Finite Group Databasebeta

← #15685187

Subgroups — #15685187

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#13093226C212yesmaximal, complemented
2#13093225C212yesmaximal, complemented
3#13092791C211yesmaximal, characteristic, complemented
4#13092683C212yesmaximal, complemented
5#13092682C212yesmaximal, complemented
6#13092599C211yesmaximal, characteristic, complemented
7#13092586C212yesmaximal, complemented
8#13092531C212yesmaximal, complemented
9C23×#456C211yesmaximal, characteristic, complemented
10C23×2−1+4C2211yescharacteristic
11#10625160C2212yescomplemented
12#10625158C2211yescharacteristic
13C23×#137C2212yescomplemented
14C23×C4⋊Q8C2211yescharacteristic, complemented
15#10625121—22no—
16#10625121C2212yes—
17#10625120—22no—
18#10625120C2212yes—
19#10625119C2212yescomplemented
20#10625113—22no—
21#10625113C2212yescomplemented
22C2×#67274—22no—
23C2×#67274C2212yescomplemented
24C2×#67274C2212yescomplemented
25#10625090—22no—
26#10625089—22no—
27#10625085—22no—
28SD16×D23—22no—
29#10625079C2212yes—
30#10625078C2212yescomplemented
31#10625045C2211yescharacteristic
32C23×#104C2212yescomplemented
33C23×#101C2211yescharacteristic, complemented
34#10625018C2211yescharacteristic, complemented
35#10625005C2212yescomplemented
36#10625004C2212yescomplemented
37#10624987C2212yescomplemented
38C4×C23⋊C8C2211yescharacteristic, complemented
39#41×C23—22no—
40#41×C23—41no—
41#41×C23C2312yes—
42C2×Q8×C23—22no—
43C2×Q8×C23C2311yescharacteristic
44C2×Q8×C23C2311yescharacteristic
45#67292—22no—
46#67292—22no—
47Q8×D23—22no—
48D4×D23—22no—
49D4×D23—42no—
50#67288—22no—
51#67288—41no—
52#67288C2312yes—
53C2×D92—22no—
54C2×D92—41no—
55C2×D92C2312yes—
56Q16×C23—22no—
57SD16×C23—22no—
58M16×C23C2312yes—
59C4⋊C4×C23—41no—
60C42×C23C2311yescharacteristic
61#67275—22no—
62#67275D412yescomplemented
63#67274—22no—
64#67274—22no—
65#67274—22no—
66#67274—22no—
67#67274—22no—
68#67274—22no—
69#67274D412yescomplemented
70#67273D412yescomplemented
71#67272—22no—
72#67272D412yescomplemented
73#67267—22no—
74#67267C2312yes—
75C2×C23⋊C8—22no—
76C2×C23⋊C8C2312yes—
77D184—22no—
78#67263—22no—
79#67262—22no—
80C8×D23—22no—
81C22×D23—22no—
82C22×D23—42no—
83Q8×C23—22no—
84Q8×C23—22no—
85Q8×C23—41no—
86Q8×C23C2×D412yes—
87D4×C23—22no—
88D4×C23—41no—
89D4×C23C2×D412yes—
90C2×C4×C23—21no—
91C2×C4×C23—22no—
92C2×C4×C23—21no—
93C2×C4×C23—21no—
94C2×C4×C23—42no—
95C2×C4×C23C2411yescharacteristic
96C22⋊D23—22no—
97C22⋊D23—42no—
98D92—22no—
99D92—22no—
100D92—42no—
101D92—41no—
102D92—82no—
103D92C2×D412yes—
104C4×D23—22no—
105C4×D23—42no—
106C4×D23—42no—
107Dic46—41no—
108Dic46C2×D412yes—
109C8×C23—22no—
110C23⋊C8—22no—
111C23⋊C8C2×D412yes—
112C23⋊C8C2×D412yes—
113#3291—231nomaximal, Sylow
114C22×C23—22no—
115C22×C23H(5,𝔽2)11yescharacteristic
116C2×D23—22no—
117C2×D23—42no—
118C2×D23—82no—
119C2×D23—162no—
120C4×C23—22no—
121C4×C23—22no—
122C4×C23—41no—
123C4×C23—41no—
124C4×C23C22×D412yes—
125Dic23—22no—
126#577—232no—
127#577—232no—
128#492—231no—
129#471—232no—
130#471—232no—
131#456—231no—
132#456D2311yescharacteristic, complemented
133#453—232no—
134#443—232no—
135C2×C23—21no—
136C2×C23—42no—
137C2×C23D4211yescharacteristic
138D23—42no—
139D23—82no—
1402−1+4—231no—
1412−1+4C2×D2311yescharacteristic
142H(5,𝔽2)—232no—
143#137—232no—
144#137—462no—
145#137—462no—
146#137C2×D2312yescomplemented
147AGL(1,ℤ/8)—232no—
148AGL(1,ℤ/8)—232no—
149AGL(1,ℤ/8)—462no—
150AGL(1,ℤ/8)—462no—
151#135—232no—
152#135—462no—
153#135—462no—
154C2×SD16—232no—
155C2×SD16—232no—
156C2×SD16—462no—
157C2×SD16—462no—
158#131—232no—
159#131—232no—
160C4⋊Q8C2×D2311yescharacteristic, complemented
161#127—231no—
162#108—232no—
163#104—232no—
164#104C2×D2312yescomplemented
165#101—231no—
166#101C2×D2311yescharacteristic, complemented
167#100—232no—
168C4×C8—231no—
169C23#329111yescharacteristic, complemented, Sylow
170#41—22no—
171#41—41no—
172#41—232no—
173#41—462no—
174#41—462no—
175#41—462no—
176#41—921no—
177#41C22×D2312yes—
178C2×Q8—22no—
179C2×Q8—462no—
180C2×Q8C22×D2311yescharacteristic
181C2×Q8C22×D2311yescharacteristic
182C2×D4—232no—
183C2×D4—462no—
184C2×D4—462no—
185C2×D4—921no—
186C2×D4—922no—
187Q16—22no—
188Q16—232no—
189Q16—462no—
190SD16—22no—
191SD16—232no—
192SD16—232no—
193SD16—462no—
194SD16—462no—
195SD16—462no—
196SD16—462no—
197SD16—462no—
198SD16—462no—
199SD16—462no—
200D8—232no—
201D8—462no—
202D8—462no—
203M16—232no—
204M16—462no—
205M16—462no—
206M16C22×D2312yes—
207C2×C8—232no—
208C2×C8—462no—
209C2×C8—462no—
210C4⋊C4—41no—
211C42C22×D2311yescharacteristic
212C23—462no—
213C23—922no—
214Q8—22no—
215Q8—22no—
216Q8—41no—
217Q8—232no—
218Q8—921no—
219Q8D4×D2312yes—
220D4—22no—
221D4—41no—
222D4—232no—
223D4—462no—
224D4—462no—
225D4—462no—
226D4—922no—
227D4—921no—
228D4—922no—
229D4—1842no—
230D4D4×D2312yes—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—42no—
236C2×C4—462no—
237C2×C4—922no—
238C2×C4—922no—
239C2×C4C23×D2311yescharacteristic
240C8—22no—
241C8—232no—
242C8—232no—
243C8—462no—
244C22—22no—
245C22—462no—
246C22—922no—
247C22—3682no—
248C22—1842no—
249C22#1062515511yescharacteristic
250C4—22no—
251C4—22no—
252C4—41no—
253C4—41no—
254C4—462no—
255C4C2×D4×D2312yes—
256C2—21no—
257C2—42no—
258C2—922no—
259C2—1842no—
260C2#1309304911yescharacteristic
subgroupG/H
centerC2#13093049
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#456C2
socleC2×C23D42
hypercenter#456D23
hypocenterC23#3291
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ #456

