Group #16845884 — subgroups

Subgroups — #16845884

Order 3968.

212 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11758407	C₂	1	1	yes	maximal, characteristic
2	C₂×#11758410	C₂	1	2	yes	maximal
3	#14521072	C₂	1	2	yes	maximal
4	C₂×#11758403	C₂	1	1	yes	maximal, characteristic
5	C₂×C₃₁×#108	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	C₃₁×#108	—	2	2	no	—
12	#11758410	—	2	4	no	—
13	#11758407	—	2	2	no	—
14	#11758403	C₄	1	4	yes	—
15	Dic₃₁⋊C₈	—	2	4	no	—
16	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
17	C₂²×Dic₃₁	Q₈	1	2	yes	—
18	M₁₆×C₃₁	—	2	2	no	—
19	M₁₆×C₃₁	—	2	2	no	—
20	C₂×C₈×C₃₁	—	2	2	no	—
21	C₂×C₈×C₃₁	C₂×C₄	1	2	yes	—
22	C₂×C₈×C₃₁	D₄	1	2	yes	—
23	C₂×C₈×C₃₁	Q₈	1	2	yes	—
24	C₄×Dic₃₁	C₂×C₄	1	2	yes	—
25	C₄×Dic₃₁	D₄	1	2	yes	—
26	#92474	—	2	2	no	—
27	#92474	—	2	2	no	—
28	C₂×C₃₁⋊C₈	—	2	2	no	—
29	C₂×C₃₁⋊C₈	C₂×C₄	1	2	yes	—
30	C₂×C₃₁⋊C₈	D₄	1	2	yes	—
31	C₂×C₃₁⋊C₈	Q₈	1	2	yes	—
32	C₂³×C₃₁	C₂×Q₈	1	1	yes	characteristic
33	C₂×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
38	C₂×C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
39	C₂×Dic₃₁	—	4	2	no	—
40	C₂×Dic₃₁	C₄⋊C₄	1	4	yes	—
41	C₈×C₃₁	—	4	2	no	—
42	C₈×C₃₁	C₄⋊C₄	1	4	yes	—
43	C₃₁⋊C₈	—	4	2	no	—
44	C₃₁⋊C₈	C₄⋊C₄	1	4	yes	—
45	#1849	—	31	1	no	maximal, Sylow
46	C₂²×C₃₁	—	2	2	no	—
47	C₂²×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₂²×C₃₁	C₄⋊Q₈	1	1	yes	characteristic
49	C₂²×C₃₁	C₄⋊Q₈	1	1	yes	characteristic
50	C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
51	C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
52	C₄×C₃₁	#127	1	1	yes	characteristic
53	C₄×C₃₁	C₄⋊Q₈	1	1	yes	characteristic
54	Dic₃₁	—	2	4	no	—
55	C₂×#108	—	31	2	no	—
56	C₂×#108	—	31	1	no	—
57	C₂×#108	D₃₁	1	1	yes	characteristic
58	#423	—	31	2	no	—
59	C₂×#97	—	31	1	no	—
60	C₂×C₃₁	—	2	1	no	—
61	C₂×C₃₁	—	2	1	no	—
62	C₂×C₃₁	#384	1	1	yes	characteristic
63	C₂×C₃₁	#430	1	2	yes	—
64	C₂×M₁₆	—	31	2	no	—
65	C₂×M₁₆	C₂×D₃₁	1	2	yes	—
66	C₂²×C₈	—	31	1	no	—
67	C₂²×C₈	C₂×D₃₁	1	1	yes	characteristic
68	C₂×C₄²	—	31	1	no	—
69	#108	—	2	2	no	—
70	#108	—	62	4	no	—
71	#108	—	62	2	no	—
72	C₄⋊C₈	—	62	4	no	—
73	#97	—	31	4	no	—
74	C₃₁	#1849	1	1	yes	characteristic, complemented, Sylow
75	C₂²×C₄	—	31	2	no	—
76	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
77	M₁₆	—	2	2	no	—
78	M₁₆	—	2	2	no	—
79	M₁₆	—	62	2	no	—
80	M₁₆	—	62	2	no	—
81	C₂×C₈	—	2	2	no	—
82	C₂×C₈	—	31	2	no	—
83	C₂×C₈	—	31	2	no	—
84	C₂×C₈	—	31	2	no	—
85	C₂×C₈	—	62	2	no	—
86	C₂×C₈	Dic₆₂	1	2	yes	—
87	C₂×C₈	C₄×D₃₁	1	2	yes	—
88	C₂×C₈	C₂²⋊D₃₁	1	2	yes	—
89	C₄²	—	31	2	no	—
90	C₄²	—	31	2	no	—
91	C₂³	Q₈×D₃₁	1	1	yes	characteristic
92	C₂×C₄	—	31	4	no	—
93	C₂×C₄	—	124	2	no	—
94	C₂×C₄	C₂×Dic₆₂	1	1	yes	characteristic
95	C₂×C₄	C₂×C₄×D₃₁	1	1	yes	characteristic
96	C₂×C₄	D₄×D₃₁	1	1	yes	characteristic
97	C₂×C₄	D₄×D₃₁	1	1	yes	characteristic
98	C₂×C₄	Q₈×D₃₁	1	1	yes	characteristic
99	C₂×C₄	C₂×C₂²⋊D₃₁	1	1	yes	characteristic
100	C₈	—	4	2	no	—
101	C₈	—	31	4	no	—
102	C₈	—	124	2	no	—
103	C₈	Dic₃₁⋊C₄	1	4	yes	—
104	C₂²	—	2	2	no	—
105	C₂²	#11758465	1	1	yes	characteristic
106	C₂²	C₄⋊C₄×D₃₁	1	1	yes	characteristic
107	C₂²	#11758521	1	1	yes	characteristic
108	C₄	—	62	4	no	—
109	C₄	#11758465	1	1	yes	characteristic
110	C₄	C₄⋊C₄×D₃₁	1	1	yes	characteristic
111	C₄	C₂×Dic₃₁⋊C₄	1	1	yes	characteristic
112	C₄	#11758517	1	1	yes	characteristic
113	C₂	—	2	1	no	—
114	C₂	—	2	1	no	—
115	C₂	#14520918	1	1	yes	characteristic
116	C₂	#14521096	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11758407

