Finite Group Databasebeta

← #15671722

Subgroups — #15671722

Order 2944.

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

normal subgroups only

This group has 440 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
1C2×C22⋊C4×D23C211yesmaximal, characteristic
2#13092379C212yesmaximal, complemented
3#13092141C211yesmaximal, characteristic, complemented
4#13092140C212yesmaximal, complemented
5C23×#323C211yesmaximal, characteristic, complemented
6C24×D23C411yescharacteristic
7C22×C4×D23C411yescharacteristic
8C22×C4×D23C2211yescharacteristic
9C2×C22⋊C4×C23C2211yescharacteristic
10C2×C22⋊Dic23C411yescharacteristic
11C2×(C2×D23)⋊C4C411yescharacteristic
12C2×(C2×D23)⋊C4C2211yescharacteristic
13C2×#67262—22no—
14C22⋊C4×D23—22no—
15C22⋊C4×D23—22no—
16C23×C22⋊C8C2212yescomplemented
17C22⋊(C23⋊C8)C2212yescomplemented
18(C2×D23)⋊C8—22no—
19C24×C23C2×C411yescharacteristic
20C23×D23—22no—
21C23×D23—21no—
22C23×D23—21no—
23C23×D23—22no—
24C23×D23—42no—
25C23×D23—42no—
26C23×D23C2×C411yescharacteristic
27C23×D23C2×C411yescharacteristic
28C22×C4×C23C2×C411yescharacteristic
29C22×C4×C23C2311yescharacteristic
30C22×Dic23C2×C411yescharacteristic
31C22×Dic23C2×C411yescharacteristic
32C2×C4×D23—21no—
33C2×C4×D23—21no—
34C2×C4×D23—42no—
35C2×C4×D23—42no—
36C2×C4×D23D412yes—
37C2×C4×D23D412yes—
38C2×C8×C23—22no—
39C22⋊C4×C23—22no—
40C22⋊Dic23—22no—
41(C2×D23)⋊C4—22no—
42(C2×D23)⋊C4—22no—
43C2×C23⋊C8—22no—
44#67262—44no—
45C23×C23—21no—
46C23×C23—21no—
47C23×C23—41no—
48C23×C23—41no—
49C23×C23M1612yescomplemented
50C23×C23C22×C411yescharacteristic
51C22×D23—21no—
52C22×D23—21no—
53C22×D23—22no—
54C22×D23—22no—
55C22×D23—24no—
56C22×D23—24no—
57C22×D23—21no—
58C22×D23—21no—
59C22×D23—48no—
60C22×D23—48no—
61C22×D23—42no—
62C22×D23—42no—
63C22×D23—42no—
64C22×D23—42no—
65C22×D23—41no—
66C22×D23—41no—
67C22×D23C22⋊C411yescharacteristic
68C22×D23C22⋊C411yescharacteristic
69C22×D23M1612yescomplemented
70C2×C4×C23—21no—
71C2×C4×C23—41no—
72C2×C4×C23—41no—
73C2×C4×C23C2×D412yes—
74C2×Dic23—21no—
75C2×Dic23—41no—
76C2×Dic23—41no—
77C2×Dic23C22⋊C412yes—
78C4×D23—24no—
79C4×D23—42no—
80C4×D23—42no—
81C4×D23—42no—
82C8×C23—42no—
83C23⋊C8—42no—
84#1462—231nomaximal, Sylow
85C22×C23—21no—
86C22×C23—21no—
87C22×C23—22no—
88C22×C23—42no—
89C22×C23—42no—
90C22×C23—41no—
91C22×C23—41no—
92C22×C23C2×C22⋊C411yescharacteristic
93C22×C23C2×M1611yescharacteristic
94C22×C23C2×M1611yescharacteristic
95C2×D23—24no—
96C2×D23—24no—
97C2×D23—21no—
98C2×D23—21no—
99C2×D23—21no—
100C2×D23—21no—
101C2×D23—22no—
102C2×D23—48no—
103C2×D23—48no—
104C2×D23—42no—
105C2×D23—41no—
106C2×D23—41no—
107C2×D23—42no—
108C2×D23#9912yes—
109C2×D23#10012yes—
110C4×C23—22no—
111C4×C23—41no—
112Dic23—22no—
113Dic23—41no—
114C22×C22⋊C4—231no—
115#407—232no—
116#323—231no—
117#323—232no—
118#323D2311yescharacteristic, complemented
119C2×C23—21no—
120C2×C23—21no—
