Finite Group Databasebeta

← #11770969

Subgroups — #11770969

Order 1152.

684 conjugacy classes of subgroups.

The subgroup lattice has 273 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#380C211yesmaximal, characteristic
2#10592911C211yesmaximal, characteristic
3C2×#63657C211yesmaximal, characteristic
4#67625—34nomaximal
5C23×C32×C4C2211yescharacteristic
6C2×C32×C4⋊C4—21no—
7C2×C32×C22⋊C4—21no—
8C2×#3757—21no—
9C2×C4⋊(C3⋊Dic3)—21no—
10C22×C3⋊(C3⋊C8)C412yescomplemented
11C32×#95C412yescomplemented
12#63658C412yescomplemented
13#63657—21no—
14#63657—21no—
15C3×#380D314yes—
16#5212—34no—
17C2×#830—34no—
18C24×C32D411yescharacteristic
19C22×C32×C4—22no—
20C22×C32×C4—42no—
21C22×C32×C4C2×C411yescharacteristic
22C22×C32×C4C2×C411yescharacteristic
23C22×C32×C4C2×C411yescharacteristic
24C22×C32×C4D411yescharacteristic
25C22×C32×C4D411yescharacteristic
26C22×C32×C4Q811yescharacteristic
27C22×C3⋊Dic3—22no—
28C32×C4⋊C4—42no—
29C32×C22⋊C4—41no—
30C32×C22⋊C4—41no—
31#3757—41no—
32#3757—41no—
33C4⋊(C3⋊Dic3)—42no—
34C2×C3⋊(C3⋊C8)—22no—
35C2×C3⋊(C3⋊C8)—42no—
36#1289—91noSylow
37C23×C3×C4C2×D314yes—
38C2×C3×C4⋊C4—24no—
39C2×C3×C22⋊C4—24no—
40C2×#217—64no—
41C2×C4⋊Dic3—64no—
42C22×C3⋊C8—38no—
43C3×#95Dic318yescomplemented
44C3⋊#95—38no—
45#830—64no—
46#830—64no—
47C23×C32—41no—
48C23×C32—41no—
49C23×C32C22⋊C411yescharacteristic
50C23×C32C22⋊C411yescharacteristic
51C23×C32C4⋊C411yescharacteristic
52C23×C32D811yescharacteristic
53C23×C32SD1611yescharacteristic
54C23×C32SD1611yescharacteristic
55C23×C32Q1611yescharacteristic
56C2×C32×C4—22no—
57C2×C32×C4—22no—
58C2×C32×C4—22no—
59C2×C32×C4—41no—
60C2×C32×C4—41no—
61C2×C32×C4—41no—
62C2×C32×C4—42no—
63C2×C32×C4—42no—
64C2×C32×C4—42no—
65C2×C32×C4C4211yescharacteristic
66C2×C32×C4C22⋊C411yescharacteristic
67C2×C32×C4C4⋊C411yescharacteristic
68C2×C32×C4C4⋊C411yescharacteristic
69C2×C3⋊Dic3—42no—
70C2×C3⋊Dic3—42no—
71C2×C3⋊Dic3—42no—
72C3⋊(C3⋊C8)—42no—
73C2×C22⋊C8—91no—
74#380—91no—
75#380C3⋊D311yescharacteristic
76C24×C3#6714yes—
77C22×C3×C4—28no—
78C22×C3×C4—48no—
79C22×C3×C4Dic614yes—
80C22×C3×C4C4×D314yes—
81C22×C3×C4C4×D314yes—
82C22×C3×C4D1214yes—
83C22×C3×C4C2×Dic314yes—
84C22×C3×C4#6714yes—
85C22×Dic3—68no—
86C3×C4⋊C4—48no—
87C3×C22⋊C4—44no—
88C3×C22⋊C4—44no—
89#217—124no—
90#217—124no—
91C4⋊Dic3—128no—
92C2×C3⋊C8—68no—
93C2×C3⋊C8—128no—
94C22×C32—21no—
95C22×C32—21no—
96C22×C32—21no—
97C22×C32—21no—
98C22×C32—21no—
99C22×C32—21no—
100C22×C32—41no—
101C22×C32—41no—
102C22×C32—41no—
103C22×C32—41no—
104C22×C32#9511yescharacteristic
105C22×C32#10211yescharacteristic
106C22×C32#10211yescharacteristic
107C22×C32#10311yescharacteristic
108C22×C32#10311yescharacteristic
109C22×C32#10611yescharacteristic
110C22×C32#10711yescharacteristic
111C32×C4—21no—
112C32×C4—21no—
113C32×C4—21no—
114C32×C4—82no—
115C32×C4#9912yes—
116C3⋊Dic3—82no—
117C23×C4C2×C3⋊D311yescharacteristic
118C22×C8—92no—
119C2×C4⋊C4—21no—
120C2×C4⋊C4—181no—
121C2×C22⋊C4—21no—
122C2×C22⋊C4—181no—
123C22⋊C8—181no—
124C22⋊C8—181no—
125#95—92no—
126#95C3⋊Dic312yescomplemented
127C23×C3—44no—
128C23×C3—44no—
129C23×C3Dic3⋊C414yes—
130C23×C3(C2×D3)⋊C414yes—
131C23×C3#21314yes—
132C23×C3#21414yes—
133C23×C3#21514yes—
134C23×C3#21614yes—
135C23×C3#21714yes—
136C2×C3×C4—28no—
