Group #14583611 — subgroups

Subgroups — #14583611

Order 2752.

236 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 95 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	#13063323	C₂	1	1	yes	maximal, characteristic, complemented
2	#13063314	C₂	1	1	yes	maximal, characteristic, complemented
3	#13063311	C₂	1	2	yes	maximal, complemented
4	#13063298	C₂	1	2	yes	maximal, complemented
5	#13063297	C₂	1	2	yes	maximal, complemented
6	(C₂²⋊D₄₃)⋊C₄	C₂	1	2	yes	maximal, complemented
7	#13063282	C₂	1	2	yes	maximal, complemented
8	#13063281	C₂	1	2	yes	maximal, complemented
9	#124×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×Q₈×C₄₃	C₂²	1	1	yes	characteristic
11	C₂×D₄×C₄₃	C₂²	1	1	yes	characteristic
12	C₂×C₂²⋊D₄₃	C₂²	1	2	yes	—
13	C₂×C₂²⋊D₄₃	C₂²	1	2	yes	—
14	C₂²×Dic₄₃	C₂²	1	2	yes	—
15	C₂×D₁₇₂	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄₃	C₂²	1	2	yes	—
17	C₂×Dic₈₆	C₂²	1	1	yes	characteristic
18	C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
19	C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
20	C₄²×C₄₃	C₂²	1	1	yes	characteristic
21	C₂²⋊Dic₄₃	C₂²	1	2	yes	—
22	(C₂×D₄₃)⋊C₄	C₂²	1	2	yes	—
23	(C₂×D₄₃)⋊C₄	C₂²	1	2	yes	—
24	(C₂×D₄₃)⋊C₄	C₂²	1	2	yes	—
25	Dic₄₃⋊C₄	C₂²	1	2	yes	—
26	Dic₄₃⋊C₄	C₂²	1	2	yes	—
27	Dic₄₃⋊C₄	C₂²	1	2	yes	—
28	C₄×Dic₄₃	C₂²	1	1	yes	characteristic
29	C₄×Dic₄₃	C₂²	1	2	yes	—
30	C₄×Dic₄₃	C₂²	1	1	yes	characteristic
31	C₂³×C₄₃	C₂³	1	2	yes	—
32	C₂²×D₄₃	C₂³	1	2	yes	—
33	Q₈×C₄₃	—	4	1	no	—
34	D₄×C₄₃	—	4	1	no	—
35	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
36	C₂×C₄×C₄₃	C₂³	1	2	yes	—
37	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
38	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
39	C₂²⋊D₄₃	—	2	4	no	—
40	C₂²⋊D₄₃	—	4	2	no	—
41	C₂×Dic₄₃	—	2	4	no	—
42	C₂×Dic₄₃	C₂³	1	2	yes	—
43	C₂×Dic₄₃	C₂³	1	2	yes	—
44	C₂×Dic₄₃	C₂³	1	2	yes	—
45	D₁₇₂	—	4	1	no	—
46	C₄×D₄₃	—	2	4	no	—
47	Dic₈₆	—	4	1	no	—
48	C₂²×C₄₃	—	2	2	no	—
49	C₂²×C₄₃	—	2	2	no	—
50	C₂²×C₄₃	—	2	2	no	—
51	C₂²×C₄₃	C₂⁴	1	1	yes	characteristic
52	C₂×D₄₃	—	2	2	no	—
53	C₂×D₄₃	—	2	2	no	—
