Subgroups — #20294822

Order 6976.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812688	C₂	1	1	yes	maximal, characteristic
2	#16812618	C₂	1	1	yes	maximal, characteristic, complemented
3	#101×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄₃₆	C₄	1	1	yes	characteristic
5	#13182013	—	2	1	no	—
6	#13182006	—	2	1	no	—
7	#13182006	—	2	1	no	—
8	C₄×Dic₁₀₉	C₄	1	1	yes	characteristic
9	C₂×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic
10	M₁₆×C₁₀₉	—	2	1	no	—
11	C₂²×D₁₀₉	—	2	1	no	—
12	Q₈×C₁₀₉	—	4	1	no	—
13	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₁₀₉	D₄	1	1	yes	characteristic
15	C₂×C₄×C₁₀₉	D₄	1	1	yes	characteristic
16	C₂×Dic₁₀₉	—	2	1	no	—
17	D₄₃₆	—	4	1	no	—
18	C₈×C₁₀₉	—	4	1	no	—
19	#11724784	—	4	1	no	—
20	C₂²×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×D₁₀₉	—	4	2	no	—
22	C₂×D₁₀₉	—	4	1	no	—
23	C₄×C₁₀₉	—	2	1	no	—
24	C₄×C₁₀₉	—	2	1	no	—
25	C₄×C₁₀₉	—	2	1	no	—
26	Dic₁₀₉	—	4	1	no	—
27	C₂×C₁₀₉	—	2	1	no	—
28	C₂×C₁₀₉	#99	1	1	yes	characteristic
29	D₁₀₉	—	8	1	no	—
30	C₁₀₉	#355	1	1	yes	characteristic, complemented, Sylow
31	#355	—	109	1	no	maximal, Sylow
32	#124	—	109	1	no	—
33	#101	—	109	1	no	—
34	#101	D₁₀₉	1	1	yes	characteristic, complemented
35	C₂×Q₈	C₂×D₁₀₉	1	1	yes	characteristic
36	C₂×D₄	—	109	1	no	—
37	M₁₆	—	2	1	no	—
38	M₁₆	—	218	1	no	—
39	C₂²⋊C₄	—	218	1	no	—
40	C₂²⋊C₄	—	218	1	no	—
41	C₄²	—	109	1	no	—
42	C₂³	—	218	1	no	—
43	Q₈	—	4	1	no	—
44	D₄	—	436	1	no	—
45	C₂×C₄	—	218	1	no	—
46	C₂×C₄	C₄×D₁₀₉	1	1	yes	characteristic
47	C₂×C₄	D₄₃₆	1	1	yes	characteristic
48	C₂×C₄	C₂²⋊D₁₀₉	1	1	yes	characteristic
49	C₈	—	4	1	no	—
50	C₈	—	436	1	no	—
51	C₂²	—	436	2	no	—
52	C₂²	—	436	1	no	—
53	C₂²	#13182006	1	1	yes	characteristic
54	C₄	—	2	1	no	—
55	C₄	—	2	1	no	—
56	C₄	—	2	1	no	—
57	C₄	—	436	1	no	—
58	C₂	—	2	1	no	—
59	C₂	—	872	1	no	—
60	C₂	#16812613	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16812613
commutator	C₂×C₄×C₁₀₉	C₂×C₄
Frattini	C₂×Q₈	C₂×D₁₀₉
Fitting	#101×C₁₀₉	C₂
socle	C₂×C₁₀₉	#99
hypercenter	#101	D₁₀₉
hypocenter	C₁₀₉	#355
LCS	G ▷ C₂×C₄×C₁₀₉ ▷ C₂²×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×Q₈ ◁ #101

Complements

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

N	H ≅ G/N	type
2. #16812618	C₂	semidirect
3. #101×C₁₀₉	C₂	semidirect
30. C₁₀₉	#355	semidirect
34. #101	D₁₀₉	semidirect