Subgroups — C₂×C₈×#89137 #20295980

Order 6976.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₈	#89137
commutator, hypocenter	C₁₀₉	C₂×C₄×C₈
Frattini	C₄	C₂²×#89137
Fitting	C₂×C₈×C₁₀₉	C₄
socle	C₂²×C₁₀₉	C₄²
LCS	G ▷ C₁₀₉
UCS	C₁ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
3. C₈×#89137	C₂	direct (N × H)
6. D₁₀₉⋊C₈	C₄	semidirect
8. C₂×#11724786	C₄	semidirect
12. C₂×#11724784	C₄	semidirect
13. C₈×D₁₀₉	C₄	semidirect
15. C₂×C₈×C₁₀₉	C₄	semidirect
17. C₂×#89137	C₈	direct (N × H)
25. #11724786	C₂×C₄	semidirect
26. C₈×C₁₀₉	C₂×C₄	semidirect
27. #11724784	C₂×C₄	semidirect
32. #89137	C₂×C₈	direct (N × H)
37. C₂×C₁₀₉	C₄×C₈	semidirect
39. D₁₀₉	C₄×C₈	semidirect
41. C₁₀₉	C₂×C₄×C₈	semidirect
55. C₂×C₈	#89137	direct (N × H)
69. C₈	C₂×#89137	direct (N × H)
81. C₂	C₈×#89137	direct (N × H)

Subgroups — C2×C8×#89137 #20295980

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₈×#89137 #20295980