Group #46846703 — subgroups

Subgroups — C₂×#31774265 #46846703

Order 34688.

384 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 149 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×#22576152	C₂	1	1	yes	maximal, characteristic
2	#31774265	C₂	1	8	yes	maximal, direct product factor
3	C₂×#22576084	C₂	1	4	yes	maximal
4	C₂×#22576071	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊Q₈×C₂₇₁	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₂₇₁⋊C₈	C₂²	1	2	yes	—
7	#22576152	—	2	2	no	—
8	#22576152	C₂²	1	4	yes	—
9	C₂×C₄⋊Dic₂₇₁	C₂²	1	2	yes	—
10	C₂×Dic₂₇₁⋊C₄	—	2	2	no	—
11	#22576084	C₂²	1	16	yes	—
12	#22576071	C₂²	1	4	yes	—
13	C₂²×Q₈×C₂₇₁	C₂²	1	2	yes	—
14	C₄⋊Q₈×C₂₇₁	—	2	2	no	—
15	C₄⋊Q₈×C₂₇₁	C₂²	1	4	yes	—
16	C₂×C₄⋊C₄×C₂₇₁	—	2	2	no	—
17	C₂×C₄²×C₂₇₁	C₂²	1	1	yes	characteristic
18	C₂²×Dic₂₇₁	—	2	2	no	—
19	C₂×C₂₇₁⋊C₈	—	2	4	no	—
20	C₂×C₂₇₁⋊C₈	C₂³	1	4	yes	—
21	C₄⋊Dic₂₇₁	—	2	2	no	—
22	C₄⋊Dic₂₇₁	C₂³	1	4	yes	—
23	Dic₂₇₁⋊C₄	—	2	8	no	—
24	C₂×Q₈×C₂₇₁	—	2	2	no	—
25	C₂×Q₈×C₂₇₁	—	2	8	no	—
26	C₂×Q₈×C₂₇₁	C₂³	1	4	yes	—
27	C₂²×C₄×C₂₇₁	—	2	2	no	—
28	C₂²×C₄×C₂₇₁	D₄	1	2	yes	—
29	C₂²×C₄×C₂₇₁	C₂³	1	1	yes	characteristic
30	C₄⋊C₄×C₂₇₁	—	2	8	no	—
31	C₄²×C₂₇₁	D₄	1	2	yes	—
32	C₄²×C₂₇₁	C₂³	1	2	yes	—
33	C₂×Dic₂₇₁	—	2	4	no	—
34	C₂×Dic₂₇₁	—	4	4	no	—
35	C₂₇₁⋊C₈	—	2	4	no	—
36	C₂³×C₂₇₁	C₂×D₄	1	1	yes	characteristic
37	Q₈×C₂₇₁	—	2	8	no	—
38	Q₈×C₂₇₁	—	4	4	no	—
39	C₂×C₄×C₂₇₁	—	2	4	no	—
40	C₂×C₄×C₂₇₁	—	2	4	no	—
41	C₂×C₄×C₂₇₁	—	4	4	no	—
42	C₂×C₄×C₂₇₁	C₂×D₄	1	4	yes	—
43	C₂×C₄×C₂₇₁	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₂₇₁	#41	1	4	yes	—
45	C₂×C₄×C₂₇₁	C₂⁴	1	1	yes	characteristic
46	C₂²×C₂₇₁	#124	1	2	yes	—
47	C₂²×C₂₇₁	#137	1	4	yes	—
48	C₂²×C₂₇₁	C₂²×D₄	1	1	yes	characteristic
49	C₄×C₂₇₁	—	2	4	no	—
50	C₄×C₂₇₁	—	4	4	no	—
51	C₄×C₂₇₁	#124	1	2	yes	—
52	C₄×C₂₇₁	C₂×#41	1	2	yes	—
