Finite Group Databasebeta

← #15673807

Subgroups — #15673807

Order 2944.

386 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 83 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×#10625100C211yesmaximal, characteristic
2#13092890C211yesmaximal, characteristic
3C2×#10624988C211yesmaximal, characteristic
4#13092280C211yesmaximal, characteristic, complemented
5#13092184C211yesmaximal, characteristic, complemented
6#13092183C211yesmaximal, characteristic, complemented
7C23×#381C211yesmaximal, characteristic, complemented
8C23×C4×C23C2211yescharacteristic
9C22×C22⋊D23C2211yescharacteristic
10C2×C22⋊C4×C23C2211yescharacteristic
11C2×C22⋊C4×C23C2211yescharacteristic
12C2×C22⋊Dic23C2211yescharacteristic
13C2×C22⋊Dic23C2211yescharacteristic
14C2×C22⋊Dic23C2211yescharacteristic
15#10625100—22no—
16#10625100C414yescomplemented
17C4×C22⋊D23—22no—
18C2×(C2×D23)⋊C4—21no—
19C2×Dic23⋊C4—21no—
20(C22⋊D23)⋊C4—22no—
21C22⋊C4×D23—21no—
22#10625048—21no—
23C23×#95—22no—
24C23⋊#95—22no—
25#10624988—22no—
26C24×C23C2311yescharacteristic
27C23×D23D411yescharacteristic
28C22×C4×C23—21no—
29C22×C4×C23—21no—
30C22×C4×C23—21no—
31C22×C4×C23—21no—
32C22×C4×C23—21no—
33C22×C4×C23—21no—
34C22×C4×C23—21no—
35C22×C4×C23C2×C412yescomplemented
36C22×C4×C23D412yes—
37C2×C22⋊D23—21no—
38C2×C22⋊D23—21no—
39C2×C22⋊D23—21no—
40C2×C22⋊D23—21no—
41C2×C22⋊D23C2×C412yes—
42C2×C22⋊D23D412yes—
43C22×Dic23—21no—
44C22×Dic23—21no—
45C22×Dic23D411yescharacteristic
46C22×Dic23D412yes—
47C2×C4×D23—22no—
48C22⋊C4×C23—21no—
49C22⋊C4×C23—21no—
50C22⋊C4×C23—21no—
51C22⋊C4×C23—21no—
52C22⋊Dic23—21no—
53C22⋊Dic23—21no—
54C22⋊Dic23—21no—
55C22⋊Dic23—21no—
56C22⋊Dic23—21no—
57C22⋊Dic23C2×C412yescomplemented
58(C2×D23)⋊C4—22no—
59(C2×D23)⋊C4—24no—
60Dic23⋊C4—22no—
61Dic23⋊C4—24no—
62C4×Dic23—22no—
63C23×C23—42no—
64C23×C23C22×C411yescharacteristic
65C23×C23C2×D411yescharacteristic
66C23×C23C2×D411yescharacteristic
67C23×C23C2×D411yescharacteristic
68C23×C23C2×D411yescharacteristic
69C23×C23#4111yescharacteristic
70C23×C23#4111yescharacteristic
71C22×D23—21no—
72C22×D23—21no—
73C22×D23—42no—
74C22×D23C22⋊C412yes—
75C2×C4×C23—22no—
76C2×C4×C23—22no—
77C2×C4×C23—22no—
78C2×C4×C23—22no—
79C2×C4×C23—41no—
80C2×C4×C23—41no—
81C2×C4×C23—41no—
82C2×C4×C23—41no—
83C2×C4×C23—42no—
84C2×C4×C23—42no—
85C2×C4×C23—41no—
86C22⋊D23—22no—
87C22⋊D23—22no—
88C22⋊D23—22no—
89C22⋊D23—22no—
90C2×Dic23—21no—
91C2×Dic23—21no—
92C2×Dic23—22no—
93C2×Dic23—22no—
94C2×Dic23—42no—
95C2×Dic23—42no—
96C2×Dic23—42no—
97C2×Dic23—41no—
98C2×Dic23C22⋊C412yes—
99C4×D23—82no—
100#1890—231nomaximal, Sylow
101C22×C23—22no—
102C22×C23—22no—
103C22×C23—22no—
104C22×C23—41no—
105C22×C23—41no—
106C22×C23—41no—
107C22×C23—41no—
108C22×C23C2×C22⋊C411yescharacteristic
109C22×C23C4×D411yescharacteristic
110C22×C23C4×D411yescharacteristic
111C22×C23#12011yescharacteristic
112C22×C23#12111yescharacteristic
113C22×C23#12111yescharacteristic
114C22×C23#12311yescharacteristic
115C2×D23—22no—
116C2×D23—42no—
117C2×D23—42no—
118C2×D23—81no—
119C4×C23—42no—
120C4×C23—42no—
121C4×C23—81no—
122Dic23—22no—
123Dic23—42no—
124Dic23—42no—
125Dic23—81no—
126C2×#123—231no—
127#518—231no—
128C2×#99—231no—
129#381—231no—
