Finite Group Databasebeta

← #15671890

Subgroups — #15671890

Order 2944.

284 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 71 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#13092467C211yesmaximal, characteristic, complemented
3#13092268C211yesmaximal, 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×Dic23⋊C4—21no—
15C2×C4×Dic23—21no—
16C2×C4×Dic23C2211yescharacteristic
17#10625064C411yescharacteristic, complemented
18#10625059C411yescharacteristic, complemented
19#10625056—21no—
20(C22⋊D23)⋊C4—21no—
21C23×C22⋊C8C2211yescharacteristic
22C23×#95C2211yescharacteristic
23C23⋊#95C2211yescharacteristic
24C22⋊(C23⋊C8)C2211yescharacteristic
25Dic23⋊C8—21no—
26C8×Dic23—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—24no—
51Dic23⋊C4—21no—
52C4×Dic23—42no—
53C4×Dic23C2×C411yescharacteristic
54C4×Dic23C2×C411yescharacteristic
55C4×Dic23D411yescharacteristic
56C4×Dic23D411yescharacteristic
57C2×C23⋊C8—21no—
58C23×C23—21no—
59C23×C23C2×D411yescharacteristic
60C22×D23—21no—
61D4×C23—41no—
62D4×C23—41no—
63D4×C23—41no—
64C2×C4×C23—22no—
65C2×C4×C23—21no—
66C2×C4×C23—41no—
67C2×C4×C23—41no—
68C2×C4×C23—41no—
69C2×C4×C23C22×C411yescharacteristic
70C2×C4×C23C2×D411yescharacteristic
71C22⋊D23—41no—
72C22⋊D23—41no—
73C22⋊D23—42no—
74C22⋊D23—42no—
75C2×Dic23—22no—
76C2×Dic23—22no—
77C2×Dic23—21no—
78C2×Dic23—41no—
79C2×Dic23—41no—
80C2×Dic23—42no—
81C2×Dic23C22⋊C411yescharacteristic
82C2×Dic23C22⋊C411yescharacteristic
83C2×Dic23C22⋊C411yescharacteristic
84C2×Dic23C22⋊C411yescharacteristic
85C2×Dic23D812yes—
86C2×Dic23SD1612yes—
87D92—41no—
88C4×D23—42no—
89Dic46—42no—
90C8×C23—41no—
91C23⋊C8—41no—
92#1502—231nomaximal, Sylow
93C22×C23—21no—
94C22×C23—21no—
95C22×C23—41no—
96C22×C23—41no—
97C22×C23—41no—
98C22×C23C2×C22⋊C411yescharacteristic
99C22×C23C2×D811yescharacteristic
100C22×C23C2×SD1611yescharacteristic
101C2×D23—41no—
102C2×D23—41no—
103C2×D23—41no—
104C4×C23—21no—
105C4×C23—21no—
106C4×C23—42no—
107C4×C23—41no—
108Dic23—21no—
109Dic23—42no—
110Dic23—41no—
111Dic23#10212yes—
112Dic23#10212yes—
113Dic23#10412yes—
114#532—231no—
115#431—231no—
116C4×C4⋊C4—231no—
117#327—231no—
118#327—231no—
119#327—231no—
120#327D2311yescharacteristic, complemented
121C2×C23—21no—
122C2×C23—21no—
123C2×C23—81no—
124C2×C23#41011yescharacteristic
125C2×C23C2×#10211yescharacteristic
126C2×C23C2×#10411yescharacteristic
127D23—81no—
128C2×#41—461no—
129C4⋊Q8—231no—
130#127—231no—
131#124—461no—
132#121—231no—
133#121—461no—
134#121C2×D2311yescharacteristic
135C4×D4—231no—
136C4×D4—231no—
137C4×D4—461no—
138C2×C4⋊C4—461no—
139C2×C42—231no—
140C2×C42—461no—
141C4⋊C8—461no—
142C22⋊C8—231no—
143C22⋊C8C2×D2311yescharacteristic
144C4×C8—461no—
145#95—231no—
146#95C2×D2311yescharacteristic
147C23#150211yescharacteristic, complemented, Sylow
148#41—922no—
149#41—922no—
150C2×Q8—461no—
151C2×D4—21no—
152C2×D4—231no—
153C2×D4—461no—
154C2×D4—461no—
155C2×D4—461no—
156C2×D4C4×D2311yescharacteristic
157C22×C4—21no—
158C22×C4—231no—
159C22×C4—231no—
160C22×C4—461no—
161C22×C4—461no—
162C22×C4—461no—
163C22×C4C22×D2311yescharacteristic
164C2×C8—21no—
165C2×C8—461no—
166C4⋊C4—231no—
167C4⋊C4—461no—
168C4⋊C4—464no—
169C4⋊C4C4×D2311yescharacteristic
170C22⋊C4—21no—
171C22⋊C4—461no—
172C22⋊C4—461no—
173C22⋊C4—461no—
174C42—231no—
175C42—231no—
176C42—231no—
177C42—231no—
178C42—922no—
179C23—21no—
180C23—461no—
181C23D4×D2311yescharacteristic
182Q8—922no—
183D4—41no—
184D4—41no—
185D4—41no—
186D4—921no—
187D4—922no—
188D4—922no—
189D4—921no—
190D4—921no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—231no—
197C2×C4—231no—
198C2×C4—231no—
199C2×C4—232no—
200C2×C4—232no—
201C2×C4—231no—
202C2×C4—462no—
203C2×C4—462no—
204C2×C4—461no—
205C2×C4—922no—
206C2×C4—922no—
207C2×C4—921no—
208C2×C4—921no—
209C2×C4C2×C4×D2311yescharacteristic
210C2×C4D4×D2311yescharacteristic
211C8—41no—
212C8—921no—
213C22—21no—
214C22—21no—
215C22—41no—
216C22—41no—
217C22—41no—
218C22—921no—
219C22—921no—
220C22—921no—
221C22C22⋊C4×D2311yescharacteristic
222C22D8×D2311yescharacteristic
223C22SD16×D2311yescharacteristic
224C4—21no—
225C4—21no—
226C4—42no—
227C4—41no—
228C4—232no—
229C4—232no—
230C4—232no—
231C4—461no—
232C4—922no—
233C4—921no—
234C2—21no—
235C2—21no—
236C2—81no—
237C2—1841no—
238C2#1309238911yescharacteristic
239C2#102×D2311yescharacteristic
240C2#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#1502
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. #13092467C2semidirect
3. #13092268C2semidirect
4. #13092152C2semidirect
5. #13092151C2semidirect
6. #13092150C2semidirect
7. C23×#327C2semidirect
10. #10625111C4semidirect
12. D4×Dic23C4semidirect
17. #10625064C4semidirect
18. #10625059C4semidirect
120. #327D23semidirect
147. C23#1502semidirect

Maximal subgroups

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

subgroupindex
#130929622
#130924672
#130922682
#130921522
#130921512
#130921502
C23×#3272
#150223