Finite Group Databasebeta

← #15683320

Subgroups — #15683320

Order 2944.

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

normal subgroups only

This group has 458 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
1#13092928C211yesmaximal, characteristic
2#13092752C212yesmaximal, complemented
3#13092747C212yesmaximal, complemented
4#13092735C212yesmaximal, complemented
5#13092730C212yesmaximal, complemented
6#13092457C212yesmaximal, complemented
7#13092416C212yesmaximal, complemented
8#13092381C211yesmaximal, characteristic, complemented
9C22×C4⋊C4×C23C211yesmaximal, characteristic, complemented
10C23×C4×C23—21no—
11C23×C4×C23C2211yescharacteristic
12C2×#67288C2211yescharacteristic
13C2×C4⋊C4×C23—21no—
14C2×C4⋊C4×C23—21no—
15C2×C4⋊C4×C23—21no—
16C2×C4⋊C4×C23C2212yes—
17C2×C4⋊C4×C23C2212yes—
18C2×C4⋊C4×C23C2212yes—
19#10625124—21no—
20#10625101C2211yescharacteristic
21#10625101C2211yescharacteristic
22#10625100—21no—
23C4×C22⋊D23—21no—
24C4×C22⋊D23—21no—
25#10625097C2211yescharacteristic
26#10625095C2211yescharacteristic
27#10625095C2211yescharacteristic
28C2×#67267C2212yes—
29C22⋊(C23⋊C8)C2212yes—
30C22⋊(C23⋊C8)C2212yes—
31#10624992C2214yescomplemented
32#10624991C2214yescomplemented
33#10624990C2214yescomplemented
34#10624989C2214yescomplemented
35C24×C23D411yescharacteristic
36C22×C4×C23—24no—
37C22×C4×C23—22no—
38C22×C4×C23—22no—
39C22×C4×C23—22no—
40C22×C4×C23—44no—
41C22×C4×C23D411yescharacteristic
42C22×C4×C23D411yescharacteristic
43C22×C4×C23D411yescharacteristic
44C22×C4×C23C2311yescharacteristic
45C22×C4×C23C2311yescharacteristic
46C22×C4×C23C2311yescharacteristic
47C2×C22⋊D23—21no—
48C2×C22⋊D23—21no—
49C2×C22⋊D23—21no—
50#67288—24no—
51C2×D92C2311yescharacteristic
52C2×C4×D23—21no—
53C2×Dic46C2311yescharacteristic
54C4⋊C4×C23—22no—
55C4⋊C4×C23—22no—
56C4⋊C4×C23—22no—
57C4⋊C4×C23C2314yes—
58C22⋊Dic23—21no—
59C22⋊Dic23—21no—
60C22⋊Dic23—21no—
61(C2×D23)⋊C4—21no—
62(C2×D23)⋊C4—21no—
63C4⋊Dic23C2311yescharacteristic
64C4⋊Dic23C2311yescharacteristic
65Dic23⋊C4—21no—
66Dic23⋊C4—21no—
67C4×Dic23—21no—
68#67267—24no—
69C2×C23⋊C8C2314yes—
70C23×C23—22no—
71C23×C23—22no—
72C23×C23—22no—
73C23×C23C2×D411yescharacteristic
74C23×C23C2×D411yescharacteristic
75C23×C23C2×D411yescharacteristic
76C22×D23—21no—
77C2×C4×C23—22no—
78C2×C4×C23—22no—
79C2×C4×C23—22no—
80C2×C4×C23—22no—
81C2×C4×C23—22no—
82C2×C4×C23—24no—
83C2×C4×C23—44no—
84C2×C4×C23—44no—
85C2×C4×C23—44no—
86C2×C4×C23C2×D411yescharacteristic
87C2×C4×C23C2×D411yescharacteristic
88C2×C4×C23C2×D411yescharacteristic
89C2×C4×C23#4114yes—
90C2×C4×C23C2411yescharacteristic
91C22⋊D23—42no—
92C22⋊D23—42no—
93C22⋊D23—42no—
94C2×Dic23—21no—
95C2×Dic23—21no—
96C2×Dic23—21no—
97D92—22no—
98C4×D23—42no—
99Dic46—22no—
100C23⋊C8—24no—
101#3092—231nomaximal, Sylow
102C22×C23—28no—
103C22×C23—21no—
104C22×C23—21no—
105C22×C23—21no—
106C22×C23—21no—
107C22×C23—21no—
108C22×C23—21no—
109C22×C23#12312yes—
110C22×C23AGL(1,ℤ/8)12yes—
111C22×C23#13712yes—
112C22×C23C22×D411yescharacteristic
113C2×D23—41no—
114C2×D23—41no—
115C2×D23—41no—
116C4×C23—21no—
117C4×C23—21no—
118C4×C23—44no—
119C4×C23#12312yes—
120C4×C23C2×#4112yes—
121Dic23—41no—
122Dic23—41no—
123Dic23—41no—
124#525—231no—
125C22×C4⋊C4D2311yescharacteristic, complemented
126#484—232no—
127#483—232no—
128#481—232no—
