Subgroups — #20295940

Order 6976.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₀₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#16812770	C₂	1	1	yes	maximal, characteristic, complemented
3	#16812718	C₂	1	1	yes	maximal, characteristic
4	#13182039	—	2	1	no	—
5	#13182032	—	2	1	no	—
6	#13182028	—	2	1	no	—
7	Dic₄₃₆	C₄	1	1	yes	characteristic
8	#13182017	—	2	1	no	—
9	C₈×D₁₀₉	C₂²	1	1	yes	characteristic
10	D₈×C₁₀₉	C₄	1	1	yes	characteristic
11	D₄×C₁₀₉	—	2	1	no	—
12	C₂²⋊D₁₀₉	—	4	1	no	—
13	C₂×Dic₁₀₉	—	4	1	no	—
14	C₄×D₁₀₉	D₄	1	1	yes	characteristic
15	Dic₂₁₈	—	2	1	no	—
16	#11724786	—	4	1	no	—
17	C₈×C₁₀₉	C₂×C₄	1	1	yes	characteristic
18	#11724784	D₄	1	1	yes	characteristic
19	C₂²×C₁₀₉	—	4	1	no	—
20	C₂×D₁₀₉	SD₁₆	1	1	yes	characteristic
21	C₄×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
22	Dic₁₀₉	—	4	1	no	—
23	Dic₁₀₉	D₈	1	1	yes	characteristic
24	C₂×C₁₀₉	—	8	1	no	—
25	C₂×C₁₀₉	#102	1	1	yes	characteristic
26	D₁₀₉	—	2	1	no	—
27	C₁₀₉	#359	1	1	yes	characteristic, complemented, Sylow
28	#359	—	109	1	no	maximal, Sylow
29	#135	—	109	1	no	—
30	C₂×C₁₆	—	109	1	no	—
31	#108	—	109	1	no	—
32	#41	—	218	1	no	—
33	Q₁₆	—	109	1	no	—
34	SD₁₆	—	218	1	no	—
35	D₈	#89137	1	1	yes	characteristic
36	M₁₆	—	218	1	no	—
37	C₂×C₈	—	109	1	no	—
38	C₁₆	—	218	1	no	—
39	Q₈	—	218	1	no	—
40	D₄	—	2	1	no	—
41	D₄	—	436	1	no	—
42	C₂×C₄	—	109	1	no	—
43	C₂×C₄	—	436	1	no	—
44	C₈	—	109	1	no	—
45	C₈	—	436	1	no	—
46	C₈	C₂×#89137	1	1	yes	characteristic
47	C₂²	—	4	1	no	—
48	C₂²	—	109	1	no	—
49	C₄	—	109	1	no	—
50	C₄	—	436	1	no	—
51	C₄	C₂²⋊#89137	1	1	yes	characteristic
52	C₂	—	8	1	no	—
53	C₂	—	218	1	no	—
54	C₂	#16812761	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16812761
commutator	C₈×C₁₀₉	C₂×C₄
Frattini	C₈	C₂×#89137
Fitting	D₈×C₁₀₉	C₄
socle	C₂×C₁₀₉	#102
hypercenter	D₈	#89137
hypocenter	C₁₀₉	#359
LCS	G ▷ C₈×C₁₀₉ ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. D₁₀₉⋊C₁₆	C₂	semidirect
2. #16812770	C₂	semidirect
27. C₁₀₉	#359	semidirect