C₂

yes

maximal, characteristic

C₂×#11758410

C₂

yes

maximal

#14521072

C₂

yes

maximal

C₂×#11758403

C₂

yes

maximal, characteristic

C₂×C₃₁×#108

C₂

yes

maximal, characteristic

C₂×M₁₆×C₃₁

C₂²

yes

—

C₂²×C₈×C₃₁

C₂²

yes

characteristic

C₂×C₄×Dic₃₁

C₂²

yes

characteristic

C₂×#92474

C₂²

yes

—

C₂²×C₃₁⋊C₈

C₂²

yes

characteristic

C₃₁×#108

—

#11758410

—

#11758407

—

#11758403

C₄

yes

—

Dic₃₁⋊C₈

—

C₂²×C₄×C₃₁

C₂³

yes

characteristic

C₂²×Dic₃₁

Q₈

yes

—

M₁₆×C₃₁

—

M₁₆×C₃₁

—

C₂×C₈×C₃₁

—

C₂×C₈×C₃₁

C₂×C₄

yes

—

C₂×C₈×C₃₁

D₄

yes

—

C₂×C₈×C₃₁

Q₈

yes

—

C₄×Dic₃₁

C₂×C₄

yes

—

C₄×Dic₃₁

D₄

yes

—

#92474

—

#92474

—

C₂×C₃₁⋊C₈

—

C₂×C₃₁⋊C₈

C₂×C₄

yes

—

C₂×C₃₁⋊C₈

D₄

yes

—

C₂×C₃₁⋊C₈

Q₈

yes

—

C₂³×C₃₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₃₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₃₁

