Finite Group Databasebeta

← #11774677

Subgroups — #11774677

Order 1152.

948 conjugacy classes of subgroups; only the 257 normal subgroups are shown.

normal subgroups only

This group has 948 conjugacy classes of subgroups — too many to draw. Only its 257 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×C32×C4×D4C211yesmaximal, characteristic
2#10592625C211yesmaximal, characteristic, complemented
3C4×#3748C211yesmaximal, characteristic, complemented
4D4⋊(C3⋊(C3⋊C8))C214yesmaximal, complemented
5#71599—34nomaximal
6C22×C32×D4C411yescharacteristic
7C23×C32×C4—21no—
8C32×C4×D4—21no—
9C32×C4×D4—21no—
10C32×C4×D4C412yes—
11C32×C4×D4C2212yes—
12C2×C32×C4⋊C4C411yescharacteristic
13C2×C32×C22⋊C4—21no—
14C2×C32×C42C2211yescharacteristic
15C2×#3748—21no—
16#63657—21no—
17C4⋊(C3⋊(C3⋊C8))C2212yescomplemented
18#63630—21no—
19#63630—21no—
20C4×C3⋊(C3⋊C8)C2212yescomplemented
21C2×C3×C4×D4D314yes—
22#4926—34no—
23C4×#208—34no—
24D4⋊(C3⋊C8)—316no—
25C24×C32—21no—
26C2×C32×D4—24no—
27C2×C32×D4—21no—
28C2×C32×D4C2×C412yes—
29C22×C32×C4—21no—
30C22×C32×C4—22no—
31C22×C32×C4—22no—
32C22×C32×C4—44no—
33C22×C32×C4C2×C411yescharacteristic
34C22×C32×C4D411yescharacteristic
35C22×C32×C4D411yescharacteristic
36C32×C4⋊C4—21no—
37C32×C4⋊C4C2×C412yes—
38C32×C22⋊C4—22no—
39C32×C22⋊C4—22no—
40C32×C42C2×C411yescharacteristic
41C32×C42D411yescharacteristic
42C32×C42D411yescharacteristic
43C32×C42C2311yescharacteristic
44#3748—24no—
45C2×C3⋊(C3⋊C8)—22no—
46C2×C3⋊(C3⋊C8)—22no—
47#1490—91noSylow
48C22×C3×D4Dic314yes—
49C23×C3×C4—24no—
50C3×C4×D4—24no—
51C3×C4×D4—24no—
52C3×C4×D4Dic318yes—
53C3×C4×D4C2×D318yes—
54C2×C3×C4⋊C4Dic314yes—
55C2×C3×C22⋊C4—24no—
56C2×C3×C42C2×D314yes—
57C2×#208—64no—
58#830—64no—
59C4⋊(C3⋊C8)—38no—
60#803—64no—
61#803—64no—
62C4×C3⋊C8—38no—
63C23×C32—24no—
64C23×C32—22no—
65C23×C32—42no—
66C23×C32—42no—
67C23×C32C22⋊C411yescharacteristic
68C32×D4—24no—
69C32×D4—22no—
70C32×D4M1614yescomplemented
71C2×C32×C4—22no—
72C2×C32×C4—22no—
73C2×C32×C4—22no—
74C2×C32×C4—22no—
75C2×C32×C4—44no—
76C2×C32×C4—42no—
77C2×C32×C4—44no—
78C2×C32×C4C22⋊C411yescharacteristic
79C2×C32×C4C22⋊C411yescharacteristic
80C2×C32×C4C22⋊C411yescharacteristic
81C2×C32×C4C22×C411yescharacteristic
82C2×C32×C4C2×D411yescharacteristic
83C2×C32×C4C2×D411yescharacteristic
84C3⋊(C3⋊C8)—24no—
85C3⋊(C3⋊C8)—42no—
86C2×C4×D4C3⋊D311yescharacteristic
87#432—91no—
88C4×M16—91no—
89D4⋊C8—94no—
90C24×C3—24no—
91C2×C3×D4—216no—
92C2×C3×D4—24no—
93C2×C3×D4C2×Dic318yes—
94C22×C3×C4—24no—
95C22×C3×C4—28no—
96C22×C3×C4—28no—
97C22×C3×C4—416no—
98C22×C3×C4C2×Dic314yes—
99C22×C3×C4#6714yes—
100C22×C3×C4#6714yes—
101C3×C4⋊C4—24no—
102C3×C4⋊C4C2×Dic318yes—
103C3×C22⋊C4—28no—
104C3×C22⋊C4—28no—
105C3×C42C2×Dic314yes—
106C3×C42#6714yes—
107C3×C42#6714yes—
108C3×C42C22×D314yes—
109#208—616no—
110C2×C3⋊C8—68no—
111C2×C3⋊C8—68no—
112C22×C32—21no—
113C22×C32—21no—
114C22×C32—24no—
115C22×C32—48no—
116C22×C32—42no—
117C22×C32—42no—
118C22×C32#10412yes—
119C22×C32C2×C22⋊C411yescharacteristic
120C32×C4—21no—
121C32×C4—21no—
122C32×C4—21no—
123C32×C4—21no—
124C32×C4—42no—
125C32×C4C2×M1612yes—
126C32×C4AGL(1,ℤ/8)12yes—
127C22×D4C3⋊Dic311yescharacteristic
128C23×C4—21no—
129C2×M16—181no—
