Finite Group Databasebeta

← #15683879

Subgroups — #15683879

Order 2944.

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

normal subgroups only

This group has 596 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×#10625085C212yesmaximal, complemented
2C2×#10625090C211yesmaximal, characteristic, complemented
3C2×D8×D23C211yesmaximal, characteristic, complemented
4#13092985C212yesmaximal, complemented
5#13092807C212yesmaximal, complemented
6#13092803C212yesmaximal, complemented
7#13092802C211yesmaximal, characteristic, complemented
8#13092794C211yesmaximal, characteristic, complemented
9#13092792C211yesmaximal, characteristic, complemented
10#13092371C211yesmaximal, characteristic, complemented
11C23×#495C211yesmaximal, characteristic, complemented
12C2×#67292C2212yes—
13C2×D4×D23C2212yes—
14C2×Q16×C23C2211yescharacteristic, complemented
15C2×SD16×C23C2212yescomplemented
16C2×D8×C23C2211yescharacteristic
17C23×#124C2212yescomplemented
18#10625118C2212yescomplemented
19C2×#67274C2212yescomplemented
20C2×#67274C2212yescomplemented
21#10625111C2212yescomplemented
22C2×#67272C2212yes—
23C2×#67272C2212yescomplemented
24#10625090—24no—
25#10625085—28no—
26D8×D23—24no—
27C2×D184C2211yescharacteristic
28C2×D184C2211yescharacteristic, complemented
29C2×D184C2212yescomplemented
30C2×#67262C2211yescharacteristic
31C2×C8×D23C2211yescharacteristic
32#10625055—24no—
33#10625053—24no—
34#10625045C2212yescomplemented
35#10625043C2211yescharacteristic
36C4×C8×C23C2211yescharacteristic, complemented
37#10624997C2211yescharacteristic, complemented
38C8×Dic23C2211yescharacteristic, complemented
39#10624985C2211yescharacteristic, complemented
40C23×D23—22no—
41C2×Q8×C23C2312yes—
42C2×D4×C23C2312yes—
43C2×C22⋊D23—22no—
44C2×C22⋊D23—24no—
45#67292—24no—
46#67292—24no—
47D4×D23—24no—
48D4×D23—24no—
49C2×D92—22no—
50C2×D92—24no—
51C2×D92C2312yes—
52C2×D92C2312yes—
53C2×C4×D23—22no—
54C2×C4×D23C2311yescharacteristic
55Q16×C23—22no—
56SD16×C23—24no—
57D8×C23—22no—
58C2×C8×C23C2311yescharacteristic
59C2×C8×C23C2311yescharacteristic
60C22⋊C4×C23—24no—
61C42×C23C2311yescharacteristic
62#67274—24no—
63#67274—24no—
64#67272—24no—
65#67272—24no—
66(C2×D23)⋊C4—24no—
67(C2×D23)⋊C4D412yes—
68Dic23⋊C4D412yes—
69C4×Dic23C2311yescharacteristic
70C2×C23⋊C8C2311yescharacteristic
71C2×C23⋊C8C2311yescharacteristic
72D184—22no—
73D184—24no—
74D184—22no—
75#67262D414yescomplemented
76C8×D23D414yescomplemented
77C23×C23—22no—
78C22×D23—22no—
79C22×D23—22no—
80C22×D23—44no—
81C22×D23—84no—
82C22×D23C2×D411yescharacteristic
83Q8×C23—22no—
84Q8×C23—22no—
85D4×C23—22no—
86D4×C23—22no—
87C2×C4×C23—22no—
88C2×C4×C23C2×D412yes—
89C2×C4×C23C2411yescharacteristic
90C22⋊D23—44no—
91C22⋊D23—84no—
92C2×Dic23C2×D412yes—
93C2×Dic23C2×D411yescharacteristic
94D92—22no—
95D92—22no—
96D92—22no—
97D92—22no—
98D92—44no—
99D92—84no—
100C4×D23—44no—
101C4×D23C2×D412yes—
102C4×D23C2×D412yes—
103C8×C23C2×D412yes—
104C8×C23C2×D412yes—
105C23⋊C8C2×D412yes—
106C23⋊C8C2×D412yes—
107#3155—231nomaximal, Sylow
108C22×C23—42no—
109C22×C23—44no—
110C22×C23C22×D411yescharacteristic
111C2×D23—22no—
112C2×D23—42no—
113C2×D23—42no—
114C2×D23—44no—
115C2×D23—44no—
116C2×D23—88no—
117C2×D23#12712yes—
118C4×C23—22no—
119C4×C23—42no—
120C4×C23C22×D411yescharacteristic
121C4×C23C22×D411yescharacteristic
122Dic23—22no—
123Dic23#12712yes—
124C2×AGL(1,ℤ/8)—232no—
125C2×#135—231no—
126C22×D8—231no—
127#535—232no—
128#496—232no—
129#496—232no—
130#495—231no—
131#495D2311yescharacteristic, complemented
132#493—231no—