121C2×C23—42no—
122C2×C23#40711yescharacteristic
123C2×C23C2×#9911yescharacteristic
124C2×C23C2×#10011yescharacteristic
125D23—22no—
126D23—22no—
127D23—42no—
128C25—231no—
129C23×C4—231no—
130C23×C4—231no—
131C2×M16—462no—
132C2×C22⋊C4—231no—
133C2×C22⋊C4—231no—
134C2×C22⋊C4—231no—
135C2×C22⋊C4—462no—
136C2×C22⋊C4—462no—
137C2×C22⋊C4C2×D2311yescharacteristic
138C22⋊C8—232no—
139C22⋊C8—462no—
140C22⋊C8C2×D2312yescomplemented
141C23#146211yescharacteristic, complemented, Sylow
142C24—231no—
143C24—231no—
144C24—461no—
145C24—461no—
146C24—462no—
147C24—462no—
148C24—922no—
149C24—922no—
150C24C4×D2311yescharacteristic
151C22×C4—231no—
152C22×C4—232no—
153C22×C4—232no—
154C22×C4—231no—
155C22×C4—461no—
156C22×C4—461no—
157C22×C4—922no—
158C22×C4—922no—
159C22×C4C4×D2311yescharacteristic
160C22×C4C22×D2311yescharacteristic
161M16—924no—
162C2×C8—22no—
163C2×C8—462no—
164C22⋊C4—22no—
165C22⋊C4—462no—
166C22⋊C4—462no—
167C22⋊C4—462no—
168C23—21no—
169C23—21no—
170C23—41no—
171C23—41no—
172C23—231no—
173C23—231no—
174C23—232no—
175C23—462no—
176C23—462no—
177C23—464no—
178C23—464no—
179C23—461no—
180C23—461no—
181C23—461no—
182C23—461no—
183C23—921no—
184C23—921no—
185C23—922no—
186C23—922no—
187C23—928no—
188C23—928no—
189C23—922no—
190C23—922no—
191C23#6726212yescomplemented
192C23C2×C4×D2311yescharacteristic
193C2×C4—21no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—232no—
197C2×C4—464no—
198C2×C4—461no—
199C2×C4—922no—
200C2×C4—922no—
201C2×C4—922no—
202C2×C4—921no—
203C2×C4—921no—
204C2×C4D4×D2312yes—
205C8—42no—
206C8—922no—
207C22—21no—
208C22—21no—
209C22—22no—
210C22—42no—
211C22—42no—
212C22—41no—
213C22—41no—
214C22—232no—
215C22—232no—
216C22—464no—
217C22—464no—
218C22—461no—
219C22—461no—
220C22—461no—
221C22—461no—
222C22—462no—
223C22—922no—
224C22—922no—
225C22—928no—
226C22—928no—
227C22—921no—
228C22—921no—
229C22C22⋊C4×D2311yescharacteristic
230C22C2×#6726211yescharacteristic
231C22M16×D2311yescharacteristic
232C4—22no—
233C4—41no—
234C4—462no—
235C4—921no—
236C2—21no—
237C2—21no—
238C2—42no—
239C2—462no—
240C2—462no—
241C2—922no—
242C2#1309237911yescharacteristic
243C2#99×D2311yescharacteristic
244C2#100×D2311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D23
commutatorC23×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#323C2
socleC22×C23C2×C22⋊C4
prime radicalC24×D23C4
cosocleC22×C4×C23C23
hypercenter#323D23
hypocenterC23#1462
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. #13092141C2semidirect
4. #13092140C2semidirect
5. C23×#323C2semidirect
16. C23×C22⋊C8C22semidirect
17. C22⋊(C23⋊C8)C22semidirect
49. C23×C23M16semidirect
69. C22×D23M16semidirect
118. #323D23semidirect
140. C22⋊C8C2×D23semidirect
141. C23#1462semidirect
191. C23#67262semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×D232
#130923792
#130921412
#130921402
C23×#3232
#146223