Subgroups — #20295053

Order 6976.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13182013	C₂	1	1	yes	maximal, characteristic
2	C₂²×#11724784	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#11724784	C₂	1	4	yes	maximal, complemented
4	#117×C₁₀₉	C₂	1	1	yes	maximal, characteristic
5	#13182013	—	2	2	no	—
6	C₂×#11724784	—	2	2	no	—
7	C₂×#11724784	C₂²	1	2	yes	—
8	C₂×#11724784	C₂²	1	2	yes	—
9	C₂²×C₄×C₁₀₉	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×C₁₀₉	C₄	1	2	yes	—
11	C₂²⋊C₄×C₁₀₉	C₄	1	2	yes	—
12	C₄²×C₁₀₉	C₂²	1	2	yes	—
13	C₂³×C₁₀₉	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₁₀₉	C₂×C₄	1	4	yes	—
15	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₁₀₉	D₄	1	2	yes	—
17	C₂×C₄×C₁₀₉	Q₈	1	2	yes	—
18	C₂×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
19	#11724784	—	2	2	no	—
20	#11724784	—	2	2	no	—
21	C₂²×C₁₀₉	—	2	2	no	—
22	C₂²×C₁₀₉	C₄⋊C₄	1	2	yes	—
23	C₂²×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₁₀₉	—	2	4	no	—
25	C₄×C₁₀₉	C₄⋊C₄	1	2	yes	—
26	C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
27	C₄×C₁₀₉	C₂×Q₈	1	1	yes	characteristic
28	C₂×C₁₀₉	—	2	2	no	—
29	C₂×C₁₀₉	C₂×C₄⋊C₄	1	1	yes	characteristic
30	C₂×C₁₀₉	#131	1	2	yes	—
31	C₁₀₉	#424	1	1	yes	characteristic, complemented, Sylow
32	#424	—	109	1	no	maximal, Sylow
33	C₂×M₁₆	—	109	1	no	—
34	C₂²×C₈	—	109	1	no	—
35	#117	D₁₀₉	1	1	yes	characteristic
36	C₄⋊C₈	—	109	4	no	—
37	C₂²×C₄	C₂×D₁₀₉	1	1	yes	characteristic
38	M₁₆	—	218	2	no	—
39	C₂×C₈	—	109	2	no	—
40	C₂×C₈	—	109	2	no	—
41	C₂×C₈	—	218	2	no	—
42	C₄⋊C₄	Dic₁₀₉	1	2	yes	—
43	C₂²⋊C₄	Dic₁₀₉	1	2	yes	—
44	C₄²	C₂×D₁₀₉	1	2	yes	—
45	C₂³	C₂×Dic₁₀₉	1	1	yes	characteristic
46	C₂×C₄	Dic₂₁₈	1	2	yes	—
47	C₂×C₄	D₄₃₆	1	2	yes	—
48	C₂×C₄	C₂×Dic₁₀₉	1	4	yes	—
49	C₂×C₄	C₂×Dic₁₀₉	1	1	yes	characteristic
50	C₂×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
51	C₈	—	218	2	no	—
52	C₈	—	218	2	no	—
53	C₂²	—	2	2	no	—
54	C₂²	C₄⋊Dic₁₀₉	1	2	yes	—
55	C₂²	C₂²×Dic₁₀₉	1	1	yes	characteristic
56	C₄	—	2	4	no	—
57	C₄	C₄⋊Dic₁₀₉	1	2	yes	—
58	C₄	C₂×D₄₃₆	1	1	yes	characteristic
59	C₄	C₂×Dic₂₁₈	1	1	yes	characteristic
60	C₂	—	2	2	no	—
61	C₂	C₂×C₄⋊Dic₁₀₉	1	1	yes	characteristic
62	C₂	#16812706	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₁₀₉
commutator, socle	C₂²×C₁₀₉	C₂²×C₄
Fitting	#117×C₁₀₉	C₂
hypercenter	#117	D₁₀₉
hypocenter	C₁₀₉	#424
LCS	G ▷ C₂²×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
3. C₄⋊#11724784	C₂	semidirect
31. C₁₀₉	#424	semidirect