Finite Group Databasebeta

← #15683860

Subgroups — #15683860

Order 2944.

572 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 137 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×#10625089C212yesmaximal, complemented
2C2×#10625085C212yesmaximal, complemented
3#13092968C211yesmaximal, characteristic, complemented
4#124×D23C211yesmaximal, characteristic, complemented
5#13092809C211yesmaximal, characteristic, complemented
6#13092807C211yesmaximal, characteristic, complemented
7#13092806C211yesmaximal, characteristic, complemented
8#13092802C212yesmaximal, complemented
9#13092798C212yesmaximal, complemented
10#13092369C211yesmaximal, characteristic, complemented
11C23×#497C211yesmaximal, characteristic, complemented
12C2×#67292C2212yes—
13C2×Q8×D23C2211yescharacteristic
14C2×D4×D23C2211yescharacteristic
15C2×Q16×C23C2212yescomplemented
16C2×SD16×C23C2212yes—
17C23×C4⋊Q8C2211yescharacteristic, complemented
18C23×#124C2211yescharacteristic
19#10625118C2211yescharacteristic
20#10625118C2212yescomplemented
21C2×#67275C2212yescomplemented
22C2×#67274C2212yes—
23C2×#67274C2212yescomplemented
24#10625107C2211yescharacteristic
25C2×#67272C2212yes—
26#10625089—28no—
27#10625085—28no—
28C2×D184C2212yes—
29C2×#67263C2212yescomplemented
30C2×#67262C2212yes—
31#10625066—22no—
32#10625064—22no—
33#10625056—22no—
34C22⋊C4×D23—22no—
35#10625046C2211yescharacteristic
36#10625045C2211yescharacteristic, complemented
37C42×D23C2211yescharacteristic
38C23×#97C2211yescharacteristic, complemented
39C8×Dic23C2212yescomplemented
40#10624985C2211yescharacteristic, complemented
41C23×D23—21no—
42C2×Q8×C23C2312yes—
43C2×Q8×C23C2311yescharacteristic
44C2×D4×C23C2311yescharacteristic
45C2×C22⋊D23—21no—
46#67292—24no—
47#67292—24no—
48Q8×D23—24no—
49D4×D23—24no—
50C2×D92—22no—
51C2×D92—22no—
52C2×D92C2312yes—
53C2×D92C2311yescharacteristic
54C2×C4×D23—21no—
55C2×C4×D23—22no—
56C2×C4×D23D412yes—
57C2×C4×D23C2311yescharacteristic
58C2×Dic46—21no—
59C2×Dic46C2311yescharacteristic
60Q16×C23—24no—
61SD16×C23—24no—
62C2×C8×C23C2312yes—
63C4⋊C4×C23—22no—
64C22⋊C4×C23—22no—
65C42×C23C2311yescharacteristic
66C22⋊Dic23—22no—
67#67275—24no—
68#67274—24no—
69#67274—24no—
70#67272—24no—
71(C2×D23)⋊C4—22no—
72(C2×D23)⋊C4—22no—
73(C2×D23)⋊C4—24no—
74C4×Dic23D412yes—
75C4×Dic23C2311yescharacteristic
76C2×C23⋊C8C2312yes—
77D184—24no—
78#67263—24no—
79#67262D418yescomplemented
80C23×C23—21no—
81C22×D23—21no—
82C22×D23—22no—
83C22×D23—44no—
84C22×D23—42no—
85C22×D23C2×D411yescharacteristic
86Q8×C23—22no—
87Q8×C23—22no—
88Q8×C23—22no—
89D4×C23—22no—
90C2×C4×C23—21no—
91C2×C4×C23—22no—
92C2×C4×C23C2×D412yes—
93C2×C4×C23C2411yescharacteristic
94C22⋊D23—42no—
95C2×Dic23—21no—
96C2×Dic23C2×D412yes—
97C2×Dic23C2×D411yescharacteristic
98D92—22no—
99D92—22no—
100D92—22no—
101D92—44no—
102D92—44no—
103C4×D23—42no—
104C4×D23—42no—
105C4×D23—44no—
106C4×D23C2×D414yes—
107Dic46—22no—
108Dic46—42no—
109C8×C23C2×D414yes—
110C23⋊C8C2×D414yes—
111#3153—231nomaximal, Sylow
112C22×C23—41no—
113C22×C23—42no—
114C22×C23C22×D411yescharacteristic
115C2×D23—22no—
116C2×D23—42no—
117C2×D23—41no—
118C2×D23—44no—
119C2×D23—42no—
120C2×D23—84no—
121C2×D23#12712yes—
122C4×C23—22no—
123C4×C23—41no—
124C4×C23—42no—
125C4×C23C22×D412yes—
126Dic23—22no—
127Dic23—41no—
128Dic23#12712yes—
129C2×#137—232no—
130C2×AGL(1,ℤ/8)—232no—
131#532—231no—
132C2×#124—231no—
133#497—231no—
134#497D2311yescharacteristic, complemented
