Group #49174885 — subgroups

Subgroups — #49174885

Order 37504.

248 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 94 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×C₄⋊#14556880	C₂	1	2	yes	maximal
2	C₂×C₄⋊#14556880	C₂	1	1	yes	maximal, characteristic
3	C₂×#22627679	C₂	1	1	yes	maximal, characteristic
4	#34036995	C₂	1	2	yes	maximal
5	#34035980	C₂	1	1	yes	maximal, characteristic
6	C₂²×#14556880	C₂²	1	2	yes	—
7	C₂²×#14556880	C₂²	1	1	yes	characteristic
8	C₂²×#14556880	C₂²	1	1	yes	characteristic
9	C₄⋊#14556880	—	2	4	no	—
10	C₄⋊#14556880	—	2	2	no	—
11	#22627679	—	2	2	no	—
12	C₂×#17989781	C₄	1	2	yes	—
13	C₂×C₄×Dic₂₉₃	C₂²	1	2	yes	—
14	C₂×C₄×Dic₂₉₃	C₂²	1	1	yes	characteristic
15	#22627531	C₄	1	1	yes	characteristic
16	#95×C₂₉₃	C₄	1	1	yes	characteristic
17	C₂×#14556880	—	2	1	no	—
18	C₂×#14556880	—	2	1	no	—
19	C₂×#14556880	—	2	2	no	—
20	C₂×#14556880	—	2	2	no	—
21	C₂×#14556880	—	2	1	no	—
22	C₂×#14556880	—	2	1	no	—
23	C₂×#14556880	—	2	2	no	—
24	C₂×#14556880	D₄	1	2	yes	—
25	C₂×#14556880	Q₈	1	2	yes	—
26	C₂²×Dic₂₉₃	C₂×C₄	1	2	yes	—
27	C₂²×Dic₂₉₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×Dic₂₉₃	C₂³	1	1	yes	characteristic
29	#17989781	—	2	4	no	—
30	C₄×Dic₂₉₃	—	2	2	no	—
31	C₄×Dic₂₉₃	—	2	2	no	—
32	C₄×Dic₂₉₃	D₄	1	2	yes	—
33	C₄×Dic₂₉₃	Q₈	1	2	yes	—
34	C₂²×C₄×C₂₉₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₄×C₂₉₃	C₂×C₄	1	2	yes	—
36	#14556880	—	2	2	no	—
37	#14556880	—	2	2	no	—
38	#14556880	—	4	2	no	—
39	C₂×Dic₂₉₃	—	2	2	no	—
40	C₂×Dic₂₉₃	—	2	2	no	—
41	C₂×Dic₂₉₃	—	2	2	no	—
42	C₂×Dic₂₉₃	—	2	2	no	—
43	C₂×Dic₂₉₃	C₄⋊C₄	1	2	yes	—
44	C₂×Dic₂₉₃	C₂×D₄	1	1	yes	characteristic
45	C₂×Dic₂₉₃	C₂×D₄	1	1	yes	characteristic
46	C₂×Dic₂₉₃	C₂×Q₈	1	1	yes	characteristic
47	C₂×Dic₂₉₃	C₂×Q₈	1	1	yes	characteristic
48	C₂×Dic₂₉₃	#41	1	1	yes	characteristic
49	C₂×Dic₂₉₃	#41	1	1	yes	characteristic
50	C₂³×C₂₉₃	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₄×C₂₉₃	—	2	2	no	—
52	C₂×C₄×C₂₉₃	—	2	2	no	—
53	C₂×C₄×C₂₉₃	—	2	2	no	—
54	C₂×C₄×C₂₉₃	C₄⋊C₄	1	2	yes	—
55	C₂×C₄×C₂₉₃	M₁₆	1	4	yes	—
56	C₂²×C₂₉₃	C₂×C₄⋊C₄	1	1	yes	characteristic
57	C₂²×C₂₉₃	C₄×D₄	1	1	yes	characteristic
58	C₂²×C₂₉₃	C₄×Q₈	1	1	yes	characteristic
59	C₂²×C₂₉₃	C₂×M₁₆	1	2	yes	—
60	C₂²×C₂₉₃	#131	1	2	yes	—
61	C₄×C₂₉₃	—	2	2	no	—
62	C₄×C₂₉₃	—	2	4	no	—
63	Dic₂₉₃	—	2	2	no	—
64	Dic₂₉₃	—	4	2	no	—
65	Dic₂₉₃	#121	1	1	yes	characteristic