133#493—231no—
134#405—231no—
135C2×C23—82no—
136C2×C23C2×#12711yescharacteristic
137C2×C23#57612yes—
138D23—22no—
139D23—82no—
140D23—82no—
141C2×#41—232no—
142C22×D4—232no—
143AGL(1,ℤ/8)—468no—
144#135—464no—
145C2×Q16C2×D2311yescharacteristic, complemented
146C2×SD16—232no—
147C2×SD16—232no—
148C2×SD16C2×D2312yescomplemented
149C2×D8—232no—
150C2×D8—232no—
151C2×D8—231no—
152C2×D8—231no—
153C2×D8—232no—
154C2×D8—464no—
155C2×D8C2×D2311yescharacteristic
156C2×M16—231no—
157C22×C8—231no—
158#127—232no—
159#127—232no—
160#124—232no—
161#124C2×D2312yescomplemented
162#121—464no—
163#120—464no—
164#117—231no—
165#97—231no—
166#97—231no—
167C4×C8—231no—
168C4×C8C2×D2311yescharacteristic, complemented
169C23#315511yescharacteristic, complemented, Sylow
170C24—462no—
171#41—464no—
172#41—464no—
173C2×Q8C22×D2312yes—
174C2×D4—232no—
175C2×D4—232no—
176C2×D4—462no—
177C2×D4—464no—
178C2×D4—464no—
179C2×D4—462no—
180C2×D4—464no—
181C2×D4—464no—
182C2×D4C22×D2312yes—
183C22×C4—231no—
184C22×C4—462no—
185Q16—22no—
186SD16—24no—
187SD16—464no—
188SD16—464no—
189D8—22no—
190D8—464no—
191D8—464no—
192D8—462no—
193D8—462no—
194D8—464no—
195M16—234no—
196C2×C8—231no—
197C2×C8—231no—
198C2×C8—234no—
199C2×C8C22×D2311yescharacteristic
200C2×C8C22×D2311yescharacteristic
201C4⋊C4—232no—
202C22⋊C4—24no—
203C22⋊C4—232no—
204C22⋊C4—464no—
205C42—231no—
206C42C22×D2311yescharacteristic
207C23—22no—
208C23—231no—
209C23—462no—
210C23—462no—
211C23—924no—
212C23—1844no—
213Q8—22no—
214Q8—22no—
215D4—22no—
216D4—22no—
217D4—462no—
218D4—462no—
219D4—462no—
220D4—462no—
221D4—924no—
222D4—924no—
223D4—1844no—
224D4—1844no—
225C2×C4—22no—
226C2×C4—231no—
227C2×C4—232no—
228C2×C4—232no—
229C2×C4—232no—
230C2×C4—924no—
231C2×C4D4×D2312yes—
232C2×C4C23×D2311yescharacteristic
233C8—232no—
234C8—232no—
235C8D4×D2312yes—
236C8D4×D2312yes—
237C22—42no—
238C22—44no—
239C22—232no—
240C22—462no—
241C22—922no—
242C22—922no—
243C22—924no—
244C22—924no—
245C22—1848no—
246C22C2×D4×D2311yescharacteristic
247C4—22no—
248C4—42no—
249C4—232no—
250C4—462no—
251C4C2×D4×D2311yescharacteristic
252C4C2×D4×D2311yescharacteristic
253C2—82no—
254C2—462no—
255C2—1842no—
256C2—1842no—
257C2#127×D2311yescharacteristic
258C2#1309321912yes—
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#495C2
socleC22×C23C22×D4
hypercenter#495D23
hypocenterC23#3155
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C2×#10625085C2semidirect
2. C2×#10625090C2semidirect
3. C2×D8×D23C2semidirect
4. #13092985C2semidirect
5. #13092807C2semidirect
6. #13092803C2semidirect
7. #13092802C2semidirect
8. #13092794C2semidirect
9. #13092792C2semidirect
10. #13092371C2semidirect
11. C23×#495C2semidirect
14. C2×Q16×C23C22semidirect
15. C2×SD16×C23C22semidirect
17. C23×#124C22semidirect
18. #10625118C22semidirect
19. C2×#67274C22semidirect
20. C2×#67274C22semidirect
21. #10625111C22semidirect
23. C2×#67272C22semidirect
28. C2×D184C22semidirect
29. C2×D184C22semidirect
34. #10625045C22semidirect
36. C4×C8×C23C22semidirect
37. #10624997C22semidirect
38. C8×Dic23C22semidirect
39. #10624985C22semidirect
75. #67262D4semidirect
76. C8×D23D4semidirect
131. #495D23semidirect
145. C2×Q16C2×D23semidirect
148. C2×SD16C2×D23semidirect
161. #124C2×D23semidirect
168. C4×C8C2×D23semidirect
169. C23#3155semidirect

Maximal subgroups

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

subgroupindex
C2×#106250852
C2×#106250902
C2×D8×D232
#130929852
#130928072
#130928032
#130928022
#130927942
#130927922
#130923712
C23×#4952
#315523