Group #14582813 — subgroups

Subgroups — #14582813

Order 2752.

238 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 65 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×Dic₄₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂²⋊Dic₄₃	C₂	1	2	yes	maximal, complemented
3	C₂×C₂²⋊Dic₄₃	C₂	1	2	yes	maximal, complemented
4	C₄₃⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₄×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂⁴×C₄₃	C₂²	1	2	yes	—
7	C₂×D₄×C₄₃	—	2	2	no	—
8	C₂×D₄×C₄₃	—	2	4	no	—
9	C₂²×C₄×C₄₃	C₂²	1	1	yes	characteristic
10	C₂²×Dic₄₃	C₂²	1	2	yes	—
11	C₂²×Dic₄₃	C₂²	1	1	yes	characteristic
12	C₂²×Dic₄₃	C₂²	1	1	yes	characteristic
13	C₂²⋊Dic₄₃	—	2	4	no	—
14	C₂²⋊Dic₄₃	—	2	4	no	—
15	Dic₄₃⋊C₄	—	2	2	no	—
16	C₂³×C₄₃	—	2	2	no	—
17	C₂³×C₄₃	—	2	2	no	—
18	C₂³×C₄₃	—	2	2	no	—
19	C₂³×C₄₃	—	2	2	no	—
20	C₂³×C₄₃	—	2	2	no	—
21	C₂³×C₄₃	—	2	2	no	—
22	C₂³×C₄₃	D₄	1	4	yes	—
23	C₂³×C₄₃	C₂³	1	1	yes	characteristic
24	D₄×C₄₃	—	2	8	no	—
25	C₂×C₄×C₄₃	—	2	2	no	—
26	C₂×C₄×C₄₃	D₄	1	2	yes	—
27	C₂×Dic₄₃	—	2	1	no	—
28	C₂×Dic₄₃	—	2	1	no	—
29	C₂×Dic₄₃	—	2	1	no	—
30	C₂×Dic₄₃	—	2	2	no	—
31	C₂×Dic₄₃	—	2	2	no	—
32	C₂×Dic₄₃	—	2	2	no	—
33	C₂×Dic₄₃	—	2	2	no	—
34	C₂×Dic₄₃	D₄	1	2	yes	complemented
35	C₂²×C₄₃	—	2	4	no	—
36	C₂²×C₄₃	—	2	4	no	—
37	C₂²×C₄₃	—	2	4	no	—
38	C₂²×C₄₃	—	4	2	no	—
39	C₂²×C₄₃	—	4	2	no	—
40	C₂²×C₄₃	—	4	2	no	—
41	C₂²×C₄₃	—	4	2	no	—
42	C₂²×C₄₃	C₂×D₄	1	1	yes	characteristic
43	C₂²×C₄₃	C₂×D₄	1	2	yes	—
44	C₂²×C₄₃	C₂×D₄	1	1	yes	characteristic
45	C₂²×C₄₃	#41	1	1	yes	characteristic
46	C₂²×C₄₃	#41	1	2	yes	—
47	C₄×C₄₃	—	2	2	no	—
48	Dic₄₃	—	2	2	no	—
49	Dic₄₃	—	4	1	no	—
50	Dic₄₃	—	4	2	no	—
51	C₂×C₄₃	—	4	4	no	—
52	C₂×C₄₃	#120	1	1	yes	characteristic
53	C₂×C₄₃	#121	1	1	yes	characteristic
54	C₂×C₄₃	#121	1	2	yes	—
55	C₂×C₄₃	#123	1	2	yes	—
56	C₂×C₄₃	#124	1	1	yes	characteristic
57	#394	—	43	1	no	maximal, Sylow
58	C₄₃	#394	1	1	yes	characteristic, complemented, Sylow
59	C₂²×D₄	D₄₃	1	1	yes	characteristic
60	C₂×C₄⋊C₄	—	43	1	no	—
61	C₂×C₂²⋊C₄	—	43	2	no	—
62	C₂×C₂²⋊C₄	—	43	2	no	—
63	#95	—	43	1	no	—
64	C₂⁴	C₂×D₄₃	1	2	yes	—
65	C₂×D₄	—	2	4	no	—
66	C₂×D₄	—	2	2	no	—
67	C₂²×C₄	—	43	1	no	—
68	C₂²×C₄	—	43	2	no	—
69	C₂²×C₄	—	43	1	no	—
70	C₂²×C₄	C₂×D₄₃	1	1	yes	characteristic
71	C₄⋊C₄	—	86	2	no	—
72	C₂²⋊C₄	—	86	4	no	—
73	C₂²⋊C₄	—	86	4	no	—
74	C₂³	—	2	2	no	—
75	C₂³	—	2	2	no	—
76	C₂³	—	2	2	no	—
77	C₂³	—	2	2	no	—
78	C₂³	—	2	2	no	—
79	C₂³	—	2	2	no	—
80	C₂³	C₂²⋊D₄₃	1	4	yes	—
81	C₂³	C₂²×D₄₃	1	1	yes	characteristic
82	D₄	—	2	8	no	—
83	C₂×C₄	—	2	2	no	—
84	C₂×C₄	—	43	2	no	—
85	C₂×C₄	—	86	1	no	—
86	C₂×C₄	—	86	1	no	—
87	C₂×C₄	—	86	2	no	—
88	C₂×C₄	—	86	2	no	—
89	C₂×C₄	—	86	2	no	—
90	C₂×C₄	—	86	2	no	—
91	C₂×C₄	—	86	1	no	—
92	C₂×C₄	C₂²⋊D₄₃	1	2	yes	—
93	C₂²	—	2	4	no	—
94	C₂²	—	2	4	no	—
95	C₂²	—	2	4	no	—
96	C₂²	—	4	2	no	—
97	C₂²	—	4	2	no	—
98	C₂²	—	4	2	no	—
99	C₂²	—	4	2	no	—
100	C₂²	D₄×D₄₃	1	1	yes	characteristic
101	C₂²	#10621900	1	1	yes	characteristic
102	C₂²	#10621900	1	2	yes	—
103	C₂²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
104	C₂²	C₂×C₂²⋊D₄₃	1	2	yes	—
105	C₄	—	2	2	no	—
106	C₄	—	86	2	no	—
107	C₄	—	172	1	no	—
108	C₄	—	172	2	no	—
109	C₂	—	4	4	no	—
110	C₂	#13063294	1	1	yes	characteristic
111	C₂	#13063296	1	1	yes	characteristic
112	C₂	#13063297	1	2	yes	—
113	C₂	#13063306	1	2	yes	—
114	C₂	#13063312	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₄₃⋊C₄

