Subgroups — #14521602

Order 1984.

222 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#117	C₂	1	1	yes	maximal, characteristic
2	#11758503	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×Dic₃₁	C₂	1	1	yes	maximal, characteristic
4	#11758467	C₂	1	2	yes	maximal, complemented
5	#11758465	C₂	1	2	yes	maximal, complemented
6	#11758455	C₂	1	4	yes	maximal
7	C₄×Dic₆₂	C₂	1	4	yes	maximal, complemented
8	C₂²×C₄×C₃₁	C₂²	1	1	yes	characteristic
9	C₂²×Dic₃₁	C₂²	1	2	yes	—
10	C₂×Dic₆₂	C₂²	1	4	yes	—
11	C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
12	C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
13	C₄²×C₃₁	C₂²	1	2	yes	—
14	C₂²⋊Dic₃₁	C₂²	1	2	yes	—
15	C₄⋊Dic₃₁	C₂²	1	4	yes	—
16	C₄⋊Dic₃₁	C₂²	1	2	yes	—
17	Dic₃₁⋊C₄	C₂²	1	4	yes	—
18	Dic₃₁⋊C₄	C₂²	1	4	yes	—
19	C₄×Dic₃₁	C₂²	1	2	yes	—
20	C₄×Dic₃₁	C₂²	1	2	yes	—
21	C₄×Dic₃₁	C₂²	1	1	yes	characteristic
22	C₄×Dic₃₁	C₂²	1	1	yes	characteristic
23	C₂³×C₃₁	C₂³	1	1	yes	characteristic
24	C₂×C₄×C₃₁	Q₈	1	4	yes	complemented
25	C₂×C₄×C₃₁	C₂³	1	4	yes	—
26	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
27	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
28	C₂×Dic₃₁	—	2	4	no	—
29	C₂×Dic₃₁	C₂³	1	2	yes	—
30	C₂×Dic₃₁	C₂³	1	4	yes	—
31	C₂×Dic₃₁	C₂³	1	2	yes	—
32	Dic₆₂	—	2	8	no	—
33	C₂²×C₃₁	—	2	2	no	—
34	C₂²×C₃₁	C₂×Q₈	1	2	yes	—
35	C₂²×C₃₁	C₂⁴	1	1	yes	characteristic
36	C₄×C₃₁	—	2	4	no	—
37	C₄×C₃₁	C₂×Q₈	1	2	yes	—
38	C₄×C₃₁	C₂×Q₈	1	2	yes	—
39	Dic₃₁	—	2	4	no	—
40	Dic₃₁	—	2	2	no	—
41	Dic₃₁	#41	1	4	yes	—
42	#533	—	31	1	no	maximal, Sylow
43	C₂×C₃₁	—	2	2	no	—
44	C₂×C₃₁	C₂²×Q₈	1	1	yes	characteristic
45	C₂×C₃₁	C₂×#41	1	2	yes	—
46	C₄⋊Q₈	—	31	2	no	—
47	#125	—	31	2	no	—
48	C₂²⋊Q₈	—	31	4	no	—
49	C₄×Q₈	—	31	4	no	—
50	#117	—	31	1	no	—
51	#117	D₃₁	1	1	yes	characteristic
52	C₂×C₄²	—	31	1	no	—
53	C₃₁	#533	1	1	yes	characteristic, complemented, Sylow
54	C₂×Q₈	—	31	4	no	—
55	C₂²×C₄	—	31	2	no	—
56	C₂²×C₄	C₂×D₃₁	1	1	yes	characteristic
57	C₄⋊C₄	—	31	4	no	—
58	C₄⋊C₄	—	31	4	no	—
59	C₄⋊C₄	—	31	2	no	—
60	C₄⋊C₄	—	31	4	no	—
61	C₄⋊C₄	C₂×D₃₁	1	2	yes	—
62	C₂²⋊C₄	—	31	2	no	—
63	C₂²⋊C₄	C₂×D₃₁	1	2	yes	—
64	C₄²	—	31	1	no	—
65	C₄²	—	31	1	no	—
66	C₄²	—	31	2	no	—
67	C₄²	—	31	2	no	—
68	C₄²	C₂×D₃₁	1	2	yes	—
69	C₂³	C₂²×D₃₁	1	1	yes	characteristic
70	Q₈	—	62	8	no	—
71	C₂×C₄	—	31	2	no	—
72	C₂×C₄	—	31	2	no	—
73	C₂×C₄	—	31	4	no	—
74	C₂×C₄	—	62	4	no	—
75	C₂×C₄	Dic₆₂	1	4	yes	complemented
76	C₂×C₄	C₂²×D₃₁	1	4	yes	—
77	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
78	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
79	C₂²	—	2	2	no	—
80	C₂²	C₂×Dic₆₂	1	2	yes	—
81	C₂²	C₂³×D₃₁	1	1	yes	characteristic
82	C₄	—	2	4	no	—
83	C₄	—	31	4	no	—
84	C₄	—	62	2	no	—
85	C₄	—	62	4	no	—
86	C₄	C₂×Dic₆₂	1	2	yes	—
87	C₄	C₂×Dic₆₂	1	2	yes	—
88	C₂	—	2	2	no	—
89	C₂	C₂²×Dic₆₂	1	1	yes	characteristic
90	C₂	#41×D₃₁	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²×D₃₁
commutator, socle, cosocle	C₂²×C₃₁	C₂⁴
Frattini	C₂²	C₂³×D₃₁
Fitting	C₃₁×#117	C₂
prime radical	C₂³×C₃₁	C₂³
hypercenter	#117	D₃₁
hypocenter	C₃₁	#533
LCS	G ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
4. #11758467	C₂	semidirect
5. #11758465	C₂	semidirect
7. C₄×Dic₆₂	C₂	semidirect
24. C₂×C₄×C₃₁	Q₈	semidirect
53. C₃₁	#533	semidirect
75. C₂×C₄	Dic₆₂	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#117	2
#11758503	2
C₂×C₄×Dic₃₁	2
#11758467	2
#11758465	2
#11758455	2
C₄×Dic₆₂	2
#533	31