Finite Group Databasebeta

← #15682661

Subgroups — #15682661

Order 2944.

784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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×#10625155C211yesmaximal, characteristic, complemented
2C2×#10625103C211yesmaximal, characteristic, complemented
3#13092984C211yesmaximal, characteristic, complemented
4#13092559C214yesmaximal, complemented
5#13092549C214yesmaximal, complemented
6#13092422C211yesmaximal, characteristic, complemented
7#13092414C211yesmaximal, characteristic, complemented
8#13092383C211yesmaximal, characteristic, complemented
9C22×D8×C23C211yesmaximal, characteristic, complemented
10C22×D4×C23C2211yescharacteristic
11C22×D4×C23C2211yescharacteristic, complemented
12C22×C22⋊D23—22no—
13#10625155—24no—
14#10625155—24no—
15C2×#67290—21no—
16C2×#67290C2212yescomplemented
17C2×D4×D23—21no—
18C2×D4×D23C2212yescomplemented
19C2×#67288C2211yescharacteristic
20C2×#67288C2211yescharacteristic
21C2×D8×C23—24no—
22C2×D8×C23C2214yescomplemented
23C22×C8×C23C2211yescharacteristic, complemented
24#10625124—22no—
25#10625111—21no—
26#10625109C2214yescomplemented
27#10625107—21no—
28C2×#67273C2212yescomplemented
29#10625103—24no—
30C2×#67272C2212yescomplemented
31#10625097C2211yescharacteristic, complemented
32C2×#67267C2211yescharacteristic, complemented
33#10625014C2214yescomplemented
34#10625003C2212yescomplemented
35(C2×D23)⋊C8C2214yescomplemented
36#10624998C2212yescomplemented
37C24×C23—21no—
38C24×C23—21no—
39C23×D23—22no—
40C2×D4×C23—21no—
41C2×D4×C23—22no—
42C2×D4×C23—22no—
43C2×D4×C23—22no—
44C2×D4×C23—21no—
45C2×D4×C23D414yescomplemented
46C2×D4×C23C2312yes—
47C2×D4×C23C2312yes—
48C22×C4×C23C2311yescharacteristic
49C2×C22⋊D23—216no—
50C2×C22⋊D23—21no—
51C2×C22⋊D23—22no—
52C2×C22⋊D23—24no—
53C2×C22⋊D23—22no—
54C2×C22⋊D23D412yes—
55C22×Dic23—22no—
56#67290—28no—
57#67290—24no—
58#67290—24no—
59D4×D23—28no—
60D4×D23—24no—
61D4×D23—24no—
62#67288—22no—
63#67288—22no—
64#67288—22no—
65#67288D414yescomplemented
66C2×D92D411yescharacteristic
67C2×D92C2311yescharacteristic
68C2×C4×D23—21no—
69C2×C4×D23C2312yes—
70C2×Dic46D411yescharacteristic
71C2×Dic46C2311yescharacteristic
72D8×C23—28no—
73C2×C8×C23—22no—
74C2×C8×C23C2312yes—
75C22⋊Dic23—21no—
76C22⋊Dic23—24no—
77#67273—24no—
78#67272—24no—
79C4⋊Dic23C2312yes—
80C4×Dic23—21no—
81#67267—22no—
82C2×C23⋊C8C2312yes—
83C23×C23—22no—
84C23×C23—24no—
85C23×C23—22no—
86C23×C23—42no—
87C23×C23—82no—
88C23×C23—82no—
89C23×C23C2×D411yescharacteristic
90C22×D23—21no—
91C22×D23—28no—
92C22×D23—84no—
93C22×D23C2×D412yes—
94D4×C23—24no—
95D4×C23—22no—
96D4×C23—22no—
97D4×C23—22no—
98D4×C23—42no—
99D4×C23C2×D414yes—
100C2×C4×C23C2×D411yescharacteristic
101C2×C4×C23C2×D412yes—
102C2×C4×C23C2×D412yes—
103C2×C4×C23C2411yescharacteristic
104C22⋊D23—28no—
105C22⋊D23—28no—
106C22⋊D23—24no—
107C22⋊D23—24no—
108C22⋊D23—84no—
109C2×Dic23—28no—
110C2×Dic23—21no—
111C2×Dic23—22no—
112C2×Dic23C2×D412yes—
113D92—22no—
114D92—21no—
115D92C2×D412yes—
116C4×D23—24no—
117C4×D23—22no—
118C4×D23—22no—
119Dic46—22no—
120Dic46—21no—
121Dic46C2×D412yes—
122C8×C23—22no—
123C23⋊C8—22no—
124#3008—231nomaximal, Sylow
125C22×C23—22no—
126C22×C23—24no—
127C22×C23—44no—
128C22×C23—42no—
129C22×C23—44no—
130C22×C23—84no—
131C22×C23—84no—
132C22×C23#12012yes—
133C22×C23C22×D411yescharacteristic
134C2×D23—22no—
135C2×D23—22no—
136C2×D23—24no—
137C2×D23—42no—
138C2×D23—88no—
139C4×C23#12012yes—
140C4×C23C22×D411yescharacteristic
141C4×C23C22×D411yescharacteristic
142Dic23—22no—
143Dic23—22no—
144Dic23—42no—
145C2×H(5,𝔽2)—231no—
146C2×AGL(1,ℤ/8)—231no—
147C22×D8D2311yescharacteristic, complemented
148#535—231no—
149#449—234no—
150#447—234no—
151#418—231no—
152#416—231no—
153#408—231no—
154C2×C23—22no—
155C2×C23—44no—
156C2×C23—82no—
