Finite Group Databasebeta

← #15671903

Subgroups — #15671903

Order 2944.

272 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 63 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#13092962C211yesmaximal, characteristic
2#13092471C211yesmaximal, characteristic, complemented
3#13092262C211yesmaximal, characteristic, complemented
4#13092152C211yesmaximal, characteristic, complemented
5#13092151C211yesmaximal, characteristic, complemented
6#13092150C211yesmaximal, characteristic, complemented
7C23×#327C211yesmaximal, characteristic, complemented
8C2×#67290—21no—
9C23×#121C2211yescharacteristic
10#10625111C411yescharacteristic, complemented
11#10625110—21no—
12D4×Dic23C411yescharacteristic, complemented
13#10625101C2211yescharacteristic
14C2×C4×Dic23—21no—
15C2×C4×Dic23C2211yescharacteristic
16#10625064C411yescharacteristic, complemented
17#10625059C411yescharacteristic, complemented
18#10625056—21no—
19(C22⋊D23)⋊C4—21no—
20C23×C22⋊C8C2211yescharacteristic
21C23×#95C2211yescharacteristic
22C23⋊#95—21no—
23C23⋊#95C2211yescharacteristic
24C22⋊(C23⋊C8)C2211yescharacteristic
25#10624997—21no—
26Dic23⋊C8—21no—
27C2×D4×C23—21no—
28C2×D4×C23C2×C411yescharacteristic
29C22×C4×C23—21no—
30C22×C4×C23C2311yescharacteristic
31C2×C22⋊D23—21no—
32C2×C22⋊D23—21no—
33C2×C22⋊D23—21no—
34C22×Dic23—21no—
35C22×Dic23—21no—
36C22×Dic23D411yescharacteristic
37C22×Dic23D411yescharacteristic
38#67290—42no—
39#67290—42no—
40C2×D92C2×C411yescharacteristic
41C2×C4×D23—21no—
42C2×Dic46—21no—
43C2×C8×C23—21no—
44C4⋊C4×C23C2×C411yescharacteristic
45C22⋊C4×C23—21no—
46C22⋊Dic23—21no—
47(C2×D23)⋊C4—21no—
48(C2×D23)⋊C4—21no—
49C4⋊Dic23C2×C411yescharacteristic
50Dic23⋊C4—21no—
51C4×Dic23—24no—
52C4×Dic23C2×C411yescharacteristic
53C4×Dic23C2×C411yescharacteristic
54C4×Dic23D411yescharacteristic
55C4×Dic23D411yescharacteristic
56C2×C23⋊C8—21no—
57C23×C23—21no—
58C23×C23C2×D411yescharacteristic
59C22×D23—21no—
60D4×C23—41no—
61D4×C23—41no—
62D4×C23—41no—
63C2×C4×C23—22no—
64C2×C4×C23—21no—
65C2×C4×C23—41no—
66C2×C4×C23—41no—
67C2×C4×C23—41no—
68C2×C4×C23C22×C411yescharacteristic
69C2×C4×C23C2×D411yescharacteristic
70C22⋊D23—42no—
71C22⋊D23—41no—
72C22⋊D23—41no—
73C22⋊D23—42no—
74C2×Dic23—21no—
75C2×Dic23—21no—
76C2×Dic23—22no—
77C2×Dic23—22no—
78C2×Dic23—21no—
79C2×Dic23—42no—
80C2×Dic23—41no—
81C2×Dic23—41no—
82C2×Dic23C22⋊C411yescharacteristic
83C2×Dic23C22⋊C411yescharacteristic
84C2×Dic23C22⋊C411yescharacteristic
85C2×Dic23C22⋊C411yescharacteristic
86D92—41no—
87C4×D23—42no—
88Dic46—42no—
89C8×C23—41no—
90C23⋊C8—41no—
91#1505—231nomaximal, Sylow
92C22×C23—21no—
93C22×C23—21no—
94C22×C23—41no—
95C22×C23—41no—
96C22×C23—41no—
97C22×C23C2×C22⋊C411yescharacteristic
98C22×C23AGL(1,ℤ/8)11yescharacteristic
99C22×C23AGL(1,ℤ/8)11yescharacteristic
100C2×D23—41no—
101C2×D23—41no—
102C2×D23—41no—
103C4×C23—21no—
104C4×C23—21no—
105C4×C23—42no—
106C4×C23—41no—
107Dic23—21no—
108Dic23—21no—
109Dic23—21no—
110Dic23—42no—
111Dic23—41no—
112Dic23#10412yes—
