Group #23809437 — subgroups

Subgroups — C₄₁×#33236 #23809437

Order 10496.

910 conjugacy classes of subgroups; only the 318 normal subgroups are shown.

normal subgroups only

This group has 910 conjugacy classes of subgroups — too many to draw. Only its 318 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×C₄₁×#487	C₂	1	4	yes	maximal
2	C₄₁×#2868	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#2862	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#1960	C₂	1	8	yes	maximal
5	C₄×#97×C₄₁	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊Q₈×C₄₁	C₂²	1	2	yes	—
7	C₂×C₄⋊Q₈×C₄₁	C₂²	1	4	yes	—
8	C₂×C₄⋊Q₈×C₄₁	C₂²	1	2	yes	—
9	C₄₁×#487	—	2	16	no	—
10	C₂×#103×C₄₁	C₂²	1	16	yes	—
11	C₂×#97×C₄₁	C₂²	1	4	yes	—
12	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
13	C₄₁×#391	—	2	4	no	—
14	C₄₁×#384	—	2	4	no	—
15	C₄₁×#382	C₂²	1	4	yes	—
16	C₄³×C₄₁	C₂²	1	1	yes	characteristic
17	C₂²×Q₈×C₄₁	—	2	2	no	—
18	C₂²×Q₈×C₄₁	C₂³	1	4	yes	—
19	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
20	C₄⋊Q₈×C₄₁	—	2	8	no	—
21	C₄⋊Q₈×C₄₁	—	2	8	no	—
22	C₄⋊Q₈×C₄₁	—	2	16	no	—
23	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
24	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
25	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
26	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
27	C₂×C₄²×C₄₁	D₄	1	4	yes	—
28	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
29	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
30	#103×C₄₁	—	2	32	no	—
31	#97×C₄₁	—	2	8	no	—
32	C₄×C₈×C₄₁	D₄	1	8	yes	—
33	#95×C₄₁	—	2	8	no	—
34	C₂×Q₈×C₄₁	—	2	8	no	—
35	C₂×Q₈×C₄₁	—	2	16	no	—
36	C₂×Q₈×C₄₁	—	4	4	no	—
37	C₂×Q₈×C₄₁	—	4	8	no	—
38	C₂²×C₄×C₄₁	—	2	4	no	—
39	C₂²×C₄×C₄₁	—	2	4	no	—
40	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
41	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
42	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
43	C₂×C₈×C₄₁	—	2	8	no	—
44	C₂×C₈×C₄₁	C₂×D₄	1	8	yes	—
45	C₄⋊C₄×C₄₁	—	2	8	no	—
46	C₄⋊C₄×C₄₁	—	4	16	no	—
47	C₄⋊C₄×C₄₁	—	4	4	no	—
48	C₄⋊C₄×C₄₁	—	4	8	no	—
49	C₄²×C₄₁	—	2	8	no	—
50	C₄²×C₄₁	C₂×D₄	1	4	yes	—
51	C₄²×C₄₁	#41	1	8	yes	—
52	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
53	Q₈×C₄₁	—	4	16	no	—
54	Q₈×C₄₁	—	8	8	no	—
55	C₂×C₄×C₄₁	—	2	8	no	—
56	C₂×C₄×C₄₁	—	4	8	no	—
57	C₂×C₄×C₄₁	—	4	4	no	—
58	C₂×C₄×C₄₁	—	4	4	no	—
59	C₂×C₄×C₄₁	—	4	8	no	—
60	C₂×C₄×C₄₁	#124	1	8	yes	—
61	C₂×C₄×C₄₁	#127	1	4	yes	—
62	C₂×C₄×C₄₁	#137	1	8	yes	—
63	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
64	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
65	C₈×C₄₁	—	2	8	no	—
66	#33236	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
67	C₂²×C₄₁	C₂×#124	1	2	yes	—
68	C₂²×C₄₁	C₂×#127	1	1	yes	characteristic
