Subgroups — #20295403

Order 6976.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₈₇₂	C₂	1	4	yes	maximal, complemented
2	#16812696	C₂	1	2	yes	maximal, complemented
3	C₄×C₈×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄₃₆	—	2	4	no	—
5	C₂×D₄₃₆	C₂²	1	4	yes	—
6	D₈₇₂	—	2	8	no	—
7	C₂×C₈×C₁₀₉	C₂²	1	2	yes	—
8	C₄²×C₁₀₉	C₂²	1	1	yes	characteristic
9	C₂²×D₁₀₉	—	2	4	no	—
10	C₂×C₄×C₁₀₉	D₄	1	2	yes	—
11	C₂×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
12	D₄₃₆	—	2	8	no	—
13	D₄₃₆	—	4	8	no	—
14	C₈×C₁₀₉	D₄	1	4	yes	complemented
15	C₂²×C₁₀₉	C₂×D₄	1	1	yes	characteristic
16	C₂×D₁₀₉	—	4	4	no	—
17	C₂×D₁₀₉	—	4	8	no	—
18	C₄×C₁₀₉	D₈	1	4	yes	complemented
19	C₄×C₁₀₉	C₂×D₄	1	2	yes	—
20	C₂×C₁₀₉	#127	1	1	yes	characteristic
21	C₂×C₁₀₉	C₂×D₈	1	2	yes	—
22	D₁₀₉	—	8	4	no	—
23	C₁₀₉	#493	1	1	yes	characteristic, complemented, Sylow
24	#493	—	109	1	no	maximal, Sylow
25	C₂×D₈	—	109	4	no	—
26	#127	—	109	2	no	—
27	C₄×C₈	D₁₀₉	1	1	yes	characteristic, complemented
28	C₂×D₄	—	109	4	no	—
29	C₂×D₄	—	218	4	no	—
30	D₈	—	218	8	no	—
31	C₂×C₈	C₂×D₁₀₉	1	2	yes	—
32	C₄²	C₂×D₁₀₉	1	1	yes	characteristic
33	C₂³	—	218	4	no	—
34	D₄	—	436	8	no	—
35	D₄	—	218	8	no	—
36	C₂×C₄	D₄₃₆	1	2	yes	—
37	C₂×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
38	C₈	D₄₃₆	1	4	yes	complemented
39	C₂²	—	436	4	no	—
40	C₂²	—	436	8	no	—
41	C₂²	C₂×D₄₃₆	1	1	yes	characteristic
42	C₄	D₈₇₂	1	4	yes	complemented
43	C₄	C₂×D₄₃₆	1	2	yes	—
44	C₂	—	872	4	no	—
45	C₂	#16812696	1	1	yes	characteristic
46	C₂	C₂×D₈₇₂	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₄₃₆
commutator	C₂×C₄×C₁₀₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₉
Fitting	C₄×C₈×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂×D₄
hypercenter	C₄×C₈	D₁₀₉
hypocenter	C₁₀₉	#493
LCS	G ▷ C₂×C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×D₈₇₂	C₂	semidirect
2. #16812696	C₂	semidirect
3. C₄×C₈×C₁₀₉	C₂	semidirect
14. C₈×C₁₀₉	D₄	semidirect
18. C₄×C₁₀₉	D₈	semidirect
23. C₁₀₉	#493	semidirect
27. C₄×C₈	D₁₀₉	semidirect
38. C₈	D₄₃₆	semidirect
42. C₄	D₈₇₂	semidirect