66	Dic₂₉₃	C₂²⋊Q₈	1	1	yes	characteristic
67	Dic₂₉₃	#125	1	1	yes	characteristic
68	Dic₂₉₃	C₄⋊Q₈	1	1	yes	characteristic
69	C₂×C₂₉₃	#389	1	1	yes	characteristic
70	C₂×C₂₉₃	#423	1	1	yes	characteristic
71	C₂×C₂₉₃	#424	1	1	yes	characteristic
72	C₂×C₂₉₃	#435	1	2	yes	—
73	C₂×C₂₉₃	#446	1	2	yes	—
74	C₂₉₃	#1940	1	1	yes	characteristic, complemented, Sylow
75	#1940	—	293	1	no	maximal, Sylow
76	C₂×C₄⋊C₈	—	293	1	no	—
77	C₂×C₄⋊C₈	—	293	2	no	—
78	C₂×#97	—	293	1	no	—
79	C₄×C₄⋊C₄	—	293	1	no	—
80	#336	—	293	2	no	—
81	C₂²×C₈	—	293	1	no	—
82	C₂²×C₈	—	293	1	no	—
83	C₂²×C₈	—	293	2	no	—
84	C₂×C₄⋊C₄	—	293	2	no	—
85	C₂×C₄²	—	293	1	no	—
86	C₂×C₄²	—	293	2	no	—
87	C₄⋊C₈	—	586	2	no	—
88	C₄⋊C₈	—	586	4	no	—
89	#97	—	586	2	no	—
90	#95	—	293	1	no	—
91	#95	#11924078	1	1	yes	characteristic
92	C₂²×C₄	—	293	1	no	—
93	C₂²×C₄	—	293	1	no	—
94	C₂²×C₄	—	293	2	no	—
95	C₂²×C₄	C₂×#11924078	1	1	yes	characteristic
96	C₂²×C₄	C₂×#11924078	1	2	yes	—
97	C₂×C₈	—	293	2	no	—
98	C₂×C₈	—	293	2	no	—
99	C₂×C₈	—	586	1	no	—
100	C₂×C₈	—	586	1	no	—
101	C₂×C₈	—	586	1	no	—
102	C₂×C₈	—	586	1	no	—
103	C₂×C₈	—	586	2	no	—
104	C₂×C₈	—	586	2	no	—
105	C₂×C₈	—	586	2	no	—
106	C₄⋊C₄	—	586	4	no	—
107	C₄²	—	293	2	no	—
108	C₄²	—	293	2	no	—
109	C₄²	—	586	2	no	—
110	C₄²	—	586	2	no	—
111	C₂³	C₂²×#11924078	1	1	yes	characteristic
112	C₂×C₄	—	2	2	no	—
113	C₂×C₄	—	2	2	no	—
114	C₂×C₄	—	2	2	no	—
115	C₂×C₄	—	293	1	no	—
116	C₂×C₄	—	293	1	no	—
117	C₂×C₄	—	293	1	no	—
118	C₂×C₄	—	293	1	no	—
119	C₂×C₄	—	293	1	no	—
120	C₂×C₄	—	293	1	no	—
121	C₂×C₄	—	293	2	no	—
122	C₂×C₄	—	586	2	no	—
123	C₂×C₄	—	586	2	no	—
124	C₂×C₄	—	586	2	no	—
125	C₂×C₄	—	586	2	no	—
126	C₂×C₄	C₄⋊#11924078	1	2	yes	—
127	C₂×C₄	#17989812	1	4	yes	—
128	C₈	—	586	2	no	—
129	C₈	—	586	2	no	—
130	C₈	—	1172	2	no	—
131	C₂²	C₂×C₄⋊#11924078	1	1	yes	characteristic
132	C₂²	D₄×#11924078	1	1	yes	characteristic
133	C₂²	Q₈×#11924078	1	1	yes	characteristic
134	C₂²	C₂×#17989812	1	2	yes	—
135	C₂²	#22627711	1	2	yes	—
136	C₄	—	2	2	no	—
137	C₄	—	2	4	no	—
138	C₄	—	293	1	no	—
139	C₄	—	293	1	no	—
140	C₄	—	293	1	no	—
141	C₄	—	293	1	no	—
142	C₄	—	586	2	no	—
143	C₄	—	1172	2	no	—
144	C₂	#34037080	1	1	yes	characteristic
145	C₂	#34037133	1	1	yes	characteristic
146	C₂	#34037135	1	1	yes	characteristic
147	C₂	#34037158	1	2	yes	—
148	C₂	#34037179	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊#14556880

