Finite Group Databasebeta

← #37544876

Subgroups — #37544876

Order 23168.

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

normal subgroups only

This group has 326 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#26041836C211yesmaximal, characteristic
2#26041682C211yesmaximal, characteristic, complemented
3#26041675C211yesmaximal, characteristic, complemented
4#26041629C211yesmaximal, characteristic, complemented
5#26041629C211yesmaximal, characteristic, complemented
6#26041617C214yesmaximal
7#26041586C214yesmaximal, complemented
8#26041332C211yesmaximal, characteristic
9#533×C181C211yesmaximal, characteristic
10#19153816C2211yescharacteristic
11#19153816C2211yescharacteristic
12#19153808C2212yes—
13#19153795—21no—
14#19153795—21no—
15C4×Dic362—21no—
16C4×Dic362—21no—
17#19153775C2212yes—
18#19153749C2214yes—
19#19153747C2214yes—
20C4⋊#13089678C2212yes—
21#19153740C2214yes—
22#19153740C2214yes—
23C22⋊#13089678C2212yes—
24C4×#13089678C2211yescharacteristic
25C4×#13089678C2211yescharacteristic
26C4⋊Q8×C181C2211yescharacteristic
27C4⋊Q8×C181C2211yescharacteristic
28#125×C181—21no—
29C22⋊Q8×C181—21no—
30C22⋊Q8×C181C2212yes—
31C4×Q8×C181—21no—
32C4×Q8×C181C2212yes—
33#117×C181—21no—
34C2×C42×C181C2211yescharacteristic
35C2×Dic362—21no—
36C2×Dic362—21no—
37C2×#13089678C2312yes—
38C2×#13089678C2312yes—
39C4⋊Dic181—21no—
40C4⋊Dic181—21no—
41C4⋊Dic181C2312yes—
42C4⋊Dic181C2312yes—
43#15668428—22no—
44#15668428—22no—
45C22⋊Dic181—22no—
46C4×Dic181—22no—
47C2×Q8×C181—21no—
48C2×Q8×C181C2312yes—
49C22×C4×C181D411yescharacteristic
50C22×C4×C181D411yescharacteristic
51C22×C4×C181C2311yescharacteristic
52C4⋊C4×C181—21no—
53C4⋊C4×C181—21no—
54C4⋊C4×C181—21no—
55C4⋊C4×C181—22no—
56C4⋊C4×C181—22no—
57C4⋊C4×C181C2312yes—
58C22⋊C4×C181—22no—
59C42×C181—22no—
60C42×C181D411yescharacteristic
61C42×C181D411yescharacteristic
62C42×C181C2311yescharacteristic
63C42×C181C2311yescharacteristic
64Dic362—42no—
65Dic362—42no—
66C2×Dic181—22no—
67C2×Dic181—22no—
68#13089678—22no—
69#13089678—22no—
70C23×C181C2×D411yescharacteristic
71Q8×C181—24no—
72Q8×C181—42no—
73C2×C4×C181—22no—
74C2×C4×C181—22no—
75C2×C4×C181—22no—
76C2×C4×C181—22no—
77C2×C4×C181—22no—
78C2×C4×C181C2×D411yescharacteristic
79C2×C4×C181C2×D411yescharacteristic
80C2×C4×C181C2×D411yescharacteristic
81C2×C4×C181C2×D411yescharacteristic
82C2×C4×C181C2×D411yescharacteristic
83C2×C4×C181C2411yescharacteristic
84C22×C181—21no—
85C22×C181—21no—
86C22×C181—21no—
87C22×C181C22×D411yescharacteristic
88C4×C181—21no—
89C4×C181—21no—
90C4×C181—21no—
91C4×C181—42no—
92C4×C181—42no—
93C4×C181#13512yes—
94C4×C181#13712yes—
95C4×C1812−1+412yes—
96Dic181—42no—
97Dic181—42no—
98C2×C181—41no—
99C2×C181#53611yescharacteristic
100C2×C181C2×#13511yescharacteristic
101C2×C181C2×#13711yescharacteristic
102C181#323111yescharacteristic, complemented, Sylow
103#3231—1811nomaximal, Sylow
104#533—1811no—
105#533D18111yescharacteristic
106#500—1811no—
107#498—1811no—
108#487—1811no—
109#487—1811no—
110#485—1814no—
111#479—1814no—
112#431—1811no—
113C4⋊Q8—1811no—
114C4⋊Q8—1811no—
115C4⋊Q8C2×D18111yescharacteristic
116C4⋊Q8C2×D18111yescharacteristic
117#125—21no—
118#125—1812no—
119C22⋊Q8—21no—
120C22⋊Q8—3621no—
121C22⋊Q8—3621no—
122C22⋊Q8C2×D18112yes—
123C4×Q8—21no—
124C4×Q8—3621no—
125C4×Q8—3621no—
126C4×Q8C2×D18112yes—
127#117—21no—
128#117—1812no—
129C2×C42C2×D18111yescharacteristic
130#107—1814no—
131#106—1814no—
132C4⋊C8—1812no—
133#103—1814no—
134#103—1814no—
135C22⋊C8—1812no—
136C4×C8—1811no—
137C4×C8—1811no—
138C2×Q8—21no—
139C2×Q8—3621no—
140C2×Q8—3621no—
141C2×Q8C22×D18112yes—
142C22×C4C22⋊D18111yescharacteristic
143C22×C4C22⋊D18111yescharacteristic
144C22×C4C22×D18111yescharacteristic
145C2×C8—1812no—
146C2×C8—1812no—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—3622no—
153C4⋊C4—3622no—
154C4⋊C4—3621no—
155C4⋊C4—3621no—
156C4⋊C4—1812no—
157C4⋊C4—1812no—
158C4⋊C4C22×D18112yes—
159C22⋊C4—22no—
160C22⋊C4—3622no—
161C42—22no—
162C42—3622no—
163C42C22⋊D18111yescharacteristic
164C42C22⋊D18111yescharacteristic
165C42C22×D18111yescharacteristic
166C42C22×D18111yescharacteristic
167C23C2×C22⋊D18111yescharacteristic
168Q8—24no—
169Q8—42no—
170Q8—7242no—
171Q8—7242no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—3622no—
178C2×C4—3622no—
179C2×C4C2×C22⋊D18111yescharacteristic
180C2×C4C2×C22⋊D18111yescharacteristic
181C2×C4C2×C22⋊D18111yescharacteristic
182C2×C4C2×C22⋊D18111yescharacteristic
183C2×C4C2×C22⋊D18111yescharacteristic
184C2×C4C23×D18111yescharacteristic
185C8—3622no—
186C8—3622no—
187C22—21no—
188C22—21no—
189C22—21no—
190C22C22×C22⋊D18111yescharacteristic
191C4—21no—
192C4—21no—
193C4—21no—
194C4—42no—
195C4—42no—
196C4—7242no—
197C4—7242no—
198C4#1915383612yes—
199C4#1915384712yes—
200C4#1915386312yes—
201C2—41no—
202C2#2604185011yescharacteristic
203C2C2×#1915383611yescharacteristic
204C2C2×#1915384711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#533×C181C2
socleC22×C181C22×D4
prime radicalC23×C181C2×D4
hypercenter#533D181
hypocenterC181#3231
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #26041682C2semidirect
3. #26041675C2semidirect
4. #26041629C2semidirect
5. #26041629C2semidirect
7. #26041586C2semidirect
102. C181#3231semidirect

Maximal subgroups

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

subgroupindex
#260418362
#260416822
#260416752
#260416292
#260416172
#260415862
#260413322
#533×C1812
#3231181