Finite Group Databasebeta

← #11775258

Subgroups — #11775258

Order 1152.

726 conjugacy classes of subgroups.

The subgroup lattice has 297 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#529C211yesmaximal, characteristic
2C4×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
3#10592625C211yesmaximal, characteristic, complemented
4#10589404C212yesmaximal, complemented
5#10589403C212yesmaximal
6#71755—34nomaximal
7C32×#126—21no—
8C32×#125C411yescharacteristic, complemented
9C32×#124C411yescharacteristic, complemented
10C32×#123—21no—
11C32×C22⋊Q8C2211yescharacteristic
12C32×#121C2211yescharacteristic
13C32×C4×Q8C411yescharacteristic, complemented
14C32×C4×D4—21no—
15C32×C4×D4C411yescharacteristic, complemented
16C32×#117—21no—
17C2×C32×C42C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)—21no—
19C2×C4×C3⋊Dic3—21no—
20#63658C2212yes—
21#63657C2212yes—
22C4⋊(C3⋊(C3⋊C8))—21no—
23#63630—21no—
24C3×#529D314yes—
25C4×C4⋊Dic3—34no—
26#4926—34no—
27#4538—38no—
28#4537—38no—
29C2×C32×Q8C2×C411yescharacteristic
30C2×C32×D4—21no—
31C2×C32×D4C2×C411yescharacteristic
32C22×C32×C4—21no—
33C22×C32×C4D411yescharacteristic
34C22×C32×C4D411yescharacteristic
35C22×C32×C4C2311yescharacteristic
36C22×C3⋊Dic3—22no—
37C32×C4⋊C4—21no—
38C32×C4⋊C4—21no—
39C32×C4⋊C4—21no—
40C32×C4⋊C4—21no—
41C32×C4⋊C4C2×C411yescharacteristic
42C32×C4⋊C4C2×C411yescharacteristic
43C32×C22⋊C4—21no—
44C32×C22⋊C4—21no—
45C32×C22⋊C4—21no—
46C32×C22⋊C4—21no—
47C32×C22⋊C4—21no—
48C32×C42—21no—
49C32×C42C2×C411yescharacteristic
50C32×C42C2×C411yescharacteristic
51C32×C42D411yescharacteristic
52C32×C42D411yescharacteristic
53C4⋊(C3⋊Dic3)—24no—
54C4×C3⋊Dic3—42no—
55C2×C3⋊(C3⋊C8)—22no—
56#1509—91noSylow
57C3×#126—24no—
58C3×#125Dic314yescomplemented
59C3×#124Dic314yescomplemented
60C3×#123—24no—
61C3×C22⋊Q8C2×D314yes—
62C3×#121C2×D314yes—
63C3×C4×Q8Dic314yescomplemented
64C3×C4×D4—24no—
65C3×C4×D4Dic314yescomplemented
66C3×#117—24no—
67C2×C3×C42C2×D314yes—
68C2×C4⋊Dic3—64no—
69C2×C4×Dic3—64no—
70C3⋊#95—38no—
71#830—38no—
72C4⋊(C3⋊C8)—64no—
73#803—64no—
74C23×C32—21no—
75C23×C32C2×D411yescharacteristic
76C32×Q8—41no—
77C32×D4—41no—
78C32×D4—41no—
79C32×D4—41no—
80C2×C32×C4—21no—
81C2×C32×C4—21no—
82C2×C32×C4—22no—
83C2×C32×C4—21no—
84C2×C32×C4—21no—
85C2×C32×C4—21no—
86C2×C32×C4—41no—
87C2×C32×C4—42no—
88C2×C32×C4C22⋊C411yescharacteristic
89C2×C32×C4C22⋊C411yescharacteristic
90C2×C32×C4C22⋊C411yescharacteristic
91C2×C32×C4C22⋊C411yescharacteristic
92C2×C32×C4C22×C411yescharacteristic
