Finite Group Databasebeta

← #15671900

Subgroups — #15671900

Order 2944.

334 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 65 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#13092930C211yesmaximal, characteristic
2#13092379C211yesmaximal, characteristic, complemented
3#95×D23C211yesmaximal, characteristic, complemented
4#13092154C211yesmaximal, characteristic, complemented
5#13092152C211yesmaximal, characteristic, complemented
6#13092150C211yesmaximal, characteristic, complemented
7C23×#328C211yesmaximal, characteristic, complemented
8C2×#67292C411yescharacteristic, complemented
9C22×C4×D23—21no—
10C22×C4×D23C2211yescharacteristic
11C23×C22⋊Q8C2211yescharacteristic
12#10625117C411yescharacteristic, complemented
13#10625101C2211yescharacteristic
14C2×#67262—21no—
15#10625066C411yescharacteristic, complemented
16#10625065—21no—
17#10625064—21no—
18#10625063C411yescharacteristic, complemented
19#10625053—21no—
20(C22⋊D23)⋊C4—21no—
21C23×C22⋊C8C2211yescharacteristic
22C23×#95C2211yescharacteristic
23C23⋊#95—21no—
24C23⋊#95C2211yescharacteristic
25C22⋊(C23⋊C8)C2211yescharacteristic
26(C2×D23)⋊C8—21no—
27C23×D23D411yescharacteristic
28C2×Q8×C23C2×C411yescharacteristic, complemented
29C22×C4×C23—21no—
30C22×C4×C23C2311yescharacteristic
31C2×C22⋊D23—21no—
32C22×Dic23—21no—
33C22×Dic23D411yescharacteristic
34#67292—42no—
35C2×D92—21no—
36C2×D92—21no—
37C2×D92C2×C411yescharacteristic, complemented
38C2×C4×D23—24no—
39C2×C4×D23—21no—
40C2×C4×D23—42no—
41C2×C4×D23—42no—
42C2×C4×D23—42no—
43C2×C4×D23C2×C411yescharacteristic
44C2×C4×D23C2×C411yescharacteristic
45C2×C4×D23D411yescharacteristic
46C2×C4×D23D411yescharacteristic
47C2×C8×C23—21no—
48C4⋊C4×C23—21no—
49C4⋊C4×C23C2×C411yescharacteristic, complemented
50C22⋊C4×C23—21no—
51(C2×D23)⋊C4—21no—
52(C2×D23)⋊C4—21no—
53(C2×D23)⋊C4—21no—
54(C2×D23)⋊C4—21no—
55C4⋊Dic23C2×C411yescharacteristic, complemented
56Dic23⋊C4—21no—
57C4×Dic23—21no—
58C2×C23⋊C8—21no—
59#67262—42no—
60C23×C23C2×D411yescharacteristic
61C22×D23—21no—
62C22×D23—21no—
63C22×D23—22no—
64C22×D23—22no—
65C22×D23—21no—
66C22×D23C22⋊C411yescharacteristic
67C22×D23C22⋊C411yescharacteristic
68Q8×C23—41no—
69C2×C4×C23—22no—
70C2×C4×C23—21no—
71C2×C4×C23—21no—
72C2×C4×C23—41no—
73C2×C4×C23—41no—
74C2×C4×C23—41no—
75C2×C4×C23C22×C411yescharacteristic
76C2×C4×C23C2×D411yescharacteristic
77C22⋊D23—41no—
78C22⋊D23—41no—
79C2×Dic23—22no—
80C2×Dic23—21no—
81C2×Dic23—41no—
82C2×Dic23—41no—
83C2×Dic23—41no—
84C2×Dic23C22⋊C411yescharacteristic
85C2×Dic23C22⋊C411yescharacteristic
86D92—41no—
87D92—42no—
88D92—42no—
89C4×D23—22no—
90C4×D23—22no—
91C4×D23—41no—
92C4×D23—41no—
93C4×D23—42no—
94C4×D23—48no—
95C8×C23—41no—
96C23⋊C8—41no—
97#1504—231nomaximal, Sylow
98C22×C23—21no—
99C22×C23—21no—
100C22×C23C2×C22⋊C411yescharacteristic
101C22×C23AGL(1,ℤ/8)11yescharacteristic
102C22×C23#13711yescharacteristic
103C2×D23—24no—
104C2×D23—24no—
105C2×D23—21no—
106C2×D23—21no—
107C2×D23—21no—
108C2×D23—21no—
109C2×D23—41no—
110C2×D23—41no—
111C2×D23—41no—
112C2×D23#9912yes—
113C2×D23#10412yes—
114C4×C23—21no—
115C4×C23—21no—
116C4×C23—42no—
117C4×C23—41no—
118C4×C23—41no—
119Dic23—21no—
120Dic23—21no—
121Dic23—42no—
122Dic23—41no—
123#525—231no—
124#407—231no—
125C2×#95—231no—
126#328—231no—
