Group #19145118 — subgroups

Subgroups — #19145118

Order 5504.

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

normal subgroups only

This group has 348 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	#14583452	C₂	1	2	yes	maximal
2	#14583307	C₂	1	4	yes	maximal, complemented
3	#14583306	C₂	1	4	yes	maximal, complemented
4	#14582937	C₂	1	1	yes	maximal, characteristic
5	#14582935	C₂	1	2	yes	maximal
6	C₂×#13063235	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#427	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
9	#13063324	C₂²	1	4	yes	—
10	#13063316	C₂²	1	4	yes	—
11	#13063302	—	2	4	no	—
12	C₄×Dic₈₆	—	2	4	no	—
13	#13063284	C₂²	1	2	yes	—
14	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
15	#13063259	C₂²	1	2	yes	—
16	#13063258	C₂²	1	4	yes	—
17	#13063257	C₂²	1	2	yes	—
18	#13063256	C₂²	1	4	yes	—
19	#13063235	C₂²	1	2	yes	—
20	#13063235	C₂²	1	2	yes	—
21	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
22	#117×C₄₃	C₂²	1	2	yes	—
23	#107×C₄₃	C₂²	1	2	yes	—
24	#106×C₄₃	C₂²	1	2	yes	—
25	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
26	C₂²×Dic₄₃	D₄	1	2	yes	—
27	C₂×Dic₈₆	—	2	4	no	—
28	C₂×C₈×C₄₃	Q₈	1	4	yes	complemented
29	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
30	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
31	C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
32	C₂²⋊C₄×C₄₃	—	2	2	no	—
33	C₄²×C₄₃	—	2	2	no	—
34	C₂²⋊Dic₄₃	—	2	2	no	—
35	C₄⋊Dic₄₃	—	2	4	no	—
36	C₄⋊Dic₄₃	C₂³	1	4	yes	—
37	Dic₄₃⋊C₄	—	2	4	no	—
38	Dic₄₃⋊C₄	—	2	4	no	—
39	C₄×Dic₄₃	—	2	2	no	—
40	C₄×Dic₄₃	D₄	1	2	yes	—
41	C₄×Dic₄₃	C₂³	1	2	yes	—
42	C₂×C₄₃⋊C₈	Q₈	1	4	yes	complemented
43	C₂×C₄₃⋊C₈	C₂³	1	2	yes	—
44	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₄₃	—	2	4	no	—
46	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
48	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
49	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
50	C₂×Dic₄₃	—	2	4	no	—
51	C₂×Dic₄₃	—	4	2	no	—
52	C₂×Dic₄₃	C₂×D₄	1	4	yes	—
53	Dic₈₆	—	4	8	no	—
54	C₈×C₄₃	C₂×Q₈	1	2	yes	—
55	C₈×C₄₃	C₂×Q₈	1	2	yes	—
56	C₄₃⋊C₈	C₂×Q₈	1	4	yes	—
57	C₂²×C₄₃	—	2	2	no	—
58	C₂²×C₄₃	C₄⋊Q₈	1	2	yes	—
59	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
60	C₄×C₄₃	—	4	4	no	—
61	C₄×C₄₃	C₄⋊Q₈	1	2	yes	—
62	C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
