Subgroups — #27194758

Order 13184.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20268168	C₂	1	1	yes	maximal, characteristic, complemented
2	#20268167	C₂	1	4	yes	maximal, complemented
3	C₈×C₁₀₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#493×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₈₂₄	—	2	2	no	—
6	C₂×#13110090	—	2	8	no	—
7	#15693018	C₂²	1	2	yes	—
8	C₄×C₁₀₃⋊C₈	C₂²	1	2	yes	—
9	C₂×D₈×C₁₀₃	—	2	2	no	—
10	#127×C₁₀₃	C₂²	1	2	yes	—
11	C₄×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
12	C₂×D₄₁₂	—	2	4	no	—
13	C₂×D₄₁₂	—	2	2	no	—
14	D₈₂₄	—	4	4	no	—
15	#13110090	—	4	16	no	—
16	C₂×C₁₀₃⋊C₈	D₄	1	4	yes	—
17	C₂×D₄×C₁₀₃	—	2	2	no	—
18	C₂×D₄×C₁₀₃	—	2	4	no	—
19	D₈×C₁₀₃	—	4	4	no	—
20	C₂×C₈×C₁₀₃	D₄	1	2	yes	—
21	C₄²×C₁₀₃	C₂³	1	1	yes	characteristic
22	C₂³×C₁₀₃	—	4	2	no	—
23	C₂²×D₁₀₃	—	4	2	no	—
24	D₄×C₁₀₃	—	4	4	no	—
25	D₄×C₁₀₃	—	4	8	no	—
26	C₂×C₄×C₁₀₃	C₂×D₄	1	2	yes	—
27	C₂×C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
28	D₄₁₂	—	4	8	no	—
29	D₄₁₂	—	4	4	no	—
30	C₈×C₁₀₃	D₈	1	4	yes	complemented
31	C₁₀₃⋊C₈	D₈	1	8	yes	complemented
32	C₂²×C₁₀₃	—	8	4	no	—
33	C₂²×C₁₀₃	—	8	2	no	—
34	C₂²×C₁₀₃	#127	1	1	yes	characteristic
35	C₂×D₁₀₃	—	8	4	no	—
36	C₂×D₁₀₃	—	8	2	no	—
37	C₄×C₁₀₃	C₂×D₈	1	4	yes	—
38	C₄×C₁₀₃	C₂×D₈	1	2	yes	—
39	C₂×C₁₀₃	—	16	2	no	—
40	C₂×C₁₀₃	#493	1	2	yes	—
41	C₂×C₁₀₃	#493	1	1	yes	characteristic
42	D₁₀₃	—	16	2	no	—
43	#1712	—	103	1	no	maximal, Sylow
44	C₁₀₃	#1712	1	1	yes	characteristic, complemented, Sylow
45	#493	—	103	4	no	—
46	#493	—	103	1	no	—
47	#493	D₁₀₃	1	1	yes	characteristic, complemented
48	C₈²	—	103	1	no	—
49	C₂×D₈	—	2	2	no	—
50	C₂×D₈	—	206	8	no	—
51	C₂×D₈	—	206	2	no	—
52	#127	—	103	2	no	—
53	#127	C₂×D₁₀₃	1	2	yes	—
54	C₄×C₈	—	103	2	no	—
55	C₄×C₈	C₂×D₁₀₃	1	1	yes	characteristic
56	C₂×D₄	—	2	4	no	—
57	C₂×D₄	—	2	2	no	—
58	C₂×D₄	—	206	4	no	—
59	C₂×D₄	—	206	2	no	—
60	D₈	—	4	4	no	—
61	D₈	—	412	16	no	—
62	D₈	—	412	4	no	—
63	C₂×C₈	—	103	4	no	—
64	C₂×C₈	C₂²⋊D₁₀₃	1	2	yes	—
65	C₄²	C₂²×D₁₀₃	1	1	yes	characteristic
66	C₂³	—	4	2	no	—
67	C₂³	—	412	2	no	—
68	D₄	—	4	8	no	—
69	D₄	—	4	4	no	—
70	D₄	—	412	8	no	—
71	D₄	—	412	4	no	—
72	C₂×C₄	D₄×D₁₀₃	1	2	yes	—
73	C₂×C₄	C₂×C₂²⋊D₁₀₃	1	1	yes	characteristic
74	C₈	—	103	8	no	—
75	C₈	#13110090	1	4	yes	complemented
76	C₂²	—	8	4	no	—
77	C₂²	—	8	2	no	—
78	C₂²	—	824	4	no	—
79	C₂²	—	824	2	no	—
80	C₂²	#15693017	1	1	yes	characteristic
81	C₄	D₈×D₁₀₃	1	4	yes	—
82	C₄	C₂×#13110090	1	2	yes	—
83	C₂	—	16	2	no	—
84	C₂	—	1648	2	no	—
85	C₂	#20268166	1	2	yes	—
86	C₂	#20268167	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#15693017
commutator, cosocle	C₄²×C₁₀₃	C₂³
Frattini	C₄²	C₂²×D₁₀₃
Fitting	#493×C₁₀₃	C₂
socle	C₂²×C₁₀₃	#127
hypercenter	#493	D₁₀₃
hypocenter	C₁₀₃	#1712
LCS	G ▷ C₄²×C₁₀₃ ▷ C₂²×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #493

Complements

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

N	H ≅ G/N	type
1. #20268168	C₂	semidirect
2. #20268167	C₂	semidirect
3. C₈×C₁₀₃⋊C₈	C₂	semidirect
4. #493×C₁₀₃	C₂	semidirect
30. C₈×C₁₀₃	D₈	semidirect
31. C₁₀₃⋊C₈	D₈	semidirect
44. C₁₀₃	#1712	semidirect
47. #493	D₁₀₃	semidirect
75. C₈	#13110090	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#20268168	2
#20268167	2
C₈×C₁₀₃⋊C₈	2
#493×C₁₀₃	2
#1712	103