Subgroups — #28388649

Order 14464.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20298419	C₂	1	1	yes	maximal, characteristic
2	C₄×#14268622	C₂	1	1	yes	maximal, characteristic
3	#364×C₁₁₃	C₂	1	1	yes	maximal, characteristic
4	#16813562	—	2	1	no	—
5	C₂×#14268622	C₄	1	1	yes	characteristic
6	C₂×#14268622	C₄	1	1	yes	characteristic
7	M₃₂×C₁₁₃	—	2	1	no	—
8	C₄×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
9	#14268622	—	2	1	no	—
10	#14268622	—	4	1	no	—
11	#14268622	C₈	1	2	yes	—
12	C₂×C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₁₁₃	D₄	1	1	yes	characteristic
14	C₄²×C₁₁₃	Q₈	1	1	yes	characteristic
15	C₁₆×C₁₁₃	—	4	1	no	—
16	C₂×C₄×C₁₁₃	—	2	1	no	—
17	C₂×C₄×C₁₁₃	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₁₁₃	C₂×C₈	1	1	yes	characteristic
19	C₈×C₁₁₃	M₁₆	1	1	yes	characteristic
20	C₈×C₁₁₃	D₈	1	1	yes	characteristic
21	C₈×C₁₁₃	Q₁₆	1	1	yes	characteristic
22	C₂²×C₁₁₃	#108	1	1	yes	characteristic
23	C₄×C₁₁₃	—	2	2	no	—
24	C₄×C₁₁₃	C₄⋊C₈	1	1	yes	characteristic
25	C₄×C₁₁₃	#107	1	1	yes	characteristic
26	C₂×C₁₁₃	—	2	1	no	—
27	C₂×C₁₁₃	#335	1	1	yes	characteristic
28	#1373	—	113	1	no	maximal, Sylow
29	C₁₁₃	#1373	1	1	yes	characteristic, complemented, Sylow
30	#364	—	113	1	no	—
31	#364	D₁₁₃	1	1	yes	characteristic
32	C₄×C₁₆	—	113	1	no	—
33	M₃₂	—	2	1	no	—
34	M₃₂	—	226	1	no	—
35	C₂×C₁₆	—	113	1	no	—
36	C₂×C₁₆	—	113	1	no	—
37	C₄×C₈	C₂×D₁₁₃	1	1	yes	characteristic
38	C₂×C₈	C₄×D₁₁₃	1	1	yes	characteristic
39	C₂×C₈	C₂²⋊D₁₁₃	1	1	yes	characteristic
40	C₄²	Dic₂₂₆	1	1	yes	characteristic
41	C₁₆	—	4	1	no	—
42	C₁₆	—	113	2	no	—
43	C₁₆	—	452	1	no	—
44	C₁₆	—	226	1	no	—
45	C₂×C₄	—	2	1	no	—
46	C₂×C₄	#14268626	1	1	yes	characteristic
47	C₈	C₈×D₁₁₃	1	1	yes	characteristic
48	C₈	#14268630	1	1	yes	characteristic
49	C₈	#14268632	1	1	yes	characteristic
50	C₈	#14268637	1	1	yes	characteristic
51	C₂²	#16813557	1	1	yes	characteristic
52	C₄	—	2	2	no	—
53	C₄	#16813551	1	1	yes	characteristic
54	C₄	#16813555	1	1	yes	characteristic
55	C₂	—	2	1	no	—
56	C₂	#20298350	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#14268632
commutator	C₈×C₁₁₃	C₂×C₈
Frattini	C₄×C₈	C₂×D₁₁₃
Fitting	#364×C₁₁₃	C₂
socle	C₂×C₁₁₃	#335
prime radical	C₂²×C₁₁₃	#108
cosocle	C₄×C₈×C₁₁₃	C₂²
hypercenter	#364	D₁₁₃
hypocenter	C₁₁₃	#1373
LCS	G ▷ C₈×C₁₁₃ ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
29. C₁₁₃	#1373	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#20298419	2
C₄×#14268622	2
#364×C₁₁₃	2
#1373	113