Group #34046184 — subgroups

Subgroups — #34046184

Order 19072.

224 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 89 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×#18011845	C₂	1	1	yes	maximal, characteristic
2	#23749523	C₂	1	2	yes	maximal
3	#23749388	C₂	1	2	yes	maximal
4	#23749388	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊C₈×C₁₄₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊Dic₁₄₉	C₂²	1	2	yes	—
7	C₂×C₄⋊Dic₁₄₉	C₂²	1	2	yes	—
8	C₂×#14558715	—	2	2	no	—
9	#18011845	—	2	2	no	—
10	#18011818	—	2	2	no	—
11	C₂²×C₈×C₁₄₉	C₂²	1	1	yes	characteristic
12	C₂²×C₈×C₁₄₉	C₂²	1	1	yes	characteristic
13	C₂×C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
14	C₄⋊C₈×C₁₄₉	—	2	2	no	—
15	C₂²×Dic₁₄₉	—	2	2	no	—
16	C₂²×Dic₁₄₉	—	2	2	no	—
17	C₄⋊Dic₁₄₉	—	2	2	no	—
18	C₄⋊Dic₁₄₉	—	2	2	no	—
19	C₄⋊Dic₁₄₉	—	2	2	no	—
20	C₄⋊Dic₁₄₉	Q₈	1	4	yes	—
21	#14558715	—	4	4	no	—
22	C₂²×C₄×C₁₄₉	D₄	1	1	yes	characteristic
23	C₂²×C₄×C₁₄₉	D₄	1	1	yes	characteristic
24	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
25	C₂×C₈×C₁₄₉	—	2	2	no	—
26	C₂×C₈×C₁₄₉	—	2	1	no	—
27	C₂×C₈×C₁₄₉	—	2	2	no	—
28	C₂×C₈×C₁₄₉	D₄	1	2	yes	—
29	C₄²×C₁₄₉	—	2	1	no	—
30	C₄²×C₁₄₉	—	2	1	no	—
31	C₂×Dic₁₄₉	—	2	4	no	—
32	C₂×Dic₁₄₉	—	4	2	no	—
33	C₂×Dic₁₄₉	—	4	2	no	—
34	C₂×Dic₁₄₉	—	4	2	no	—
35	C₂×Dic₁₄₉	—	4	2	no	—
36	C₂×Dic₁₄₉	—	4	2	no	—
37	C₂³×C₁₄₉	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₁₄₉	—	2	1	no	—
39	C₂×C₄×C₁₄₉	—	2	1	no	—
40	C₂×C₄×C₁₄₉	—	2	1	no	—
41	C₂×C₄×C₁₄₉	—	2	2	no	—
42	C₂×C₄×C₁₄₉	Q₁₆	1	2	yes	—
43	C₂×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₁₄₉	C₂×Q₈	1	2	yes	—
45	C₂×C₄×C₁₄₉	#41	1	2	yes	—
46	C₂×C₄×C₁₄₉	#41	1	1	yes	characteristic
47	C₈×C₁₄₉	—	2	2	no	—
48	C₈×C₁₄₉	—	4	1	no	—
49	C₂²×C₁₄₉	#121	1	1	yes	characteristic
50	C₂²×C₁₄₉	C₂²⋊Q₈	1	2	yes	—
51	C₂²×C₁₄₉	C₂×Q₁₆	1	1	yes	characteristic
52	C₂²×C₁₄₉	#135	1	1	yes	characteristic
53	C₂²×C₁₄₉	AGL(1,ℤ/8)	1	2	yes	—
54	C₄×C₁₄₉	—	2	2	no	—
55	C₄×C₁₄₉	—	4	1	no	—
56	C₄×C₁₄₉	#123	1	1	yes	characteristic
57	C₄×C₁₄₉	#125	1	2	yes	—
58	C₄×C₁₄₉	C₄⋊Q₈	1	1	yes	characteristic
59	Dic₁₄₉	—	4	4	no	—
60	Dic₁₄₉	—	8	2	no	—
61	C₂×C₁₄₉	#398	1	1	yes	characteristic
