Finite Group Databasebeta

← #15683030

Subgroups — #15683030

Order 2944.

496 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 135 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×#10625122C211yesmaximal, characteristic, complemented
2C2×M16×D23C211yesmaximal, characteristic, complemented
3#13092924C211yesmaximal, characteristic
4C2×#10625068C211yesmaximal, characteristic, complemented
5#13092674C212yesmaximal, complemented
6#13092662C212yesmaximal, complemented
7#13092657C212yesmaximal, complemented
8#13092645C212yesmaximal, complemented
9#13092457C211yesmaximal, characteristic, complemented
10#13092427C211yesmaximal, characteristic, complemented
11C23×#417C211yesmaximal, characteristic, complemented
12C2×#41×C23C2211yescharacteristic
13C22×C4×D23C2211yescharacteristic
14C22×Dic46C2211yescharacteristic
15C2×M16×C23C2211yescharacteristic
16C2×C4⋊C4×C23C2211yescharacteristic
17#10625122—24no—
18#10625117C2211yescharacteristic
19#10625117C2211yescharacteristic
20C2×#67275C2212yescomplemented
21#10625109C2211yescharacteristic
22#10625109C2211yescharacteristic
23#10625108—21no—
24#10625106—21no—
25C2×#67273C2212yescomplemented
26C4×C22⋊D23—21no—
27C4×C22⋊D23—21no—
28C2×(C2×D23)⋊C4—21no—
29#10625097C2211yescharacteristic
30C2×C4⋊Dic23—21no—
31C2×#67267C2211yescharacteristic
32M16×D23—24no—
33C2×#67262C2212yes—
34C2×C8×D23C2212yes—
35#10625068—21no—
36#10625068—21no—
37#10625068C2212yes—
38#10625068C2212yes—
39C23×#103C2212yescomplemented
40C23×#102C2212yescomplemented
41#10624998C2212yescomplemented
42#10624998C2212yescomplemented
43#10624990C2212yescomplemented
44#10624989C2212yescomplemented
45C23×D23D411yescharacteristic
46#41×C23—22no—
47#41×C23—22no—
48C2×Q8×C23C2311yescharacteristic
49C2×D4×C23—21no—
50C2×D4×C23C2311yescharacteristic
51C22×C4×C23—21no—
52C22×C4×C23—21no—
53C22×C4×C23C2311yescharacteristic
54C2×C22⋊D23—21no—
55C2×C22⋊D23—21no—
56C22×Dic23—21no—
57C22×Dic23D411yescharacteristic
58C2×C4×D23—22no—
59C2×C4×D23—22no—
60C2×C4×D23D411yescharacteristic
61C2×C4×D23D411yescharacteristic
62C2×C4×D23C2311yescharacteristic
63C2×C4×D23C2311yescharacteristic
64C2×Dic46—22no—
65C2×Dic46—22no—
66C2×Dic46—21no—
67C2×Dic46C2312yes—
68M16×C23—22no—
69C2×C8×C23C2312yes—
70C4⋊C4×C23—21no—
71C4⋊C4×C23C2312yes—
72C22⋊Dic23—21no—
73C22⋊Dic23—21no—
74C22⋊Dic23—21no—
75#67275—24no—
76#67273—24no—
77(C2×D23)⋊C4—22no—
78(C2×D23)⋊C4—22no—
79(C2×D23)⋊C4—21no—
80(C2×D23)⋊C4—21no—
81C4⋊Dic23—22no—
82C4⋊Dic23—22no—
83C4⋊Dic23C2311yescharacteristic
84C4⋊Dic23C2311yescharacteristic
85Dic23⋊C4—21no—
86Dic23⋊C4—21no—
87C4×Dic23—21no—
88#67267D414yescomplemented
89C2×C23⋊C8C2312yes—
90#67262—24no—
91C8×D23—24no—
92C23×C23—21no—
93C23×C23C2×D411yescharacteristic
