Subgroups — #20295900

Order 6976.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊#89137	C₂	1	2	yes	maximal
2	C₂×C₈×D₁₀₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×#89137	—	2	2	no	—
4	C₄⋊#89137	—	2	2	no	—
5	C₄⋊#89137	C₄	1	4	yes	complemented
6	C₂×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
7	C₂×#11724784	C₄	1	1	yes	characteristic, complemented
8	C₈×D₁₀₉	—	2	2	no	—
9	C₂×C₈×C₁₀₉	C₄	1	1	yes	characteristic, complemented
10	C₂²×D₁₀₉	D₄	1	1	yes	characteristic
11	C₂×#89137	—	2	4	no	—
12	C₂×#89137	—	4	2	no	—
13	C₂×#89137	—	4	2	no	—
14	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
15	C₂×Dic₁₀₉	Q₈	1	1	yes	characteristic
16	C₄×D₁₀₉	C₂×C₄	1	2	yes	—
17	C₄×D₁₀₉	D₄	1	2	yes	—
18	C₈×C₁₀₉	—	2	1	no	—
19	#11724784	—	2	1	no	—
20	C₂²×C₁₀₉	C₄⋊C₄	1	1	yes	characteristic
21	C₂×D₁₀₉	C₂²⋊C₄	1	2	yes	—
22	C₂×D₁₀₉	D₈	1	1	yes	characteristic
23	C₂×D₁₀₉	SD₁₆	1	2	yes	—
24	C₂×D₁₀₉	Q₁₆	1	1	yes	characteristic
25	#89137	—	4	4	no	—
26	C₄×C₁₀₉	C₄²	1	1	yes	characteristic
27	C₄×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
28	Dic₁₀₉	C₄⋊C₄	1	2	yes	—
29	C₂×C₁₀₉	#95	1	1	yes	characteristic
30	C₂×C₁₀₉	#106	1	1	yes	characteristic
31	C₂×C₁₀₉	#107	1	1	yes	characteristic
32	D₁₀₉	#102	1	2	yes	—
33	D₁₀₉	#103	1	2	yes	—
34	C₁₀₉	#340	1	1	yes	characteristic, complemented, Sylow
35	#340	—	109	1	no	maximal, Sylow
36	C₂²×C₈	—	109	1	no	—
37	C₂×C₄⋊C₄	—	109	2	no	—
38	C₂²×C₄	—	109	1	no	—
39	C₂²×C₄	—	218	2	no	—
40	C₂×C₈	—	109	1	no	—
41	C₂×C₈	—	218	2	no	—
42	C₂×C₈	#89137	1	1	yes	characteristic, complemented
43	C₄⋊C₄	—	109	4	no	—
44	C₄⋊C₄	—	218	2	no	—
45	C₂³	—	109	1	no	—
46	C₂×C₄	—	109	1	no	—
47	C₂×C₄	—	109	2	no	—
48	C₂×C₄	—	109	2	no	—
49	C₂×C₄	—	436	2	no	—
50	C₂×C₄	—	436	2	no	—
51	C₂×C₄	—	218	4	no	—
52	C₂×C₄	C₂×#89137	1	1	yes	characteristic
53	C₈	—	2	1	no	—
54	C₈	—	218	1	no	—
55	C₂²	—	109	2	no	—
56	C₂²	—	109	2	no	—
57	C₂²	—	109	1	no	—
58	C₂²	—	109	1	no	—
59	C₂²	C₄⋊#89137	1	1	yes	characteristic
60	C₄	—	109	2	no	—
61	C₄	—	436	4	no	—
62	C₄	C₄×#89137	1	1	yes	characteristic
63	C₄	C₂²⋊#89137	1	1	yes	characteristic
64	C₂	—	109	2	no	—
65	C₂	—	109	2	no	—
66	C₂	(C₂×#89137)⋊C₄	1	1	yes	characteristic
67	C₂	#16812767	1	1	yes	characteristic
68	C₂	#16812768	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊#89137
commutator	C₄×C₁₀₉	C₄²
Frattini	C₂×C₄	C₂×#89137
Fitting	C₂×C₈×C₁₀₉	C₄
socle	C₂²×C₁₀₉	C₄⋊C₄
hypercenter	C₂×C₈	#89137
hypocenter	C₁₀₉	#340
LCS	G ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
5. C₄⋊#89137	C₄	semidirect
7. C₂×#11724784	C₄	semidirect
9. C₂×C₈×C₁₀₉	C₄	semidirect
34. C₁₀₉	#340	semidirect
42. C₂×C₈	#89137	semidirect