Group #34060792 — subgroups

Subgroups — #34060792

Order 19072.

248 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 90 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×#18011978	C₂	1	2	yes	maximal
2	C₂×C₄⋊#11924753	C₂	1	1	yes	maximal, characteristic
3	C₂×#18011966	C₂	1	1	yes	maximal, characteristic
4	#23750491	C₂	1	2	yes	maximal
5	#23749476	C₂	1	1	yes	maximal, characteristic
6	C₂²×#11924753	C₂²	1	2	yes	—
7	C₂²×#11924753	C₂²	1	1	yes	characteristic
8	C₂²×#11924753	C₂²	1	1	yes	characteristic
9	#18011978	—	2	4	no	—
10	C₄⋊#11924753	—	2	2	no	—
11	#18011966	—	2	2	no	—
12	C₂×#14558715	C₄	1	2	yes	—
13	C₂×C₄×Dic₁₄₉	C₂²	1	2	yes	—
14	C₂×C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
15	#18011818	C₄	1	1	yes	characteristic
16	#95×C₁₄₉	C₄	1	1	yes	characteristic
17	C₂×#11924753	—	2	1	no	—
18	C₂×#11924753	—	2	1	no	—
19	C₂×#11924753	—	2	2	no	—
20	C₂×#11924753	—	2	2	no	—
21	C₂×#11924753	—	2	1	no	—
22	C₂×#11924753	—	2	1	no	—
23	C₂×#11924753	—	2	2	no	—
24	C₂×#11924753	D₄	1	2	yes	—
25	C₂×#11924753	Q₈	1	2	yes	—
26	C₂²×Dic₁₄₉	C₂×C₄	1	1	yes	characteristic
27	C₂²×Dic₁₄₉	C₂×C₄	1	2	yes	—
28	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
29	#14558715	—	2	4	no	—
30	C₄×Dic₁₄₉	—	2	2	no	—
31	C₄×Dic₁₄₉	—	2	2	no	—
32	C₄×Dic₁₄₉	D₄	1	2	yes	—
33	C₄×Dic₁₄₉	Q₈	1	2	yes	—
34	C₂²×C₄×C₁₄₉	C₂×C₄	1	2	yes	—
35	C₂²×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
36	#11924753	—	2	2	no	—
37	#11924753	—	2	2	no	—
38	#11924753	—	4	2	no	—
39	C₂×Dic₁₄₉	—	2	2	no	—
40	C₂×Dic₁₄₉	—	2	2	no	—
41	C₂×Dic₁₄₉	—	2	2	no	—
42	C₂×Dic₁₄₉	C₄⋊C₄	1	2	yes	—
43	C₂×Dic₁₄₉	M₁₆	1	4	yes	—
44	C₂×Dic₁₄₉	C₂×D₄	1	1	yes	characteristic
45	C₂×Dic₁₄₉	C₂×D₄	1	1	yes	characteristic
46	C₂×Dic₁₄₉	C₂×Q₈	1	1	yes	characteristic
47	C₂×Dic₁₄₉	C₂×Q₈	1	1	yes	characteristic
48	C₂×Dic₁₄₉	#41	1	1	yes	characteristic
49	C₂×Dic₁₄₉	#41	1	1	yes	characteristic
50	C₂³×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₄×C₁₄₉	—	2	2	no	—
52	C₂×C₄×C₁₄₉	—	2	2	no	—
53	C₂×C₄×C₁₄₉	—	2	2	no	—
54	C₂×C₄×C₁₄₉	—	2	2	no	—
55	C₂×C₄×C₁₄₉	C₄⋊C₄	1	2	yes	—
56	C₂²×C₁₄₉	C₂×C₄⋊C₄	1	1	yes	characteristic
57	C₂²×C₁₄₉	C₄×D₄	1	1	yes	characteristic
58	C₂²×C₁₄₉	C₄×Q₈	1	1	yes	characteristic
59	C₂²×C₁₄₉	C₂×M₁₆	1	2	yes	—
60	C₂²×C₁₄₉	#131	1	2	yes	—
61	C₄×C₁₄₉	—	2	2	no	—
62	C₄×C₁₄₉	—	4	2	no	—
63	Dic₁₄₉	—	2	2	no	—
64	Dic₁₄₉	—	2	4	no	—