93C2×C32×C4C2×D411yescharacteristic
94C2×C3⋊Dic3—24no—
95C2×C3⋊Dic3—42no—
96C2×C3⋊Dic3—42no—
97C3⋊(C3⋊C8)—42no—
98#529C3⋊D311yescharacteristic
99#432—91no—
100C4×C4⋊C4—91no—
101#328—92no—
102#327—92no—
103C2×C3×Q8C2×Dic314yes—
104C2×C3×D4—24no—
105C2×C3×D4C2×Dic314yes—
106C22×C3×C4—24no—
107C22×C3×C4#6714yes—
108C22×C3×C4#6714yes—
109C22×C3×C4C22×D314yes—
110C22×Dic3—68no—
111C3×C4⋊C4—24no—
112C3×C4⋊C4—24no—
113C3×C4⋊C4—24no—
114C3×C4⋊C4—24no—
115C3×C4⋊C4C2×Dic314yes—
116C3×C4⋊C4C2×Dic314yes—
117C3×C22⋊C4—24no—
118C3×C22⋊C4—24no—
119C3×C22⋊C4—24no—
120C3×C22⋊C4—24no—
121C3×C22⋊C4—24no—
122C3×C42—24no—
123C3×C42C2×Dic314yes—
124C3×C42C2×Dic314yes—
125C3×C42#6714yes—
126C3×C42#6714yes—
127C4⋊Dic3—616no—
128C4×Dic3—128no—
129C2×C3⋊C8—68no—
130C22×C32—21no—
131C22×C32—21no—
132C22×C32—41no—
133C22×C32—41no—
134C22×C32—41no—
135C22×C32C2×C22⋊C411yescharacteristic
136C22×C32AGL(1,ℤ/8)11yescharacteristic
137C22×C32#13711yescharacteristic
138C32×C4—21no—
139C32×C4—21no—
140C32×C4—21no—
141C32×C4—21no—
142C32×C4—21no—
143C32×C4—41no—
144C32×C4—41no—
145C32×C4—41no—
146C32×C4#10412yes—
147C3⋊Dic3—44no—
148#126—21no—
149#125C3⋊Dic311yescharacteristic, complemented
150#124C3⋊Dic311yescharacteristic, complemented
151#123—21no—
152C22⋊Q8C2×C3⋊D311yescharacteristic
153#121C2×C3⋊D311yescharacteristic
154C4×Q8C3⋊Dic311yescharacteristic, complemented
155C4×D4—21no—
156C4×D4C3⋊Dic311yescharacteristic, complemented
157#117—21no—
158C2×C4⋊C4—181no—
159C2×C42—181no—
160C2×C42C2×C3⋊D311yescharacteristic
161C4⋊C8—181no—
162C22⋊C8—92no—
163#97—181no—
164#95—92no—
165C23×C3—24no—
166C23×C3C2×#6714yes—
167C3×Q8—44no—
168C3×D4—44no—
169C3×D4—44no—
170C3×D4—44no—
171C2×C3×C4—24no—
172C2×C3×C4—24no—
173C2×C3×C4—28no—
174C2×C3×C4—24no—
175C2×C3×C4—24no—
176C2×C3×C4—24no—
177C2×C3×C4—44no—
178C2×C3×C4—48no—
179C2×C3×C4#21714yes—
180C2×C3×C4#21714yes—
181C2×C3×C4#21714yes—
182C2×C3×C4#21714yes—
183C2×C3×C4C22×Dic314yes—
184C2×C3×C4C2×#6714yes—
185C2×Dic3—616no—
186C2×Dic3—128no—
187C2×Dic3—128no—
188C3⋊C8—128no—
189C2×C32—21no—
190C2×C32—21no—
191C2×C32—81no—
192C2×C32#41011yescharacteristic
193C2×C32#41711yescharacteristic
194C2×C32C2×#10411yescharacteristic
195C2×Q8C2×C3⋊Dic311yescharacteristic
196C2×D4—21no—
197C2×D4C2×C3⋊Dic311yescharacteristic
198C22×C4—21no—
199C22×C4—182no—
200C22×C4#63811yescharacteristic
201C22×C4#63811yescharacteristic
202C22×C4C22×C3⋊D311yescharacteristic
203C2×C8—182no—
204C4⋊C4—21no—
205C4⋊C4—21no—
206C4⋊C4—21no—
207C4⋊C4—21no—
208C4⋊C4—184no—
