Subgroups — #14521482

Order 1984.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11758496	C₂	1	2	yes	maximal, complemented
2	C₃₁×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#11758416	C₂	1	2	yes	maximal, complemented
4	D₄₉₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₆×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#92499	—	2	2	no	—
7	Q₁₆×C₃₁	C₂²	1	2	yes	—
8	#92481	—	2	2	no	—
9	D₂₄₈	C₂²	1	2	yes	—
10	C₈×D₃₁	C₂²	1	1	yes	characteristic
11	C₁₆×C₃₁	C₂²	1	1	yes	characteristic
12	C₃₁⋊C₁₆	C₂²	1	1	yes	characteristic
13	Q₈×C₃₁	—	2	2	no	—
14	D₁₂₄	—	2	2	no	—
15	D₁₂₄	—	4	2	no	—
16	C₄×D₃₁	—	4	2	no	—
17	C₄×D₃₁	D₄	1	1	yes	characteristic
18	C₈×C₃₁	C₂³	1	1	yes	characteristic
19	C₃₁⋊C₈	D₄	1	1	yes	characteristic
20	C₂×D₃₁	—	4	2	no	—
21	C₂×D₃₁	D₈	1	1	yes	characteristic
22	C₄×C₃₁	—	4	2	no	—
23	C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
24	Dic₃₁	D₈	1	1	yes	characteristic
25	#508	—	31	1	no	maximal, Sylow
26	C₂×C₃₁	C₂×D₈	1	1	yes	characteristic
27	D₃₁	—	2	1	no	—
28	D₃₁	—	8	2	no	—
29	#135	—	31	2	no	—
30	Q₃₂	D₃₁	1	1	yes	characteristic, complemented
31	SD₃₂	—	31	2	no	—
32	D₁₆	—	31	1	no	—
33	C₂×C₁₆	—	31	1	no	—
34	C₃₁	#508	1	1	yes	characteristic, complemented, Sylow
35	#41	—	62	2	no	—
36	Q₁₆	C₂×D₃₁	1	2	yes	—
37	SD₁₆	—	62	2	no	—
38	D₈	—	31	2	no	—
39	C₂×C₈	—	31	1	no	—
40	C₁₆	—	31	1	no	—
41	C₁₆	C₂×D₃₁	1	1	yes	characteristic
42	Q₈	—	2	2	no	—
43	D₄	—	62	2	no	—
44	D₄	—	124	2	no	—
45	C₂×C₄	—	31	1	no	—
46	C₂×C₄	—	124	2	no	—
47	C₈	—	31	1	no	—
48	C₈	C₂²×D₃₁	1	1	yes	characteristic
49	C₂²	—	31	1	no	—
50	C₂²	—	124	2	no	—
51	C₄	—	4	2	no	—
52	C₄	—	31	1	no	—
53	C₄	D₄×D₃₁	1	1	yes	characteristic
54	C₂	—	62	1	no	—
55	C₂	—	248	2	no	—
56	C₂	D₈×D₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₃₁
commutator, cosocle	C₈×C₃₁	C₂³
Frattini	C₈	C₂²×D₃₁
Fitting	C₃₁×Q₃₂	C₂
socle	C₂×C₃₁	C₂×D₈
hypercenter	Q₃₂	D₃₁
hypocenter	C₃₁	#508
LCS	G ▷ C₈×C₃₁ ▷ C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
1. #11758496	C₂	semidirect
2. C₃₁×Q₃₂	C₂	semidirect
3. #11758416	C₂	semidirect
4. D₄₉₆	C₂	semidirect
5. C₁₆×D₃₁	C₂	semidirect
30. Q₃₂	D₃₁	semidirect
34. C₃₁	#508	semidirect

Maximal subgroups

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

subgroup	index
#11758496	2
C₃₁×Q₃₂	2
#11758416	2
D₄₉₆	2
C₁₆×D₃₁	2
#508	31