C₂

yes

maximal, characteristic, complemented

C₂×C₂²⋊Dic₄₃

C₂

yes

maximal, complemented

C₂×C₂²⋊Dic₄₃

C₂

yes

maximal, complemented

C₄₃⋊#95

C₂

yes

maximal, characteristic, complemented

C₂²×D₄×C₄₃

C₂

yes

maximal, characteristic

C₂⁴×C₄₃

C₂²

yes

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂²×C₄×C₄₃

C₂²

yes

characteristic

C₂²×Dic₄₃

C₂²

yes

—

C₂²×Dic₄₃

C₂²

yes

characteristic

C₂²×Dic₄₃

C₂²

yes

characteristic

C₂²⋊Dic₄₃

—

C₂²⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

D₄

yes

—

C₂³×C₄₃

C₂³

yes

characteristic

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

D₄

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

D₄

yes

complemented

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×D₄

yes

characteristic

C₂²×C₄₃

C₂×D₄

yes

—

C₂²×C₄₃

C₂×D₄

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×C₄₃

#123

yes

—

C₂×C₄₃

yes

—

C₄₃

yes

characteristic, complemented, Sylow

C₂²×D₄

D₄₃

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

#95

—

C₂⁴

C₂×D₄₃

yes

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₄₃

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂²⋊D₄₃

yes

—

C₂³

C₂²×D₄₃

yes

characteristic

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊D₄₃

yes

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

100

C₂²

D₄×D₄₃

yes

characteristic

101

C₂²

#10621900

yes

characteristic

102

C₂²

#10621900

yes

—

103

C₂²

C₂×C₂²⋊D₄₃

yes

characteristic

104

C₂²

C₂×C₂²⋊D₄₃

yes

—

105

C₄

—

106

C₄

—

107

C₄

—

172

—

108

C₄

—

172

—

109

C₂

—

110

C₂

#13063294

yes

characteristic

111

C₂

#13063296

yes

characteristic

112

C₂

#13063297

yes

—

113

C₂

#13063306

yes

—

114

C₂

#13063312

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₄₃
commutator, socle, cosocle	C₂³×C₄₃	C₂³
Fitting, prime radical	C₂²×D₄×C₄₃	C₂
hypercenter	C₂²×D₄	D₄₃
hypocenter	C₄₃	#394
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂²×D₄

subgroup

G/H

center, Frattini

C₂³

C₂²×D₄₃

commutator, socle, cosocle

C₂³×C₄₃

C₂³

Fitting, prime radical

C₂²×D₄×C₄₃

C₂

hypercenter

C₂²×D₄

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ C₂²×D₄

N	H ≅ G/N	type
1. C₂×Dic₄₃⋊C₄	C₂	semidirect
2. C₂×C₂²⋊Dic₄₃	C₂	semidirect
3. C₂×C₂²⋊Dic₄₃	C₂	semidirect
4. C₄₃⋊#95	C₂	semidirect
34. C₂×Dic₄₃	D₄	semidirect
58. C₄₃	#394	semidirect

H ≅ G/N

type

1. C₂×Dic₄₃⋊C₄

C₂

semidirect

2. C₂×C₂²⋊Dic₄₃

C₂

semidirect

3. C₂×C₂²⋊Dic₄₃

C₂

semidirect

4. C₄₃⋊#95

C₂

semidirect

34. C₂×Dic₄₃

D₄

semidirect

58. C₄₃

#394

semidirect

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

subgroup	index
C₂×Dic₄₃⋊C₄	2
C₂×C₂²⋊Dic₄₃	2
C₄₃⋊#95	2
C₂²×D₄×C₄₃	2
#394	43

subgroup

index

C₂×Dic₄₃⋊C₄

C₂×C₂²⋊Dic₄₃

C₄₃⋊#95

C₂²×D₄×C₄₃

#394

Subgroups — #14582813

Conjugacy classes of subgroups

Complements

Maximal subgroups