Subgroups — C₃₂×#90673 #28405677

Order 14464.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299529	C₂	1	1	yes	maximal, characteristic
2	C₁₆×#90673	C₂	1	1	yes	maximal, characteristic
3	C₃₂×D₁₁₃	C₂	1	1	yes	maximal, characteristic
4	#16813695	C₄	1	1	yes	characteristic
5	C₈×#90673	C₄	1	1	yes	characteristic
6	#16813672	C₄	1	2	yes	complemented
7	C₁₆×D₁₁₃	C₂²	1	1	yes	characteristic
8	#16813528	C₄	1	1	yes	characteristic, complemented
9	C₃₂×C₁₁₃	C₄	1	1	yes	characteristic, complemented
10	#14268655	C₈	1	1	yes	characteristic
11	C₄×#90673	C₈	1	1	yes	characteristic
12	#14268650	C₈	1	2	yes	—
13	C₈×D₁₁₃	C₂×C₄	1	1	yes	characteristic
14	#14268622	C₂×C₄	1	1	yes	characteristic
15	C₁₆×C₁₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂×#90673	C₁₆	1	2	yes	—
17	C₄×D₁₁₃	C₂×C₈	1	1	yes	characteristic
18	#11744753	C₁₆	1	2	yes	—
19	C₈×C₁₁₃	C₄²	1	1	yes	characteristic
20	#11744751	C₂×C₈	1	1	yes	characteristic
21	C₂×D₁₁₃	C₂×C₁₆	1	1	yes	characteristic
22	#90673	C₃₂	1	4	yes	direct product factor
23	C₄×C₁₁₃	C₄×C₈	1	1	yes	characteristic
24	Dic₁₁₃	C₂×C₁₆	1	1	yes	characteristic
25	C₂×C₁₁₃	C₄×C₁₆	1	1	yes	characteristic
26	D₁₁₃	C₂×C₃₂	1	2	yes	—
27	C₄×C₃₂	—	113	1	no	maximal, Sylow
28	C₁₁₃	C₄×C₃₂	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃₂	—	113	1	no	—
30	C₂×C₃₂	—	113	1	no	—
31	C₄×C₁₆	—	113	1	no	—
32	C₂×C₁₆	—	113	1	no	—
33	C₂×C₁₆	—	113	1	no	—
34	C₄×C₈	—	113	1	no	—
35	C₃₂	—	113	2	no	—
36	C₃₂	—	113	1	no	—
37	C₃₂	#90673	1	1	yes	characteristic, direct product factor
38	C₂×C₈	—	113	1	no	—
39	C₂×C₈	—	113	1	no	—
40	C₄²	—	113	1	no	—
41	C₁₆	—	113	2	no	—
42	C₁₆	—	113	1	no	—
43	C₁₆	C₂×#90673	1	1	yes	characteristic
44	C₂×C₄	—	113	2	no	—
45	C₂×C₄	—	113	1	no	—
46	C₈	—	113	2	no	—
47	C₈	—	113	1	no	—
48	C₈	C₄×#90673	1	1	yes	characteristic
49	C₂²	—	113	1	no	—
50	C₄	—	113	4	no	—
51	C₄	—	113	1	no	—
52	C₄	C₈×#90673	1	1	yes	characteristic
53	C₂	—	113	2	no	—
54	C₂	C₁₆×#90673	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃₂	#90673
commutator, hypocenter	C₁₁₃	C₄×C₃₂
Frattini	C₁₆	C₂×#90673
Fitting	C₃₂×C₁₁₃	C₄
socle	C₂×C₁₁₃	C₄×C₁₆
prime radical	C₂×D₁₁₃	C₂×C₁₆
cosocle	C₁₆×D₁₁₃	C₂²
LCS	G ▷ C₁₁₃
UCS	C₁ ◁ C₃₂

Complements

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

N	H ≅ G/N	type
6. #16813672	C₄	semidirect
8. #16813528	C₄	semidirect
9. C₃₂×C₁₁₃	C₄	semidirect
22. #90673	C₃₂	direct (N × H)
28. C₁₁₃	C₄×C₃₂	semidirect
37. C₃₂	#90673	direct (N × H)

Maximal subgroups

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

subgroup	index
#20299529	2
C₁₆×#90673	2
C₃₂×D₁₁₃	2
C₄×C₃₂	113

Subgroups — C32×#90673 #28405677

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₂×#90673 #28405677