Group #14583621 — subgroups

Subgroups — #14583621

Order 2752.

212 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 97 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	#13063320	C₂	1	2	yes	maximal, complemented
3	#13063319	C₂	1	2	yes	maximal, complemented
4	#13063314	C₂	1	1	yes	maximal, characteristic
5	#13063313	C₂	1	1	yes	maximal, characteristic
6	#13063303	C₂	1	2	yes	maximal, complemented
7	C₄×Dic₈₆	C₂	1	1	yes	maximal, characteristic, complemented
8	#13063290	C₂	1	1	yes	maximal, characteristic, complemented
9	#13063287	C₂	1	1	yes	maximal, characteristic
10	#13063282	C₂	1	2	yes	maximal, complemented
11	C₄×Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×D₁₇₂	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄₃	C₂²	1	2	yes	—
15	C₂×Dic₈₆	C₂²	1	1	yes	characteristic
16	C₂×Dic₈₆	C₂²	1	1	yes	characteristic
17	C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
19	C₄²×C₄₃	C₂²	1	2	yes	—
20	C₄²×C₄₃	C₂²	1	1	yes	characteristic
21	(C₂×D₄₃)⋊C₄	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	(C₂×D₄₃)⋊C₄	C₂²	1	2	yes	—
26	C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
27	Dic₄₃⋊C₄	C₂²	1	1	yes	characteristic
28	Dic₄₃⋊C₄	C₂²	1	2	yes	—
29	Dic₄₃⋊C₄	C₂²	1	2	yes	—
30	Dic₄₃⋊C₄	C₂²	1	1	yes	characteristic
31	Dic₄₃⋊C₄	C₂²	1	2	yes	—
32	C₄×Dic₄₃	C₂²	1	2	yes	—
33	C₄×Dic₄₃	C₂²	1	1	yes	characteristic
34	C₄×Dic₄₃	C₂²	1	1	yes	characteristic
35	C₂²×D₄₃	C₂³	1	2	yes	—
36	Q₈×C₄₃	—	2	2	no	—
37	C₂×C₄×C₄₃	C₂³	1	2	yes	—
38	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
39	C₂×C₄×C₄₃	C₂³	1	2	yes	—
40	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
41	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
42	C₂×Dic₄₃	C₂³	1	1	yes	characteristic
43	C₂×Dic₄₃	C₂³	1	1	yes	characteristic
44	C₂×Dic₄₃	C₂³	1	2	yes	—
45	C₂×Dic₄₃	C₂³	1	1	yes	characteristic
46	C₂×Dic₄₃	C₂³	1	1	yes	characteristic
47	D₁₇₂	—	2	2	no	—
48	C₄×D₄₃	—	2	4	no	—
49	Dic₈₆	—	2	2	no	—
50	Dic₈₆	—	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	1	no	—
56	C₄×C₄₃	—	2	2	no	—
57	C₄×C₄₃	—	2	2	no	—
58	C₄×C₄₃	—	2	1	no	—
59	C₄×C₄₃	#41	1	2	yes	—
60	Dic₄₃	—	2	1	no	—
61	Dic₄₃	—	2	2	no	—
