Subgroups — #14521486

Order 1984.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11758496	C₂	1	1	yes	maximal, characteristic, complemented
2	D₈×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#11758416	C₂	1	1	yes	maximal, characteristic, complemented
5	#11758414	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄₉₆	C₂	1	1	yes	maximal, characteristic, complemented
7	#11758386	C₂	1	1	yes	maximal, characteristic, complemented
8	#92499	—	2	1	no	—
9	D₄×D₃₁	—	2	1	no	—
10	Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
11	D₈×C₃₁	C₂²	1	1	yes	characteristic
12	#92481	—	2	1	no	—
13	#92479	—	2	1	no	—
14	D₂₄₈	C₂²	1	1	yes	characteristic
15	D₂₄₈	C₂²	1	1	yes	characteristic, complemented
16	C₈×D₃₁	C₂²	1	1	yes	characteristic
17	C₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
18	C₃₁⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
19	C₂²×D₃₁	—	4	1	no	—
20	Q₈×C₃₁	—	2	1	no	—
21	D₄×C₃₁	—	2	1	no	—
22	C₂²⋊D₃₁	—	4	1	no	—
23	D₁₂₄	—	2	1	no	—
24	D₁₂₄	—	2	1	no	—
25	D₁₂₄	—	4	1	no	—
26	C₄×D₃₁	—	4	1	no	—
27	C₄×D₃₁	D₄	1	1	yes	characteristic
28	C₈×C₃₁	C₂³	1	1	yes	characteristic
29	C₃₁⋊C₈	D₄	1	1	yes	characteristic
30	C₂²×C₃₁	—	4	1	no	—
31	C₂×D₃₁	—	4	1	no	—
32	C₂×D₃₁	—	4	1	no	—
33	C₂×D₃₁	—	8	2	no	—
34	C₂×D₃₁	D₈	1	1	yes	characteristic
35	C₄×C₃₁	—	4	1	no	—
36	C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
37	Dic₃₁	D₈	1	1	yes	characteristic
38	#509	—	31	1	no	maximal, Sylow
39	C₂×C₃₁	—	8	1	no	—
40	C₂×C₃₁	C₂×D₈	1	1	yes	characteristic
41	D₃₁	—	2	1	no	—
42	D₃₁	—	8	1	no	—
43	D₃₁	—	8	1	no	—
44	#135	—	31	1	no	—
45	C₂×D₈	—	31	1	no	—
46	SD₃₂	—	31	1	no	—
47	SD₃₂	D₃₁	1	1	yes	characteristic, complemented
48	D₁₆	—	31	1	no	—
49	D₁₆	—	31	1	no	—
50	M₃₂	—	31	1	no	—
51	C₃₁	#509	1	1	yes	characteristic, complemented, Sylow
52	#41	—	62	1	no	—
53	C₂×D₄	—	62	1	no	—
54	Q₁₆	C₂×D₃₁	1	1	yes	characteristic, complemented
55	SD₁₆	—	62	1	no	—
56	D₈	—	31	1	no	—
57	D₈	—	31	1	no	—
58	D₈	—	62	1	no	—
59	D₈	C₂×D₃₁	1	1	yes	characteristic
60	C₂×C₈	—	31	1	no	—
61	C₁₆	—	31	1	no	—
62	C₁₆	C₂×D₃₁	1	1	yes	characteristic, complemented
63	C₂³	—	124	1	no	—
64	Q₈	—	2	1	no	—
65	D₄	—	2	1	no	—
66	D₄	—	62	1	no	—
67	D₄	—	62	1	no	—
68	D₄	—	124	1	no	—
69	D₄	—	124	1	no	—
70	C₂×C₄	—	31	1	no	—
71	C₂×C₄	—	124	1	no	—
72	C₈	—	31	1	no	—
73	C₈	C₂²×D₃₁	1	1	yes	characteristic
74	C₂²	—	4	1	no	—
75	C₂²	—	31	1	no	—
76	C₂²	—	124	1	no	—
77	C₂²	—	124	1	no	—
78	C₂²	—	248	2	no	—
79	C₄	—	4	1	no	—
80	C₄	—	31	1	no	—
81	C₄	D₄×D₃₁	1	1	yes	characteristic
82	C₂	—	8	1	no	—
83	C₂	—	62	1	no	—
84	C₂	—	248	1	no	—
85	C₂	—	248	1	no	—
86	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×SD₃₂	C₂
socle	C₂×C₃₁	C₂×D₈
hypercenter	SD₃₂	D₃₁
hypocenter	C₃₁	#509
LCS	G ▷ C₈×C₃₁ ▷ C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ SD₃₂

Complements

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

N	H ≅ G/N	type
1. #11758496	C₂	semidirect
2. D₈×D₃₁	C₂	semidirect
3. C₃₁×SD₃₂	C₂	semidirect
4. #11758416	C₂	semidirect
5. #11758414	C₂	semidirect
6. D₄₉₆	C₂	semidirect
7. #11758386	C₂	semidirect
10. Q₁₆×C₃₁	C₂²	semidirect
15. D₂₄₈	C₂²	semidirect
17. C₁₆×C₃₁	C₂²	semidirect
18. C₃₁⋊C₁₆	C₂²	semidirect
47. SD₃₂	D₃₁	semidirect
51. C₃₁	#509	semidirect
54. Q₁₆	C₂×D₃₁	semidirect
62. C₁₆	C₂×D₃₁	semidirect

Maximal subgroups

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

subgroup	index
#11758496	2
D₈×D₃₁	2
C₃₁×SD₃₂	2
#11758416	2
#11758414	2
D₄₉₆	2
#11758386	2
#509	31