Subgroups — #20295931

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	#16812696	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊#89137	—	2	2	no	—
4	C₂×D₄₃₆	—	2	2	no	—
5	C₂×D₄₃₆	C₄	1	1	yes	characteristic, complemented
6	C₂×D₄₃₆	C₂²	1	1	yes	characteristic
7	C₄²×C₁₀₉	C₄	1	1	yes	characteristic, complemented
8	C₂²×D₁₀₉	—	2	1	no	—
9	C₂²×D₁₀₉	D₄	1	2	yes	—
10	C₂×#89137	—	4	2	no	—
11	C₂×C₄×C₁₀₉	—	2	1	no	—
12	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
13	D₄₃₆	—	4	1	no	—
14	D₄₃₆	—	4	1	no	—
15	D₄₃₆	—	4	4	no	—
16	C₂²×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
17	C₂×D₁₀₉	—	2	2	no	—
18	C₂×D₁₀₉	—	4	2	no	—
19	C₂×D₁₀₉	—	4	2	no	—
20	C₂×D₁₀₉	—	4	1	no	—
21	#89137	—	8	2	no	—
22	C₄×C₁₀₉	—	2	2	no	—
23	C₄×C₁₀₉	—	2	1	no	—
24	C₂×C₁₀₉	—	2	1	no	—
25	C₂×C₁₀₉	#99	1	1	yes	characteristic
26	D₁₀₉	—	4	2	no	—
27	D₁₀₉	—	8	1	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	—	109	1	no	—
34	C₂×D₄	—	218	2	no	—
35	C₂²⋊C₄	—	218	2	no	—
36	C₄²	#89137	1	1	yes	characteristic, complemented
37	C₂³	—	109	2	no	—
38	C₂³	—	218	1	no	—
39	D₄	—	436	1	no	—
40	D₄	—	436	4	no	—
41	D₄	—	436	1	no	—
42	C₂×C₄	—	2	1	no	—
43	C₂×C₄	—	436	2	no	—
44	C₂×C₄	C₂×#89137	1	1	yes	characteristic
45	C₂²	—	436	2	no	—
46	C₂²	—	436	2	no	—
47	C₂²	—	436	1	no	—
48	C₂²	—	218	2	no	—
49	C₂²	C₂²⋊#89137	1	1	yes	characteristic
50	C₄	—	2	2	no	—
51	C₄	—	2	1	no	—
52	C₄	—	872	2	no	—
53	C₂	—	2	1	no	—
54	C₂	—	872	1	no	—
55	C₂	—	436	2	no	—
56	C₂	#16812758	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16812758
commutator	C₂×C₄×C₁₀₉	C₂×C₄
Frattini	C₂×C₄	C₂×#89137
Fitting	C₄²×C₁₀₉	C₄
socle	C₂×C₁₀₉	#99
hypercenter	C₄²	#89137
hypocenter	C₁₀₉	#353
LCS	G ▷ C₂×C₄×C₁₀₉ ▷ C₂²×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
1. #16812758	C₂	semidirect
5. C₂×D₄₃₆	C₄	semidirect
7. C₄²×C₁₀₉	C₄	semidirect
28. C₁₀₉	#353	semidirect
36. C₄²	#89137	semidirect