Finite Group Databasebeta

← #37544883

Subgroups — #37544883

Order 23168.

326 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 117 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#26041834C211yesmaximal, characteristic
2#26041834C211yesmaximal, characteristic
3#26041682C211yesmaximal, characteristic, complemented
4#26041631C211yesmaximal, characteristic, complemented
5#26041630C211yesmaximal, characteristic, complemented
6#26041623C214yesmaximal
7#26041589C214yesmaximal, complemented
8#26041330C211yesmaximal, characteristic
9#498×C181C211yesmaximal, characteristic, complemented
10#19153816C2211yescharacteristic
11#19153816C2211yescharacteristic
12#19153807—21no—
13#19153807C2212yes—
14#19153796—21no—
15#19153796C2212yes—
16#19153792—21no—
17#19153792—21no—
18Q8×Dic181—21no—
19Q8×Dic181—21no—
20#19153781—21no—
21#19153781C2212yes—
22#19153774—21no—
23#19153774C2212yes—
24C42×D181C2211yescharacteristic
25#19153749C2214yes—
26#19153745C2212yes—
27#19153741C2214yes—
28#19153739C2214yes—
29#19153728C2212yes—
30C4×#13089678C2211yescharacteristic
31C4⋊Q8×C181C2211yescharacteristic
32C4⋊Q8×C181C2211yescharacteristic
33#106×C181C2214yes—
34C4×C8×C181C2211yescharacteristic
35C2×Dic362—21no—
36C2×Dic362C2312yes—
37C2×C4×D181D411yescharacteristic
38C2×C4×D181D411yescharacteristic
39C2×C4×D181C2311yescharacteristic
40C2×#13089678C2312yes—
41C4⋊Dic181—22no—
42C4⋊Dic181—22no—
43C4⋊Dic181—21no—
44C4⋊Dic181—21no—
45C4⋊Dic181—21no—
46C4⋊Dic181C2312yes—
47#15668428—22no—
48#15668428—22no—
49#15668426—22no—
50#15668426—22no—
51C4×Dic181—22no—
52C4×Dic181—22no—
53C4×Dic181D411yescharacteristic
54C4×Dic181D411yescharacteristic
55C4×Dic181C2311yescharacteristic
56C2×Q8×C181—21no—
57C2×Q8×C181—21no—
58C2×C8×C181C2312yes—
59C4⋊C4×C181—21no—
60C4⋊C4×C181—21no—
61C4⋊C4×C181C2312yes—
62C4⋊C4×C181C2312yes—
63C42×C181C2311yescharacteristic
64C22×D181C2×D411yescharacteristic
65Dic362—24no—
66Dic362—42no—
67C2×Dic181—22no—
68C2×Dic181—22no—
69C2×Dic181C2×D411yescharacteristic
70C2×Dic181C2×D411yescharacteristic
71C2×Dic181C2×D411yescharacteristic
72C4×D181—22no—
73C4×D181—22no—
74C4×D181—22no—
75#13089678—22no—
76Q8×C181—42no—
77Q8×C181—42no—
78C2×C4×C181—22no—
79C2×C4×C181—22no—
80C2×C4×C181C2×D411yescharacteristic
81C2×C4×C181C2×D411yescharacteristic
82C2×C4×C181C2411yescharacteristic
83C8×C181—22no—
84C22×C181C22×D411yescharacteristic
85C2×D181—21no—
86C2×D181—21no—
87C2×D181—21no—
88C4×C181—42no—
89C4×C181—42no—
90C4×C181#13512yes—
91C4×C181#13712yes—
92C4×C1812−1+412yes—
93Dic181—21no—
94Dic181—21no—
95Dic181—21no—
96Dic181—42no—
97Dic181—42no—
98C2×C181#53611yescharacteristic
99C2×C181C2×#13511yescharacteristic
100C2×C181C2×#13711yescharacteristic
101D181—41no—
102C181#323111yescharacteristic, complemented, Sylow
103#3231—1811nomaximal, Sylow
104#533—1811no—
105#533—1811no—
106#500—1811no—
107#498D18111yescharacteristic, complemented
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—3621no—
118#125—1812no—
119C22⋊Q8—3621no—
120C22⋊Q8—3621no—
121C22⋊Q8—3621no—
122C22⋊Q8—1812no—
123C4×Q8—3621no—
124C4×Q8—3621no—
125C4×Q8—3621no—
126C4×Q8—1812no—
127#117—3621no—
128#117—1812no—
129C2×C42—1811no—
130#107—1814no—
131#106C2×D18114yes—
132C4⋊C8—1812no—
133#103—1814no—
134#103—1814no—
135C22⋊C8—1812no—
136C4×C8—1811no—
137C4×C8C2×D18111yescharacteristic
138C2×Q8—21no—
139C2×Q8—21no—
140C2×Q8—3621no—
141C2×Q8—1812no—
142C22×C4—1811no—
143C22×C4—1811no—
144C22×C4—1811no—
145C2×C8—1812no—
146C2×C8C22×D18112yes—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4—3622no—
150C4⋊C4—3622no—
151C4⋊C4—3622no—
152C4⋊C4—3622no—
153C4⋊C4—3621no—
154C4⋊C4—3621no—
155C4⋊C4—3621no—
156C4⋊C4—1812no—
157C4⋊C4C22×D18112yes—
158C4⋊C4C22×D18112yes—
159C22⋊C4—3622no—
160C22⋊C4—3622no—
161C42—3622no—
162C42—3622no—
163C42—1811no—
164C42—1811no—
165C42—1811no—
166C42C22×D18111yescharacteristic
167C23—1811no—
168Q8—42no—
169Q8—42no—
170Q8—3624no—
171Q8—7242no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—3622no—
175C2×C4—3622no—
176C2×C4—3622no—
177C2×C4—3622no—
178C2×C4—3622no—
179C2×C4—1811no—
180C2×C4—1811no—
181C2×C4—1811no—
182C2×C4D4×D18111yescharacteristic
183C2×C4D4×D18111yescharacteristic
184C2×C4C23×D18111yescharacteristic
185C8—22no—
186C8—3622no—
187C22—3621no—
188C22—3621no—
189C22—3621no—
190C22C2×D4×D18111yescharacteristic
191C4—42no—
192C4—42no—
193C4—3621no—
194C4—3621no—
195C4—3621no—
196C4—7242no—
197C4—7242no—
198C4#1915383712yes—
199C4#1915384512yes—
200C4#1915386412yes—
201C2—7241no—
202C2#2604185411yescharacteristic
203C2C2×#1915383711yescharacteristic
204C2C2×#1915384511yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#498×C181C2
socleC22×C181C22×D4
prime radicalC22×D181C2×D4
hypercenter#498D181
hypocenterC181#3231
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
3. #26041682C2semidirect
4. #26041631C2semidirect
5. #26041630C2semidirect
7. #26041589C2semidirect
9. #498×C181C2semidirect
102. C181#3231semidirect
107. #498D181semidirect

Maximal subgroups

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

subgroupindex
#260418342
#260416822
#260416312
#260416302
#260416232
#260415892
#260413302
#498×C1812
#3231181