Finite Group Databasebeta

← #15673384

Subgroups — #15673384

Order 2944.

380 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C2×(C22⋊D23)⋊C4C211yesmaximal, characteristic
2C2×#10624988C212yesmaximal
3#13092275C212yesmaximal, complemented
4#13092184C211yesmaximal, characteristic, complemented
5C23×#342C211yesmaximal, characteristic, complemented
6C22×C22⋊D23C2211yescharacteristic
7C23×Dic23C2211yescharacteristic
8C22×C4×D23C411yescharacteristic, complemented
9C2×C22⋊C4×C23C2212yes—
10C2×C22⋊C4×C23C2211yescharacteristic
11C2×C22⋊Dic23C2212yes—
12C2×(C2×D23)⋊C4C411yescharacteristic, complemented
13C2×Dic23⋊C4—22no—
14C2×Dic23⋊C4C411yescharacteristic, complemented
15C2×C4×Dic23C411yescharacteristic, complemented
16(C22⋊D23)⋊C4—22no—
17(C22⋊D23)⋊C4—22no—
18C23⋊#95—22no—
19#10624988—24no—
20C24×C23C2311yescharacteristic
21C23×D23C2×C411yescharacteristic
22C22×C4×C23—22no—
23C22×C4×C23C2×C411yescharacteristic
24C22×C4×C23C2×C411yescharacteristic
25C2×C22⋊D23—22no—
26C2×C22⋊D23—22no—
27C2×C22⋊D23D412yes—
28C2×C22⋊D23Q812yes—
29C22×Dic23—22no—
30C22×Dic23—42no—
31C22×Dic23C2×C411yescharacteristic
32C22×Dic23C2×C411yescharacteristic
33C22×Dic23C2×C411yescharacteristic
34C22×Dic23D412yes—
35C22×Dic23D412yes—
36C2×C4×D23—21no—
37C2×C4×D23—21no—
38C2×C4×D23—42no—
39C22⋊C4×C23—22no—
40C22⋊C4×C23—22no—
41C22⋊C4×C23—22no—
42C22⋊Dic23—22no—
43C22⋊Dic23—22no—
44(C2×D23)⋊C4—22no—
45Dic23⋊C4—22no—
46Dic23⋊C4—44no—
47C4×Dic23—21no—
48C4×Dic23—21no—
49C23×C23—41no—
50C23×C23—41no—
51C23×C23C22×C411yescharacteristic
52C23×C23C2×D412yes—
53C23×C23C2×D411yescharacteristic
54C23×C23C2×Q811yescharacteristic
55C23×C23#4112yes—
56C22×D23—21no—
57C22×D23—21no—
58C22×D23—41no—
59C22×D23—41no—
60C22×D23C4⋊C412yescomplemented
61C2×C4×C23—21no—
62C2×C4×C23—21no—
63C2×C4×C23—41no—
64C2×C4×C23—41no—
65C2×C4×C23—42no—
66C2×C4×C23—42no—
67C2×C4×C23—42no—
68C22⋊D23—24no—
69C22⋊D23—24no—
70C2×Dic23—21no—
71C2×Dic23—21no—
72C2×Dic23—24no—
73C2×Dic23—22no—
74C2×Dic23—41no—
75C2×Dic23—42no—
76C2×Dic23—42no—
77C2×Dic23—42no—
78C2×Dic23—42no—
79C2×Dic23C22⋊C411yescharacteristic
80C2×Dic23C22⋊C412yes—
81C2×Dic23C22⋊C411yescharacteristic
82C2×Dic23C4⋊C412yescomplemented
83C4×D23—42no—
84C4×D23—42no—
85#1799—231nomaximal, Sylow
86C22×C23—22no—
87C22×C23—21no—
88C22×C23—22no—
89C22×C23—21no—
90C22×C23—41no—
91C22×C23—41no—
92C22×C23—42no—
93C22×C23C2×C22⋊C411yescharacteristic
94C22×C23C2×C4⋊C411yescharacteristic
95C22×C23#11711yescharacteristic
96C22×C23#12112yes—
97C22×C23C22⋊Q812yes—
98C2×D23—22no—
99C2×D23—42no—
100C2×D23—41no—
101C2×D23—41no—
102C2×D23—42no—
103C4×C23—41no—
104C4×C23—41no—
105C4×C23—82no—
106Dic23—22no—
107Dic23—21no—
108Dic23—22no—
109Dic23—82no—
110Dic23#9912yescomplemented
111C2×C4×D4—231no—
112C2×#99—232no—
113#380—232no—
114#342—231no—
115#342D2311yescharacteristic, complemented
116C2×C23—22no—
117C2×C23—21no—