65	Dic₁₄₉	#121	1	1	yes	characteristic
66	Dic₁₄₉	C₂²⋊Q₈	1	1	yes	characteristic
67	Dic₁₄₉	#125	1	1	yes	characteristic
68	Dic₁₄₉	C₄⋊Q₈	1	1	yes	characteristic
69	C₂×C₁₄₉	#389	1	1	yes	characteristic
70	C₂×C₁₄₉	#423	1	1	yes	characteristic
71	C₂×C₁₄₉	#424	1	1	yes	characteristic
72	C₂×C₁₄₉	#435	1	2	yes	—
73	C₂×C₁₄₉	#446	1	2	yes	—
74	C₁₄₉	#1940	1	1	yes	characteristic, complemented, Sylow
75	#1940	—	149	1	no	maximal, Sylow
76	C₂×C₄⋊C₈	—	149	1	no	—
77	C₂×C₄⋊C₈	—	149	2	no	—
78	C₂×#97	—	149	1	no	—
79	C₄×C₄⋊C₄	—	149	1	no	—
80	#336	—	149	2	no	—
81	C₂²×C₈	—	149	2	no	—
82	C₂²×C₈	—	149	1	no	—
83	C₂²×C₈	—	149	1	no	—
84	C₂×C₄⋊C₄	—	149	2	no	—
85	C₂×C₄²	—	149	2	no	—
86	C₂×C₄²	—	149	1	no	—
87	C₄⋊C₈	—	298	4	no	—
88	C₄⋊C₈	—	298	2	no	—
89	#97	—	298	2	no	—
90	#95	—	149	1	no	—
91	#95	#10597010	1	1	yes	characteristic
92	C₂²×C₄	—	149	2	no	—
93	C₂²×C₄	—	149	1	no	—
94	C₂²×C₄	—	149	1	no	—
95	C₂²×C₄	C₂×#10597010	1	2	yes	—
96	C₂²×C₄	C₂×#10597010	1	1	yes	characteristic
97	C₂×C₈	—	298	1	no	—
98	C₂×C₈	—	298	1	no	—
99	C₂×C₈	—	298	1	no	—
100	C₂×C₈	—	298	1	no	—
101	C₂×C₈	—	298	2	no	—
102	C₂×C₈	—	298	2	no	—
103	C₂×C₈	—	298	2	no	—
104	C₂×C₈	—	149	2	no	—
105	C₂×C₈	—	149	2	no	—
106	C₄⋊C₄	—	298	4	no	—
107	C₄²	—	298	2	no	—
108	C₄²	—	298	2	no	—
109	C₄²	—	149	2	no	—
110	C₄²	—	149	2	no	—
111	C₂³	C₂²×#10597010	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	—	2	2	no	—
116	C₂×C₄	—	298	2	no	—
117	C₂×C₄	—	298	2	no	—
118	C₂×C₄	—	298	2	no	—
119	C₂×C₄	—	149	2	no	—
120	C₂×C₄	—	149	4	no	—
121	C₂×C₄	—	149	1	no	—
122	C₂×C₄	—	149	1	no	—
123	C₂×C₄	—	149	1	no	—
124	C₂×C₄	—	149	1	no	—
125	C₂×C₄	—	149	1	no	—
126	C₂×C₄	—	149	1	no	—
127	C₂×C₄	C₄⋊#10597010	1	2	yes	—
128	C₈	—	298	2	no	—
129	C₈	—	298	2	no	—
130	C₈	—	596	2	no	—
131	C₂²	C₂×C₄⋊#10597010	1	1	yes	characteristic
132	C₂²	D₄×#10597010	1	1	yes	characteristic
133	C₂²	Q₈×#10597010	1	1	yes	characteristic
134	C₂²	D₁₄₉⋊M₁₆	1	2	yes	—
135	C₂²	#18011998	1	2	yes	—
136	C₄	—	2	2	no	—
137	C₄	—	4	2	no	—
138	C₄	—	298	4	no	—
139	C₄	—	298	2	no	—
140	C₄	—	149	1	no	—
141	C₄	—	149	1	no	—
142	C₄	—	149	1	no	—
143	C₄	—	149	1	no	—
144	C₂	#23750576	1	1	yes	characteristic
145	C₂	#23750630	1	1	yes	characteristic
146	C₂	#23750631	1	1	yes	characteristic
147	C₂	#23750657	1	2	yes	—
148	C₂	#23750677	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#18011978

