Finite Group Databasebeta

← #15685183

Subgroups — #15685183

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#13093225C212yesmaximal, complemented
2#13093219C211yesmaximal, characteristic, complemented
3#13092802C211yesmaximal, characteristic, complemented
4#13092689C211yesmaximal, characteristic, complemented
5#13092687C211yesmaximal, characteristic, complemented
6#13092682C212yesmaximal, complemented
7#13092593C212yesmaximal, complemented
8#13092590C212yesmaximal, complemented
9#13092534C211yesmaximal, characteristic, complemented
10#13092532C211yesmaximal, characteristic, complemented
11C23×#578C211yesmaximal, characteristic, complemented
12C23×2−1+4C2212yescomplemented
13#10625160C2212yes—
14C23×#137—22no—
15C23×#137C2212yescomplemented
16C23×#135—21no—
17C23×#135C2211yescharacteristic
18C2×Q16×C23—21no—
19C2×Q16×C23C2211yescharacteristic, complemented
20C23×#131C2211yescharacteristic, complemented
21#10625121—22no—
22#10625121C2211yescharacteristic
23#10625120—22no—
24#10625120C2212yes—
25#10625120C2212yescomplemented
26#10625119C2212yescomplemented
27#10625118C2212yescomplemented
28#10625113—22no—
29#10625113C2212yes—
30C2×#67274—22no—
31C2×#67274C2212yescomplemented
32#10625090—21no—
33#10625085—22no—
34D8×D23—21no—
35C2×D184C2211yescharacteristic
36#10625072C2211yescharacteristic
37#10625019C2211yescharacteristic, complemented
38#10625019C2212yescomplemented
39#10625018C2212yescomplemented
40#10625007C2211yescharacteristic
41#10625005C2212yescomplemented
42#10625004C2211yescharacteristic, complemented
43#10625001C2211yescharacteristic, complemented
44C8×Dic23C2211yescharacteristic, complemented
45#41×C23—22no—
46#41×C23—22no—
47#41×C23—42no—
48#41×C23C2312yes—
49#41×C23C2311yescharacteristic
50C2×Q8×C23—22no—
51C2×Q8×C23—22no—
52C2×Q8×C23C2312yes—
53#67292—22no—
54D4×D23—22no—
55D4×D23—42no—
56#67288—22no—
57#67288C2311yescharacteristic
58C2×D92—22no—
59C2×D92C2312yes—
60Q16×C23—22no—
61Q16×C23—21no—
62Q16×C23—21no—
63Q16×C23D411yescharacteristic
64SD16×C23—22no—
65SD16×C23D412yes—
66D8×C23D411yescharacteristic
67M16×C23—21no—
68M16×C23C2311yescharacteristic
69C2×C8×C23—21no—
70C2×C8×C23C2311yescharacteristic
71#67275—22no—
72#67275D411yescharacteristic
73#67274—22no—
74#67274—22no—
75#67274—22no—
76#67274—22no—
77#67274—22no—
78#67274D411yescharacteristic
79#67273D411yescharacteristic
80#67272—22no—
81#67272—22no—
82#67272D411yescharacteristic
83(C2×D23)⋊C4—42no—
84C4×Dic23C2311yescharacteristic
85#67267—22no—
86#67267C2311yescharacteristic
87#67267C2312yes—
88C2×C23⋊C8—22no—
89C2×C23⋊C8C2311yescharacteristic
90D184—21no—
91D184—21no—
92#67262—21no—
93C8×D23—21no—
94C22×D23—22no—
95C22×D23—42no—
96Q8×C23—22no—
97Q8×C23—22no—
98Q8×C23—42no—
99Q8×C23C2×D411yescharacteristic
100Q8×C23C2×D412yes—
101D4×C23—22no—
102D4×C23—21no—
103D4×C23—42no—
104D4×C23C2×D411yescharacteristic
105D4×C23C2×D412yes—
106C2×C4×C23—22no—
107C2×C4×C23—21no—
108C2×C4×C23—22no—
109C2×C4×C23—42no—
110C2×C4×C23—42no—
111C2×C4×C23C2411yescharacteristic
112C22⋊D23—21no—
113C22⋊D23—42no—
114C2×Dic23—21no—
115D92—22no—
116D92—22no—
117D92—42no—
118D92C2×D411yescharacteristic
119C4×D23—21no—
120C4×D23—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×C23H(5,𝔽2)11yescharacteristic
133C2×D23—21no—
134C2×D23—42no—
135C2×D23—82no—
136C2×D23—162no—
137C4×C23—22no—
138C4×C23—21no—
139C4×C23—42no—
140C4×C23C22×D411yescharacteristic
141C4×C23C22×D411yescharacteristic
142Dic23—21no—
143Dic23—41no—
144#578D2311yescharacteristic, complemented
145#577—232no—
146#576—231no—
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×C23D4211yescharacteristic
159D23—41no—
160D23—82no—
1612−1+4C2×D2312yescomplemented
162H(5,𝔽2)—232no—
163#137—22no—
164#137—232no—
165#137—462no—
166#137C2×D2312yescomplemented
167AGL(1,ℤ/8)—232no—
168AGL(1,ℤ/8)—232no—
169AGL(1,ℤ/8)—462no—
170AGL(1,ℤ/8)—462no—
171#135—21no—
172#135—231no—
173#135—462no—
174#135—461no—
175#135C2×D2311yescharacteristic
176C2×Q16—21no—
177C2×Q16C2×D2311yescharacteristic, complemented
178C2×SD16—232no—
179C2×SD16—462no—
180C2×D8—231no—
181C2×D8—461no—
182#131—232no—
183#131—231no—
184#131C2×D2311yescharacteristic, complemented
185#124—232no—
186#108—231no—
187#108—231no—
188#104—231no—
189#104—232no—
190#104—231no—
191#101—232no—
192#100—232no—
193C4×C8—231no—
194C23#329011yescharacteristic, complemented, Sylow
195#41—22no—
196#41—22no—
197#41—42no—
198#41—231no—
199#41—462no—
200#41—462no—
201#41C22×D2311yescharacteristic
202#41C22×D2312yes—
203C2×Q8—22no—
204C2×Q8—22no—
205C2×Q8C22×D2312yes—
206C2×D4—232no—
207C2×D4—462no—
208C2×D4—462no—
209C2×D4—922no—
210Q16—22no—
211Q16—21no—
212Q16—21no—
213Q16—231no—
214Q16—462no—
215Q16C22⋊D2311yescharacteristic
216SD16—22no—
217SD16—231no—
218SD16—231no—
219SD16—462no—
220SD16—462no—
221SD16—462no—
222SD16—462no—
223SD16—462no—
224SD16C22⋊D2312yes—
225D8—231no—
226D8—462no—
227D8—462no—
228D8—461no—
229D8—461no—
230D8C22⋊D2311yescharacteristic
231M16—21no—
232M16—232no—
233M16—231no—
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—462no—
245C23—922no—
246Q8—22no—
247Q8—22no—
248Q8—42no—
249Q8—231no—
250Q8D4×D2311yescharacteristic
251Q8C2×C22⋊D2312yes—
252D4—22no—
253D4—21no—
254D4—42no—
255D4—231no—
256D4—461no—
257D4—462no—
258D4—462no—
259D4—922no—
260D4—922no—
261D4D4×D2311yescharacteristic
262D4C2×C22⋊D2312yes—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—461no—
269C2×C4—461no—
270C2×C4—922no—
271C2×C4C23×D2311yescharacteristic
272C8—21no—
273C8—231no—
274C8—231no—
275C8—462no—
276C8—461no—
277C8C2×C22⋊D2311yescharacteristic
278C8C2×C22⋊D2311yescharacteristic
279C22—21no—
280C22—22no—
281C22—461no—
282C22—922no—
283C22—3682no—
284C22—1842no—
285C22#1062515511yescharacteristic
286C4—21no—
287C4—22no—
288C4—42no—
289C4—461no—
290C4—921no—
291C4C2×D4×D2311yescharacteristic
292C4C22×C22⋊D2311yescharacteristic
293C2—21no—
294C2—42no—
295C2—41no—
296C2—921no—
297C2—1842no—
298C2D4×C22⋊D2311yescharacteristic
subgroupG/H
centerC2D4×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#578C2
socleC2×C23D42
hypercenter#578D23
hypocenterC23#3290
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ #578

