Finite Group Databasebeta

← #11773803

Subgroups — #11773803

Order 1152.

936 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 936 conjugacy classes of subgroups — too many to draw. Only its 157 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×#64090C211yesmaximal, characteristic
2#10592417C212yesmaximal, complemented
3C32×#323C211yesmaximal, characteristic, complemented
4#10589391C211yesmaximal, characteristic, complemented
5#10589334C212yesmaximal, complemented
6#68101—34nomaximal
7C22×#638C411yescharacteristic
8C23×C3⋊Dic3C411yescharacteristic
9C22×C4×C3⋊D3C411yescharacteristic
10C2×C32×C22⋊C4C2211yescharacteristic
11C2×#3752C2211yescharacteristic
12C2×#3750C411yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14#64090—22no—
15#64090—22no—
16C32×C22⋊C8C2212yes—
17#63657C2212yes—
18#63641—22no—
19C8×C3⋊Dic3—22no—
20C2×#67⋊C4—34no—
21#4718—38no—
22C3×#323D314yescomplemented
23#4525—34no—
24#4468—38no—
25C24×C32C2×C411yescharacteristic
26C23×C3⋊D3C2×C411yescharacteristic
27C22×C32×C4C2×C411yescharacteristic
28C22×C32×C4C2311yescharacteristic
29C2×#638—22no—
30C2×#638—22no—
31C2×#638C814yescomplemented
32C22×C3⋊Dic3—21no—
33C22×C3⋊Dic3—21no—
34C22×C3⋊Dic3—42no—
35C22×C3⋊Dic3C2×C411yescharacteristic
36C22×C3⋊Dic3C2×C411yescharacteristic
37C22×C3⋊Dic3C2×C411yescharacteristic
38C2×C4×C3⋊D3—21no—
39C2×C4×C3⋊D3—21no—
40C2×C4×C3⋊D3—42no—
41C2×C32×C8—22no—
42C32×C22⋊C4—22no—
43#3752—22no—
44#3750—22no—
45C4×C3⋊Dic3D412yes—
46C4×C3⋊Dic3D412yes—
47C2×C3⋊(C3⋊C8)—22no—
48#1460—91noSylow
49C22×#67—34no—
50C23×Dic3—34no—
51C22×C4×D3—34no—
52C2×C3×C22⋊C4C2×D314yes—
53C2×(C2×D3)⋊C4—34no—
54C2×Dic3⋊C4—34no—
55C2×C4×Dic3—34no—
56#67⋊C4—68no—
57#67⋊C4—68no—
58C3×C22⋊C8C2×D318yes—
59#830—38no—
60Dic3⋊C8—68no—
61C8×Dic3—68no—
62C23×C32—21no—
63C23×C32—21no—
64C23×C32—41no—
65C23×C32—41no—
66C23×C32C2×C812yes—
67C23×C32C22×C411yescharacteristic
68C22×C3⋊D3—21no—
69C22×C3⋊D3—21no—
70C22×C3⋊D3—41no—
71C22×C3⋊D3—41no—
72C22×C3⋊D3C2×C812yes—
73C2×C32×C4—21no—
74C2×C32×C4—41no—
75C2×C32×C4—41no—
76C2×C32×C4C2×D412yes—
77#638—28no—
78C2×C3⋊Dic3—22no—
79C2×C3⋊Dic3—21no—
80C2×C3⋊Dic3—42no—
81C2×C3⋊Dic3—42no—
82C2×C3⋊Dic3—41no—
83C2×C3⋊Dic3C22⋊C411yescharacteristic
84C2×C3⋊Dic3C22⋊C412yes—
85C2×C3⋊Dic3C22⋊C411yescharacteristic
86C2×C3⋊Dic3C2×C812yes—
87C2×C3⋊Dic3M1612yes—
88C4×C3⋊D3—42no—
89C4×C3⋊D3—42no—
90C32×C8—42no—
91C3⋊(C3⋊C8)—42no—
92C2×C4×D4—91no—
93#431—92no—
94#323—91no—
95#323—92no—
96#323C3⋊D311yescharacteristic, complemented
97C24×C3C4×D314yes—
98C23×D3—34no—
99C22×C3×C4C4×D314yes—
100C22×C3×C4C22×D314yes—
101C2×#67—316no—
102C2×#67—68no—
103C2×#67—68no—
104C22×Dic3—34no—
105C22×Dic3—34no—
106C22×Dic3—34no—
107C22×Dic3—64no—
108C22×Dic3—64no—
109C22×Dic3—128no—
110C2×C4×D3—64no—
111C2×C4×D3—64no—
112C2×C4×D3—128no—
113C2×C3×C8—28no—
114C3×C22⋊C4—28no—
115(C2×D3)⋊C4—68no—
116Dic3⋊C4—68no—
117C4×Dic3—38no—
118C4×Dic3—38no—
119C2×C3⋊C8—68no—
120C22×C32—21no—
121C22×C32—21no—
122C22×C32—22no—
123C22×C32—42no—
124C22×C32—42no—
125C22×C32—41no—
126C22×C32—41no—
127C22×C32C2×C22⋊C411yescharacteristic
128C22×C32C22×C811yescharacteristic
129C22×C32C2×M1611yescharacteristic
130C2×C3⋊D3—22no—
131C2×C3⋊D3—42no—
132C2×C3⋊D3—41no—
133C2×C3⋊D3—41no—
134C2×C3⋊D3—42no—
135C32×C4—22no—
136C32×C4—41no—
137C3⋊Dic3—21no—
138C3⋊Dic3—41no—
139C3⋊Dic3C22⋊C814yes—
140C3⋊Dic3#10012yes—
141C22×D4—91no—
142C23×C4—91no—
143C23×C4—91no—
144C4×D4—182no—
145C4×D4—182no—
146C2×C4⋊C4—91no—
