Finite Group Databasebeta

← #13072106

Subgroups — #13072106

Order 1408.

596 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66991C211yesmaximal, characteristic
2C2×D4×Dic11C211yesmaximal, characteristic, complemented
3C11×#390C211yesmaximal, characteristic, complemented
4#10622600C211yesmaximal, characteristic, complemented
5#10622598C211yesmaximal, characteristic, complemented
6#10622574C212yesmaximal, complemented
7#10622571C212yesmaximal, complemented
8#10622566C212yesmaximal, complemented
9#10622556C212yesmaximal, complemented
10C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
11#10622549C211yesmaximal, characteristic, complemented
12C22×D4×C11C2211yescharacteristic
13C22×C22⋊D11C2212yes—
14C23×Dic11C2212yes—
15C22×C4×D11C2211yescharacteristic
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C11×C22⋊C4C2212yes—
18C2×C11×C22⋊C4C2212yes—
19C2×C42×C11C2211yescharacteristic
20C2×C22⋊Dic11C2212yes—
21C2×C22⋊Dic11C2212yes—
22#66991—24no—
23D4×Dic11—24no—
24C2×(C2×D11)⋊C4C2211yescharacteristic
25C2×(C2×D11)⋊C4C2211yescharacteristic
26C2×(C2×D11)⋊C4C2212yes—
27C2×C4⋊Dic11C2211yescharacteristic
28C2×C4⋊Dic11C2211yescharacteristic
29C2×C4⋊Dic11C2212yes—
30C2×C4×Dic11C2211yescharacteristic
31C11⋊#95C2212yes—
32C11⋊#95C2212yes—
33C11⋊#95C2211yescharacteristic
34C11⋊#95C2211yescharacteristic
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C24×C11C2312yes—
38C23×D11C2311yescharacteristic
39C2×D4×C11—22no—
40C2×D4×C11—22no—
41C2×D4×C11D414yes—
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2311yescharacteristic
44C22×C4×C11C2312yes—
45C22×C4×C11C2311yescharacteristic
46C2×C22⋊D11—24no—
47C2×C22⋊D11—24no—
48C2×C22⋊D11—42no—
49C22×Dic11—24no—
50C22×Dic11—24no—
51C22×Dic11—42no—
52C22×Dic11C2311yescharacteristic
53C22×Dic11C2312yes—
54C22×Dic11C2312yes—
55C22×Dic11C2311yescharacteristic
56C22×Dic11C2311yescharacteristic
57C2×C4×D11—22no—
58C2×C4×D11—22no—
59C2×C4×D11—22no—
60C11×C4⋊C4—22no—
61C11×C22⋊C4—42no—
62C11×C22⋊C4—42no—
63C42×C11—22no—
64C22⋊Dic11—24no—
65C22⋊Dic11—24no—
66(C2×D11)⋊C4—22no—
67(C2×D11)⋊C4—22no—
68(C2×D11)⋊C4—42no—
69C4⋊Dic11—22no—
70C4⋊Dic11—22no—
71C4⋊Dic11—42no—
72C4×Dic11—22no—
73#2420—111nomaximal, Sylow
74C23×C11—22no—
75C23×C11—22no—
76C23×C11—22no—
77C23×C11—22no—
78C23×C11—22no—
79C23×C11—22no—
80C23×C11C2×D414yes—
81C23×C11C2411yescharacteristic
82C22×D11—21no—
83C22×D11—21no—
84C22×D11—21no—
85C22×D11—21no—
86C22×D11—21no—
87C22×D11—21no—
88C22×D11#4112yes—
89D4×C11—28no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—22no—
95C2×C4×C11—22no—
96C2×C4×C11—22no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11C2×D412yes—
100C2×C4×C11#4112yes—
101C2×C4×C11#4112yes—
102C22⋊D11—48no—
103C2×Dic11—21no—
104C2×Dic11—21no—
105C2×Dic11—21no—
106C2×Dic11—22no—
107C2×Dic11—22no—
108C2×Dic11—21no—
109C2×Dic11—21no—
110C2×Dic11—21no—
111C2×Dic11—21no—
112C2×Dic11—22no—
113C2×Dic11—22no—
114C2×Dic11—21no—
115C2×Dic11—22no—
116C2×Dic11—22no—
117C2×Dic11—48no—
118C2×Dic11#4112yes—
119C4×D11—44no—
120C2×#121—111no—
121C2×C4×D4—111no—
122#397—112no—
123#394—112no—
124#390D1111yescharacteristic, complemented
125#389—111no—
126#386—112no—
127#382—111no—
128#381—112no—
129#380—111no—
130C4×C22⋊C4—111no—
131C22×C11—24no—
132C22×C11—24no—
133C22×C11—24no—
134C22×C11—42no—
135C22×C11—42no—
136C22×C11—42no—
137C22×C11—42no—
138C22×C11C22×D411yescharacteristic
139C22×C11C2×#4111yescharacteristic
140C22×C11C2×#4111yescharacteristic
141C22×C11C2×#4111yescharacteristic
142C22×C11C2×#4111yescharacteristic
143C22×C11H(5,𝔽2)11yescharacteristic
144C22×C11H(5,𝔽2)11yescharacteristic
145C2×D11—22no—
146C2×D11—22no—
147C2×D11—22no—
148C2×D11—41no—
149C2×D11—41no—
150C2×D11—41no—
151C2×D11—41no—
152C4×C11—42no—
