Finite Group Databasebeta

← #37534871

Subgroups — #37534871

Order 23168.

258 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#19153807C211yesmaximal, characteristic
2C2×#19153741C211yesmaximal, characteristic
3C2×#19153739C211yesmaximal, characteristic
4#26041184C211yesmaximal, characteristic
5#26041041C211yesmaximal, characteristic
6#26041033C211yesmaximal, characteristic
7#340×C181C211yesmaximal, characteristic
8C22×Dic362C2211yescharacteristic
9C22×#13089678C2211yescharacteristic
10#19153807—22no—
11#19153807—22no—
12C2×C4⋊Dic181—21no—
13C2×C4⋊Dic181C2211yescharacteristic
14C2×#15668428—21no—
15C2×C4×Dic181C2211yescharacteristic
16#19153741—22no—
17#19153739—22no—
18#19153723—21no—
19#19153723—21no—
20C22×C8×C181C2211yescharacteristic
21C2×C4⋊C4×C181C2211yescharacteristic
22C2×C4⋊C4×C181C2211yescharacteristic
23C2×Dic362—21no—
24C2×Dic362—21no—
25C2×Dic362—21no—
26C2×Dic362—21no—
27C2×Dic362—21no—
28C2×Dic362Q812yes—
29C22×Dic181—21no—
30C22×Dic181—21no—
31C22×Dic181D411yescharacteristic
32C22×Dic181D411yescharacteristic
33C2×#13089678—21no—
34C2×#13089678—21no—
35C2×#13089678—21no—
36C4⋊Dic181—24no—
37C4⋊Dic181—21no—
38C4⋊Dic181D412yes—
39#15668428—24no—
40C4×Dic181—21no—
41C4×Dic181—21no—
42C22×C4×C181—21no—
43C22×C4×C181—21no—
44C22×C4×C181C2311yescharacteristic
45C2×C8×C181—21no—
46C2×C8×C181—21no—
47C2×C8×C181—21no—
48C4⋊C4×C181—21no—
49C4⋊C4×C181—21no—
50C4⋊C4×C181—21no—
51C4⋊C4×C181D412yes—
52Dic362—22no—
53Dic362—22no—
54Dic362—41no—
55Dic362—41no—
56C2×Dic181—21no—
57C2×Dic181—21no—
58C2×Dic181—22no—
59C2×Dic181—22no—
60C2×Dic181—21no—
61C2×Dic181—21no—
62C2×Dic181—21no—
63C2×Dic181—21no—
64C2×Dic181—41no—
65C2×Dic181—41no—
66C2×Dic181—41no—
67C2×Dic181—41no—
68#13089678—41no—
69C23×C181C2×D411yescharacteristic
70C2×C4×C181—22no—
71C2×C4×C181—41no—
72C2×C4×C181—41no—
73C2×C4×C181—41no—
74C2×C4×C181—41no—
75C2×C4×C181—41no—
76C2×C4×C181C2×D411yescharacteristic
77C2×C4×C181C2×D411yescharacteristic
78C2×C4×C181C2×Q811yescharacteristic
79C2×C4×C181#4111yescharacteristic
80C2×C4×C181#4111yescharacteristic
81C2×C4×C181#4111yescharacteristic
82C8×C181—41no—
83C22×C181#12011yescharacteristic
84C22×C181C22⋊Q811yescharacteristic
85C22×C181#12411yescharacteristic
86C22×C181#13511yescharacteristic
87C22×C181#13511yescharacteristic
88C22×C181#13711yescharacteristic
89C22×C181#13711yescharacteristic
90C4×C181—42no—
91C4×C181—81no—
92C4×C181C22⋊Q811yescharacteristic
93C4×C181C22⋊Q811yescharacteristic
94C4×C181#12411yescharacteristic
95C4×C181#12411yescharacteristic
96Dic181—42no—
97Dic181—41no—
98Dic181—41no—
99Dic181—42no—
100C2×C181#39311yescharacteristic
101C2×C181#45211yescharacteristic
102C2×C181#45211yescharacteristic
103C2×C181#47911yescharacteristic
104C2×C181#47911yescharacteristic
105C2×C181#48811yescharacteristic
106C2×C181#49111yescharacteristic