135#496—231no—
136#496—231no—
137#495—232no—
138#495—232no—
139C4×M16—231no—
140C2×C23—81no—
141C2×C23C2×#12711yescharacteristic
142C2×C23#57512yes—
143D23—22no—
144D23—82no—
145D23—81no—
146C2×#41—232no—
147C22×Q8—231no—
148C22×D4—231no—
149#137—468no—
150AGL(1,ℤ/8)—468no—
151C2×Q16—232no—
152C2×Q16C2×D2312yescomplemented
153C2×SD16—232no—
154C2×SD16—232no—
155C2×SD16—232no—
156C2×SD16C2×D2312yes—
157C2×D8—232no—
158C2×D8—232no—
159C2×M16—232no—
160C4⋊Q8C2×D2311yescharacteristic, complemented
161#127—231no—
162#124—231no—
163#124—232no—
164#124—231no—
165#124—231no—
166#124—462no—
167#124C2×D2311yescharacteristic
168#121—462no—
169C4×D4—462no—
170C2×C22⋊C4—462no—
171C2×C42—231no—
172#97—231no—
173#97C2×D2311yescharacteristic, complemented
174C4×C8—232no—
175C23#315311yescharacteristic, complemented, Sylow
176C24—461no—
177#41—464no—
178#41—464no—
179C2×Q8—231no—
180C2×Q8—461no—
181C2×Q8—464no—
182C2×Q8C22×D2311yescharacteristic
183C2×Q8C22×D2312yes—
184C2×D4—231no—
185C2×D4—232no—
186C2×D4—462no—
187C2×D4—464no—
188C2×D4—461no—
189C2×D4—462no—
190C2×D4C22×D2311yescharacteristic
191C22×C4—231no—
192C22×C4—232no—
193C22×C4—462no—
194C22×C4—461no—
195Q16—24no—
196Q16—464no—
197SD16—24no—
198SD16—464no—
199SD16—464no—
200SD16—464no—
201D8—464no—
202D8—464no—
203M16—238no—
204C2×C8—232no—
205C2×C8C22×D2312yes—
206C4⋊C4—22no—
207C22⋊C4—22no—
208C22⋊C4—462no—
209C22⋊C4—464no—
210C22⋊C4—462no—
211C22⋊C4—462no—
212C42—232no—
213C42—231no—
214C42C22×D2311yescharacteristic
215C23—21no—
216C23—231no—
217C23—461no—
218C23—462no—
219C23—922no—
220C23—924no—
221Q8—22no—
222Q8—22no—
223Q8—22no—
224Q8—462no—
225Q8—922no—
226D4—22no—
227D4—462no—
228D4—462no—
229D4—462no—
230D4—924no—
231D4—924no—
232D4—922no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—231no—
236C2×C4—234no—
237C2×C4—232no—
238C2×C4—461no—
239C2×C4—922no—
240C2×C4—924no—
241C2×C4—922no—
242C2×C4D4×D2312yes—
243C2×C4C23×D2311yescharacteristic
244C8—234no—
245C8D4×D2314yes—
246C22—41no—
247C22—42no—
248C22—232no—
249C22—462no—
250C22—922no—
251C22—921no—
252C22—924no—
253C22—922no—
254C22—1844no—
255C22C2×D4×D2311yescharacteristic
256C4—22no—
257C4—42no—
258C4—41no—
259C4—232no—
260C4—462no—
261C4—921no—
262C4C2×D4×D2312yes—
263C2—81no—
264C2—462no—
265C2—1841no—
266C2—1842no—
267C2#127×D2311yescharacteristic
268C2#1309321612yes—
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#497C2
socleC22×C23C22×D4
hypercenter#497D23
hypocenterC23#3153
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. C2×#10625089C2semidirect
2. C2×#10625085C2semidirect
3. #13092968C2semidirect
4. #124×D23C2semidirect
5. #13092809C2semidirect
6. #13092807C2semidirect
7. #13092806C2semidirect
8. #13092802C2semidirect
9. #13092798C2semidirect
10. #13092369C2semidirect
11. C23×#497C2semidirect
15. C2×Q16×C23C22semidirect
17. C23×C4⋊Q8C22semidirect
20. #10625118C22semidirect
21. C2×#67275C22semidirect
23. C2×#67274C22semidirect
29. C2×#67263C22semidirect
36. #10625045C22semidirect
38. C23×#97C22semidirect
39. C8×Dic23C22semidirect
40. #10624985C22semidirect
79. #67262D4semidirect
134. #497D23semidirect
152. C2×Q16C2×D23semidirect
160. C4⋊Q8C2×D23semidirect
173. #97C2×D23semidirect
175. C23#3153semidirect

Maximal subgroups

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

subgroupindex
C2×#106250892
C2×#106250852
#130929682
#124×D232
#130928092
#130928072
#130928062
#130928022
#130927982
#130923692
C23×#4972
#315323