Finite Group Databasebeta

← #37546611

Subgroups — #37546611

Order 23168.

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

normal subgroups only

This group has 324 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#26042008C211yesmaximal, characteristic
2#26042004C211yesmaximal, characteristic
3#26041682C211yesmaximal, characteristic
4#26041679C212yesmaximal
5#26041589C212yesmaximal
6#26041584C212yesmaximal
7#26041565C211yesmaximal, characteristic
8#26041403C211yesmaximal, characteristic
9C4×#15668439C211yesmaximal, characteristic
10#26041371C212yesmaximal
11#475×C181C211yesmaximal, characteristic
12C2×#15668439C2211yescharacteristic
13#19153816—21no—
14#19153816C2211yescharacteristic
15#19153814—21no—
16#19153807—22no—
17#19153807C2212yes—
18#19153807C2212yes—
19#19153806—22no—
20Q8×Dic181—21no—
21Q8×Dic181C2212yes—
22C4×Dic362—21no—
23C4×Dic362C2211yescharacteristic
24C4×Dic362C2211yescharacteristic
25#19153781C2212yes—
26#19153749C2212yes—
27#19153749C2211yescharacteristic
28#19153749C2212yes—
29#19153748C2212yes—
30#19153745C2212yes—
31#19153741C2212yes—
32#19153740C2211yescharacteristic
33#19153739C2211yescharacteristic
34C4×#13089678C2211yescharacteristic
35C8×Dic181C2212yes—
36C4⋊Q8×C181C2211yescharacteristic
37C4×Q8×C181C2211yescharacteristic
38#106×C181C2212yes—
39C4⋊C8×C181C2211yescharacteristic
40#103×C181C2212yes—
41C2×Dic362—21no—
42C2×Dic362D411yescharacteristic
43C2×Dic362C2311yescharacteristic
44#15668439Q814yescomplemented
45C2×#13089678C2311yescharacteristic
46C2×#13089678C2311yescharacteristic
47C4⋊Dic181—22no—
48C4⋊Dic181—22no—
49C4⋊Dic181—22no—
50C4⋊Dic181—21no—
51C4⋊Dic181D411yescharacteristic
52C4⋊Dic181C2311yescharacteristic
53C4⋊Dic181C2312yes—
54#15668428—22no—
55#15668428—22no—
56#15668428—22no—
57#15668428—21no—
58#15668428D412yes—
59C4×Dic181—22no—
60C4×Dic181—22no—
61C4×Dic181—21no—
62C4×Dic181C2312yes—
63C2×Q8×C181—21no—
64C2×Q8×C181C2311yescharacteristic
65C2×C8×C181C2312yes—
66C4⋊C4×C181—21no—
67C4⋊C4×C181—21no—
68C4⋊C4×C181C2312yes—
69C4⋊C4×C181C2311yescharacteristic
70C42×C181—21no—
71C42×C181C2311yescharacteristic
72Dic362—22no—
73Dic362—21no—
74Dic362—42no—
75Dic362C2×Q812yes—
76C2×Dic181—21no—
77C2×Dic181—21no—
78C2×Dic181—22no—
79C2×Dic181C2×D412yes—
80C2×Dic181C2×D412yes—
81#13089678—21no—
82#13089678C2×Q812yes—
83Q8×C181—21no—
84Q8×C181—42no—
85Q8×C181C2×Q812yes—
86C2×C4×C181—21no—
87C2×C4×C181—21no—
88C2×C4×C181—22no—
89C2×C4×C181C2×D411yescharacteristic
90C2×C4×C181C2×D411yescharacteristic
91C2×C4×C181C2411yescharacteristic
92C8×C181—22no—
93C22×C181C22×D411yescharacteristic
94C4×C181—22no—
95C4×C181—21no—
96C4×C181—42no—
97C4×C181—41no—
98C4×C181#13512yes—
99C4×C181C22×Q811yescharacteristic
100C4×C1812−1+411yescharacteristic
101Dic181—22no—
