Finite Group Databasebeta

← #15683846

Subgroups — #15683846

Order 2944.

656 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 141 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×#10625082C212yesmaximal, complemented
3#13092966C211yesmaximal, characteristic, complemented
4#127×D23C211yesmaximal, characteristic, complemented
5#13092807C211yesmaximal, characteristic, complemented
6#13092806C211yesmaximal, characteristic, complemented
7#13092804C211yesmaximal, characteristic, complemented
8#13092792C212yesmaximal, complemented
9#13092788C212yesmaximal, complemented
10#13092369C211yesmaximal, characteristic, complemented
11C23×#496C211yesmaximal, characteristic, complemented
12C2×#67292C2211yescharacteristic
13C2×#67290C2211yescharacteristic
14C2×D4×D23—22no—
15C2×D4×D23C2212yes—
16C2×SD16×C23C2212yescomplemented
17C2×D8×C23C2212yescomplemented
18C23×#127C2211yescharacteristic
19C23×#124C2211yescharacteristic, complemented
20#10625115C2211yescharacteristic, complemented
21C2×#67274C2212yescomplemented
22#10625111—22no—
23#10625111C2212yes—
24#10625111C2211yescharacteristic, complemented
25C2×#67273C2212yescomplemented
26C2×#67272C2212yescomplemented
27C2×#67272C2212yescomplemented
28#10625085—28no—
29#10625082—28no—
30C2×D184C2212yescomplemented
31C2×#67263C2212yescomplemented
32C2×#67262C2212yes—
33#10625055—22no—
34(C22⋊D23)⋊C4—22no—
35#10625046C2211yescharacteristic, complemented
36#10625045C2211yescharacteristic
37C42×D23C2211yescharacteristic
38C23×#97C2211yescharacteristic, complemented
39C8×Dic23C2212yescomplemented
40#10624985C2211yescharacteristic, complemented
41C23×D23—22no—
42C2×Q8×C23C2311yescharacteristic
43C2×D4×C23—22no—
44C2×D4×C23C2311yescharacteristic
45C2×D4×C23C2312yes—
46C2×C22⋊D23—21no—
47C2×C22⋊D23—22no—
48C2×C22⋊D23—22no—
49C2×C22⋊D23—24no—
50C22×Dic23—21no—
51#67292—24no—
52#67290—24no—
53D4×D23—24no—
54D4×D23—24no—
55D4×D23—48no—
56C2×D92—21no—
57C2×D92—22no—
58C2×D92C2312yes—
59C2×D92C2311yescharacteristic
60C2×C4×D23—21no—
61C2×C4×D23D412yes—
62C2×C4×D23C2311yescharacteristic
63C2×Dic46C2311yescharacteristic
64SD16×C23—24no—
65D8×C23—24no—
66C2×C8×C23C2312yes—
67C22⋊C4×C23—22no—
68C42×C23C2311yescharacteristic
69#67274—24no—
70#67273—24no—
71#67272—24no—
72#67272—24no—
73(C2×D23)⋊C4—22no—
74Dic23⋊C4—22no—
75C4×Dic23D412yes—
76C4×Dic23C2311yescharacteristic
77C2×C23⋊C8C2312yes—
78D184—24no—
79#67263—24no—
80#67262D418yescomplemented
81C23×C23—21no—
82C23×C23—22no—
83C22×D23—21no—
84C22×D23—22no—
85C22×D23—48no—
86C22×D23—44no—
87C22×D23C2×D411yescharacteristic
88Q8×C23—22no—
89D4×C23—22no—
90D4×C23—22no—
91D4×C23—22no—
92D4×C23—44no—
93C2×C4×C23—21no—
94C2×C4×C23C2×D412yes—
95C2×C4×C23C2411yescharacteristic
96C22⋊D23—42no—
97C22⋊D23—44no—
98C22⋊D23—48no—
99C22⋊D23—44no—
100C2×Dic23—21no—
101C2×Dic23—42no—
102C2×Dic23C2×D411yescharacteristic
103C2×Dic23C2×D412yes—
104D92—22no—
105D92—22no—
106D92—22no—
107D92—44no—
108D92—42no—
109C4×D23—24no—
110C4×D23—42no—
111C4×D23C2×D414yes—
112Dic46—22no—
113C8×C23C2×D414yescomplemented
114C23⋊C8C2×D414yescomplemented
115#3151—231nomaximal, Sylow
116C22×C23—41no—
117C22×C23—42no—
118C22×C23—44no—
119C22×C23—42no—
120C22×C23C22×D411yescharacteristic
121C2×D23—22no—
122C2×D23—41no—
123C2×D23—42no—
124C2×D23—44no—
125C2×D23—42no—
126C2×D23—88no—
127C2×D23#12712yes—
128C4×C23—22no—
129C4×C23—41no—
130C4×C23C22×D412yes—
131Dic23—41no—
132Dic23#12712yes—
133Dic23AGL(1,ℤ/8)14yescomplemented
134C2×AGL(1,ℤ/8)—232no—
135C2×AGL(1,ℤ/8)—232no—
136#532—231no—
137C2×#127—231no—
138#496—231no—
139#496—231no—
140#496—231no—
141#496D2311yescharacteristic, complemented
142#493—232no—
143#492—232no—
144C4×M16—231no—
145C2×C23—82no—
146C2×C23—81no—
