Subgroups — D₈×#89137 #20296062

Order 6976.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#89137	C₂	1	2	yes	maximal, complemented
2	#16812768	C₂	1	1	yes	maximal, characteristic, complemented
3	#16812761	C₂	1	2	yes	maximal, complemented
4	C₈×#89137	C₂	1	1	yes	maximal, characteristic, complemented
5	D₈×D₁₀₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×#89137	—	2	2	no	—
7	D₁₀₉⋊C₈	C₂²	1	1	yes	characteristic
8	C₄⋊#89137	C₂²	1	2	yes	—
9	C₂²⋊#89137	—	2	2	no	—
10	C₄×#89137	C₂²	1	1	yes	characteristic
11	D₄×D₁₀₉	C₂²	1	2	yes	—
12	D₈₇₂	C₄	1	1	yes	characteristic, complemented
13	#13182014	C₄	1	2	yes	complemented
14	C₈×D₁₀₉	C₂²	1	1	yes	characteristic
15	D₈×C₁₀₉	C₄	1	1	yes	characteristic, complemented
16	C₂²×D₁₀₉	—	2	2	no	—
17	C₂×#89137	—	2	2	no	—
18	C₂×#89137	—	4	4	no	—
19	C₂×#89137	D₄	1	1	yes	characteristic
20	C₂×#89137	D₄	1	1	yes	characteristic
21	D₄×C₁₀₉	C₂×C₄	1	2	yes	complemented
22	C₂²⋊D₁₀₉	—	2	2	no	—
23	D₄₃₆	C₂×C₄	1	2	yes	complemented
24	C₄×D₁₀₉	C₂³	1	1	yes	characteristic
25	#11724786	—	2	1	no	—
26	C₈×C₁₀₉	C₂×C₄	1	1	yes	characteristic, complemented
27	#11724784	C₂×C₄	1	1	yes	characteristic, complemented
28	C₂²×C₁₀₉	—	2	2	no	—
29	C₂×D₁₀₉	—	2	2	no	—
30	C₂×D₁₀₉	—	4	2	no	—
31	C₂×D₁₀₉	—	4	2	no	—
32	C₂×D₁₀₉	C₂×D₄	1	1	yes	characteristic
33	#89137	—	2	1	no	—
34	#89137	—	4	2	no	—
35	#89137	D₈	1	2	yes	direct product factor
36	C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
37	Dic₁₀₉	#41	1	1	yes	characteristic
38	C₂×C₁₀₉	—	4	2	no	—
39	C₂×C₁₀₉	C₄×D₄	1	1	yes	characteristic
40	D₁₀₉	—	4	2	no	—
41	D₁₀₉	C₂×D₈	1	1	yes	characteristic
42	D₁₀₉	#135	1	1	yes	characteristic
43	C₁₀₉	C₄×D₈	1	1	yes	characteristic, complemented, Sylow
44	C₄×D₈	—	109	1	no	maximal, Sylow
45	C₂×D₈	—	109	1	no	—
46	C₄×D₄	—	109	2	no	—
47	#107	—	109	1	no	—
48	#102	—	109	2	no	—
49	C₄×C₈	—	109	1	no	—
50	C₂×D₄	—	109	2	no	—
51	C₂²×C₄	—	218	2	no	—
52	D₈	—	109	2	no	—
53	D₈	—	109	1	no	—
54	D₈	#89137	1	1	yes	characteristic, direct product factor
55	C₂×C₈	—	109	1	no	—
56	C₂×C₈	—	109	1	no	—
57	C₄⋊C₄	—	109	2	no	—
58	C₂²⋊C₄	—	218	2	no	—
59	C₄²	—	109	1	no	—
60	C₂³	—	218	2	no	—
61	D₄	—	109	2	no	—
62	D₄	—	218	2	no	—
63	D₄	C₂×#89137	1	2	yes	complemented
64	C₂×C₄	—	109	1	no	—
65	C₂×C₄	—	109	1	no	—
66	C₂×C₄	—	109	1	no	—
67	C₂×C₄	—	436	4	no	—
68	C₂×C₄	—	218	2	no	—
69	C₈	—	109	1	no	—
70	C₈	—	218	1	no	—
71	C₈	C₂×#89137	1	1	yes	characteristic, complemented
72	C₂²	—	2	2	no	—
73	C₂²	—	109	1	no	—
74	C₂²	—	436	2	no	—
75	C₂²	—	436	2	no	—
76	C₂²	—	218	2	no	—
77	C₄	—	109	2	no	—
78	C₄	—	109	1	no	—
79	C₄	—	436	2	no	—
80	C₄	—	218	1	no	—
81	C₄	C₂²×#89137	1	1	yes	characteristic
82	C₂	—	4	2	no	—
83	C₂	—	109	1	no	—
84	C₂	—	109	1	no	—
85	C₂	—	436	2	no	—
86	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	C₄×D₈
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. D₄×#89137	C₂	semidirect
2. #16812768	C₂	semidirect
3. #16812761	C₂	semidirect
4. C₈×#89137	C₂	semidirect
12. D₈₇₂	C₄	semidirect
13. #13182014	C₄	semidirect
15. D₈×C₁₀₉	C₄	semidirect
21. D₄×C₁₀₉	C₂×C₄	semidirect
23. D₄₃₆	C₂×C₄	semidirect
26. C₈×C₁₀₉	C₂×C₄	semidirect
27. #11724784	C₂×C₄	semidirect
35. #89137	D₈	direct (N × H)
43. C₁₀₉	C₄×D₈	semidirect
54. D₈	#89137	direct (N × H)
63. D₄	C₂×#89137	semidirect
71. C₈	C₂×#89137	semidirect

Subgroups — D8×#89137 #20296062

Conjugacy classes of subgroups

Complements

Subgroups — D₈×#89137 #20296062