Finite Group Databasebeta

← #15685191

Subgroups — #15685191

Order 2944.

460 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 125 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#13093229C212yesmaximal, complemented
2#13093224C212yesmaximal, complemented
3#13092790C211yesmaximal, characteristic, complemented
4#13092681C212yesmaximal, complemented
5#13092680C212yesmaximal, complemented
6#13092601C212yesmaximal, complemented
7#13092586C212yesmaximal, complemented
8#13092535C211yesmaximal, characteristic, complemented
9C23×#443C211yesmaximal, characteristic, complemented
10#10625161C2212yes—
11#10625160C2212yescomplemented
12C23×#135C2211yescharacteristic
13C23×#131C2212yescomplemented
14#10625122C2212yescomplemented
15#10625120C2212yes—
16#10625089—22no—
17#10625087—22no—
18SD16×D23—22no—
19#10625082—22no—
20#10625080—22no—
21#10625080C2212yescomplemented
22#10625079—22no—
23#10625079C2212yes—
24#10625075—22no—
25#10625075C2211yescharacteristic
26C2×#67263—22no—
27C2×#67263C2212yescomplemented
28C2×#67263C2212yescomplemented
29#10625072C2212yescomplemented
30#10625045C2211yescharacteristic
31#10625040C2211yescharacteristic, complemented
32C23×#108C2211yescharacteristic, complemented
33C23×#104C2212yescomplemented
34C4×C8×C23C2211yescharacteristic, complemented
35#10625006C2212yescomplemented
36#10625005C2212yescomplemented
37#10625001C2211yescharacteristic, complemented
38#10624987C2212yescomplemented
39#41×C23C2312yes—
40#67292—22no—
41Q8×D23—22no—
42#67290—22no—
43#67290—42no—
44D4×D23—22no—
45D4×D23—42no—
46#67288—22no—
47#67288—22no—
48#67288C2312yes—
49C2×D92—22no—
50C2×D92—41no—
51C2×D92C2312yes—
52C2×Dic46—22no—
53C2×Dic46C2312yes—
54Q16×C23D411yescharacteristic, complemented
55SD16×C23D412yescomplemented
56D8×C23D411yescharacteristic, complemented
57M16×C23—22no—
58M16×C23C2312yes—
59C2×C8×C23—22no—
60C2×C8×C23C2311yescharacteristic
61C2×C8×C23C2311yescharacteristic
62C42×C23C2311yescharacteristic
63#67275—22no—
64#67274—22no—
65#67273—22no—
66#67272—22no—
67C4⋊Dic23—41no—
68#67267C2312yes—
69Dic92—22no—
70Dic92D411yescharacteristic, complemented
71D184—22no—
72D184D411yescharacteristic, complemented
73#67263—22no—
74#67263—22no—
75#67263—22no—
76#67263—22no—
77#67263—22no—
78#67263—22no—
79#67263D412yescomplemented
80#67262—22no—
81C8×D23—22no—
82C22×D23—22no—
83C22×D23—42no—
84Q8×C23C2×D412yes—
85D4×C23—22no—
86D4×C23C2×D412yes—
87C2×C4×C23—21no—
88C2×C4×C23—22no—
89C2×C4×C23C2411yescharacteristic
90C22⋊D23—22no—
91C22⋊D23—42no—
92C22⋊D23—42no—
93C2×Dic23—22no—
94C2×Dic23—42no—
95D92—22no—
96D92—22no—
97D92—42no—
98D92—82no—
99D92C2×D412yes—
100C4×D23—22no—
101C4×D23—42no—
102C4×D23—42no—
103Dic46—22no—
104Dic46—22no—
105Dic46—42no—
106Dic46C2×D412yes—
107C8×C23—22no—
108C8×C23C2×D411yescharacteristic
109C8×C23C2×D411yescharacteristic
110C8×C23C2×D411yescharacteristic
111C8×C23C2×D411yescharacteristic
112C23⋊C8—22no—
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×C23C22×D411yescharacteristic
123C4×C23C22×D411yescharacteristic
124Dic23—22no—
125Dic23—42no—
126#577—232no—
127#577—232no—
128#492—231no—
129#471—232no—
130#471—232no—
131#456—232no—
132#453—232no—
133#443—231no—
134#443D2311yescharacteristic, complemented
135C2×C23—21no—
136C2×C23—42no—
137C2×C23D4211yescharacteristic
138D23—42no—
139D23—82no—
1402−1+4—232no—
141H(5,𝔽2)—232no—
142#137—232no—
143#137—232no—
144#137—462no—
145#137—462no—
146AGL(1,ℤ/8)—232no—
147AGL(1,ℤ/8)—232no—
148AGL(1,ℤ/8)—462no—
149AGL(1,ℤ/8)—462no—
150#135—231no—
151#135—462no—
152#135—462no—
153#135C2×D2311yescharacteristic
154C2×SD16—232no—
155C2×SD16—232no—
156C2×SD16—462no—
157C2×SD16—462no—
158#131—232no—
159#131C2×D2312yescomplemented
160C4⋊Q8—231no—
161#127—231no—
162#108—231no—
163#108C2×D2311yescharacteristic, complemented
164#104—232no—
165#104C2×D2312yescomplemented
166#101—232no—
167#100—232no—
168C4×C8C2×D2311yescharacteristic, complemented
169C23#329111yescharacteristic, complemented, Sylow
170#41—232no—
171#41—462no—
172#41—462no—
173#41—462no—
174#41—462no—
175#41—922no—
176#41C22×D2312yes—
177C2×Q8—232no—
178C2×Q8—462no—
179C2×Q8—462no—
180C2×D4—232no—
181C2×D4—462no—
182C2×D4—462no—
183C2×D4—921no—
184C2×D4—922no—
185Q16—231no—
186Q16—462no—
187Q16—462no—
188Q16D9211yescharacteristic, complemented
189SD16—232no—
190SD16—462no—
191SD16—462no—
192SD16—462no—
193SD16—462no—
194SD16—462no—
195SD16—462no—
196SD16—462no—
197SD16—462no—
198SD16D9212yescomplemented
199D8—231no—
200D8—462no—
201D8—462no—
202D8D9211yescharacteristic, complemented
203M16—22no—
204M16—232no—
205M16—462no—
206M16C22×D2312yes—
207C2×C8—22no—
208C2×C8—462no—
209C2×C8C22×D2311yescharacteristic
210C2×C8C22×D2311yescharacteristic
211C4⋊C4—921no—
212C42C22×D2311yescharacteristic
213C23—462no—
214C23—922no—
215Q8—232no—
216Q8—462no—
217Q8—462no—
218Q8—922no—
219Q8C2×D9212yes—
220D4—22no—
221D4—232no—
222D4—462no—
223D4—462no—
224D4—462no—
225D4—922no—
226D4—922no—
227D4—922no—
228D4—1842no—
229D4C2×D9212yes—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—462no—
233C2×C4—462no—
234C2×C4—922no—
235C2×C4—922no—
236C2×C4—922no—
237C2×C4C23×D2311yescharacteristic
238C8—22no—
239C8—462no—
240C8C2×D9211yescharacteristic
241C8C2×D9211yescharacteristic
242C8D4×D2311yescharacteristic
243C8D4×D2311yescharacteristic
244C22—22no—
245C22—462no—
246C22—922no—
247C22—3682no—
248C22—1842no—
249C22#1062516011yescharacteristic
250C4—22no—
251C4—22no—
252C4—462no—
253C4—922no—
254C4C22×D9211yescharacteristic
255C4C2×D4×D2311yescharacteristic
256C2—21no—
257C2—42no—
258C2—922no—
259C2—1842no—
260C2D4×D9211yescharacteristic
subgroupG/H
centerC2D4×D92
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#443C2
socleC2×C23D42
hypercenter#443D23
hypocenterC23#3291
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443