157C2×C23C2×#12011yescharacteristic
158C2×C23#57612yes—
159D23—42no—
160D23—42no—
161H(5,𝔽2)—464no—
162H(5,𝔽2)—464no—
163C2×#41—231no—
164C2×#41—232no—
165C2×#41—231no—
166C2×#41—461no—
167C22×D4—232no—
168C22×D4—461no—
169C22×D4—462no—
170C22×D4C2×D2311yescharacteristic
171C22×D4C2×D2311yescharacteristic, complemented
172AGL(1,ℤ/8)—464no—
173C2×SD16—232no—
174C2×D8—24no—
175C2×D8—232no—
176C2×D8C2×D2314yescomplemented
177C2×M16—231no—
178C22×C8C2×D2311yescharacteristic, complemented
179#127—461no—
180#124—461no—
181#121—234no—
182#120—462no—
183#117—231no—
184#103—232no—
185#102—234no—
186#102—232no—
187C22⋊C8—234no—
188C23#300811yescharacteristic, complemented, Sylow
189C24—21no—
190C24—21no—
191C24—462no—
192#41—234no—
193#41—464no—
194#41—468no—
195#41—464no—
196#41—462no—
197#41—462no—
198#41—462no—
199C2×Q8—231no—
200C2×Q8—231no—
201C2×D4—21no—
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—21no—
205C2×D4—22no—
206C2×D4—232no—
207C2×D4—231no—
208C2×D4—231no—
209C2×D4—462no—
210C2×D4—464no—
211C2×D4—468no—
212C2×D4—462no—
213C2×D4—4616no—
214C2×D4—461no—
215C2×D4—464no—
216C2×D4—464no—
217C2×D4C22⋊D2314yescomplemented
218C2×D4C22×D2312yes—
219C2×D4C22×D2312yes—
220C22×C4—232no—
221C22×C4—462no—
222C22×C4—461no—
223C22×C4C22×D2311yescharacteristic
224SD16—464no—
225D8—28no—
226D8—464no—
227M16—462no—
228C2×C8—22no—
229C2×C8—232no—
230C2×C8C22×D2312yes—
231C4⋊C4—232no—
232C22⋊C4—464no—
233C22⋊C4—461no—
234C42—461no—
235C23—22no—
236C23—24no—
237C23—22no—
238C23—42no—
239C23—82no—
240C23—82no—
241C23—232no—
242C23—468no—
243C23—461no—
244C23—1844no—
245C23D4×D2311yescharacteristic
246Q8—232no—
247Q8—462no—
248Q8—461no—
249D4—24no—
250D4—22no—
251D4—22no—
252D4—22no—
253D4—42no—
254D4—232no—
255D4—468no—
256D4—468no—
257D4—464no—
258D4—464no—
259D4—462no—
260D4—461no—
261D4—1844no—
262D4C2×C22⋊D2314yes—
263C2×C4—232no—
264C2×C4—468no—
265C2×C4—461no—
266C2×C4—464no—
267C2×C4—462no—
268C2×C4—462no—
269C2×C4—462no—
270C2×C4D4×D2311yescharacteristic
271C2×C4D4×D2312yes—
272C2×C4C2×C22⋊D2312yes—
273C2×C4C23×D2311yescharacteristic
274C8—22no—
275C8—462no—
276C22—22no—
277C22—24no—
278C22—44no—
279C22—42no—
280C22—44no—
281C22—84no—
282C22—84no—
283C22—462no—
284C22—462no—
285C22—464no—
286C22—922no—
287C22—1848no—
288C22#1062510812yes—
289C22C2×D4×D2311yescharacteristic
290C4—462no—
291C4—462no—
292C4—922no—
293C4#1062510812yes—
294C4C2×D4×D2311yescharacteristic
295C4C22×C22⋊D2311yescharacteristic
296C2—22no—
297C2—44no—
298C2—82no—
299C2—922no—
300C2—922no—
301C2C2×#1062510811yescharacteristic
302C2#1309321812yes—
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC22×D8×C23C2
socleC22×C23C22×D4
hypercenterC22×D8D23
hypocenterC23#3008
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×#10625155C2semidirect
2. C2×#10625103C2semidirect
3. #13092984C2semidirect
4. #13092559C2semidirect
5. #13092549C2semidirect
6. #13092422C2semidirect
7. #13092414C2semidirect
8. #13092383C2semidirect
9. C22×D8×C23C2semidirect
11. C22×D4×C23C22semidirect
16. C2×#67290C22semidirect
18. C2×D4×D23C22semidirect
22. C2×D8×C23C22semidirect
23. C22×C8×C23C22semidirect
26. #10625109C22semidirect
28. C2×#67273C22semidirect
30. C2×#67272C22semidirect
31. #10625097C22semidirect
32. C2×#67267C22semidirect
33. #10625014C22semidirect
34. #10625003C22semidirect
35. (C2×D23)⋊C8C22semidirect
36. #10624998C22semidirect
45. C2×D4×C23D4semidirect
65. #67288D4semidirect
147. C22×D8D23semidirect
171. C22×D4C2×D23semidirect
176. C2×D8C2×D23semidirect
178. C22×C8C2×D23semidirect
188. C23#3008semidirect
217. C2×D4C22⋊D23semidirect

Maximal subgroups

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

subgroupindex
C2×#106251552
C2×#106251032
#130929842
#130925592
#130925492
#130924222
#130924142
#130923832
C22×D8×C232
#300823