Subgroups — #20295458

Order 6976.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812721	C₂	1	2	yes	maximal, complemented
2	Dic₈₇₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#16812644	C₂	1	2	yes	maximal, complemented
4	D₁₇₄₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₆×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#13182029	—	2	2	no	—
7	Dic₄₃₆	C₂²	1	2	yes	—
8	#13182018	—	2	2	no	—
9	D₈₇₂	C₂²	1	2	yes	—
10	C₂×C₈×C₁₀₉	C₂²	1	1	yes	characteristic
11	C₁₆×C₁₀₉	C₂²	1	1	yes	characteristic
12	C₁₆×C₁₀₉	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₁₀₉	D₄	1	1	yes	characteristic
14	C₂²⋊D₁₀₉	—	4	2	no	—
15	D₄₃₆	—	2	2	no	—
16	C₄×D₁₀₉	—	4	2	no	—
17	Dic₂₁₈	—	2	2	no	—
18	C₈×C₁₀₉	D₄	1	1	yes	characteristic
19	C₈×C₁₀₉	C₂³	1	1	yes	characteristic
20	C₂²×C₁₀₉	D₈	1	1	yes	characteristic
21	C₂×D₁₀₉	—	4	2	no	—
22	C₄×C₁₀₉	D₈	1	1	yes	characteristic
23	C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
24	Dic₁₀₉	—	4	2	no	—
25	C₂×C₁₀₉	—	2	1	no	—
26	C₂×C₁₀₉	C₂×D₈	1	1	yes	characteristic
27	D₁₀₉	—	8	2	no	—
28	C₁₀₉	#508	1	1	yes	characteristic, complemented, Sylow
29	#508	—	109	1	no	maximal, Sylow
30	#135	—	109	2	no	—
31	Q₃₂	—	109	1	no	—
32	SD₃₂	—	109	2	no	—
33	D₁₆	—	109	1	no	—
34	C₂×C₁₆	D₁₀₉	1	1	yes	characteristic, complemented
35	#41	—	218	2	no	—
36	Q₁₆	—	109	2	no	—
37	SD₁₆	—	218	2	no	—
38	D₈	—	109	2	no	—
39	C₂×C₈	C₂×D₁₀₉	1	1	yes	characteristic
40	C₁₆	C₂×D₁₀₉	1	1	yes	characteristic
41	C₁₆	C₂×D₁₀₉	1	1	yes	characteristic
42	Q₈	—	218	2	no	—
43	D₄	—	436	2	no	—
44	D₄	—	218	2	no	—
45	C₂×C₄	—	436	2	no	—
46	C₂×C₄	D₄₃₆	1	1	yes	characteristic
47	C₈	D₄₃₆	1	1	yes	characteristic
48	C₈	C₂²×D₁₀₉	1	1	yes	characteristic
49	C₂²	—	436	2	no	—
50	C₂²	D₈₇₂	1	1	yes	characteristic
51	C₄	—	436	2	no	—
52	C₄	D₈₇₂	1	1	yes	characteristic
53	C₄	C₂×D₄₃₆	1	1	yes	characteristic
54	C₂	—	2	1	no	—
55	C₂	—	872	2	no	—
56	C₂	C₂×D₈₇₂	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₈₇₂
commutator	C₈×C₁₀₉	C₂³
Frattini	C₈	C₂²×D₁₀₉
Fitting	C₂×C₁₆×C₁₀₉	C₂
socle	C₂×C₁₀₉	C₂×D₈
hypercenter	C₂×C₁₆	D₁₀₉
hypocenter	C₁₀₉	#508
LCS	G ▷ C₈×C₁₀₉ ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
1. #16812721	C₂	semidirect
2. Dic₈₇₂	C₂	semidirect
3. #16812644	C₂	semidirect
4. D₁₇₄₄	C₂	semidirect
5. C₂×C₁₆×C₁₀₉	C₂	semidirect
28. C₁₀₉	#508	semidirect
34. C₂×C₁₆	D₁₀₉	semidirect