Complements

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

NH ≅ G/Ntype
1. #13093229C2semidirect
2. #13093224C2semidirect
3. #13092790C2semidirect
4. #13092681C2semidirect
5. #13092680C2semidirect
6. #13092601C2semidirect
7. #13092586C2semidirect
8. #13092535C2semidirect
9. C23×#443C2semidirect
11. #10625160C22semidirect
13. C23×#131C22semidirect
14. #10625122C22semidirect
21. #10625080C22semidirect
27. C2×#67263C22semidirect
28. C2×#67263C22semidirect
29. #10625072C22semidirect
31. #10625040C22semidirect
32. C23×#108C22semidirect
33. C23×#104C22semidirect
34. C4×C8×C23C22semidirect
35. #10625006C22semidirect
36. #10625005C22semidirect
37. #10625001C22semidirect
38. #10624987C22semidirect
54. Q16×C23D4semidirect
55. SD16×C23D4semidirect
56. D8×C23D4semidirect
70. Dic92D4semidirect
72. D184D4semidirect
79. #67263D4semidirect
134. #443D23semidirect
159. #131C2×D23semidirect
163. #108C2×D23semidirect
165. #104C2×D23semidirect
168. C4×C8C2×D23semidirect
169. C23#3291semidirect
188. Q16D92semidirect
198. SD16D92semidirect
202. D8D92semidirect

Maximal subgroups

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

subgroupindex
#130932292
#130932242
#130927902
#130926812
#130926802
#130926012
#130925862
#130925352
C23×#4432
#329123