Finite Group Databasebeta

← #15685213

Subgroups — #15685213

Order 2944.

494 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 123 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#13093072C211yesmaximal, characteristic, complemented
2#13093052C211yesmaximal, characteristic, complemented
3#13092763C211yesmaximal, characteristic, complemented
4#13092729C212yesmaximal, complemented
5#13092698C211yesmaximal, characteristic, complemented
6#13092650C212yesmaximal, complemented
7#13092549C212yesmaximal, complemented
8C4×#67272C211yesmaximal, characteristic, complemented
9#13092482C211yesmaximal, characteristic, complemented
10#102×D23C212yesmaximal, complemented
11C23×#459C211yesmaximal, characteristic, complemented
12C2×D4×D23—21no—
13C2×D4×D23C2212yes—
14C2×#67288—21no—
15C2×D8×C23C2212yescomplemented
16C23×#127C2211yescharacteristic
17C4×D4×C23C2211yescharacteristic, complemented
18#10625109—21no—
19#10625109C2212yes—
20#10625109C2212yescomplemented
21#10625108—22no—
22C2×#67272C2211yescharacteristic
23#10625095—21no—
24C2×C8×D23C2212yescomplemented
25C4⋊C4×D23C2212yescomplemented
26#10625054—22no—
27C4×D92C2211yescharacteristic
28C4×D92C2211yescharacteristic
29#10625040C2211yescharacteristic, complemented
30C23×C4⋊C8C2211yescharacteristic, complemented
31C23×#102C2212yescomplemented
32#10625014C2211yescharacteristic, complemented
33#10625014C2212yescomplemented
34#10625014C2212yescomplemented
35#10625003C2212yes—
36(C2×D23)⋊C8C2212yescomplemented
37#10625000C2212yescomplemented
38#10624991C2211yescharacteristic
39#10624989C2211yescharacteristic, complemented
40C4×C23⋊C8C2211yescharacteristic, complemented
41C23×D23—22no—
42C2×D4×C23—21no—
43C2×D4×C23—21no—
44C2×D4×C23C2312yes—
45C2×D4×C23C2311yescharacteristic
46C22×C4×C23—21no—
47C2×C22⋊D23—22no—
48C2×C22⋊D23—22no—
49C2×C22⋊D23—22no—
50D4×D23—24no—
51D4×D23—42no—
52D4×D23—44no—
53#67288—44no—
54C2×D92D411yescharacteristic
55C2×D92C2311yescharacteristic
56C2×C4×D23—22no—
57C2×C4×D23—21no—
58C2×C4×D23C2312yes—
59C2×Dic46—21no—
60D8×C23—42no—
61C2×C8×C23C2312yes—
62C4⋊C4×C23C2311yescharacteristic
63C22⋊C4×C23—21no—
64C42×C23C2311yescharacteristic
65C22⋊Dic23—22no—
66C22⋊Dic23—22no—
67#67272—22no—
68(C2×D23)⋊C4—21no—
69(C2×D23)⋊C4D412yes—
70C4⋊Dic23—21no—
71C4⋊Dic23D411yescharacteristic
72C4⋊Dic23C2312yes—
73C4⋊Dic23C2311yescharacteristic
74Dic23⋊C4—22no—
75C2×C23⋊C8C2311yescharacteristic
76C2×C23⋊C8C2311yescharacteristic
77C8×D23—42no—
78C23×C23—21no—
79C23×C23—22no—
80C22×D23—21no—
81C22×D23—44no—
82C22×D23—44no—
83C22×D23—82no—
84C22×D23C2×D412yes—
85D4×C23—21no—
86D4×C23—22no—
87D4×C23—21no—
88D4×C23—22no—
89D4×C23—42no—
90D4×C23—81no—
91C2×C4×C23—21no—
92C2×C4×C23—42no—
93C2×C4×C23C2×D411yescharacteristic
94C2×C4×C23C2×D411yescharacteristic
95C2×C4×C23C2411yescharacteristic
96C22⋊D23—44no—
97C22⋊D23—44no—
98C22⋊D23—44no—
99C2×Dic23—22no—
100C2×Dic23—21no—
101C2×Dic23C2×D412yes—
102D92—21no—
103D92D814yescomplemented
104D92#4112yescomplemented
105C4×D23—22no—
106C4×D23—22no—
107C4×D23—44no—
108C4×D23—42no—
109Dic46—42no—
110C8×C23—22no—
111C23⋊C8—21no—
112C23⋊C8—21no—
113#3294—231nomaximal, Sylow
114C22×C23—42no—
115C22×C23—41no—
116C22×C23—41no—
117C22×C23—42no—
118C22×C23—42no—
119C22×C23—41no—
120C22×C23C22×D411yescharacteristic
121C2×D23—22no—
122C2×D23—22no—
123C2×D23—22no—
124C2×D23—41no—
125C2×D23—41no—
126C2×D23—88no—
127C2×D23C2×D814yes—
128C4×C23—21no—
129C4×C23—41no—
130C4×C23C2×D812yes—
131C4×C23C2×#4111yescharacteristic
132C4×C23H(5,𝔽2)11yescharacteristic
133Dic23—22no—
134Dic23—42no—
135Dic23—41no—
136#547—231no—
137D42—231no—
138#486—231no—
139#480—232no—
140#474—231no—
141#466—232no—
142#459D2311yescharacteristic, complemented
143#447—232no—
144C4×D8—231no—
145C8×D4—231no—
146C2×#102—232no—
147C2×C23—82no—
