Finite Group Databasebeta

← #37544931

Subgroups — #37544931

Order 23168.

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

normal subgroups only

This group has 322 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
2#26041685C212yesmaximal, complemented
3#26041647C212yesmaximal, complemented
4#26041617C214yesmaximal
5#26041574C212yesmaximal, complemented
6#26041564C212yesmaximal, complemented
7#26041336C211yesmaximal, characteristic
8#533×C181C211yesmaximal, characteristic
9#19153816C2211yescharacteristic
10#19153816C2211yescharacteristic
11#19153808C2212yes—
12#19153795—21no—
13#19153795—21no—
14C4×Dic362—21no—
15C4×Dic362—21no—
16#19153775C2212yes—
17#19153749C2214yes—
18#19153747C2214yes—
19C4⋊#13089678C2212yes—
20#19153740C2214yes—
21#19153740C2214yes—
22C22⋊#13089678C2212yes—
23#19153727C2212yes—
24C4⋊Q8×C181C2211yescharacteristic
25C4⋊Q8×C181C2211yescharacteristic
26#125×C181—21no—
27C22⋊Q8×C181—21no—
28C22⋊Q8×C181C2212yes—
29C4×Q8×C181—21no—
30C4×Q8×C181C2212yes—
31#117×C181—21no—
32C2×C42×C181C2211yescharacteristic
33C2×Dic362—21no—
34C2×Dic362—21no—
35C2×#13089678C2314yes—
36C4⋊Dic181—21no—
37C4⋊Dic181—21no—
38C4⋊Dic181C2312yes—
39C4⋊Dic181C2312yes—
40#15668428—22no—
41#15668428—22no—
42C22⋊Dic181—22no—
43C4×Dic181—22no—
44C2×Q8×C181—21no—
45C2×Q8×C181C2312yes—
46C22×C4×C181D411yescharacteristic
47C22×C4×C181D411yescharacteristic
48C22×C4×C181C2311yescharacteristic
49C4⋊C4×C181—21no—
50C4⋊C4×C181—21no—
51C4⋊C4×C181—21no—
52C4⋊C4×C181—22no—
53C4⋊C4×C181—22no—
54C4⋊C4×C181C2312yes—
55C22⋊C4×C181—22no—
56C42×C181—22no—
57C42×C181D411yescharacteristic
58C42×C181D411yescharacteristic
59C42×C181C2311yescharacteristic
60C42×C181C2311yescharacteristic
61Dic362—42no—
62Dic362—42no—
63C2×Dic181—22no—
64C2×Dic181—22no—
65#13089678—24no—
66C23×C181C2×D411yescharacteristic
67Q8×C181—24no—
68Q8×C181—42no—
69C2×C4×C181—22no—
70C2×C4×C181—22no—
71C2×C4×C181—22no—
72C2×C4×C181—22no—
73C2×C4×C181—41no—
74C2×C4×C181C2×D411yescharacteristic
75C2×C4×C181C2×D411yescharacteristic
76C2×C4×C181C2×D411yescharacteristic
77C2×C4×C181C2×D411yescharacteristic
78C2×C4×C181C2×D411yescharacteristic
79C2×C4×C181C2411yescharacteristic
80C22×C181—21no—
81C22×C181—21no—
82C22×C181—21no—
83C22×C181C22×D411yescharacteristic
84C4×C181—21no—
85C4×C181—21no—
86C4×C181—21no—
87C4×C181—21no—
88C4×C181—42no—
89C4×C181—42no—
90C4×C181#13712yes—
91C4×C1812−1+412yes—
92Dic181—42no—
93Dic181—42no—
94C2×C181—41no—
95C2×C181#53611yescharacteristic
96C2×C181C2×#13711yescharacteristic
97C2×C181#57511yescharacteristic
98C181#323711yescharacteristic, complemented, Sylow
99#3237—1811nomaximal, Sylow
100#533—1811no—
101#533D18111yescharacteristic
102#501—1812no—
103#491—1812no—
104#485—1814no—
105#477—1812no—
106#475—1812no—
107#432—1811no—
108C4⋊Q8—1811no—
109C4⋊Q8—1811no—
110C4⋊Q8C2×D18111yescharacteristic
111C4⋊Q8C2×D18111yescharacteristic
112#125—21no—
113#125—1812no—
114C22⋊Q8—21no—
115C22⋊Q8—3621no—
116C22⋊Q8—3621no—
117C22⋊Q8C2×D18112yes—
118C4×Q8—21no—
119C4×Q8—3621no—
120C4×Q8—3621no—
121C4×Q8C2×D18112yes—
122#117—21no—
123#117—1812no—
124C2×C42C2×D18111yescharacteristic
125#107—1814no—
126#106—1814no—
127C4⋊C8—1812no—
128#103—1814no—
129#103—1814no—
130C22⋊C8—1812no—
131#97—1812no—
132C2×Q8—21no—
133C2×Q8—3621no—
134C2×Q8—3621no—
135C2×Q8C22×D18112yes—
136C22×C4C22⋊D18111yescharacteristic
137C22×C4C22⋊D18111yescharacteristic
138C22×C4C22×D18111yescharacteristic
139C2×C8—1814no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—22no—
144C4⋊C4—22no—
145C4⋊C4—3622no—
146C4⋊C4—3622no—
147C4⋊C4—3621no—
148C4⋊C4—3621no—
149C4⋊C4—1812no—
150C4⋊C4—1812no—
151C4⋊C4C22×D18112yes—
152C22⋊C4—22no—
153C22⋊C4—3622no—
154C42—22no—
155C42—3622no—
156C42C22⋊D18111yescharacteristic
157C42C22⋊D18111yescharacteristic
158C42C22×D18111yescharacteristic
159C42C22×D18111yescharacteristic
160C23C2×C22⋊D18111yescharacteristic
161Q8—24no—
162Q8—42no—
163Q8—7242no—
164Q8—7242no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—41no—
170C2×C4—3622no—
171C2×C4—3622no—
172C2×C4C2×C22⋊D18111yescharacteristic
173C2×C4C2×C22⋊D18111yescharacteristic
174C2×C4C2×C22⋊D18111yescharacteristic
175C2×C4C2×C22⋊D18111yescharacteristic
176C2×C4C2×C22⋊D18111yescharacteristic
177C2×C4C23×D18111yescharacteristic
178C8—3624no—
179C22—21no—
180C22—21no—
181C22—21no—
182C22C22×C22⋊D18111yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—21no—
187C4—42no—
188C4—42no—
189C4—7242no—
190C4—7242no—
191C4#1915384712yes—
192C4#1915386312yes—
193C2—41no—
194C2#2604185011yescharacteristic
195C2C2×#1915384711yescharacteristic
196C2#2604207711yescharacteristic
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#3237
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. #26041685C2semidirect
3. #26041647C2semidirect
5. #26041574C2semidirect
6. #26041564C2semidirect
98. C181#3237semidirect

Maximal subgroups

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

subgroupindex
#260418362
#260416852
#260416472
#260416172
#260415742
#260415642
#260413362
#533×C1812
#3237181