69	C₂²×C₄₁	C₂×#137	1	4	yes	—
70	C₄×C₄₁	—	2	8	no	—
71	C₄×C₄₁	—	8	4	no	—
72	C₄×C₄₁	—	8	4	no	—
73	C₄×C₄₁	#497	1	8	yes	—
74	C₄×C₄₁	#532	1	4	yes	—
75	C₂×#487	C₂×C₄₁	1	4	yes	—
76	#2868	C₂×C₄₁	1	1	yes	characteristic
77	#2862	C₂×C₄₁	1	1	yes	characteristic
78	#1960	C₂×C₄₁	1	8	yes	—
79	C₄×#97	C₂×C₄₁	1	1	yes	characteristic
80	C₂×C₄₁	#2858	1	1	yes	characteristic
81	C₂×C₄₁	#3139	1	4	yes	—
82	C₂×C₄₁	C₂×#497	1	2	yes	—
83	C₂×C₄⋊Q₈	C₂²×C₄₁	1	2	yes	—
84	C₂×C₄⋊Q₈	C₂²×C₄₁	1	4	yes	—
85	C₂×C₄⋊Q₈	C₂²×C₄₁	1	2	yes	—
86	#487	—	2	16	no	—
87	C₂×#103	C₂²×C₄₁	1	16	yes	—
88	C₂×#97	C₂²×C₄₁	1	4	yes	—
89	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
90	#391	—	2	4	no	—
91	#384	—	2	4	no	—
92	#382	C₂²×C₄₁	1	4	yes	—
93	C₄³	C₂²×C₄₁	1	1	yes	characteristic
94	C₄₁	#33236	1	1	yes	characteristic, direct product factor, Sylow
95	C₂²×Q₈	—	2	2	no	—
96	C₂²×Q₈	C₂³×C₄₁	1	4	yes	—
97	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
98	C₄⋊Q₈	—	2	8	no	—
99	C₄⋊Q₈	—	2	8	no	—
100	C₄⋊Q₈	—	2	16	no	—
101	C₂×C₄⋊C₄	—	2	8	no	—
102	C₂×C₄⋊C₄	—	2	4	no	—
103	C₂×C₄⋊C₄	—	2	2	no	—
104	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
105	C₂×C₄²	D₄×C₄₁	1	4	yes	—
106	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
107	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
108	#103	—	2	32	no	—
109	#97	—	2	8	no	—
110	C₄×C₈	D₄×C₄₁	1	8	yes	—
111	#95	—	2	8	no	—
112	C₂×Q₈	—	2	8	no	—
113	C₂×Q₈	—	2	16	no	—
114	C₂×Q₈	—	4	4	no	—
115	C₂×Q₈	—	4	8	no	—
116	C₂²×C₄	—	2	4	no	—
117	C₂²×C₄	—	2	4	no	—
118	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
119	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
120	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
121	C₂×C₈	—	2	8	no	—
122	C₂×C₈	C₂×D₄×C₄₁	1	8	yes	—
123	C₄⋊C₄	—	2	8	no	—
124	C₄⋊C₄	—	4	16	no	—
125	C₄⋊C₄	—	4	4	no	—
126	C₄⋊C₄	—	4	8	no	—
127	C₄²	—	2	8	no	—
128	C₄²	C₂×D₄×C₄₁	1	4	yes	—
129	C₄²	#41×C₄₁	1	8	yes	—
130	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
131	Q₈	—	4	16	no	—
132	Q₈	—	8	8	no	—
133	C₂×C₄	—	2	8	no	—
134	C₂×C₄	—	4	8	no	—
135	C₂×C₄	—	4	4	no	—
136	C₂×C₄	—	4	4	no	—
137	C₂×C₄	—	4	8	no	—
138	C₂×C₄	#124×C₄₁	1	8	yes	—
139	C₂×C₄	#127×C₄₁	1	4	yes	—
140	C₂×C₄	#137×C₄₁	1	8	yes	—
141	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
142	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
143	C₈	—	2	8	no	—
144	C₂²	C₂×#124×C₄₁	1	2	yes	—
145	C₂²	C₂×#127×C₄₁	1	1	yes	characteristic
146	C₂²	C₂×#137×C₄₁	1	4	yes	—
147	C₄	—	2	8	no	—
148	C₄	—	8	4	no	—
149	C₄	—	8	4	no	—
150	C₄	C₄₁×#497	1	8	yes	—
151	C₄	C₄₁×#532	1	4	yes	—
152	C₂	C₄₁×#2858	1	1	yes	characteristic
153	C₂	C₄₁×#3139	1	4	yes	—
154	C₂	C₂×C₄₁×#497	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄₁×#487