147C2×C22⋊C4—91no—
148C2×C22⋊C4C2×C3⋊D311yescharacteristic
149C2×C42—91no—
150C4⋊C8—182no—
151C22⋊C8—92no—
152C22⋊C8C2×C3⋊D312yes—
153C4×C8—182no—
154C23×C3—24no—
155C23×C3—24no—
156C23×C3—44no—
157C23×C3—44no—
158C23×C3D3×C818yes—
159C23×C3C2×C4×D314yes—
160C22×D3—38no—
161C22×D3—64no—
162C22×D3—64no—
163C22×D3—124no—
164C22×D3—124no—
165C2×C3×C4—24no—
166C2×C3×C4—44no—
167C2×C3×C4—44no—
168C2×C3×C4D3×D418yes—
169#67—632no—
170C2×Dic3—38no—
171C2×Dic3—34no—
172C2×Dic3—38no—
173C2×Dic3—38no—
174C2×Dic3—34no—
175C2×Dic3—68no—
176C2×Dic3—64no—
177C2×Dic3—128no—
178C2×Dic3—128no—
179C2×Dic3—124no—
180C4×D3—128no—
181C4×D3—128no—
182C3×C8—48no—
183C3⋊C8—128no—
184C2×C32—21no—
185C2×C32—21no—
186C2×C32—42no—
187C2×C32C2×C22⋊C811yescharacteristic
188C2×C32#41011yescharacteristic
189C2×C32C2×#10011yescharacteristic
190C3⋊D3—42no—
191C24—91no—
192C24C4×C3⋊D311yescharacteristic
193C2×D4—94no—
194C2×D4—182no—
195C2×D4—182no—
196C22×C4—91no—
197C22×C4—91no—
198C22×C4—91no—
199C22×C4—181no—
200C22×C4—181no—
201C22×C4—181no—
202C22×C4—181no—
203C22×C4—362no—
204C22×C4—362no—
205C22×C4C4×C3⋊D311yescharacteristic
206C22×C4C22×C3⋊D311yescharacteristic
207C2×C8—22no—
208C2×C8—182no—
209C4⋊C4—182no—
210C22⋊C4—22no—
211C22⋊C4—182no—
212C42—92no—
213C42—92no—
214C22×C3—24no—
215C22×C3—24no—
216C22×C3—28no—
217C22×C3—48no—
218C22×C3—48no—
219C22×C3—44no—
220C22×C3—44no—
221C22×C3D3×C22⋊C414yes—
222C22×C3C2×D3×C814yes—
223C22×C3D3×M1614yes—
224C2×D3—68no—
225C2×D3—128no—
226C2×D3—124no—
227C2×D3—124no—
228C2×D3—128no—
229C3×C4—28no—
230C3×C4—44no—
231Dic3—316no—
232Dic3—38no—
233Dic3—64no—
234Dic3—124no—
235C32#146011yescharacteristic, complemented, Sylow
236C23—21no—
237C23—21no—
238C23—41no—
239C23—41no—
240C23—92no—
241C23—181no—
242C23—181no—
243C23—361no—
244C23—361no—
245C23C8×C3⋊D312yes—
246C23C2×C4×C3⋊D311yescharacteristic
247D4—188no—
248C2×C4—21no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—92no—
252C2×C4—91no—
253C2×C4—92no—
254C2×C4—92no—
255C2×C4—91no—
256C2×C4—182no—
257C2×C4—181no—
258C2×C4—362no—
259C2×C4—362no—
260C2×C4—362no—
261C2×C4—362no—
262C2×C4—361no—
263C2×C4D4×C3⋊D312yes—
264C8—42no—
265C8—362no—
266C2×C3—24no—
267C2×C3—24no—
268C2×C3—48no—
269C2×C3D3×C22⋊C814yes—
270C2×C3#474014yes—
271C2×C3D3×#10014yes—
272D3—128no—
273C22—21no—
274C22—21no—
275C22—22no—
276C22—42no—
277C22—42no—
278C22—41no—
279C22—41no—
280C22—182no—
281C22—362no—
282C22—362no—
283C22—361no—
284C22—361no—
285C22C22⋊C4×C3⋊D311yescharacteristic
286C22C2×C8×C3⋊D311yescharacteristic
287C22M16×C3⋊D311yescharacteristic
288C4—22no—
289C4—41no—
290C4—94no—
291C4—92no—
292C4—181no—
293C4—361no—
294C3#6810114yescomplemented
295C2—21no—
296C2—21no—
297C2—42no—
298C2—362no—
299C2C3⋊D3×C22⋊C811yescharacteristic
300C2#1059243911yescharacteristic
301C2C3⋊D3×#10011yescharacteristic
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC22×C32C22×C8
FrattiniC22×C4C22×C3⋊D3
FittingC32×#323C2
socleC22×C32C2×C22⋊C4
prime radicalC22×#638C4
cosocleC22×C32×C4C23
hypercenter#323C3⋊D3
hypocenterC32#1460
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #10592417C2semidirect
3. C32×#323C2semidirect
4. #10589391C2semidirect
5. #10589334C2semidirect
22. C3×#323D3semidirect
31. C2×#638C8semidirect
96. #323C3⋊D3semidirect
235. C32#1460semidirect
294. C3#68101semidirect

Maximal subgroups

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

subgroupindex
C2×#640902
#105924172
C32×#3232
#105893912
#105893342
#681013