Subgroups — #20295874

Order 6976.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11724786	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#11724786	C₂	1	1	yes	maximal, characteristic, complemented
3	#16812661	C₂	1	1	yes	maximal, characteristic
4	C₂×#11724786	—	2	1	no	—
5	C₂×#11724786	—	2	1	no	—
6	C₂×D₄₃₆	C₄	1	1	yes	characteristic
7	C₂×C₄×D₁₀₉	—	2	1	no	—
8	#13182006	—	2	1	no	—
9	C₄×Dic₁₀₉	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×C₁₀₉	C₄	1	1	yes	characteristic
11	C₂²×D₁₀₉	—	2	1	no	—
12	C₂×C₄×C₁₀₉	—	2	1	no	—
13	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
14	C₂×Dic₁₀₉	D₄	1	1	yes	characteristic
15	C₂×Dic₁₀₉	D₄	1	1	yes	characteristic
16	D₄₃₆	—	2	1	no	—
17	D₄₃₆	C₈	1	2	yes	complemented
18	C₄×D₁₀₉	—	4	1	no	—
19	C₄×D₁₀₉	—	4	1	no	—
20	#11724786	—	2	2	no	—
21	#11724786	—	4	1	no	—
22	C₂²×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×D₁₀₉	—	2	2	no	—
24	C₂×D₁₀₉	—	4	1	no	—
25	C₂×D₁₀₉	—	4	1	no	—
26	C₄×C₁₀₉	—	4	1	no	—
27	C₄×C₁₀₉	C₂×C₈	1	1	yes	characteristic
28	C₄×C₁₀₉	M₁₆	1	1	yes	characteristic
29	Dic₁₀₉	—	2	1	no	—
30	Dic₁₀₉	D₈	1	1	yes	characteristic
31	Dic₁₀₉	SD₁₆	1	1	yes	characteristic
32	C₂×C₁₀₉	C₂²⋊C₈	1	1	yes	characteristic
33	C₂×C₁₀₉	#102	1	1	yes	characteristic
34	C₂×C₁₀₉	#104	1	1	yes	characteristic
35	D₁₀₉	—	4	2	no	—
36	C₁₀₉	D₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
37	D₄⋊C₈	—	109	1	no	maximal, Sylow
38	C₄×D₄	—	109	1	no	—
39	C₄⋊C₈	—	109	1	no	—
40	C₄×C₈	—	109	1	no	—
41	C₂×D₄	—	109	1	no	—
42	C₂²×C₄	—	218	1	no	—
43	C₂×C₈	—	218	1	no	—
44	C₂×C₈	—	218	1	no	—
45	C₄⋊C₄	#89137	1	1	yes	characteristic
46	C₂²⋊C₄	—	218	1	no	—
47	C₄²	—	109	1	no	—
48	C₂³	—	218	1	no	—
49	D₄	—	109	2	no	—
50	D₄	—	218	1	no	—
51	C₂×C₄	—	2	1	no	—
52	C₂×C₄	—	109	1	no	—
53	C₂×C₄	—	109	1	no	—
54	C₂×C₄	—	436	1	no	—
55	C₂×C₄	—	436	1	no	—
56	C₂×C₄	C₂×#89137	1	1	yes	characteristic
57	C₈	—	436	1	no	—
58	C₈	—	218	2	no	—
59	C₂²	—	436	1	no	—
60	C₂²	—	436	1	no	—
61	C₂²	—	218	2	no	—
62	C₂²	C₂²⋊#89137	1	1	yes	characteristic
63	C₄	—	4	1	no	—
64	C₄	—	109	1	no	—
65	C₄	—	109	1	no	—
66	C₄	—	218	1	no	—
67	C₄	D₁₀₉⋊C₈	1	1	yes	characteristic
68	C₄	#13182039	1	1	yes	characteristic
69	C₂	—	436	2	no	—
70	C₂	#16812756	1	1	yes	characteristic
71	C₂	#16812761	1	1	yes	characteristic
72	C₂	#16812764	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#89137
commutator	C₄×C₁₀₉	C₂×C₈
Frattini	C₂×C₄	C₂×#89137
Fitting	C₄⋊C₄×C₁₀₉	C₄
socle	C₂²×C₁₀₉	C₂²⋊C₄
hypercenter	C₄⋊C₄	#89137
hypocenter	C₁₀₉	D₄⋊C₈
LCS	G ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₄⋊#11724786	C₂	semidirect
2. C₄×#11724786	C₂	semidirect
17. D₄₃₆	C₈	semidirect
36. C₁₀₉	D₄⋊C₈	semidirect