62	Dic₄₃	—	2	1	no	—
63	Dic₄₃	—	2	1	no	—
64	Dic₄₃	#41	1	2	yes	—
65	C₂×C₄₃	C₂×#41	1	1	yes	characteristic
66	C₂×C₄₃	C₂×#41	1	1	yes	characteristic
67	C₂×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
68	D₄₃	—	4	2	no	—
69	#556	—	43	1	no	maximal, Sylow
70	C₄₃	#556	1	1	yes	characteristic, complemented, Sylow
71	C₄⋊Q₈	—	43	1	no	—
72	#126	—	43	2	no	—
73	#126	—	43	2	no	—
74	#124	—	43	1	no	—
75	#124	—	43	1	no	—
76	C₂²⋊Q₈	—	43	2	no	—
77	C₄×Q₈	—	43	1	no	—
78	C₄×Q₈	—	43	1	no	—
79	C₄×Q₈	D₄₃	1	1	yes	characteristic, complemented
80	C₄×D₄	—	43	1	no	—
81	#117	—	43	2	no	—
82	C₂×Q₈	—	43	1	no	—
83	C₂×Q₈	—	43	1	no	—
84	C₂×Q₈	C₂×D₄₃	1	1	yes	characteristic
85	C₂×D₄	—	43	1	no	—
86	C₂²×C₄	—	43	2	no	—
87	C₄⋊C₄	—	43	1	no	—
88	C₄⋊C₄	—	43	2	no	—
89	C₄⋊C₄	—	43	2	no	—
90	C₄⋊C₄	—	43	1	no	—
91	C₄⋊C₄	—	43	1	no	—
92	C₄⋊C₄	—	43	2	no	—
93	C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
94	C₄⋊C₄	C₂×D₄₃	1	2	yes	—
95	C₂²⋊C₄	—	43	2	no	—
96	C₂²⋊C₄	—	43	2	no	—
97	C₂²⋊C₄	—	43	2	no	—
98	C₂²⋊C₄	—	43	2	no	—
99	C₂²⋊C₄	—	43	2	no	—
100	C₄²	—	43	2	no	—
101	C₄²	—	43	1	no	—
102	C₄²	—	43	1	no	—
103	C₄²	C₂×D₄₃	1	2	yes	—
104	C₄²	C₂×D₄₃	1	1	yes	characteristic
105	C₂³	—	43	2	no	—
106	Q₈	—	2	2	no	—
107	Q₈	—	86	2	no	—
108	Q₈	—	86	2	no	—
109	D₄	—	86	2	no	—
110	C₂×C₄	—	43	1	no	—
111	C₂×C₄	—	43	1	no	—
112	C₂×C₄	—	43	1	no	—
113	C₂×C₄	—	43	1	no	—
114	C₂×C₄	—	43	2	no	—
115	C₂×C₄	—	86	4	no	—
116	C₂×C₄	C₂²×D₄₃	1	2	yes	—
117	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
118	C₂×C₄	C₂²×D₄₃	1	2	yes	—
119	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
120	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
121	C₂²	—	86	2	no	—
122	C₂²	—	86	2	no	—
123	C₂²	—	86	2	no	—
124	C₂²	C₂³×D₄₃	1	1	yes	characteristic
125	C₄	—	2	2	no	—
126	C₄	—	2	1	no	—
127	C₄	—	2	2	no	—
128	C₄	—	2	1	no	—
129	C₄	—	43	2	no	—
130	C₄	—	86	1	no	—
131	C₄	—	86	2	no	—
132	C₄	—	86	1	no	—
133	C₄	—	86	1	no	—
134	C₄	#10621898	1	2	yes	—
135	C₂	—	172	2	no	—
136	C₂	#41×D₄₃	1	1	yes	characteristic
137	C₂	C₂×#10621898	1	1	yes	characteristic
138	C₂	#13063373	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13063323