62	C₂×C₁₄₉	#467	1	1	yes	characteristic
63	C₂×C₁₄₉	#469	1	1	yes	characteristic
64	C₂×C₁₄₉	#477	1	2	yes	—
65	C₂×C₁₄₉	#478	1	2	yes	—
66	C₁₄₉	#2087	1	1	yes	characteristic, complemented, Sylow
67	#2087	—	149	1	no	maximal, Sylow
68	C₂×#107	—	149	1	no	—
69	C₂×C₄⋊C₈	D₁₄₉	1	1	yes	characteristic
70	#389	—	149	2	no	—
71	#340	—	149	2	no	—
72	#340	—	149	1	no	—
73	C₂²×C₈	C₂×D₁₄₉	1	1	yes	characteristic
74	C₂²×C₈	C₂×D₁₄₉	1	1	yes	characteristic
75	C₂×C₄⋊C₄	—	298	2	no	—
76	C₂×C₄⋊C₄	—	149	2	no	—
77	C₂×C₄⋊C₄	—	149	2	no	—
78	C₂×C₄²	C₂×D₁₄₉	1	1	yes	characteristic
79	#107	—	298	2	no	—
80	C₄⋊C₈	—	2	2	no	—
81	#95	—	298	2	no	—
82	C₂²×C₄	—	298	2	no	—
83	C₂²×C₄	—	298	2	no	—
84	C₂²×C₄	D₅₉₆	1	1	yes	characteristic
85	C₂²×C₄	D₅₉₆	1	1	yes	characteristic
86	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
87	C₂×C₈	—	2	2	no	—
88	C₂×C₈	—	2	1	no	—
89	C₂×C₈	—	2	2	no	—
90	C₂×C₈	C₂²⋊D₁₄₉	1	2	yes	—
91	C₄⋊C₄	—	298	2	no	—
92	C₄⋊C₄	—	298	2	no	—
93	C₄⋊C₄	—	298	2	no	—
94	C₄⋊C₄	—	596	4	no	—
95	C₄⋊C₄	—	149	4	no	—
96	C₄²	—	2	1	no	—
97	C₄²	—	2	1	no	—
98	C₂³	C₂×D₅₉₆	1	1	yes	characteristic
99	C₂×C₄	—	2	1	no	—
100	C₂×C₄	—	2	1	no	—
101	C₂×C₄	—	2	2	no	—
102	C₂×C₄	—	2	1	no	—
103	C₂×C₄	—	298	4	no	—
104	C₂×C₄	—	596	2	no	—
105	C₂×C₄	—	596	2	no	—
106	C₂×C₄	—	596	2	no	—
107	C₂×C₄	—	596	2	no	—
108	C₂×C₄	—	596	2	no	—
109	C₂×C₄	Dic₅₉₆	1	2	yes	—
110	C₂×C₄	C₂×C₂²⋊D₁₄₉	1	1	yes	characteristic
111	C₂×C₄	Q₈×D₁₄₉	1	2	yes	—
112	C₂×C₄	#14558735	1	2	yes	—
113	C₂×C₄	#14558736	1	1	yes	characteristic
114	C₈	—	2	2	no	—
115	C₈	—	4	1	no	—
116	C₂²	#18011885	1	1	yes	characteristic
117	C₂²	#18011891	1	2	yes	—
118	C₂²	C₂×Dic₅₉₆	1	1	yes	characteristic
119	C₂²	#18011933	1	1	yes	characteristic
120	C₂²	#18011939	1	2	yes	—
121	C₄	—	2	2	no	—
122	C₄	—	4	1	no	—
123	C₄	—	596	4	no	—
124	C₄	—	1192	2	no	—
125	C₄	#18011892	1	1	yes	characteristic
126	C₄	#18011901	1	2	yes	—
127	C₄	#18011909	1	1	yes	characteristic
128	C₂	#23749555	1	1	yes	characteristic
129	C₂	#23749866	1	1	yes	characteristic
130	C₂	#23749878	1	1	yes	characteristic
131	C₂	#23749921	1	2	yes	—
132	C₂	#23749926	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#18011845