Complements

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

NH ≅ G/Ntype
1. #13093225C2semidirect
2. #13093219C2semidirect
3. #13092802C2semidirect
4. #13092689C2semidirect
5. #13092687C2semidirect
6. #13092682C2semidirect
7. #13092593C2semidirect
8. #13092590C2semidirect
9. #13092534C2semidirect
10. #13092532C2semidirect
11. C23×#578C2semidirect
12. C23×2−1+4C22semidirect
15. C23×#137C22semidirect
19. C2×Q16×C23C22semidirect
20. C23×#131C22semidirect
25. #10625120C22semidirect
26. #10625119C22semidirect
27. #10625118C22semidirect
31. C2×#67274C22semidirect
37. #10625019C22semidirect
38. #10625019C22semidirect
39. #10625018C22semidirect
41. #10625005C22semidirect
42. #10625004C22semidirect
43. #10625001C22semidirect
44. C8×Dic23C22semidirect
144. #578D23semidirect
161. 2−1+4C2×D23semidirect
166. #137C2×D23semidirect
177. C2×Q16C2×D23semidirect
184. #131C2×D23semidirect
194. C23#3290semidirect

Maximal subgroups

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

subgroupindex
#130932252
#130932192
#130928022
#130926892
#130926872
#130926822
#130925932
#130925902
#130925342
#130925322
C23×#5782
#329023