C₂×D₄

yes

characteristic

C₂×C₄×C₃₁

C₂×D₄

yes

characteristic

C₂×C₄×C₃₁

C₂×D₄

yes

characteristic

C₂×C₄×C₃₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₃₁

C₂×Q₈

yes

characteristic

C₂×Dic₃₁

—

C₂×Dic₃₁

C₄⋊C₄

yes

—

C₈×C₃₁

—

C₈×C₃₁

C₄⋊C₄

yes

—

C₃₁⋊C₈

—

C₃₁⋊C₈

C₄⋊C₄

yes

—

#1849

—

maximal, Sylow

C₂²×C₃₁

—

C₂²×C₃₁

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₃₁

C₄⋊Q₈

yes

characteristic

C₂²×C₃₁

C₄⋊Q₈

yes

characteristic

C₄×C₃₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₃₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₃₁

#127

yes

characteristic

C₄×C₃₁

C₄⋊Q₈

yes

characteristic

Dic₃₁

—

C₂×#108

—

C₂×#108

—

C₂×#108

D₃₁

yes

characteristic

#423

—

C₂×#97

—

C₂×C₃₁

—

C₂×C₃₁

—

C₂×C₃₁

#384

yes

characteristic

C₂×C₃₁

#430

yes

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₃₁

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₃₁

yes

characteristic

C₂×C₄²

—

#108

—

#108

—

#108

—

C₄⋊C₈

—

#97

—

C₃₁

#1849

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₂²×D₃₁

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₆₂

yes

—

C₂×C₈

C₄×D₃₁

yes

—

C₂×C₈

C₂²⋊D₃₁

yes

—

C₄²

—

C₄²

—

C₂³

Q₈×D₃₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

124

—

C₂×C₄

C₂×Dic₆₂

yes

characteristic

C₂×C₄

C₂×C₄×D₃₁

yes

characteristic

C₂×C₄

D₄×D₃₁

yes

characteristic

C₂×C₄

D₄×D₃₁

yes

characteristic

C₂×C₄

Q₈×D₃₁

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₃₁

yes

characteristic

100

C₈

—

101

C₈

—

102

C₈

—

124

—

103

C₈

Dic₃₁⋊C₄

yes

—

104

C₂²

—

105

C₂²

#11758465

yes

characteristic

106

C₂²

C₄⋊C₄×D₃₁

yes

characteristic

107

C₂²

#11758521

yes

characteristic

108

C₄

—

109

C₄

#11758465

yes

characteristic

110

C₄

C₄⋊C₄×D₃₁

yes

characteristic

111

C₄

C₂×Dic₃₁⋊C₄

yes

characteristic

112

C₄

#11758517

yes

characteristic

113

C₂

—

114

C₂

—

115

C₂

#14520918

yes

characteristic

116

C₂

#14521096

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₃₁
commutator	C₂×C₄×C₃₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₃₁
Fitting	C₂×C₃₁×#108	C₂
socle	C₂²×C₃₁	C₂×C₄⋊C₄
prime radical	C₂³×C₃₁	C₂×Q₈
cosocle	C₂²×C₄×C₃₁	C₂³
hypercenter	C₂×#108	D₃₁
hypocenter	C₃₁	#1849
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₂×C₄

D₄×D₃₁

commutator

C₂×C₄×C₃₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₃₁

Fitting

C₂×C₃₁×#108

C₂

socle

C₂²×C₃₁

C₂×C₄⋊C₄

prime radical

C₂³×C₃₁

C₂×Q₈

cosocle

C₂²×C₄×C₃₁

C₂³

D₃₁

C₃₁

G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
74. C₃₁	#1849	semidirect

H ≅ G/N

type

74. C₃₁

#1849

semidirect

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

subgroup	index
C₂×#11758407	2
C₂×#11758410	2
#14521072	2
C₂×#11758403	2
C₂×C₃₁×#108	2
#1849	31

subgroup

index

C₂×C₃₁×#108

Subgroups — #16845884

Conjugacy classes of subgroups

Complements

Maximal subgroups