94C22×D23—22no—
95C22×D23—22no—
96C22×D23—41no—
97C22×D23C2×D411yescharacteristic
98C22×D23C2×D411yescharacteristic
99Q8×C23—21no—
100Q8×C23—21no—
101D4×C23—21no—
102D4×C23—21no—
103D4×C23—42no—
104C2×C4×C23—21no—
105C2×C4×C23—22no—
106C2×C4×C23—42no—
107C2×C4×C23—42no—
108C2×C4×C23C2×D411yescharacteristic
109C2×C4×C23C2×D412yes—
110C2×C4×C23#4112yes—
111C2×C4×C23C2411yescharacteristic
112C22⋊D23—42no—
113C22⋊D23—42no—
114C2×Dic23—22no—
115C2×Dic23—21no—
116C2×Dic23—21no—
117C2×Dic23—22no—
118C2×Dic23—42no—
119C2×Dic23C2×D411yescharacteristic
120C2×Dic23C2×D411yescharacteristic
121C4×D23—22no—
122C4×D23—22no—
123C4×D23—21no—
124C4×D23—21no—
125C4×D23—21no—
126C4×D23—21no—
127Dic46—22no—
128Dic46—22no—
129Dic46—42no—
130C8×C23—22no—
131C23⋊C8C2×D414yes—
132#3056—231nomaximal, Sylow
133C22×C23—21no—
134C22×C23—21no—
135C22×C23—41no—
136C22×C23—41no—
137C22×C23—41no—
138C22×C23#12112yes—
139C22×C23C22×D411yescharacteristic
140C2×D23—21no—
141C2×D23—21no—
142C2×D23—21no—
143C2×D23—21no—
144C2×D23—21no—
145C2×D23—44no—
146C2×D23#13712yescomplemented
147C4×C23—41no—
148C4×C23—42no—
149C4×C23#12112yes—
150C4×C23C22×D411yescharacteristic
151C4×C23C2×#4111yescharacteristic
152Dic23—21no—
153Dic23—21no—
154Dic23—42no—
155Dic23—41no—
156Dic23—41no—
157C2×#137—231no—
158C22×M16—231no—
159#525—231no—
160C2×C22⋊Q8—231no—
161#470—232no—
162#468—232no—
163#467—232no—
164#465—232no—
165#428—231no—
166#419—231no—
167#417D2311yescharacteristic, complemented
168C2×C23—22no—
169C2×C23—81no—
170C2×C23C2×#12111yescharacteristic
171C2×C23C2×#13711yescharacteristic
172C2×C23#57511yescharacteristic
173D23—22no—
174D23—41no—
175C2×#41C2×D2311yescharacteristic
176C22×Q8—231no—
177C23×C4—231no—
178#137—464no—
179C2×Q16—232no—
180C2×SD16—232no—
181C2×M16—231no—
182C2×M16—232no—
183C2×M16—464no—
184C2×M16C2×D2311yescharacteristic
185C22×C8—232no—
186#123—461no—
187C22⋊Q8—231no—
188C22⋊Q8—231no—
189C22⋊Q8—232no—
190C22⋊Q8—232no—
191C22⋊Q8—461no—
192C22⋊Q8—461no—
193#121—231no—
194#121—231no—
195#120—461no—
196C4×D4—461no—
197C4×D4—461no—
198#117—231no—
199C2×C4⋊C4—461no—
200C2×C4⋊C4C2×D2311yescharacteristic
201C2×C22⋊C4—461no—
202#107—232no—
203#106—232no—
204#103—232no—
205#103—232no—
206#103C2×D2312yescomplemented
207#102C2×D2312yescomplemented
208C23#305611yescharacteristic, complemented, Sylow
209C24—231no—
210#41—22no—
211#41—22no—
212C2×Q8—232no—
213C2×Q8—461no—
214C2×Q8—462no—
215C2×Q8—462no—
216C2×Q8C22×D2311yescharacteristic
217C2×D4—21no—
218C2×D4—461no—
219C2×D4—461no—
220C2×D4C22×D2311yescharacteristic
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—231no—
224C22×C4—231no—
225C22×C4—231no—
226C22×C4—231no—
227C22×C4—231no—
228C22×C4—462no—
