Finite Group Databasebeta

← #37541909

Subgroups — #37541909

Order 23168.

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

normal subgroups only

This group has 380 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
1#26041221C212yesmaximal, complemented
2#26041220C212yesmaximal, complemented
3#26041217C212yesmaximal, complemented
4#26041207C212yesmaximal
5#26041204C211yesmaximal, characteristic
6#26041199C212yesmaximal, complemented
7#26041191C211yesmaximal, characteristic
8#26041152C212yesmaximal
9#385×C181C211yesmaximal, characteristic
10C22×Dic362C2211yescharacteristic
11C2×C4⋊Dic181C2211yescharacteristic
12C2×#15668428C2212yes—
13C2×#15668428C2212yes—
14C2×#15668428C2212yes—
15C2×C22⋊Dic181C2212yes—
16C2×C22⋊Dic181C2212yes—
17#19153723C2212yes—
18#19153723C2212yes—
19#19153723C2211yescharacteristic
20#19153723C2212yes—
21#19153723C2212yes—
22#19153723C2212yes—
23#19153723C2212yes—
24#19153723C2211yescharacteristic
25#19153723C2212yes—
26C23×C4×C181C2211yescharacteristic
27C2×C4⋊C4×C181C2212yes—
28C2×C22⋊C4×C181C2211yescharacteristic
29C2×C22⋊C4×C181C2211yescharacteristic
30#95×C181C2212yes—
31C2×Dic362—41no—
32C2×Dic362—42no—
33C22×Dic181C2312yes—
34C22×Dic181C2312yes—
35C22×Dic181C2312yes—
36C22×Dic181C2312yes—
37C4⋊Dic181—41no—
38#15668428—42no—
39#15668428—42no—
40#15668428—42no—
41C22⋊Dic181—24no—
42C22⋊Dic181—42no—
43C24×C181C2311yescharacteristic
44C22×C4×C181—42no—
45C22×C4×C181—41no—
46C22×C4×C181C2311yescharacteristic
47C22×C4×C181C2312yes—
48C22×C4×C181C2312yes—
49C22×C4×C181C2311yescharacteristic
50C4⋊C4×C181—42no—
51C22⋊C4×C181—22no—
52C22⋊C4×C181—41no—
53Dic362—44no—
54C2×Dic181—22no—
55C2×Dic181—22no—
56C2×Dic181—22no—
57C2×Dic181—22no—
58C2×Dic181—22no—
59C2×Dic181—22no—
60C2×Dic181—22no—
61C2×Dic181—22no—
62C2×Dic181—22no—
63C2×Dic181—22no—
64C2×Dic181—22no—
65C2×Dic181—22no—
66C23×C181—21no—
67C23×C181—22no—
68C23×C181—22no—
69C23×C181—21no—
70C23×C181#4112yes—
71C23×C181C2411yescharacteristic
72C2×C4×C181—22no—
73C2×C4×C181—21no—
74C2×C4×C181—21no—
75C2×C4×C181—22no—
76C2×C4×C181—22no—
77C2×C4×C181—22no—
78C2×C4×C181—22no—
79C2×C4×C181—22no—
80C2×C4×C181—22no—
81C2×C4×C181—22no—
82C2×C4×C181—44no—
83C22×C181—24no—
84C22×C181—22no—
85C22×C181—41no—
86C22×C181—42no—
87C22×C181—41no—
88C22×C181C2×#4111yescharacteristic
89C22×C181H(5,𝔽2)12yes—
90C22×C181H(5,𝔽2)11yescharacteristic
91C22×C1812−1+412yes—
92C22×C1812−1+411yescharacteristic
93C4×C181—42no—
94C4×C181—42no—
95C4×C181—41no—
96C4×C181—41no—
97Dic181—42no—
98Dic181—42no—
99Dic181—42no—
100Dic181—42no—
101C2×C181—42no—
102C2×C181#53912yes—
103C2×C181#53911yescharacteristic
104C2×C181H(3,𝔽4)11yescharacteristic
105C2×C181#56312yes—
106C2×C181#56311yescharacteristic
107C181#283511yescharacteristic, complemented, Sylow
108#2835—1811nomaximal, Sylow
109#400—1812no—
110#400—1812no—
111#400—1812no—
112#397—1811no—
113#397—1812no—
114#395—1812no—
115#393—1811no—
116#385—1812no—
117#385D18111yescharacteristic
118C22×Q8—1811no—
119C23×C4C2×D18111yescharacteristic
120C2×C4⋊C4—1812no—
121C2×C4⋊C4—1812no—
122C2×C4⋊C4—1812no—
123C2×C4⋊C4—1811no—
124C2×C4⋊C4C2×D18112yes—
125C2×C22⋊C4—1812no—
126C2×C22⋊C4—1812no—
127C2×C22⋊C4C2×D18111yescharacteristic
128C2×C22⋊C4C2×D18111yescharacteristic
129#95—1812no—
130#95—1812no—
131#95—1811no—
132#95—1812no—
133#95—1812no—
134#95—1812no—
135#95—1812no—
136#95—1812no—
137#95—1811no—
138#95C2×D18112yes—
139C24C22×D18111yescharacteristic
140C2×Q8—7241no—
141C2×Q8—7242no—
142C22×C4—42no—
143C22×C4—41no—
144C22×C4—1812no—
145C22×C4—1812no—
146C22×C4—1812no—
147C22×C4—1812no—
148C22×C4C22×D18111yescharacteristic
149C22×C4C22×D18112yes—
150C22×C4C22×D18111yescharacteristic
151C22×C4C22×D18112yes—
152C4⋊C4—42no—
153C4⋊C4—7242no—
154C4⋊C4—7242no—
155C4⋊C4—7242no—
156C4⋊C4—7241no—
157C22⋊C4—22no—
158C22⋊C4—41no—
159C22⋊C4—3624no—
160C22⋊C4—7242no—
161C23—21no—
162C23—22no—
163C23—22no—
164C23—21no—
165C23#1566844912yes—
166C23C23×D18111yescharacteristic
167Q8—7244no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—44no—
179C2×C4—3622no—
180C2×C4—3622no—
181C2×C4—3622no—
182C2×C4—3622no—
183C2×C4—3622no—
184C2×C4—3622no—
185C2×C4—3622no—
186C2×C4—3622no—
187C2×C4—3622no—
188C2×C4—3622no—
189C2×C4—3622no—
190C2×C4—3622no—
191C22—24no—
192C22—22no—
193C22—41no—
194C22—42no—
195C22—41no—
196C22C2×#1566844911yescharacteristic
197C22#1915386112yes—
198C22#1915386111yescharacteristic
199C22#1915386312yes—
200C22#1915386411yescharacteristic
201C4—42no—
202C4—42no—
203C4—41no—
204C4—41no—
205C4—7242no—
206C4—7242no—
207C4—7242no—
208C4—7242no—
209C2—42no—
210C2#2604187112yes—
211C2#2604187611yescharacteristic
212C2#2604202211yescharacteristic
213C2#2604203012yes—
214C2#2604203211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D181
commutator, socle, cosocleC23×C181C24
Fitting#385×C181C2
prime radicalC24×C181C23
hypercenter#385D181
hypocenterC181#2835
LCSG ▷ C23×C181 ▷ C181
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. #26041221C2semidirect
2. #26041220C2semidirect
3. #26041217C2semidirect
6. #26041199C2semidirect
107. C181#2835semidirect

Maximal subgroups

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

subgroupindex
#260412212
#260412202
#260412172
#260412072
#260412042
#260411992
#260411912
#260411522
#385×C1812
#2835181