53	Dic₂₇₁	—	4	4	no	—
54	C₂×C₂₇₁	#491	1	4	yes	complemented
55	C₂×C₂₇₁	C₂×#124	1	1	yes	characteristic
56	C₂×C₂₇₁	C₂×#137	1	2	yes	—
57	C₂₇₁	C₂×#491	1	1	yes	characteristic, complemented, Sylow
58	C₂×#491	—	271	1	no	maximal, Sylow
59	C₂×C₄⋊Q₈	D₂₇₁	1	1	yes	characteristic
60	C₂×#125	—	271	1	no	—
61	#491	—	271	8	no	—
62	C₂×#103	—	271	4	no	—
63	C₂×#97	—	271	1	no	—
64	C₂²×Q₈	C₂×D₂₇₁	1	2	yes	—
65	C₂²×C₈	—	271	2	no	—
66	C₄⋊Q₈	—	2	2	no	—
67	C₄⋊Q₈	C₂×D₂₇₁	1	4	yes	—
68	#125	—	271	4	no	—
69	#125	—	542	2	no	—
70	C₂×C₄⋊C₄	—	2	2	no	—
71	C₂×C₄⋊C₄	—	271	2	no	—
72	C₂×C₄⋊C₄	—	542	2	no	—
73	C₂×C₄²	C₂×D₂₇₁	1	1	yes	characteristic
74	#103	—	271	16	no	—
75	#97	—	271	4	no	—
76	C₂×Q₈	—	2	2	no	—
77	C₂×Q₈	—	2	8	no	—
78	C₂×Q₈	C₂²×D₂₇₁	1	4	yes	—
79	C₂²×C₄	—	2	2	no	—
80	C₂²×C₄	—	542	2	no	—
81	C₂²×C₄	C₂²⋊D₂₇₁	1	2	yes	—
82	C₂²×C₄	C₂²×D₂₇₁	1	1	yes	characteristic
83	C₂×C₈	—	271	4	no	—
84	C₂×C₈	—	542	4	no	—
85	C₄⋊C₄	—	2	8	no	—
86	C₄⋊C₄	—	271	4	no	—
87	C₄⋊C₄	—	542	2	no	—
88	C₄⋊C₄	—	542	8	no	—
89	C₄²	C₂²⋊D₂₇₁	1	2	yes	—
90	C₄²	C₂²×D₂₇₁	1	2	yes	—
91	C₂³	C₂×C₂²⋊D₂₇₁	1	1	yes	characteristic
92	Q₈	—	2	8	no	—
93	Q₈	—	4	4	no	—
94	C₂×C₄	—	2	4	no	—
95	C₂×C₄	—	2	4	no	—
96	C₂×C₄	—	4	4	no	—
97	C₂×C₄	—	542	4	no	—
98	C₂×C₄	—	1084	4	no	—
99	C₂×C₄	C₂×C₂²⋊D₂₇₁	1	4	yes	—
100	C₂×C₄	C₂×C₂²⋊D₂₇₁	1	1	yes	characteristic
101	C₂×C₄	#16864653	1	4	yes	—
102	C₂×C₄	C₂³×D₂₇₁	1	1	yes	characteristic
103	C₈	—	542	4	no	—
104	C₂²	#22576147	1	2	yes	—
105	C₂²	#22576191	1	4	yes	—
106	C₂²	C₂²×C₂²⋊D₂₇₁	1	1	yes	characteristic
107	C₄	—	2	4	no	—
108	C₄	—	4	4	no	—
109	C₄	—	1084	4	no	—
110	C₄	#22576147	1	2	yes	—
111	C₄	C₂×#16864653	1	2	yes	—
112	C₂	#31774265	1	4	yes	direct product factor
113	C₂	C₂×#22576147	1	1	yes	characteristic
114	C₂	C₂×#22576191	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#22576152

