Subgroups — #20296068

Order 6976.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812786	C₂	1	2	yes	maximal, complemented
2	#16812770	C₂	1	1	yes	maximal, characteristic, complemented
3	#16812763	C₂	1	2	yes	maximal, complemented
4	C₈×#89137	C₂	1	1	yes	maximal, characteristic, complemented
5	#16812718	C₂	1	1	yes	maximal, characteristic
6	#13182039	C₂²	1	2	yes	—
7	#13182038	—	2	2	no	—
8	D₁₀₉⋊C₈	C₂²	1	1	yes	characteristic
9	C₂×#11724786	—	2	2	no	—
10	C₄×#89137	C₂²	1	1	yes	characteristic
11	#13182028	C₂²	1	2	yes	—
12	Dic₄₃₆	C₄	1	1	yes	characteristic, complemented
13	#13182017	C₄	1	2	yes	complemented
14	C₈×D₁₀₉	C₂²	1	1	yes	characteristic
15	D₈×C₁₀₉	C₄	1	1	yes	characteristic, complemented
16	C₂×#89137	—	2	1	no	—
17	D₄×C₁₀₉	C₂×C₄	1	2	yes	—
18	C₂²⋊D₁₀₉	—	2	2	no	—
19	C₂×Dic₁₀₉	—	2	2	no	—
20	C₄×D₁₀₉	C₂³	1	1	yes	characteristic
21	Dic₂₁₈	C₂×C₄	1	2	yes	—
22	#11724786	—	2	2	no	—
23	#11724786	D₄	1	1	yes	characteristic
24	#11724786	D₄	1	1	yes	characteristic
25	C₈×C₁₀₉	C₂×C₄	1	1	yes	characteristic
26	#11724784	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₁₀₉	—	2	2	no	—
28	C₂×D₁₀₉	#41	1	1	yes	characteristic
29	#89137	—	2	2	no	—
30	C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
31	Dic₁₀₉	—	2	2	no	—
32	Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
33	C₂×C₁₀₉	—	4	2	no	—
34	C₂×C₁₀₉	C₄×D₄	1	1	yes	characteristic
35	D₁₀₉	—	2	1	no	—
36	C₁₀₉	#443	1	1	yes	characteristic, complemented, Sylow
37	#443	—	109	1	no	maximal, Sylow
38	#135	—	109	1	no	—
39	#131	—	109	2	no	—
40	#108	—	109	1	no	—
41	#104	—	109	2	no	—
42	C₄×C₈	—	109	1	no	—
43	#41	—	109	2	no	—
44	Q₁₆	—	109	1	no	—
45	SD₁₆	—	109	2	no	—
46	D₈	#89137	1	1	yes	characteristic, complemented
47	M₁₆	—	109	2	no	—
48	M₁₆	—	218	2	no	—
49	C₂×C₈	—	109	1	no	—
50	C₂×C₈	—	109	1	no	—
51	C₂×C₈	—	218	2	no	—
52	C₄²	—	109	1	no	—
53	Q₈	—	109	2	no	—
54	D₄	—	218	2	no	—
55	D₄	C₂×#89137	1	2	yes	—
56	C₂×C₄	—	109	1	no	—
57	C₂×C₄	—	218	2	no	—
58	C₂×C₄	—	218	1	no	—
59	C₈	—	109	1	no	—
60	C₈	—	109	1	no	—
61	C₈	—	109	1	no	—
62	C₈	—	218	2	no	—
63	C₈	C₂×#89137	1	1	yes	characteristic
64	C₂²	—	2	2	no	—
65	C₂²	—	109	1	no	—
66	C₄	—	109	1	no	—
67	C₄	—	218	2	no	—
68	C₄	—	218	2	no	—
69	C₄	C₂²×#89137	1	1	yes	characteristic
70	C₂	—	4	2	no	—
71	C₂	—	218	1	no	—
72	C₂	D₄×#89137	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#89137
commutator	C₄×C₁₀₉	C₂²×C₄
Frattini	C₄	C₂²×#89137
Fitting	D₈×C₁₀₉	C₄
socle	C₂×C₁₀₉	C₄×D₄
hypercenter	D₈	#89137
hypocenter	C₁₀₉	#443
LCS	G ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. #16812786	C₂	semidirect
2. #16812770	C₂	semidirect
3. #16812763	C₂	semidirect
4. C₈×#89137	C₂	semidirect
12. Dic₄₃₆	C₄	semidirect
13. #13182017	C₄	semidirect
15. D₈×C₁₀₉	C₄	semidirect
36. C₁₀₉	#443	semidirect
46. D₈	#89137	semidirect