Subgroups — #20294840

Order 6976.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₈₇₂	C₂	1	1	yes	maximal, characteristic
2	#16812635	C₂	1	1	yes	maximal, characteristic, complemented
3	M₃₂×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄₃₆	—	2	1	no	—
5	D₈₇₂	—	2	1	no	—
6	D₈₇₂	C₄	1	2	yes	—
7	#13182013	—	2	1	no	—
8	C₂×C₈×C₁₀₉	C₂²	1	1	yes	characteristic
9	C₁₆×C₁₀₉	—	2	1	no	—
10	C₂²×D₁₀₉	—	4	1	no	—
11	C₂×C₄×C₁₀₉	D₄	1	1	yes	characteristic
12	D₄₃₆	—	2	2	no	—
13	D₄₃₆	—	4	1	no	—
14	C₈×C₁₀₉	C₂×C₄	1	1	yes	characteristic
15	C₈×C₁₀₉	D₄	1	1	yes	characteristic
16	#11724784	—	4	1	no	—
17	C₂²×C₁₀₉	SD₁₆	1	1	yes	characteristic
18	C₂×D₁₀₉	—	4	2	no	—
19	C₂×D₁₀₉	—	8	2	no	—
20	C₄×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₁₀₉	D₈	1	1	yes	characteristic
22	C₂×C₁₀₉	—	2	1	no	—
23	C₂×C₁₀₉	#102	1	1	yes	characteristic
24	D₁₀₉	—	8	2	no	—
25	C₁₀₉	#361	1	1	yes	characteristic, complemented, Sylow
26	#361	—	109	1	no	maximal, Sylow
27	C₂×D₈	—	109	1	no	—
28	M₃₂	D₁₀₉	1	1	yes	characteristic, complemented
29	#108	—	109	1	no	—
30	C₂×D₄	—	218	1	no	—
31	D₈	—	109	2	no	—
32	D₈	—	218	1	no	—
33	M₁₆	—	218	1	no	—
34	C₂×C₈	C₂×D₁₀₉	1	1	yes	characteristic
35	C₁₆	—	2	1	no	—
36	C₂³	—	436	1	no	—
37	D₄	—	436	1	no	—
38	D₄	—	218	2	no	—
39	C₂×C₄	D₄₃₆	1	1	yes	characteristic
40	C₈	—	436	1	no	—
41	C₈	C₄×D₁₀₉	1	1	yes	characteristic
42	C₈	C₂²⋊D₁₀₉	1	1	yes	characteristic
43	C₂²	—	872	2	no	—
44	C₂²	—	436	2	no	—
45	C₂²	#13182018	1	1	yes	characteristic
46	C₄	#13182006	1	1	yes	characteristic
47	C₄	D₈₇₂	1	1	yes	characteristic
48	C₂	—	2	1	no	—
49	C₂	—	872	2	no	—
50	C₂	#16812621	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16812621
commutator	C₈×C₁₀₉	C₂×C₄
Frattini	C₂×C₈	C₂×D₁₀₉
Fitting	M₃₂×C₁₀₉	C₂
socle	C₂×C₁₀₉	#102
hypercenter	M₃₂	D₁₀₉
hypocenter	C₁₀₉	#361
LCS	G ▷ C₈×C₁₀₉ ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
2. #16812635	C₂	semidirect
3. M₃₂×C₁₀₉	C₂	semidirect
25. C₁₀₉	#361	semidirect
28. M₃₂	D₁₀₉	semidirect