Finite Group Databasebeta

← #15676634

Subgroups — #15676634

Order 2944.

696 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 696 conjugacy classes of subgroups — too many to draw. Only its 151 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×#10625064C211yesmaximal, characteristic, complemented
2C2×(C22⋊D23)⋊C4C212yesmaximal, complemented
3C2×#10625048C211yesmaximal, characteristic, complemented
4#13092348C211yesmaximal, characteristic, complemented
5#13092341C212yesmaximal, complemented
6#13092335C211yesmaximal, characteristic, complemented
7#13092332C212yesmaximal, complemented
8#13092326C211yesmaximal, characteristic
9#13092268C211yesmaximal, characteristic, complemented
10#13092264C212yesmaximal, complemented
11C23×#397C211yesmaximal, characteristic, complemented
12C22×C22⋊D23C2212yes—
13C23×Dic23C2211yescharacteristic
14C22×D92C2211yescharacteristic
15C22×C4×D23C2212yes—
16C2×C4⋊C4×C23C2211yescharacteristic
17C2×C22⋊C4×C23C2211yescharacteristic
18C2×C22⋊C4×C23C2212yes—
19C2×C22⋊Dic23C2211yescharacteristic
20C2×(C2×D23)⋊C4C2212yes—
21C2×(C2×D23)⋊C4C2212yes—
22C2×(C2×D23)⋊C4C2212yes—
23C2×(C2×D23)⋊C4C2212yes—
24C2×Dic23⋊C4C2211yescharacteristic
25C2×Dic23⋊C4C2211yescharacteristic
26C2×Dic23⋊C4C2212yes—
27C2×Dic23⋊C4C2212yes—
28C2×C4×Dic23C2211yescharacteristic
29C2×C4×Dic23C2212yes—
30C2×C4×Dic23C2211yescharacteristic
31#10625064—24no—
32(C22⋊D23)⋊C4—28no—
33#10625048—24no—
34C23×#95C2212yes—
35C23×#95C2211yescharacteristic
36C23⋊#95C2212yes—
37C23⋊#95C2211yescharacteristic
38C24×C23C2311yescharacteristic
39C23×D23C2312yes—
40C22×C4×C23C2311yescharacteristic
41C22×C4×C23C2312yes—
42C22×C4×C23C2312yes—
43C22×C4×C23C2311yescharacteristic
44C2×C22⋊D23—24no—
45C2×C22⋊D23—24no—
46C2×C22⋊D23—24no—
47C22×Dic23—22no—
48C22×Dic23—22no—
49C22×Dic23D414yescomplemented
50C22×Dic23C2311yescharacteristic
51C22×Dic23C2311yescharacteristic
52C22×Dic23C2311yescharacteristic
53C22×Dic23C2312yes—
54C22×Dic23C2311yescharacteristic
55C2×D92—24no—
56C2×D92—22no—
57C2×C4×D23—24no—
58C2×C4×D23—24no—
59C2×C4×D23—24no—
60C4⋊C4×C23—22no—
61C22⋊C4×C23—24no—
62C22⋊C4×C23—22no—
63C22⋊Dic23—22no—
64(C2×D23)⋊C4—24no—
65(C2×D23)⋊C4—24no—
66(C2×D23)⋊C4—24no—
67(C2×D23)⋊C4—24no—
68Dic23⋊C4—22no—
69Dic23⋊C4—22no—
70Dic23⋊C4—24no—
71Dic23⋊C4—24no—
72C4×Dic23—22no—
73C4×Dic23—24no—
74C4×Dic23D414yescomplemented
75C23×C23—21no—
76C23×C23—21no—
77C23×C23—22no—
78C23×C23—22no—
79C23×C23C2×D412yes—
80C23×C23C2411yescharacteristic
81C22×D23—22no—
82C22×D23—22no—
83C22×D23—22no—
84C22×D23—22no—
85C22×D23—22no—
86C22×D23—22no—
87C22×D23#4114yes—
88C2×C4×C23—22no—
89C2×C4×C23—21no—
90C2×C4×C23—22no—
91C2×C4×C23—22no—
92C2×C4×C23—22no—
93C2×C4×C23—22no—
94C2×C4×C23—22no—
95C2×C4×C23—22no—
96C2×C4×C23—22no—
97C2×C4×C23C2×D412yes—
98C22⋊D23—216no—
99C2×Dic23—22no—
100C2×Dic23—21no—
101C2×Dic23—22no—
102C2×Dic23—21no—
103C2×Dic23—22no—
104C2×Dic23—28no—
105C2×Dic23—21no—
106C2×Dic23—22no—
107C2×Dic23C2×D412yes—
108C2×Dic23C2×D412yes—
109C2×Dic23C2×D412yes—
110C2×Dic23C2×D412yes—
111C2×Dic23#4114yes—
112C2×Dic23#4112yes—
113D92—28no—
114C4×D23—48no—
115#2392—231nomaximal, Sylow
116C22×C23—22no—
117C22×C23—24no—
118C22×C23—41no—
119C22×C23—42no—
120C22×C23—41no—
121C22×C23C22×D411yescharacteristic
122C22×C23C22×D411yescharacteristic
123C22×C23C2×#4111yescharacteristic
124C22×C23C2×#4112yes—
125C22×C23C2×#4112yes—
126C2×D23—24no—
127C2×D23—24no—
128C2×D23—24no—
129C2×D23—42no—
130C2×D23—42no—
131C2×D23—42no—
132C2×D23—42no—
133C4×C23—22no—
134C4×C23—42no—
135C4×C23—42no—
136C4×C23—41no—
137Dic23—22no—
138Dic23—24no—
139Dic23—22no—
140Dic23—41no—