153C4×C11—41no—
154C4×C11—41no—
155C4×C11#12314yes—
156Dic11—22no—
157Dic11—41no—
158Dic11—41no—
159Dic11—42no—
160Dic11—42no—
161C22×D4—112no—
162C22×D4C2×D1111yescharacteristic
163C23×C4—112no—
164C23×C4—111no—
165#121—224no—
166C4×D4—224no—
167C2×C4⋊C4—111no—
168C2×C4⋊C4—111no—
169C2×C4⋊C4—112no—
170C2×C4⋊C4C2×D1111yescharacteristic
171C2×C22⋊C4—112no—
172C2×C22⋊C4—112no—
173C2×C22⋊C4—111no—
174C2×C22⋊C4—111no—
175C2×C22⋊C4—112no—
176C2×C22⋊C4C2×D1112yes—
177C2×C22⋊C4C2×D1112yes—
178C2×C42—111no—
179C2×C42C2×D1111yescharacteristic
180#95—111no—
181#95—111no—
182#95—112no—
183#95—112no—
184#95—112no—
185#95—112no—
186C2×C11—44no—
187C2×C11C2×#12311yescharacteristic
188C2×C11#52911yescharacteristic
189C2×C11#54011yescharacteristic
190C2×C11#54611yescharacteristic
191C2×C11#54611yescharacteristic
192C2×C11#55311yescharacteristic
193C2×C11#55511yescharacteristic
194D11—42no—
195C24—111no—
196C24C22×D1112yes—
197C2×D4—22no—
198C2×D4—22no—
199C2×D4—224no—
200C2×D4—224no—
201C2×D4—442no—
202C2×D4D4414yes—
203C22×C4—111no—
204C22×C4—111no—
205C22×C4—112no—
206C22×C4—112no—
207C22×C4—111no—
208C22×C4—224no—
209C22×C4—224no—
210C22×C4—222no—
211C22×C4—222no—
212C22×C4—222no—
213C22×C4—442no—
214C22×C4C22×D1111yescharacteristic
215C22×C4C22×D1111yescharacteristic
216C22×C4C22×D1112yes—
217C22×C4C22×D1111yescharacteristic
218C4⋊C4—22no—
219C4⋊C4—222no—
220C4⋊C4—222no—
221C4⋊C4—442no—
222C22⋊C4—42no—
223C22⋊C4—42no—
224C22⋊C4—222no—
225C22⋊C4—222no—
226C22⋊C4—224no—
227C22⋊C4—224no—
228C22⋊C4—442no—
229C42—22no—
230C42—222no—
231C11#242011yescharacteristic, complemented, Sylow
232C23—22no—
233C23—22no—
234C23—22no—
235C23—22no—
236C23—22no—
237C23—22no—
238C23—112no—
239C23—221no—
240C23—221no—
241C23—221no—
242C23—221no—
243C23—221no—
244C23—221no—
245C23C2×D4414yes—
246C23C23×D1111yescharacteristic
247D4—28no—
248D4—448no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—112no—
259C2×C4—221no—
260C2×C4—221no—
261C2×C4—221no—
262C2×C4—221no—
263C2×C4—222no—
264C2×C4—222no—
265C2×C4—221no—
266C2×C4—221no—
267C2×C4—222no—
268C2×C4—221no—
269C2×C4—222no—
270C2×C4—221no—
271C2×C4—222no—
272C2×C4—222no—
273C2×C4—448no—
274C2×C4—444no—
275C2×C4C2×D4412yes—
276C2×C4#434112yes—
277C2×C4#434112yes—
278C22—24no—
279C22—24no—
280C22—24no—
281C22—42no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—222no—
286C22—222no—
287C22—222no—
288C22—441no—
289C22—441no—
290C22—441no—
291C22—441no—
292C22C22×D4411yescharacteristic
293C22C2×#434111yescharacteristic
294C22C2×#434111yescharacteristic
295C22#6703711yescharacteristic
296C22#6703711yescharacteristic
297C22#41×D1111yescharacteristic
298C22#41×D1111yescharacteristic
299C4—42no—
300C4—41no—
301C4—41no—
302C4—222no—
303C4—441no—
304C4—442no—
305C4—442no—
306C4—441no—
307C4#6693914yes—
308C2—44no—
309C2—442no—
310C2C2×#6693911yescharacteristic
311C2#1062308511yescharacteristic
312C2#1062308511yescharacteristic
313C2#1062314511yescharacteristic
314C2#1062314711yescharacteristic
315C2#1062321111yescharacteristic
316C2#1062325011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#390C2
prime radicalC2×#66991C2
hypercenter#390D11
hypocenterC11#2420
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×D4×Dic11C2semidirect
3. C11×#390C2semidirect
4. #10622600C2semidirect
5. #10622598C2semidirect
6. #10622574C2semidirect
7. #10622571C2semidirect
8. #10622566C2semidirect
9. #10622556C2semidirect
10. C4×(C2×D11)⋊C4C2semidirect
11. #10622549C2semidirect
124. #390D11semidirect
231. C11#2420semidirect

Maximal subgroups

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

subgroupindex
C2×#669912
C2×D4×Dic112
C11×#3902
#106226002
#106225982
#106225742
#106225712
#106225662
#106225562
C4×(C2×D11)⋊C42
#106225492
#242011