Group #19135384 — subgroups

Subgroups — #19135384

Order 5504.

184 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 79 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	#14582948	C₂	1	1	yes	maximal, characteristic
2	#14582947	C₂	1	1	yes	maximal, characteristic
3	C₂×#13063260	C₂	1	1	yes	maximal, characteristic
4	C₂×#13063260	C₂	1	1	yes	maximal, characteristic
5	#14582855	C₂	1	1	yes	maximal, characteristic
6	#14582669	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#344	C₂	1	1	yes	maximal, characteristic
8	C₂×#10621877	C₂²	1	1	yes	characteristic
9	C₂×#10621877	C₂²	1	1	yes	characteristic
10	C₂×#10621877	C₂²	1	1	yes	characteristic
11	C₂²×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
12	#13063261	—	2	2	no	—
13	#13063260	—	2	2	no	—
14	#13063260	—	2	1	no	—
15	#13063260	—	2	1	no	—
16	#13063260	C₄	1	4	yes	complemented
17	#13063236	—	2	1	no	—
18	C₄×C₄₃⋊C₈	—	2	1	no	—
19	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
21	#117×C₄₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
23	M₁₆×C₄₃	—	2	1	no	—
24	M₁₆×C₄₃	—	2	1	no	—
25	M₁₆×C₄₃	—	2	1	no	—
26	M₁₆×C₄₃	C₂×C₄	1	2	yes	—
27	C₂×C₈×C₄₃	—	2	1	no	—
28	C₂×C₈×C₄₃	—	2	1	no	—
29	C₄⋊C₄×C₄₃	—	2	1	no	—
30	C₂²⋊C₄×C₄₃	Q₈	1	2	yes	—
31	C₄²×C₄₃	—	2	1	no	—
32	#10621877	—	2	1	no	—
33	#10621877	—	2	1	no	—
34	#10621877	—	2	1	no	—
35	#10621877	—	2	1	no	—
36	#10621877	C₂×C₄	1	2	yes	—
37	#10621877	D₄	1	2	yes	—
38	C₂×C₄₃⋊C₈	—	2	1	no	—
39	C₂×C₄₃⋊C₈	—	2	1	no	—
40	C₂×C₄₃⋊C₈	—	2	1	no	—
41	C₂×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
42	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
43	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
44	C₂×C₄₃⋊C₈	Q₈	1	2	yes	—
45	C₂³×C₄₃	C₂×Q₈	1	1	yes	characteristic
46	C₂×C₄×C₄₃	—	2	2	no	—
47	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
48	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
51	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
52	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
53	C₈×C₄₃	—	2	2	no	—
54	C₈×C₄₃	—	4	1	no	—
55	C₄₃⋊C₈	—	2	2	no	—
56	C₄₃⋊C₈	—	2	2	no	—
57	C₄₃⋊C₈	—	4	1	no	—
58	C₄₃⋊C₈	C₄⋊C₄	1	2	yes	—
59	C₄₃⋊C₈	C₄⋊C₄	1	2	yes	—
60	C₂²×C₄₃	—	4	1	no	—
61	C₂²×C₄₃	C₄×Q₈	1	1	yes	characteristic
62	C₂²×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
63	C₂²×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
64	C₄×C₄₃	—	4	2	no	—
65	C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
66	C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
67	C₄×C₄₃	#121	1	1	yes	characteristic
68	C₄×C₄₃	#125	1	1	yes	characteristic
69	#1953	—	43	1	no	maximal, Sylow
70	C₂×C₄₃	—	2	1	no	—
71	C₂×C₄₃	—	2	1	no	—
72	C₂×C₄₃	—	2	1	no	—
73	C₂×C₄₃	#389	1	1	yes	characteristic
74	#430	—	43	1	no	—
75	#430	—	43	1	no	—
76	C₂×#108	—	43	1	no	—
77	C₂×#108	—	43	1	no	—
78	#405	—	43	1	no	—
79	#344	—	43	1	no	—
80	#344	D₄₃	1	1	yes	characteristic
81	C₄₃	#1953	1	1	yes	characteristic, complemented, Sylow
82	C₂×M₁₆	—	43	1	no	—
83	C₂×M₁₆	—	43	1	no	—
84	C₂×M₁₆	—	43	1	no	—
85	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic
86	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic
87	C₂²×C₈	—	43	1	no	—
88	#117	C₂×D₄₃	1	1	yes	characteristic
89	#108	—	43	4	no	—
90	#108	—	86	2	no	—
91	#108	—	86	1	no	—
92	#108	—	86	1	no	—
93	#108	—	86	2	no	—
94	#97	—	86	1	no	—
95	C₄×C₈	—	86	1	no	—
96	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
97	M₁₆	—	2	1	no	—
98	M₁₆	—	2	1	no	—
99	M₁₆	—	2	1	no	—
100	M₁₆	—	43	2	no	—
101	M₁₆	—	43	2	no	—
102	M₁₆	—	86	1	no	—
103	M₁₆	—	86	1	no	—
104	M₁₆	—	86	1	no	—
105	M₁₆	—	86	1	no	—
106	M₁₆	C₄×D₄₃	1	2	yes	—
107	C₂×C₈	—	2	1	no	—
108	C₂×C₈	—	2	1	no	—
109	C₂×C₈	—	43	2	no	—
110	C₂×C₈	—	43	1	no	—
111	C₂×C₈	—	43	1	no	—
112	C₂×C₈	—	43	2	no	—
113	C₂×C₈	—	86	1	no	—
114	C₂×C₈	—	86	1	no	—
115	C₂×C₈	—	86	1	no	—
116	C₄⋊C₄	—	2	1	no	—
117	C₂²⋊C₄	Dic₈₆	1	2	yes	—
118	C₄²	—	2	1	no	—
119	C₂³	C₂×Dic₈₆	1	1	yes	characteristic
120	C₂×C₄	—	2	2	no	—
121	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
122	C₂×C₄	#10621898	1	1	yes	characteristic
123	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
124	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
125	C₂×C₄	#10621900	1	1	yes	characteristic
126	C₂×C₄	Q₈×D₄₃	1	1	yes	characteristic
127	C₈	—	2	2	no	—
128	C₈	—	4	1	no	—
129	C₈	—	43	2	no	—
130	C₈	—	43	2	no	—
131	C₈	—	86	2	no	—
132	C₈	—	86	2	no	—
133	C₈	—	172	1	no	—
134	C₂²	—	4	1	no	—
135	C₂²	C₄×Dic₈₆	1	1	yes	characteristic
136	C₂²	#13063302	1	1	yes	characteristic
137	C₂²	#13063324	1	1	yes	characteristic
138	C₄	—	4	2	no	—
139	C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
140	C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
141	C₄	#13063298	1	1	yes	characteristic
142	C₄	#13063315	1	1	yes	characteristic
143	C₂	—	2	1	no	—
144	C₂	—	2	1	no	—
145	C₂	—	2	1	no	—
146	C₂	#14582796	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582948

