Finite Group Databasebeta

← #15685182

Subgroups — #15685182

Order 2944.

454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 117 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#13093230C211yesmaximal, characteristic, complemented
2#13093223C212yesmaximal, complemented
3#13093218C211yesmaximal, characteristic, complemented
4#13092689C211yesmaximal, characteristic, complemented
5#13092684C211yesmaximal, characteristic, complemented
6#13092677C212yesmaximal, complemented
7#13092594C212yesmaximal, complemented
8#13092589C212yesmaximal, complemented
9#13092535C211yesmaximal, characteristic, complemented
10#13092535C211yesmaximal, characteristic, complemented
11C23×#495C211yesmaximal, characteristic, complemented
12#10625158C2212yescomplemented
13#10625155C2212yes—
14C2×Q16×C23C2211yescharacteristic, complemented
15C2×SD16×C23C2212yescomplemented
16C2×D8×C23C2211yescharacteristic
17C23×#124C2212yescomplemented
18#10625113C2212yes—
19#10625113C2212yescomplemented
20#10625103C2212yes—
21#10625103C2212yescomplemented
22#10625090—21no—
23#10625089—22no—
24Q16×D23—21no—
25#10625087—22no—
26#10625086—22no—
27#10625085—22no—
28SD16×D23—22no—
29#10625083—21no—
30#10625082—22no—
31D8×D23—21no—
32#10625075C2211yescharacteristic
33#10625075C2211yescharacteristic
34#10625072C2211yescharacteristic
35#10625072C2212yescomplemented
36#10625072C2211yescharacteristic, complemented
37C4×C8×C23C2211yescharacteristic, complemented
38#10625018C2212yescomplemented
39#10625015C2212yescomplemented
40#10625001C2211yescharacteristic, complemented
41#10625001C2211yescharacteristic, complemented
42#10624987C2211yescharacteristic
43#10624987C2211yescharacteristic, complemented
44#10624987C2212yescomplemented
45C2×Q8×C23C2312yes—
46C2×D4×C23C2312yes—
47C2×C22⋊D23—42no—
48#67292—22no—
49#67292—22no—
50Q8×D23—22no—
51Q8×D23—22no—
52#67290—22no—
53#67290—22no—
54D4×D23—22no—
55D4×D23—22no—
56#67288—42no—
57#67288C2311yescharacteristic
58#67288C2312yes—
59#67288C2311yescharacteristic
60Q16×C23—21no—
61Q16×C23—21no—
62SD16×C23—22no—
63SD16×C23—22no—
64D8×C23—21no—
65D8×C23—21no—
66C2×C8×C23C2311yescharacteristic
67C2×C8×C23C2311yescharacteristic
68C22⋊C4×C23—42no—
69C42×C23C2311yescharacteristic
70#67275—22no—
71#67275—22no—
72#67274—22no—
73#67274—22no—
74#67273—22no—
75#67273—22no—
76#67272—22no—
77#67272—22no—
78#67267C2311yescharacteristic
79#67267C2312yes—
80#67267C2311yescharacteristic
81Dic92D411yescharacteristic
82Dic92D411yescharacteristic
83D184D411yescharacteristic
84D184D411yescharacteristic
85#67263D412yes—
86#67263D411yescharacteristic
87#67263D411yescharacteristic
88#67262—21no—
89#67262—22no—
90#67262—21no—
91C8×D23—21no—
92C8×D23—22no—
93C8×D23—21no—
94C23×C23—22no—
95C22×D23—42no—
96Q8×C23—22no—
97Q8×C23—22no—
98D4×C23—22no—
99D4×C23—22no—
100C2×C4×C23—21no—
101C2×C4×C23—22no—
102C2×C4×C23C2411yescharacteristic
103C22⋊D23—21no—
104C22⋊D23—22no—
105C22⋊D23—21no—
106C22⋊D23—42no—
107C22⋊D23—42no—
108C2×Dic23—42no—
109D92—42no—
110D92C2×D411yescharacteristic
111D92C2×D412yes—
112D92C2×D411yescharacteristic
113C4×D23—21no—
114C4×D23—22no—
115C4×D23—21no—
116C4×D23—42no—
117C4×D23—42no—
118Dic46—42no—
119Dic46C2×D411yescharacteristic
120Dic46C2×D412yes—
121Dic46C2×D411yescharacteristic
122C8×C23C2×D411yescharacteristic
123C8×C23C2×D411yescharacteristic
124C8×C23C2×D411yescharacteristic
125C8×C23C2×D411yescharacteristic
126C23⋊C8—21no—
127C23⋊C8—22no—
128C23⋊C8—21no—
129#3290—231nomaximal, Sylow
130C22×C23—42no—
131C22×C23—82no—
132C22×C23H(5,𝔽2)11yescharacteristic
133C2×D23—21no—
134C2×D23—22no—
135C2×D23—21no—
136C2×D23—162no—
137C4×C23—41no—
138C4×C23—42no—
139C4×C23C22×D411yescharacteristic
140C4×C23C22×D411yescharacteristic
141Dic23—21no—
142Dic23—22no—
143Dic23—21no—
144#578—231no—
145#577—232no—
146#576—231no—
147#495D2311yescharacteristic, complemented
