Subgroups — #14521363

Order 1984.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11758507	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#11758409	C₂	1	2	yes	maximal, complemented
5	#11758406	C₂	1	2	yes	maximal, complemented
6	C₂²×C₄×C₃₁	C₂²	1	1	yes	characteristic
7	C₂×C₂²⋊D₃₁	—	2	1	no	—
8	C₂²×Dic₃₁	—	2	1	no	—
9	C₂×D₁₂₄	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₃₁	C₂²	1	2	yes	—
11	(C₂×D₃₁)⋊C₄	—	2	1	no	—
12	C₄⋊Dic₃₁	—	2	1	no	—
13	C₄⋊Dic₃₁	C₂²	1	1	yes	characteristic
14	C₄⋊Dic₃₁	C₂²	1	2	yes	—
15	C₂³×C₃₁	D₄	1	1	yes	characteristic
16	C₂²×D₃₁	—	2	1	no	—
17	C₂×C₄×C₃₁	—	2	2	no	—
18	C₂×C₄×C₃₁	D₄	1	1	yes	characteristic
19	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
20	C₂²⋊D₃₁	—	4	2	no	—
21	C₂×Dic₃₁	—	2	2	no	—
22	C₂×Dic₃₁	—	2	1	no	—
23	C₂×Dic₃₁	—	4	2	no	—
24	D₁₂₄	—	2	2	no	—
25	C₈×C₃₁	—	2	2	no	—
26	C₂²×C₃₁	—	2	1	no	—
27	C₂²×C₃₁	—	2	1	no	—
28	C₂²×C₃₁	D₈	1	2	yes	—
29	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
30	C₂×D₃₁	—	4	1	no	—
31	C₂×D₃₁	—	4	1	no	—
32	C₂×D₃₁	—	4	1	no	—
33	C₄×C₃₁	—	2	1	no	—
34	C₄×C₃₁	#41	1	2	yes	—
35	Dic₃₁	—	4	2	no	—
36	Dic₃₁	—	4	1	no	—
37	#480	—	31	1	no	maximal, Sylow
38	C₂×C₃₁	—	2	2	no	—
39	C₂×C₃₁	#123	1	1	yes	characteristic
40	C₂×C₃₁	C₂×D₈	1	1	yes	characteristic
41	C₂×C₃₁	#137	1	1	yes	characteristic
42	D₃₁	—	8	1	no	—
43	#121	—	31	1	no	—
44	C₂×C₄⋊C₄	—	31	1	no	—
45	#107	—	31	2	no	—
46	#102	—	31	2	no	—
47	C₂²⋊C₈	D₃₁	1	1	yes	characteristic, complemented
48	C₃₁	#480	1	1	yes	characteristic, complemented, Sylow
49	C₂×D₄	—	31	1	no	—
50	C₂×D₄	—	62	1	no	—
51	C₂²×C₄	—	62	1	no	—
52	C₂²×C₄	C₂×D₃₁	1	1	yes	characteristic
53	C₂×C₈	C₂×D₃₁	1	2	yes	—
54	C₄⋊C₄	—	31	2	no	—
55	C₄⋊C₄	—	31	1	no	—
56	C₄⋊C₄	—	62	1	no	—
57	C₂²⋊C₄	—	62	1	no	—
58	C₂³	—	62	1	no	—
59	C₂³	D₁₂₄	1	1	yes	characteristic
60	D₄	—	62	2	no	—
61	D₄	—	124	2	no	—
62	C₂×C₄	—	2	2	no	—
63	C₂×C₄	—	62	1	no	—
64	C₂×C₄	—	62	2	no	—
65	C₂×C₄	—	124	2	no	—
66	C₂×C₄	D₁₂₄	1	1	yes	characteristic
67	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
68	C₈	—	2	2	no	—
69	C₂²	—	2	1	no	—
70	C₂²	—	2	1	no	—
71	C₂²	—	124	1	no	—
72	C₂²	—	124	1	no	—
73	C₂²	—	124	1	no	—
74	C₂²	D₂₄₈	1	2	yes	—
75	C₂²	C₂×D₁₂₄	1	1	yes	characteristic
76	C₄	—	2	1	no	—
77	C₄	—	124	2	no	—
78	C₄	—	124	1	no	—
79	C₄	#92497	1	2	yes	—
80	C₂	—	2	2	no	—
81	C₂	—	248	1	no	—
82	C₂	#11758463	1	1	yes	characteristic
83	C₂	C₂×D₂₄₈	1	1	yes	characteristic
84	C₂	#11758486	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₂₄
commutator, cosocle	C₂×C₄×C₃₁	C₂³
Frattini	C₂×C₄	C₂²×D₃₁
Fitting	C₃₁×C₂²⋊C₈	C₂
socle	C₂²×C₃₁	C₂×D₄
prime radical	#11758507	C₂
hypercenter	C₂²⋊C₈	D₃₁
hypocenter	C₃₁	#480
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₄⋊Dic₃₁	C₂	semidirect
3. C₃₁×C₂²⋊C₈	C₂	semidirect
4. #11758409	C₂	semidirect
5. #11758406	C₂	semidirect
47. C₂²⋊C₈	D₃₁	semidirect
48. C₃₁	#480	semidirect

Maximal subgroups

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

subgroup	index
#11758507	2
C₂×C₄⋊Dic₃₁	2
C₃₁×C₂²⋊C₈	2
#11758409	2
#11758406	2
#480	31