147C2×C23C2×#12711yescharacteristic
148C2×C23C2×AGL(1,ℤ/8)12yes—
149D23—22no—
150D23—81no—
151D23—82no—
152C2×#41—231no—
153C2×#41—231no—
154C22×D4—232no—
155C22×D4—462no—
156AGL(1,ℤ/8)—468no—
157AGL(1,ℤ/8)—468no—
158C2×SD16—232no—
159C2×SD16—232no—
160C2×SD16—232no—
161C2×SD16C2×D2312yescomplemented
162C2×D8—232no—
163C2×D8—232no—
164C2×D8—232no—
165C2×D8C2×D2312yescomplemented
166C2×M16—232no—
167C4⋊Q8—231no—
168#127—232no—
169#127—231no—
170#127—231no—
171#127—462no—
172#127C2×D2311yescharacteristic
173#124—231no—
174#124C2×D2311yescharacteristic, complemented
175#121—462no—
176C4×D4—462no—
177C2×C42—231no—
178#97—231no—
179#97C2×D2311yescharacteristic, complemented
180C4×C8—232no—
181C23#315111yescharacteristic, complemented, Sylow
182C24—462no—
183#41—464no—
184#41—464no—
185C2×Q8—231no—
186C2×Q8C22×D2311yescharacteristic
187C2×D4—22no—
188C2×D4—231no—
189C2×D4—232no—
190C2×D4—461no—
191C2×D4—464no—
192C2×D4—464no—
193C2×D4—462no—
194C2×D4—464no—
195C2×D4—462no—
196C2×D4—461no—
197C2×D4—462no—
198C2×D4—928no—
199C2×D4C22×D2311yescharacteristic
200C2×D4C22×D2312yes—
201C22×C4—231no—
202C22×C4—232no—
203C22×C4—461no—
204C22×C4—461no—
205SD16—24no—
206SD16—464no—
207SD16—464no—
208SD16—464no—
209D8—24no—
210D8—464no—
211D8—464no—
212D8—464no—
213M16—238no—
214C2×C8—232no—
215C2×C8C22×D2312yes—
216C4⋊C4—462no—
217C22⋊C4—22no—
218C22⋊C4—462no—
219C42—232no—
220C42—231no—
221C42C22×D2311yescharacteristic
222C23—21no—
223C23—22no—
224C23—231no—
225C23—461no—
226C23—462no—
227C23—924no—
228C23—928no—
229Q8—22no—
230Q8—462no—
231D4—22no—
232D4—22no—
233D4—22no—
234D4—44no—
235D4—462no—
236D4—462no—
237D4—462no—
238D4—924no—
239D4—922no—
240D4—924no—
241D4—928no—
242D4—924no—
243D4—922no—
244C2×C4—21no—
245C2×C4—232no—
246C2×C4—231no—
247C2×C4—234no—
248C2×C4—464no—
249C2×C4—461no—
250C2×C4—922no—
251C2×C4—922no—
252C2×C4D4×D2312yes—
253C2×C4C23×D2311yescharacteristic
254C8—234no—
255C8D4×D2314yescomplemented
256C22—44no—
257C22—42no—
258C22—41no—
259C22—42no—
260C22—232no—
261C22—462no—
262C22—924no—
263C22—922no—
264C22—921no—
265C22—922no—
266C22—1848no—
267C22C2×D4×D2311yescharacteristic
268C4—22no—
269C4—41no—
270C4—234no—
271C4—232no—
272C4—921no—
273C4C2×D4×D2312yes—
274C2—82no—
275C2—81no—
276C2—462no—
277C2—1842no—
278C2—1841no—
279C2#127×D2311yescharacteristic
280C2AGL(1,ℤ/8)×D2312yes—
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#496C2
socleC22×C23C22×D4
hypercenter#496D23
hypocenterC23#3151
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×#10625085C2semidirect
2. C2×#10625082C2semidirect
3. #13092966C2semidirect
4. #127×D23C2semidirect
5. #13092807C2semidirect
6. #13092806C2semidirect
7. #13092804C2semidirect
8. #13092792C2semidirect
9. #13092788C2semidirect
10. #13092369C2semidirect
11. C23×#496C2semidirect
16. C2×SD16×C23C22semidirect
17. C2×D8×C23C22semidirect
19. C23×#124C22semidirect
20. #10625115C22semidirect
21. C2×#67274C22semidirect
24. #10625111C22semidirect
25. C2×#67273C22semidirect
26. C2×#67272C22semidirect
27. C2×#67272C22semidirect
30. C2×D184C22semidirect
31. C2×#67263C22semidirect
35. #10625046C22semidirect
38. C23×#97C22semidirect
39. C8×Dic23C22semidirect
40. #10624985C22semidirect
80. #67262D4semidirect
113. C8×C23C2×D4semidirect
114. C23⋊C8C2×D4semidirect
133. Dic23AGL(1,ℤ/8)semidirect
141. #496D23semidirect
161. C2×SD16C2×D23semidirect
165. C2×D8C2×D23semidirect
174. #124C2×D23semidirect
179. #97C2×D23semidirect
181. C23#3151semidirect
255. C8D4×D23semidirect

Maximal subgroups

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

subgroupindex
C2×#106250852
C2×#106250822
#130929662
#127×D232
#130928072
#130928062
#130928042
#130927922
#130927882
#130923692
C23×#4962
#315123