Finite Group Databasebeta

← #15671723

Subgroups — #15671723

Order 2944.

440 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 81 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
1C22×(C2×D23)⋊C4C211yesmaximal, characteristic
2#13092381C211yesmaximal, characteristic, complemented
3#13092140C214yesmaximal, complemented
4C23×#407C211yesmaximal, characteristic, complemented
5C24×D23C411yescharacteristic
6C23×C4×C23C2211yescharacteristic
7C23×Dic23C411yescharacteristic
8C2×M16×C23—21no—
9C2×(C2×D23)⋊C4—21no—
10C2×(C2×D23)⋊C4—21no—
11C2×(C2×D23)⋊C4—21no—
12C2×(C2×D23)⋊C4—21no—
13C2×(C2×D23)⋊C4C412yes—
14C2×(C2×D23)⋊C4C2212yes—
15C2×#67267—21no—
16C23×C22⋊C8—21no—
17C23×C22⋊C8C2212yescomplemented
18C22⋊(C23⋊C8)—21no—
19C22⋊(C23⋊C8)C2212yescomplemented
20C24×C23C2×C411yescharacteristic
21C23×D23—21no—
22C23×D23—21no—
23C23×D23—24no—
24C23×D23—42no—
25C23×D23—42no—
26C23×D23C2×C412yes—
27C22×C4×C23—42no—
28C22×C4×C23C2×C411yescharacteristic
29C22×C4×C23D411yescharacteristic
30C22×C4×C23D411yescharacteristic
31C22×C4×C23D411yescharacteristic
32C22×C4×C23D411yescharacteristic
33C22×C4×C23C2311yescharacteristic
34C22×Dic23—21no—
35C22×Dic23—21no—
36C22×Dic23—42no—
37C22×Dic23C2×C412yes—
38M16×C23—42no—
39C2×C8×C23—22no—
40(C2×D23)⋊C4—22no—
41(C2×D23)⋊C4—22no—
42(C2×D23)⋊C4—22no—
43(C2×D23)⋊C4—22no—
44#67267—42no—
45C2×C23⋊C8—22no—
46C23×C23—22no—
47C23×C23—22no—
48C23×C23—22no—
49C23×C23C22⋊C411yescharacteristic
50C23×C23C22⋊C411yescharacteristic
51C23×C23C22×C411yescharacteristic
52C22×D23—24no—
53C22×D23—24no—
54C22×D23—22no—
55C22×D23—22no—
56C22×D23—416no—
57C22×D23—42no—
58C22×D23—42no—
59C22×D23—42no—
60C22×D23—42no—
61C22×D23—42no—
62C22×D23—42no—
63C22×D23M1614yescomplemented
64C2×C4×C23—22no—
65C2×C4×C23—22no—
66C2×C4×C23—41no—
67C2×C4×C23—41no—
68C2×C4×C23—41no—
69C2×C4×C23—41no—
70C2×C4×C23C22⋊C411yescharacteristic
71C2×C4×C23C22⋊C411yescharacteristic
72C2×C4×C23C2×D411yescharacteristic
73C2×C4×C23C2×D411yescharacteristic
74C2×Dic23—22no—
75C2×Dic23—42no—
76C2×Dic23—42no—
77C2×Dic23—42no—
78C8×C23—42no—
79C23⋊C8—42no—
80#1462—231nomaximal, Sylow
81C22×C23—28no—
82C22×C23—21no—
83C22×C23—21no—
84C22×C23—21no—
85C22×C23—21no—
86C22×C23—21no—
87C22×C23—21no—
88C22×C23#9912yes—
89C22×C23#10012yes—
90C22×C23C2×C22⋊C411yescharacteristic
91C22×C23C2×M1612yes—
92C2×D23—24no—
93C2×D23—48no—
94C2×D23—48no—
95C2×D23—44no—
96C2×D23—42no—
97C2×D23—42no—
98C2×D23—44no—
99C4×C23—21no—
100C4×C23—21no—
101C4×C23—21no—
102C4×C23—21no—
103Dic23—42no—
104C22×C22⋊C4—231no—
105#407—231no—
106#407D2311yescharacteristic, complemented
107#323—234no—
108C2×C23—22no—
109C2×C23—22no—
110C2×C23—22no—
111C2×C23#40711yescharacteristic
112C2×C23C2×#9911yescharacteristic
