Finite Group Databasebeta

← #11776124

Subgroups — #11776124

Order 1152.

768 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 768 conjugacy classes of subgroups — too many to draw. Only its 149 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
1#10596196C211yesmaximal, characteristic
2#10592532C211yesmaximal, characteristic, complemented
3C3⋊D3×C4⋊C8C211yesmaximal, characteristic, complemented
4C32×#332C211yesmaximal, characteristic, complemented
5#10589413C211yesmaximal, characteristic, complemented
6#10589351C211yesmaximal, characteristic, complemented
7#10589351C211yesmaximal, characteristic, complemented
8#68417—34nomaximal
9C2×#3832—21no—
10C32×C4⋊Q8C2211yescharacteristic
11#64156—21no—
12C2×C8×C3⋊D3—21no—
13#64104—21no—
14#64104C412yes—
15#64102—21no—
16#64102C412yes—
17#64083C2211yescharacteristic
18C42×C3⋊D3C2211yescharacteristic
19C32×C4⋊C8C2211yescharacteristic
20C32×C4⋊C8C2211yescharacteristic
21#63647—21no—
22#63641—21no—
23C8×C3⋊Dic3—21no—
24C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
25C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
26#5725—34no—
27#4833—34no—
28D3×C4⋊C8—34no—
29C3×#332D314yescomplemented
30#4547—34no—
31#4485—34no—
32#4485—34no—
33C2×C32×Q8—21no—
34#3832—42no—
35#3832—42no—
36C2×C4⋊(C3⋊D3)—22no—
37C2×C4⋊(C3⋊D3)—21no—
38C2×C4⋊(C3⋊D3)—21no—
39C2×C4⋊(C3⋊D3)C2×C412yes—
40C2×C4×C3⋊D3—22no—
41C2×C4×C3⋊D3C2×C411yescharacteristic
42C2×C4×C3⋊D3D411yescharacteristic
43C2×C4×C3⋊D3D411yescharacteristic
44C2×C32×C8—21no—
45C2×C32×C8—21no—
46C32×C4⋊C4—21no—
47C32×C4⋊C4C2×C412yes—
48C32×C42C2311yescharacteristic
49#3752—22no—
50#3752—22no—
51C4×C3⋊Dic3C2×C411yescharacteristic
52C4×C3⋊Dic3D411yescharacteristic
53C4×C3⋊Dic3D411yescharacteristic
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C8×C3⋊D3—42no—
57#1540—91noSylow
58C2×#239—64no—
59C3×C4⋊Q8C2×D314yes—
60#947—64no—
61C2×D3×C8—64no—
62#895—38no—
63#895—64no—
64#893—38no—
65#893—64no—
66#874—34no—
67C42×D3—34no—
68C3×C4⋊C8C2×D314yes—
69C3×C4⋊C8C2×D314yes—
70(C2×D3)⋊C8—64no—
71Dic3⋊C8—64no—
72C8×Dic3—64no—
73C4⋊(C3⋊C8)—34no—
74C4⋊(C3⋊C8)—34no—
75C22×C3⋊D3—22no—
76C22×C3⋊D3C22⋊C411yescharacteristic
77C32×Q8—41no—
78C32×Q8—41no—
79C2×C32×C4—22no—
80C2×C32×C4C22×C411yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C2×C32×C4C2×D411yescharacteristic
83C2×C3⋊Dic3C22⋊C411yescharacteristic
84C2×C3⋊Dic3C22⋊C411yescharacteristic
85C2×C3⋊Dic3C22⋊C411yescharacteristic
86C4⋊(C3⋊D3)—42no—
87C4⋊(C3⋊D3)—44no—
88C4⋊(C3⋊D3)—41no—
89C4⋊(C3⋊D3)—41no—
90C4⋊(C3⋊D3)—41no—
91C4⋊(C3⋊D3)—41no—
92C4×C3⋊D3—21no—
93C4×C3⋊D3—21no—
94C4×C3⋊D3—41no—
95C4×C3⋊D3—44no—
96C4×C3⋊D3D812yes—
97C4×C3⋊D3SD1612yes—
98C32×C8—41no—
99C32×C8—41no—
100C3⋊(C3⋊C8)—41no—
101C3⋊(C3⋊C8)—41no—
102#532—91no—
103#431—91no—
104C2×C4⋊C8—91no—
105#332—91no—
106#332C3⋊D311yescharacteristic, complemented
107#331—91no—
108#331—91no—
109C2×C3×Q8—24no—
110#239—128no—
111#239—128no—
112C2×D12—38no—
113C2×D12—68no—
114C2×D12—64no—
115C2×D12—64no—
116C2×C4×D3—34no—
117C2×C4×D3—34no—
118C2×C4×D3—34no—
119C2×C4×D3—68no—
120C2×C3×C8—24no—
121C2×C3×C8—24no—
122C3×C4⋊C4—24no—
123C3×C4⋊C4C4×D318yes—
124C3×C42C22×D314yes—
125(C2×D3)⋊C4—68no—
126(C2×D3)⋊C4—68no—
127C4×Dic3—34no—
128C4×Dic3—34no—
129C4×Dic3—34no—
130C2×C3⋊C8—64no—
131C2×C3⋊C8—64no—
132D3×C8—128no—
133C22×C32C2×C22⋊C411yescharacteristic
134C2×C3⋊D3—21no—
135C2×C3⋊D3—21no—
136C2×C3⋊D3—42no—
137C2×C3⋊D3—42no—
138C2×C3⋊D3—42no—
139C2×C3⋊D3#10212yes—
140C32×C4—21no—
141C32×C4—42no—