C₂

yes

maximal

C₄₁×#2868

C₂

yes

maximal, characteristic

C₄₁×#2862

C₂

yes

maximal, characteristic

C₄₁×#1960

C₂

yes

maximal

C₄×#97×C₄₁

C₂

yes

maximal, characteristic

C₂×C₄⋊Q₈×C₄₁

C₂²

yes

—

C₂×C₄⋊Q₈×C₄₁

C₂²

yes

—

C₂×C₄⋊Q₈×C₄₁

C₂²

yes

—

C₄₁×#487

—

C₂×#103×C₄₁

C₂²

yes

—

C₂×#97×C₄₁

C₂²

yes

—

C₂×C₄×C₈×C₄₁

C₂²

yes

—

C₄₁×#391

—

C₄₁×#384

—

C₄₁×#382

C₂²

yes

—

C₄³×C₄₁

C₂²

yes

characteristic

C₂²×Q₈×C₄₁

—

C₂²×Q₈×C₄₁

C₂³

yes

—

C₂²×C₈×C₄₁

C₂³

yes

—

C₄⋊Q₈×C₄₁

—

C₄⋊Q₈×C₄₁

—

C₄⋊Q₈×C₄₁

—

C₂×C₄⋊C₄×C₄₁

—

C₂×C₄⋊C₄×C₄₁

—

C₂×C₄⋊C₄×C₄₁

—

C₂×C₄⋊C₄×C₄₁

C₂³

yes

—

C₂×C₄²×C₄₁

D₄

yes

—

C₂×C₄²×C₄₁

C₂³

yes

characteristic

C₂×C₄²×C₄₁

C₂³

yes

—

#103×C₄₁

—

#97×C₄₁

—

C₄×C₈×C₄₁

D₄

yes

—

#95×C₄₁

—

C₂×Q₈×C₄₁

—

C₂×Q₈×C₄₁

—

C₂×Q₈×C₄₁

—

C₂×Q₈×C₄₁

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

C₂×D₄

yes

—

C₂²×C₄×C₄₁

C₂×D₄

yes

—

C₂²×C₄×C₄₁

C₂⁴

yes

characteristic

C₂×C₈×C₄₁

—

C₂×C₈×C₄₁

C₂×D₄

yes

—

C₄⋊C₄×C₄₁

—

C₄⋊C₄×C₄₁

—

C₄⋊C₄×C₄₁

—

C₄⋊C₄×C₄₁

—

C₄²×C₄₁

—

C₄²×C₄₁

C₂×D₄

yes

—

C₄²×C₄₁

#41

yes

—

C₂³×C₄₁

C₂²×D₄

yes

characteristic

Q₈×C₄₁

—

Q₈×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

#124

yes

—

C₂×C₄×C₄₁

#127

yes

—

C₂×C₄×C₄₁

#137

yes

—

C₂×C₄×C₄₁

C₂²×D₄

yes

—

C₂×C₄×C₄₁

C₂×#41

yes

—

C₈×C₄₁

—

#33236

C₄₁

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₄₁

C₂×#124

yes

—

C₂²×C₄₁

C₂×#127

yes

characteristic

C₂²×C₄₁

C₂×#137

yes

—

C₄×C₄₁

—

C₄×C₄₁

—

C₄×C₄₁

—

C₄×C₄₁

#497

yes

—

C₄×C₄₁

#532

yes

—

C₂×#487

C₂×C₄₁

yes

—

#2868

C₂×C₄₁

yes

characteristic

#2862

C₂×C₄₁

yes

characteristic

#1960

C₂×C₄₁

yes

—

C₄×#97

C₂×C₄₁

yes

C₂×C₄₁

yes

C₂×C₄₁

yes

—

C₂×C₄₁

C₂×#497

yes

—

C₂×C₄⋊Q₈

C₂²×C₄₁

yes

—

C₂×C₄⋊Q₈

C₂²×C₄₁

yes

—

C₂×C₄⋊Q₈

C₂²×C₄₁

yes

—

#487

—

C₂×#103

C₂²×C₄₁

yes

—

C₂×#97

C₂²×C₄₁

yes

—

C₂×C₄×C₈

C₂²×C₄₁

yes

—

#391

—

#384

—

#382

C₂²×C₄₁

yes

—

C₄³

C₂²×C₄₁

yes

characteristic

C₄₁

#33236

yes

characteristic, direct product factor, Sylow

C₂²×Q₈

—

C₂²×Q₈

C₂³×C₄₁

yes

—

C₂²×C₈

C₂³×C₄₁

