Subgroups — #20298355

Order 7232.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813581	C₂	1	2	yes	maximal
2	C₂×M₁₆×C₁₁₃	C₂	1	1	yes	maximal, characteristic
3	C₄⋊Dic₁₁₃	—	2	2	no	—
4	C₂²⋊Dic₁₁₃	—	2	2	no	—
5	C₄×Dic₁₁₃	C₄	1	4	yes	complemented
6	C₂²×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
7	M₁₆×C₁₁₃	—	2	2	no	—
8	C₂×C₈×C₁₁₃	C₄	1	2	yes	complemented
9	C₂³×C₁₁₃	D₄	1	1	yes	characteristic
10	C₂×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
11	C₂×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₁₁₃	D₄	1	2	yes	—
13	C₂×C₄×C₁₁₃	Q₈	1	1	yes	characteristic
14	C₂×Dic₁₁₃	—	2	4	no	—
15	C₈×C₁₁₃	—	2	2	no	—
16	C₂²×C₁₁₃	—	4	1	no	—
17	C₂²×C₁₁₃	C₂²⋊C₄	1	2	yes	—
18	C₂²×C₁₁₃	C₄⋊C₄	1	1	yes	characteristic
19	C₄×C₁₁₃	C₄²	1	1	yes	characteristic
20	C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₁₁₃	C₄⋊C₄	1	2	yes	—
22	Dic₁₁₃	—	4	4	no	—
23	C₂×C₁₁₃	—	2	2	no	—
24	C₂×C₁₁₃	—	2	1	no	—
25	C₂×C₁₁₃	#95	1	1	yes	characteristic
26	C₁₁₃	H(3,ℤ/4)	1	1	yes	characteristic, complemented, Sylow
27	H(3,ℤ/4)	—	113	1	no	maximal, Sylow
28	C₂×M₁₆	D₁₁₃	1	1	yes	characteristic
29	#117	—	113	2	no	—
30	C₂²×C₄	C₂×D₁₁₃	1	1	yes	characteristic
31	M₁₆	—	2	2	no	—
32	C₂×C₈	Dic₁₁₃	1	2	yes	complemented
33	C₄⋊C₄	—	226	2	no	—
34	C₂²⋊C₄	—	226	2	no	—
35	C₄²	—	113	4	no	—
36	C₂³	D₄₅₂	1	1	yes	characteristic
37	C₂×C₄	—	226	4	no	—
38	C₂×C₄	Dic₂₂₆	1	1	yes	characteristic
39	C₂×C₄	C₄×D₁₁₃	1	2	yes	—
40	C₂×C₄	C₂×Dic₁₁₃	1	1	yes	characteristic
41	C₂×C₄	C₂²⋊D₁₁₃	1	2	yes	—
42	C₈	—	2	2	no	—
43	C₂²	—	4	1	no	—
44	C₂²	#14268624	1	2	yes	—
45	C₂²	C₄⋊Dic₁₁₃	1	1	yes	characteristic
46	C₄	—	452	4	no	—
47	C₄	C₄×Dic₁₁₃	1	1	yes	characteristic
48	C₄	C₂²⋊Dic₁₁₃	1	1	yes	characteristic
49	C₄	#14268626	1	2	yes	—
50	C₂	—	2	2	no	—
51	C₂	—	2	1	no	—
52	C₂	#16813529	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄×Dic₁₁₃
commutator	C₄×C₁₁₃	C₄²
Frattini	C₂²×C₄	C₂×D₁₁₃
Fitting	C₂×M₁₆×C₁₁₃	C₂
socle	C₂×C₁₁₃	#95
hypercenter	C₂×M₁₆	D₁₁₃
hypocenter	C₁₁₃	H(3,ℤ/4)
LCS	G ▷ C₄×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
5. C₄×Dic₁₁₃	C₄	semidirect
8. C₂×C₈×C₁₁₃	C₄	semidirect
26. C₁₁₃	H(3,ℤ/4)	semidirect
32. C₂×C₈	Dic₁₁₃	semidirect