113#532—231no—
114#432—231no—
115#376—231no—
116#327—231no—
117#327—231no—
118#327—231no—
119#327D2311yescharacteristic, complemented
120C2×C23—21no—
121C2×C23—21no—
122C2×C23—81no—
123C2×C23#41011yescharacteristic
124C2×C23#41811yescharacteristic
125C2×C23C2×#10411yescharacteristic
126D23—81no—
127C2×#41—461no—
128C4⋊Q8—231no—
129#127—231no—
130#124—461no—
131#121—231no—
132#121—461no—
133#121C2×D2311yescharacteristic
134C4×D4—231no—
135C4×D4—231no—
136C4×D4—461no—
137C2×C42—231no—
138C2×C42—461no—
139C4⋊C8—461no—
140C22⋊C8—231no—
141C22⋊C8C2×D2311yescharacteristic
142#97—461no—
143#95—231no—
144#95—461no—
145#95C2×D2311yescharacteristic
146C23#150511yescharacteristic, complemented, Sylow
147#41—922no—
148#41—922no—
149C2×Q8—461no—
150C2×D4—21no—
151C2×D4—231no—
152C2×D4—461no—
153C2×D4—461no—
154C2×D4—461no—
155C2×D4C4×D2311yescharacteristic
156C22×C4—21no—
157C22×C4—231no—
158C22×C4—231no—
159C22×C4—461no—
160C22×C4—461no—
161C22×C4—461no—
162C22×C4C22×D2311yescharacteristic
163C2×C8—21no—
164C2×C8—461no—
165C4⋊C4—231no—
166C4⋊C4—461no—
167C4⋊C4C4×D2311yescharacteristic
168C22⋊C4—21no—
169C22⋊C4—461no—
170C22⋊C4—461no—
171C22⋊C4—461no—
172C42—231no—
173C42—231no—
174C42—231no—
175C42—231no—
176C42—464no—
177C23—21no—
178C23—461no—
179C23D4×D2311yescharacteristic
180Q8—922no—
181D4—41no—
182D4—41no—
183D4—41no—
184D4—921no—
185D4—922no—
186D4—922no—
187D4—921no—
188D4—921no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—231no—
195C2×C4—231no—
196C2×C4—231no—
197C2×C4—231no—
198C2×C4—462no—
199C2×C4—461no—
200C2×C4—461no—
201C2×C4—462no—
202C2×C4—461no—
203C2×C4—922no—
204C2×C4—922no—
205C2×C4—921no—
206C2×C4—921no—
207C2×C4C2×C4×D2311yescharacteristic
208C2×C4D4×D2311yescharacteristic
209C8—41no—
210C8—921no—
211C22—21no—
212C22—21no—
213C22—41no—
214C22—41no—
215C22—41no—
216C22—921no—
217C22—921no—
218C22—921no—
219C22C22⋊C4×D2311yescharacteristic
220C22#1062508211yescharacteristic
221C22#1062508511yescharacteristic
222C4—21no—
223C4—21no—
224C4—42no—
225C4—41no—
226C4—232no—
227C4—461no—
228C4—461no—
229C4—461no—
230C4—922no—
231C4—921no—
232C2—21no—
233C2—21no—
234C2—81no—
235C2—1841no—
236C2#1309238911yescharacteristic
237C2#1309242011yescharacteristic
238C2#104×D2311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D23
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#327C2
socleC22×C23C2×C22⋊C4
prime radical#13092962C2
cosocleC22×C4×C23C23
hypercenter#327D23
hypocenterC23#1505
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #13092471C2semidirect
3. #13092262C2semidirect
4. #13092152C2semidirect
5. #13092151C2semidirect
6. #13092150C2semidirect
7. C23×#327C2semidirect
10. #10625111C4semidirect
12. D4×Dic23C4semidirect
16. #10625064C4semidirect
17. #10625059C4semidirect
119. #327D23semidirect
146. C23#1505semidirect

Maximal subgroups

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

subgroupindex
#130929622
#130924712
#130922622
#130921522
#130921512
#130921502
C23×#3272
#150523