C₂

yes

maximal

C₂×C₄⋊#14556880

C₂

yes

maximal, characteristic

C₂×#22627679

C₂

yes

maximal, characteristic

#34036995

C₂

yes

maximal

#34035980

C₂

yes

maximal, characteristic

C₂²×#14556880

C₂²

yes

—

C₂²×#14556880

C₂²

yes

characteristic

C₂²×#14556880

C₂²

yes

—

—

—

C₄

yes

—

C₂×C₄×Dic₂₉₃

C₂²

yes

—

C₂×C₄×Dic₂₉₃

C₂²

yes

characteristic

#22627531

C₄

yes

characteristic

#95×C₂₉₃

C₄

yes

—

—

—

—

—

—

—

D₄

yes

—

C₂×#14556880

Q₈

yes

—

C₂²×Dic₂₉₃

C₂×C₄

yes

—

C₂²×Dic₂₉₃

C₂×C₄

yes

characteristic

C₂²×Dic₂₉₃

C₂³

yes

characteristic

#17989781

—

C₄×Dic₂₉₃

—

C₄×Dic₂₉₃

—

C₄×Dic₂₉₃

D₄

yes

—

C₄×Dic₂₉₃

Q₈

yes

—

C₂²×C₄×C₂₉₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₂₉₃

C₂×C₄

yes

—

#14556880

—

#14556880

—

#14556880

—

C₂×Dic₂₉₃

—

C₂×Dic₂₉₃

—

C₂×Dic₂₉₃

—

C₂×Dic₂₉₃

—

C₂×Dic₂₉₃

C₄⋊C₄

yes

—

C₂×Dic₂₉₃

C₂×D₄

yes

characteristic

C₂×Dic₂₉₃

C₂×D₄

yes

characteristic

C₂×Dic₂₉₃

C₂×Q₈

yes

characteristic

C₂×Dic₂₉₃

C₂×Q₈

yes

C₂×Dic₂₉₃

yes

C₂×Dic₂₉₃

yes

C₂³×C₂₉₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉₃

—

C₂×C₄×C₂₉₃

—

C₂×C₄×C₂₉₃

—

C₂×C₄×C₂₉₃

C₄⋊C₄

yes

—

C₂×C₄×C₂₉₃

M₁₆

yes

—

C₂²×C₂₉₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₂₉₃

C₄×D₄

yes

characteristic

C₂²×C₂₉₃

C₄×Q₈

yes

characteristic

C₂²×C₂₉₃

C₂×M₁₆

yes

—

C₂²×C₂₉₃

#131

yes

—

C₄×C₂₉₃

—

C₄×C₂₉₃

—

Dic₂₉₃

—

Dic₂₉₃

—

Dic₂₉₃

#121

yes

characteristic

Dic₂₉₃

C₂²⋊Q₈

yes

characteristic

Dic₂₉₃

#125

yes

characteristic

Dic₂₉₃

C₄⋊Q₈

yes

C₂×C₂₉₃

yes

C₂×C₂₉₃

yes

C₂×C₂₉₃

yes

C₂×C₂₉₃

yes

—

C₂×C₂₉₃

#446

yes

—

C₂₉₃

#1940

yes

characteristic, complemented, Sylow

#1940

—

293

maximal, Sylow

C₂×C₄⋊C₈

—

293

—

C₂×C₄⋊C₈

—

293

—

C₂×#97

—

293

—

C₄×C₄⋊C₄

—

293

—

#336

—

293

—

C₂²×C₈

—

293

—

C₂²×C₈

—

293

—

C₂²×C₈

—

293

—

C₂×C₄⋊C₄

—

293

—

C₂×C₄²

—

293

—

C₂×C₄²

—

293

—

C₄⋊C₈

—

586

—

C₄⋊C₈

—

586

—

#97

—

586

—

#95

—

293

—

#95

#11924078

yes

characteristic

C₂²×C₄

—

293

—

C₂²×C₄

—

293

—

C₂²×C₄

—

293

—

C₂²×C₄

