Subgroups — #14520973

Order 1984.

186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×(C₂×D₃₁)⋊C₄	C₂	1	3	yes	maximal
2	C₂×Dic₃₁⋊C₄	C₂	1	3	yes	maximal, complemented
3	C₃₁×#95	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×D₃₁	C₂²	1	1	yes	characteristic
5	C₂²×C₄×C₃₁	C₂²	1	3	yes	—
6	C₂²×Dic₃₁	C₂²	1	3	yes	—
7	(C₂×D₃₁)⋊C₄	—	2	6	no	—
8	Dic₃₁⋊C₄	—	2	6	no	—
9	C₂³×C₃₁	C₂³	1	1	yes	characteristic
10	C₂²×D₃₁	—	2	3	no	—
11	C₂²×D₃₁	—	2	3	no	—
12	C₂²×D₃₁	Q₈	1	2	yes	—
13	C₂×C₄×C₃₁	—	2	3	no	—
14	C₂×C₄×C₃₁	—	2	3	no	—
15	C₂×C₄×C₃₁	—	2	3	no	—
16	C₂×Dic₃₁	—	2	3	no	—
17	C₂×Dic₃₁	—	2	3	no	—
18	C₂×Dic₃₁	D₄	1	6	yes	—
19	C₂²×C₃₁	C₂×D₄	1	3	yes	—
20	C₂²×C₃₁	C₂×Q₈	1	1	yes	characteristic
21	C₂²×C₃₁	#41	1	3	yes	—
22	C₂×D₃₁	—	2	6	no	—
23	C₂×D₃₁	—	4	3	no	—
24	C₂×D₃₁	—	4	1	no	—
25	C₄×C₃₁	—	4	3	no	—
26	Dic₃₁	—	2	6	no	—
27	#396	—	31	1	no	maximal, Sylow
28	C₂×C₃₁	#121	1	3	yes	—
29	C₂×C₃₁	C₂²⋊Q₈	1	3	yes	—
30	C₂×C₃₁	#126	1	1	yes	characteristic
31	D₃₁	—	4	2	no	—
32	C₂×C₄⋊C₄	—	31	3	no	—
33	C₂×C₂²⋊C₄	—	31	3	no	—
34	#95	D₃₁	1	1	yes	characteristic, complemented
35	C₃₁	#396	1	1	yes	characteristic, complemented, Sylow
36	C₂⁴	—	31	1	no	—
37	C₂²×C₄	—	31	3	no	—
38	C₂²×C₄	C₂×D₃₁	1	3	yes	—
39	C₄⋊C₄	—	62	6	no	—
40	C₂²⋊C₄	—	62	6	no	—
41	C₂³	—	31	2	no	—
42	C₂³	—	62	3	no	—
43	C₂³	—	62	3	no	—
44	C₂³	C₂²×D₃₁	1	1	yes	characteristic
45	C₂×C₄	—	2	3	no	—
46	C₂×C₄	—	2	3	no	—
47	C₂×C₄	—	2	3	no	—
48	C₂×C₄	—	31	6	no	—
49	C₂×C₄	—	62	3	no	—
50	C₂×C₄	—	62	3	no	—
51	C₂²	—	62	6	no	—
52	C₂²	—	124	1	no	—
53	C₂²	—	124	3	no	—
54	C₂²	#92495	1	3	yes	—
55	C₂²	D₄×D₃₁	1	3	yes	—
56	C₂²	Q₈×D₃₁	1	1	yes	characteristic
57	C₄	—	4	3	no	—
58	C₄	—	62	6	no	—
59	C₂	—	124	2	no	—
60	C₂	#11758453	1	1	yes	characteristic
61	C₂	#11758461	1	3	yes	—
62	C₂	#11758473	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₃₁
commutator, socle, cosocle	C₂³×C₃₁	C₂³
Fitting	C₃₁×#95	C₂
prime radical	C₂³×D₃₁	C₂²
hypercenter	#95	D₃₁
hypocenter	C₃₁	#396
LCS	G ▷ C₂³×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₃₁⋊C₄	C₂	semidirect
3. C₃₁×#95	C₂	semidirect
34. #95	D₃₁	semidirect
35. C₃₁	#396	semidirect

Maximal subgroups

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

subgroup	index
C₂×(C₂×D₃₁)⋊C₄	2
C₂×Dic₃₁⋊C₄	2
C₃₁×#95	2
#396	31