209C4⋊C4C2×C3⋊Dic311yescharacteristic
210C4⋊C4C2×C3⋊Dic311yescharacteristic
211C22⋊C4—21no—
212C22⋊C4—21no—
213C22⋊C4—21no—
214C22⋊C4—21no—
215C22⋊C4—21no—
216C42—21no—
217C42—362no—
218C42C2×C3⋊Dic311yescharacteristic
219C42C2×C3⋊Dic311yescharacteristic
220C42#63811yescharacteristic
221C42#63811yescharacteristic
222C22×C3—24no—
223C22×C3—24no—
224C22×C3—44no—
225C22×C3—44no—
226C22×C3—44no—
227C22×C3#94914yes—
228C22×C3#95114yes—
229C22×C3C2×#21714yes—
230C3×C4—24no—
231C3×C4—24no—
232C3×C4—24no—
233C3×C4—24no—
234C3×C4—24no—
235C3×C4—44no—
236C3×C4—44no—
237C3×C4—44no—
238C3×C4#83718yes—
239Dic3—1216no—
240C32#150911yescharacteristic, complemented, Sylow
241C23—21no—
242C23C2×#63811yescharacteristic
243Q8—41no—
244D4—41no—
245D4—41no—
246D4—41no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—184no—
256C2×C4—362no—
257C2×C4—362no—
258C2×C4#375711yescharacteristic
259C2×C4#375711yescharacteristic
260C2×C4#375711yescharacteristic
261C2×C4#375711yescharacteristic
262C2×C4C22×C3⋊Dic311yescharacteristic
263C2×C4C2×#63811yescharacteristic
264C8—362no—
265C2×C3—24no—
266C2×C3—24no—
267C2×C3—84no—
268C2×C3#523214yes—
269C2×C3C2×#83714yes—
270C2×C3#524014yes—
271C22—21no—
272C22—21no—
273C22—41no—
274C22—41no—
275C22—41no—
276C22#6415811yescharacteristic
277C22#6416011yescharacteristic
278C22C2×#375711yescharacteristic
279C4—21no—
280C4—21no—
281C4—21no—
282C4—21no—
283C4—21no—
284C4—41no—
285C4—41no—
286C4—41no—
287C4—364no—
288C4#6366412yes—
289C3#7175514yescomplemented
290C2—21no—
291C2—21no—
292C2—81no—
293C2#1059293111yescharacteristic
294C2C2×#6366411yescharacteristic
295C2#1059293911yescharacteristic
subgroupG/H
centerC22C2×#3757
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#529C2
socleC22×C32C2×C22⋊C4
prime radicalC32×#121C22
cosocleC22×C32×C4C23
hypercenter#529C3⋊D3
hypocenterC32#1509
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
2. C4×C4⋊(C3⋊Dic3)C2semidirect
3. #10592625C2semidirect
4. #10589404C2semidirect
8. C32×#125C4semidirect
9. C32×#124C4semidirect
13. C32×C4×Q8C4semidirect
15. C32×C4×D4C4semidirect
58. C3×#125Dic3semidirect
59. C3×#124Dic3semidirect
63. C3×C4×Q8Dic3semidirect
65. C3×C4×D4Dic3semidirect
149. #125C3⋊Dic3semidirect
150. #124C3⋊Dic3semidirect
154. C4×Q8C3⋊Dic3semidirect
156. C4×D4C3⋊Dic3semidirect
240. C32#1509semidirect
289. C3#71755semidirect

Maximal subgroups

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

subgroupindex
C32×#5292
C4×C4⋊(C3⋊Dic3)2
#105926252
#105894042
#105894032
#717553