Subgroups — #20295922

Order 6976.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812773	C₂	1	2	yes	maximal, complemented
2	C₂×#13182013	C₂	1	1	yes	maximal, characteristic
3	#13182032	—	2	2	no	—
4	#13182013	—	2	2	no	—
5	C₂×#11724784	C₄	1	1	yes	characteristic
6	C₂×#11724784	C₂²	1	1	yes	characteristic
7	C₂²×C₄×C₁₀₉	C₄	1	1	yes	characteristic
8	C₂³×C₁₀₉	C₈	1	1	yes	characteristic
9	C₂×C₄×C₁₀₉	—	2	1	no	—
10	C₂×C₄×C₁₀₉	—	2	1	no	—
11	C₂×C₄×C₁₀₉	C₈	1	1	yes	characteristic
12	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
13	#11724784	—	2	1	no	—
14	#11724784	D₄	1	2	yes	—
15	C₂²×C₁₀₉	—	2	1	no	—
16	C₂²×C₁₀₉	—	4	1	no	—
17	C₂²×C₁₀₉	C₂×C₈	1	1	yes	characteristic
18	C₄×C₁₀₉	—	2	1	no	—
19	C₄×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
20	C₄×C₁₀₉	M₁₆	1	1	yes	characteristic
21	C₂×C₁₀₉	—	2	1	no	—
22	C₂×C₁₀₉	—	4	1	no	—
23	C₂×C₁₀₉	C₂²⋊C₈	1	1	yes	characteristic
24	C₁₀₉	#349	1	1	yes	characteristic, complemented, Sylow
25	#349	—	109	1	no	maximal, Sylow
26	C₂×M₁₆	—	109	1	no	—
27	M₃₂	—	109	2	no	—
28	C₂²×C₄	#89137	1	1	yes	characteristic
29	M₁₆	—	218	2	no	—
30	C₂×C₈	—	109	1	no	—
31	C₂×C₈	—	109	1	no	—
32	C₁₆	—	218	2	no	—
33	C₂³	#11724786	1	1	yes	characteristic
34	C₂×C₄	—	2	1	no	—
35	C₂×C₄	—	2	1	no	—
36	C₂×C₄	#11724786	1	1	yes	characteristic
37	C₂×C₄	C₂×#89137	1	1	yes	characteristic
38	C₈	—	109	2	no	—
39	C₈	—	218	1	no	—
40	C₂²	—	2	1	no	—
41	C₂²	—	4	1	no	—
42	C₂²	C₂×#11724786	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	C₂²⋊#89137	1	1	yes	characteristic
45	C₄	#13182038	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	4	1	no	—
48	C₂	C₂²⋊#11724786	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊#89137
commutator	C₂²×C₁₀₉	C₂×C₈
Frattini	C₂×C₄	C₂×#89137
Fitting	C₂²×C₄×C₁₀₉	C₄
socle	C₂×C₁₀₉	C₂²⋊C₈
hypercenter	C₂²×C₄	#89137
hypocenter	C₁₀₉	#349
LCS	G ▷ C₂²×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
1. #16812773	C₂	semidirect
24. C₁₀₉	#349	semidirect