54	C₂×D₄₃	—	2	2	no	—
55	C₄×C₄₃	—	2	2	no	—
56	C₄×C₄₃	—	2	1	no	—
57	C₄×C₄₃	—	2	1	no	—
58	C₄×C₄₃	—	2	1	no	—
59	Dic₄₃	—	2	2	no	—
60	Dic₄₃	—	2	2	no	—
61	Dic₄₃	#41	1	4	yes	—
62	C₂×C₄₃	—	4	2	no	—
63	C₂×C₄₃	C₂×#41	1	2	yes	—
64	C₂×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
65	D₄₃	—	4	2	no	—
66	#555	—	43	1	no	maximal, Sylow
67	C₄₃	#555	1	1	yes	characteristic, complemented, Sylow
68	C₄⋊Q₈	—	43	1	no	—
69	#124	—	43	1	no	—
70	#124	—	43	2	no	—
71	#124	D₄₃	1	1	yes	characteristic, complemented
72	#121	—	43	2	no	—
73	#121	—	43	2	no	—
74	C₄×D₄	—	43	2	no	—
75	#117	—	43	2	no	—
76	#117	—	43	2	no	—
77	C₂×Q₈	—	43	1	no	—
78	C₂×Q₈	C₂×D₄₃	1	1	yes	characteristic
79	C₂×D₄	—	43	2	no	—
80	C₂×D₄	—	43	2	no	—
81	C₂×D₄	—	43	1	no	—
82	C₂×D₄	C₂×D₄₃	1	1	yes	characteristic
83	C₂²×C₄	—	43	2	no	—
84	C₂²×C₄	—	43	2	no	—
85	C₄⋊C₄	—	43	2	no	—
86	C₄⋊C₄	—	43	2	no	—
87	C₄⋊C₄	—	43	2	no	—
88	C₂²⋊C₄	—	43	2	no	—
89	C₂²⋊C₄	—	43	2	no	—
90	C₂²⋊C₄	—	43	2	no	—
91	C₂²⋊C₄	—	43	2	no	—
92	C₂²⋊C₄	C₂×D₄₃	1	2	yes	—
93	C₂²⋊C₄	C₂×D₄₃	1	2	yes	—
94	C₄²	—	43	1	no	—
95	C₄²	—	43	2	no	—
96	C₄²	—	43	1	no	—
97	C₄²	C₂×D₄₃	1	1	yes	characteristic
98	C₂³	—	43	2	no	—
99	C₂³	C₂²×D₄₃	1	2	yes	—
100	Q₈	—	4	1	no	—
101	Q₈	—	172	1	no	—
102	D₄	—	4	1	no	—
103	D₄	—	86	4	no	—
104	D₄	—	172	1	no	—
105	D₄	—	172	2	no	—
106	C₂×C₄	—	43	2	no	—
107	C₂×C₄	—	43	2	no	—
108	C₂×C₄	—	43	2	no	—
109	C₂×C₄	—	86	4	no	—
110	C₂×C₄	—	86	4	no	—
111	C₂×C₄	C₂²×D₄₃	1	2	yes	—
112	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
113	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
114	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
115	C₂²	—	2	2	no	—
116	C₂²	—	2	2	no	—
117	C₂²	—	2	2	no	—
118	C₂²	—	86	2	no	—
119	C₂²	—	86	2	no	—
120	C₂²	—	86	2	no	—
121	C₂²	C₂³×D₄₃	1	1	yes	characteristic
122	C₄	—	2	2	no	—
123	C₄	—	2	1	no	—
124	C₄	—	2	1	no	—
125	C₄	—	2	1	no	—
126	C₄	—	43	4	no	—
127	C₄	—	86	2	no	—
128	C₄	—	86	2	no	—
129	C₂	—	4	2	no	—
130	C₂	—	172	2	no	—
131	C₂	#41×D₄₃	1	2	yes	—
132	C₂	#13063370	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13063323

