Subgroups — #20295947

Order 6976.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13182032	C₂	1	2	yes	maximal
2	C₈×Dic₁₀₉	C₂	1	1	yes	maximal, characteristic
3	#13182032	—	2	2	no	—
4	C₂×#11724784	C₂²	1	1	yes	characteristic
5	C₄×Dic₁₀₉	C₄	1	1	yes	characteristic
6	C₂×C₈×C₁₀₉	C₄	1	1	yes	characteristic
7	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
8	C₂×Dic₁₀₉	C₈	1	1	yes	characteristic
9	C₂×Dic₁₀₉	C₈	1	1	yes	characteristic
10	C₈×C₁₀₉	—	2	1	no	—
11	#11724784	D₄	1	1	yes	characteristic
12	#11724784	Q₈	1	1	yes	characteristic
13	C₂²×C₁₀₉	C₂×C₈	1	1	yes	characteristic
14	C₄×C₁₀₉	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₁₀₉	M₁₆	1	1	yes	characteristic
16	Dic₁₀₉	—	2	1	no	—
17	Dic₁₀₉	C₁₆	1	2	yes	complemented
18	C₂×C₁₀₉	C₄⋊C₈	1	1	yes	characteristic
19	C₂×C₁₀₉	C₂×C₁₆	1	1	yes	characteristic
20	C₂×C₁₀₉	M₃₂	1	1	yes	characteristic
21	C₁₀₉	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₄⋊C₁₆	—	109	1	no	maximal, Sylow
23	C₂×C₁₆	—	109	2	no	—
24	C₄×C₈	—	109	1	no	—
25	C₂×C₈	—	109	1	no	—
26	C₂×C₈	#89137	1	1	yes	characteristic
27	C₄²	—	109	1	no	—
28	C₁₆	—	218	2	no	—
29	C₂×C₄	—	109	1	no	—
30	C₂×C₄	—	109	1	no	—
31	C₂×C₄	C₂×#89137	1	1	yes	characteristic
32	C₈	—	2	1	no	—
33	C₈	—	109	1	no	—
34	C₈	—	109	1	no	—
35	C₂²	D₁₀₉⋊C₈	1	1	yes	characteristic
36	C₄	—	109	2	no	—
37	C₄	—	218	1	no	—
38	C₄	C₄⋊#89137	1	1	yes	characteristic
39	C₄	#13182038	1	1	yes	characteristic
40	C₂	#16812766	1	1	yes	characteristic
41	C₂	D₁₀₉⋊C₁₆	1	1	yes	characteristic
42	C₂	#16812774	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#89137
commutator	C₂×C₁₀₉	C₂×C₁₆
Fitting	C₂×C₈×C₁₀₉	C₄
socle	C₂²×C₁₀₉	C₂×C₈
hypercenter	C₂×C₈	#89137
hypocenter	C₁₀₉	C₄⋊C₁₆
LCS	G ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
17. Dic₁₀₉	C₁₆	semidirect
21. C₁₀₉	C₄⋊C₁₆	semidirect