142C32×C4C2×D811yescharacteristic
143C32×C4C2×SD1611yescharacteristic
144C32×C4#13511yescharacteristic
145C32×C4#13511yescharacteristic
146C3⋊Dic3—21no—
147C3⋊Dic3—21no—
148C3⋊Dic3#10212yes—
149C2×#41—181no—
150C22×C8—181no—
151C4⋊Q8C2×C3⋊D311yescharacteristic
152#127—91no—
153#124—181no—
154#121—92no—
155#121—181no—
156C4×D4—92no—
157C4×D4—181no—
158C2×C42—91no—
159C4⋊C8—91no—
160C4⋊C8—91no—
161C4⋊C8—181no—
162C4⋊C8C2×C3⋊D311yescharacteristic
163C4⋊C8C2×C3⋊D311yescharacteristic
164C22⋊C8—181no—
165C4×C8—181no—
166C22×D3—34no—
167C22×D3—68no—
168C3×Q8—44no—
169C3×Q8—44no—
170C2×C3×C4—28no—
171C2×C3×C4C2×C4×D314yes—
172C2×C3×C4D3×D414yes—
173C2×C3×C4D3×D414yes—
174C2×Dic3—34no—
175C2×Dic3—34no—
176C2×Dic3—34no—
177D12—128no—
178D12—1216no—
179D12—124no—
180D12—124no—
181D12—124no—
182D12—124no—
183C4×D3—38no—
184C4×D3—38no—
185C4×D3—64no—
186C4×D3—64no—
187C4×D3—1216no—
188C4×D3—124no—
189C3×C8—44no—
190C3×C8—44no—
191C3⋊C8—124no—
192C3⋊C8—124no—
193C2×C32#41311yescharacteristic
194C2×C32C2×#10211yescharacteristic
195C2×C32#41611yescharacteristic
196C3⋊D3—22no—
197C3⋊D3—82no—
198#41—362no—
199#41—362no—
200C2×Q8—21no—
201C2×D4—92no—
202C2×D4—182no—
203C2×D4—181no—
204C2×D4—181no—
205C22×C4—91no—
206C22×C4—91no—
207C22×C4—91no—
208C22×C4—182no—
209C2×C8—21no—
210C2×C8—21no—
211C2×C8—181no—
212C2×C8—181no—
213C2×C8—362no—
214C4⋊C4—21no—
215C4⋊C4C4×C3⋊D312yes—
216C22⋊C4—182no—
217C22⋊C4—182no—
218C42—91no—
219C42—91no—
220C42—91no—
221C42C22×C3⋊D311yescharacteristic
222C22×C3D3×C22⋊C414yes—
223C2×D3—38no—
224C2×D3—64no—
225C2×D3—64no—
226C2×D3—128no—
227C2×D3—128no—
228C2×D3—128no—
229C3×C4—24no—
230C3×C4—48no—
231C3×C4D3×D814yes—
232C3×C4D3×SD1614yes—
233C3×C4#91614yes—
234C3×C4#91914yes—
235Dic3—38no—
236Dic3—64no—
237Dic3—64no—
238C32#154011yescharacteristic, complemented, Sylow
239C23—91no—
240C23—182no—
241Q8—41no—
242Q8—41no—
243D4—362no—
244D4—364no—
245D4—361no—
246D4—361no—
247D4—361no—
248D4—361no—
249C2×C4—22no—
250C2×C4—91no—
251C2×C4—92no—
252C2×C4—92no—
253C2×C4—91no—
254C2×C4—91no—
255C2×C4—181no—
256C2×C4—181no—
257C2×C4—361no—
258C2×C4—364no—
259C2×C4C2×C4×C3⋊D311yescharacteristic
260C2×C4D4×C3⋊D311yescharacteristic
261C2×C4D4×C3⋊D311yescharacteristic
262C8—41no—
263C8—41no—
264C8—361no—
265C8—361no—
266C2×C3#475114yes—
267C2×C3D3×#10214yes—
268C2×C3#480414yes—
269D3—68no—
270D3—248no—
271C22—92no—
272C22—181no—
273C22—181no—
274C22—362no—
275C22—362no—
276C22—362no—
277C22C22⋊C4×C3⋊D311yescharacteristic
278C4—21no—
279C4—42no—
280C4—92no—
281C4—181no—
282C4—181no—
283C4D8×C3⋊D311yescharacteristic
284C4SD16×C3⋊D311yescharacteristic
285C4#6412511yescharacteristic
286C4#6412811yescharacteristic
287C3#6841714yescomplemented
288C2—182no—
289C2—722no—
290C2#1059245011yescharacteristic
291C2C3⋊D3×#10211yescharacteristic
292C2#1059250311yescharacteristic
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC42C22×C3⋊D3
FittingC32×#332C2
socleC22×C32C2×C22⋊C4
prime radical#10596196C2
cosocleC32×C42C23
hypercenter#332C3⋊D3
hypocenterC32#1540
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #10592532C2semidirect
3. C3⋊D3×C4⋊C8C2semidirect
4. C32×#332C2semidirect
5. #10589413C2semidirect
6. #10589351C2semidirect
7. #10589351C2semidirect
29. C3×#332D3semidirect
106. #332C3⋊D3semidirect
238. C32#1540semidirect
287. C3#68417semidirect

Maximal subgroups

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

subgroupindex
#105961962
#105925322
C3⋊D3×C4⋊C82
C32×#3322
#105894132
#105893512
#684173