Finite Group Databasebeta

← #37541987

Subgroups — #37541987

Order 23168.

348 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 125 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
1#26041220C212yesmaximal
2#26041218C211yesmaximal, characteristic
3#26041213C212yesmaximal
4#26041212C212yesmaximal
5#26041210C212yesmaximal
6#26041198C212yesmaximal
7#26041148C211yesmaximal, characteristic
8#26041146C212yesmaximal
9#395×C181C211yesmaximal, characteristic
10C2×C4⋊Dic181C2211yescharacteristic
11C2×C4⋊Dic181C2211yescharacteristic
12C2×#15668428C2212yes—
13C2×#15668428C2212yes—
14C2×#15668428C2212yes—
15C2×#15668428C2212yes—
16C2×#15668428C2212yes—
17C2×C4×Dic181C2211yescharacteristic
18#19153723C2212yes—
19#19153723C2212yes—
20#19153723C2212yes—
21#19153723C2212yes—
22#19153723C2212yes—
23#19153723C2212yes—
24#19153723C2211yescharacteristic
25#19153723C2212yes—
26C22×Q8×C181C2211yescharacteristic
27C2×C4⋊C4×C181C2211yescharacteristic
28C2×C4⋊C4×C181C2212yes—
29#95×C181C2212yes—
30#95×C181C2211yescharacteristic
31C22×Dic181C2312yes—
32C22×Dic181C2312yes—
33C22×Dic181C2312yes—
34C22×Dic181C2312yes—
35C4⋊Dic181—41no—
36C4⋊Dic181—41no—
37#15668428—42no—
38#15668428—42no—
39#15668428—42no—
40#15668428—42no—
41#15668428—42no—
42C4×Dic181Q814yescomplemented
43C2×Q8×C181—42no—
44C2×Q8×C181—41no—
45C22×C4×C181C2312yes—
46C22×C4×C181C2312yes—
47C22×C4×C181C2311yescharacteristic
48C22×C4×C181C2311yescharacteristic
49C22×C4×C181C2311yescharacteristic
50C4⋊C4×C181—41no—
51C4⋊C4×C181—42no—
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×Dic181C2×Q814yes—
63C23×C181C2411yescharacteristic
64Q8×C181—44no—
65C2×C4×C181—21no—
66C2×C4×C181—21no—
67C2×C4×C181—22no—
68C2×C4×C181—21no—
69C2×C4×C181—22no—
70C2×C4×C181—22no—
71C2×C4×C181—21no—
72C2×C4×C181—22no—
73C2×C4×C181—22no—
74C2×C4×C181—22no—
75C2×C4×C181—22no—
76C2×C4×C181—22no—
77C2×C4×C181C2×Q812yes—
78C22×C181C22×Q811yescharacteristic
79C22×C181H(5,𝔽2)12yes—
80C22×C181H(5,𝔽2)11yescharacteristic
81C22×C1812−1+411yescharacteristic
82C22×C1812−1+412yes—
83C4×C181—22no—
84C4×C181—41no—
85C4×C181—42no—
86C4×C181—41no—
87C4×C181—42no—
88Dic181—24no—
89Dic181—42no—
90Dic181—42no—
91Dic181—42no—
92C2×C181#54412yes—
93C2×C181#54411yescharacteristic
94C2×C181#56011yescharacteristic
95C2×C181#56311yescharacteristic
96C2×C181#56312yes—
97C181#284311yescharacteristic, complemented, Sylow
98#2843—1811nomaximal, Sylow
99#400—1811no—
100#400—1812no—
101#398—1812no—
102#398—1812no—
103#398—1812no—
104#395—1812no—
105#395D18111yescharacteristic
106#384—1811no—
107#383—1812no—
108C22×Q8C2×D18111yescharacteristic
109C2×C4⋊C4—1812no—
110C2×C4⋊C4—1812no—
111C2×C4⋊C4—1812no—
112C2×C4⋊C4—1812no—
113C2×C4⋊C4—1812no—
114C2×C4⋊C4—1811no—
115C2×C4⋊C4—1811no—
116C2×C4⋊C4C2×D18111yescharacteristic
117C2×C4⋊C4C2×D18112yes—
118C2×C42—1811no—
119#95—1812no—
120#95—1812no—
121#95—1812no—
122#95—1812no—
123#95—1812no—
124#95—1812no—
125#95—1811no—
126#95—1812no—
127#95C2×D18112yes—
128#95C2×D18111yescharacteristic
129C2×Q8—42no—
130C2×Q8—41no—
131C22×C4—1812no—
132C22×C4—1812no—
133C22×C4—1812no—
134C22×C4—1812no—
135C22×C4C22×D18112yes—
136C22×C4C22×D18112yes—
137C22×C4C22×D18111yescharacteristic
138C22×C4C22×D18111yescharacteristic
139C22×C4C22×D18111yescharacteristic
140C4⋊C4—41no—
141C4⋊C4—42no—
142C4⋊C4—7242no—
143C4⋊C4—7242no—
144C4⋊C4—7242no—
145C4⋊C4—7242no—
146C4⋊C4—7242no—
147C4⋊C4—7241no—
148C4⋊C4—7241no—
149C42—1814no—
150C23C23×D18111yescharacteristic
151Q8—44no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—22no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—3622no—
165C2×C4—3622no—
166C2×C4—3622no—
167C2×C4—3622no—
168C2×C4—3622no—
169C2×C4—3622no—
170C2×C4—3622no—
171C2×C4—3622no—
172C2×C4—3624no—
173C2×C4—3622no—
174C2×C4—1814no—
175C2×C4Q8×D18112yes—
176C22C2×Q8×D18111yescharacteristic
177C22#1915386112yes—
178C22#1915386111yescharacteristic
179C22#1915386311yescharacteristic
180C22#1915386412yes—
181C4—22no—
182C4—42no—
183C4—41no—
184C4—41no—
185C4—42no—
186C4—3624no—
187C4—7242no—
188C4—7242no—
189C4—7242no—
190C2#2604190612yes—
191C2#2604190811yescharacteristic
192C2#2604201811yescharacteristic
193C2#2604202811yescharacteristic
194C2#2604203012yes—
subgroupG/H
center, FrattiniC23C23×D181
commutator, socle, prime radical, cosocleC23×C181C24
Fitting#395×C181C2
hypercenter#395D181
hypocenterC181#2843
LCSG ▷ C23×C181 ▷ C181
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
42. C4×Dic181Q8semidirect
97. C181#2843semidirect

Maximal subgroups

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

subgroupindex
#260412202
#260412182
#260412132
#260412122
#260412102
#260411982
#260411482
#260411462
#395×C1812
#2843181