Subgroups — #20295930

Order 6976.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812758	C₂	1	2	yes	maximal, complemented
2	#16812695	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊#89137	—	2	2	no	—
4	C₂×D₄₃₆	C₂²	1	1	yes	characteristic
5	C₂×C₂²⋊D₁₀₉	—	2	2	no	—
6	C₄×Dic₁₀₉	C₄	1	1	yes	characteristic, complemented
7	C₂×D₄×C₁₀₉	C₄	1	1	yes	characteristic, complemented
8	C₂³×C₁₀₉	—	2	1	no	—
9	C₂²×D₁₀₉	D₄	1	2	yes	—
10	C₂×#89137	—	4	2	no	—
11	D₄×C₁₀₉	—	4	1	no	—
12	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
13	C₂²⋊D₁₀₉	—	4	4	no	—
14	C₂×Dic₁₀₉	—	2	1	no	—
15	D₄₃₆	—	4	1	no	—
16	C₂²×C₁₀₉	—	4	2	no	—
17	C₂²×C₁₀₉	—	4	1	no	—
18	C₂²×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×D₁₀₉	—	2	2	no	—
20	C₂×D₁₀₉	—	4	2	no	—
21	#89137	—	8	2	no	—
22	C₄×C₁₀₉	—	2	1	no	—
23	Dic₁₀₉	—	2	2	no	—
24	C₂×C₁₀₉	—	2	1	no	—
25	C₂×C₁₀₉	—	8	1	no	—
26	C₂×C₁₀₉	#99	1	1	yes	characteristic
27	D₁₀₉	—	4	2	no	—
28	C₁₀₉	#353	1	1	yes	characteristic, complemented, Sylow
29	#353	—	109	1	no	maximal, Sylow
30	#127	—	109	1	no	—
31	#99	—	109	2	no	—
32	C₂×D₄	—	109	1	no	—
33	C₂×D₄	—	218	2	no	—
34	C₂×D₄	#89137	1	1	yes	characteristic, complemented
35	C₂²⋊C₄	—	218	2	no	—
36	C₄²	—	109	1	no	—
37	C₂³	—	2	1	no	—
38	C₂³	—	109	2	no	—
39	D₄	—	4	1	no	—
40	D₄	—	436	1	no	—
41	D₄	—	436	4	no	—
42	C₂×C₄	—	436	2	no	—
43	C₂×C₄	—	218	1	no	—
44	C₂×C₄	C₂×#89137	1	1	yes	characteristic
45	C₂²	—	4	2	no	—
46	C₂²	—	4	1	no	—
47	C₂²	—	436	2	no	—
48	C₂²	—	218	2	no	—
49	C₂²	C₂²⋊#89137	1	1	yes	characteristic
50	C₄	—	2	1	no	—
51	C₄	—	872	2	no	—
52	C₄	—	218	2	no	—
53	C₂	—	2	1	no	—
54	C₂	—	8	1	no	—
55	C₂	—	436	2	no	—
56	C₂	#16812757	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16812757
commutator	C₂×C₄×C₁₀₉	C₂×C₄
Frattini	C₂×C₄	C₂×#89137
Fitting	C₂×D₄×C₁₀₉	C₄
socle	C₂×C₁₀₉	#99
hypercenter	C₂×D₄	#89137
hypocenter	C₁₀₉	#353
LCS	G ▷ C₂×C₄×C₁₀₉ ▷ C₂²×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
1. #16812758	C₂	semidirect
6. C₄×Dic₁₀₉	C₄	semidirect
7. C₂×D₄×C₁₀₉	C₄	semidirect
28. C₁₀₉	#353	semidirect
34. C₂×D₄	#89137	semidirect