Subgroups — #20295921

Order 6976.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13182032	C₂	1	2	yes	maximal, complemented
2	C₂×C₈×D₁₀₉	C₂	1	1	yes	maximal, characteristic
3	#13182032	—	2	2	no	—
4	C₂×C₄×D₁₀₉	C₄	1	1	yes	characteristic
5	C₂×#11724784	C₂²	1	1	yes	characteristic
6	C₈×D₁₀₉	—	2	2	no	—
7	C₂×C₈×C₁₀₉	C₄	1	1	yes	characteristic
8	C₂²×D₁₀₉	C₈	1	1	yes	characteristic
9	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
10	C₂×Dic₁₀₉	C₈	1	1	yes	characteristic
11	C₄×D₁₀₉	—	2	1	no	—
12	C₄×D₁₀₉	—	2	1	no	—
13	C₈×C₁₀₉	—	2	1	no	—
14	#11724784	D₄	1	2	yes	—
15	C₂²×C₁₀₉	C₂×C₈	1	1	yes	characteristic
16	C₂×D₁₀₉	—	2	1	no	—
17	C₂×D₁₀₉	—	2	1	no	—
18	C₂×D₁₀₉	C₁₆	1	2	yes	complemented
19	C₄×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
20	C₄×C₁₀₉	M₁₆	1	1	yes	characteristic
21	Dic₁₀₉	—	2	1	no	—
22	C₂×C₁₀₉	C₂²⋊C₈	1	1	yes	characteristic
23	C₂×C₁₀₉	C₂×C₁₆	1	1	yes	characteristic
24	C₂×C₁₀₉	M₃₂	1	1	yes	characteristic
25	D₁₀₉	—	2	2	no	—
26	C₁₀₉	C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
27	C₂²⋊C₁₆	—	109	1	no	maximal, Sylow
28	C₂²×C₈	—	109	1	no	—
29	C₂×C₁₆	—	109	2	no	—
30	C₂²×C₄	—	109	1	no	—
31	C₂×C₈	—	109	1	no	—
32	C₂×C₈	—	218	2	no	—
33	C₂×C₈	#89137	1	1	yes	characteristic
34	C₁₆	—	218	2	no	—
35	C₂³	—	109	1	no	—
36	C₂×C₄	—	109	1	no	—
37	C₂×C₄	—	218	1	no	—
38	C₂×C₄	—	218	1	no	—
39	C₂×C₄	C₂×#89137	1	1	yes	characteristic
40	C₈	—	2	1	no	—
41	C₈	—	109	2	no	—
42	C₂²	—	109	2	no	—
43	C₂²	—	218	1	no	—
44	C₂²	—	218	1	no	—
45	C₂²	D₁₀₉⋊C₈	1	1	yes	characteristic
46	C₄	—	218	1	no	—
47	C₄	C₂²⋊#89137	1	1	yes	characteristic
48	C₄	#13182039	1	1	yes	characteristic
49	C₂	—	218	2	no	—
50	C₂	#16812756	1	1	yes	characteristic
51	C₂	D₁₀₉⋊C₁₆	1	1	yes	characteristic
52	C₂	#16812774	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#89137
commutator	C₂×C₁₀₉	C₂×C₁₆
Fitting	C₂×C₈×C₁₀₉	C₄
socle	C₂²×C₁₀₉	C₂×C₈
hypercenter	C₂×C₈	#89137
hypocenter	C₁₀₉	C₂²⋊C₁₆
LCS	G ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#13182032	C₂	semidirect
18. C₂×D₁₀₉	C₁₆	semidirect
26. C₁₀₉	C₂²⋊C₁₆	semidirect