C₂×#11924078

yes

characteristic

C₂²×C₄

C₂×#11924078

yes

—

C₂×C₈

—

293

—

C₂×C₈

—

293

—

C₂×C₈

—

586

—

100

C₂×C₈

—

586

—

101

C₂×C₈

—

586

—

102

C₂×C₈

—

586

—

103

C₂×C₈

—

586

—

104

C₂×C₈

—

586

—

105

C₂×C₈

—

586

—

106

C₄⋊C₄

—

586

—

107

C₄²

—

293

—

108

C₄²

—

293

—

109

C₄²

—

586

—

110

C₄²

—

586

—

111

C₂³

C₂²×#11924078

yes

characteristic

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

293

—

116

C₂×C₄

—

293

—

117

C₂×C₄

—

293

—

118

C₂×C₄

—

293

—

119

C₂×C₄

—

293

—

120

C₂×C₄

—

293

—

121

C₂×C₄

—

293

—

122

C₂×C₄

—

586

—

123

C₂×C₄

—

586

—

124

C₂×C₄

—

586

—

125

C₂×C₄

—

586

—

126

C₂×C₄

C₄⋊#11924078

yes

—

127

C₂×C₄

#17989812

yes

—

128

C₈

—

586

—

129

C₈

—

586

—

130

C₈

—

1172

—

131

C₂²

C₂×C₄⋊#11924078

yes

characteristic

132

C₂²

D₄×#11924078

yes

characteristic

133

C₂²

Q₈×#11924078

yes

characteristic

134

C₂²

C₂×#17989812

yes

—

135

C₂²

#22627711

yes

—

136

C₄

—

137

C₄

—

138

C₄

—

293

—

139

C₄

—

293

—

140

C₄

—

293

—

141

C₄

—

293

—

142

C₄

—

586

—

143

C₄

—

1172

—

144

C₂

#34037080

yes

characteristic

145

C₂

#34037133

yes

characteristic

146

C₂

#34037135

yes

characteristic

147

C₂

#34037158

yes

—

148

C₂

#34037179

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#11924078
commutator, socle, prime radical	C₂³×C₂₉₃	C₂²×C₄
Fitting	#95×C₂₉₃	C₄
cosocle	C₂²×Dic₂₉₃	C₂³
hypercenter	#95	#11924078
hypocenter	C₂₉₃	#1940
LCS	G ▷ C₂³×C₂₉₃ ▷ C₂₉₃
UCS	C₁ ◁ C₂³ ◁ #95

subgroup

G/H

center, Frattini

C₂³

C₂²×#11924078

commutator, socle, prime radical

C₂³×C₂₉₃

C₂²×C₄

Fitting

#95×C₂₉₃

C₄

cosocle

C₂²×Dic₂₉₃

C₂³

C₂₉₃

G ▷ C₂³×C₂₉₃ ▷ C₂₉₃

C₁ ◁ C₂³ ◁ #95

N	H ≅ G/N	type
74. C₂₉₃	#1940	semidirect

H ≅ G/N

type

74. C₂₉₃

#1940

semidirect

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

subgroup	index
C₂×C₄⋊#14556880	2
C₂×#22627679	2
#34036995	2
#34035980	2
#1940	293

subgroup

index

293

Subgroups — #49174885

Conjugacy classes of subgroups

Complements

Maximal subgroups