63	C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
64	Dic₄₃	—	2	4	no	—
65	Dic₄₃	—	4	4	no	—
66	#3162	—	43	1	no	maximal, Sylow
67	C₂×C₄₃	—	2	2	no	—
68	C₂×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
69	C₂×C₄₃	#575	1	2	yes	—
70	#533	—	43	2	no	—
71	#501	—	43	4	no	—
72	#501	—	43	4	no	—
73	#427	—	43	1	no	—
74	#427	—	43	2	no	—
75	#427	D₄₃	1	1	yes	characteristic
76	C₂×#97	—	43	1	no	—
77	C₄₃	#3162	1	1	yes	characteristic, complemented, Sylow
78	C₂²×C₈	—	43	1	no	—
79	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
80	C₄⋊Q₈	—	43	4	no	—
81	#125	—	43	4	no	—
82	C₂²⋊Q₈	—	86	4	no	—
83	C₄×Q₈	—	86	4	no	—
84	#117	—	43	2	no	—
85	#117	C₂×D₄₃	1	2	yes	—
86	C₂×C₄²	—	43	1	no	—
87	#107	—	43	2	no	—
88	#107	—	43	4	no	—
89	#107	C₂×D₄₃	1	2	yes	—
90	#106	—	43	2	no	—
91	#106	—	43	4	no	—
92	#106	C₂×D₄₃	1	2	yes	—
93	#97	—	43	2	no	—
94	#97	—	43	2	no	—
95	C₂×Q₈	—	86	4	no	—
96	C₂²×C₄	—	43	2	no	—
97	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
98	C₂×C₈	—	43	4	no	—
99	C₂×C₈	—	43	2	no	—
100	C₂×C₈	Dic₈₆	1	4	yes	complemented
101	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
102	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
103	C₄⋊C₄	—	43	4	no	—
104	C₄⋊C₄	—	86	4	no	—
105	C₄⋊C₄	—	86	4	no	—
106	C₄⋊C₄	—	86	4	no	—
107	C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
108	C₂²⋊C₄	—	2	2	no	—
109	C₂²⋊C₄	—	86	2	no	—
110	C₄²	—	2	2	no	—
111	C₄²	—	43	2	no	—
112	C₄²	—	43	2	no	—
113	C₄²	—	86	2	no	—
114	C₂³	D₄×D₄₃	1	1	yes	characteristic
115	Q₈	—	172	8	no	—
116	C₂×C₄	—	2	4	no	—
117	C₂×C₄	—	43	4	no	—
118	C₂×C₄	—	86	4	no	—
119	C₂×C₄	—	172	2	no	—
120	C₂×C₄	C₂×Dic₈₆	1	2	yes	—
121	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
122	C₂×C₄	Q₈×D₄₃	1	2	yes	—
123	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
124	C₈	—	43	4	no	—
125	C₈	C₂×Dic₈₆	1	2	yes	—
126	C₈	C₂×Dic₈₆	1	2	yes	—
127	C₂²	—	2	2	no	—
128	C₂²	#13063324	1	2	yes	—
129	C₂²	C₂×D₄×D₄₃	1	1	yes	characteristic
130	C₄	—	4	4	no	—
131	C₄	—	86	4	no	—
132	C₄	—	172	4	no	—
133	C₄	#13063324	1	2	yes	—
134	C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
135	C₄	C₂²×Dic₈₆	1	1	yes	characteristic
136	C₂	—	2	2	no	—
137	C₂	C₂×#13063324	1	1	yes	characteristic
138	C₂	#14583696	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14583452