130C4×D4—21no—
131C4×D4—21no—
132C4×D4C3⋊Dic312yes—
133C4×D4C2×C3⋊D312yes—
134C2×C4⋊C4C3⋊Dic311yescharacteristic
135C2×C22⋊C4—21no—
136C2×C42C2×C3⋊D311yescharacteristic
137C4⋊C8—92no—
138C22⋊C8—181no—
139#97—181no—
140#97—181no—
141C4×C8—92no—
142C23×C3—216no—
143C23×C3—28no—
144C23×C3—48no—
145C23×C3—48no—
146C23×C3#21714yes—
147C3×D4—216no—
148C3×D4—28no—
149C3×D4#208116yescomplemented
150C2×C3×C4—28no—
151C2×C3×C4—28no—
152C2×C3×C4—28no—
153C2×C3×C4—28no—
154C2×C3×C4—416no—
155C2×C3×C4—48no—
156C2×C3×C4—416no—
157C2×C3×C4#21714yes—
158C2×C3×C4#21714yes—
159C2×C3×C4#21714yes—
160C2×C3×C4C22×Dic314yes—
161C2×C3×C4C2×#6714yes—
162C2×C3×C4C2×#6714yes—
163C3⋊C8—616no—
164C3⋊C8—128no—
165C2×C32—22no—
166C2×C32—44no—
167C2×C32#40711yescharacteristic
168C2×C32#41811yescharacteristic
169C2×C32C2×#10411yescharacteristic
170C24—21no—
171C2×D4—24no—
172C2×D4—21no—
173C2×D4C2×C3⋊Dic312yes—
174C22×C4—21no—
175C22×C4—22no—
176C22×C4—22no—
177C22×C4—44no—
178C22×C4C2×C3⋊Dic311yescharacteristic
179C22×C4#63811yescharacteristic
180C22×C4#63811yescharacteristic
181M16—184no—
182C2×C8—182no—
183C2×C8—182no—
184C4⋊C4—21no—
185C4⋊C4C2×C3⋊Dic312yes—
186C22⋊C4—22no—
187C22⋊C4—22no—
188C42C2×C3⋊Dic311yescharacteristic
189C42#63811yescharacteristic
190C42#63811yescharacteristic
191C42C22×C3⋊D311yescharacteristic
192C22×C3—24no—
193C22×C3—24no—
194C22×C3—216no—
195C22×C3—432no—
196C22×C3—48no—
197C22×C3—48no—
198C22×C3#83718yes—
199C22×C3C2×#21714yes—
200C3×C4—24no—
201C3×C4—24no—
202C3×C4—24no—
203C3×C4—24no—
204C3×C4—48no—
205C3×C4C2×#20818yes—
206C3×C4#93218yes—
207C32#149011yescharacteristic, complemented, Sylow
208C23—24no—
209C23—22no—
210C23—42no—
211C23—42no—
212C23#375711yescharacteristic
213D4—24no—
214D4—22no—
215D4#374814yescomplemented
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—44no—
221C2×C4—42no—
222C2×C4—44no—
223C2×C4#375711yescharacteristic
224C2×C4#375711yescharacteristic
225C2×C4#375711yescharacteristic
226C2×C4C22×C3⋊Dic311yescharacteristic
227C2×C4C2×#63811yescharacteristic
228C2×C4C2×#63811yescharacteristic
229C8—184no—
230C8—362no—
231C2×C3—28no—
232C2×C3—416no—
233C2×C3#520714yes—
234C2×C3#521514yes—
235C2×C3C2×#83714yes—
236C22—21no—
237C22—21no—
238C22—24no—
239C22—48no—
240C22—42no—
241C22—42no—
242C22#6366412yes—
243C22C2×#375711yescharacteristic
244C4—21no—
245C4—21no—
246C4—21no—
247C4—21no—
248C4—42no—
249C4C2×#374812yes—
250C4#6414112yes—
251C3#7159914yescomplemented
252C2—22no—
253C2—44no—
254C2#1059290611yescharacteristic
255C2#1059291411yescharacteristic
256C2C2×#6366411yescharacteristic
subgroupG/H
centerC2×C4C2×#638
commutatorC2×C32×C4C22×C4
FrattiniC42C22×C3⋊D3
FittingC2×C32×C4×D4C2
socleC22×C32C2×C22⋊C4
prime radicalC22×C32×D4C4
cosocleC32×C42C23
hypercenterC2×C4×D4C3⋊D3
hypocenterC32#1490
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. #10592625C2semidirect
3. C4×#3748C2semidirect
4. D4⋊(C3⋊(C3⋊C8))C2semidirect
17. C4⋊(C3⋊(C3⋊C8))C22semidirect
20. C4×C3⋊(C3⋊C8)C22semidirect
70. C32×D4M16semidirect
149. C3×D4#208semidirect
207. C32#1490semidirect
215. D4#3748semidirect
251. C3#71599semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
#105926252
C4×#37482
D4⋊(C3⋊(C3⋊C8))2
#715993