Subgroups — #27197454

Order 13184.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20268224	C₂	1	2	yes	maximal, complemented
2	#20267628	C₂	1	2	yes	maximal, complemented
3	D₃₂₉₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₂×D₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
5	Q₆₄×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#15693044	—	2	2	no	—
7	#15692964	—	2	2	no	—
8	D₁₆₄₈	C₂²	1	2	yes	—
9	C₁₆×D₁₀₃	C₂²	1	1	yes	characteristic
10	C₁₀₃⋊C₃₂	C₂²	1	1	yes	characteristic
11	Q₃₂×C₁₀₃	C₂²	1	2	yes	—
12	C₃₂×C₁₀₃	C₂²	1	1	yes	characteristic
13	#13110106	—	4	2	no	—
14	#13110092	—	4	2	no	—
15	D₈₂₄	—	2	2	no	—
16	C₈×D₁₀₃	D₄	1	1	yes	characteristic
17	C₁₀₃⋊C₁₆	D₄	1	1	yes	characteristic
18	Q₁₆×C₁₀₃	—	2	2	no	—
19	C₁₆×C₁₀₃	C₂³	1	1	yes	characteristic
20	Q₈×C₁₀₃	—	4	2	no	—
21	D₄₁₂	—	4	2	no	—
22	D₄₁₂	—	8	2	no	—
23	C₄×D₁₀₃	—	8	2	no	—
24	C₄×D₁₀₃	D₈	1	1	yes	characteristic
25	C₈×C₁₀₃	C₂×D₄	1	1	yes	characteristic
26	C₁₀₃⋊C₈	D₈	1	1	yes	characteristic
27	C₂×D₁₀₃	—	8	2	no	—
28	C₂×D₁₀₃	D₁₆	1	1	yes	characteristic
29	C₄×C₁₀₃	—	8	2	no	—
30	C₄×C₁₀₃	C₂×D₈	1	1	yes	characteristic
31	Dic₁₀₃	D₁₆	1	1	yes	characteristic
32	C₂×C₁₀₃	C₂×D₁₆	1	1	yes	characteristic
33	D₁₀₃	—	2	1	no	—
34	D₁₀₃	—	16	2	no	—
35	#2262	—	103	1	no	maximal, Sylow
36	C₁₀₃	#2262	1	1	yes	characteristic, complemented, Sylow
37	#508	—	103	2	no	—
38	Q₆₄	D₁₀₃	1	1	yes	characteristic, complemented
39	SD₆₄	—	103	2	no	—
40	D₃₂	—	103	1	no	—
41	C₂×C₃₂	—	103	1	no	—
42	#135	—	206	2	no	—
43	Q₃₂	C₂×D₁₀₃	1	2	yes	—
44	SD₃₂	—	206	2	no	—
45	D₁₆	—	103	2	no	—
46	C₂×C₁₆	—	103	1	no	—
47	C₃₂	—	103	1	no	—
48	C₃₂	C₂×D₁₀₃	1	1	yes	characteristic
49	#41	—	412	2	no	—
50	Q₁₆	—	2	2	no	—
51	SD₁₆	—	412	2	no	—
52	D₈	—	206	2	no	—
53	C₂×C₈	—	103	1	no	—
54	C₁₆	—	103	1	no	—
55	C₁₆	C₂²×D₁₀₃	1	1	yes	characteristic
56	Q₈	—	4	2	no	—
57	D₄	—	824	2	no	—
58	D₄	—	412	2	no	—
59	C₂×C₄	—	824	2	no	—
60	C₂×C₄	—	103	1	no	—
61	C₈	—	103	1	no	—
62	C₈	D₄×D₁₀₃	1	1	yes	characteristic
63	C₂²	—	824	2	no	—
64	C₂²	—	103	1	no	—
65	C₄	—	8	2	no	—
66	C₄	—	103	1	no	—
67	C₄	D₈×D₁₀₃	1	1	yes	characteristic
68	C₂	—	1648	2	no	—
69	C₂	—	206	1	no	—
70	C₂	D₁₆×D₁₀₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₆×D₁₀₃
commutator, cosocle	C₁₆×C₁₀₃	C₂³
Frattini	C₁₆	C₂²×D₁₀₃
Fitting	Q₆₄×C₁₀₃	C₂
socle	C₂×C₁₀₃	C₂×D₁₆
hypercenter	Q₆₄	D₁₀₃
hypocenter	C₁₀₃	#2262
LCS	G ▷ C₁₆×C₁₀₃ ▷ C₈×C₁₀₃ ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₆₄

Complements

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

N	H ≅ G/N	type
1. #20268224	C₂	semidirect
2. #20267628	C₂	semidirect
3. D₃₂₉₆	C₂	semidirect
4. C₃₂×D₁₀₃	C₂	semidirect
5. Q₆₄×C₁₀₃	C₂	semidirect
36. C₁₀₃	#2262	semidirect
38. Q₆₄	D₁₀₃	semidirect

Maximal subgroups

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

subgroup	index
#20268224	2
#20267628	2
D₃₂₉₆	2
C₃₂×D₁₀₃	2
Q₆₄×C₁₀₃	2
#2262	103