Finite Group Databasebeta

← #15682683

Subgroups — #15682683

Order 2944.

732 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 732 conjugacy classes of subgroups — too many to draw. Only its 165 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×#10625120C211yesmaximal, characteristic, complemented
2C22×#67274C211yesmaximal, characteristic, complemented
3#13092981C211yesmaximal, characteristic, complemented
4#13092562C214yesmaximal, complemented
5#13092556C214yesmaximal, complemented
6#13092426C211yesmaximal, characteristic, complemented
7#13092413C211yesmaximal, characteristic, complemented
8#13092384C211yesmaximal, characteristic, complemented
9C2×C23×2−1+4C211yesmaximal, characteristic, complemented
10C23×2−1+4—24no—
11C23×2−1+4—24no—
12C2×#41×C23—22no—
13C2×#41×C23—21no—
14C2×#41×C23C2211yescharacteristic
15C2×#41×C23C2211yescharacteristic
16C2×#41×C23C2212yescomplemented
17C22×Q8×C23—21no—
18C22×Q8×C23C2211yescharacteristic
19C22×Q8×C23C2212yescomplemented
20C22×D92C2211yescharacteristic
21#10625120—24no—
22#10625118—21no—
23C2×#67274—24no—
24C2×#67274C2214yes—
25C2×#67274C2212yes—
26#10625111—21no—
27#10625108—22no—
28C2×#67272C2212yes—
29#10625101C2214yes—
30#10625097C2211yescharacteristic
31C2×#67267C2211yescharacteristic
32C22×C23⋊C8C2211yescharacteristic
33#10625017C2212yescomplemented
34#10625017C2214yescomplemented
35#10625014C2212yescomplemented
36C22⋊(C23⋊C8)C2214yescomplemented
37C23×D23—21no—
38#41×C23—216no—
39#41×C23—28no—
40#41×C23—24no—
41#41×C23—24no—
42#41×C23—22no—
43#41×C23—22no—
44#41×C23—22no—
45#41×C23D414yescomplemented
46C2×Q8×C23—28no—
47C2×Q8×C23—24no—
48C2×Q8×C23—24no—
49C2×Q8×C23—21no—
50C2×Q8×C23—22no—
51C2×Q8×C23—22no—
52C2×Q8×C23D411yescharacteristic
53C2×Q8×C23D414yescomplemented
54C2×Q8×C23C2312yes—
55C2×Q8×C23C2311yescharacteristic
56C2×D4×C23—21no—
57C2×D4×C23—22no—
58C2×D4×C23D412yes—
59C2×D4×C23D411yescharacteristic
60C2×D4×C23C2311yescharacteristic
61C22×C4×C23—21no—
62C22×C4×C23—22no—
63C22×C4×C23—21no—
64C22×C4×C23—22no—
65C22×C4×C23C2312yes—
66C22×C4×C23C2311yescharacteristic
67C2×C22⋊D23—24no—
68C2×D92—22no—
69C2×D92—22no—
70C2×D92—21no—
71C2×D92C2312yes—
72C22⋊Dic23—21no—
73#67274—28no—
74#67274—24no—
75#67272—24no—
76(C2×D23)⋊C4—24no—
77C4⋊Dic23C2312yes—
78C4×Dic23—21no—
79#67267—22no—
80C2×C23⋊C8—22no—
81C2×C23⋊C8C2312yes—
82C2×C23⋊C8C2312yes—
83C23×C23—21no—
84C23×C23C2×D412yes—
85C23×C23C2×D411yescharacteristic
86C22×D23—22no—
87C22×D23—42no—
88C22×D23—82no—
89Q8×C23—28no—
90Q8×C23—22no—
91Q8×C23—24no—
92Q8×C23—21no—
93Q8×C23—22no—
94Q8×C23C2×D412yes—
95Q8×C23C2×D414yes—
96D4×C23—28no—
97D4×C23—24no—
98D4×C23—24no—
99D4×C23—22no—
100D4×C23—21no—
101D4×C23C2×D412yes—
102C2×C4×C23—28no—
103C2×C4×C23—28no—
104C2×C4×C23—24no—
105C2×C4×C23—22no—
106C2×C4×C23—21no—
107C2×C4×C23—24no—
108C2×C4×C23—22no—
109C2×C4×C23—22no—
110C2×C4×C23C2×D412yes—
111C2×C4×C23C2×D411yescharacteristic
112C2×C4×C23C2×D412yes—
113C2×C4×C23C2×D412yes—
114C2×C4×C23C2411yescharacteristic
115C22⋊D23—84no—
116C2×Dic23—22no—
117D92—22no—
118D92—22no—
119D92—42no—
120C23⋊C8—22no—
121C23⋊C8—22no—
122#3010—231nomaximal, Sylow
123C22×C23—22no—
124C22×C23—22no—
125C22×C23—22no—
126C22×C23—24no—
127C22×C23—42no—
128C22×C23#12012yes—
129C22×C23C22×D411yescharacteristic
130C2×D23—42no—
131C2×D23—44no—
132C2×D23—84no—
133C4×C23—24no—
134C4×C23—22no—
135C4×C23—22no—
136C4×C23#12012yes—
137C4×C23C22×D411yescharacteristic
138C4×C23C22×D411yescharacteristic
139Dic23—42no—
140C2×2−1+4D2311yescharacteristic, complemented
141C2×AGL(1,ℤ/8)—231no—
142C22×SD16—231no—
143#535—231no—
144#449—234no—
145#448—234no—
146#419—231no—
147#416—231no—
148#408—231no—