127#328D2311yescharacteristic, complemented
128#327—231no—
129#327—231no—
130C2×C23—21no—
131C2×C23—21no—
132C2×C23C2×#9911yescharacteristic
133C2×C23#41711yescharacteristic
134C2×C23C2×#10411yescharacteristic
135D23—22no—
136D23—22no—
137D23—81no—
138C2×#41—231no—
139C23×C4—231no—
140C23×C4—461no—
141C2×M16—461no—
142#123—461no—
143C22⋊Q8—231no—
144C22⋊Q8C2×D2311yescharacteristic
145#121—231no—
146#121—231no—
147#120—461no—
148C4×D4—461no—
149C4×D4—461no—
150#117—231no—
151C22⋊C8—231no—
152C22⋊C8—461no—
153C22⋊C8C2×D2311yescharacteristic
154#95—231no—
155#95—461no—
156#95C2×D2311yescharacteristic
157C23#150411yescharacteristic, complemented, Sylow
158C24—231no—
159#41—922no—
160C2×Q8C4×D2311yescharacteristic, complemented
161C2×D4—231no—
162C2×D4—461no—
163C2×D4—461no—
164C2×D4—461no—
165C22×C4—21no—
166C22×C4—231no—
167C22×C4—231no—
168C22×C4—231no—
169C22×C4—231no—
170C22×C4—231no—
171C22×C4—461no—
172C22×C4—464no—
173C22×C4—461no—
174C22×C4—922no—
175C22×C4—922no—
176C22×C4—922no—
177C22×C4C22×D2311yescharacteristic
178M16—922no—
179C2×C8—21no—
180C2×C8—461no—
181C4⋊C4—21no—
182C4⋊C4—231no—
183C4⋊C4—461no—
184C4⋊C4C4×D2311yescharacteristic, complemented
185C22⋊C4—21no—
186C22⋊C4—461no—
187C22⋊C4—461no—
188C22⋊C4—461no—
189C22⋊C4—461no—
190C42—461no—
191C23—231no—
192C23—231no—
193C23—462no—
194C23—462no—
195C23—461no—
196C23—461no—
197C23—461no—
198C23D4×D2311yescharacteristic
199Q8—41no—
200D4—921no—
201D4—922no—
202D4—922no—
203D4—921no—
204D4—921no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—231no—
212C2×C4—231no—
213C2×C4—462no—
214C2×C4—462no—
215C2×C4—462no—
216C2×C4—461no—
217C2×C4—921no—
218C2×C4—921no—
219C2×C4—922no—
220C2×C4—928no—
221C2×C4—921no—
222C2×C4—921no—
223C2×C4—921no—
224C2×C4C2×C4×D2311yescharacteristic
225C2×C4D4×D2311yescharacteristic
226C8—41no—
227C8—921no—
228C22—21no—
229C22—21no—
230C22—232no—
231C22—232no—
232C22—464no—
233C22—464no—
234C22—461no—
235C22—461no—
236C22—461no—
237C22—461no—
238C22—921no—
239C22—921no—
240C22—921no—
241C22C22⋊C4×D2311yescharacteristic
242C22#1062508511yescharacteristic
243C22#1062508911yescharacteristic
244C4—21no—
245C4—21no—
246C4—42no—
247C4—41no—
248C4—41no—
249C4—461no—
250C4—461no—
251C4—922no—
252C4—921no—
253C2—21no—
254C2—21no—
255C2—462no—
256C2—462no—
257C2—1841no—
258C2#99×D2311yescharacteristic
259C2#1309241711yescharacteristic
260C2#104×D2311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D23
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#328C2
socleC22×C23C2×C22⋊C4
prime radical#13092930C2
cosocleC22×C4×C23C23
hypercenter#328D23
hypocenterC23#1504
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #13092379C2semidirect
3. #95×D23C2semidirect
4. #13092154C2semidirect
5. #13092152C2semidirect
6. #13092150C2semidirect
7. C23×#328C2semidirect
8. C2×#67292C4semidirect
12. #10625117C4semidirect
15. #10625066C4semidirect
18. #10625063C4semidirect
28. C2×Q8×C23C2×C4semidirect
37. C2×D92C2×C4semidirect
49. C4⋊C4×C23C2×C4semidirect
55. C4⋊Dic23C2×C4semidirect
127. #328D23semidirect
157. C23#1504semidirect
160. C2×Q8C4×D23semidirect
184. C4⋊C4C4×D23semidirect

Maximal subgroups

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

subgroupindex
#130929302
#130923792
#95×D232
#130921542
#130921522
#130921502
C23×#3282
#150423