Subgroups — #20295075

Order 6976.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13182013	C₂	1	2	yes	maximal
2	#16812635	C₂	1	4	yes	maximal, complemented
3	C₂×M₁₆×C₁₀₉	C₂	1	1	yes	maximal, characteristic
4	#13182013	—	2	2	no	—
5	#13182013	C₂²	1	4	yes	—
6	C₂×#11724784	—	2	2	no	—
7	C₂²×C₄×C₁₀₉	C₂²	1	1	yes	characteristic
8	M₁₆×C₁₀₉	C₄	1	4	yes	—
9	C₂×C₈×C₁₀₉	C₂²	1	2	yes	—
10	C₂³×C₁₀₉	Q₈	1	1	yes	characteristic
11	C₂×C₄×C₁₀₉	C₂×C₄	1	2	yes	—
12	C₂×C₄×C₁₀₉	D₄	1	2	yes	—
13	C₂×C₄×C₁₀₉	Q₈	1	1	yes	characteristic
14	C₂×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
15	C₈×C₁₀₉	C₂×C₄	1	4	yes	—
16	#11724784	—	2	4	no	—
17	C₂²×C₁₀₉	—	4	1	no	—
18	C₂²×C₁₀₉	C₄⋊C₄	1	2	yes	—
19	C₂²×C₁₀₉	C₂×Q₈	1	1	yes	characteristic
20	C₄×C₁₀₉	C₄⋊C₄	1	2	yes	—
21	C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
22	C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
23	C₂×C₁₀₉	—	2	2	no	—
24	C₂×C₁₀₉	—	2	1	no	—
25	C₂×C₁₀₉	C₂×C₄⋊C₄	1	1	yes	characteristic
26	C₁₀₉	#430	1	1	yes	characteristic, complemented, Sylow
27	#430	—	109	1	no	maximal, Sylow
28	C₂×M₁₆	—	109	2	no	—
29	C₂×M₁₆	D₁₀₉	1	1	yes	characteristic
30	#108	—	109	4	no	—
31	C₂²×C₄	C₂×D₁₀₉	1	1	yes	characteristic
32	M₁₆	—	109	4	no	—
33	M₁₆	—	218	2	no	—
34	M₁₆	Dic₁₀₉	1	4	yes	—
35	C₂×C₈	—	218	2	no	—
36	C₂×C₈	C₂×D₁₀₉	1	2	yes	—
37	C₂³	Dic₂₁₈	1	1	yes	characteristic
38	C₂×C₄	Dic₂₁₈	1	1	yes	characteristic
39	C₂×C₄	D₄₃₆	1	2	yes	—
40	C₂×C₄	C₂×Dic₁₀₉	1	2	yes	—
41	C₂×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
42	C₈	—	218	4	no	—
43	C₈	C₂×Dic₁₀₉	1	4	yes	—
44	C₂²	—	4	1	no	—
45	C₂²	C₄⋊Dic₁₀₉	1	2	yes	—
46	C₂²	C₂×Dic₂₁₈	1	1	yes	characteristic
47	C₄	C₄⋊Dic₁₀₉	1	2	yes	—
48	C₄	C₂²×Dic₁₀₉	1	1	yes	characteristic
49	C₄	C₂×D₄₃₆	1	1	yes	characteristic
50	C₂	—	2	2	no	—
51	C₂	—	2	1	no	—
52	C₂	C₂×C₄⋊Dic₁₀₉	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₄₃₆
commutator	C₄×C₁₀₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₀₉
Fitting	C₂×M₁₆×C₁₀₉	C₂
socle	C₂×C₁₀₉	C₂×C₄⋊C₄
hypercenter	C₂×M₁₆	D₁₀₉
hypocenter	C₁₀₉	#430
LCS	G ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
2. #16812635	C₂	semidirect
26. C₁₀₉	#430	semidirect