Subgroups — #28405492

Order 14464.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299486	C₂	1	1	yes	maximal, characteristic
2	#20299486	C₂	1	1	yes	maximal, characteristic
3	#20298320	C₂	1	1	yes	maximal, characteristic
4	C₂×#14268650	C₄	1	2	yes	—
5	C₂×#14268650	C₄	1	2	yes	—
6	C₄×#11744751	C₄	1	1	yes	characteristic
7	C₄×#11744751	C₂²	1	1	yes	characteristic
8	C₄×C₈×C₁₁₃	C₄	1	1	yes	characteristic
9	#14268650	—	2	2	no	—
10	#14268650	C₈	1	4	yes	complemented
11	C₂×#11744751	—	2	1	no	—
12	C₂×#11744751	C₂×C₄	1	1	yes	characteristic
13	C₂×#11744751	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₁₁₃	—	2	1	no	—
15	C₄²×C₁₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₁₁₃	C₄²	1	1	yes	characteristic
17	C₂×C₄×C₁₁₃	M₁₆	1	1	yes	characteristic
18	C₂×C₄×C₁₁₃	M₁₆	1	1	yes	characteristic
19	C₈×C₁₁₃	—	4	1	no	—
20	#11744751	—	4	1	no	—
21	#11744751	C₂×C₈	1	2	yes	—
22	#11744751	M₁₆	1	2	yes	—
23	C₂²×C₁₁₃	#97	1	1	yes	characteristic
24	C₄×C₁₁₃	—	2	1	no	—
25	C₄×C₁₁₃	—	2	1	no	—
26	C₄×C₁₁₃	C₄×C₈	1	1	yes	characteristic
27	C₄×C₁₁₃	#97	1	1	yes	characteristic
28	C₂×C₁₁₃	#322	1	1	yes	characteristic
29	C₂×C₁₁₃	#347	1	1	yes	characteristic
30	C₂×C₁₁₃	#347	1	1	yes	characteristic
31	#1313	—	113	1	no	maximal, Sylow
32	C₁₁₃	#1313	1	1	yes	characteristic, complemented, Sylow
33	#346	—	113	1	no	—
34	#346	—	113	1	no	—
35	#322	—	113	1	no	—
36	C₂×C₁₆	—	113	2	no	—
37	C₂×C₁₆	—	113	2	no	—
38	C₄×C₈	—	113	1	no	—
39	C₄×C₈	—	113	1	no	—
40	C₄×C₈	#90673	1	1	yes	characteristic
41	C₂×C₈	—	2	1	no	—
42	C₂×C₈	—	113	1	no	—
43	C₂×C₈	—	113	1	no	—
44	C₂×C₈	—	226	1	no	—
45	C₄²	C₂×#90673	1	1	yes	characteristic
46	C₁₆	—	113	4	no	—
47	C₁₆	—	226	2	no	—
48	C₂×C₄	C₄×#90673	1	1	yes	characteristic
49	C₂×C₄	#14268656	1	1	yes	characteristic
50	C₂×C₄	#14268657	1	1	yes	characteristic
51	C₈	—	4	1	no	—
52	C₈	—	113	2	no	—
53	C₈	—	113	2	no	—
54	C₈	—	452	1	no	—
55	C₂²	#16813677	1	1	yes	characteristic
56	C₄	—	2	1	no	—
57	C₄	—	2	1	no	—
58	C₄	C₈×#90673	1	1	yes	characteristic
59	C₄	#16813676	1	1	yes	characteristic
60	C₂	#20299440	1	1	yes	characteristic
61	C₂	#20299490	1	1	yes	characteristic
62	C₂	#20299491	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₄×#90673
commutator	C₄×C₁₁₃	C₄×C₈
Frattini	C₄²	C₂×#90673
Fitting	C₄×C₈×C₁₁₃	C₄
socle, prime radical	C₂²×C₁₁₃	#97
cosocle	C₄×#11744751	C₂²
hypercenter	C₄×C₈	#90673
hypocenter	C₁₁₃	#1313
LCS	G ▷ C₄×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
10. #14268650	C₈	semidirect
32. C₁₁₃	#1313	semidirect

Maximal subgroups

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

subgroup	index
#20299486	2
#20298320	2
#1313	113