₂²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
29	C₂×D₁₀₃	—	4	2	no	—
30	C₂×D₁₀₃	—	4	4	no	—
31	C₄×C₁₀₃	—	2	2	no	—
32	C₄×C₁₀₃	—	4	1	no	—
33	C₄×C₁₀₃	C₂×D₄	1	2	yes	—
34	C₂×C₁₀₃	—	8	1	no	—
35	C₂×C₁₀₃	#127	1	1	yes	characteristic
36	C₂×C₁₀₃	AGL(1,ℤ/8)	1	2	yes	—
37	D₁₀₃	—	8	2	no	—
38	C₁₀₃	#496	1	1	yes	characteristic, complemented, Sylow
39	#496	—	103	1	no	maximal, Sylow
40	C₂×SD₁₆	—	103	2	no	—
41	C₂×D₈	—	103	2	no	—
42	#127	—	103	1	no	—
43	#124	D₁₀₃	1	1	yes	characteristic, complemented
44	#97	—	103	1	no	—
45	C₂×Q₈	C₂×D₁₀₃	1	1	yes	characteristic
46	C₂×D₄	—	103	2	no	—
47	C₂×D₄	—	206	2	no	—
48	C₂×D₄	C₂×D₁₀₃	1	1	yes	characteristic
49	SD₁₆	—	206	4	no	—
50	D₈	—	206	4	no	—
51	C₂×C₈	—	103	2	no	—
52	C₂²⋊C₄	—	2	2	no	—
53	C₄²	C₂×D₁₀₃	1	1	yes	characteristic
54	C₂³	—	2	1	no	—
55	C₂³	—	206	2	no	—
56	Q₈	—	2	2	no	—
57	D₄	—	2	2	no	—
58	D₄	—	412	4	no	—
59	D₄	—	206	2	no	—
60	D₄	—	206	2	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	C₂²⋊D₁₀₃	1	2	yes	—
63	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
64	C₈	—	103	4	no	—
65	C₂²	—	4	1	no	—
66	C₂²	—	4	2	no	—
67	C₂²	—	412	2	no	—
68	C₂²	—	412	4	no	—
69	C₂²	C₂×C₂²⋊D₁₀₃	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	—	4	1	no	—
72	C₄	D₄×D₁₀₃	1	2	yes	—
73	C₂	—	8	1	no	—
74	C₂	—	824	2	no	—
75	C₂	#15693017	1	1	yes	characteristic
76	C₂	#15693046	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₁₀₃
commutator	C₂×C₄×C₁₀₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₃
Fitting	#124×C₁₀₃	C₂
socle	C₂²×C₁₀₃	C₂×D₄
hypercenter	#124	D₁₀₃
hypocenter	C₁₀₃	#496
LCS	G ▷ C₂×C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #124

Complements

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

N	H ≅ G/N	type
1. C₂×#13110092	C₂	semidirect
2. C₂×#13110090	C₂	semidirect
3. #15693018	C₂	semidirect
4. #15692932	C₂	semidirect
5. #124×C₁₀₃	C₂	semidirect
25. C₁₀₃⋊C₈	D₄	semidirect
38. C₁₀₃	#496	semidirect
43. #124	D₁₀₃	semidirect