Subgroups — #28388648

Order 14464.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20298351	C₂	1	2	yes	maximal
2	C₄×C₁₆×C₁₁₃	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#11744751	—	2	2	no	—
4	C₂×C₁₆×C₁₁₃	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₁₁₃	C₄	1	1	yes	characteristic
6	C₄×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
7	C₂×#11744751	—	4	2	no	—
8	C₂×C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
9	C₂×C₈×C₁₁₃	Q₈	1	1	yes	characteristic
10	C₄²×C₁₁₃	D₄	1	1	yes	characteristic
11	C₁₆×C₁₁₃	—	2	1	no	—
12	C₁₆×C₁₁₃	C₈	1	2	yes	complemented
13	C₂×C₄×C₁₁₃	C₄⋊C₄	1	1	yes	characteristic
14	C₂×C₄×C₁₁₃	D₈	1	1	yes	characteristic
15	C₂×C₄×C₁₁₃	Q₁₆	1	1	yes	characteristic
16	C₈×C₁₁₃	—	2	1	no	—
17	C₈×C₁₁₃	C₂×C₈	1	1	yes	characteristic
18	C₈×C₁₁₃	M₁₆	1	1	yes	characteristic
19	#11744751	—	8	2	no	—
20	C₂²×C₁₁₃	#107	1	1	yes	characteristic
21	C₄×C₁₁₃	—	2	1	no	—
22	C₄×C₁₁₃	C₄⋊C₈	1	1	yes	characteristic
23	C₄×C₁₁₃	#108	1	1	yes	characteristic
24	C₄×C₁₁₃	SD₃₂	1	2	yes	—
25	C₂×C₁₁₃	#335	1	1	yes	characteristic
26	C₂×C₁₁₃	#367	1	1	yes	characteristic
27	C₂×C₁₁₃	#368	1	1	yes	characteristic
28	#1372	—	113	1	no	maximal, Sylow
29	C₁₁₃	#1372	1	1	yes	characteristic, complemented, Sylow
30	C₄×C₁₆	D₁₁₃	1	1	yes	characteristic
31	#335	—	113	2	no	—
32	C₂×C₁₆	Dic₁₁₃	1	1	yes	characteristic
33	C₂×C₁₆	Dic₁₁₃	1	1	yes	characteristic
34	C₄⋊C₈	—	226	2	no	—
35	C₄×C₈	C₂×D₁₁₃	1	1	yes	characteristic
36	C₂×C₈	—	452	2	no	—
37	C₂×C₈	Dic₂₂₆	1	1	yes	characteristic
38	C₂×C₈	C₂×Dic₁₁₃	1	1	yes	characteristic
39	C₄²	D₄₅₂	1	1	yes	characteristic
40	C₁₆	—	2	1	no	—
41	C₁₆	#11744751	1	2	yes	complemented
42	C₂×C₄	C₄⋊Dic₁₁₃	1	1	yes	characteristic
43	C₂×C₄	D₉₀₄	1	1	yes	characteristic
44	C₂×C₄	Dic₄₅₂	1	1	yes	characteristic
45	C₈	—	2	1	no	—
46	C₈	—	904	2	no	—
47	C₈	C₂×#11744751	1	1	yes	characteristic
48	C₈	#14268631	1	1	yes	characteristic
49	C₂²	#16813556	1	1	yes	characteristic
50	C₄	—	2	1	no	—
51	C₄	C₄⋊#11744751	1	1	yes	characteristic
52	C₄	#16813558	1	1	yes	characteristic
53	C₄	#16813567	1	2	yes	—
54	C₂	#20298351	1	1	yes	characteristic
55	C₂	#20298426	1	1	yes	characteristic
56	C₂	#20298428	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₉₀₄
commutator	C₈×C₁₁₃	C₂×C₈
Frattini	C₄×C₈	C₂×D₁₁₃
Fitting	C₄×C₁₆×C₁₁₃	C₂
socle, prime radical	C₂²×C₁₁₃	#107
cosocle	C₄×C₈×C₁₁₃	C₂²
hypercenter	C₄×C₁₆	D₁₁₃
hypocenter	C₁₁₃	#1372
LCS	G ▷ C₈×C₁₁₃ ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
12. C₁₆×C₁₁₃	C₈	semidirect
29. C₁₁₃	#1372	semidirect
41. C₁₆	#11744751	semidirect

Maximal subgroups

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

subgroup	index
#20298351	2
C₄×C₁₆×C₁₁₃	2
#1372	113