Finite Group Databasebeta

← #37544929

Subgroups — #37544929

Order 23168.

324 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 121 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
2C2×#19153808C211yesmaximal, characteristic
3#26041688C212yesmaximal, complemented
4#26041648C212yesmaximal, complemented
5#26041615C212yesmaximal
6#26041610C212yesmaximal
7#26041587C214yesmaximal, complemented
8#432×C181C211yesmaximal, characteristic
9#19153816C2211yescharacteristic
10#19153816C2211yescharacteristic
11#19153808—21no—
12#19153808—21no—
13#19153808—21no—
14#19153808C2212yes—
15#19153808C2212yes—
16#19153795—21no—
17#19153795C2212yes—
18C4×Dic362—21no—
19C4×Dic362C2212yes—
20#19153775—21no—
21C2×C4⋊Dic181C2211yescharacteristic
22C2×C4⋊Dic181C2211yescharacteristic
23C2×#15668428—21no—
24C2×#15668428—21no—
25#19153750C2214yes—
26#19153748C2214yes—
27#19153741C2214yes—
28#19153741C2214yes—
29C2×C42×C181C2211yescharacteristic
30C4⋊C8×C181C2212yes—
31C22⋊C8×C181C2212yes—
32#97×C181C2212yes—
33C2×Dic362—21no—
34C2×Dic362C2312yes—
35C22×Dic181—21no—
36C22×Dic181—21no—
37C4⋊Dic181—21no—
38C4⋊Dic181—21no—
39C4⋊Dic181—21no—
40C4⋊Dic181—21no—
41C4⋊Dic181—21no—
42C4⋊Dic181C2312yes—
43C4⋊Dic181C2312yes—
44C4⋊Dic181C2312yes—
45#15668428—22no—
46#15668428—22no—
47#15668428—22no—
48#15668428—22no—
49#15668428—22no—
50#15668428—22no—
51C22⋊Dic181—22no—
52C4×Dic181—22no—
53C22×C4×C181D411yescharacteristic
54C22×C4×C181D411yescharacteristic
55C22×C4×C181C2311yescharacteristic
56C2×C8×C181C2314yes—
57C42×C181D411yescharacteristic
58C42×C181D411yescharacteristic
59C42×C181C2311yescharacteristic
60C42×C181C2311yescharacteristic
61Dic362—24no—
62Dic362—42no—
63C2×Dic181—22no—
64C2×Dic181—22no—
65C2×Dic181—22no—
66C2×Dic181—22no—
67C2×Dic181—42no—
68C2×Dic181—42no—
69C23×C181C2×D411yescharacteristic
70C2×C4×C181—22no—
71C2×C4×C181—22no—
72C2×C4×C181—41no—
73C2×C4×C181C2×D411yescharacteristic
74C2×C4×C181C2×D411yescharacteristic
75C2×C4×C181C2×D411yescharacteristic
76C2×C4×C181C2×D411yescharacteristic
77C2×C4×C181C2×D411yescharacteristic
78C2×C4×C181C2411yescharacteristic
79C8×C181—24no—
80C22×C181—21no—
81C22×C181—21no—
82C22×C181#13712yes—
83C22×C181C22×D411yescharacteristic
84C4×C181—21no—
85C4×C181—21no—
86C4×C181—21no—
87C4×C181—21no—
88C4×C181—21no—
89C4×C1812−1+412yes—
90Dic181—42no—
91Dic181—42no—
92Dic181—42no—
93Dic181—42no—
94C2×C181—22no—
95C2×C181#53611yescharacteristic
96C2×C181C2×#13711yescharacteristic
97C2×C181#57511yescharacteristic
98C181#323611yescharacteristic, complemented, Sylow
99#3236—1811nomaximal, Sylow
100#533—1811no—
101C2×#125—1811no—
102#501—1812no—
103#491—1812no—
104#484—1812no—
105#483—1812no—
106#479—1814no—
107#432D18111yescharacteristic
108C4⋊Q8—1811no—
109C4⋊Q8—1811no—
110#125—3621no—
111#125—3621no—
112#125—3621no—
113#125—1812no—
114#125—1812no—
115C22⋊Q8—3621no—
116C22⋊Q8—1812no—
117C4×Q8—3621no—
118C4×Q8—1812no—
119#117—3621no—
120C2×C4⋊C4—3621no—
121C2×C4⋊C4—3621no—
122C2×C4⋊C4—1811no—
123C2×C4⋊C4—1811no—
124C2×C42C2×D18111yescharacteristic
125#107—1814no—
126#106—1814no—
127C4⋊C8C2×D18112yes—
128#103—1814no—
129#103—1814no—
130C22⋊C8C2×D18112yes—
131#97C2×D18112yes—
132C2×Q8—3621no—
133C2×Q8—1812no—
134C22×C4—3621no—
135C22×C4—3621no—
136C22×C4D72411yescharacteristic
137C22×C4D72411yescharacteristic
138C22×C4C22×D18111yescharacteristic
139C2×C8C22×D18114yes—
140C4⋊C4—3622no—
141C4⋊C4—3622no—
142C4⋊C4—3622no—
143C4⋊C4—3622no—
144C4⋊C4—3621no—
145C4⋊C4—3621no—
146C4⋊C4—3621no—
147C4⋊C4—3621no—
148C4⋊C4—3621no—
149C4⋊C4—3622no—
150C4⋊C4—3622no—
151C4⋊C4—1812no—
152C4⋊C4—1812no—
153C4⋊C4—1812no—
154C22⋊C4—3622no—
155C42—3622no—
156C42D72411yescharacteristic
157C42D72411yescharacteristic
158C42C22×D18111yescharacteristic
159C42C22×D18111yescharacteristic
160C23C2×D72411yescharacteristic
161Q8—3624no—
162Q8—7242no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—41no—
166C2×C4—3622no—
167C2×C4—3622no—
168C2×C4—3622no—
169C2×C4—3622no—
170C2×C4—7242no—
171C2×C4—7242no—
172C2×C4C2×D72411yescharacteristic
173C2×C4C2×D72411yescharacteristic
174C2×C4C2×D72411yescharacteristic
175C2×C4C2×D72411yescharacteristic
176C2×C4C2×D72411yescharacteristic
177C2×C4C23×D18111yescharacteristic
178C8—24no—
179C22—21no—
180C22—21no—
181C22#1915384912yes—
182C22C22×D72411yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—21no—
187C4—21no—
188C4—7242no—
189C4—7242no—
190C4—7242no—
191C4—7242no—
192C4#1915386312yes—
193C2—22no—
194C2#2604185511yescharacteristic
195C2C2×#1915384911yescharacteristic
196C2#2604207911yescharacteristic
subgroupG/H
centerC22C22×D724
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#432×C181C2
socleC22×C181C22×D4
prime radicalC23×C181C2×D4
hypercenter#432D181
hypocenterC181#3236
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
3. #26041688C2semidirect
4. #26041648C2semidirect
7. #26041587C2semidirect
98. C181#3236semidirect

Maximal subgroups

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

subgroupindex
#260418362
C2×#191538082
#260416882
#260416482
#260416152
#260416102
#260415872
#432×C1812
#3236181