141Dic23#12114yes—
142C2×C4×D4—231no—
143C2×C4×D4—232no—
144C2×#117—231no—
145#398—231no—
146#397D2311yescharacteristic, complemented
147#396—232no—
148#394—232no—
149#394—231no—
150#392—231no—
151C4×C4⋊C4—231no—
152C4×C22⋊C4—232no—
153C2×C23—42no—
154C2×C23C2×#12111yescharacteristic
155C2×C23#52512yes—
156C2×C23#52511yescharacteristic
157C2×C23#52912yes—
158C2×C23#53211yescharacteristic
159D23—44no—
160C22×D4—232no—
161C22×D4—231no—
162C23×C4—231no—
163C23×C4—232no—
164C4×D4—464no—
165C4×D4—468no—
166#117—464no—
167C2×C4⋊C4—231no—
168C2×C4⋊C4—231no—
169C2×C4⋊C4—232no—
170C2×C4⋊C4—232no—
171C2×C4⋊C4C2×D2311yescharacteristic
172C2×C22⋊C4—231no—
173C2×C22⋊C4—232no—
174C2×C22⋊C4—232no—
175C2×C22⋊C4—232no—
176C2×C22⋊C4—232no—
177C2×C22⋊C4C2×D2311yescharacteristic
178C2×C22⋊C4C2×D2312yes—
179C2×C42—231no—
180C2×C42—231no—
181C2×C42—232no—
182#95—232no—
183#95—231no—
184#95C2×D2312yes—
185#95C2×D2311yescharacteristic
186C23#239211yescharacteristic, complemented, Sylow
187C24—232no—
188C24C22×D2311yescharacteristic
189C2×D4—464no—
190C2×D4—464no—
191C2×D4—464no—
192C2×D4—464no—
193C2×D4—462no—
194C22×C4—231no—
195C22×C4—234no—
196C22×C4—232no—
197C22×C4—231no—
198C22×C4—231no—
199C22×C4—231no—
200C22×C4—464no—
201C22×C4—464no—
202C22×C4—464no—
203C22×C4—462no—
204C22×C4—462no—
205C22×C4C22×D2312yes—
206C22×C4C22×D2312yes—
207C22×C4C22×D2311yescharacteristic
208C22×C4C22×D2311yescharacteristic
209C4⋊C4—22no—
210C4⋊C4—462no—
211C4⋊C4—464no—
212C4⋊C4—464no—
213C4⋊C4—462no—
214C22⋊C4—24no—
215C22⋊C4—22no—
216C22⋊C4—464no—
217C22⋊C4—464no—
218C22⋊C4—464no—
219C22⋊C4—464no—
220C22⋊C4—462no—
221C42—234no—
222C42—462no—
223C42—464no—
224C23—21no—
225C23—21no—
226C23—22no—
227C23—22no—
228C23—234no—
229C23—462no—
230C23—462no—
231C23—462no—
232C23—462no—
233C23—462no—
234C23—462no—
235C23D4×D2312yes—
236C23C23×D2311yescharacteristic
237D4—468no—
238D4—4616no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—232no—
249C2×C4—232no—
250C2×C4—232no—
251C2×C4—232no—
252C2×C4—232no—
253C2×C4—234no—
254C2×C4—468no—
255C2×C4—462no—
256C2×C4—461no—
257C2×C4—462no—
258C2×C4—461no—
259C2×C4—462no—
260C2×C4—461no—
261C2×C4—462no—
262C2×C4—928no—
263C2×C4D4×D2312yes—
264C22—22no—
265C22—24no—
266C22—41no—
267C22—42no—
268C22—41no—
269C22—464no—
270C22—464no—
271C22—464no—
272C22—922no—
273C22—922no—
274C22—922no—
275C22—922no—
276C22C2×D4×D2311yescharacteristic
277C22C2×D4×D2311yescharacteristic
278C22#41×D2311yescharacteristic
279C22#41×D2312yes—
280C22#41×D2312yes—
281C4—22no—
282C4—42no—
283C4—42no—
284C4—41no—
285C4—234no—
286C4—462no—
287C4—464no—
288C4—462no—
289C4—921no—
290C2—42no—
291C2—924no—
292C2#121×D2311yescharacteristic
293C2#1309292511yescharacteristic
294C2#1309292512yes—
295C2#1309295012yes—
296C2#1309296611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D23
commutator, socle, cosocleC23×C23C24
FittingC23×#397C2
prime radical#13092326C2
hypercenter#397D23
hypocenterC23#2392
LCSG ▷ C23×C23 ▷ C23
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#10625064C2semidirect
2. C2×(C22⋊D23)⋊C4C2semidirect
3. C2×#10625048C2semidirect
4. #13092348C2semidirect
5. #13092341C2semidirect
6. #13092335C2semidirect
7. #13092332C2semidirect
9. #13092268C2semidirect
10. #13092264C2semidirect
11. C23×#397C2semidirect
49. C22×Dic23D4semidirect
74. C4×Dic23D4semidirect
146. #397D23semidirect
186. C23#2392semidirect

Maximal subgroups

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

subgroupindex
C2×#106250642
C2×(C22⋊D23)⋊C42
C2×#106250482
#130923482
#130923412
#130923352
#130923322
#130923262
#130922682
#130922642
C23×#3972
#239223