Finite Group Databasebeta

← #11776228

Subgroups — #11776228

Order 1152.

524 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 120 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
1C3×#5725C211yesmaximal, characteristic
2#10590248C212yesmaximal, complemented
3#10589412C211yesmaximal, characteristic, complemented
4C3×#4546C211yesmaximal, characteristic, complemented
5#10589090C212yesmaximal, complemented
6#71805—31nomaximal
7#68482—31nomaximal
8C2×C3×#239C412yes—
9C32×C4⋊Q8C2211yescharacteristic
10C3×#947C412yes—
11C3×#895—22no—
12C3×#893—22no—
13C3×#874C2211yescharacteristic
14C3×C42×D3C2211yescharacteristic
15C4⋊(C3⋊(C3⋊C8))C2212yes—
16C3×C4⋊(C3⋊C8)C2212yes—
17(C2×D3)⋊(C3⋊C8)—22no—
18Dic3×C3⋊C8—22no—
19C3×#532—31no—
20#5725D311yescharacteristic
21#4925—32no—
22#4833—32no—
23C3×#333—31no—
24#4546—31no—
25#4546—31no—
26#4546—61no—
27#4546D311yescharacteristic, complemented
28#4544—32no—
29#4485—32no—
30C2×C32×Q8C2×C412yes—
31C3×#239—44no—
32C2×C3×D12—22no—
33C2×C3×D12—22no—
34C2×C3×D12C2×C412yes—
35C2×C3×C4×D3—22no—
36C2×C3×C4×D3C2×C411yescharacteristic
37C2×C3×C4×D3D412yes—
38C32×C4⋊C4—22no—
39C32×C42C2311yescharacteristic
40C2×C3⋊(C3⋊C8)—22no—
41C3×(C2×D3)⋊C4—24no—
42C3×C4×Dic3C2×C411yescharacteristic
43C3×C4×Dic3D412yes—
44C2×C3×C3⋊C8—22no—
45#1543—91noSylow
46C2×C3×#41—32no—
47C2×#239Dic312yes—
48C3×C4⋊Q8—21no—
49C3×C4⋊Q8C2×D311yescharacteristic
50C3×C4⋊Q8C2×D311yescharacteristic
51C3×#127—31no—
52C3×#124—32no—
53C3×#121—62no—
54C3×C4×D4—62no—
55C2×C3×C42—31no—
56#947Dic312yes—
57#895—22no—
58#893—22no—
59#874C2×D311yescharacteristic
60C42×D3C2×D311yescharacteristic
61C3×C4⋊C8—32no—
62#830—62no—
63(C2×D3)⋊C8—62no—
64C8×Dic3—62no—
65C4⋊(C3⋊C8)—32no—
66C4⋊(C3⋊C8)—32no—
67C4⋊(C3⋊C8)—62no—
68C4⋊(C3⋊C8)C2×D312yes—
69C4×C3⋊C8—62no—
70C22×C3×D3—22no—
71C22×C3×D3C22⋊C411yescharacteristic
72C32×Q8—42no—
73C2×C32×C4—22no—
74C2×C32×C4C22×C411yescharacteristic
75C2×C32×C4C2×D412yes—
76C2×C3×Dic3C22⋊C412yes—
77C2×C3×Dic3C22⋊C411yescharacteristic
78C3×D12—42no—
79C3×D12—44no—
80C3×D12—42no—
81C3×D12—42no—
82C3×C4×D3—22no—
83C3×C4×D3—22no—
84C3×C4×D3—22no—
85C3×C4×D3—44no—
86C3⋊(C3⋊C8)—42no—
87C3×C3⋊C8—42no—
88#532—31no—
89#431—92no—
90#333—31no—
91#333—91no—
92#331—92no—
93C3×#41—124no—
94C2×C3×Q8—22no—
95C2×C3×Q8C4×D312yes—
96C2×C3×Q8C2×Dic312yes—
97C2×C3×D4—32no—
98C2×C3×D4—62no—
99C2×C3×D4—62no—
100C22×C3×C4—31no—
101C22×C3×C4—32no—
102C22×C3×C4—62no—
103#239—44no—
104C2×D12—22no—
105C2×D12—22no—
106C2×D12C2×Dic312yes—
107C2×C4×D3—22no—
108C2×C4×D3C2×Dic311yescharacteristic
109C2×C4×D3#6712yes—
110C2×C3×C8—62no—
111C3×C4⋊C4—22no—
112C3×C4⋊C4—22no—
113C3×C4⋊C4—42no—
114C3×C22⋊C4—64no—
115C3×C42—21no—
116C3×C42—31no—
117C3×C42—32no—
118C3×C42C22×D311yescharacteristic
119C3×C42C22×D311yescharacteristic
120(C2×D3)⋊C4—24no—
121C4×Dic3C2×Dic311yescharacteristic
122C4×Dic3#6712yes—
123C2×C3⋊C8—22no—
124C2×C3⋊C8—62no—
125C2×C3⋊C8—62no—
126C2×C3⋊C8—122no—
127C22×C32C2×C22⋊C411yescharacteristic
128C2×C3×D3—21no—
129C2×C3×D3—22no—
130C2×C3×D3—42no—
131C2×C3×D3—44no—
132C32×C4—21no—
133C32×C4—42no—
134C32×C4#13512yes—
135C32×C4#13512yes—
136C3×Dic3—22no—
137C3×Dic3#10012yes—
138C2×#41—32no—
139C4⋊Q8D3211yescharacteristic