C₂

yes

maximal

C₂×C₄⋊#11924753

C₂

yes

maximal, characteristic

C₂×#18011966

C₂

yes

maximal, characteristic

#23750491

C₂

yes

maximal

#23749476

C₂

yes

maximal, characteristic

C₂²×#11924753

C₂²

yes

—

C₂²×#11924753

C₂²

yes

characteristic

C₂²×#11924753

C₂²

yes

—

—

—

C₄

yes

—

C₂×C₄×Dic₁₄₉

C₂²

yes

—

C₂×C₄×Dic₁₄₉

C₂²

yes

characteristic

#18011818

C₄

yes

characteristic

#95×C₁₄₉

C₄

yes

—

—

—

—

—

—

—

D₄

yes

—

C₂×#11924753

Q₈

yes

—

C₂²×Dic₁₄₉

C₂×C₄

yes

characteristic

C₂²×Dic₁₄₉

C₂×C₄

yes

—

C₂²×Dic₁₄₉

C₂³

yes

characteristic

#14558715

—

C₄×Dic₁₄₉

—

C₄×Dic₁₄₉

—

C₄×Dic₁₄₉

D₄

yes

—

C₄×Dic₁₄₉

Q₈

yes

—

C₂²×C₄×C₁₄₉

C₂×C₄

yes

—

C₂²×C₄×C₁₄₉

C₂×C₄

yes

—

—

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

C₄⋊C₄

yes

—

C₂×Dic₁₄₉

M₁₆

yes

—

C₂×Dic₁₄₉

C₂×D₄

yes

characteristic

C₂×Dic₁₄₉

C₂×D₄

yes

characteristic

C₂×Dic₁₄₉

C₂×Q₈

yes

characteristic

C₂×Dic₁₄₉

C₂×Q₈

yes

C₂×Dic₁₄₉

yes

C₂×Dic₁₄₉

yes

C₂³×C₁₄₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

C₄⋊C₄

yes

—

C₂²×C₁₄₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₄₉

C₄×D₄

yes

characteristic

C₂²×C₁₄₉

C₄×Q₈

yes

characteristic

C₂²×C₁₄₉

C₂×M₁₆

yes

—

C₂²×C₁₄₉

#131

yes

—

C₄×C₁₄₉

—

C₄×C₁₄₉

—

Dic₁₄₉

—

Dic₁₄₉

—

Dic₁₄₉

#121

yes

characteristic

Dic₁₄₉

C₂²⋊Q₈

yes

characteristic

Dic₁₄₉

#125

yes

characteristic

Dic₁₄₉

C₄⋊Q₈

yes

C₂×C₁₄₉

yes

C₂×C₁₄₉

yes

C₂×C₁₄₉

yes

C₂×C₁₄₉

yes

—

C₂×C₁₄₉

#446

yes

—

C₁₄₉

#1940

yes

characteristic, complemented, Sylow

#1940

—

149

maximal, Sylow

C₂×C₄⋊C₈

—

149

—

C₂×C₄⋊C₈

—

149

—

C₂×#97

—

149

—

C₄×C₄⋊C₄

—

149

—

#336

—

149

—

C₂²×C₈

—

149

—

C₂²×C₈

—

149

—

C₂²×C₈

—

149

—

C₂×C₄⋊C₄

—

149

—

C₂×C₄²

—

149

—

C₂×C₄²

—

149

—

C₄⋊C₈

—

298

—

C₄⋊C₈

—

298

—

#97

—

298

—

#95

—

149

—

#95

#10597010

yes

characteristic

C₂²×C₄

—

149

—

C₂²×C₄

—

149

—

C₂²×C₄

—

149

—

C₂²×C₄

C₂×#10597010

yes

—

C₂²×C₄

C₂×#10597010

yes

characteristic

C₂×C₈

