Finite Group Databasebeta

← #15685163

Subgroups — #15685163

Order 2944.

464 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 117 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
1#13093223C212yesmaximal, complemented
2#13093218C212yesmaximal, complemented
3#13092684C212yesmaximal, complemented
4#13092677C212yesmaximal, complemented
5#13092594C211yesmaximal, characteristic, complemented
6#13092589C211yesmaximal, characteristic, complemented
7#13092584C212yesmaximal, complemented
8#13092540C212yesmaximal, complemented
9C23×#496C211yesmaximal, characteristic, complemented
10#10625158C2211yescharacteristic, complemented
11#10625155C2211yescharacteristic
12#10625155C2212yescomplemented
13C2×SD16×C23C2212yescomplemented
14C2×D8×C23C2212yescomplemented
15C23×#127C2211yescharacteristic, complemented
16C23×#124C2211yescharacteristic, complemented
17#10625113C2212yescomplemented
18#10625103C2212yes—
19#10625103C2212yescomplemented
20#10625103C2212yescomplemented
21#10625087—22no—
22#10625086—22no—
23#10625085—22no—
24SD16×D23—22no—
25#10625083—22no—
26#10625082—22no—
27#10625082—22no—
28D8×D23—22no—
29#10625075C2212yes—
30#10625072C2212yescomplemented
31#10625072C2212yescomplemented
32C23×#97C2211yescharacteristic, complemented
33#10625018C2211yescharacteristic, complemented
34#10625015C2212yescomplemented
35#10625015C2211yescharacteristic, complemented
36#10625001C2212yescomplemented
37#10624987C2212yescomplemented
38#10624987C2212yescomplemented
39C2×Q8×C23C2311yescharacteristic
40C2×D4×C23—41no—
41C2×D4×C23C2312yes—
42C2×D4×C23C2311yescharacteristic
43C2×C22⋊D23—41no—
44C2×C22⋊D23—42no—
45#67292—22no—
46Q8×D23—22no—
47#67290—22no—
48#67290—22no—
49#67290—22no—
50D4×D23—22no—
51D4×D23—22no—
52D4×D23—22no—
53#67288—41no—
54#67288C2312yes—
55#67288C2312yes—
56SD16×C23—22no—
57SD16×C23—22no—
58D8×C23—22no—
59D8×C23—22no—
60C2×C8×C23C2312yes—
61C22⋊C4×C23—41no—
62C42×C23C2311yescharacteristic
63#67275—22no—
64#67274—22no—
65#67273—22no—
66#67273—22no—
67#67273—22no—
68#67272—22no—
69#67272—22no—
70#67272—22no—
71#67267C2312yes—
72#67267C2312yes—
73Dic92D412yescomplemented
74D184D412yescomplemented
75#67263D412yescomplemented
76#67263D412yescomplemented
77#67262—22no—
78#67262—22no—
79C8×D23—22no—
80C8×D23—22no—
81C23×C23—21no—
82C23×C23—22no—
83C22×D23—42no—
84C22×D23—41no—
85Q8×C23—22no—
86D4×C23—22no—
87D4×C23—22no—
88D4×C23—22no—
89D4×C23—82no—
90C2×C4×C23—21no—
91C2×C4×C23—21no—
92C2×C4×C23C2411yescharacteristic
93C22⋊D23—22no—
94C22⋊D23—22no—
95C22⋊D23—42no—
96C22⋊D23—42no—
97C22⋊D23—42no—
98C2×Dic23—42no—
99C2×Dic23—41no—
100D92—41no—
101D92C2×D412yes—
102D92C2×D412yes—
103C4×D23—22no—
104C4×D23—22no—
105C4×D23—42no—
106Dic46—41no—
107Dic46C2×D412yes—
108Dic46C2×D412yes—
109C8×C23C2×D412yes—
110C8×C23C2×D412yes—
111C23⋊C8—22no—
112C23⋊C8—22no—
113#3288—231nomaximal, Sylow
114C22×C23—41no—
115C22×C23—42no—
116C22×C23—82no—
117C22×C23—81no—
118C22×C23H(5,𝔽2)11yescharacteristic
119C2×D23—22no—
120C2×D23—22no—
121C2×D23—162no—
122C2×D23—161no—
123C4×C23—41no—
124C4×C23—41no—
125C4×C23C22×D412yes—
126Dic23—22no—
127Dic23—22no—
128#577—232no—
129#576—232no—
130#496D2311yescharacteristic, complemented
131#472—232no—
132#471—232no—
133#455—231no—
134#454—231no—
135#453—232no—
136#444—232no—
137C2×C23—21no—
138C2×C23—82no—
139C2×C23—81no—
140C2×C23D4211yescharacteristic
141D23—42no—
142D23—42no—
1432−1+4—231no—
144H(5,𝔽2)—231no—
145H(5,𝔽2)—232no—
146#137—232no—
