Finite Group Databasebeta

← #15675976

Subgroups — #15675976

Order 2944.

1104 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 229 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
1C22×D4×D23C211yesmaximal, characteristic
2C2×#10625063C211yesmaximal, characteristic, complemented
3C2×#10625043C211yesmaximal, characteristic, complemented
4#13092320C211yesmaximal, characteristic, complemented
5#13092319C211yesmaximal, characteristic, complemented
6#13092318C211yesmaximal, characteristic, complemented
7#13092317C214yesmaximal, complemented
8#13092272C214yesmaximal, complemented
9C23×#390C211yesmaximal, characteristic, complemented
10C24×D23C2212yes—
11C22×D4×C23C2211yescharacteristic
12C22×C22⋊D23C2212yes—
13C2×D4×D23—24no—
14C2×D4×D23—24no—
15C2×D4×D23C418yescomplemented
16C22×D92C2211yescharacteristic
17C22×C4×D23C2211yescharacteristic
18C2×C4⋊C4×C23C2211yescharacteristic, complemented
19C2×C22⋊C4×C23C2214yescomplemented
20C2×C42×C23C2211yescharacteristic, complemented
21C2×C22⋊Dic23C2214yescomplemented
22C2×(C2×D23)⋊C4C2212yes—
23C2×(C2×D23)⋊C4C2212yes—
24C2×(C2×D23)⋊C4C2214yescomplemented
25C2×(C2×D23)⋊C4C2214yescomplemented
26C2×C4⋊Dic23C2211yescharacteristic, complemented
27C2×Dic23⋊C4C2212yescomplemented
28C2×C4×Dic23C2211yescharacteristic, complemented
29C2×C4×Dic23C2212yescomplemented
30#10625063—24no—
31#10625043—24no—
32C24×C23C2312yes—
33C23×D23—24no—
34C23×D23—24no—
35C23×D23—44no—
36C23×D23—44no—
37C23×D23C2×C418yes—
38C23×D23C2312yes—
39C23×D23C2311yescharacteristic
40C2×D4×C23—22no—
41C2×D4×C23—22no—
42C2×D4×C23C2×C414yes—
43C22×C4×C23C2312yes—
44C22×C4×C23C2312yes—
45C22×C4×C23C2311yescharacteristic
46C2×C22⋊D23—24no—
47C2×C22⋊D23—24no—
48C2×C22⋊D23C2×C418yes—
49C22×Dic23C2312yes—
50C22×Dic23C2312yes—
51C22×Dic23C2311yescharacteristic
52D4×D23—232no—
53C2×D92—22no—
54C2×D92—22no—
55C2×D92C2×C414yes—
56C2×C4×D23C2×C414yes—
57C2×C4×D23D414yes—
58C2×C4×D23D414yes—
59C4⋊C4×C23—22no—
60C22⋊C4×C23—44no—
61C42×C23—22no—
62C22⋊Dic23—44no—
63(C2×D23)⋊C4—24no—
64(C2×D23)⋊C4—24no—
65(C2×D23)⋊C4—44no—
66(C2×D23)⋊C4—44no—
67C4⋊Dic23—22no—
68Dic23⋊C4—24no—
69C4×Dic23—22no—
70C4×Dic23—24no—
71C23×C23—22no—
72C23×C23—22no—
73C23×C23—24no—
74C23×C23—24no—
75C23×C23C22×C414yes—
76C23×C23C2411yescharacteristic
77C22×D23—22no—
78C22×D23—22no—
79C22×D23—22no—
80C22×D23—22no—
81C22×D23—24no—
82C22×D23—24no—
83C22×D23—216no—
84C22×D23—416no—
85C22×D23—48no—
86C22×D23—416no—
87C22×D23—48no—
88C22×D23C22×C414yes—
89C22×D23C22×C412yes—
90C22×D23C2×D412yes—
91C22×D23C2×D412yes—
92D4×C23—28no—
93C2×C4×C23—22no—
94C2×C4×C23—22no—
95C2×C4×C23—22no—
96C2×C4×C23—24no—
97C2×C4×C23—22no—
98C2×C4×C23C22×C412yes—
99C2×C4×C23C2×D412yes—
100C2×C4×C23C2×D412yes—
101C22⋊D23—216no—
102C2×Dic23—22no—
103C2×Dic23—22no—
104C2×Dic23—22no—
105C2×Dic23—24no—
106C2×Dic23—22no—
107C2×Dic23C22×C412yes—
108C2×Dic23C2×D412yes—
109C2×Dic23C2×D412yes—
110D92—28no—
111C4×D23C22⋊C4116yescomplemented
112#2309—231nomaximal, Sylow
113C22×C23—24no—
114C22×C23—28no—
115C22×C23—42no—
116C22×C23—44no—
117C22×C23—42no—
118C22×C23C23×C411yescharacteristic
119C22×C23C22×D411yescharacteristic
120C22×C23C22×D411yescharacteristic
121C22×C23H(5,𝔽2)12yes—
122C22×C23H(5,𝔽2)12yes—
123C2×D23—24no—
124C2×D23—22no—
125C2×D23—24no—
126C2×D23—22no—
127C2×D23—24no—
128C2×D23—28no—
129C2×D23—432no—
130C2×D23—42no—
131C2×D23—44no—
132C2×D23—42no—
133C2×D23C2×C22⋊C414yes—
134C4×C23—42no—
135C4×C23—42no—
136C4×C23C2×C22⋊C414yes—
137Dic23—42no—
138Dic23—42no—
139Dic23C2×C22⋊C414yes—
140C23×D4—231no—
141C2×#117—231no—
142C2×#117—231no—
143#390—231no—
144#390—231no—
145#390—234no—
146#390—231no—
147#390D2311yescharacteristic, complemented
148#379—234no—
149C2×C23—44no—