140#127—31no—
141#124—32no—
142#121—62no—
143C4×D4—62no—
144C2×C42—31no—
145C4⋊C8—32no—
146C4⋊C8—92no—
147C22⋊C8—182no—
148C4×C8—182no—
149C23×C3—31no—
150C23×C3—62no—
151C22×D3—22no—
152C22×D3#21711yescharacteristic
153C3×Q8—42no—
154C3×Q8—42no—
155C3×Q8—82no—
156C3×D4—122no—
157C3×D4—124no—
158C3×D4—122no—
159C3×D4—122no—
160C2×C3×C4—22no—
161C2×C3×C4—22no—
162C2×C3×C4—21no—
163C2×C3×C4—22no—
164C2×C3×C4—31no—
165C2×C3×C4—32no—
166C2×C3×C4—42no—
167C2×C3×C4—62no—
168C2×C3×C4—62no—
169C2×C3×C4—62no—
170C2×C3×C4—124no—
171C2×C3×C4C2×C4×D311yescharacteristic
172C2×C3×C4D3×D412yes—
173C2×C3×C4C22×Dic311yescharacteristic
174C2×C3×C4C2×#6712yes—
175C2×Dic3#21712yes—
176C2×Dic3#21711yescharacteristic
177D12—42no—
178D12—44no—
179D12—42no—
180D12—42no—
181C4×D3—22no—
182C4×D3—22no—
183C4×D3—22no—
184C4×D3—44no—
185C3×C8—122no—
186C3⋊C8—42no—
187C3⋊C8—122no—
188C3⋊C8—122no—
189C3⋊C8—242no—
190C2×C32C2×#10011yescharacteristic
191C2×C32#41612yes—
192C3×D3—41no—
193C3×D3—82no—
194#41—124no—
195C2×Q8D3×Dic312yes—
196C2×D4—32no—
197C2×D4—62no—
198C2×D4—62no—
199C22×C4—31no—
200C22×C4—32no—
201C22×C4—62no—
202C2×C8—62no—
203C2×C8—182no—
204C4⋊C4—22no—
205C22⋊C4—64no—
206C42—31no—
207C42—32no—
208C42C2×D3211yescharacteristic
209C22×C3—21no—
210C22×C3—61no—
211C22×C3—62no—
212C22×C3—122no—
213C22×C3—124no—
214C22×C3D3×C22⋊C411yescharacteristic
215C22×C3C2×#21711yescharacteristic
216C2×D3—21no—
217C2×D3—22no—
218C2×D3—42no—
219C2×D3—44no—
220C3×C4—21no—
221C3×C4—21no—
222C3×C4—22no—
223C3×C4—22no—
224C3×C4—32no—
225C3×C4—41no—
226C3×C4—42no—
227C3×C4—42no—
228C3×C4—62no—
229C3×C4—82no—
230C3×C4#91612yes—
231C3×C4#91912yes—
232C3×C4#95012yes—
233C3×C4#95012yes—
234Dic3—22no—
235Dic3#83312yes—
236C32#154311yescharacteristic, complemented, Sylow
237C23—31no—
238C23—62no—
239Q8—42no—
240D4—122no—
241D4—124no—
242D4—122no—
243D4—122no—
244C2×C4—22no—
245C2×C4—31no—
246C2×C4—32no—
247C2×C4—62no—
248C2×C4—62no—
249C2×C4—62no—
250C2×C4—124no—
251C2×C4C2×D3×Dic311yescharacteristic
252C2×C4D3×#6712yes—
253C8—122no—
254C8—362no—
255C2×C3—21no—
256C2×C3—22no—
257C2×C3—121no—
258C2×C3—242no—
259C2×C3D3×#10011yescharacteristic
260C2×C3#480412yes—
261C2×C3C2×#83311yescharacteristic
262C2×C3#523312yes—
263D3—41no—
264D3—82no—
265C22—61no—
266C22—62no—
267C22—122no—
268C22—124no—
269C22D3×#21711yescharacteristic
270C4—21no—
271C4—32no—
272C4—42no—
273C4—62no—
274C4#6394712yes—
275C4#6394912yes—
276C3—21no—
277C3#6848211yescharacteristic, complemented
278C3#7180511yescharacteristic, complemented
279C2—121no—
280C2—242no—
281C2D3×#83311yescharacteristic
282C2#1059155612yes—
subgroupG/H
centerC22D3×#217
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32C2×C22⋊C4
prime radicalC3×#5725C2
cosocleC32×C42C23
hypercenterC4⋊Q8D32
hypocenterC32#1543
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #10590248C2semidirect
3. #10589412C2semidirect
4. C3×#4546C2semidirect
5. #10589090C2semidirect
27. #4546D3semidirect
236. C32#1543semidirect
277. C3#68482semidirect
278. C3#71805semidirect

Maximal subgroups

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

subgroupindex
C3×#57252
#105902482
#105894122
C3×#45462
#105890902
#718053
#684823