Finite Group Databasebeta

← #15683322

Subgroups — #15683322

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
2C22×C4⋊Dic23C211yesmaximal, characteristic, complemented
3#13092753C212yesmaximal, complemented
4#13092748C212yesmaximal, complemented
5#13092736C212yesmaximal, complemented
6#13092731C212yesmaximal, complemented
7#13092459C212yesmaximal, complemented
8#13092419C212yesmaximal, complemented
9C23×#407C211yesmaximal, characteristic, complemented
10C23×C4×C23C2211yescharacteristic
11C23×Dic23—21no—
12C2×#67288C2211yescharacteristic
13C2×M16×C23C2212yes—
14#10625124—21no—
15#10625101C2211yescharacteristic
16#10625101C2211yescharacteristic
17#10625100—21no—
18C4×C22⋊D23—21no—
19C4×C22⋊D23—21no—
20#10625097C2211yescharacteristic
21C2×C4⋊Dic23—21no—
22C2×C4⋊Dic23—21no—
23C2×C4⋊Dic23—21no—
24C2×C4⋊Dic23C2212yes—
25C2×C4⋊Dic23C2212yes—
26C2×C4⋊Dic23C2212yes—
27#10625095C2211yescharacteristic
28#10625095C2211yescharacteristic
29C23×C22⋊C8C2212yes—
30C23×C22⋊C8C2212yes—
31#10625003C2214yescomplemented
32#10625000C2214yescomplemented
33#10624999C2214yescomplemented
34#10624998C2214yescomplemented
35C24×C23D411yescharacteristic
36C22×C4×C23—24no—
37C22×C4×C23D411yescharacteristic
38C22×C4×C23D411yescharacteristic
39C22×C4×C23D411yescharacteristic
40C22×C4×C23C2311yescharacteristic
41C22×C4×C23C2311yescharacteristic
42C22×C4×C23C2311yescharacteristic
43C2×C22⋊D23—21no—
44C2×C22⋊D23—21no—
45C2×C22⋊D23—21no—
46C22×Dic23—22no—
47C22×Dic23—22no—
48C22×Dic23—22no—
49C22×Dic23—44no—
50#67288—24no—
51C2×D92C2311yescharacteristic
52C2×C4×D23—21no—
53C2×Dic46C2311yescharacteristic
54M16×C23—24no—
55C2×C8×C23C2314yes—
56C22⋊Dic23—21no—
57C22⋊Dic23—21no—
58C22⋊Dic23—21no—
59(C2×D23)⋊C4—21no—
60(C2×D23)⋊C4—21no—
61C4⋊Dic23—22no—
62C4⋊Dic23—22no—
63C4⋊Dic23—22no—
64C4⋊Dic23C2311yescharacteristic
65C4⋊Dic23C2311yescharacteristic
66C4⋊Dic23C2314yes—
67Dic23⋊C4—21no—
68Dic23⋊C4—21no—
69C4×Dic23—21no—
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×C23C2×D411yescharacteristic
83C2×C4×C23C2×D411yescharacteristic
84C2×C4×C23C2×D411yescharacteristic
85C2×C4×C23#4114yes—
86C2×C4×C23C2411yescharacteristic
87C22⋊D23—42no—
88C22⋊D23—42no—
89C22⋊D23—42no—
90C2×Dic23—21no—
91C2×Dic23—21no—
92C2×Dic23—21no—
93C2×Dic23—24no—
94C2×Dic23—44no—
95C2×Dic23—44no—
96C2×Dic23—44no—
97D92—22no—
98C4×D23—42no—
99Dic46—22no—
100C8×C23—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#12312yes—
119C4×C23C2×#4112yes—
120Dic23—41no—
121Dic23—44no—
122Dic23—41no—
123Dic23—41no—
124#525—231no—
125C22×C4⋊C4—231no—
126#484—232no—
127#483—232no—
128#481—232no—
129#480—232no—
130#428—232no—
131#417—232no—
132#407D2311yescharacteristic, complemented
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—461no—
142C23×C4C2×D2311yescharacteristic
143C2×M16C2×D2312yes—
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—232no—
154C2×C4⋊C4—232no—
155C2×C4⋊C4—232no—
156C2×C4⋊C4—461no—
157C2×C4⋊C4—461no—
158C2×C4⋊C4—461no—
159#107—234no—
160#106—234no—
161#103—234no—
162#102—234no—
163C22⋊C8C2×D2312yes—
164C22⋊C8C2×D2312yes—
165C23#309211yescharacteristic, complemented, Sylow
166C24D9211yescharacteristic
167#41—464no—
168C2×Q8—231no—
169C2×D4—231no—
170C2×D4—461no—
171C2×D4—461no—
172C2×D4—461no—
173C22×C4—24no—
174C22×C4—462no—
175C22×C4—462no—
176C22×C4—462no—
177C22×C4—461no—
178C22×C4—924no—
179C22×C4D9211yescharacteristic
180C22×C4D9211yescharacteristic
181C22×C4D9211yescharacteristic
182C22×C4C22×D2311yescharacteristic
183C22×C4C22×D2311yescharacteristic
184C22×C4C22×D2311yescharacteristic
185M16—24no—
186C2×C8C22×D2314yes—
187C4⋊C4—234no—
188C4⋊C4—231no—
189C4⋊C4—231no—
190C4⋊C4—462no—
191C4⋊C4—462no—
192C4⋊C4—462no—
193C4⋊C4—461no—
194C4⋊C4—461no—
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×D9211yescharacteristic
206C23C2×D9211yescharacteristic
207C23C2×D9211yescharacteristic
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—461no—
219C2×C4—461no—
220C2×C4—461no—
221C2×C4—464no—
222C2×C4—924no—
223C2×C4—924no—
224C2×C4—924no—
225C2×C4—922no—
226C2×C4C2×D9211yescharacteristic
227C2×C4C2×D9211yescharacteristic
228C2×C4C2×D9211yescharacteristic
229C2×C4#6729014yes—
230C2×C4C23×D2311yescharacteristic
231C8—24no—
232C22—28no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—921no—
240C22—921no—
241C22—921no—
242C22#1062505712yes—
243C22#1062507912yes—
244C22#1062508012yes—
245C22C22×D9211yescharacteristic
246C4—21no—
247C4—21no—
248C4—921no—
249C4—924no—
250C4—921no—
251C4—921no—
252C4#1062505712yes—
253C4C2×#6729012yes—
254C2—22no—
255C2—22no—
256C2—22no—
257C2—1841no—
258C2C2×#1062505711yescharacteristic
259C2C2×#1062507911yescharacteristic
260C2C2×#1062508011yescharacteristic
subgroupG/H
centerC22C22×D92
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#407C2
socleC22×C23C22×D4
prime radical#13092928C2
hypercenter#407D23
hypocenterC23#3092
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊Dic23C2semidirect
3. #13092753C2semidirect
4. #13092748C2semidirect
5. #13092736C2semidirect
6. #13092731C2semidirect
7. #13092459C2semidirect
8. #13092419C2semidirect
9. C23×#407C2semidirect
31. #10625003C22semidirect
32. #10625000C22semidirect
33. #10624999C22semidirect
34. #10624998C22semidirect
132. #407D23semidirect
165. C23#3092semidirect

Maximal subgroups

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

subgroupindex
#130929282
C22×C4⋊Dic232
#130927532
#130927482
#130927362
#130927312
#130924592
#130924192
C23×#4072
#309223