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

100

C₄⋊Q₈

—

101

C₂×C₄⋊C₄

—

102

C₂×C₄⋊C₄

—

103

C₂×C₄⋊C₄

—

104

C₂×C₄⋊C₄

C₂³×C₄₁

yes

—

105

C₂×C₄²

D₄×C₄₁

yes

—

106

C₂×C₄²

C₂³×C₄₁

yes

characteristic

107

C₂×C₄²

C₂³×C₄₁

yes

—

108

#103

—

109

#97

—

110

C₄×C₈

D₄×C₄₁

yes

—

111

#95

—

112

C₂×Q₈

—

113

C₂×Q₈

—

114

C₂×Q₈

—

115

C₂×Q₈

—

116

C₂²×C₄

—

117

C₂²×C₄

—

118

C₂²×C₄

C₂×D₄×C₄₁

yes

—

119

C₂²×C₄

C₂×D₄×C₄₁

yes

—

120

C₂²×C₄

C₂⁴×C₄₁

yes

characteristic

121

C₂×C₈

—

122

C₂×C₈

C₂×D₄×C₄₁

yes

—

123

C₄⋊C₄

—

124

C₄⋊C₄

—

125

C₄⋊C₄

—

126

C₄⋊C₄

—

127

C₄²

—

128

C₄²

C₂×D₄×C₄₁

yes

—

129

C₄²

#41×C₄₁

yes

—

130

C₂³

C₂²×D₄×C₄₁

yes

characteristic

131

Q₈

—

132

Q₈

—

133

C₂×C₄

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

138

C₂×C₄

#124×C₄₁

yes

—

139

C₂×C₄

#127×C₄₁

yes

—

140

C₂×C₄

#137×C₄₁

yes

—

141

C₂×C₄

C₂²×D₄×C₄₁

yes

—

142

C₂×C₄

C₂×#41×C₄₁

yes

—

143

C₈

—

144

C₂²

C₂×#124×C₄₁

yes

—

145

C₂²

C₂×#127×C₄₁

yes

characteristic

146

C₂²

C₂×#137×C₄₁

yes

—

147

C₄

—

148

C₄

—

149

C₄

—

150

C₄

C₄₁×#497

yes

—

151

C₄

C₄₁×#532

yes

—

152

C₂

C₄₁×#2858

yes

characteristic

153

C₂

C₄₁×#3139

yes

—

154

C₂

C₂×C₄₁×#497

yes

—

	subgroup	G/H
center, socle, prime radical	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₄³×C₄₁ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₄₁

C₂²×D₄

commutator, Frattini, cosocle

C₂²×C₄

C₂⁴×C₄₁

LCS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₄₁ ◁ C₄³×C₄₁ ◁ G

N	H ≅ G/N	type
66. #33236	C₄₁	direct (N × H)
94. C₄₁	#33236	direct (N × H)

H ≅ G/N

type

66. #33236

C₄₁

direct (N × H)

94. C₄₁

#33236

direct (N × H)

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

subgroup	index
C₂×C₄₁×#487	2
C₄₁×#2868	2
C₄₁×#2862	2
C₄₁×#1960	2
C₄×#97×C₄₁	2
#33236	41

subgroup

index

C₂×C₄₁×#487

C₄₁×#2868

C₄₁×#2862

C₄₁×#1960

C₄×#97×C₄₁

#33236

Subgroups — C₄₁×#33236 #23809437

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C41×#33236 #23809437

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#33236 #23809437