Finite Group Databasebeta

← #37541901

Subgroups — #37541901

Order 23168.

332 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C181⋊#401C212yesmaximal
2#26041221C212yesmaximal
3#26041219C212yesmaximal
4#26041218C211yesmaximal, characteristic
5#26041212C212yesmaximal
6#26041199C212yesmaximal
7#26041184C211yesmaximal, characteristic
8#26041165C212yesmaximal
9#398×C181C211yesmaximal, characteristic
10C22×Dic362C2211yescharacteristic
11C2×C4⋊Dic181C2212yes—
12C2×C4⋊Dic181C2211yescharacteristic
13C2×#15668428C2212yes—
14C2×#15668428C2212yes—
15C2×C4×Dic181C2211yescharacteristic
16#19153723C2212yes—
17#19153723C2212yes—
18#19153723C2212yes—
19#19153723C2212yes—
20#19153723C2212yes—
21#19153723C2212yes—
22#19153723C2212yes—
23#19153723C2212yes—
24#19153723C2212yes—
25#19153723C2211yescharacteristic
26C2×C4⋊C4×C181C2212yes—
27C2×C4⋊C4×C181C2211yescharacteristic
28C2×C4⋊C4×C181C2211yescharacteristic
29#95×C181C2212yes—
30#95×C181C2211yescharacteristic
31C2×Dic362—22no—
32C2×Dic362—41no—
33C2×Dic362—41no—
34C22×Dic181C2312yes—
35C22×Dic181C2312yes—
36C22×Dic181C2312yes—
37C22×Dic181C2312yes—
38C4⋊Dic181—41no—
39C4⋊Dic181—42no—
40#15668428—42no—
41#15668428—42no—
42C4×Dic181—41no—
43C22×C4×C181C2312yes—
44C22×C4×C181C2311yescharacteristic
45C22×C4×C181C2311yescharacteristic
46C22×C4×C181C2312yes—
47C22×C4×C181C2311yescharacteristic
48C4⋊C4×C181—24no—
49C4⋊C4×C181—41no—
50C4⋊C4×C181—41no—
51Dic362—44no—
52C2×Dic181—22no—
53C2×Dic181—22no—
54C2×Dic181—22no—
55C2×Dic181—22no—
56C2×Dic181—22no—
57C2×Dic181—22no—
58C2×Dic181—22no—
59C2×Dic181—22no—
60C2×Dic181—22no—
61C2×Dic181—24no—
62C2×Dic181—22no—
63C23×C181C2411yescharacteristic
64C2×C4×C181—21no—
65C2×C4×C181—21no—
66C2×C4×C181—22no—
67C2×C4×C181—22no—
68C2×C4×C181—21no—
69C2×C4×C181—22no—
70C2×C4×C181—21no—
71C2×C4×C181—22no—
72C2×C4×C181—22no—
73C2×C4×C181—22no—
74C2×C4×C181—22no—
75C2×C4×C181—22no—
76C2×C4×C181#4112yes—
77C22×C181C2×#4111yescharacteristic
78C22×C181H(5,𝔽2)11yescharacteristic
79C22×C181H(5,𝔽2)11yescharacteristic
80C22×C1812−1+412yes—
81C22×C1812−1+412yes—
82C4×C181—22no—
83C4×C181—42no—
84C4×C181—42no—
85C4×C181—41no—
86C4×C181—41no—
87Dic181—42no—
88Dic181—42no—
89Dic181—42no—
90Dic181—42no—
91C2×C181#53811yescharacteristic
92C2×C181#54112yes—
93C2×C181#56311yescharacteristic
94C2×C181#56311yescharacteristic
95C2×C181#56312yes—
96C181#283311yescharacteristic, complemented, Sylow
97#2833—1811nomaximal, Sylow
98#401—1812no—
99#400—1811no—
100#400—1812no—
101#400—1812no—
102#398—1812no—
103#398D18111yescharacteristic
104#395—1812no—
105#391—1811no—
106#387—1812no—
107C22×Q8—1811no—
108C2×C4⋊C4—1812no—
109C2×C4⋊C4—1812no—
110C2×C4⋊C4—1812no—
111C2×C4⋊C4—1811no—
112C2×C4⋊C4C2×D18112yes—
113C2×C4⋊C4C2×D18111yescharacteristic
114C2×C4⋊C4C2×D18111yescharacteristic
115C2×C42—1811no—
116#95—1812no—
117#95—1812no—
118#95—1812no—
119#95—1812no—
120#95—1812no—
121#95—1812no—
122#95—1812no—
123#95—1812no—
124#95—1812no—
125#95—1811no—
126#95C2×D18112yes—
127#95C2×D18111yescharacteristic
128C2×Q8—3622no—
129C2×Q8—7241no—
130C2×Q8—7241no—
131C22×C4—1812no—
132C22×C4—1812no—
133C22×C4—1812no—
134C22×C4—1812no—
135C22×C4C22×D18112yes—
136C22×C4C22×D18111yescharacteristic
137C22×C4C22×D18111yescharacteristic
138C22×C4C22×D18112yes—
139C22×C4C22×D18111yescharacteristic
140C4⋊C4—24no—
141C4⋊C4—41no—
142C4⋊C4—41no—
143C4⋊C4—7242no—
144C4⋊C4—7242no—
145C4⋊C4—7241no—
146C4⋊C4—7242no—
147C42—7241no—
148C23C23×D18111yescharacteristic
149Q8—7244no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—3622no—
163C2×C4—3622no—
164C2×C4—3622no—
165C2×C4—3622no—
166C2×C4—3622no—
167C2×C4—3622no—
168C2×C4—3622no—
169C2×C4—3622no—
170C2×C4—3624no—
171C2×C4—3622no—
172C2×C4—3622no—
173C2×C4#1566844812yes—
174C22C2×#1566844811yescharacteristic
175C22#1915386111yescharacteristic
176C22#1915386211yescharacteristic
177C22#1915386312yes—
178C22#1915386412yes—
179C4—22no—
180C4—42no—
181C4—42no—
182C4—41no—
183C4—41no—
184C4—7242no—
185C4—7242no—
186C4—7242no—
187C4—7242no—
188C2#2604186611yescharacteristic
189C2#2604188912yes—
190C2#2604202811yescharacteristic
191C2#2604203211yescharacteristic
192C2#2604203312yes—
subgroupG/H
center, FrattiniC23C23×D181
commutator, socle, prime radical, cosocleC23×C181C24
Fitting#398×C181C2
hypercenter#398D181
hypocenterC181#2833
LCSG ▷ C23×C181 ▷ C181
UCSC1 ◁ C23 ◁ #398

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
96. C181#2833semidirect

Maximal subgroups

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

subgroupindex
C181⋊#4012
#260412212
#260412192
#260412182
#260412122
#260411992
#260411842
#260411652
#398×C1812
#2833181