Subgroups — #28407658

Order 14464.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299705	C₂	1	2	yes	maximal
2	C₁₆×#90673	C₂	1	1	yes	maximal, characteristic
3	#16813712	C₄	1	4	yes	complemented
4	#16813695	C₂²	1	1	yes	characteristic
5	C₈×#90673	C₄	1	1	yes	characteristic
6	C₁₆×D₁₁₃	C₄	1	1	yes	characteristic
7	#14268655	C₈	1	1	yes	characteristic
8	C₄×#90673	C₈	1	1	yes	characteristic
9	#14268650	C₂×C₄	1	2	yes	—
10	C₈×D₁₁₃	C₂×C₄	1	1	yes	characteristic
11	#14268622	C₈	1	1	yes	characteristic
12	C₁₆×C₁₁₃	C₈	1	1	yes	characteristic
13	C₂×#90673	C₁₆	1	2	yes	—
14	C₄×D₁₁₃	C₂×C₈	1	1	yes	characteristic
15	#11744753	C₁₆	1	2	yes	—
16	C₈×C₁₁₃	C₂×C₈	1	1	yes	characteristic
17	#11744751	C₄²	1	1	yes	characteristic
18	C₂×D₁₁₃	C₂×C₁₆	1	1	yes	characteristic
19	#90673	C₃₂	1	4	yes	complemented
20	C₄×C₁₁₃	C₄×C₈	1	1	yes	characteristic
21	Dic₁₁₃	C₂×C₁₆	1	1	yes	characteristic
22	C₂×C₁₁₃	C₄×C₁₆	1	1	yes	characteristic
23	D₁₁₃	C₂×C₃₂	1	2	yes	—
24	C₄×C₃₂	—	113	1	no	maximal, Sylow
25	C₁₁₃	C₄×C₃₂	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₃₂	—	113	2	no	—
27	C₄×C₁₆	—	113	1	no	—
28	C₂×C₁₆	—	113	1	no	—
29	C₂×C₁₆	—	113	1	no	—
30	C₄×C₈	—	113	1	no	—
31	C₃₂	—	113	4	no	—
32	C₂×C₈	—	113	1	no	—
33	C₂×C₈	—	113	1	no	—
34	C₄²	—	113	1	no	—
35	C₁₆	—	113	2	no	—
36	C₁₆	—	113	1	no	—
37	C₁₆	#11744762	1	1	yes	characteristic
38	C₂×C₄	—	113	2	no	—
39	C₂×C₄	—	113	1	no	—
40	C₈	—	113	2	no	—
41	C₈	—	113	1	no	—
42	C₈	C₂×#11744762	1	1	yes	characteristic
43	C₂²	—	113	1	no	—
44	C₄	—	113	4	no	—
45	C₄	—	113	1	no	—
46	C₄	C₄×#11744762	1	1	yes	characteristic
47	C₂	—	113	2	no	—
48	C₂	#20299691	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₁₆	#11744762
commutator, hypocenter	C₁₁₃	C₄×C₃₂
Frattini	C₈	C₂×#11744762
Fitting	C₁₆×C₁₁₃	C₈
socle	C₂×C₁₁₃	C₄×C₁₆
prime radical	C₂×D₁₁₃	C₂×C₁₆
cosocle	#16813695	C₂²
LCS	G ▷ C₁₁₃
UCS	C₁ ◁ C₁₆

Complements

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

N	H ≅ G/N	type
3. #16813712	C₄	semidirect
19. #90673	C₃₂	semidirect
25. C₁₁₃	C₄×C₃₂	semidirect

Maximal subgroups

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

subgroup	index
#20299705	2
C₁₆×#90673	2
C₄×C₃₂	113