C₂

yes

maximal, characteristic, complemented

#13063320

C₂

yes

maximal, complemented

#13063319

C₂

yes

maximal, complemented

#13063314

C₂

yes

maximal, characteristic

#13063313

C₂

yes

maximal, characteristic

#13063303

C₂

yes

maximal, complemented

C₄×Dic₈₆

C₂

yes

maximal, characteristic, complemented

#13063290

C₂

yes

maximal, characteristic, complemented

#13063287

C₂

yes

maximal, characteristic

#13063282

C₂

yes

maximal, complemented

C₄×Q₈×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂×Q₈×C₄₃

C₂²

yes

characteristic

C₂×D₁₇₂

C₂²

yes

characteristic

C₂×C₄×D₄₃

C₂²

yes

—

C₂×Dic₈₆

C₂²

yes

characteristic

C₂×Dic₈₆

C₂²

yes

characteristic

C₄⋊C₄×C₄₃

C₂²

yes

characteristic

C₄⋊C₄×C₄₃

C₂²

yes

—

C₄²×C₄₃

C₂²

yes

—

C₄²×C₄₃

C₂²

yes

characteristic

(C₂×D₄₃)⋊C₄

C₂²

yes

—

(C₂×D₄₃)⋊C₄

C₂²

yes

—

(C₂×D₄₃)⋊C₄

C₂²

yes

—

(C₂×D₄₃)⋊C₄

C₂²

yes

—

(C₂×D₄₃)⋊C₄

C₂²

yes

—

C₄⋊Dic₄₃

C₂²

yes

characteristic

Dic₄₃⋊C₄

C₂²

yes

characteristic

Dic₄₃⋊C₄

C₂²

yes

—

Dic₄₃⋊C₄

C₂²

yes

—

Dic₄₃⋊C₄

C₂²

yes

characteristic

Dic₄₃⋊C₄

C₂²

yes

—

C₄×Dic₄₃

C₂²

yes

—

C₄×Dic₄₃

C₂²

yes

characteristic

C₄×Dic₄₃

C₂²

yes

characteristic

C₂²×D₄₃

C₂³

yes

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

C₂³

yes

—

C₂×C₄×C₄₃

C₂³

yes

characteristic

C₂×C₄×C₄₃

C₂³

yes

—

C₂×C₄×C₄₃

C₂³

yes

characteristic

C₂×C₄×C₄₃

C₂³

yes

characteristic

C₂×Dic₄₃

C₂³

yes

characteristic

C₂×Dic₄₃

C₂³

yes

characteristic

C₂×Dic₄₃

C₂³

yes

—

C₂×Dic₄₃

C₂³

yes

characteristic

C₂×Dic₄₃

C₂³

yes

characteristic

D₁₇₂

—

C₄×D₄₃

—

Dic₈₆

—

Dic₈₆

—

C₂²×C₄₃

C₂⁴

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#41

yes

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

#41

yes

—

C₂×C₄₃

C₂×#41

yes

characteristic

C₂×C₄₃

C₂×#41

yes

characteristic

C₂×C₄₃

2₋¹⁺⁴

yes

characteristic

D₄₃

—

#556

—

maximal, Sylow

C₄₃

#556

yes

characteristic, complemented, Sylow

C₄⋊Q₈

—

—

—

—

—

C₂²⋊Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

D₄₃

yes

characteristic, complemented

C₄×D₄

—

#117

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂×D₄₃

yes

characteristic

C₂×D₄

—

C₂²×C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂×D₄₃

yes

characteristic

C₄⋊C₄

C₂×D₄₃

yes

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

100

C₄²

—

101

C₄²

—

102

C₄²

—

103

C₄²

C₂×D₄₃

yes

—

104

C₄²

C₂×D₄₃

yes

characteristic

105

C₂³

—

106

Q₈

—

107

Q₈

—

108

Q₈

—

109

D₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

C₂²×D₄₃

yes

—

117

C₂×C₄

C₂²×D₄₃

yes

characteristic

118

C₂×C₄

C₂²×D₄₃

yes

—

119

C₂×C₄

C₂²×D₄₃

yes

characteristic

120

C₂×C₄

C₂²×D₄₃

yes

characteristic

121

C₂²

—

122

C₂²

—

123

C₂²

—

124

C₂²

C₂³×D₄₃

yes

characteristic

125

C₄

—

126

C₄

—

127

C₄

—

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

—

132

C₄

—

133

C₄

—

134

C₄

#10621898

yes

—

135

C₂

—

172

—

136

C₂

#41×D₄₃

yes

characteristic

137

C₂

C₂×#10621898

yes

characteristic

138

C₂

#13063373

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₄₃
commutator, socle, cosocle	C₂²×C₄₃	C₂⁴
Fitting	C₄×Q₈×C₄₃	C₂
prime radical	C₂×D₁₇₂	C₂²
hypercenter	C₄×Q₈	D₄₃
hypocenter	C₄₃	#556
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄×Q₈

subgroup

G/H

center, Frattini

C₂²

C₂³×D₄₃

commutator, socle, cosocle

C₂²×C₄₃

C₂⁴

Fitting

C₄×Q₈×C₄₃

C₂

prime radical

C₂×D₁₇₂

C₂²

hypercenter

C₄×Q₈

D₄₃

C₄₃

G ▷ C₂²×C₄₃ ▷ C₄₃

C₁ ◁ C₂² ◁ C₄×Q₈

N	H ≅ G/N	type
1. #13063323	C₂	semidirect
2. #13063320	C₂	semidirect
3. #13063319	C₂	semidirect
6. #13063303	C₂	semidirect
7. C₄×Dic₈₆	C₂	semidirect
8. #13063290	C₂	semidirect
10. #13063282	C₂	semidirect
11. C₄×Q₈×C₄₃	C₂	semidirect
70. C₄₃	#556	semidirect
79. C₄×Q₈	D₄₃	semidirect

H ≅ G/N

type

1. #13063323

C₂

semidirect

2. #13063320

C₂

semidirect

3. #13063319

C₂

semidirect

6. #13063303

C₂

semidirect

7. C₄×Dic₈₆

C₂

semidirect

8. #13063290

C₂

semidirect

10. #13063282

C₂

semidirect

11. C₄×Q₈×C₄₃

C₂

semidirect

70. C₄₃

#556

semidirect

79. C₄×Q₈

D₄₃

semidirect

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

subgroup	index
#13063323	2
#13063320	2
#13063319	2
#13063314	2
#13063313	2
#13063303	2
C₄×Dic₈₆	2
#13063290	2
#13063287	2
#13063282	2
C₄×Q₈×C₄₃	2
#556	43

subgroup

index

C₄×Dic₈₆

C₄×Q₈×C₄₃

Subgroups — #14583621

Conjugacy classes of subgroups

Complements

Maximal subgroups