Finite Group Databasebeta

← #15671746

Subgroups — #15671746

Order 2944.

280 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 73 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×#10625100C211yesmaximal, characteristic
2C2×C22⋊(C23⋊C8)C211yesmaximal, characteristic, complemented
3#13092142C212yesmaximal, complemented
4#13092140C212yesmaximal, complemented
5C23×#407C211yesmaximal, characteristic, complemented
6C23×C4×C23C2211yescharacteristic
7C22×C22⋊D23C411yescharacteristic
8C2×M16×C23—21no—
9C2×C22⋊Dic23C411yescharacteristic
10#10625100—21no—
11#10625100—21no—
12#10625100—21no—
13#10625100—21no—
14C2×(C2×D23)⋊C4C411yescharacteristic
15C2×(C2×D23)⋊C4C2211yescharacteristic
16C2×Dic23⋊C4C411yescharacteristic
17C2×Dic23⋊C4C2211yescharacteristic
18C22×C23⋊C8—21no—
19C23×C22⋊C8—21no—
20C23×C22⋊C8C2212yes—
21C22⋊(C23⋊C8)—21no—
22C22⋊(C23⋊C8)C2212yes—
23C24×C23C2×C411yescharacteristic
24C23×D23C2×C411yescharacteristic
25C22×C4×C23—42no—
26C22×C4×C23C2×C411yescharacteristic
27C22×C4×C23D411yescharacteristic
28C22×C4×C23D411yescharacteristic
29C22×C4×C23D411yescharacteristic
30C22×C4×C23D411yescharacteristic
31C22×C4×C23C2311yescharacteristic
32C2×C22⋊D23—21no—
33C2×C22⋊D23—21no—
34C2×C22⋊D23—42no—
35C22×Dic23C2×C411yescharacteristic
36C22×Dic23C2×C411yescharacteristic
37C22×Dic23C2×C411yescharacteristic
38M16×C23—42no—
39C2×C8×C23—22no—
40C22⋊Dic23—21no—
41C22⋊Dic23—21no—
42(C2×D23)⋊C4—21no—
43(C2×D23)⋊C4—21no—
44(C2×D23)⋊C4—21no—
45(C2×D23)⋊C4—21no—
46Dic23⋊C4—21no—
47Dic23⋊C4—21no—
48Dic23⋊C4—21no—
49Dic23⋊C4—21no—
50C2×C23⋊C8—22no—
51C2×C23⋊C8—42no—
52C23×C23—22no—
53C23×C23—22no—
54C23×C23—41no—
55C23×C23C22⋊C411yescharacteristic
56C23×C23C22⋊C411yescharacteristic
57C23×C23C22×C411yescharacteristic
58C22×D23—21no—
59C22×D23—22no—
60C22×D23—41no—
61C22×D23—41no—
62C2×C4×C23—22no—
63C2×C4×C23—22no—
64C2×C4×C23—41no—
65C2×C4×C23—41no—
66C2×C4×C23—41no—
67C2×C4×C23—41no—
68C2×C4×C23C22⋊C411yescharacteristic
69C2×C4×C23C22⋊C411yescharacteristic
70C2×C4×C23C2×D411yescharacteristic
71C2×C4×C23C2×D411yescharacteristic
72C22⋊D23—42no—
73C22⋊D23—42no—
74C2×Dic23—21no—
75C2×Dic23—21no—
76C2×Dic23—21no—
77C2×Dic23—22no—
78C2×Dic23—41no—
79C2×Dic23—41no—
80C8×C23—42no—
81C23⋊C8—42no—
82#1468—231nomaximal, Sylow
83C22×C23—21no—
84C22×C23—21no—
85C22×C23—21no—
86C22×C23—21no—
87C22×C23—21no—
88C22×C23—21no—
89C22×C23—21no—
90C22×C23—44no—
91C22×C23#9912yes—
92C22×C23C2×C22⋊C411yescharacteristic
93C22×C23#13112yes—
94C2×D23—41no—
95C2×D23—41no—
96C2×D23—41no—
97C2×D23—82no—
98C4×C23—21no—
99C4×C23—21no—
100C4×C23—21no—
101C4×C23—21no—
102Dic23—41no—
103Dic23—41no—
104Dic23—41no—
105C2×#123—231no—
106#407D2311yescharacteristic, complemented
107C2×C22⋊C8—231no—
108#324—232no—
