Finite Group Databasebeta

← #15685179

Subgroups — #15685179

Order 2944.

454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 125 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#13093231C211yesmaximal, characteristic, complemented
2#13093228C212yesmaximal, complemented
3#13092800C211yesmaximal, characteristic, complemented
4#13092692C211yesmaximal, characteristic, complemented
5#13092684C211yesmaximal, characteristic, complemented
6#13092678C212yesmaximal, complemented
7#13092595C212yesmaximal, complemented
8#13092588C212yesmaximal, complemented
9#13092534C211yesmaximal, characteristic, complemented
10#13092532C211yesmaximal, characteristic, complemented
11C23×#576C211yesmaximal, characteristic, complemented
12C23×H(5,𝔽2)C2212yes—
13#10625161C2212yescomplemented
14C23×AGL(1,ℤ/8)—22no—
15C23×AGL(1,ℤ/8)C2212yes—
16C23×#135—21no—
17C23×#135C2211yescharacteristic
18C2×D8×C23—21no—
19C2×D8×C23C2211yescharacteristic
20C23×#131C2211yescharacteristic
21#10625122—22no—
22#10625122C2212yes—
23#10625122C2212yescomplemented
24#10625121—22no—
25#10625121C2211yescharacteristic
26#10625119C2212yescomplemented
27#10625107C2212yescomplemented
28C2×#67273—22no—
29C2×#67273C2212yescomplemented
30#10625103—22no—
31#10625103C2212yescomplemented
32Q16×D23—21no—
33#10625086—22no—
34#10625083—21no—
35C2×Dic92C2211yescharacteristic, complemented
36#10625072C2211yescharacteristic, complemented
37#10625019C2211yescharacteristic
38#10625019C2212yescomplemented
39#10625015C2212yescomplemented
40#10625007C2211yescharacteristic, complemented
41#10625006C2212yescomplemented
42#10625004C2211yescharacteristic, complemented
43#10625001C2211yescharacteristic, complemented
44C8×Dic23C2211yescharacteristic, complemented
45#41×C23—22no—
46#41×C23—22no—
47#41×C23C2312yes—
48#41×C23C2311yescharacteristic
49C2×D4×C23—22no—
50C2×D4×C23—22no—
51C2×D4×C23—42no—
52C2×D4×C23C2312yes—
53Q8×D23—22no—
54#67290—22no—
55#67290—42no—
56#67288—22no—
57#67288C2311yescharacteristic
58C2×Dic46—22no—
59C2×Dic46C2312yes—
60Q16×C23D411yescharacteristic
61SD16×C23—22no—
62SD16×C23D412yes—
63D8×C23—22no—
64D8×C23—21no—
65D8×C23—21no—
66D8×C23D411yescharacteristic
67M16×C23—21no—
68M16×C23C2311yescharacteristic
69C2×C8×C23—21no—
70C2×C8×C23C2311yescharacteristic
71C22⋊Dic23—42no—
72#67275—22no—
73#67275—22no—
74#67275D411yescharacteristic
75#67274D411yescharacteristic
76#67273—22no—
77#67273—22no—
78#67273—22no—
79#67273—22no—
80#67273—22no—
81#67273D411yescharacteristic
82#67272—22no—
83#67272D411yescharacteristic
84C4×Dic23C2311yescharacteristic
85#67267—22no—
86#67267C2311yescharacteristic
87#67267C2312yes—
88C2×C23⋊C8—22no—
89C2×C23⋊C8C2311yescharacteristic
90Dic92—21no—
91Dic92—21no—
92#67262—21no—
93C8×D23—21no—
94C23×C23—22no—
95C23×C23—42no—
96Q8×C23C2×D411yescharacteristic
97Q8×C23C2×D412yes—
98D4×C23—22no—
99D4×C23—21no—
100D4×C23—22no—
101D4×C23—22no—
102D4×C23—42no—
103D4×C23—42no—
104D4×C23C2×D411yescharacteristic
105D4×C23C2×D412yes—
106C2×C4×C23—22no—
107C2×C4×C23—21no—
108C2×C4×C23—42no—
109C2×C4×C23C2411yescharacteristic
110C22⋊D23—21no—
111C22⋊D23—42no—
112C2×Dic23—21no—
113C2×Dic23—22no—
114C2×Dic23—42no—
115D92C2×D411yescharacteristic
116C4×D23—21no—
117C4×D23—42no—
118Dic46—22no—
119Dic46—22no—
120Dic46—42no—
121Dic46C2×D411yescharacteristic
122C8×C23—21no—
123C8×C23C2×D411yescharacteristic
124C8×C23C2×D411yescharacteristic
125C23⋊C8—21no—
126C23⋊C8—22no—
127C23⋊C8C2×D411yescharacteristic
128C23⋊C8C2×D411yescharacteristic
129#3290—231nomaximal, Sylow
130C22×C23—22no—
131C22×C23—21no—
132C22×C23—42no—
133C22×C23—82no—
134C22×C23—162no—
135C22×C23H(5,𝔽2)11yescharacteristic
136C2×D23—21no—
137C4×C23—22no—
138C4×C23—21no—
139C4×C23C22×D411yescharacteristic
140C4×C23C22×D411yescharacteristic
141Dic23—21no—
142Dic23—41no—
143Dic23—42no—
144#578—231no—
145#577—232no—
146#576D2311yescharacteristic, complemented
147#495—231no—
