Subgroups — #20295894

Order 6976.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812778	C₂	1	2	yes	maximal
2	C₂×#13182012	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#89137	—	2	2	no	—
4	C₂²⋊#89137	—	2	2	no	—
5	C₄×#89137	C₄	1	4	yes	complemented
6	C₂×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
7	#13182012	—	2	2	no	—
8	C₂×#11724784	C₄	1	1	yes	characteristic, complemented
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×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
13	C₂×Dic₁₀₉	Q₈	1	1	yes	characteristic
14	C₄×D₁₀₉	C₂×C₄	1	2	yes	—
15	C₄×D₁₀₉	D₄	1	2	yes	—
16	C₈×C₁₀₉	—	2	1	no	—
17	#11724784	—	2	1	no	—
18	C₂²×C₁₀₉	C₄⋊C₄	1	1	yes	characteristic
19	C₂×D₁₀₉	—	4	1	no	—
20	C₂×D₁₀₉	C₂²⋊C₄	1	2	yes	—
21	#89137	—	4	4	no	—
22	C₄×C₁₀₉	C₄²	1	1	yes	characteristic
23	C₄×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
24	Dic₁₀₉	C₄⋊C₄	1	2	yes	—
25	C₂×C₁₀₉	—	2	1	no	—
26	C₂×C₁₀₉	#95	1	1	yes	characteristic
27	D₁₀₉	—	2	2	no	—
28	C₁₀₉	H(3,ℤ/4)	1	1	yes	characteristic, complemented, Sylow
29	H(3,ℤ/4)	—	109	1	no	maximal, Sylow
30	C₂×M₁₆	—	109	1	no	—
31	#117	—	109	2	no	—
32	C₂²×C₄	—	109	1	no	—
33	M₁₆	—	218	2	no	—
34	C₂×C₈	—	109	1	no	—
35	C₂×C₈	#89137	1	1	yes	characteristic, complemented
36	C₄⋊C₄	—	218	2	no	—
37	C₂²⋊C₄	—	218	2	no	—
38	C₄²	—	109	4	no	—
39	C₂³	—	109	1	no	—
40	C₂×C₄	—	109	1	no	—
41	C₂×C₄	—	109	2	no	—
42	C₂×C₄	—	109	2	no	—
43	C₂×C₄	—	218	4	no	—
44	C₂×C₄	C₂×#89137	1	1	yes	characteristic
45	C₈	—	2	1	no	—
46	C₈	—	218	1	no	—
47	C₂²	—	109	2	no	—
48	C₂²	—	436	1	no	—
49	C₂²	C₄⋊#89137	1	1	yes	characteristic
50	C₄	—	109	2	no	—
51	C₄	—	436	4	no	—
52	C₄	C₄×#89137	1	1	yes	characteristic
53	C₄	C₂²⋊#89137	1	1	yes	characteristic
54	C₂	—	2	1	no	—
55	C₂	—	218	2	no	—
56	C₂	(C₂×#89137)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄×#89137
commutator	C₄×C₁₀₉	C₄²
Frattini	C₂×C₄	C₂×#89137
Fitting	C₂×C₈×C₁₀₉	C₄
socle	C₂×C₁₀₉	#95
hypercenter	C₂×C₈	#89137
hypocenter	C₁₀₉	H(3,ℤ/4)
LCS	G ▷ C₄×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
5. C₄×#89137	C₄	semidirect
8. C₂×#11724784	C₄	semidirect
9. C₂×C₈×C₁₀₉	C₄	semidirect
28. C₁₀₉	H(3,ℤ/4)	semidirect
35. C₂×C₈	#89137	semidirect