Finite Group Databasebeta

← #15683043

Subgroups — #15683043

Order 2944.

524 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 127 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×D8×D23C211yesmaximal, characteristic, complemented
2C2×#10625078C211yesmaximal, characteristic, complemented
3#13092983C212yesmaximal, complemented
4#13092671C211yesmaximal, characteristic, complemented
5#13092670C211yesmaximal, characteristic, complemented
6#13092667C211yesmaximal, characteristic, complemented
7#13092652C212yesmaximal, complemented
8#13092651C212yesmaximal, complemented
9#13092452C211yesmaximal, characteristic, complemented
10#13092420C212yesmaximal, complemented
11C23×#469C211yesmaximal, characteristic, complemented
12C2×D4×D23C2212yes—
13C2×#67288C2211yescharacteristic
14C2×D8×C23C2211yescharacteristic
15C2×M16×C23C2211yescharacteristic, complemented
16C23×#121C2212yescomplemented
17#10625111—22no—
18#10625109C2212yescomplemented
19#10625108—22no—
20C2×#67272C2212yes—
21#10625101C2212yescomplemented
22C22×C23⋊C8C2211yescharacteristic, complemented
23D8×D23—24no—
24#10625078—24no—
25C2×D184C2211yescharacteristic
26C2×#67262C2211yescharacteristic
27C2×#67262C2211yescharacteristic, complemented
28C2×C8×D23C2211yescharacteristic
29C2×C8×D23C2211yescharacteristic, complemented
30#10625066C2212yescomplemented
31#10625063C2212yes—
32#10625056—22no—
33#10625053—22no—
34C23×#106C2211yescharacteristic, complemented
35C23×#102C2212yescomplemented
36#10625014C2212yescomplemented
37#10625003C2212yescomplemented
38#10624999C2211yescharacteristic, complemented
39#10624991C2212yescomplemented
40#10624989C2212yescomplemented
41C23×D23—22no—
42C2×D4×C23—22no—
43C2×D4×C23C2312yes—
44C22×C4×C23C2311yescharacteristic
45C2×C22⋊D23—22no—
46C2×C22⋊D23—22no—
47C2×C22⋊D23—22no—
48C2×C22⋊D23D411yescharacteristic
49C2×C22⋊D23D411yescharacteristic
50D4×D23—24no—
51D4×D23—24no—
52#67288—22no—
53#67288—22no—
54C2×D92—22no—
55C2×D92D411yescharacteristic
56C2×D92C2312yes—
57C2×C4×D23C2311yescharacteristic
58C2×C4×D23C2311yescharacteristic
59C2×Dic46D411yescharacteristic
60D8×C23—22no—
61M16×C23—22no—
62C2×C8×C23C2311yescharacteristic
63C2×C8×C23C2311yescharacteristic
64C4⋊C4×C23C2312yes—
65C22⋊C4×C23—22no—
66C22⋊Dic23—22no—
67#67272—24no—
68(C2×D23)⋊C4—22no—
69(C2×D23)⋊C4—22no—
70(C2×D23)⋊C4—22no—
71C4⋊Dic23C2312yes—
72C4×Dic23—22no—
73C2×C23⋊C8—22no—
74C2×C23⋊C8C2311yescharacteristic
75C2×C23⋊C8C2311yescharacteristic
76D184—22no—
77#67262—22no—
78#67262—22no—
79C8×D23—22no—
80C8×D23D414yescomplemented
81C23×C23—22no—
82C23×C23C2×D411yescharacteristic
83C22×D23—22no—
84C22×D23—44no—
85C22×D23—82no—
86C22×D23—82no—
87C22×D23C2×D411yescharacteristic
88C22×D23C2×D411yescharacteristic
89D4×C23—22no—
90D4×C23—22no—
91D4×C23—82no—
92C2×C4×C23—21no—
93C2×C4×C23—21no—
94C2×C4×C23—22no—
95C2×C4×C23C2×D411yescharacteristic
96C2×C4×C23C2411yescharacteristic
97C22⋊D23—22no—
98C22⋊D23—22no—
99C22⋊D23—44no—
100C22⋊D23—82no—
101C22⋊D23—82no—
102C2×Dic23—22no—
103C2×Dic23C2×D411yescharacteristic
104C2×Dic23C2×D411yescharacteristic
105D92—22no—
106D92—22no—
107D92—22no—
108D92—82no—
109C4×D23—21no—
110C4×D23—21no—
111C4×D23C2×D412yes—
112C4×D23#4112yes—
113Dic46—22no—
114C8×C23—21no—
115C8×C23C2×D412yes—
116C23⋊C8—21no—
117C23⋊C8C2×D412yes—
118#3058—231nomaximal, Sylow
119C22×C23—21no—
120C22×C23—22no—
121C22×C23—42no—
122C22×C23—42no—
123C22×C23—42no—
124C22×C23C22×D411yescharacteristic
125C2×D23—22no—
126C2×D23—21no—
127C2×D23—22no—
128C2×D23—42no—
129C2×D23—42no—
130C2×D23—42no—
131C2×D23—88no—
132C2×D23#12112yes—
133C4×C23—21no—
134C4×C23—42no—
135C4×C23C22×D411yescharacteristic
136C4×C23C2×#4111yescharacteristic
137Dic23—21no—
138Dic23—42no—
139Dic23#12112yes—
140C22×D8—231no—
141C2×#131—231no—
142#535—232no—
143#469—231no—
144#469—231no—
145#469—231no—
