Finite Group Databasebeta

← #15683040

Subgroups — #15683040

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×#10625072C211yesmaximal, characteristic, complemented
3#13092983C212yesmaximal, complemented
4#13092669C212yesmaximal, complemented
5#13092668C212yesmaximal, complemented
6#13092654C211yesmaximal, characteristic, complemented
7#13092653C211yesmaximal, characteristic, complemented
8#13092650C211yesmaximal, characteristic, complemented
9#13092454C211yesmaximal, characteristic, complemented
10#13092420C212yesmaximal, complemented
11C23×#466C211yesmaximal, characteristic, complemented
12C2×D4×D23C2212yes—
13C2×#67288C2211yescharacteristic
14C2×D8×C23C2211yescharacteristic
15C22×C8×C23C2211yescharacteristic, complemented
16C23×#121C2212yescomplemented
17#10625111—22no—
18#10625109C2212yescomplemented
19#10625108—22no—
20C2×#67272C2212yes—
21#10625101C2212yescomplemented
22C2×#67267C2211yescharacteristic, complemented
23D8×D23—24no—
24C2×D184C2211yescharacteristic
25#10625072—24no—
26C2×#67262C2211yescharacteristic
27C2×#67262C2211yescharacteristic, complemented
28C2×C8×D23C2211yescharacteristic
29C2×C8×D23C2211yescharacteristic, complemented
30#10625066C2212yescomplemented
31#10625063C2212yes—
32#10625056—22no—
33#10625053—22no—
34C23×#107C2211yescharacteristic, complemented
35C23×#102C2212yescomplemented
36#10625014C2212yescomplemented
37#10625003C2212yescomplemented
38#10625000C2211yescharacteristic, complemented
39#10624991C2212yescomplemented
40#10624990C2212yescomplemented
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—
61C2×C8×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—
73#67267—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—21no—
121C22×C23—21no—
122C22×C23—42no—
123C22×C23—42no—
124C22×C23—42no—
125C22×C23C22×D411yescharacteristic
126C2×D23—21no—
127C2×D23—21no—
128C2×D23—21no—
129C2×D23—21no—
130C2×D23—21no—
131C2×D23—42no—
132C2×D23—42no—
133C2×D23—42no—
134C2×D23—88no—
135C2×D23#12112yes—
136C4×C23—21no—
137C4×C23—42no—
138C4×C23C22×D411yescharacteristic
139C4×C23C2×#4111yescharacteristic
140Dic23—21no—
141Dic23—42no—
142Dic23#12112yes—
143C22×D8—231no—
144C2×#131—231no—
145#535—232no—
146#469—232no—
147#469—232no—
148#466—231no—
149#466—231no—
150#466—231no—
151#466D2311yescharacteristic, complemented
152#427—231no—
153#418—232no—
154C2×C23—41no—
155C2×C23—82no—
156C2×C23C2×#12111yescharacteristic
157C2×C23#57611yescharacteristic
158C2×C23#57611yescharacteristic
159D23—22no—
160D23—41no—
161D23—82no—
162C2×#41—231no—
163C22×D4—232no—
164C2×D8—232no—
165C2×D8—231no—
166C2×D8—464no—
167C2×D8C2×D2311yescharacteristic
168#131—464no—
169C2×M16—231no—
170C2×M16—231no—
171C2×M16—231no—
172C22×C8—231no—
173C22×C8—231no—
174C22×C8C2×D2311yescharacteristic, complemented
175#127—462no—
176#124—462no—
177#121—232no—
178#121—232no—
179#121—232no—
180#121C2×D2312yescomplemented
181#120—462no—
182#120—462no—
183#117—232no—
184#107—231no—
185#107C2×D2311yescharacteristic, complemented
186#106—232no—
187#102—232no—
188#102—232no—
189#102—232no—
190#102C2×D2312yescomplemented
