Subgroups — #20298647

Order 7232.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14268631	C₂	1	2	yes	maximal
2	#16813558	C₂	1	4	yes	maximal, complemented
3	C₂×M₁₆×C₁₁₃	C₂	1	1	yes	maximal, characteristic
4	#14268631	—	2	2	no	—
5	#14268631	C₂²	1	4	yes	—
6	C₂×#11744751	—	2	2	no	—
7	C₂²×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
8	M₁₆×C₁₁₃	C₄	1	4	yes	—
9	C₂×C₈×C₁₁₃	C₂²	1	2	yes	—
10	C₂³×C₁₁₃	Q₈	1	1	yes	characteristic
11	C₂×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
12	C₂×C₄×C₁₁₃	D₄	1	2	yes	—
13	C₂×C₄×C₁₁₃	Q₈	1	1	yes	characteristic
14	C₂×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
15	C₈×C₁₁₃	C₂×C₄	1	4	yes	—
16	#11744751	—	2	4	no	—
17	C₂²×C₁₁₃	—	4	1	no	—
18	C₂²×C₁₁₃	C₄⋊C₄	1	2	yes	—
19	C₂²×C₁₁₃	C₂×Q₈	1	1	yes	characteristic
20	C₄×C₁₁₃	C₄⋊C₄	1	2	yes	—
21	C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
22	C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
23	C₂×C₁₁₃	—	2	2	no	—
24	C₂×C₁₁₃	—	2	1	no	—
25	C₂×C₁₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
26	C₁₁₃	#430	1	1	yes	characteristic, complemented, Sylow
27	#430	—	113	1	no	maximal, Sylow
28	C₂×M₁₆	—	113	2	no	—
29	C₂×M₁₆	D₁₁₃	1	1	yes	characteristic
30	#108	—	113	4	no	—
31	C₂²×C₄	C₂×D₁₁₃	1	1	yes	characteristic
32	M₁₆	—	113	4	no	—
33	M₁₆	—	226	2	no	—
34	M₁₆	Dic₁₁₃	1	4	yes	—
35	C₂×C₈	—	226	2	no	—
36	C₂×C₈	C₂×D₁₁₃	1	2	yes	—
37	C₂³	Dic₂₂₆	1	1	yes	characteristic
38	C₂×C₄	Dic₂₂₆	1	1	yes	characteristic
39	C₂×C₄	D₄₅₂	1	2	yes	—
40	C₂×C₄	C₂×Dic₁₁₃	1	2	yes	—
41	C₂×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
42	C₈	—	226	4	no	—
43	C₈	C₂×Dic₁₁₃	1	4	yes	—
44	C₂²	—	4	1	no	—
45	C₂²	C₄⋊Dic₁₁₃	1	2	yes	—
46	C₂²	C₂×Dic₂₂₆	1	1	yes	characteristic
47	C₄	C₄⋊Dic₁₁₃	1	2	yes	—
48	C₄	C₂²×Dic₁₁₃	1	1	yes	characteristic
49	C₄	C₂×D₄₅₂	1	1	yes	characteristic
50	C₂	—	2	2	no	—
51	C₂	—	2	1	no	—
52	C₂	C₂×C₄⋊Dic₁₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₄₅₂
commutator	C₄×C₁₁₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₁₃
Fitting	C₂×M₁₆×C₁₁₃	C₂
socle	C₂×C₁₁₃	C₂×C₄⋊C₄
hypercenter	C₂×M₁₆	D₁₁₃
hypocenter	C₁₁₃	#430
LCS	G ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
2. #16813558	C₂	semidirect
26. C₁₁₃	#430	semidirect