129#480—232no—
130#428—232no—
131#417—232no—
132#407—231no—
133C2×C23—22no—
134C2×C23—22no—
135C2×C23—22no—
136C2×C23C2×#12311yescharacteristic
137C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C23C2×#13711yescharacteristic
139D23—81no—
140C2×#41—231no—
141C23×C4—21no—
142C23×C4C2×D2311yescharacteristic
143C2×M16—232no—
144#123—461no—
145C22⋊Q8—231no—
146C22⋊Q8—231no—
147#121—231no—
148#121—231no—
149#120—461no—
150C4×D4—461no—
151C4×D4—461no—
152#117—231no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4C2×D2312yes—
157C2×C4⋊C4C2×D2312yes—
158C2×C4⋊C4C2×D2312yes—
159#107—234no—
160#106—234no—
161#103—234no—
162#102—234no—
163C22⋊C8—232no—
164C22⋊C8—232no—
165C23#309211yescharacteristic, complemented, Sylow
166C24C22⋊D2311yescharacteristic
167#41—464no—
168C2×Q8—231no—
169C2×D4—231no—
170C2×D4—461no—
171C2×D4—461no—
172C2×D4—461no—
173C22×C4—24no—
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—22no—
177C22×C4—44no—
178C22×C4—461no—
179C22×C4C22⋊D2311yescharacteristic
180C22×C4C22⋊D2311yescharacteristic
181C22×C4C22⋊D2311yescharacteristic
182C22×C4C22×D2311yescharacteristic
183C22×C4C22×D2311yescharacteristic
184C22×C4C22×D2311yescharacteristic
185M16—464no—
186C2×C8—234no—
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—22no—
190C4⋊C4—231no—
191C4⋊C4—231no—
192C4⋊C4—461no—
193C4⋊C4—461no—
194C4⋊C4C22×D2314yes—
195C22⋊C4—461no—
196C22⋊C4—461no—
197C22⋊C4—461no—
198C22⋊C4—461no—
199C22⋊C4—461no—
200C42—461no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—461no—
205C23C2×C22⋊D2311yescharacteristic
206C23C2×C22⋊D2311yescharacteristic
207C23C2×C22⋊D2311yescharacteristic
208Q8—462no—
209D4—462no—
210D4—922no—
211D4—922no—
212D4—922no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—24no—
219C2×C4—44no—
220C2×C4—44no—
221C2×C4—44no—
222C2×C4—461no—
223C2×C4—461no—
224C2×C4—461no—
225C2×C4—922no—
226C2×C4#6728814yes—
227C2×C4C2×C22⋊D2311yescharacteristic
228C2×C4C2×C22⋊D2311yescharacteristic
229C2×C4C2×C22⋊D2311yescharacteristic
230C2×C4C23×D2311yescharacteristic
231C8—464no—
232C22—28no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—921no—
240C22—921no—
241C22—921no—
242C22#1062510012yes—
243C22#1062510312yes—
244C22#1062511312yes—
245C22C22×C22⋊D2311yescharacteristic
246C4—21no—
247C4—21no—
248C4—44no—
249C4—921no—
250C4—921no—
251C4—921no—
252C4#1062510012yes—
253C4C2×#6728812yes—
254C2—22no—
255C2—22no—
256C2—22no—
257C2—1841no—
258C2C2×#1062510011yescharacteristic
259C2C2×#1062510311yescharacteristic
260C2C2×#1062511311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC22×C4⋊C4×C23C2
socleC22×C23C22×D4
prime radical#13092928C2
hypercenterC22×C4⋊C4D23
hypocenterC23#3092
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13092752C2semidirect
3. #13092747C2semidirect
4. #13092735C2semidirect
5. #13092730C2semidirect
6. #13092457C2semidirect
7. #13092416C2semidirect
8. #13092381C2semidirect
9. C22×C4⋊C4×C23C2semidirect
31. #10624992C22semidirect
32. #10624991C22semidirect
33. #10624990C22semidirect
34. #10624989C22semidirect
125. C22×C4⋊C4D23semidirect
165. C23#3092semidirect

Maximal subgroups

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

subgroupindex
#130929282
#130927522
#130927472
#130927352
#130927302
#130924572
#130924162
#130923812
C22×C4⋊C4×C232
#309223