Subgroups — #16845794

Order 3968.

272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14521013	C₂	1	2	yes	maximal
2	#14520818	C₂	1	4	yes	maximal, complemented
3	C₂×C₃₁×#117	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₄×C₃₁	C₂²	1	1	yes	characteristic
5	C₃₁×#117	—	2	4	no	—
6	C₂×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
7	C₂×C₂²⋊C₄×C₃₁	C₄	1	2	yes	—
8	C₂×C₄²×C₃₁	C₄	1	2	yes	—
9	C₂×#92474	C₂²	1	4	yes	—
10	C₂²⋊(C₃₁⋊C₈)	—	2	4	no	—
11	C₂⁴×C₃₁	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₄×C₃₁	—	2	4	no	—
13	C₂²×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₄×C₃₁	C₂×C₄	1	4	yes	—
15	C₂²×C₄×C₃₁	D₄	1	4	yes	—
16	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
17	C₄⋊C₄×C₃₁	—	2	4	no	—
18	C₂²⋊C₄×C₃₁	—	2	4	no	—
19	C₄²×C₃₁	—	2	4	no	—
20	#92474	—	2	8	no	—
21	C₂×C₃₁⋊C₈	—	2	4	no	—
22	C₂³×C₃₁	—	2	2	no	—
23	C₂³×C₃₁	—	4	2	no	—
24	C₂³×C₃₁	C₂²⋊C₄	1	2	yes	—
25	C₂³×C₃₁	C₂²×C₄	1	1	yes	characteristic
26	C₂×C₄×C₃₁	—	2	2	no	—
27	C₂×C₄×C₃₁	—	2	8	no	—
28	C₂×C₄×C₃₁	—	2	4	no	—
29	C₂×C₄×C₃₁	—	4	4	no	—
30	C₂×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
31	C₂×C₄×C₃₁	C₂×D₄	1	2	yes	—
32	C₂×C₄×C₃₁	#41	1	4	yes	—
33	C₃₁⋊C₈	—	4	4	no	—
34	#1822	—	31	1	no	maximal, Sylow
35	C₂²×C₃₁	—	2	2	no	—
36	C₂²×C₃₁	—	2	2	no	—
37	C₂²×C₃₁	—	2	4	no	—
38	C₂²×C₃₁	—	4	4	no	—
39	C₂²×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
40	C₂²×C₃₁	#117	1	2	yes	—
41	C₄×C₃₁	—	2	2	no	—
42	C₄×C₃₁	—	4	4	no	—
43	C₄×C₃₁	#123	1	4	yes	—
44	C₂×#117	D₃₁	1	1	yes	characteristic
45	#407	—	31	2	no	—
46	#343	—	31	4	no	—
47	C₂×C₃₁	—	2	2	no	—
48	C₂×C₃₁	—	4	2	no	—
49	C₂×C₃₁	#381	1	1	yes	characteristic
50	C₂×C₃₁	#413	1	2	yes	—
51	C₂³×C₄	C₂×D₃₁	1	1	yes	characteristic
52	C₂×M₁₆	—	31	4	no	—
53	#117	—	2	4	no	—
54	C₂×C₄⋊C₄	C₂×D₃₁	1	2	yes	—
55	C₂×C₂²⋊C₄	Dic₃₁	1	2	yes	—
56	C₂×C₄²	Dic₃₁	1	2	yes	—
57	C₂²⋊C₈	—	62	4	no	—
58	C₃₁	#1822	1	1	yes	characteristic, complemented, Sylow
59	C₂⁴	C₂×Dic₃₁	1	1	yes	characteristic
60	C₂²×C₄	—	2	4	no	—
61	C₂²×C₄	C₂×Dic₃₁	1	1	yes	characteristic
62	C₂²×C₄	C₂×Dic₃₁	1	4	yes	—
63	C₂²×C₄	C₂²⋊D₃₁	1	4	yes	—
64	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
65	M₁₆	—	62	8	no	—
66	C₂×C₈	—	62	4	no	—
67	C₄⋊C₄	—	2	4	no	—
68	C₂²⋊C₄	—	2	4	no	—
69	C₄²	—	2	4	no	—
70	C₂³	—	2	2	no	—
71	C₂³	—	4	2	no	—
72	C₂³	C₂²⋊Dic₃₁	1	2	yes	—
73	C₂³	C₂²×Dic₃₁	1	1	yes	characteristic
74	C₂×C₄	—	2	2	no	—
75	C₂×C₄	—	2	8	no	—
76	C₂×C₄	—	2	4	no	—
77	C₂×C₄	—	4	4	no	—
78	C₂×C₄	C₂²⋊Dic₃₁	1	2	yes	—
79	C₂×C₄	#92495	1	4	yes	—
80	C₂×C₄	C₂×C₂²⋊D₃₁	1	2	yes	—
81	C₈	—	124	4	no	—
82	C₂²	—	2	2	no	—
83	C₂²	—	2	2	no	—
84	C₂²	—	2	4	no	—
85	C₂²	—	4	4	no	—
86	C₂²	#11758503	1	2	yes	—
87	C₂²	C₂×C₂²⋊Dic₃₁	1	1	yes	characteristic
88	C₄	—	2	2	no	—
89	C₄	—	4	4	no	—
90	C₄	#11758506	1	4	yes	—
91	C₂	—	2	2	no	—
92	C₂	—	4	2	no	—
93	C₂	#14520912	1	1	yes	characteristic
94	C₂	#14521033	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊Dic₃₁
commutator	C₂³×C₃₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₃₁
Fitting	C₂×C₃₁×#117	C₂
socle	C₂²×C₃₁	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₃₁	C₂×C₄
cosocle	C₂²×C₄×C₃₁	C₂³
hypercenter	C₂×#117	D₃₁
hypocenter	C₃₁	#1822
LCS	G ▷ C₂³×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#117

Complements

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

N	H ≅ G/N	type
2. #14520818	C₂	semidirect
58. C₃₁	#1822	semidirect

Maximal subgroups

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

subgroup	index
#14521013	2
#14520818	2
C₂×C₃₁×#117	2
#1822	31