113C2×C23C2×#10011yescharacteristic
114D23—44no—
115C25—231no—
116C23×C4—231no—
117C23×C4C2×D2311yescharacteristic
118C2×M16—21no—
119C2×M16—461no—
120C2×C22⋊C4—232no—
121C2×C22⋊C4—232no—
122C2×C22⋊C4—461no—
123C2×C22⋊C4—461no—
124C2×C22⋊C4—461no—
125C2×C22⋊C4—461no—
126C22⋊C8—21no—
127C22⋊C8—232no—
128C22⋊C8—461no—
129C22⋊C8C2×D2312yescomplemented
130C23#146211yescharacteristic, complemented, Sylow
131C24—232no—
132C24—464no—
133C24—461no—
134C24—461no—
135C24—922no—
136C24—922no—
137C24C4×D2311yescharacteristic
138C22×C4—42no—
139C22×C4—232no—
140C22×C4—461no—
141C22×C4—461no—
142C22×C4—922no—
143C22×C4C4×D2311yescharacteristic
144C22×C4D9211yescharacteristic
145C22×C4D9211yescharacteristic
146C22×C4C22⋊D2311yescharacteristic
147C22×C4C22⋊D2311yescharacteristic
148C22×C4C22×D2311yescharacteristic
149M16—42no—
150M16—922no—
151C2×C8—22no—
152C2×C8—462no—
153C22⋊C4—462no—
154C22⋊C4—462no—
155C22⋊C4—462no—
156C22⋊C4—462no—
157C23—22no—
158C23—22no—
159C23—22no—
160C23—234no—
161C23—464no—
162C23—464no—
163C23—462no—
164C23—462no—
165C23—922no—
166C23—922no—
167C23—9216no—
168C23—922no—
169C23—922no—
170C23—922no—
171C23—922no—
172C23(C2×D23)⋊C411yescharacteristic
173C23(C2×D23)⋊C411yescharacteristic
174C23C2×C4×D2311yescharacteristic
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—462no—
182C2×C4—922no—
183C2×C4—922no—
184C2×C4—922no—
185C2×C4(C2×D23)⋊C411yescharacteristic
186C2×C4(C2×D23)⋊C411yescharacteristic
187C2×C4C2×D9211yescharacteristic
188C2×C4C2×C22⋊D2311yescharacteristic
189C8—42no—
190C8—922no—
191C22—28no—
192C22—21no—
193C22—21no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—464no—
199C22—924no—
200C22—924no—
201C22—928no—
202C22—928no—
203C22—922no—
204C22—922no—
205C22#1062498812yes—
206C22#1062500512yes—
207C22M16×D2312yes—
208C22C2×(C2×D23)⋊C411yescharacteristic
209C4—21no—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—922no—
214C2—22no—
215C2—22no—
216C2—22no—
217C2—924no—
218C2#1309238011yescharacteristic
219C2C2×#1062498811yescharacteristic
220C2C2×#1062500511yescharacteristic
subgroupG/H
centerC22C2×(C2×D23)⋊C4
commutatorC23×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#407C2
socleC22×C23C2×C22⋊C4
prime radicalC24×D23C4
cosocleC22×C4×C23C23
hypercenter#407D23
hypocenterC23#1462
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. #13092381C2semidirect
3. #13092140C2semidirect
4. C23×#407C2semidirect
17. C23×C22⋊C8C22semidirect
19. C22⋊(C23⋊C8)C22semidirect
63. C22×D23M16semidirect
106. #407D23semidirect
129. C22⋊C8C2×D23semidirect
130. C23#1462semidirect

Maximal subgroups

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

subgroupindex
C22×(C2×D23)⋊C42
#130923812
#130921402
C23×#4072
#146223