Subgroups — #20295895

Order 6976.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₀₉⋊M₁₆	C₂	1	2	yes	maximal
2	C₂×#13182012	C₂	1	1	yes	maximal, characteristic
3	#13182039	—	2	2	no	—
4	#13182038	—	2	2	no	—
5	D₁₀₉⋊C₈	C₄	1	4	yes	—
6	C₂×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
7	#13182012	—	2	2	no	—
8	C₂×#11724784	C₄	1	1	yes	characteristic
9	C₂×C₈×C₁₀₉	C₄	1	1	yes	characteristic
10	C₂²×D₁₀₉	Q₈	1	1	yes	characteristic
11	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
12	C₂×Dic₁₀₉	D₄	1	1	yes	characteristic
13	C₄×D₁₀₉	C₂×C₄	1	2	yes	—
14	C₄×D₁₀₉	D₄	1	2	yes	—
15	#11724786	—	2	4	no	—
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	C₄⋊C₄	1	2	yes	—
21	C₄×C₁₀₉	C₄²	1	1	yes	characteristic
22	C₄×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
23	Dic₁₀₉	C₂²⋊C₄	1	2	yes	—
24	C₂×C₁₀₉	—	2	1	no	—
25	C₂×C₁₀₉	#95	1	1	yes	characteristic
26	D₁₀₉	—	2	2	no	—
27	C₁₀₉	#338	1	1	yes	characteristic, complemented, Sylow
28	#338	—	109	1	no	maximal, Sylow
29	C₂×M₁₆	—	109	2	no	—
30	C₂×M₁₆	—	109	1	no	—
31	C₂²×C₄	—	109	1	no	—
32	M₁₆	—	218	2	no	—
33	M₁₆	—	218	2	no	—
34	M₁₆	—	218	2	no	—
35	C₂×C₈	—	109	4	no	—
36	C₂×C₈	—	109	1	no	—
37	C₂×C₈	#89137	1	1	yes	characteristic
38	C₂³	—	109	1	no	—
39	C₂×C₄	—	109	1	no	—
40	C₂×C₄	—	109	2	no	—
41	C₂×C₄	—	109	2	no	—
42	C₂×C₄	C₂×#89137	1	1	yes	characteristic
43	C₈	—	2	1	no	—
44	C₈	—	218	4	no	—
45	C₈	—	218	1	no	—
46	C₂²	—	109	2	no	—
47	C₂²	—	436	1	no	—
48	C₂²	C₄⋊#89137	1	1	yes	characteristic
49	C₄	—	109	2	no	—
50	C₄	C₄×#89137	1	1	yes	characteristic
51	C₄	C₂²⋊#89137	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	218	2	no	—
54	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	#338
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
27. C₁₀₉	#338	semidirect