Subgroups — #20296073

Order 6976.

104 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	#16812769	C₂	1	1	yes	maximal, characteristic, complemented
3	#16812763	C₂	1	2	yes	maximal, complemented
4	#16812753	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	2	yes	—
24	C₈×C₁₀₉	C₂×C₄	1	1	yes	characteristic
25	#11724784	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₁₀₉	—	2	2	no	—
27	C₂×D₁₀₉	#41	1	1	yes	characteristic
28	#89137	—	4	1	no	—
29	C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
30	Dic₁₀₉	—	2	2	no	—
31	Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
32	C₂×C₁₀₉	—	4	2	no	—
33	C₂×C₁₀₉	C₄×D₄	1	1	yes	characteristic
34	D₁₀₉	—	2	1	no	—
35	C₁₀₉	#444	1	1	yes	characteristic, complemented, Sylow
36	#444	—	109	1	no	maximal, Sylow
37	#135	—	109	1	no	—
38	#131	—	109	2	no	—
39	#108	—	109	1	no	—
40	#104	—	109	2	no	—
41	#97	—	109	1	no	—
42	#41	—	109	2	no	—
43	Q₁₆	—	109	1	no	—
44	SD₁₆	—	109	2	no	—
45	D₈	#89137	1	1	yes	characteristic, complemented
46	M₁₆	—	109	2	no	—
47	M₁₆	—	218	2	no	—
48	C₂×C₈	—	109	1	no	—
49	C₂×C₈	—	109	1	no	—
50	C₂×C₈	—	218	2	no	—
51	C₄²	—	109	1	no	—
52	Q₈	—	109	2	no	—
53	D₄	—	218	2	no	—
54	D₄	C₂×#89137	1	2	yes	—
55	C₂×C₄	—	109	1	no	—
56	C₂×C₄	—	218	2	no	—
57	C₂×C₄	—	218	1	no	—
58	C₈	—	109	2	no	—
59	C₈	—	109	1	no	—
60	C₈	—	218	2	no	—
61	C₈	C₂×#89137	1	1	yes	characteristic
62	C₂²	—	2	2	no	—
63	C₂²	—	109	1	no	—
64	C₄	—	109	1	no	—
65	C₄	—	436	1	no	—
66	C₄	—	218	2	no	—
67	C₄	C₂²×#89137	1	1	yes	characteristic
68	C₂	—	4	2	no	—
69	C₂	—	218	1	no	—
70	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	#444
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. #16812769	C₂	semidirect
3. #16812763	C₂	semidirect
4. #16812753	C₂	semidirect
12. Dic₄₃₆	C₄	semidirect
13. #13182017	C₄	semidirect
15. D₈×C₁₀₉	C₄	semidirect
35. C₁₀₉	#444	semidirect
45. D₈	#89137	semidirect