C₂

yes

maximal

#14583307

C₂

yes

maximal, complemented

#14583306

C₂

yes

maximal, complemented

#14582937

C₂

yes

maximal, characteristic

#14582935

C₂

yes

maximal

C₂×#13063235

C₂

yes

maximal, characteristic

C₄₃×#427

C₂

yes

maximal, characteristic

C₂²×C₄₃⋊C₈

C₂²

yes

characteristic

#13063324

C₂²

yes

—

#13063316

C₂²

yes

—

#13063302

—

C₄×Dic₈₆

—

#13063284

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

characteristic

#13063259

C₂²

yes

—

#13063258

C₂²

yes

—

#13063257

C₂²

yes

—

#13063256

C₂²

yes

—

#13063235

C₂²

yes

—

#13063235

C₂²

yes

—

C₂²×C₈×C₄₃

C₂²

yes

characteristic

#117×C₄₃

C₂²

yes

—

#107×C₄₃

C₂²

yes

—

#106×C₄₃

C₂²

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

D₄

yes

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

Q₈

yes

complemented

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄⋊C₄×C₄₃

C₂³

yes

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

C₂³

yes

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

D₄

yes

—

C₄×Dic₄₃

C₂³

yes

—

C₂×C₄₃⋊C₈

Q₈

yes

complemented

C₂×C₄₃⋊C₈

C₂³

yes

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂×D₄

yes

—

Dic₈₆

—

C₈×C₄₃

C₂×Q₈

yes

—

C₈×C₄₃

C₂×Q₈

yes

—

C₄₃⋊C₈

C₂×Q₈

yes

—

C₂²×C₄₃

—

C₂²×C₄₃

C₄⋊Q₈

yes

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

C₄⋊Q₈

yes

—

C₄×C₄₃

C₂²×Q₈

yes

characteristic

C₄×C₄₃

C₂²×Q₈

yes

characteristic

Dic₄₃

—

Dic₄₃

—

#3162

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₄₃

#575

yes

—

—

—

—

—

—

D₄₃

yes

characteristic

C₂×#97

—

C₄₃

#3162

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₄₃

yes

characteristic

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

#117

C₂×D₄₃

yes

—

C₂×C₄²

—

#107

—

#107

—

#107

C₂×D₄₃

yes

—

#106

—

#106

—

#106

C₂×D₄₃

yes

—

#97

—

#97

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

Dic₈₆

yes

complemented

101

C₂×C₈

C₂²×D₄₃

yes

characteristic

102

C₂×C₈

C₂²×D₄₃

yes

characteristic

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

C₂²×D₄₃

yes

—

108

C₂²⋊C₄

—

109

C₂²⋊C₄

—

110

C₄²

—

111

C₄²

—

112

C₄²

—

113

C₄²

—

114

C₂³

D₄×D₄₃

yes

characteristic

115

Q₈

—

172

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

172

—

120

C₂×C₄

C₂×Dic₈₆

yes

—

121

C₂×C₄

D₄×D₄₃

yes

characteristic

122

C₂×C₄

Q₈×D₄₃

yes

—

123

C₂×C₄

C₂³×D₄₃

yes

characteristic

124

C₈

—

125

C₈

C₂×Dic₈₆

yes

—

126

C₈

C₂×Dic₈₆

yes

—

127

C₂²

—

128

C₂²

#13063324

yes

—

129

C₂²

C₂×D₄×D₄₃

yes

characteristic

130

C₄

—

131

C₄

—

132

C₄

—

172

—

133

C₄

#13063324

yes

—

134

C₄

C₂×Q₈×D₄₃

yes

characteristic

135

C₄

C₂²×Dic₈₆

yes

characteristic

136

C₂

—

137

C₂

C₂×#13063324

yes

characteristic

138

C₂

#14583696

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₄₃×#427	C₂
socle	C₂²×C₄₃	C₂²×D₄
hypercenter	#427	D₄₃
hypocenter	C₄₃	#3162
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #427

subgroup

G/H

center

C₂×C₄

D₄×D₄₃

commutator

C₂×C₄×C₄₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₃

Fitting

C₄₃×#427

C₂

socle

C₂²×C₄₃

C₂²×D₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #427

N	H ≅ G/N	type
2. #14583307	C₂	semidirect
3. #14583306	C₂	semidirect
28. C₂×C₈×C₄₃	Q₈	semidirect
42. C₂×C₄₃⋊C₈	Q₈	semidirect
77. C₄₃	#3162	semidirect
100. C₂×C₈	Dic₈₆	semidirect

H ≅ G/N

type

2. #14583307

C₂

semidirect

3. #14583306

C₂

semidirect

28. C₂×C₈×C₄₃

Q₈

semidirect

42. C₂×C₄₃⋊C₈

Q₈

semidirect

77. C₄₃

#3162

semidirect

100. C₂×C₈

Dic₈₆

semidirect

Subgroups — #19145118

Conjugacy classes of subgroups

Complements