—

298

—

C₂×C₈

—

298

—

C₂×C₈

—

298

—

100

C₂×C₈

—

298

—

101

C₂×C₈

—

298

—

102

C₂×C₈

—

298

—

103

C₂×C₈

—

298

—

104

C₂×C₈

—

149

—

105

C₂×C₈

—

149

—

106

C₄⋊C₄

—

298

—

107

C₄²

—

298

—

108

C₄²

—

298

—

109

C₄²

—

149

—

110

C₄²

—

149

—

111

C₂³

C₂²×#10597010

yes

characteristic

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

298

—

117

C₂×C₄

—

298

—

118

C₂×C₄

—

298

—

119

C₂×C₄

—

149

—

120

C₂×C₄

—

149

—

121

C₂×C₄

—

149

—

122

C₂×C₄

—

149

—

123

C₂×C₄

—

149

—

124

C₂×C₄

—

149

—

125

C₂×C₄

—

149

—

126

C₂×C₄

—

149

—

127

C₂×C₄

C₄⋊#10597010

yes

—

128

C₈

—

298

—

129

C₈

—

298

—

130

C₈

—

596

—

131

C₂²

C₂×C₄⋊#10597010

yes

characteristic

132

C₂²

D₄×#10597010

yes

characteristic

133

C₂²

Q₈×#10597010

yes

characteristic

134

C₂²

D₁₄₉⋊M₁₆

yes

—

135

C₂²

#18011998

yes

—

136

C₄

—

137

C₄

—

138

C₄

—

298

—

139

C₄

—

298

—

140

C₄

—

149

—

141

C₄

—

149

—

142

C₄

—

149

—

143

C₄

—

149

—

144

C₂

#23750576

yes

characteristic

145

C₂

#23750630

yes

characteristic

146

C₂

#23750631

yes

characteristic

147

C₂

#23750657

yes

—

148

C₂

#23750677

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#10597010
commutator, socle, prime radical	C₂³×C₁₄₉	C₂²×C₄
Fitting	#95×C₁₄₉	C₄
cosocle	C₂²×Dic₁₄₉	C₂³
hypercenter	#95	#10597010
hypocenter	C₁₄₉	#1940
LCS	G ▷ C₂³×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂³ ◁ #95

subgroup

G/H

center, Frattini

C₂³

C₂²×#10597010

commutator, socle, prime radical

C₂³×C₁₄₉

C₂²×C₄

Fitting

#95×C₁₄₉

C₄

cosocle

C₂²×Dic₁₄₉

C₂³

C₁₄₉

G ▷ C₂³×C₁₄₉ ▷ C₁₄₉

C₁ ◁ C₂³ ◁ #95

N	H ≅ G/N	type
74. C₁₄₉	#1940	semidirect

H ≅ G/N

type

74. C₁₄₉

#1940

semidirect

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

subgroup	index
C₂×#18011978	2
C₂×C₄⋊#11924753	2
C₂×#18011966	2
#23750491	2
#23749476	2
#1940	149

subgroup

index

149

Subgroups — #34060792

Conjugacy classes of subgroups

Complements

Maximal subgroups