150C2×C23C22×C22⋊C411yescharacteristic
151C2×C23#51812yes—
152C2×C23#53511yescharacteristic
153C2×C23#53512yes—
154C2×C23#53511yescharacteristic
155D23—24no—
156D23—44no—
157C25—232no—
158C22×D4—232no—
159C22×D4—238no—
160C22×D4—231no—
161C22×D4—464no—
162C22×D4—464no—
163C22×D4C2×D2311yescharacteristic
164C23×C4—231no—
165#117—464no—
166#117—464no—
167C2×C4⋊C4—232no—
168C2×C4⋊C4—231no—
169C2×C4⋊C4C2×D2311yescharacteristic, complemented
170C2×C22⋊C4—232no—
171C2×C22⋊C4—232no—
172C2×C22⋊C4—234no—
173C2×C22⋊C4—234no—
174C2×C22⋊C4—234no—
175C2×C22⋊C4C2×D2314yescomplemented
176C2×C42—232no—
177C2×C42—231no—
178C2×C42C2×D2311yescharacteristic, complemented
179C23#230911yescharacteristic, complemented, Sylow
180C24—231no—
181C24—232no—
182C24—238no—
183C24—464no—
184C24—464no—
185C24—924no—
186C24—924no—
187C24C22×D2312yes—
188C2×D4—22no—
189C2×D4—22no—
190C2×D4—238no—
191C2×D4—234no—
192C2×D4—4632no—
193C2×D4—464no—
194C2×D4—464no—
195C2×D4—462no—
196C2×D4—462no—
197C2×D4C4×D2314yes—
198C22×C4—231no—
199C22×C4—234no—
200C22×C4—234no—
201C22×C4—234no—
202C22×C4—232no—
203C22×C4—232no—
204C22×C4C22×D2312yes—
205C22×C4C22×D2312yes—
206C22×C4C22×D2311yescharacteristic
207C4⋊C4—22no—
208C4⋊C4—464no—
209C4⋊C4—462no—
210C22⋊C4—44no—
211C22⋊C4—464no—
212C22⋊C4—464no—
213C22⋊C4—924no—
214C22⋊C4—924no—
215C22⋊C4—924no—
216C42—22no—
217C42—464no—
218C42—462no—
219C23—22no—
220C23—22no—
221C23—24no—
222C23—24no—
223C23—232no—
224C23—232no—
225C23—232no—
226C23—234no—
227C23—4616no—
228C23—462no—
229C23—462no—
230C23—462no—
231C23—462no—
232C23—464no—
233C23—464no—
234C23—9216no—
235C23—928no—
236C23—9216no—
237C23—928no—
238C23C2×C4×D2314yes—
239C23C23×D2311yescharacteristic
240D4—28no—
241D4—4616no—
242D4—468no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—24no—
247C2×C4—22no—
248C2×C4—232no—
249C2×C4—232no—
250C2×C4—232no—
251C2×C4—2316no—
252C2×C4—462no—
253C2×C4—462no—
254C2×C4—462no—
255C2×C4—462no—
256C2×C4—464no—
257C2×C4C2×C4×D2312yes—
258C2×C4D4×D2312yes—
259C2×C4D4×D2312yes—
260C22—28no—
261C22—24no—
262C22—42no—
263C22—44no—
264C22—42no—
265C22—234no—
266C22—464no—
267C22—462no—
268C22—464no—
269C22—462no—
270C22—468no—
271C22—464no—
272C22—9232no—
273C22—922no—
274C22—924no—
275C22—922no—
276C22C22×C4×D2311yescharacteristic
277C22C2×D4×D2311yescharacteristic
278C22C2×D4×D2311yescharacteristic
279C22#1062515512yes—
280C22#1062516012yes—
281C4—42no—
282C4—42no—
283C4—234no—
284C4—922no—
285C4—922no—
286C4C22⋊C4×D2314yes—
287C2—44no—
288C2—464no—
289C2—924no—
290C2C2×C22⋊C4×D2311yescharacteristic
291C2#1309288912yes—
292C2#1309298011yescharacteristic
293C2#1309298312yes—
294C2#1309298511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D23
commutatorC22×C23C23×C4
FittingC23×#390C2
socle, cosocleC23×C23C24
prime radicalC22×D4×D23C2
hypercenter#390D23
hypocenterC23#2309
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×#10625063C2semidirect
3. C2×#10625043C2semidirect
4. #13092320C2semidirect
5. #13092319C2semidirect
6. #13092318C2semidirect
7. #13092317C2semidirect
8. #13092272C2semidirect
9. C23×#390C2semidirect
15. C2×D4×D23C4semidirect
18. C2×C4⋊C4×C23C22semidirect
19. C2×C22⋊C4×C23C22semidirect
20. C2×C42×C23C22semidirect
21. C2×C22⋊Dic23C22semidirect
24. C2×(C2×D23)⋊C4C22semidirect
25. C2×(C2×D23)⋊C4C22semidirect
26. C2×C4⋊Dic23C22semidirect
27. C2×Dic23⋊C4C22semidirect
28. C2×C4×Dic23C22semidirect
29. C2×C4×Dic23C22semidirect
111. C4×D23C22⋊C4semidirect
147. #390D23semidirect
169. C2×C4⋊C4C2×D23semidirect
175. C2×C22⋊C4C2×D23semidirect
178. C2×C42C2×D23semidirect
179. C23#2309semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D232
C2×#106250632
C2×#106250432
#130923202
#130923192
#130923182
#130923172
#130922722
C23×#3902
#230923