107C181#202611yescharacteristic, complemented, Sylow
108#2026—1811nomaximal, Sylow
109C2×#125—1811no—
110C2×#103—1811no—
111C2×#103—1811no—
112#391—1811no—
113#340—1811no—
114#340D18111yescharacteristic
115#336—1811no—
116C22×Q8—1811no—
117C22×C8—1811no—
118C22×C8C2×D18111yescharacteristic
119#125—3622no—
120#125—3622no—
121C2×C4⋊C4—3621no—
122C2×C4⋊C4—3621no—
123C2×C4⋊C4—1811no—
124C2×C4⋊C4C2×D18111yescharacteristic
125C2×C4⋊C4C2×D18111yescharacteristic
126C2×C42—1811no—
127#103—3622no—
128#103—3622no—
129#95—3621no—
130#95—3621no—
131C2×Q8—3621no—
132C2×Q8—3621no—
133C2×Q8—3621no—
134C2×Q8—3621no—
135C2×Q8—3621no—
136C2×Q8—1812no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—3621no—
140C22×C4—3621no—
141C22×C4—1811no—
142C22×C4—1811no—
143C22×C4C22×D18111yescharacteristic
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—3621no—
148C2×C8—3621no—
149C2×C8—3621no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—3624no—
154C4⋊C4—3624no—
155C4⋊C4—3621no—
156C4⋊C4—1812no—
157C4⋊C4D72412yes—
158C42—3621no—
159C42—3621no—
160C23D4×D18111yescharacteristic
161Q8—3622no—
162Q8—3622no—
163Q8—7241no—
164Q8—7241no—
165C2×C4—22no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—3621no—
172C2×C4—3621no—
173C2×C4—3622no—
174C2×C4—3622no—
175C2×C4—3621no—
176C2×C4—3621no—
177C2×C4—3621no—
178C2×C4—3621no—
179C2×C4—7241no—
180C2×C4—7241no—
181C2×C4—7241no—
182C2×C4—7241no—
183C2×C4D4×D18111yescharacteristic
184C2×C4C2×D72411yescharacteristic
185C2×C4Q8×D18111yescharacteristic
186C2×C4#1566844811yescharacteristic
187C2×C4#1566844911yescharacteristic
188C2×C4#1566844911yescharacteristic
189C8—41no—
190C8—7241no—
191C22#1915378611yescharacteristic
192C22#1915379411yescharacteristic
193C22#1915380211yescharacteristic
194C22#1915383511yescharacteristic
195C22#1915383711yescharacteristic
196C22#1915384511yescharacteristic
197C22#1915384811yescharacteristic
198C4—42no—
199C4—81no—
200C4—7241no—
201C4—7241no—
202C4—7242no—
203C4—7242no—
204C4#1915379411yescharacteristic
205C4#1915379611yescharacteristic
206C4#1915380211yescharacteristic
207C4#1915380411yescharacteristic
208C2#2604119211yescharacteristic
209C2#2604144211yescharacteristic
210C2#2604144411yescharacteristic
211C2#2604158511yescharacteristic
212C2#2604158911yescharacteristic
213C2#2604163211yescharacteristic
214C2#2604164611yescharacteristic
subgroupG/H
centerC23D4×D181
commutator, cosocleC22×C4×C181C23
FrattiniC22×C4C22×D181
Fitting#340×C181C2
socle, prime radicalC23×C181C2×D4
hypercenter#340D181
hypocenterC181#2026
LCSG ▷ C22×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
107. C181#2026semidirect

Maximal subgroups

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

subgroupindex
C2×#191538072
C2×#191537412
C2×#191537392
#260411842
#260410412
#260410332
#340×C1812
#2026181