C₂

yes

maximal, characteristic, complemented

#13063314

C₂

yes

maximal, characteristic, complemented

#13063311

C₂

yes

maximal, complemented

#13063298

C₂

yes

maximal, complemented

#13063297

C₂

yes

maximal, complemented

(C₂²⋊D₄₃)⋊C₄

C₂

yes

maximal, complemented

#13063282

C₂

yes

maximal, complemented

#13063281

C₂

yes

maximal, complemented

#124×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂×Q₈×C₄₃

C₂²

yes

characteristic

C₂×D₄×C₄₃

C₂²

yes

characteristic

C₂×C₂²⋊D₄₃

C₂²

yes

—

C₂×C₂²⋊D₄₃

C₂²

yes

—

C₂²×Dic₄₃

C₂²

yes

—

C₂×D₁₇₂

C₂²

yes

characteristic

C₂×C₄×D₄₃

C₂²

yes

—

C₂×Dic₈₆

C₂²

yes

characteristic

C₂²⋊C₄×C₄₃

C₂²

yes

—

C₂²⋊C₄×C₄₃

C₂²

yes

—

C₄²×C₄₃

C₂²

yes

characteristic

C₂²⋊Dic₄₃

C₂²

yes

—

(C₂×D₄₃)⋊C₄

C₂²

yes

—

(C₂×D₄₃)⋊C₄

C₂²

yes

—

(C₂×D₄₃)⋊C₄

C₂²

yes

—

Dic₄₃⋊C₄

C₂²

yes

—

Dic₄₃⋊C₄

C₂²

yes

—

Dic₄₃⋊C₄

C₂²

yes

—

C₄×Dic₄₃

C₂²

yes

characteristic

C₄×Dic₄₃

C₂²

yes

—

C₄×Dic₄₃

C₂²

yes

characteristic

C₂³×C₄₃

C₂³

yes

—

C₂²×D₄₃

C₂³

yes

—

Q₈×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

C₂³

yes

characteristic

C₂×C₄×C₄₃

C₂³

yes

—

C₂×C₄×C₄₃

C₂³

yes

characteristic

C₂×C₄×C₄₃

C₂³

yes

characteristic

C₂²⋊D₄₃

—

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂³

yes

—

C₂×Dic₄₃

C₂³

yes

—

C₂×Dic₄₃

C₂³

yes

—

D₁₇₂

—

C₄×D₄₃

—

Dic₈₆

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂⁴

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

#41

yes

—

C₂×C₄₃

—

C₂×C₄₃

C₂×#41

yes

—

C₂×C₄₃

H(5,𝔽₂)

yes

characteristic

D₄₃

—

#555

—

maximal, Sylow

C₄₃

#555

yes

characteristic, complemented, Sylow

C₄⋊Q₈

—

#124

—

#124

—

#124

D₄₃

yes

characteristic, complemented

#121

—

#121

—

C₄×D₄

—

#117

—

#117

—

C₂×Q₈

—

C₂×Q₈

C₂×D₄₃

yes

characteristic

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

C₂×D₄₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

C₂×D₄₃

yes

—

C₂²⋊C₄

C₂×D₄₃

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×D₄₃

yes

characteristic

C₂³

—

C₂³

C₂²×D₄₃

yes

—

100

Q₈

—

101

Q₈

—

172

—

102

D₄

—

103

D₄

—

104

D₄

—

172

—

105

D₄

—

172

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

C₂²×D₄₃

yes

—

112

C₂×C₄

C₂²×D₄₃

yes

characteristic

113

C₂×C₄

C₂²×D₄₃

yes

characteristic

114

C₂×C₄

C₂²×D₄₃

yes

characteristic

115

C₂²

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

C₂³×D₄₃

yes

characteristic

122

C₄

—

123

C₄

—

124

C₄

—

125

C₄

—

126

C₄

—

127

C₄

—

128

C₄

—

129

C₂

—

130

C₂

—

172

—

131

C₂

#41×D₄₃

yes

—

132

C₂

#13063370

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₄₃
commutator, socle, cosocle	C₂²×C₄₃	C₂⁴
Fitting	#124×C₄₃	C₂
hypercenter	#124	D₄₃
hypocenter	C₄₃	#555
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #124

subgroup

G/H

center, Frattini

C₂²

C₂³×D₄₃

commutator, socle, cosocle

C₂²×C₄₃

C₂⁴

Fitting

#124×C₄₃

C₂

D₄₃

C₄₃

G ▷ C₂²×C₄₃ ▷ C₄₃

C₁ ◁ C₂² ◁ #124

N	H ≅ G/N	type
1. #13063323	C₂	semidirect
2. #13063314	C₂	semidirect
3. #13063311	C₂	semidirect
4. #13063298	C₂	semidirect
5. #13063297	C₂	semidirect
6. (C₂²⋊D₄₃)⋊C₄	C₂	semidirect
7. #13063282	C₂	semidirect
8. #13063281	C₂	semidirect
9. #124×C₄₃	C₂	semidirect
67. C₄₃	#555	semidirect
71. #124	D₄₃	semidirect

H ≅ G/N

type

1. #13063323

C₂

semidirect

2. #13063314

C₂

semidirect

3. #13063311

C₂

semidirect

4. #13063298

C₂

semidirect

5. #13063297

C₂

semidirect

6. (C₂²⋊D₄₃)⋊C₄

C₂

semidirect

7. #13063282

C₂

semidirect

8. #13063281

C₂

semidirect

9. #124×C₄₃

C₂

semidirect

67. C₄₃

#555

semidirect

71. #124

D₄₃

semidirect

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

subgroup	index
#13063323	2
#13063314	2
#13063311	2
#13063298	2
#13063297	2
(C₂²⋊D₄₃)⋊C₄	2
#13063282	2
#13063281	2
#124×C₄₃	2
#555	43

subgroup

index

(C₂²⋊D₄₃)⋊C₄

#124×C₄₃

Subgroups — #14583611

Conjugacy classes of subgroups

Complements

Maximal subgroups