149C2×C23—22no—
150C2×C23—42no—
151C2×C23—42no—
152C2×C23C2×#12011yescharacteristic
153C2×C23#57712yes—
154D23—82no—
1552−1+4—24no—
1562−1+4—24no—
157C2×#41—22no—
158C2×#41—21no—
159C2×#41C2×D2311yescharacteristic
160C2×#41C2×D2311yescharacteristic
161C2×#41C2×D2312yescomplemented
162C22×Q8—21no—
163C22×Q8C2×D2311yescharacteristic
164C22×Q8C2×D2312yescomplemented
165C22×D4—231no—
166AGL(1,ℤ/8)—464no—
167C2×SD16—234no—
168C2×SD16—232no—
169C2×SD16—464no—
170C2×D8—232no—
171C2×M16—231no—
172C22×C8—231no—
173#127—461no—
174#124—461no—
175#121—234no—
176#120—462no—
177#117—231no—
178#103—232no—
179#103—234no—
180#102—232no—
181C22⋊C8—234no—
182C23#301011yescharacteristic, complemented, Sylow
183C24—461no—
184#41—216no—
185#41—28no—
186#41—24no—
187#41—24no—
188#41—22no—
189#41—22no—
190#41—22no—
191#41C22⋊D2314yescomplemented
192C2×Q8—28no—
193C2×Q8—24no—
194C2×Q8—24no—
195C2×Q8—21no—
196C2×Q8—22no—
197C2×Q8—22no—
198C2×Q8C22⋊D2311yescharacteristic
199C2×Q8C22⋊D2314yescomplemented
200C2×Q8C22×D2312yes—
201C2×Q8C22×D2311yescharacteristic
202C2×D4—21no—
203C2×D4—22no—
204C2×D4—232no—
205C2×D4—464no—
206C2×D4—462no—
207C2×D4—462no—
208C2×D4—461no—
209C2×D4C22⋊D2312yes—
210C2×D4C22⋊D2311yescharacteristic
211C2×D4C22×D2311yescharacteristic
212C22×C4—21no—
213C22×C4—22no—
214C22×C4—21no—
215C22×C4—22no—
216C22×C4C22×D2312yes—
217C22×C4C22×D2311yescharacteristic
218SD16—468no—
219SD16—464no—
220D8—464no—
221M16—462no—
222C2×C8—232no—
223C2×C8—232no—
224C2×C8—462no—
225C4⋊C4—232no—
226C22⋊C4—461no—
227C22⋊C4—464no—
228C42—461no—
229C23—21no—
230C23—462no—
231C23—922no—
232C23—1842no—
233C23C2×C22⋊D2312yes—
234C23C2×C22⋊D2311yescharacteristic
235Q8—28no—
236Q8—22no—
237Q8—24no—
238Q8—21no—
239Q8—22no—
240Q8C2×C22⋊D2312yes—
241Q8C2×C22⋊D2314yes—
242D4—28no—
243D4—24no—
244D4—24no—
245D4—22no—
246D4—21no—
247D4—462no—
248D4—462no—
249D4—922no—
250D4—1844no—
251D4C2×C22⋊D2312yes—
252C2×C4—28no—
253C2×C4—28no—
254C2×C4—24no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—24no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—462no—
261C2×C4C2×C22⋊D2312yes—
262C2×C4C2×C22⋊D2311yescharacteristic
263C2×C4C2×C22⋊D2312yes—
264C2×C4C2×C22⋊D2312yes—
265C2×C4C23×D2311yescharacteristic
266C8—462no—
267C8—462no—
268C22—22no—
269C22—22no—
270C22—22no—
271C22—24no—
272C22—42no—
273C22—922no—
274C22—924no—
275C22—1844no—
276C22#1062512412yes—
277C22C22×C22⋊D2311yescharacteristic
278C4—24no—
279C4—22no—
280C4—22no—
281C4—922no—
282C4#1062512412yes—
283C4C22×C22⋊D2311yescharacteristic
284C4C22×C22⋊D2311yescharacteristic
285C2—22no—
286C2—42no—
287C2—42no—
288C2—1842no—
289C2C2×#1062512411yescharacteristic
290C2#1309322512yes—
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC2×C23×2−1+4C2
socleC22×C23C22×D4
hypercenterC2×2−1+4D23
hypocenterC23#3010
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. C2×#10625120C2semidirect
2. C22×#67274C2semidirect
3. #13092981C2semidirect
4. #13092562C2semidirect
5. #13092556C2semidirect
6. #13092426C2semidirect
7. #13092413C2semidirect
8. #13092384C2semidirect
9. C2×C23×2−1+4C2semidirect
16. C2×#41×C23C22semidirect
19. C22×Q8×C23C22semidirect
33. #10625017C22semidirect
34. #10625017C22semidirect
35. #10625014C22semidirect
36. C22⋊(C23⋊C8)C22semidirect
45. #41×C23D4semidirect
53. C2×Q8×C23D4semidirect
140. C2×2−1+4D23semidirect
161. C2×#41C2×D23semidirect
164. C22×Q8C2×D23semidirect
182. C23#3010semidirect
191. #41C22⋊D23semidirect
199. C2×Q8C22⋊D23semidirect

Maximal subgroups

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

subgroupindex
C2×#106251202
C22×#672742
#130929812
#130925622
#130925562
#130924262
#130924132
#130923842
C2×C23×2−1+42
#301023