Finite Group Databasebeta

← #11774547

Subgroups — #11774547

Order 1152.

936 conjugacy classes of subgroups.

The subgroup lattice has 270 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic
2#10592624C211yesmaximal, characteristic, complemented
3#10592623C211yesmaximal, characteristic, complemented
4D4⋊(C3⋊(C3⋊C8))C214yesmaximal, complemented
5#71598—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))—21no—
18C4⋊(C3⋊(C3⋊C8))—21no—
19C4⋊(C3⋊(C3⋊C8))C2212yescomplemented
20C4×C3⋊(C3⋊C8)C2212yescomplemented
21C2×C3×C4×D4D314yes—
22#4925—34no—
23#4924—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—42no—
33C22×C32×C4—42no—
34C22×C32×C4C2×C411yescharacteristic
35C22×C32×C4D411yescharacteristic
36C22×C32×C4D411yescharacteristic
37C32×C4⋊C4—21no—
38C32×C4⋊C4C2×C412yes—
39C32×C22⋊C4—22no—
40C32×C22⋊C4—22no—
41C32×C42C2×C411yescharacteristic
42C32×C42D411yescharacteristic
43C32×C42D411yescharacteristic
44C32×C42C2311yescharacteristic
45#3748—42no—
46C2×C3⋊(C3⋊C8)—22no—
47C2×C3⋊(C3⋊C8)—22no—
48#1486—91noSylow
49C22×C3×D4Dic314yes—
50C23×C3×C4—24no—
51C3×C4×D4—24no—
52C3×C4×D4—24no—
53C3×C4×D4Dic318yes—
54C3×C4×D4C2×D318yes—
55C2×C3×C4⋊C4Dic314yes—
56C2×C3×C22⋊C4—24no—
57C2×C3×C42C2×D314yes—
58C2×#208—64no—
59#830—64no—
60C4⋊(C3⋊C8)—38no—
61C4⋊(C3⋊C8)—64no—
62C4⋊(C3⋊C8)—64no—
63C4×C3⋊C8—38no—
64C23×C32—24no—
65C23×C32—22no—
66C23×C32—42no—
67C23×C32—42no—
68C23×C32C22⋊C411yescharacteristic
69C32×D4—24no—
70C32×D4—22no—
71C32×D4M1614yescomplemented
72C2×C32×C4—22no—
73C2×C32×C4—22no—
74C2×C32×C4—41no—
75C2×C32×C4—42no—
76C2×C32×C4—44no—
77C2×C32×C4—42no—
78C2×C32×C4—42no—
79C2×C32×C4C22⋊C411yescharacteristic
80C2×C32×C4C22⋊C411yescharacteristic
81C2×C32×C4C22⋊C411yescharacteristic
82C2×C32×C4D812yes—
83C2×C32×C4SD1612yes—
84C2×C32×C4C22×C411yescharacteristic
85C2×C32×C4C2×D411yescharacteristic
86C2×C32×C4C2×D411yescharacteristic
87C3⋊(C3⋊C8)—42no—
88C3⋊(C3⋊C8)—42no—
89C2×C4×D4C3⋊D311yescharacteristic
90#431—91no—
91#423—91no—
92D4⋊C8—94no—
93C24×C3—24no—
94C2×C3×D4—216no—
95C2×C3×D4—24no—
96C2×C3×D4C2×Dic318yes—
97C22×C3×C4—24no—
98C22×C3×C4—28no—
99C22×C3×C4—28no—
100C22×C3×C4—48no—
101C22×C3×C4—48no—
102C22×C3×C4C2×Dic314yes—
103C22×C3×C4#6714yes—
104C22×C3×C4#6714yes—
105C3×C4⋊C4—24no—
106C3×C4⋊C4C2×Dic318yes—
107C3×C22⋊C4—28no—
108C3×C22⋊C4—28no—
109C3×C42C2×Dic314yes—
110C3×C42#6714yes—
111C3×C42#6714yes—
112C3×C42C22×D314yes—
113#208—128no—
114C2×C3⋊C8—68no—
115C2×C3⋊C8—68no—
116C22×C32—21no—
117C22×C32—21no—
118C22×C32—24no—
119C22×C32—48no—
120C22×C32—42no—
121C22×C32—42no—
122C22×C32#10212yes—
123C22×C32C2×C22⋊C411yescharacteristic
124C32×C4—21no—
125C32×C4—21no—
126C32×C4—21no—
127C32×C4—42no—
128C32×C4#10212yes—
129C32×C4C2×M1612yes—
130C32×C4C2×D811yescharacteristic
131C32×C4C2×SD1611yescharacteristic
132C22×D4C3⋊Dic311yescharacteristic
133C23×C4—21no—
134C2×M16—181no—
135C4×D4—21no—
136C4×D4—21no—
137C4×D4C3⋊Dic312yes—
138C4×D4C2×C3⋊D312yes—
139C2×C4⋊C4C3⋊Dic311yescharacteristic
140C2×C22⋊C4—21no—
141C2×C42C2×C3⋊D311yescharacteristic
142C4⋊C8—92no—
143C4⋊C8—181no—
