Finite Group Databasebeta

← #15685192

Subgroups — #15685192

Order 2944.

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

normal subgroups only

This group has 460 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#13093228C212yesmaximal, complemented
2#13093227C212yesmaximal, complemented
3#13092789C211yesmaximal, characteristic, complemented
4#13092679C212yesmaximal, complemented
5#13092678C212yesmaximal, complemented
6#13092601C212yesmaximal, complemented
7#13092584C211yesmaximal, characteristic, complemented
8#13092531C212yesmaximal, complemented
9C23×#453C211yesmaximal, characteristic, complemented
10C23×H(5,𝔽2)C2211yescharacteristic, complemented
11#10625161C2212yes—
12#10625155C2211yescharacteristic, complemented
13C23×AGL(1,ℤ/8)C2212yes—
14C23×#127C2211yescharacteristic
15#10625122—22no—
16#10625122C2212yescomplemented
17#10625121—22no—
18#10625121C2212yes—
19#10625119C2212yescomplemented
20C2×#67273—22no—
21C2×#67273C2212yescomplemented
22C2×#67273C2212yescomplemented
23#10625103—22no—
24#10625103C2212yes—
25#10625086—22no—
26SD16×D23—22no—
27#10625083—22no—
28#10625082—22no—
29#10625080C2212yescomplemented
30#10625078C2212yescomplemented
31#10625040C2211yescharacteristic, complemented
32C23×#104C2212yescomplemented
33C23×#100C2211yescharacteristic, complemented
34#10625015C2211yescharacteristic, complemented
35#10625006C2212yescomplemented
36#10625004C2212yescomplemented
37#10624987C2212yescomplemented
38C4×C23⋊C8C2211yescharacteristic, complemented
39#41×C23—22no—
40#41×C23C2312yes—
41C2×D4×C23—22no—
42C2×D4×C23—41no—
43C2×D4×C23—41no—
44C2×D4×C23C2311yescharacteristic
45C2×D4×C23C2311yescharacteristic
46C2×C22⋊D23—41no—
47Q8×D23—22no—
48#67290—22no—
49#67290—22no—
50#67290—42no—
51D4×D23—22no—
52#67288—22no—
53#67288C2312yes—
54C2×Dic46—22no—
55C2×Dic46C2312yes—
56SD16×C23—22no—
57D8×C23—22no—
58M16×C23C2312yes—
59C42×C23C2311yescharacteristic
60#67275—22no—
61#67275D412yescomplemented
62#67274D412yescomplemented
63#67273—22no—
64#67273—22no—
65#67273—22no—
66#67273—22no—
67#67273—22no—
68#67273—22no—
69#67273D412yescomplemented
70#67272—22no—
71#67272D412yescomplemented
72C4⋊Dic23—41no—
73#67267—22no—
74#67267C2312yes—
75C2×C23⋊C8—22no—
76C2×C23⋊C8C2312yes—
77Dic92—22no—
78#67263—22no—
79#67262—22no—
80C8×D23—22no—
81C23×C23—21no—
82C23×C23—21no—
83C23×C23—41no—
84C22×D23—41no—
85Q8×C23C2×D412yes—
86D4×C23—22no—
87D4×C23—22no—
88D4×C23—22no—
89D4×C23—42no—
90D4×C23—82no—
91D4×C23C2×D412yes—
92C2×C4×C23—21no—
93C2×C4×C23—22no—
94C2×C4×C23—41no—
95C2×C4×C23C2411yescharacteristic
96C22⋊D23—22no—
97C22⋊D23—42no—
98C22⋊D23—42no—
99C2×Dic23—22no—
100C2×Dic23—41no—
101C2×Dic23—42no—
102D92C2×D412yes—
103C4×D23—22no—
104C4×D23—42no—
105Dic46—22no—
106Dic46—22no—
107Dic46—42no—
108Dic46C2×D412yes—
109C8×C23—22no—
110C23⋊C8—22no—
111C23⋊C8C2×D412yes—
112C23⋊C8C2×D412yes—
113#3291—231nomaximal, Sylow
114C22×C23—22no—
115C22×C23—41no—
116C22×C23—41no—
117C22×C23—81no—
118C22×C23—81no—
119C22×C23—161no—
120C22×C23H(5,𝔽2)11yescharacteristic
121C2×D23—22no—
122C2×D23—161no—
123C4×C23—22no—
124C4×C23—22no—
125C4×C23C22×D412yes—
126Dic23—22no—
127Dic23—42no—
128#577—232no—
129#577—232no—
130#492—231no—
131#471—232no—
132#471—232no—
133#456—232no—
134#453—231no—
135#453D2311yescharacteristic, complemented
136#443—232no—
137C2×C23—21no—
138C2×C23—42no—
139C2×C23—81no—
140C2×C23—81no—
141C2×C23D4211yescharacteristic