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—82no—
157C2×C23D4211yescharacteristic
158D23—41no—
159D23—42no—
160D23—41no—
1612−1+4—232no—
162H(5,𝔽2)—232no—
163#137—232no—
164#137—232no—
165#137—462no—
166#137—462no—
167AGL(1,ℤ/8)—232no—
168AGL(1,ℤ/8)—232no—
169AGL(1,ℤ/8)—462no—
170AGL(1,ℤ/8)—462no—
171#135—231no—
172#135—231no—
173#135—461no—
174#135—461no—
175#135—462no—
176C2×Q16—461no—
177C2×Q16C2×D2311yescharacteristic, complemented
178C2×SD16—462no—
179C2×SD16C2×D2312yescomplemented
180C2×D8—461no—
181C2×D8C2×D2311yescharacteristic
182#131—231no—
183#131—232no—
184#131—231no—
185#124C2×D2312yescomplemented
186#108—231no—
187#108—231no—
188#104—231no—
189#104—232no—
190#104—231no—
191#101—232no—
192#100—232no—
193C4×C8C2×D2311yescharacteristic, complemented
194C23#329011yescharacteristic, complemented, Sylow
195#41—231no—
196#41—232no—
197#41—231no—
198#41—462no—
199#41—462no—
200#41—462no—
201#41—462no—
202#41—922no—
203C2×Q8—462no—
204C2×Q8—462no—
205C2×Q8C22×D2312yes—
206C2×D4—462no—
207C2×D4—462no—
208C2×D4—922no—
209C2×D4C22×D2312yes—
210Q16—21no—
211Q16—21no—
212Q16—231no—
213Q16—231no—
214Q16—462no—
215Q16—462no—
216SD16—22no—
217SD16—22no—
218SD16—231no—
219SD16—231no—
220SD16—232no—
221SD16—462no—
222SD16—462no—
223SD16—462no—
224SD16—462no—
225D8—21no—
226D8—21no—
227D8—231no—
228D8—231no—
229D8—462no—
230D8—462no—
231M16—231no—
232M16—232no—
233M16—231no—
234M16—461no—
235M16—462no—
236M16—461no—
237C2×C8—461no—
238C2×C8—462no—
239C2×C8—461no—
240C2×C8C22×D2311yescharacteristic
241C2×C8C22×D2311yescharacteristic
242C22⋊C4—42no—
243C42C22×D2311yescharacteristic
244C23—22no—
245C23—922no—
246Q8—22no—
247Q8—22no—
248Q8—231no—
249Q8—232no—
250Q8—231no—
251Q8—922no—
252D4—22no—
253D4—22no—
254D4—231no—
255D4—232no—
256D4—231no—
257D4—461no—
258D4—462no—
259D4—461no—
260D4—922no—
261D4—922no—
262D4—922no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—461no—
266C2×C4—462no—
267C2×C4—461no—
268C2×C4—922no—
269C2×C4—922no—
270C2×C4—922no—
271C2×C4C23×D2311yescharacteristic
272C8—461no—
273C8—462no—
274C8—461no—
275C8D4×D2311yescharacteristic
276C8D4×D2311yescharacteristic
277C8D4×D2311yescharacteristic
278C8D4×D2311yescharacteristic
279C22—42no—
280C22—82no—
281C22—461no—
282C22—462no—
283C22—461no—
284C22—3682no—
285C22#1062515511yescharacteristic
286C4—41no—
287C4—42no—
288C4—461no—
289C4—462no—
290C4—461no—
291C4C2×D4×D2311yescharacteristic
292C4C2×D4×D2311yescharacteristic
293C2—21no—
294C2—82no—
295C2—921no—
296C2—922no—
297C2—921no—
298C2#1309305211yescharacteristic
subgroupG/H
centerC2#13093052
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#495C2
socleC2×C23D42
hypercenter#495D23
hypocenterC23#3290
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #13093230C2semidirect
2. #13093223C2semidirect
3. #13093218C2semidirect
4. #13092689C2semidirect
5. #13092684C2semidirect
6. #13092677C2semidirect
7. #13092594C2semidirect
8. #13092589C2semidirect
9. #13092535C2semidirect
10. #13092535C2semidirect
11. C23×#495C2semidirect
12. #10625158C22semidirect
14. C2×Q16×C23C22semidirect
15. C2×SD16×C23C22semidirect
17. C23×#124C22semidirect
19. #10625113C22semidirect
21. #10625103C22semidirect
35. #10625072C22semidirect
36. #10625072C22semidirect
37. C4×C8×C23C22semidirect
38. #10625018C22semidirect
39. #10625015C22semidirect
40. #10625001C22semidirect
41. #10625001C22semidirect
43. #10624987C22semidirect
44. #10624987C22semidirect
147. #495D23semidirect
177. C2×Q16C2×D23semidirect
179. C2×SD16C2×D23semidirect
185. #124C2×D23semidirect
193. C4×C8C2×D23semidirect
194. C23#3290semidirect

Maximal subgroups

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

subgroupindex
#130932302
#130932232
#130932182
#130926892
#130926842
#130926772
#130925942
#130925892
#130925352
C23×#4952
#329023