Finite Group Databasebeta

← #37534880

Subgroups — #37534880

Order 23168.

246 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 69 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#26041907C211yesmaximal, characteristic
2#26041288C211yesmaximal, characteristic
3#26041186C211yesmaximal, characteristic
4#26041047C211yesmaximal, characteristic
5#26041040C211yesmaximal, characteristic
6#26041038C211yesmaximal, characteristic
7#419×C181C211yesmaximal, characteristic
8C2×#15668433C2211yescharacteristic
9#19153816—21no—
10#19153815—21no—
11#19153808—21no—
12#19153807—21no—
13#19153793—22no—
14#19153775C2211yescharacteristic
15C2×C4⋊Dic181C2211yescharacteristic
16C2×C4×Dic181C2211yescharacteristic
17#19153740—21no—
18#19153740—21no—
19#19153723—22no—
20C22×Q8×C181C2211yescharacteristic
21C2×M16×C181C2211yescharacteristic
22#117×C181C2211yescharacteristic
23#103×C181—21no—
24#103×C181—21no—
25C2×Dic362—22no—
26C22×Dic181—21no—
27C22×Dic181D412yes—
28#15668433—21no—
29#15668433—21no—
30C2×#13089678—21no—
31C4⋊Dic181—22no—
32C4⋊Dic181—21no—
33C4⋊Dic181—21no—
34C4⋊Dic181D411yescharacteristic
35C4⋊Dic181D411yescharacteristic
36#15668428—22no—
37#15668428—22no—
38C22⋊Dic181—21no—
39C4×Dic181—21no—
40C4×Dic181—21no—
41C4×Dic181—21no—
42C2×Q8×C181—21no—
43C2×Q8×C181—21no—
44C2×Q8×C181—21no—
45C2×Q8×C181—21no—
46C2×Q8×C181—21no—
47C2×Q8×C181Q812yescomplemented
48C22×C4×C181—21no—
49C22×C4×C181C2311yescharacteristic
50M16×C181—21no—
51M16×C181—21no—
52C2×C8×C181—21no—
53C4⋊C4×C181D411yescharacteristic
54C4⋊C4×C181D411yescharacteristic
55C22⋊C4×C181—21no—
56C42×C181—21no—
57Dic362—82no—
58C2×Dic181—22no—
59C2×Dic181—21no—
60C2×Dic181—21no—
61C2×Dic181—22no—
62C2×Dic181—41no—
63C2×Dic181—41no—
64C2×Dic181—42no—
65#13089678—41no—
66C23×C181C2×D411yescharacteristic
67Q8×C181—22no—
68Q8×C181—22no—
69Q8×C181—41no—
70Q8×C181—41no—
71C2×C4×C181—21no—
72C2×C4×C181—21no—
73C2×C4×C181—22no—
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—21no—
84C22×C181—21no—
85C22×C181#12011yescharacteristic
86C22×C181C22⋊Q811yescharacteristic
87C22×C181#12411yescharacteristic
88C4×C181—42no—
89C4×C181—41no—
90C4×C181—41no—
91C4×C181C22⋊Q811yescharacteristic
92C4×C181C22⋊Q811yescharacteristic
93C4×C181#12411yescharacteristic
94C4×C181#12411yescharacteristic
95Dic181—42no—
96Dic181—42no—
97Dic181—41no—
98Dic181—41no—
99C2×C181—21no—
100C2×C181—21no—
101C2×C181#39311yescharacteristic
102C2×C181#45511yescharacteristic
103C2×C181#45611yescharacteristic
104C181#202811yescharacteristic, complemented, Sylow
105#2028—1811nomaximal, Sylow
106#544—1811no—
107#419—1811no—
108#419D18111yescharacteristic
109#391—1811no—
110#343—1811no—
111#339—1811no—
112#339—1811no—
113C22×Q8C2×D18111yescharacteristic
114C2×M16—1811no—
115C2×M16C2×D18111yescharacteristic
116C4⋊Q8—3621no—
117C4⋊Q8—3621no—
118#125—3621no—
119#125—3621no—
120C22⋊Q8—3622no—
121#117—1811no—
122#117C2×D18111yescharacteristic
123C2×C4⋊C4—1811no—
124C2×C42—1811no—
125#103—21no—
126#103—21no—
127#103—3621no—
128#103—3621no—
129#95—3622no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—3622no—
136C2×Q8Dic36212yescomplemented
137C22×C4—21no—
138C22×C4—3621no—
139C22×C4—1812no—
140C22×C4C22×D18111yescharacteristic
141M16—21no—
142M16—21no—
143M16—3621no—
144M16—3621no—
145C2×C8—21no—
146C2×C8—3621no—
147C4⋊C4—3622no—
148C4⋊C4—3622no—
149C4⋊C4—3622no—
150C4⋊C4—3621no—
151C4⋊C4—3621no—
152C4⋊C4—1811no—
153C4⋊C4—1811no—
154C4⋊C4C22⋊D18111yescharacteristic
155C4⋊C4C22⋊D18111yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—3621no—
158C42—21no—
159C42—3621no—
160C42—3621no—
161C42—3621no—
162C23D4×D18111yescharacteristic
163Q8—22no—
164Q8—22no—
165Q8—41no—
166Q8—41no—
167Q8—14482no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—3622no—
174C2×C4—3621no—
175C2×C4—3621no—
176C2×C4—3622no—
177C2×C4—7241no—
178C2×C4—7241no—
179C2×C4—7242no—
180C2×C4D4×D18111yescharacteristic
181C2×C4C2×C22⋊D18111yescharacteristic
182C2×C4C2×Dic36211yescharacteristic
183C2×C4#1566844811yescharacteristic
184C2×C4#1566844811yescharacteristic
185C2×C4#1566844911yescharacteristic
186C8—41no—
187C8—7241no—
188C22—21no—
189C22—21no—
190C22#1915378411yescharacteristic
191C22#1915379311yescharacteristic
192C22#1915380211yescharacteristic
193C4—42no—
194C4—41no—
195C4—41no—
196C4—7242no—
197C4—7242no—
198C4—7241no—
199C4—7241no—
200C4#1915379311yescharacteristic
201C4#1915379511yescharacteristic
202C4#1915380211yescharacteristic
203C4#1915380311yescharacteristic
204C2—21no—
205C2—21no—
206C2#2604119111yescharacteristic
207C2#2604145511yescharacteristic
208C2#2604146011yescharacteristic
subgroupG/H
centerC22#19153784
commutator, cosocleC22×C4×C181C23
FrattiniC22×C4C22×D181
Fitting#419×C181C2
socleC22×C181#120
prime radicalC23×C181C2×D4
hypercenter#419D181
hypocenterC181#2028
LCSG ▷ C22×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
47. C2×Q8×C181Q8semidirect
104. C181#2028semidirect
136. C2×Q8Dic362semidirect

Maximal subgroups

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

subgroupindex
#260419072
#260412882
#260411862
#260410472
#260410402
#260410382
#419×C1812
#2028181