144C4⋊C8—181no—
145C22⋊C8—181no—
146C4×C8—92no—
147C23×C3—216no—
148C23×C3—28no—
149C23×C3—48no—
150C23×C3—48no—
151C23×C3#21714yes—
152C3×D4—216no—
153C3×D4—28no—
154C3×D4#208116yescomplemented
155C2×C3×C4—28no—
156C2×C3×C4—28no—
157C2×C3×C4—44no—
158C2×C3×C4—48no—
159C2×C3×C4—416no—
160C2×C3×C4—48no—
161C2×C3×C4—48no—
162C2×C3×C4#21318yes—
163C2×C3×C4#21418yes—
164C2×C3×C4#21714yes—
165C2×C3×C4#21714yes—
166C2×C3×C4#21714yes—
167C2×C3×C4C22×Dic314yes—
168C2×C3×C4C2×#6714yes—
169C2×C3×C4C2×#6714yes—
170C3⋊C8—128no—
171C3⋊C8—128no—
172C2×C32—22no—
173C2×C32—44no—
174C2×C32#40711yescharacteristic
175C2×C32C2×#10211yescharacteristic
176C2×C32#42111yescharacteristic
177C24—21no—
178C2×D4—24no—
179C2×D4—21no—
180C2×D4C2×C3⋊Dic312yes—
181C22×C4—21no—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—42no—
185C22×C4—42no—
186C22×C4C2×C3⋊Dic311yescharacteristic
187C22×C4#63811yescharacteristic
188C22×C4#63811yescharacteristic
189M16—362no—
190C2×C8—182no—
191C2×C8—182no—
192C4⋊C4—21no—
193C4⋊C4C2×C3⋊Dic312yes—
194C22⋊C4—22no—
195C22⋊C4—22no—
196C42C2×C3⋊Dic311yescharacteristic
197C42#63811yescharacteristic
198C42#63811yescharacteristic
199C42C22×C3⋊D311yescharacteristic
200C22×C3—24no—
201C22×C3—24no—
202C22×C3—216no—
203C22×C3—432no—
204C22×C3—48no—
205C22×C3—48no—
206C22×C3#83218yes—
207C22×C3C2×#21714yes—
208C3×C4—24no—
209C3×C4—24no—
210C3×C4—24no—
211C3×C4—48no—
212C3×C4#83218yes—
213C3×C4C2×#20818yes—
214C3×C4C2×#21314yes—
215C3×C4C2×#21414yes—
216C32#148611yescharacteristic, complemented, Sylow
217C23—24no—
218C23—22no—
219C23—42no—
220C23—42no—
221C23#375711yescharacteristic
222D4—24no—
223D4—22no—
224D4#374814yescomplemented
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—41no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—44no—
232C2×C4#375312yes—
233C2×C4#375412yes—
234C2×C4#375711yescharacteristic
235C2×C4#375711yescharacteristic
236C2×C4#375711yescharacteristic
237C2×C4C22×C3⋊Dic311yescharacteristic
238C2×C4C2×#63811yescharacteristic
239C2×C4C2×#63811yescharacteristic
240C8—362no—
241C8—362no—
242C2×C3—28no—
243C2×C3—416no—
244C2×C3#520714yes—
245C2×C3C2×#83214yes—
246C2×C3#523614yes—
247C22—21no—
248C22—21no—
249C22—24no—
250C22—48no—
251C22—42no—
252C22—42no—
253C22#6365912yes—
254C22C2×#375711yescharacteristic
255C4—21no—
256C4—21no—
257C4—21no—
258C4—42no—
259C4#6365912yes—
260C4C2×#374812yes—
261C4C2×#375311yescharacteristic
262C4C2×#375411yescharacteristic
263C3#7159814yescomplemented
264C2—22no—
265C2—44no—
266C2#1059290611yescharacteristic
267C2C2×#6365911yescharacteristic
268C2#1059293511yescharacteristic
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#1486
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. #10592624C2semidirect
3. #10592623C2semidirect
4. D4⋊(C3⋊(C3⋊C8))C2semidirect
19. C4⋊(C3⋊(C3⋊C8))C22semidirect
20. C4×C3⋊(C3⋊C8)C22semidirect
71. C32×D4M16semidirect
154. C3×D4#208semidirect
216. C32#1486semidirect
224. D4#3748semidirect
263. C3#71598semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
#105926242
#105926232
D4⋊(C3⋊(C3⋊C8))2
#715983