Finite Group Databasebeta

← #15671742

Subgroups — #15671742

Order 2944.

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

normal subgroups only

This group has 280 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
1C2×#10625054C211yesmaximal, characteristic
2#13092379C211yesmaximal, characteristic, complemented
3C22⋊C8×D23C211yesmaximal, characteristic, complemented
4#13092142C211yesmaximal, characteristic, complemented
5#13092142C211yesmaximal, characteristic, complemented
6#13092141C211yesmaximal, characteristic, complemented
7C23×#323C211yesmaximal, characteristic, complemented
8C22×C22⋊D23C411yescharacteristic
9C22×C4×D23C2211yescharacteristic
10C2×C22⋊C4×C23C2211yescharacteristic
11C2×C22⋊Dic23C411yescharacteristic
12C2×(C2×D23)⋊C4C411yescharacteristic
13C2×C4⋊Dic23C411yescharacteristic
14C2×Dic23⋊C4C2211yescharacteristic
15C2×#67262—21no—
16C2×C8×D23—21no—
17#10625054—21no—
18#10625054—21no—
19#10625054—21no—
20#10625054—21no—
21C23×C22⋊C8C2211yescharacteristic
22C23×C22⋊C8C2211yescharacteristic
23C22⋊(C23⋊C8)C2211yescharacteristic
24C22⋊(C23⋊C8)C2211yescharacteristic
25(C2×D23)⋊C8—21no—
26(C2×D23)⋊C8—21no—
27C24×C23C2×C411yescharacteristic
28C23×D23C2×C411yescharacteristic
29C22×C4×C23C2×C411yescharacteristic
30C22×C4×C23C2311yescharacteristic
31C2×C22⋊D23—21no—
32C2×C22⋊D23—21no—
33C2×C22⋊D23—42no—
34C22×Dic23C2×C411yescharacteristic
35C22×Dic23C2×C411yescharacteristic
36C22×Dic23C2×C411yescharacteristic
37C2×C4×D23—42no—
38C2×C4×D23D411yescharacteristic
39C2×C4×D23D411yescharacteristic
40C2×C4×D23D411yescharacteristic
41C2×C4×D23D411yescharacteristic
42C2×C8×C23—21no—
43C2×C8×C23—21no—
44C22⋊C4×C23—21no—
45C22⋊C4×C23—21no—
46C22⋊Dic23—21no—
47C22⋊Dic23—21no—
48(C2×D23)⋊C4—21no—
49(C2×D23)⋊C4—21no—
50C4⋊Dic23—21no—
51C4⋊Dic23—21no—
52Dic23⋊C4—21no—
53Dic23⋊C4—21no—
54C2×C23⋊C8—21no—
55C2×C23⋊C8—21no—
56#67262—42no—
57C8×D23—42no—
58C23×C23—21no—
59C23×C23—21no—
60C23×C23—21no—
61C23×C23—41no—
62C23×C23—41no—
63C23×C23C22×C411yescharacteristic
64C22×D23—21no—
65C22×D23—21no—
66C22×D23—22no—
67C22×D23—41no—
68C22×D23C22⋊C411yescharacteristic
69C22×D23C22⋊C411yescharacteristic
70C2×C4×C23—21no—
71C2×C4×C23—41no—
72C2×C4×C23—41no—
73C2×C4×C23C2×D411yescharacteristic
74C2×C4×C23C2×D411yescharacteristic
75C22⋊D23—42no—
76C22⋊D23—42no—
77C2×Dic23—21no—
78C2×Dic23—21no—
79C2×Dic23—21no—
80C2×Dic23—21no—
81C2×Dic23—41no—
82C2×Dic23—41no—
83C2×Dic23C22⋊C411yescharacteristic
84C2×Dic23C22⋊C411yescharacteristic
85C4×D23—22no—
86C4×D23—22no—
87C4×D23—41no—
88C4×D23—41no—
89C8×C23—41no—
90C8×C23—41no—
91C23⋊C8—41no—
92C23⋊C8—41no—
93#1468—231nomaximal, Sylow
94C22×C23—21no—
95C22×C23—21no—
96C22×C23—41no—
97C22×C23—41no—
98C22×C23—41no—
99C22×C23—81no—
100C22×C23—81no—
101C22×C23C2×C22⋊C411yescharacteristic
102C22×C23#13111yescharacteristic
103C22×C23#13111yescharacteristic
104C2×D23—21no—
105C2×D23—21no—
106C2×D23—21no—
107C2×D23—21no—
108C2×D23—21no—
109C2×D23—42no—
110C2×D23—42no—
111C2×D23#9912yes—
112C4×C23—21no—
113C4×C23—21no—
114C4×C23—41no—
115Dic23—21no—
116Dic23—21no—
117Dic23—41no—
118Dic23—41no—