109#323—232no—
110C2×C23—22no—
111C2×C23—22no—
112C2×C23—41no—
113C2×C23#40811yescharacteristic
114C2×C23C2×#9911yescharacteristic
115C2×C23#41311yescharacteristic
116D23—81no—
117C22×D4—231no—
118C23×C4C2×D2311yescharacteristic
119C2×M16—21no—
120C22×C8—461no—
121#123—461no—
122#123—461no—
123#123—461no—
124#123—461no—
125C2×C4⋊C4—231no—
126C2×C4⋊C4—231no—
127C2×C22⋊C4—231no—
128C2×C22⋊C4—231no—
129C2×C22⋊C4—231no—
130C22⋊C8—21no—
131C22⋊C8—232no—
132C22⋊C8—461no—
133C22⋊C8C2×D2312yes—
134C23#146811yescharacteristic, complemented, Sylow
135C24—231no—
136C24C4×D2311yescharacteristic
137C2×D4—461no—
138C2×D4—461no—
139C2×D4—922no—
140C22×C4—42no—
141C22×C4—231no—
142C22×C4—231no—
143C22×C4—231no—
144C22×C4C4×D2311yescharacteristic
145C22×C4D9211yescharacteristic
146C22×C4D9211yescharacteristic
147C22×C4C22⋊D2311yescharacteristic
148C22×C4C22⋊D2311yescharacteristic
149C22×C4C22×D2311yescharacteristic
150M16—42no—
151C2×C8—22no—
152C2×C8—462no—
153C2×C8—922no—
154C4⋊C4—461no—
155C4⋊C4—461no—
156C4⋊C4—461no—
157C4⋊C4—461no—
158C22⋊C4—461no—
159C22⋊C4—461no—
160C22⋊C4—461no—
161C22⋊C4—461no—
162C22⋊C4—461no—
163C22⋊C4—461no—
164C23—22no—
165C23—22no—
166C23—41no—
167C23—461no—
168C23—462no—
169C23—921no—
170C23—921no—
171C23(C2×D23)⋊C411yescharacteristic
172C23(C2×D23)⋊C411yescharacteristic
173C23C2×C4×D2311yescharacteristic
174D4—922no—
175D4—922no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—462no—
183C2×C4—461no—
184C2×C4—461no—
185C2×C4—461no—
186C2×C4—921no—
187C2×C4—921no—
188C2×C4(C2×D23)⋊C411yescharacteristic
189C2×C4(C2×D23)⋊C411yescharacteristic
190C2×C4C2×D9211yescharacteristic
191C2×C4C2×C22⋊D2311yescharacteristic
192C8—42no—
193C8—922no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—44no—
202C22—921no—
203C22—921no—
204C22—921no—
205C22—1842no—
206C22#1062498812yes—
207C22#1062507812yes—
208C22C2×(C2×D23)⋊C411yescharacteristic
209C4—21no—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—921no—
214C4—921no—
215C4—921no—
216C2—22no—
217C2—22no—
218C2—41no—
219C2—1841no—
220C2#1309238511yescharacteristic
221C2C2×#1062498811yescharacteristic
222C2#1309239911yescharacteristic
subgroupG/H
centerC22C2×(C2×D23)⋊C4
commutatorC23×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#407C2
socleC22×C23C2×C22⋊C4
prime radicalC22×C22⋊D23C4
cosocleC22×C4×C23C23
hypercenter#407D23
hypocenterC23#1468
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. C2×C22⋊(C23⋊C8)C2semidirect
3. #13092142C2semidirect
4. #13092140C2semidirect
5. C23×#407C2semidirect
106. #407D23semidirect
134. C23#1468semidirect

Maximal subgroups

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

subgroupindex
C2×#106251002
C2×C22⋊(C23⋊C8)2
#130921422
#130921402
C23×#4072
#146823