229C22×C4—462no—
230C22×C4—461no—
231C22×C4C22×D2311yescharacteristic
232Q16—464no—
233SD16—464no—
234M16—22no—
235M16—234no—
236M16—464no—
237C2×C8—232no—
238C2×C8—464no—
239C2×C8C22×D2312yes—
240C4⋊C4—21no—
241C4⋊C4—231no—
242C4⋊C4—231no—
243C4⋊C4—462no—
244C4⋊C4—462no—
245C4⋊C4—461no—
246C4⋊C4—461no—
247C4⋊C4C22×D2312yes—
248C22⋊C4—462no—
249C22⋊C4—462no—
250C22⋊C4—461no—
251C22⋊C4—461no—
252C22⋊C4—461no—
253C22⋊C4—461no—
254C22⋊C4—461no—
255C42—461no—
256C23—21no—
257C23—231no—
258C23—231no—
259C23—462no—
260C23—462no—
261C23—921no—
262C23D4×D2311yescharacteristic
263Q8—21no—
264Q8—21no—
265Q8—462no—
266Q8—462no—
267Q8—922no—
268D4—21no—
269D4—21no—
270D4—42no—
271D4—922no—
272D4—922no—
273C2×C4—22no—
274C2×C4—21no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—231no—
278C2×C4—231no—
279C2×C4—462no—
280C2×C4—462no—
281C2×C4—462no—
282C2×C4—461no—
283C2×C4—461no—
284C2×C4—461no—
285C2×C4—461no—
286C2×C4—461no—
287C2×C4—461no—
288C2×C4—462no—
289C2×C4—922no—
290C2×C4#6728812yes—
291C2×C4D4×D2311yescharacteristic
292C2×C4D4×D2312yes—
293C2×C4C23×D2311yescharacteristic
294C8—22no—
295C8—234no—
296C22—21no—
297C22—21no—
298C22—41no—
299C22—41no—
300C22—41no—
301C22—232no—
302C22—461no—
303C22—461no—
304C22—461no—
305C22—461no—
306C22—461no—
307C22—924no—
308C22#1062505512yes—
309C22C2×D4×D2311yescharacteristic
310C4—41no—
311C4—42no—
312C4—461no—
313C4—461no—
314C4—922no—
315C4—921no—
316C4—921no—
317C4#1062505512yes—
318C4C2×#6728811yescharacteristic
319C4C2×D4×D2311yescharacteristic
320C2—22no—
321C2—81no—
322C2—462no—
323C2—921no—
324C2C2×#1062505511yescharacteristic
325C2#137×D2311yescharacteristic
326C2#1309321311yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#417C2
socleC22×C23C22×D4
prime radical#13092924C2
hypercenter#417D23
hypocenterC23#3056
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. C2×#10625122C2semidirect
2. C2×M16×D23C2semidirect
4. C2×#10625068C2semidirect
5. #13092674C2semidirect
6. #13092662C2semidirect
7. #13092657C2semidirect
8. #13092645C2semidirect
9. #13092457C2semidirect
10. #13092427C2semidirect
11. C23×#417C2semidirect
20. C2×#67275C22semidirect
25. C2×#67273C22semidirect
39. C23×#103C22semidirect
40. C23×#102C22semidirect
41. #10624998C22semidirect
42. #10624998C22semidirect
43. #10624990C22semidirect
44. #10624989C22semidirect
88. #67267D4semidirect
146. C2×D23#137semidirect
167. #417D23semidirect
206. #103C2×D23semidirect
207. #102C2×D23semidirect
208. C23#3056semidirect

Maximal subgroups

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

subgroupindex
C2×#106251222
C2×M16×D232
#130929242
C2×#106250682
#130926742
#130926622
#130926572
#130926452
#130924572
#130924272
C23×#4172
#305623