148#473—231no—
149#472—231no—
150#471—232no—
151#455—232no—
152#454—232no—
153#443—231no—
154#443—231no—
155C2×C23—21no—
156C2×C23—42no—
157C2×C23—41no—
158C2×C23—82no—
159C2×C23D4211yescharacteristic
160D23—41no—
1612−1+4—232no—
162H(5,𝔽2)C2×D2312yes—
163#137—232no—
164#137—232no—
165#137—462no—
166#137—462no—
167AGL(1,ℤ/8)—22no—
168AGL(1,ℤ/8)—232no—
169AGL(1,ℤ/8)—462no—
170AGL(1,ℤ/8)C2×D2312yes—
171#135—21no—
172#135—231no—
173#135—462no—
174#135—461no—
175#135C2×D2311yescharacteristic
176C2×Q16—231no—
177C2×Q16—461no—
178C2×SD16—232no—
179C2×SD16—462no—
180C2×D8—21no—
181C2×D8C2×D2311yescharacteristic
182#131—232no—
183#131—231no—
184#131C2×D2311yescharacteristic
185#124—232no—
186#108—231no—
187#108—231no—
188#104—232no—
189#104—231no—
190#104—231no—
191#101—232no—
192#100—232no—
193C4×C8—231no—
194C23#329011yescharacteristic, complemented, Sylow
195#41—22no—
196#41—22no—
197#41—231no—
198#41—462no—
199#41—462no—
200#41—922no—
201#41C22×D2311yescharacteristic
202#41C22×D2312yes—
203C2×Q8—232no—
204C2×Q8—462no—
205C2×Q8—462no—
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—42no—
209C2×D4C22×D2312yes—
210Q16—231no—
211Q16—462no—
212Q16—462no—
213Q16—461no—
214Q16—461no—
215Q16C22⋊D2311yescharacteristic
216SD16—22no—
217SD16—231no—
218SD16—231no—
219SD16—462no—
220SD16—462no—
221SD16—462no—
222SD16—462no—
223SD16—462no—
224SD16C22⋊D2312yes—
225D8—22no—
226D8—21no—
227D8—21no—
228D8—231no—
229D8—462no—
230D8C22⋊D2311yescharacteristic
231M16—21no—
232M16—231no—
233M16—232no—
234M16—462no—
235M16—461no—
236M16C22×D2311yescharacteristic
237C2×C8—21no—
238C2×C8—231no—
239C2×C8—462no—
240C2×C8—461no—
241C2×C8C22×D2311yescharacteristic
242C22⋊C4—922no—
243C42—231no—
244C23—22no—
245C23—42no—
246Q8—231no—
247Q8—462no—
248Q8—462no—
249Q8—922no—
250Q8D4×D2311yescharacteristic
251Q8C2×C22⋊D2312yes—
252D4—21no—
253D4—22no—
254D4—22no—
255D4—22no—
256D4—42no—
257D4—42no—
258D4—231no—
259D4—461no—
260D4—922no—
261D4D4×D2311yescharacteristic
262D4C2×C22⋊D2312yes—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—42no—
266C2×C4—461no—
267C2×C4—461no—
268C2×C4—462no—
269C2×C4—922no—
270C2×C4—922no—
271C2×C4C23×D2311yescharacteristic
272C8—21no—
273C8—231no—
274C8—231no—
275C8—462no—
276C8—461no—
277C8C2×C22⋊D2311yescharacteristic
278C8C2×C22⋊D2311yescharacteristic
279C22—22no—
280C22—21no—
281C22—42no—
282C22—82no—
283C22—162no—
284C22—461no—
285C22#1062515511yescharacteristic
286C4—21no—
287C4—22no—
288C4—461no—
289C4—921no—
290C4—922no—
291C4C2×D4×D2311yescharacteristic
292C4C22×C22⋊D2311yescharacteristic
293C2—21no—
294C2—41no—
295C2—42no—
296C2—82no—
297C2—921no—
298C2D4×C22⋊D2311yescharacteristic
subgroupG/H
centerC2D4×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#576C2
socleC2×C23D42
hypercenter#576D23
hypocenterC23#3290
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ #576

Complements

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

NH ≅ G/Ntype
1. #13093231C2semidirect
2. #13093228C2semidirect
3. #13092800C2semidirect
4. #13092692C2semidirect
5. #13092684C2semidirect
6. #13092678C2semidirect
7. #13092595C2semidirect
8. #13092588C2semidirect
9. #13092534C2semidirect
10. #13092532C2semidirect
11. C23×#576C2semidirect
13. #10625161C22semidirect
23. #10625122C22semidirect
26. #10625119C22semidirect
27. #10625107C22semidirect
29. C2×#67273C22semidirect
31. #10625103C22semidirect
35. C2×Dic92C22semidirect
36. #10625072C22semidirect
38. #10625019C22semidirect
39. #10625015C22semidirect
40. #10625007C22semidirect
41. #10625006C22semidirect
42. #10625004C22semidirect
43. #10625001C22semidirect
44. C8×Dic23C22semidirect
146. #576D23semidirect
194. C23#3290semidirect

Maximal subgroups

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

subgroupindex
#130932312
#130932282
#130928002
#130926922
#130926842
#130926782
#130925952
#130925882
#130925342
#130925322
C23×#5762
#329023