147#137—462no—
148AGL(1,ℤ/8)—232no—
149AGL(1,ℤ/8)—232no—
150AGL(1,ℤ/8)—232no—
151AGL(1,ℤ/8)—462no—
152AGL(1,ℤ/8)—462no—
153AGL(1,ℤ/8)—462no—
154#135—232no—
155#135—462no—
156#135—462no—
157C2×SD16—462no—
158C2×SD16C2×D2312yescomplemented
159C2×D8—462no—
160C2×D8C2×D2312yescomplemented
161#131—232no—
162#131—232no—
163#127C2×D2311yescharacteristic, complemented
164#124C2×D2311yescharacteristic, complemented
165#108—232no—
166#104—232no—
167#104—232no—
168#101—231no—
169#100—232no—
170#100—231no—
171#97C2×D2311yescharacteristic, complemented
172C23#328811yescharacteristic, complemented, Sylow
173#41—232no—
174#41—232no—
175#41—462no—
176#41—462no—
177#41—462no—
178#41—462no—
179#41—921no—
180C2×Q8—462no—
181C2×Q8C22×D2311yescharacteristic
182C2×D4—41no—
183C2×D4—462no—
184C2×D4—462no—
185C2×D4—462no—
186C2×D4—921no—
187C2×D4—922no—
188C2×D4C22×D2311yescharacteristic
189C2×D4C22×D2312yes—
190Q16—232no—
191Q16—462no—
192SD16—22no—
193SD16—22no—
194SD16—232no—
195SD16—232no—
196SD16—462no—
197SD16—462no—
198SD16—462no—
199SD16—462no—
200D8—22no—
201D8—22no—
202D8—232no—
203D8—462no—
204D8—462no—
205D8—462no—
206M16—232no—
207M16—232no—
208M16—462no—
209M16—462no—
210C2×C8—462no—
211C2×C8—462no—
212C2×C8C22×D2312yes—
213C22⋊C4—41no—
214C42C22×D2311yescharacteristic
215C23—21no—
216C23—22no—
217C23—922no—
218C23—921no—
219Q8—22no—
220Q8—232no—
221Q8—232no—
222Q8—921no—
223D4—22no—
224D4—22no—
225D4—22no—
226D4—82no—
227D4—232no—
228D4—232no—
229D4—462no—
230D4—462no—
231D4—921no—
232D4—922no—
233D4—922no—
234D4—922no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—462no—
238C2×C4—462no—
239C2×C4—922no—
240C2×C4—921no—
241C2×C4—922no—
242C2×C4C23×D2311yescharacteristic
243C8—462no—
244C8—462no—
245C8D4×D2312yes—
246C8D4×D2312yes—
247C22—41no—
248C22—42no—
249C22—82no—
250C22—81no—
251C22—462no—
252C22—462no—
253C22—3681no—
254C22—3682no—
255C22#1062515511yescharacteristic
256C4—41no—
257C4—41no—
258C4—462no—
259C4—462no—
260C4C2×D4×D2312yes—
261C2—21no—
262C2—82no—
263C2—81no—
264C2—922no—
265C2—922no—
266C2#1309305211yescharacteristic
subgroupG/H
centerC2#13093052
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#496C2
socleC2×C23D42
hypercenter#496D23
hypocenterC23#3288
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #13093223C2semidirect
2. #13093218C2semidirect
3. #13092684C2semidirect
4. #13092677C2semidirect
5. #13092594C2semidirect
6. #13092589C2semidirect
7. #13092584C2semidirect
8. #13092540C2semidirect
9. C23×#496C2semidirect
10. #10625158C22semidirect
12. #10625155C22semidirect
13. C2×SD16×C23C22semidirect
14. C2×D8×C23C22semidirect
15. C23×#127C22semidirect
16. C23×#124C22semidirect
17. #10625113C22semidirect
19. #10625103C22semidirect
20. #10625103C22semidirect
30. #10625072C22semidirect
31. #10625072C22semidirect
32. C23×#97C22semidirect
33. #10625018C22semidirect
34. #10625015C22semidirect
35. #10625015C22semidirect
36. #10625001C22semidirect
37. #10624987C22semidirect
38. #10624987C22semidirect
73. Dic92D4semidirect
74. D184D4semidirect
75. #67263D4semidirect
76. #67263D4semidirect
130. #496D23semidirect
158. C2×SD16C2×D23semidirect
160. C2×D8C2×D23semidirect
163. #127C2×D23semidirect
164. #124C2×D23semidirect
171. #97C2×D23semidirect
172. C23#3288semidirect

Maximal subgroups

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

subgroupindex
#130932232
#130932182
#130926842
#130926772
#130925942
#130925892
#130925842
#130925402
C23×#4962
#328823