191C23#305811yescharacteristic, complemented, Sylow
192C24—462no—
193#41—462no—
194#41—462no—
195C2×Q8—231no—
196C2×D4—22no—
197C2×D4—231no—
198C2×D4—231no—
199C2×D4—231no—
200C2×D4—232no—
201C2×D4—462no—
202C2×D4—464no—
203C2×D4—464no—
204C2×D4—462no—
205C2×D4—462no—
206C2×D4—462no—
207C2×D4C22×D2312yes—
208C22×C4—231no—
209C22×C4—231no—
210C22×C4C22×D2311yescharacteristic
211D8—22no—
212D8—464no—
213D8—462no—
214M16—462no—
215M16—462no—
216M16—462no—
217C2×C8—22no—
218C2×C8—231no—
219C2×C8—234no—
220C2×C8—231no—
221C2×C8—462no—
222C2×C8C22×D2311yescharacteristic
223C2×C8C22×D2311yescharacteristic
224C4⋊C4—232no—
225C4⋊C4C22×D2312yes—
226C22⋊C4—22no—
227C22⋊C4—462no—
228C22⋊C4—462no—
229C22⋊C4—462no—
230C22⋊C4—462no—
231C42—462no—
232C23—22no—
233C23—231no—
234C23—231no—
235C23—462no—
236C23—924no—
237C23—1842no—
238C23—1842no—
239C23D4×D2311yescharacteristic
240Q8—462no—
241D4—22no—
242D4—22no—
243D4—82no—
244D4—462no—
245D4—462no—
246D4—462no—
247D4—462no—
248D4—462no—
249D4—924no—
250D4—1842no—
251D4—1842no—
252D4—1842no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—231no—
257C2×C4—232no—
258C2×C4—232no—
259C2×C4—231no—
260C2×C4—461no—
261C2×C4—461no—
262C2×C4—462no—
263C2×C4D4×D2311yescharacteristic
264C2×C4C23×D2311yescharacteristic
265C8—21no—
266C8—232no—
267C8—461no—
268C8D4×D2312yes—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—42no—
273C22—42no—
274C22—42no—
275C22—232no—
276C22—461no—
277C22—461no—
278C22—461no—
279C22—461no—
280C22—461no—
281C22—922no—
282C22—922no—
283C22—922no—
284C22—1848no—
285C22C2×D4×D2311yescharacteristic
286C4—21no—
287C4—42no—
288C4—232no—
289C4—461no—
290C4—922no—
291C4C2×D4×D2311yescharacteristic
292C4#41×D2311yescharacteristic
293C2—41no—
294C2—82no—
295C2—462no—
296C2—921no—
297C2—1842no—
298C2#121×D2311yescharacteristic
299C2#1309321811yescharacteristic
300C2#1309321911yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#466C2
socleC22×C23C22×D4
hypercenter#466D23
hypocenterC23#3058
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C2×D8×D23C2semidirect
2. C2×#10625072C2semidirect
3. #13092983C2semidirect
4. #13092669C2semidirect
5. #13092668C2semidirect
6. #13092654C2semidirect
7. #13092653C2semidirect
8. #13092650C2semidirect
9. #13092454C2semidirect
10. #13092420C2semidirect
11. C23×#466C2semidirect
15. C22×C8×C23C22semidirect
16. C23×#121C22semidirect
18. #10625109C22semidirect
21. #10625101C22semidirect
22. C2×#67267C22semidirect
27. C2×#67262C22semidirect
29. C2×C8×D23C22semidirect
30. #10625066C22semidirect
34. C23×#107C22semidirect
35. C23×#102C22semidirect
36. #10625014C22semidirect
37. #10625003C22semidirect
38. #10625000C22semidirect
39. #10624991C22semidirect
40. #10624990C22semidirect
80. C8×D23D4semidirect
151. #466D23semidirect
174. C22×C8C2×D23semidirect
180. #121C2×D23semidirect
185. #107C2×D23semidirect
190. #102C2×D23semidirect
191. 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×#106250722
#130929832
#130926692
#130926682
#130926542
#130926532
#130926502
#130924542
#130924202
C23×#4662
#305823