148C2×C23—81no—
149C2×C23#54611yescharacteristic
150C2×C23C22×D811yescharacteristic
151C2×C23#57711yescharacteristic
152D23—24no—
153D23—42no—
154C2×#41—461no—
155C22×D4—232no—
156C22×D4—461no—
157C2×D8—231no—
158C2×D8C2×D2312yescomplemented
159C22×C8—232no—
160C4⋊Q8—231no—
161#127C2×D2311yescharacteristic
162#123—462no—
163C22⋊Q8—461no—
164#121—232no—
165#121—232no—
166#121—461no—
167#120—462no—
168C4×D4—231no—
169C4×D4—231no—
170C4×D4C2×D2311yescharacteristic, complemented
171C2×C4⋊C4—232no—
172#107—232no—
173#107—231no—
174C4⋊C8C2×D2311yescharacteristic, complemented
175#102—232no—
176#102—231no—
177#102—232no—
178#102—232no—
179#102—231no—
180#102C2×D2312yescomplemented
181C22⋊C8—232no—
182C4×C8—231no—
183C23#329411yescharacteristic, complemented, Sylow
184C24—462no—
185#41—924no—
186C2×Q8—461no—
187C2×D4—21no—
188C2×D4—21no—
189C2×D4—231no—
190C2×D4—231no—
191C2×D4—462no—
192C2×D4—464no—
193C2×D4—462no—
194C2×D4—462no—
195C2×D4—922no—
196C2×D4—924no—
197C2×D4C22×D2312yes—
198C2×D4C22×D2311yescharacteristic
199C22×C4—21no—
200C22×C4—232no—
201C22×C4—462no—
202C22×C4—461no—
203D8—42no—
204D8—462no—
205C2×C8—231no—
206C2×C8—231no—
207C2×C8—922no—
208C2×C8C22×D2312yes—
209C4⋊C4—231no—
210C4⋊C4—232no—
211C4⋊C4—231no—
212C4⋊C4—462no—
213C4⋊C4—461no—
214C4⋊C4C22×D2311yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—232no—
217C22⋊C4—462no—
218C22⋊C4—462no—
219C22⋊C4—461no—
220C42C22×D2311yescharacteristic
221C23—21no—
222C23—22no—
223C23—232no—
224C23—461no—
225C23—924no—
226C23—924no—
227C23—1842no—
228Q8—922no—
229D4—21no—
230D4—22no—
231D4—21no—
232D4—22no—
233D4—42no—
234D4—81no—
235D4—234no—
236D4—232no—
237D4—461no—
238D4—924no—
239D4—924no—
240D4—924no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—232no—
244C2×C4—462no—
245C2×C4—462no—
246C2×C4—461no—
247C2×C4—462no—
248C2×C4—924no—
249C2×C4—922no—
250C2×C4D4×D2311yescharacteristic
251C2×C4D4×D2311yescharacteristic
252C2×C4C23×D2311yescharacteristic
253C8—22no—
254C8—461no—
255C8—461no—
256C22—41no—
257C22—42no—
258C22—42no—
259C22—41no—
260C22—42no—
261C22—41no—
262C22—234no—
263C22—462no—
264C22—462no—
265C22—462no—
266C22—921no—
267C22—921no—
268C22—1848no—
269C22C2×D4×D2311yescharacteristic
270C4—21no—
271C4—41no—
272C4—462no—
273C4—921no—
274C4—922no—
275C4D8×D2312yes—
276C4#1062515511yescharacteristic
277C4#41×D2311yescharacteristic
278C2—82no—
279C2—81no—
280C2—464no—
281C2—922no—
282C2#1309306411yescharacteristic
283C2C2×D8×D2311yescharacteristic
284C2#1309322711yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#459C2
socleC22×C23C22×D4
hypercenter#459D23
hypocenterC23#3294
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #13093072C2semidirect
2. #13093052C2semidirect
3. #13092763C2semidirect
4. #13092729C2semidirect
5. #13092698C2semidirect
6. #13092650C2semidirect
7. #13092549C2semidirect
8. C4×#67272C2semidirect
9. #13092482C2semidirect
10. #102×D23C2semidirect
11. C23×#459C2semidirect
15. C2×D8×C23C22semidirect
17. C4×D4×C23C22semidirect
20. #10625109C22semidirect
24. C2×C8×D23C22semidirect
25. C4⋊C4×D23C22semidirect
29. #10625040C22semidirect
30. C23×C4⋊C8C22semidirect
31. C23×#102C22semidirect
32. #10625014C22semidirect
33. #10625014C22semidirect
34. #10625014C22semidirect
36. (C2×D23)⋊C8C22semidirect
37. #10625000C22semidirect
39. #10624989C22semidirect
40. C4×C23⋊C8C22semidirect
103. D92D8semidirect
104. D92#41semidirect
142. #459D23semidirect
158. C2×D8C2×D23semidirect
170. C4×D4C2×D23semidirect
174. C4⋊C8C2×D23semidirect
180. #102C2×D23semidirect
183. C23#3294semidirect

Maximal subgroups

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

subgroupindex
#130930722
#130930522
#130927632
#130927292
#130926982
#130926502
#130925492
C4×#672722
#130924822
#102×D232
C23×#4592
#329423