146#469D2311yescharacteristic, complemented
147#466—232no—
148#466—232no—
149#427—231no—
150#418—232no—
151C2×C23—41no—
152C2×C23—82no—
153C2×C23C2×#12111yescharacteristic
154C2×C23#57612yes—
155D23—22no—
156D23—41no—
157D23—82no—
158C2×#41—231no—
159C22×D4—232no—
160C2×D8—232no—
161C2×D8—231no—
162C2×D8—464no—
163C2×D8C2×D2311yescharacteristic
164#131—464no—
165C2×M16—231no—
166C2×M16—231no—
167C2×M16C2×D2311yescharacteristic, complemented
168C22×C8—231no—
169C22×C8—231no—
170C22×C8—231no—
171#127—462no—
172#124—462no—
173#121—232no—
174#121—232no—
175#121—232no—
176#121C2×D2312yescomplemented
177#120—462no—
178#120—462no—
179#117—232no—
180#107—232no—
181#106—231no—
182#106C2×D2311yescharacteristic, complemented
183#102—232no—
184#102—232no—
185#102—232no—
186#102C2×D2312yescomplemented
187C23#305811yescharacteristic, complemented, Sylow
188C24—462no—
189#41—462no—
190#41—462no—
191C2×Q8—231no—
192C2×D4—22no—
193C2×D4—231no—
194C2×D4—231no—
195C2×D4—231no—
196C2×D4—232no—
197C2×D4—462no—
198C2×D4—464no—
199C2×D4—464no—
200C2×D4—462no—
201C2×D4—462no—
202C2×D4—462no—
203C2×D4C22×D2312yes—
204C22×C4—231no—
205C22×C4—231no—
206C22×C4C22×D2311yescharacteristic
207D8—22no—
208D8—464no—
209D8—462no—
210M16—22no—
211M16—462no—
212M16—462no—
213C2×C8—231no—
214C2×C8—234no—
215C2×C8—231no—
216C2×C8—462no—
217C2×C8—462no—
218C2×C8C22×D2311yescharacteristic
219C2×C8C22×D2311yescharacteristic
220C4⋊C4—232no—
221C4⋊C4C22×D2312yes—
222C22⋊C4—22no—
223C22⋊C4—462no—
224C22⋊C4—462no—
225C22⋊C4—462no—
226C22⋊C4—462no—
227C42—462no—
228C23—22no—
229C23—231no—
230C23—231no—
231C23—462no—
232C23—924no—
233C23—1842no—
234C23—1842no—
235C23D4×D2311yescharacteristic
236Q8—462no—
237D4—22no—
238D4—22no—
239D4—82no—
240D4—462no—
241D4—462no—
242D4—462no—
243D4—462no—
244D4—462no—
245D4—924no—
246D4—1842no—
247D4—1842no—
248D4—1842no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—231no—
253C2×C4—232no—
254C2×C4—232no—
255C2×C4—231no—
256C2×C4—461no—
257C2×C4—461no—
258C2×C4—462no—
259C2×C4D4×D2311yescharacteristic
260C2×C4C23×D2311yescharacteristic
261C8—21no—
262C8—232no—
263C8—461no—
264C8D4×D2312yes—
265C22—21no—
266C22—22no—
267C22—42no—
268C22—42no—
269C22—42no—
270C22—232no—
271C22—462no—
272C22—461no—
273C22—462no—
274C22—922no—
275C22—922no—
276C22—922no—
277C22—1848no—
278C22C2×D4×D2311yescharacteristic
279C4—21no—
280C4—42no—
281C4—232no—
282C4—461no—
283C4—922no—
284C4C2×D4×D2311yescharacteristic
285C4#41×D2311yescharacteristic
286C2—41no—
287C2—82no—
288C2—462no—
289C2—921no—
290C2—1842no—
291C2#121×D2311yescharacteristic
292C2#1309322112yes—
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#469C2
socleC22×C23C22×D4
hypercenter#469D23
hypocenterC23#3058
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. C2×D8×D23C2semidirect
2. C2×#10625078C2semidirect
3. #13092983C2semidirect
4. #13092671C2semidirect
5. #13092670C2semidirect
6. #13092667C2semidirect
7. #13092652C2semidirect
8. #13092651C2semidirect
9. #13092452C2semidirect
10. #13092420C2semidirect
11. C23×#469C2semidirect
15. C2×M16×C23C22semidirect
16. C23×#121C22semidirect
18. #10625109C22semidirect
21. #10625101C22semidirect
22. C22×C23⋊C8C22semidirect
27. C2×#67262C22semidirect
29. C2×C8×D23C22semidirect
30. #10625066C22semidirect
34. C23×#106C22semidirect
35. C23×#102C22semidirect
36. #10625014C22semidirect
37. #10625003C22semidirect
38. #10624999C22semidirect
39. #10624991C22semidirect
40. #10624989C22semidirect
80. C8×D23D4semidirect
146. #469D23semidirect
167. C2×M16C2×D23semidirect
176. #121C2×D23semidirect
182. #106C2×D23semidirect
186. #102C2×D23semidirect
187. C23#3058semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D232
C2×#106250782
#130929832
#130926712
#130926702
#130926672
#130926522
#130926512
#130924522
#130924202
C23×#4692
#305823