Subgroups — #16845850

Order 3968.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14521072	C₂	1	2	yes	maximal
2	C₂×#11758403	C₂	1	1	yes	maximal, characteristic
3	#14520814	C₂	1	1	yes	maximal, characteristic
4	#14520813	C₂	1	2	yes	maximal
5	C₃₁×#341	C₂	1	1	yes	maximal, characteristic
6	C₂×M₁₆×C₃₁	C₂²	1	2	yes	—
7	C₂²×C₈×C₃₁	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₃₁	C₂²	1	1	yes	characteristic
9	C₂×#92474	C₂²	1	2	yes	—
10	C₂²×C₃₁⋊C₈	C₂²	1	1	yes	characteristic
11	#11758403	C₄	1	4	yes	—
12	Dic₃₁⋊C₈	—	2	4	no	—
13	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
14	C₂²×Dic₃₁	Q₈	1	2	yes	—
15	M₁₆×C₃₁	—	2	2	no	—
16	M₁₆×C₃₁	—	2	2	no	—
17	C₂×C₈×C₃₁	—	2	2	no	—
18	C₂×C₈×C₃₁	—	2	2	no	—
19	C₂×C₈×C₃₁	C₂×C₄	1	2	yes	—
20	C₄×Dic₃₁	C₂×C₄	1	2	yes	—
21	C₄×Dic₃₁	D₄	1	2	yes	—
22	#92474	—	2	2	no	—
23	#92474	—	2	2	no	—
24	C₂×C₃₁⋊C₈	—	2	2	no	—
25	C₂×C₃₁⋊C₈	—	2	2	no	—
26	C₂×C₃₁⋊C₈	C₂×C₄	1	2	yes	—
27	C₂³×C₃₁	C₂×Q₈	1	1	yes	characteristic
28	C₂×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₃₁	#41	1	2	yes	—
31	C₂×C₄×C₃₁	#41	1	2	yes	—
32	C₂×Dic₃₁	—	4	2	no	—
33	C₂×Dic₃₁	C₄⋊C₄	1	4	yes	—
34	C₈×C₃₁	—	2	2	no	—
35	C₈×C₃₁	—	4	2	no	—
36	C₃₁⋊C₈	—	2	2	no	—
37	C₃₁⋊C₈	—	4	2	no	—
38	#1838	—	31	1	no	maximal, Sylow
39	C₂²×C₃₁	—	2	2	no	—
40	C₂²×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
41	C₂²×C₃₁	#125	1	2	yes	—
42	C₄×C₃₁	#117	1	1	yes	characteristic
43	C₄×C₃₁	#117	1	1	yes	characteristic
44	C₄×C₃₁	#124	1	2	yes	—
45	Dic₃₁	—	2	4	no	—
46	#423	—	31	2	no	—
47	C₂×#97	—	31	1	no	—
48	#341	—	31	2	no	—
49	#341	—	31	1	no	—
50	#341	D₃₁	1	1	yes	characteristic
51	C₂×C₃₁	—	2	2	no	—
52	C₂×C₃₁	#382	1	1	yes	characteristic
53	C₂×C₃₁	#430	1	2	yes	—
54	C₂×M₁₆	—	31	2	no	—
55	C₂×M₁₆	C₂×D₃₁	1	2	yes	—
56	C₂²×C₈	—	31	1	no	—
57	C₂²×C₈	C₂×D₃₁	1	1	yes	characteristic
58	C₂×C₄²	—	31	1	no	—
59	C₄⋊C₈	—	62	4	no	—
60	#97	—	31	4	no	—
61	C₃₁	#1838	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₄	—	31	2	no	—
63	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
64	M₁₆	—	2	2	no	—
65	M₁₆	—	2	2	no	—
66	M₁₆	—	62	2	no	—
67	M₁₆	—	62	2	no	—
68	C₂×C₈	—	2	2	no	—
69	C₂×C₈	—	2	2	no	—
70	C₂×C₈	—	31	2	no	—
71	C₂×C₈	—	62	2	no	—
72	C₂×C₈	—	62	2	no	—
73	C₂×C₈	C₄×D₃₁	1	2	yes	—
74	C₄²	—	31	2	no	—
75	C₄²	—	31	2	no	—
76	C₂³	Q₈×D₃₁	1	1	yes	characteristic
77	C₂×C₄	—	31	4	no	—
78	C₂×C₄	—	124	2	no	—
79	C₂×C₄	C₂×C₄×D₃₁	1	1	yes	characteristic
80	C₂×C₄	#92495	1	2	yes	—
81	C₂×C₄	D₄×D₃₁	1	1	yes	characteristic
82	C₂×C₄	#92497	1	2	yes	—
83	C₈	—	2	2	no	—
84	C₈	—	4	2	no	—
85	C₈	—	62	2	no	—
86	C₈	—	124	2	no	—
87	C₂²	—	2	2	no	—
88	C₂²	#11758466	1	2	yes	—
89	C₂²	C₄⋊C₄×D₃₁	1	1	yes	characteristic
90	C₄	—	62	4	no	—
91	C₄	#11758449	1	1	yes	characteristic
92	C₄	#11758454	1	1	yes	characteristic
93	C₄	#11758462	1	2	yes	—
94	C₂	—	2	2	no	—
95	C₂	#14520913	1	1	yes	characteristic
96	C₂	#14521096	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	D₄×D₃₁
commutator	C₂×C₄×C₃₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₃₁
Fitting	C₃₁×#341	C₂
socle	C₂²×C₃₁	C₂×C₄⋊C₄
prime radical	C₂³×C₃₁	C₂×Q₈
cosocle	C₂²×C₄×C₃₁	C₂³
hypercenter	#341	D₃₁
hypocenter	C₃₁	#1838
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #341

Complements

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

N	H ≅ G/N	type
61. C₃₁	#1838	semidirect

Maximal subgroups

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

subgroup	index
#14521072	2
C₂×#11758403	2
#14520814	2
#14520813	2
C₃₁×#341	2
#1838	31