Subgroups — #28405734

Order 14464.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299530	C₂	1	2	yes	maximal
2	C₁₆×Dic₁₁₃	C₂	1	1	yes	maximal, characteristic
3	#16813672	—	2	2	no	—
4	C₂×#14268622	C₂²	1	1	yes	characteristic
5	C₈×Dic₁₁₃	C₄	1	1	yes	characteristic
6	C₂×C₁₆×C₁₁₃	C₄	1	1	yes	characteristic
7	C₂×#11744751	C₈	1	1	yes	characteristic
8	C₄×Dic₁₁₃	C₈	1	1	yes	characteristic
9	#14268622	D₄	1	1	yes	characteristic
10	#14268622	Q₈	1	1	yes	characteristic
11	C₂×C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₁₁₃	—	2	1	no	—
13	C₂×C₄×C₁₁₃	C₂×C₈	1	1	yes	characteristic
14	C₂×Dic₁₁₃	—	2	1	no	—
15	C₈×C₁₁₃	C₄⋊C₄	1	1	yes	characteristic
16	C₈×C₁₁₃	M₁₆	1	1	yes	characteristic
17	#11744751	C₁₆	1	2	yes	—
18	C₂²×C₁₁₃	M₃₂	1	1	yes	characteristic
19	C₄×C₁₁₃	C₄⋊C₈	1	1	yes	characteristic
20	C₄×C₁₁₃	C₂×C₁₆	1	1	yes	characteristic
21	Dic₁₁₃	—	2	2	no	—
22	C₂×C₁₁₃	—	2	1	no	—
23	C₂×C₁₁₃	C₄⋊C₁₆	1	1	yes	characteristic
24	#1422	—	113	1	no	maximal, Sylow
25	C₁₁₃	#1422	1	1	yes	characteristic, complemented, Sylow
26	M₆₄	—	113	2	no	—
27	C₄×C₁₆	—	113	1	no	—
28	C₂×C₁₆	—	113	1	no	—
29	C₂×C₁₆	#90673	1	1	yes	characteristic
30	C₄×C₈	—	113	1	no	—
31	C₃₂	—	226	2	no	—
32	C₂×C₈	—	113	1	no	—
33	C₂×C₈	C₂×#90673	1	1	yes	characteristic
34	C₄²	—	113	1	no	—
35	C₁₆	—	2	1	no	—
36	C₁₆	—	113	1	no	—
37	C₁₆	—	113	1	no	—
38	C₂×C₄	—	226	1	no	—
39	C₂×C₄	#14268655	1	1	yes	characteristic
40	C₈	—	113	2	no	—
41	C₈	C₄⋊#90673	1	1	yes	characteristic
42	C₈	#14268656	1	1	yes	characteristic
43	C₂²	#16813697	1	1	yes	characteristic
44	C₄	—	226	2	no	—
45	C₄	#16813689	1	1	yes	characteristic
46	C₄	#16813695	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	#20299519	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₄⋊#90673
commutator	C₄×C₁₁₃	C₂×C₁₆
Frattini	C₂×C₈	C₂×#90673
Fitting	C₂×C₁₆×C₁₁₃	C₄
socle	C₂×C₁₁₃	C₄⋊C₁₆
prime radical	C₂²×C₁₁₃	M₃₂
cosocle	C₂×#14268622	C₂²
hypercenter	C₂×C₁₆	#90673
hypocenter	C₁₁₃	#1422
LCS	G ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
25. C₁₁₃	#1422	semidirect

Maximal subgroups

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

subgroup	index
#20299530	2
C₁₆×Dic₁₁₃	2
#1422	113