142D23—42no—
1432−1+4—232no—
144H(5,𝔽2)—231no—
145H(5,𝔽2)C2×D2311yescharacteristic, complemented
146#137—232no—
147#137—232no—
148#137—462no—
149#137—462no—
150AGL(1,ℤ/8)—232no—
151AGL(1,ℤ/8)—462no—
152AGL(1,ℤ/8)—462no—
153AGL(1,ℤ/8)C2×D2312yes—
154#135—232no—
155#135—462no—
156#135—462no—
157C2×SD16—232no—
158C2×SD16—232no—
159C2×SD16—462no—
160C2×SD16—462no—
161#131—232no—
162#131—232no—
163C4⋊Q8—231no—
164#127C2×D2311yescharacteristic
165#108—232no—
166#104—232no—
167#104C2×D2312yescomplemented
168#101—232no—
169#100—231no—
170#100C2×D2311yescharacteristic, complemented
171C4×C8—231no—
172C23#329111yescharacteristic, complemented, Sylow
173#41—22no—
174#41—232no—
175#41—462no—
176#41—462no—
177#41—462no—
178#41—922no—
179#41C22×D2312yes—
180C2×Q8—232no—
181C2×Q8—462no—
182C2×Q8—462no—
183C2×D4—22no—
184C2×D4—41no—
185C2×D4—41no—
186C2×D4—462no—
187C2×D4—921no—
188C2×D4C22×D2311yescharacteristic
189C2×D4C22×D2311yescharacteristic
190Q16—232no—
191Q16—462no—
192Q16—462no—
193SD16—22no—
194SD16—232no—
195SD16—232no—
196SD16—462no—
197SD16—462no—
198SD16—462no—
199SD16—462no—
200SD16—462no—
201SD16—462no—
202SD16—462no—
203D8—22no—
204D8—232no—
205D8—462no—
206M16—232no—
207M16—462no—
208M16—462no—
209M16C22×D2312yes—
210C2×C8—232no—
211C2×C8—462no—
212C2×C8—462no—
213C4⋊C4—921no—
214C42C22×D2311yescharacteristic
215C23—21no—
216C23—21no—
217C23—41no—
218C23—921no—
219Q8—232no—
220Q8—462no—
221Q8—462no—
222Q8—922no—
223Q8D4×D2312yes—
224D4—22no—
225D4—22no—
226D4—22no—
227D4—42no—
228D4—82no—
229D4—232no—
230D4—462no—
231D4—922no—
232D4—922no—
233D4D4×D2312yes—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—41no—
237C2×C4—462no—
238C2×C4—462no—
239C2×C4—922no—
240C2×C4—921no—
241C2×C4—922no—
242C2×C4C23×D2311yescharacteristic
243C8—22no—
244C8—232no—
245C8—232no—
246C8—462no—
247C22—22no—
248C22—41no—
249C22—41no—
250C22—81no—
251C22—81no—
252C22—161no—
253C22—462no—
254C22—3681no—
255C22#1062515511yescharacteristic
256C4—22no—
257C4—22no—
258C4—462no—
259C4—922no—
260C4C2×D4×D2312yes—
261C2—21no—
262C2—42no—
263C2—81no—
264C2—81no—
265C2—922no—
266C2#1309304911yescharacteristic
subgroupG/H
centerC2#13093049
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#453C2
socleC2×C23D42
hypercenter#453D23
hypocenterC23#3291
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. #13093228C2semidirect
2. #13093227C2semidirect
3. #13092789C2semidirect
4. #13092679C2semidirect
5. #13092678C2semidirect
6. #13092601C2semidirect
7. #13092584C2semidirect
8. #13092531C2semidirect
9. C23×#453C2semidirect
10. C23×H(5,𝔽2)C22semidirect
12. #10625155C22semidirect
16. #10625122C22semidirect
19. #10625119C22semidirect
21. C2×#67273C22semidirect
22. C2×#67273C22semidirect
29. #10625080C22semidirect
30. #10625078C22semidirect
31. #10625040C22semidirect
32. C23×#104C22semidirect
33. C23×#100C22semidirect
34. #10625015C22semidirect
35. #10625006C22semidirect
36. #10625004C22semidirect
37. #10624987C22semidirect
38. C4×C23⋊C8C22semidirect
61. #67275D4semidirect
62. #67274D4semidirect
69. #67273D4semidirect
71. #67272D4semidirect
135. #453D23semidirect
145. H(5,𝔽2)C2×D23semidirect
167. #104C2×D23semidirect
170. #100C2×D23semidirect
172. C23#3291semidirect

Maximal subgroups

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

subgroupindex
#130932282
#130932272
#130927892
#130926792
#130926782
#130926012
#130925842
#130925312
C23×#4532
#329123