Finite Group Databasebeta

← #13076384

Subgroups — #13076384

Order 1408.

408 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#387C211yesmaximal, characteristic, complemented
2#10622607C211yesmaximal, characteristic
3#10622602C211yesmaximal, characteristic
4#10622591C211yesmaximal, characteristic, complemented
5#10622589C211yesmaximal, characteristic, complemented
6#10622553C211yesmaximal, characteristic
7#10622541C211yesmaximal, characteristic, complemented
8#10622289C211yesmaximal, characteristic
9#10622283C211yesmaximal, characteristic
10#10622281C211yesmaximal, characteristic
11#10622281C211yesmaximal, characteristic
12#10622274C211yesmaximal, characteristic, complemented
13#10622271C211yesmaximal, characteristic, complemented
14#10622270C211yesmaximal, characteristic, complemented
15#10622270C211yesmaximal, characteristic, complemented
16C22×C4×D11C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C11×C4⋊C4C2211yescharacteristic
19C2×C42×C11C2211yescharacteristic
20C2×(C2×D11)⋊C4C2211yescharacteristic
21C2×(C2×D11)⋊C4C2211yescharacteristic
22C2×(C2×D11)⋊C4C2211yescharacteristic
23C2×(C2×D11)⋊C4C2211yescharacteristic
24C2×(C2×D11)⋊C4C2211yescharacteristic
25C2×(C2×D11)⋊C4C2211yescharacteristic
26C2×C4⋊Dic11C2211yescharacteristic
27C2×C4⋊Dic11C2211yescharacteristic
28C2×C4⋊Dic11C2211yescharacteristic
29C2×C4⋊Dic11C2211yescharacteristic
30C2×Dic11⋊C4C2211yescharacteristic
31C2×Dic11⋊C4C2211yescharacteristic
32C2×Dic11⋊C4C2211yescharacteristic
33C2×Dic11⋊C4C2211yescharacteristic
34C2×Dic11⋊C4C2211yescharacteristic
35C2×Dic11⋊C4C2211yescharacteristic
36C2×Dic11⋊C4C2211yescharacteristic
37C2×Dic11⋊C4C2211yescharacteristic
38C2×C4×Dic11C2211yescharacteristic
39C11×#95C2211yescharacteristic
40C11×#95C2211yescharacteristic
41C11×#95C2211yescharacteristic
42C11×#95C2211yescharacteristic
43C11⋊#95C2211yescharacteristic
44C11⋊#95C2211yescharacteristic
45C11⋊#95C2211yescharacteristic
46C11⋊#95C2211yescharacteristic
47C11⋊#95C2211yescharacteristic
48C11⋊#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C23×D11C2311yescharacteristic
52C22×C4×C11C2311yescharacteristic
53C22×C4×C11C2311yescharacteristic
54C22×C4×C11C2311yescharacteristic
55C22×C4×C11C2311yescharacteristic
56C22×C4×C11C2311yescharacteristic
57C22×C4×C11C2311yescharacteristic
58C22×C4×C11C2311yescharacteristic
59C22×Dic11C2311yescharacteristic
60C22×Dic11C2311yescharacteristic
61C22×Dic11C2311yescharacteristic
62C22×Dic11C2311yescharacteristic
63C22×Dic11C2311yescharacteristic
64C22×Dic11C2311yescharacteristic
65C22×Dic11C2311yescharacteristic
66C2×C4×D11—41no—
67C2×C4×D11—41no—
68C2×C4×D11—41no—
69C11×C4⋊C4—22no—
70C11×C4⋊C4—41no—
71C42×C11—41no—
72(C2×D11)⋊C4—22no—
73(C2×D11)⋊C4—22no—
74(C2×D11)⋊C4—41no—
75(C2×D11)⋊C4—41no—
76(C2×D11)⋊C4—41no—
77(C2×D11)⋊C4Q814yes—
78C4⋊Dic11—22no—
79C4⋊Dic11—41no—
80C4⋊Dic11—41no—
81C4⋊Dic11—41no—
82Dic11⋊C4—22no—
83Dic11⋊C4—41no—
84Dic11⋊C4—41no—
85Dic11⋊C4—41no—
86Dic11⋊C4—41no—
87Dic11⋊C4—41no—
88Dic11⋊C4—41no—
89Dic11⋊C4—41no—
90C4×Dic11—22no—
91#2790—111nomaximal, Sylow
92C23×C11C2411yescharacteristic
93C22×D11—21no—
94C22×D11—21no—
95C22×D11—21no—
96C22×D11—21no—
97C22×D11—21no—
98C22×D11—21no—
99C22×D11C2×Q812yes—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11C2×Q812yes—
120C2×C4×C11#4112yes—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11C2×Q812yes—
141C2×Dic11#4112yes—
142C4×D11—44no—
143#400—111no—
144#398—111no—
145#398—111no—
146#398—111no—
147#396—111no—
148#396—111no—
149#389—111no—
150#388—111no—
151#388—111no—
152#387—111no—
153#387D1111yescharacteristic, complemented
154#385—111no—
155#385—111no—
156#385—111no—
157#384—111no—
158C22×C11C22×Q811yescharacteristic
159C22×C11C2×#4111yescharacteristic
160C22×C11C2×#4111yescharacteristic
161C22×C11H(5,𝔽2)11yescharacteristic
162C22×C11H(5,𝔽2)11yescharacteristic
163C22×C11H(5,𝔽2)11yescharacteristic
164C22×C112−1+411yescharacteristic
165C2×D11—22no—
166C2×D11—22no—
167C2×D11—22no—
168C2×D11—41no—
169C2×D11—41no—
170C2×D11—41no—
171C2×D11—41no—