C₂

yes

maximal, characteristic

#23749523

C₂

yes

maximal

#23749388

C₂

yes

maximal

#23749388

C₂

yes

maximal, characteristic

C₂×C₄⋊C₈×C₁₄₉

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₁₄₉

C₂²

yes

—

C₂×C₄⋊Dic₁₄₉

C₂²

yes

—

C₂×#14558715

—

#18011845

—

#18011818

—

C₂²×C₈×C₁₄₉

C₂²

yes

characteristic

C₂²×C₈×C₁₄₉

C₂²

yes

characteristic

C₂×C₄²×C₁₄₉

C₂²

yes

characteristic

C₄⋊C₈×C₁₄₉

—

C₂²×Dic₁₄₉

—

C₂²×Dic₁₄₉

—

C₄⋊Dic₁₄₉

—

C₄⋊Dic₁₄₉

—

C₄⋊Dic₁₄₉

—

C₄⋊Dic₁₄₉

Q₈

yes

—

#14558715

—

C₂²×C₄×C₁₄₉

D₄

yes

characteristic

C₂²×C₄×C₁₄₉

D₄

yes

characteristic

C₂²×C₄×C₁₄₉

C₂³

yes

characteristic

C₂×C₈×C₁₄₉

—

C₂×C₈×C₁₄₉

—

C₂×C₈×C₁₄₉

—

C₂×C₈×C₁₄₉

D₄

yes

—

C₄²×C₁₄₉

—

C₄²×C₁₄₉

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

—

C₂³×C₁₄₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

Q₁₆

yes

—

C₂×C₄×C₁₄₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₄₉

C₂×Q₈

yes

—

C₂×C₄×C₁₄₉

#41

yes

—

C₂×C₄×C₁₄₉

#41

yes

characteristic

C₈×C₁₄₉

—

C₈×C₁₄₉

—

C₂²×C₁₄₉

#121

yes

characteristic

C₂²×C₁₄₉

C₂²⋊Q₈

yes

—

C₂²×C₁₄₉

C₂×Q₁₆

yes

C₂²×C₁₄₉

yes

C₂²×C₁₄₉

yes

—

C₄×C₁₄₉

—

C₄×C₁₄₉

—

C₄×C₁₄₉

#123

yes

characteristic

C₄×C₁₄₉

#125

yes

—

C₄×C₁₄₉

C₄⋊Q₈

yes

characteristic

Dic₁₄₉

—

Dic₁₄₉

—

C₂×C₁₄₉

yes

C₂×C₁₄₉

yes

C₂×C₁₄₉

yes

C₂×C₁₄₉

yes

—

C₂×C₁₄₉

#478

yes

—

C₁₄₉

#2087

yes

characteristic, complemented, Sylow

#2087

—

149

maximal, Sylow

C₂×#107

—

149

—

C₂×C₄⋊C₈

D₁₄₉

yes

characteristic

#389

—

149

—

#340

—

149

—

#340

—

149

—

C₂²×C₈

C₂×D₁₄₉

yes

characteristic

C₂²×C₈

C₂×D₁₄₉

yes

characteristic

C₂×C₄⋊C₄

—

298

—

C₂×C₄⋊C₄

—

149

—

C₂×C₄⋊C₄

—

149

—

C₂×C₄²

C₂×D₁₄₉

yes

characteristic

#107

—

298

—

C₄⋊C₈

—

#95

—

298

—

C₂²×C₄

—

298

—

C₂²×C₄

—

298

—

C₂²×C₄

D₅₉₆

yes

characteristic

C₂²×C₄

D₅₉₆

yes

characteristic

C₂²×C₄

C₂²×D₁₄₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₁₄₉

yes

—

C₄⋊C₄

—

298

—

C₄⋊C₄

—

298

—

C₄⋊C₄

—

298

—

C₄⋊C₄

—

596

—

C₄⋊C₄

—

149

—

C₄²

—

C₄²

—

C₂³

C₂×D₅₉₆

yes

characteristic

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

298

—

104

C₂×C₄

—

596

—

105

C₂×C₄

—

596

—

106

C₂×C₄

—

596

—

107

C₂×C₄

—

596

—

108

C₂×C₄

—

596

—

109

C₂×C₄

Dic₅₉₆

yes

—

110

C₂×C₄

C₂×C₂²⋊D₁₄₉

yes

characteristic

111

C₂×C₄

Q₈×D₁₄₉

yes

—

112

C₂×C₄

#14558735

yes

—

113

C₂×C₄

#14558736

yes

characteristic

114

C₈

—

115

C₈

—

116

C₂²

#18011885

yes

characteristic

117

C₂²

#18011891

yes

—

118

C₂²

C₂×Dic₅₉₆

yes

characteristic

119

C₂²

#18011933

yes

characteristic

120

C₂²

#18011939

yes

—

121

C₄

—

122

C₄

—

123

C₄

—

596

—

124

C₄

—

1192

—

125

C₄

#18011892

yes

characteristic

126

C₄

#18011901

yes

—

127

C₄

#18011909

yes

characteristic

128

C₂

#23749555

yes

characteristic

129

C₂

#23749866

yes

characteristic

130

C₂

#23749878

yes

characteristic

131

C₂

#23749921

yes

—

132

C₂

#23749926

yes

—

	subgroup	G/H
center	C₂³	C₂×D₅₉₆
commutator, cosocle	C₂²×C₄×C₁₄₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₄₉
Fitting	C₂×C₄⋊C₈×C₁₄₉	C₂
socle, prime radical	C₂³×C₁₄₉	C₂×D₄
hypercenter	C₂×C₄⋊C₈	D₁₄₉
hypocenter	C₁₄₉	#2087
LCS	G ▷ C₂²×C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

subgroup

G/H

center

C₂³

C₂×D₅₉₆

commutator, cosocle

C₂²×C₄×C₁₄₉

C₂³

Frattini

C₂²×C₄

C₂²×D₁₄₉

Fitting

C₂×C₄⋊C₈×C₁₄₉

C₂

socle, prime radical

C₂³×C₁₄₉

C₂×D₄

hypercenter

C₂×C₄⋊C₈

D₁₄₉

hypocenter

C₁₄₉

#2087

LCS

G ▷ C₂²×C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

N	H ≅ G/N	type
66. C₁₄₉	#2087	semidirect

H ≅ G/N

type

66. C₁₄₉

#2087

semidirect

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

subgroup	index
C₂×#18011845	2
#23749523	2
#23749388	2
C₂×C₄⋊C₈×C₁₄₉	2
#2087	149

subgroup

index

C₂×C₄⋊C₈×C₁₄₉

149

Subgroups — #34046184

Conjugacy classes of subgroups

Complements

Maximal subgroups