C₂

yes

maximal, characteristic

#31774265

C₂

yes

maximal, direct product factor

C₂×#22576084

C₂

yes

maximal

C₂×#22576071

C₂

yes

maximal, characteristic

C₂×C₄⋊Q₈×C₂₇₁

C₂

yes

maximal, characteristic

C₂²×C₂₇₁⋊C₈

C₂²

yes

—

#22576152

—

#22576152

C₂²

yes

—

C₂×C₄⋊Dic₂₇₁

C₂²

yes

—

C₂×Dic₂₇₁⋊C₄

—

#22576084

C₂²

yes

—

#22576071

C₂²

yes

—

C₂²×Q₈×C₂₇₁

C₂²

yes

—

C₄⋊Q₈×C₂₇₁

—

C₄⋊Q₈×C₂₇₁

C₂²

yes

—

C₂×C₄⋊C₄×C₂₇₁

—

C₂×C₄²×C₂₇₁

C₂²

yes

characteristic

C₂²×Dic₂₇₁

—

C₂×C₂₇₁⋊C₈

—

C₂×C₂₇₁⋊C₈

C₂³

yes

—

C₄⋊Dic₂₇₁

—

C₄⋊Dic₂₇₁

C₂³

yes

—

Dic₂₇₁⋊C₄

—

C₂×Q₈×C₂₇₁

—

C₂×Q₈×C₂₇₁

—

C₂×Q₈×C₂₇₁

C₂³

yes

—

C₂²×C₄×C₂₇₁

—

C₂²×C₄×C₂₇₁

D₄

yes

—

C₂²×C₄×C₂₇₁

C₂³

yes

characteristic

C₄⋊C₄×C₂₇₁

—

C₄²×C₂₇₁

D₄

yes

—

C₄²×C₂₇₁

C₂³

yes

—

C₂×Dic₂₇₁

—

C₂×Dic₂₇₁

—

C₂₇₁⋊C₈

—

C₂³×C₂₇₁

C₂×D₄

yes

characteristic

Q₈×C₂₇₁

—

Q₈×C₂₇₁

—

C₂×C₄×C₂₇₁

—

C₂×C₄×C₂₇₁

—

C₂×C₄×C₂₇₁

—

C₂×C₄×C₂₇₁

C₂×D₄

yes

—

C₂×C₄×C₂₇₁

C₂×D₄

yes

characteristic

C₂×C₄×C₂₇₁

#41

yes

—

C₂×C₄×C₂₇₁

C₂⁴

yes

characteristic

C₂²×C₂₇₁

#124

yes

—

C₂²×C₂₇₁

#137

yes

—

C₂²×C₂₇₁

C₂²×D₄

yes

characteristic

C₄×C₂₇₁

—

C₄×C₂₇₁

—

C₄×C₂₇₁

#124

yes

—

C₄×C₂₇₁

C₂×#41

yes

—

Dic₂₇₁

—

C₂×C₂₇₁

yes

C₂×C₂₇₁

yes

C₂×C₂₇₁

yes

—

C₂₇₁

C₂×#491

yes

characteristic, complemented, Sylow

C₂×#491

—

271

maximal, Sylow

C₂×C₄⋊Q₈

D₂₇₁

yes

characteristic

C₂×#125

—

271

—

#491

—

271

—

C₂×#103

—

271

—

C₂×#97

—

271

—

C₂²×Q₈

C₂×D₂₇₁

yes

—

C₂²×C₈

—

271

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₂₇₁

yes

—

#125

—

271

—

#125

—

542

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

271

—

C₂×C₄⋊C₄

—

542

—

C₂×C₄²

C₂×D₂₇₁

yes

characteristic

#103

—

271

—

#97

—

271

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂²×D₂₇₁

yes

—

C₂²×C₄

—

C₂²×C₄

—

542

—

C₂²×C₄

C₂²⋊D₂₇₁

yes

—

C₂²×C₄

C₂²×D₂₇₁

yes

characteristic

C₂×C₈

—

271

—

C₂×C₈

—

542

—

C₄⋊C₄

—

C₄⋊C₄

—

271

—

C₄⋊C₄

—

542

—

C₄⋊C₄

—

542

—

C₄²

C₂²⋊D₂₇₁

yes

—

C₄²

C₂²×D₂₇₁

yes

—

C₂³

C₂×C₂²⋊D₂₇₁

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

542

—

C₂×C₄

—

1084

—

C₂×C₄

C₂×C₂²⋊D₂₇₁

yes

—

100

C₂×C₄

C₂×C₂²⋊D₂₇₁

yes

characteristic

101

C₂×C₄

#16864653

yes

—

102

C₂×C₄

C₂³×D₂₇₁

yes

characteristic

103

C₈

—

542

—

104

C₂²

#22576147

yes

—

105

C₂²

#22576191

yes

—

106

C₂²

C₂²×C₂²⋊D₂₇₁

yes

characteristic

107

C₄

—

108

C₄

—

109

C₄

—

1084

—

110

C₄

#22576147

yes

—

111

C₄

C₂×#16864653

yes

—

112

C₂

#31774265

yes

direct product factor

113

C₂

C₂×#22576147

yes

characteristic

114

C₂

C₂×#22576191

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₂₇₁
commutator, cosocle	C₂×C₄×C₂₇₁	C₂⁴
Frattini	C₂×C₄	C₂³×D₂₇₁
Fitting	C₂×C₄⋊Q₈×C₂₇₁	C₂
socle, prime radical	C₂³×C₂₇₁	C₂×D₄
hypercenter	C₂×C₄⋊Q₈	D₂₇₁
hypocenter	C₂₇₁	C₂×#491
LCS	G ▷ C₂×C₄×C₂₇₁ ▷ C₂×C₂₇₁ ▷ C₂₇₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊Q₈

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₂₇₁

commutator, cosocle

C₂×C₄×C₂₇₁

C₂⁴

Frattini

C₂×C₄

C₂³×D₂₇₁

Fitting

C₂×C₄⋊Q₈×C₂₇₁

C₂

socle, prime radical

C₂³×C₂₇₁

C₂×D₄

hypercenter

C₂×C₄⋊Q₈

D₂₇₁

hypocenter

C₂₇₁

C₂×#491

LCS

G ▷ C₂×C₄×C₂₇₁ ▷ C₂×C₂₇₁ ▷ C₂₇₁

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊Q₈

N	H ≅ G/N	type
2. #31774265	C₂	direct (N × H)
54. C₂×C₂₇₁	#491	semidirect
57. C₂₇₁	C₂×#491	semidirect
112. C₂	#31774265	direct (N × H)

H ≅ G/N

type

2. #31774265

C₂

direct (N × H)

54. C₂×C₂₇₁

#491

semidirect

57. C₂₇₁

C₂×#491

semidirect

112. C₂

#31774265

direct (N × H)

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

subgroup	index
C₂×#22576152	2
#31774265	2
C₂×#22576084	2
C₂×#22576071	2
C₂×C₄⋊Q₈×C₂₇₁	2
C₂×#491	271

subgroup

index

C₂×C₄⋊Q₈×C₂₇₁

271

Subgroups — C₂×#31774265 #46846703

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#31774265 #46846703

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#31774265 #46846703