130#381D2311yescharacteristic, complemented
131#342—231no—
132#342—231no—
133C2×C23—21no—
134C2×C23—21no—
135C2×C23—21no—
136C2×C23—21no—
137C2×C23—21no—
138C2×C23—21no—
139C2×C23#38611yescharacteristic
140C2×C23#45812yes—
141D23—42no—
142C22×D4—231no—
143C23×C4C2×D2311yescharacteristic
144#123—234no—
145#123—462no—
146C4×D4—462no—
147C4×D4—462no—
148#117—461no—
149C2×C4⋊C4—461no—
150C2×C22⋊C4—231no—
151C2×C22⋊C4—231no—
152C2×C22⋊C4—231no—
153C2×C22⋊C4—461no—
154C2×C22⋊C4—461no—
155C2×C22⋊C4C2×D2311yescharacteristic
156C2×C22⋊C4C2×D2311yescharacteristic
157#99—462no—
158#95—22no—
159#95—462no—
160C23#189011yescharacteristic, complemented, Sylow
161C24—231no—
162C24C22×D2311yescharacteristic
163C2×D4—232no—
164C2×D4—232no—
165C2×D4—461no—
166C2×D4—461no—
167C2×D4—461no—
168C2×D4—461no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—231no—
177C22×C4—232no—
178C22×C4—462no—
179C22×C4—461no—
180C22×C4—461no—
181C22×C4C4×D2312yescomplemented
182C22×C4C22⋊D2312yes—
183C4⋊C4—464no—
184C4⋊C4—462no—
185C22⋊C4—21no—
186C22⋊C4—21no—
187C22⋊C4—21no—
188C22⋊C4—21no—
189C22⋊C4—232no—
190C22⋊C4—464no—
191C22⋊C4—462no—
192C22⋊C4—461no—
193C22⋊C4—461no—
194C22⋊C4—461no—
195C22⋊C4—461no—
196C22⋊C4—461no—
197C42—462no—
198C23—42no—
199C23—232no—
200C23—461no—
201C23—461no—
202C23—922no—
203C23C2×C4×D2311yescharacteristic
204C23#6728811yescharacteristic
205C23D4×D2311yescharacteristic
206C23D4×D2311yescharacteristic
207C23D4×D2311yescharacteristic
208C23#6729011yescharacteristic
209C23C2×C22⋊D2311yescharacteristic
210D4—462no—
211D4—462no—
212D4—462no—
213D4—462no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—41no—
225C2×C4—232no—
226C2×C4—461no—
227C2×C4—461no—
228C2×C4—462no—
229C2×C4—462no—
230C2×C4—922no—
231C2×C4—922no—
232C2×C4—922no—
233C2×C4—921no—
234C2×C4—1842no—
235C22—22no—
236C22—22no—
237C22—22no—
238C22—41no—
239C22—41no—
240C22—41no—
241C22—41no—
242C22—462no—
243C22—922no—
244C22—922no—
245C22—1841no—
246C22C22⋊C4×D2311yescharacteristic
247C22(C22⋊D23)⋊C411yescharacteristic
248C22#1062505411yescharacteristic
249C22#1062505511yescharacteristic
250C22C4×C22⋊D2311yescharacteristic
251C22#1062510811yescharacteristic
252C22#1062510911yescharacteristic
253C4—42no—
254C4—42no—
255C4—81no—
256C4—462no—
257C4—922no—
258C4—922no—
259C4—1841no—
260C2—21no—
261C2—21no—
262C2—21no—
263C2—21no—
264C2—21no—
265C2—21no—
266C2—922no—
267C2#1309229311yescharacteristic
268C2#1309260612yes—
subgroupG/H
centerC22#10625108
commutatorC23×C23C22×C4
FrattiniC24C22×D23
FittingC23×#381C2
socleC22×C23#120
prime radicalC22×C22⋊D23C22
cosocleC24×C23C23
hypercenter#381D23
hypocenterC23#1890
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C24 ◁ #381

Complements

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

NH ≅ G/Ntype
4. #13092280C2semidirect
5. #13092184C2semidirect
6. #13092183C2semidirect
7. C23×#381C2semidirect
16. #10625100C4semidirect
35. C22×C4×C23C2×C4semidirect
57. C22⋊Dic23C2×C4semidirect
130. #381D23semidirect
160. C23#1890semidirect
181. C22×C4C4×D23semidirect

Maximal subgroups

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

subgroupindex
C2×#106251002
#130928902
C2×#106249882
#130922802
#130921842
#130921832
C23×#3812
#189023