118C2×C23—21no—
119C2×C23—22no—
120C2×C23#38011yescharacteristic
121C2×C23C2×#9911yescharacteristic
122C2×C23#41011yescharacteristic
123D23—42no—
124C22×D4—231no—
125C23×C4—231no—
126C23×C4—231no—
127C4×D4—462no—
128C4×D4—462no—
129C2×C4⋊C4—231no—
130C2×C4⋊C4—462no—
131C2×C22⋊C4—231no—
132C2×C22⋊C4—232no—
133C2×C22⋊C4C2×D2312yes—
134C2×C22⋊C4C2×D2311yescharacteristic
135C2×C42—231no—
136#99—464no—
137#95—462no—
138C23#179911yescharacteristic, complemented, Sylow
139C24—231no—
140C24C22×D2311yescharacteristic
141C2×D4—232no—
142C2×D4—232no—
143C2×D4—462no—
144C2×D4—462no—
145C22×C4—22no—
146C22×C4—231no—
147C22×C4—231no—
148C22×C4—232no—
149C22×C4—231no—
150C22×C4—232no—
151C22×C4—461no—
152C22×C4—461no—
153C22×C4—462no—
154C22×C4—922no—
155C22×C4—922no—
156C22×C4C4×D2311yescharacteristic
157C22×C4C4×D2311yescharacteristic
158C4⋊C4—462no—
159C4⋊C4—924no—
160C22⋊C4—22no—
161C22⋊C4—22no—
162C22⋊C4—22no—
163C22⋊C4—462no—
164C22⋊C4—462no—
165C22⋊C4—462no—
166C42—461no—
167C42—461no—
168C23—41no—
169C23—41no—
170C23—232no—
171C23—461no—
172C23—461no—
173C23—921no—
174C23—921no—
175C23C2×C4×D2311yescharacteristic
176C23#6728812yes—
177C23D4×D2312yes—
178C23D4×D2311yescharacteristic
179C23Q8×D2311yescharacteristic
180D4—464no—
181D4—464no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—231no—
190C2×C4—231no—
191C2×C4—232no—
192C2×C4—232no—
193C2×C4—464no—
194C2×C4—462no—
195C2×C4—461no—
196C2×C4—461no—
197C2×C4—922no—
198C2×C4—922no—
199C2×C4—922no—
200C2×C4—921no—
201C2×C4—922no—
202C2×C4—922no—
203C2×C4—922no—
204C22—22no—
205C22—21no—
206C22—22no—
207C22—21no—
208C22—42no—
209C22—41no—
210C22—41no—
211C22—462no—
212C22—922no—
213C22—922no—
214C22—921no—
215C22—921no—
216C22#1062504311yescharacteristic
217C22C22⋊C4×D2311yescharacteristic
218C22#1062505512yes—
219C22C4⋊C4×D2311yescharacteristic
220C22#1062506712yes—
221C4—41no—
222C4—41no—
223C4—82no—
224C4—232no—
225C4—461no—
226C4—462no—
227C4—462no—
228C4—1842no—
229C2—22no—
230C2—21no—
231C2—21no—
232C2—22no—
233C2—922no—
234C2#1309227611yescharacteristic
235C2#99×D2311yescharacteristic
236C2#1309238911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D23
commutatorC23×C23C22×C4
FrattiniC24C22×D23
FittingC23×#342C2
socleC22×C23C2×C22⋊C4
prime radicalC22×C22⋊D23C22
cosocleC24×C23C23
hypercenter#342D23
hypocenterC23#1799
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
3. #13092275C2semidirect
4. #13092184C2semidirect
5. C23×#342C2semidirect
8. C22×C4×D23C4semidirect
12. C2×(C2×D23)⋊C4C4semidirect
14. C2×Dic23⋊C4C4semidirect
15. C2×C4×Dic23C4semidirect
60. C22×D23C4⋊C4semidirect
82. C2×Dic23C4⋊C4semidirect
110. Dic23#99semidirect
115. #342D23semidirect
138. C23#1799semidirect

Maximal subgroups

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

subgroupindex
C2×(C22⋊D23)⋊C42
C2×#106249882
#130922752
#130921842
C23×#3422
#179923