Subgroups — #14521405

Order 1984.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11758524	C₂	1	1	yes	maximal, characteristic
2	#11758467	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#103	C₂	1	1	yes	maximal, characteristic, complemented
4	#11758423	C₂	1	1	yes	maximal, characteristic, complemented
5	#11758409	C₂	1	1	yes	maximal, characteristic
6	C₈×Dic₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#11758397	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₈×C₃₁	C₂²	1	1	yes	characteristic
9	C₂×D₁₂₄	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₃₁	C₂²	1	1	yes	characteristic
11	C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
12	(C₂×D₃₁)⋊C₄	—	2	1	no	—
13	(C₂×D₃₁)⋊C₄	—	2	1	no	—
14	C₄⋊Dic₃₁	—	2	1	no	—
15	C₄⋊Dic₃₁	C₂²	1	1	yes	characteristic
16	Dic₃₁⋊C₄	—	2	1	no	—
17	C₄×Dic₃₁	C₂²	1	1	yes	characteristic
18	C₂×C₃₁⋊C₈	C₂²	1	1	yes	characteristic
19	C₂²×D₃₁	—	2	1	no	—
20	Q₈×C₃₁	—	2	1	no	—
21	Q₈×C₃₁	—	2	1	no	—
22	C₂×C₄×C₃₁	—	2	1	no	—
23	C₂×C₄×C₃₁	—	2	1	no	—
24	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
25	C₂×Dic₃₁	—	2	1	no	—
26	C₂×Dic₃₁	D₄	1	1	yes	characteristic
27	C₂×Dic₃₁	D₄	1	1	yes	characteristic
28	D₁₂₄	—	2	1	no	—
29	D₁₂₄	—	2	1	no	—
30	C₈×C₃₁	—	2	1	no	—
31	C₃₁⋊C₈	—	2	1	no	—
32	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
33	C₂×D₃₁	—	4	1	no	—
34	C₂×D₃₁	—	4	1	no	—
35	C₂×D₃₁	—	4	1	no	—
36	C₄×C₃₁	—	4	1	no	—
37	C₄×C₃₁	—	4	1	no	—
38	C₄×C₃₁	#41	1	1	yes	characteristic
39	C₄×C₃₁	#41	1	1	yes	characteristic
40	Dic₃₁	—	2	1	no	—
41	Dic₃₁	—	2	1	no	—
42	Dic₃₁	—	4	1	no	—
43	#488	—	31	1	no	maximal, Sylow
44	C₂×C₃₁	#124	1	1	yes	characteristic
45	C₂×C₃₁	#135	1	1	yes	characteristic
46	C₂×C₃₁	#135	1	1	yes	characteristic
47	D₃₁	—	8	1	no	—
48	#125	—	31	1	no	—
49	#124	—	31	1	no	—
50	#103	—	31	1	no	—
51	#103	D₃₁	1	1	yes	characteristic, complemented
52	#102	—	31	1	no	—
53	#102	—	31	1	no	—
54	C₄×C₈	—	31	1	no	—
55	C₃₁	#488	1	1	yes	characteristic, complemented, Sylow
56	C₂×Q₈	C₂×D₃₁	1	1	yes	characteristic
57	C₂×D₄	—	31	1	no	—
58	C₂×C₈	—	31	1	no	—
59	C₂×C₈	C₂×D₃₁	1	1	yes	characteristic
60	C₄⋊C₄	—	31	1	no	—
61	C₄⋊C₄	—	62	1	no	—
62	C₄⋊C₄	—	62	1	no	—
63	C₄⋊C₄	C₂×D₃₁	1	1	yes	characteristic
64	C₂²⋊C₄	—	62	1	no	—
65	C₂²⋊C₄	—	62	1	no	—
66	C₄²	—	31	1	no	—
67	C₂³	—	62	1	no	—
68	Q₈	—	2	1	no	—
69	Q₈	—	2	1	no	—
70	D₄	—	62	1	no	—
71	D₄	—	62	1	no	—
72	C₂×C₄	—	2	1	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	31	1	no	—
75	C₂×C₄	—	31	1	no	—
76	C₂×C₄	—	62	1	no	—
77	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	62	1	no	—
80	C₂²	—	124	1	no	—
81	C₂²	—	124	1	no	—
82	C₂²	—	124	1	no	—
83	C₂²	D₄×D₃₁	1	1	yes	characteristic
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	62	1	no	—
87	C₄	—	62	1	no	—
88	C₄	—	124	1	no	—
89	C₄	#92495	1	1	yes	characteristic
90	C₄	#92497	1	1	yes	characteristic
91	C₂	—	248	1	no	—
92	C₂	#11758462	1	1	yes	characteristic
93	C₂	#11758493	1	1	yes	characteristic
94	C₂	#11758496	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₃₁
commutator, cosocle	C₂×C₄×C₃₁	C₂³
Frattini	C₂×C₄	C₂²×D₃₁
Fitting	C₃₁×#103	C₂
socle	C₂²×C₃₁	C₂×D₄
prime radical	C₂×D₁₂₄	C₂²
hypercenter	#103	D₃₁
hypocenter	C₃₁	#488
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
2. #11758467	C₂	semidirect
3. C₃₁×#103	C₂	semidirect
4. #11758423	C₂	semidirect
6. C₈×Dic₃₁	C₂	semidirect
51. #103	D₃₁	semidirect
55. C₃₁	#488	semidirect

Maximal subgroups

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

subgroup	index
#11758524	2
#11758467	2
C₃₁×#103	2
#11758423	2
#11758409	2
C₈×Dic₃₁	2
#11758397	2
#488	31