172C4×C11—22no—
173C4×C11—22no—
174C4×C11—41no—
175C4×C11—41no—
176C4×C11—41no—
177C4×C11—41no—
178C4×C11—41no—
179Dic11—22no—
180Dic11—22no—
181Dic11—41no—
182Dic11—41no—
183Dic11—41no—
184Dic11—41no—
185Dic11—41no—
186C23×C4—111no—
187C2×C4⋊C4—111no—
188C2×C4⋊C4—111no—
189C2×C4⋊C4—111no—
190C2×C4⋊C4—111no—
191C2×C4⋊C4—111no—
192C2×C4⋊C4—111no—
193C2×C4⋊C4—111no—
194C2×C4⋊C4—111no—
195C2×C4⋊C4—111no—
196C2×C4⋊C4—111no—
197C2×C4⋊C4—111no—
198C2×C4⋊C4—111no—
199C2×C4⋊C4C2×D1111yescharacteristic
200C2×C4⋊C4C2×D1111yescharacteristic
201C2×C22⋊C4—111no—
202C2×C22⋊C4—111no—
203C2×C22⋊C4—111no—
204C2×C22⋊C4—111no—
205C2×C22⋊C4—111no—
206C2×C22⋊C4—111no—
207C2×C42—111no—
208C2×C42C2×D1111yescharacteristic
209#95—111no—
210#95—111no—
211#95—111no—
212#95—111no—
213#95—111no—
214#95—111no—
215#95—111no—
216#95—111no—
217#95C2×D1111yescharacteristic
218#95C2×D1111yescharacteristic
219#95C2×D1111yescharacteristic
220#95C2×D1111yescharacteristic
221C2×C11#53911yescharacteristic
222C2×C11#54211yescharacteristic
223C2×C11#54411yescharacteristic
224C2×C11#55311yescharacteristic
225C2×C11#55411yescharacteristic
226C2×C11#55411yescharacteristic
227C2×C11#56011yescharacteristic
228D11—42no—
229C24—111no—
230C22×C4—111no—
231C22×C4—111no—
232C22×C4—111no—
233C22×C4—111no—
234C22×C4—111no—
235C22×C4—111no—
236C22×C4—111no—
237C22×C4—441no—
238C22×C4—441no—
239C22×C4—441no—
240C22×C4C22×D1111yescharacteristic
241C22×C4C22×D1111yescharacteristic
242C22×C4C22×D1111yescharacteristic
243C22×C4C22×D1111yescharacteristic
244C22×C4C22×D1111yescharacteristic
245C22×C4C22×D1111yescharacteristic
246C22×C4C22×D1111yescharacteristic
247C4⋊C4—22no—
248C4⋊C4—41no—
249C4⋊C4—222no—
250C4⋊C4—222no—
251C4⋊C4—441no—
252C4⋊C4—441no—
253C4⋊C4—441no—
254C4⋊C4—441no—
255C4⋊C4—441no—
256C4⋊C4—441no—
257C4⋊C4—441no—
258C4⋊C4—441no—
259C4⋊C4—441no—
260C4⋊C4—441no—
261C22⋊C4—114no—
262C22⋊C4—222no—
263C22⋊C4—222no—
264C22⋊C4—441no—
265C22⋊C4—441no—
266C22⋊C4—441no—
267C42—41no—
268C42—222no—
269C11#279011yescharacteristic, complemented, Sylow
270C23—112no—
271C23—221no—
272C23—221no—
273C23—221no—
274C23—221no—
275C23—221no—
276C23—221no—
277C23C23×D1111yescharacteristic
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—112no—
298C2×C4—112no—
299C2×C4—221no—
300C2×C4—221no—
301C2×C4—221no—
302C2×C4—221no—
303C2×C4—221no—
304C2×C4—221no—
305C2×C4—221no—
306C2×C4—221no—
307C2×C4—221no—
308C2×C4—221no—
309C2×C4—221no—
310C2×C4—221no—
311C2×C4—221no—
312C2×C4—221no—
313C2×C4—221no—
314C2×C4—221no—
315C2×C4—221no—
316C2×C4—221no—
317C2×C4—221no—
318C2×C4—444no—
319C2×C4#433912yes—
320C2×C4Q8×D1112yes—
321C22—222no—
322C22—222no—
323C22—222no—
324C22—441no—
325C22—441no—
326C22—441no—
327C22—441no—
328C22C2×#433911yescharacteristic
329C22#6703711yescharacteristic
330C22C2×Q8×D1111yescharacteristic
331C22#41×D1111yescharacteristic
332C22#6704211yescharacteristic
333C22#6704211yescharacteristic
334C22#6704311yescharacteristic
335C4—22no—
336C4—22no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—222no—
343C4—222no—
344C4—441no—
345C4—441no—
346C4—441no—
347C4—441no—
348C4—441no—
349C2—442no—
350C2#1062306111yescharacteristic
351C2#1062309511yescharacteristic
352C2#1062311011yescharacteristic
353C2#1062316711yescharacteristic
354C2#1062319711yescharacteristic
355C2#1062322011yescharacteristic
356C2#1062324111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#387C2
prime radicalC23×D11C23
hypercenter#387D11
hypocenterC11#2790
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
1. C11×#387C2semidirect
4. #10622591C2semidirect
5. #10622589C2semidirect
7. #10622541C2semidirect
12. #10622274C2semidirect
13. #10622271C2semidirect
14. #10622270C2semidirect
15. #10622270C2semidirect
153. #387D11semidirect
269. C11#2790semidirect

Maximal subgroups

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

subgroupindex
C11×#3872
#106226072
#106226022
#106225912
#106225892
#106225532
#106225412
#106222892
#106222832
#106222812
#106222742
#106222712
#106222702
#279011