Subgroups — #20294839

Order 6976.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812639	C₂	1	1	yes	maximal, characteristic, complemented
2	#16812635	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₈×C₁₀₉	C₂	1	1	yes	maximal, characteristic
4	#13182013	—	2	1	no	—
5	#13182004	—	2	1	no	—
6	C₂×D₄×C₁₀₉	—	2	1	no	—
7	D₈×C₁₀₉	—	2	1	no	—
8	D₈×C₁₀₉	C₄	1	2	yes	—
9	C₂×C₈×C₁₀₉	C₂²	1	1	yes	characteristic
10	C₂³×C₁₀₉	—	4	1	no	—
11	D₄×C₁₀₉	—	2	2	no	—
12	D₄×C₁₀₉	—	4	1	no	—
13	C₂×C₄×C₁₀₉	D₄	1	1	yes	characteristic
14	C₈×C₁₀₉	C₂×C₄	1	1	yes	characteristic
15	C₈×C₁₀₉	D₄	1	1	yes	characteristic
16	#11724784	—	4	1	no	—
17	C₂²×C₁₀₉	—	4	2	no	—
18	C₂²×C₁₀₉	—	8	2	no	—
19	C₂²×C₁₀₉	SD₁₆	1	1	yes	characteristic
20	C₄×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₁₀₉	D₈	1	1	yes	characteristic
22	C₂×C₁₀₉	—	2	1	no	—
23	C₂×C₁₀₉	—	8	2	no	—
24	C₂×C₁₀₉	#102	1	1	yes	characteristic
25	C₁₀₉	#361	1	1	yes	characteristic, complemented, Sylow
26	#361	—	109	1	no	maximal, Sylow
27	C₂×D₈	D₁₀₉	1	1	yes	characteristic
28	M₃₂	—	109	1	no	—
29	#108	—	109	1	no	—
30	C₂×D₄	—	2	1	no	—
31	D₈	—	2	1	no	—
32	D₈	Dic₁₀₉	1	2	yes	—
33	M₁₆	—	218	1	no	—
34	C₂×C₈	C₂×D₁₀₉	1	1	yes	characteristic
35	C₁₆	—	218	1	no	—
36	C₂³	—	4	1	no	—
37	D₄	—	2	2	no	—
38	D₄	—	4	1	no	—
39	C₂×C₄	C₂²⋊D₁₀₉	1	1	yes	characteristic
40	C₈	—	436	1	no	—
41	C₈	C₂×Dic₁₀₉	1	1	yes	characteristic
42	C₈	C₂²⋊D₁₀₉	1	1	yes	characteristic
43	C₂²	—	4	2	no	—
44	C₂²	—	8	2	no	—
45	C₂²	#13182017	1	1	yes	characteristic
46	C₄	C₂²⋊Dic₁₀₉	1	1	yes	characteristic
47	C₄	#13182014	1	1	yes	characteristic
48	C₂	—	2	1	no	—
49	C₂	—	8	2	no	—
50	C₂	#16812620	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16812620
commutator	C₈×C₁₀₉	C₂×C₄
Frattini	C₂×C₈	C₂×D₁₀₉
Fitting	C₂×D₈×C₁₀₉	C₂
socle	C₂×C₁₀₉	#102
hypercenter	C₂×D₈	D₁₀₉
hypocenter	C₁₀₉	#361
LCS	G ▷ C₈×C₁₀₉ ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
1. #16812639	C₂	semidirect
2. #16812635	C₂	semidirect
25. C₁₀₉	#361	semidirect