C₂

yes

maximal, characteristic

#14582947

C₂

yes

maximal, characteristic

C₂×#13063260

C₂

yes

maximal, characteristic

C₂×#13063260

C₂

yes

maximal, characteristic

#14582855

C₂

yes

maximal, characteristic

#14582669

C₂

yes

maximal, characteristic

C₄₃×#344

C₂

yes

maximal, characteristic

C₂×#10621877

C₂²

yes

characteristic

C₂×#10621877

C₂²

yes

characteristic

C₂×#10621877

C₂²

yes

characteristic

C₂²×C₄₃⋊C₈

C₂²

yes

—

—

—

—

C₄

yes

complemented

#13063236

—

C₄×C₄₃⋊C₈

—

C₂×M₁₆×C₄₃

C₂²

yes

characteristic

C₂×M₁₆×C₄₃

C₂²

yes

characteristic

#117×C₄₃

C₂²

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

M₁₆×C₄₃

—

M₁₆×C₄₃

—

M₁₆×C₄₃

—

M₁₆×C₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

Q₈

yes

—

C₄²×C₄₃

—

—

—

—

—

C₂×C₄

yes

—

#10621877

D₄

yes

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

—

C₂×C₄₃⋊C₈

D₄

yes

characteristic

C₂×C₄₃⋊C₈

D₄

yes

characteristic

C₂×C₄₃⋊C₈

Q₈

yes

—

C₂³×C₄₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₈

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

C₄⋊C₄

yes

—

C₄₃⋊C₈

C₄⋊C₄

yes

—

C₂²×C₄₃

—

C₂²×C₄₃

C₄×Q₈

yes

characteristic

C₂²×C₄₃

C₂²⋊Q₈

yes

characteristic

C₂²×C₄₃

C₄⋊Q₈

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₄₃

C₄×D₄

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

—

—

—

—

—

—

D₄₃

yes

characteristic

C₄₃

#1953

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₃

yes

characteristic

C₂×M₁₆

C₂×D₄₃

yes

characteristic

C₂²×C₈

—

#117

C₂×D₄₃

yes

—

—

—

—

—

—

C₄×C₈

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

100

M₁₆

—

101

M₁₆

—

102

M₁₆

—

103

M₁₆

—

104

M₁₆

—

105

M₁₆

—

106

M₁₆

C₄×D₄₃

yes

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₂×C₈

—

116

C₄⋊C₄

—

117

C₂²⋊C₄

Dic₈₆

yes

—

118

C₄²

—

119

C₂³

C₂×Dic₈₆

yes

characteristic

120

C₂×C₄

—

121

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

122

C₂×C₄

#10621898

yes

characteristic

123

C₂×C₄

D₄×D₄₃

yes

characteristic

124

C₂×C₄

D₄×D₄₃

yes

characteristic

125

C₂×C₄

#10621900

yes

characteristic

126

C₂×C₄

Q₈×D₄₃

yes

characteristic

127

C₈

—

128

C₈

—

129

C₈

—

130

C₈

—

131

C₈

—

132

C₈

—

133

C₈

—

172

—

134

C₂²

—

135

C₂²

C₄×Dic₈₆

yes

characteristic

136

C₂²

#13063302

yes

characteristic

137

C₂²

#13063324

yes

characteristic

138

C₄

—

139

C₄

C₄⋊C₄×D₄₃

yes

characteristic

140

C₄

(C₂²⋊D₄₃)⋊C₄

yes

characteristic

141

C₄

#13063298

yes

characteristic

142

C₄

#13063315

yes

characteristic

143

C₂

—

144

C₂

—

145

C₂

—

146

C₂

#14582796

yes

characteristic

	subgroup	G/H
center	C₄	#13063298
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#344	C₂
socle	C₂×C₄₃	#389
hypercenter	#344	D₄₃
hypocenter	C₄₃	#1953
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #344

subgroup

G/H

center

C₄

#13063298

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×#344

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #344

N	H ≅ G/N	type
16. #13063260	C₄	semidirect
81. C₄₃	#1953	semidirect

H ≅ G/N

type

16. #13063260

C₄

semidirect

81. C₄₃

#1953

semidirect

Subgroups — #19135384

Conjugacy classes of subgroups

Complements