137C2×C3×C4—28no—
138C2×C3×C4—28no—
139C2×C3×C4—44no—
140C2×C3×C4—44no—
141C2×C3×C4—44no—
142C2×C3×C4—48no—
143C2×C3×C4—48no—
144C2×C3×C4—48no—
145C2×C3×C4C4×Dic314yes—
146C2×C3×C4Dic3⋊C414yes—
147C2×C3×C4C4⋊Dic314yes—
148C2×C3×C4(C2×D3)⋊C414yes—
149C2×Dic3—128no—
150C2×Dic3—128no—
151C2×Dic3—128no—
152C3⋊C8—128no—
153C2×C32—21no—
154C2×C32—21no—
155C2×C32—21no—
156C2×C32—21no—
157C2×C32—21no—
158C2×C32—21no—
159C2×C32H(3,ℤ/4)11yescharacteristic
160C2×C32#34011yescharacteristic
161C2×C32#34211yescharacteristic
162C24#63811yescharacteristic
163C22×C4—22no—
164C22×C4—42no—
165C22×C4—182no—
166C22×C4#63411yescharacteristic
167C22×C4C4×C3⋊D311yescharacteristic
168C22×C4C4×C3⋊D311yescharacteristic
169C22×C4C4⋊(C3⋊D3)11yescharacteristic
170C22×C4C2×C3⋊Dic311yescharacteristic
171C22×C4#63811yescharacteristic
172C2×C8—182no—
173C2×C8—362no—
174C4⋊C4—42no—
175C4⋊C4—362no—
176C22⋊C4—41no—
177C22⋊C4—41no—
178C22⋊C4—361no—
179C22⋊C4—361no—
180C22×C3—24no—
181C22×C3—24no—
182C22×C3—24no—
183C22×C3—24no—
184C22×C3—24no—
185C22×C3—24no—
186C22×C3—44no—
187C22×C3—44no—
188C22×C3—44no—
189C22×C3—44no—
190C22×C3#80714yes—
191C22×C3#80814yes—
192C22×C3#80914yes—
193C22×C3#81014yes—
194C22×C3C3⋊#9514yes—
195C22×C3#83214yes—
196C22×C3#83514yes—
197C3×C4—24no—
198C3×C4—24no—
199C3×C4—24no—
200C3×C4—88no—
201C3×C4#80618yes—
202Dic3—248no—
203C32#128911yescharacteristic, complemented, Sylow
204C23—41no—
205C23—41no—
206C23#375011yescharacteristic
207C23#375211yescharacteristic
208C23#375311yescharacteristic
209C23#375411yescharacteristic
210C23#375511yescharacteristic
211C23#375611yescharacteristic
212C23#375711yescharacteristic
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—362no—
223C2×C4—362no—
224C2×C4—362no—
225C2×C4C4×C3⋊Dic311yescharacteristic
226C2×C4#375011yescharacteristic
227C2×C4C4⋊(C3⋊Dic3)11yescharacteristic
228C2×C4#375211yescharacteristic
229C8—362no—
230C2×C3—24no—
231C2×C3—24no—
232C2×C3—24no—
233C2×C3—24no—
234C2×C3—24no—
235C2×C3—24no—
236C2×C3#452714yes—
237C2×C3#452914yes—
238C2×C3#453114yes—
239C22—21no—
240C22—21no—
241C22—21no—
242C22—21no—
243C22—21no—
244C22—21no—
245C22—41no—
246C22—41no—
247C22—41no—
248C22—41no—
249C22#6363411yescharacteristic
250C22#6363511yescharacteristic
251C22#6363611yescharacteristic
252C22#6363711yescharacteristic
253C22#6365811yescharacteristic
254C22#6365911yescharacteristic
255C22#6366211yescharacteristic
256C4—21no—
257C4—21no—
258C4—21no—
259C4—82no—
260C4—722no—
261C4#6363312yes—
262C3#6762514yescomplemented
263C2—21no—
264C2—21no—
265C2—21no—
266C2—21no—
267C2—21no—
268C2—21no—
269C2#1058939311yescharacteristic
270C2#1058939511yescharacteristic
271C2#1058939711yescharacteristic
subgroupG/H
centerC22#63658
commutatorC2×C32×C4C42
FrattiniC23×C4C2×C3⋊D3
FittingC32×#380C2
socleC22×C32#95
prime radicalC24×C32D4
cosocleC23×C32×C4C22
hypercenter#380C3⋊D3
hypocenterC32#1289
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
10. C22×C3⋊(C3⋊C8)C4semidirect
11. C32×#95C4semidirect
12. #63658C4semidirect
43. C3×#95Dic3semidirect
126. #95C3⋊Dic3semidirect
203. C32#1289semidirect
262. C3#67625semidirect

Maximal subgroups

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

subgroupindex
C32×#3802
#105929112
C2×#636572
#676253