119C2×#123—231no—
120#407—231no—
121C2×C22⋊C8—231no—
122#324—231no—
123#324—231no—
124#323—231no—
125#323D2311yescharacteristic, complemented
126C2×C23—21no—
127C2×C23—21no—
128C2×C23—81no—
129C2×C23#40811yescharacteristic
130C2×C23C2×#9911yescharacteristic
131C2×C23#41311yescharacteristic
132D23—22no—
133D23—41no—
134C22×D4—231no—
135C23×C4—231no—
136C2×M16—461no—
137C22×C8—461no—
138#123—461no—
139#123—461no—
140#123—461no—
141#123—461no—
142C2×C4⋊C4—231no—
143C2×C4⋊C4—231no—
144C2×C22⋊C4—231no—
145C2×C22⋊C4—231no—
146C2×C22⋊C4C2×D2311yescharacteristic
147C22⋊C8—231no—
148C22⋊C8—231no—
149C22⋊C8—461no—
150C22⋊C8—461no—
151C22⋊C8C2×D2311yescharacteristic
152C22⋊C8C2×D2311yescharacteristic
153C23#146811yescharacteristic, complemented, Sylow
154C24—231no—
155C24C4×D2311yescharacteristic
156C2×D4—461no—
157C2×D4—461no—
158C2×D4—922no—
159C22×C4—231no—
160C22×C4—231no—
161C22×C4—231no—
162C22×C4—231no—
163C22×C4—231no—
164C22×C4—231no—
165C22×C4—231no—
166C22×C4—922no—
167C22×C4C4×D2311yescharacteristic
168C22×C4C22×D2311yescharacteristic
169M16—922no—
170C2×C8—21no—
171C2×C8—21no—
172C2×C8—461no—
173C2×C8—461no—
174C2×C8—922no—
175C4⋊C4—461no—
176C4⋊C4—461no—
177C4⋊C4—461no—
178C4⋊C4—461no—
179C22⋊C4—21no—
180C22⋊C4—21no—
181C22⋊C4—461no—
182C22⋊C4—461no—
183C22⋊C4—461no—
184C22⋊C4—461no—
185C23—21no—
186C23—21no—
187C23—21no—
188C23—41no—
189C23—41no—
190C23—231no—
191C23—231no—
192C23—462no—
193C23—461no—
194C23—461no—
195C23—921no—
196C23C2×C4×D2311yescharacteristic
197D4—922no—
198D4—922no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—231no—
203C2×C4—231no—
204C2×C4—462no—
205C2×C4—462no—
206C2×C4—461no—
207C2×C4—461no—
208C2×C4—461no—
209C2×C4—461no—
210C2×C4—921no—
211C2×C4—921no—
212C2×C4—921no—
213C2×C4—921no—
214C2×C4D4×D2311yescharacteristic
215C2×C4D4×D2311yescharacteristic
216C8—41no—
217C8—41no—
218C8—921no—
219C8—921no—
220C22—21no—
221C22—21no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—81no—
226C22—81no—
227C22—232no—
228C22—461no—
229C22—461no—
230C22—461no—
231C22—461no—
232C22—461no—
233C22—922no—
234C22—922no—
235C22C22⋊C4×D2311yescharacteristic
236C22#1062507211yescharacteristic
237C22#1062507811yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—461no—
242C4—461no—
243C4—921no—
244C4—921no—
245C2—21no—
246C2—21no—
247C2—81no—
248C2—462no—
249C2—921no—
250C2#1309238211yescharacteristic
251C2#99×D2311yescharacteristic
252C2#1309239811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D23
commutatorC23×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#323C2
socleC22×C23C2×C22⋊C4
prime radicalC22×C22⋊D23C4
cosocleC22×C4×C23C23
hypercenter#323D23
hypocenterC23#1468
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #13092379C2semidirect
3. C22⋊C8×D23C2semidirect
4. #13092142C2semidirect
5. #13092142C2semidirect
6. #13092141C2semidirect
7. C23×#323C2semidirect
125. #323D23semidirect
153. C23#1468semidirect

Maximal subgroups

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

subgroupindex
C2×#106250542
#130923792
C22⋊C8×D232
#130921422
#130921412
C23×#3232
#146823