Subgroups — #20295463

Order 6976.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812722	C₂	1	1	yes	maximal, characteristic, complemented
2	D₈×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#16812642	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₇₄₄	C₂	1	1	yes	maximal, characteristic, complemented
5	#16812640	C₂	1	1	yes	maximal, characteristic, complemented
6	#16812638	C₂	1	1	yes	maximal, characteristic, complemented
7	SD₃₂×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#13182030	—	2	1	no	—
9	D₄×D₁₀₉	—	2	1	no	—
10	#13182016	—	2	1	no	—
11	D₈₇₂	C₂²	1	1	yes	characteristic
12	D₈₇₂	C₂²	1	1	yes	characteristic, complemented
13	#13182014	—	2	1	no	—
14	C₈×D₁₀₉	C₂²	1	1	yes	characteristic
15	#13182004	C₂²	1	1	yes	characteristic, complemented
16	Q₁₆×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
17	D₈×C₁₀₉	C₂²	1	1	yes	characteristic
18	C₁₆×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
19	C₂²×D₁₀₉	—	4	1	no	—
20	Q₈×C₁₀₉	—	2	1	no	—
21	D₄×C₁₀₉	—	2	1	no	—
22	C₂²⋊D₁₀₉	—	4	1	no	—
23	D₄₃₆	—	2	1	no	—
24	D₄₃₆	—	2	1	no	—
25	D₄₃₆	—	4	1	no	—
26	C₄×D₁₀₉	—	4	1	no	—
27	C₄×D₁₀₉	D₄	1	1	yes	characteristic
28	C₈×C₁₀₉	C₂³	1	1	yes	characteristic
29	#11724784	D₄	1	1	yes	characteristic
30	C₂²×C₁₀₉	—	4	1	no	—
31	C₂×D₁₀₉	—	4	1	no	—
32	C₂×D₁₀₉	—	4	1	no	—
33	C₂×D₁₀₉	—	8	2	no	—
34	C₂×D₁₀₉	D₈	1	1	yes	characteristic
35	C₄×C₁₀₉	—	4	1	no	—
36	C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
37	Dic₁₀₉	D₈	1	1	yes	characteristic
38	C₂×C₁₀₉	—	8	1	no	—
39	C₂×C₁₀₉	C₂×D₈	1	1	yes	characteristic
40	D₁₀₉	—	2	1	no	—
41	D₁₀₉	—	8	1	no	—
42	D₁₀₉	—	8	1	no	—
43	C₁₀₉	#509	1	1	yes	characteristic, complemented, Sylow
44	#509	—	109	1	no	maximal, Sylow
45	#135	—	109	1	no	—
46	C₂×D₈	—	109	1	no	—
47	SD₃₂	—	109	1	no	—
48	SD₃₂	D₁₀₉	1	1	yes	characteristic, complemented
49	D₁₆	—	109	1	no	—
50	D₁₆	—	109	1	no	—
51	M₃₂	—	109	1	no	—
52	#41	—	218	1	no	—
53	C₂×D₄	—	218	1	no	—
54	Q₁₆	C₂×D₁₀₉	1	1	yes	characteristic, complemented
55	SD₁₆	—	218	1	no	—
56	D₈	—	109	1	no	—
57	D₈	—	109	1	no	—
58	D₈	—	218	1	no	—
59	D₈	C₂×D₁₀₉	1	1	yes	characteristic
60	C₂×C₈	—	109	1	no	—
61	C₁₆	—	109	1	no	—
62	C₁₆	C₂×D₁₀₉	1	1	yes	characteristic, complemented
63	C₂³	—	436	1	no	—
64	Q₈	—	2	1	no	—
65	D₄	—	2	1	no	—
66	D₄	—	436	1	no	—
67	D₄	—	436	1	no	—
68	D₄	—	218	1	no	—
69	D₄	—	218	1	no	—
70	C₂×C₄	—	109	1	no	—
71	C₂×C₄	—	436	1	no	—
72	C₈	—	109	1	no	—
73	C₈	C₂²×D₁₀₉	1	1	yes	characteristic
74	C₂²	—	4	1	no	—
75	C₂²	—	872	2	no	—
76	C₂²	—	109	1	no	—
77	C₂²	—	436	1	no	—
78	C₂²	—	436	1	no	—
79	C₄	—	4	1	no	—
80	C₄	—	109	1	no	—
81	C₄	D₄×D₁₀₉	1	1	yes	characteristic
82	C₂	—	8	1	no	—
83	C₂	—	872	1	no	—
84	C₂	—	872	1	no	—
85	C₂	—	218	1	no	—
86	C₂	D₈×D₁₀₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₁₀₉
commutator	C₈×C₁₀₉	C₂³
Frattini	C₈	C₂²×D₁₀₉
Fitting	SD₃₂×C₁₀₉	C₂
socle	C₂×C₁₀₉	C₂×D₈
hypercenter	SD₃₂	D₁₀₉
hypocenter	C₁₀₉	#509
LCS	G ▷ C₈×C₁₀₉ ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ SD₃₂

Complements

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

N	H ≅ G/N	type
1. #16812722	C₂	semidirect
2. D₈×D₁₀₉	C₂	semidirect
3. #16812642	C₂	semidirect
4. D₁₇₄₄	C₂	semidirect
5. #16812640	C₂	semidirect
6. #16812638	C₂	semidirect
7. SD₃₂×C₁₀₉	C₂	semidirect
12. D₈₇₂	C₂²	semidirect
15. #13182004	C₂²	semidirect
16. Q₁₆×C₁₀₉	C₂²	semidirect
18. C₁₆×C₁₀₉	C₂²	semidirect
43. C₁₀₉	#509	semidirect
48. SD₃₂	D₁₀₉	semidirect
54. Q₁₆	C₂×D₁₀₉	semidirect
62. C₁₆	C₂×D₁₀₉	semidirect