102Dic181—22no—
103Dic181—22no—
104Dic181—42no—
105Dic181—41no—
106C2×C181D4×Q811yescharacteristic
107C2×C181C2×#13511yescharacteristic
108C2×C181#57811yescharacteristic
109C181#338311yescharacteristic, complemented, Sylow
110#3383—1811nomaximal, Sylow
111#557—1811no—
112#557—1811no—
113#500—1811no—
114#499—1812no—
115#479—1812no—
116#479—1812no—
117#475—1811no—
118#475D18111yescharacteristic
119C8×Q8—1811no—
120C4×Q16—1811no—
121C4×Q16—1812no—
122C2×Q16—1811no—
123C4⋊Q8—3621no—
124C4⋊Q8—3621no—
125C4⋊Q8—1811no—
126C4⋊Q8C2×D18111yescharacteristic
127#125—3622no—
128#125—3622no—
129#125—1812no—
130#125—1812no—
131C4×Q8—3621no—
132C4×Q8—3621no—
133C4×Q8—1812no—
134C4×Q8—1812no—
135C4×Q8—1811no—
136C4×Q8—1811no—
137C4×Q8C2×D18111yescharacteristic
138#107—1811no—
139#107—1812no—
140#107—1812no—
141#106—1812no—
142#106C2×D18112yes—
143C4⋊C8—1812no—
144C4⋊C8C2×D18111yescharacteristic
145#103—1811no—
146#103—1812no—
147#103—1811no—
148#103C2×D18112yes—
149C4×C8—1812no—
150C4×C8—1811no—
151C2×Q8—21no—
152C2×Q8—3621no—
153C2×Q8—1811no—
154C2×Q8—1811no—
155C2×Q8C22×D18111yescharacteristic
156Q16—1814no—
157C2×C8—1811no—
158C2×C8—1811no—
159C2×C8C22×D18112yes—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—3622no—
163C4⋊C4—3622no—
164C4⋊C4—3622no—
165C4⋊C4—3622no—
166C4⋊C4—3622no—
167C4⋊C4—3622no—
168C4⋊C4—3621no—
169C4⋊C4—3621no—
170C4⋊C4—1811no—
171C4⋊C4—1812no—
172C4⋊C4—1811no—
173C4⋊C4—1812no—
174C4⋊C4C22×D18111yescharacteristic
175C4⋊C4C22×D18112yes—
176C42—21no—
177C42—3622no—
178C42—3622no—
179C42—3621no—
180C42—1812no—
181C42C22×D18111yescharacteristic
182Q8—21no—
183Q8—42no—
184Q8—3622no—
185Q8—3621no—
186Q8—1812no—
187Q8—7242no—
188Q8Q8×D18112yes—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—3621no—
193C2×C4—3621no—
194C2×C4—3622no—
195C2×C4—1812no—
196C2×C4—1812no—
197C2×C4D4×D18111yescharacteristic
198C2×C4D4×D18111yescharacteristic
199C2×C4C23×D18111yescharacteristic
200C8—22no—
201C8—3621no—
202C8—1812no—
203C22C2×D4×D18111yescharacteristic
204C4—22no—
205C4—21no—
206C4—42no—
207C4—41no—
208C4—3622no—
209C4—3622no—
210C4—3622no—
211C4—7242no—
212C4—7241no—
213C4#1915383712yes—
214C4C2×Q8×D18111yescharacteristic
215C4#1915386311yescharacteristic
216C2#2604194211yescharacteristic
217C2C2×#1915383711yescharacteristic
218C2#2604209511yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#475×C181C2
socle, prime radicalC22×C181C22×D4
hypercenter#475D181
hypocenterC181#3383
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
44. #15668439Q8semidirect
109. C181#3383semidirect

Maximal subgroups

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

subgroupindex
#260420082
#260420042
#260416822
#260416792
#260415892
#260415842
#260415652
#260414032
C4×#156684392
#260413712
#475×C1812
#3383181