Complements

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

NH ≅ G/Ntype
1. #13093226C2semidirect
2. #13093225C2semidirect
3. #13092791C2semidirect
4. #13092683C2semidirect
5. #13092682C2semidirect
6. #13092599C2semidirect
7. #13092586C2semidirect
8. #13092531C2semidirect
9. C23×#456C2semidirect
11. #10625160C22semidirect
13. C23×#137C22semidirect
14. C23×C4⋊Q8C22semidirect
19. #10625119C22semidirect
21. #10625113C22semidirect
23. C2×#67274C22semidirect
24. C2×#67274C22semidirect
30. #10625078C22semidirect
32. C23×#104C22semidirect
33. C23×#101C22semidirect
34. #10625018C22semidirect
35. #10625005C22semidirect
36. #10625004C22semidirect
37. #10624987C22semidirect
38. C4×C23⋊C8C22semidirect
62. #67275D4semidirect
69. #67274D4semidirect
70. #67273D4semidirect
72. #67272D4semidirect
132. #456D23semidirect
146. #137C2×D23semidirect
160. C4⋊Q8C2×D23semidirect
164. #104C2×D23semidirect
166. #101C2×D23semidirect
169. C23#3291semidirect

Maximal subgroups

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

subgroupindex
#130932262
#130932252
#130927912
#130926832
#130926822
#130925992
#130925862
#130925312
C23×#4562
#329123