Finite Group Databasebeta

← #13073408

Subgroups — #13073408

Order 1408.

420 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#388C211yesmaximal, characteristic
2#10622594C211yesmaximal, characteristic, complemented
3#10622591C211yesmaximal, characteristic, complemented
4#10622565C211yesmaximal, characteristic
5#10622563C211yesmaximal, characteristic
6#10622560C211yesmaximal, characteristic
7#10622557C211yesmaximal, characteristic
8#10622556C211yesmaximal, characteristic
9C22⋊C4×Dic11C211yesmaximal, characteristic
10#10622545C211yesmaximal, characteristic, complemented
11#10622542C211yesmaximal, characteristic, complemented
12C11⋊#401C211yesmaximal, characteristic, complemented
13#10622273C211yesmaximal, characteristic, complemented
14#10622266C211yesmaximal, characteristic, complemented
15#10622259C211yesmaximal, characteristic, complemented
16C23×Dic11C2211yescharacteristic
17C22×Dic22C2211yescharacteristic
18C2×C11×C4⋊C4C2211yescharacteristic
19C2×C11×C22⋊C4C2211yescharacteristic
20C2×C11×C22⋊C4C2211yescharacteristic
21C2×C11×C22⋊C4C2211yescharacteristic
22C2×C42×C11C2211yescharacteristic
23C2×C22⋊Dic11C2211yescharacteristic
24C2×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊Dic11C2211yescharacteristic
26C2×C4⋊Dic11C2211yescharacteristic
27C2×C4⋊Dic11C2211yescharacteristic
28C2×Dic11⋊C4C2211yescharacteristic
29C2×Dic11⋊C4C2211yescharacteristic
30C2×C4×Dic11C2211yescharacteristic
31C2×C4×Dic11C2211yescharacteristic
32C2×C4×Dic11C2211yescharacteristic
33C11×#95C2211yescharacteristic
34C11×#95C2211yescharacteristic
35C11⋊#95C2211yescharacteristic
36C11⋊#95C2211yescharacteristic
37C11⋊#95C2211yescharacteristic
38C11⋊#95C2211yescharacteristic
39C11⋊#95C2211yescharacteristic
40C11⋊#95C2211yescharacteristic
41C11⋊#95C2211yescharacteristic
42C11⋊#95C2211yescharacteristic
43C11⋊#95C2211yescharacteristic
44C11⋊#95C2211yescharacteristic
45C11⋊#95C2211yescharacteristic
46C11⋊#95C2211yescharacteristic
47C11⋊#95C2211yescharacteristic
48C11⋊#95C2211yescharacteristic
49C11⋊#95C2211yescharacteristic
50C11⋊#95C2211yescharacteristic
51C24×C11C2311yescharacteristic
52C22×C4×C11C2311yescharacteristic
53C22×C4×C11C2311yescharacteristic
54C22×C4×C11C2311yescharacteristic
55C22×C4×C11C2311yescharacteristic
56C22×C4×C11C2311yescharacteristic
57C22×C4×C11C2311yescharacteristic
58C22×Dic11—22no—
59C22×Dic11—22no—
60C22×Dic11—41no—
61C22×Dic11C2311yescharacteristic
62C22×Dic11C2311yescharacteristic
63C22×Dic11C2311yescharacteristic
64C22×Dic11C2311yescharacteristic
65C22×Dic11C2311yescharacteristic
66C22×Dic11C2311yescharacteristic
67C22×Dic11C2311yescharacteristic
68C22×Dic11C2311yescharacteristic
69C2×Dic22—22no—
70C2×Dic22—22no—
71C2×Dic22—41no—
72C11×C4⋊C4—22no—
73C11×C22⋊C4—22no—
74C11×C22⋊C4—22no—
75C11×C22⋊C4—22no—
76C42×C11—22no—
77C22⋊Dic11—22no—
78C22⋊Dic11—22no—
79C22⋊Dic11—41no—
80C4⋊Dic11—22no—
81C4⋊Dic11—41no—
82Dic11⋊C4—22no—
83Dic11⋊C4—41no—
84C4×Dic11—22no—
85C4×Dic11—22no—
86C4×Dic11—41no—
87#2527—111nomaximal, Sylow
88C23×C11—21no—
89C23×C11—21no—
90C23×C11—21no—
91C23×C11—21no—
92C23×C11—21no—
93C23×C11—21no—
94C23×C11#4112yes—
95C23×C11C2411yescharacteristic
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
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#4112yes—
113C2×C4×C11#4112yes—
114C2×Dic11—21no—
115C2×Dic11—21no—
116C2×Dic11—21no—
117C2×Dic11—21no—
118C2×Dic11—21no—
119C2×Dic11—21no—
120C2×Dic11—21no—
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—44no—
137C2×Dic11#4112yes—
138C2×Dic11#4112yes—
139Dic22—44no—
140#401—111no—
141#400—111no—
142#397—111no—
143#393—111no—
144#391—111no—
145#391—111no—
146#388—111no—
147#388D1111yescharacteristic
148#387—111no—
149#387—111no—
150#387—111no—
151#385—111no—
152#381—111no—
153C4×C22⋊C4—111no—
154#376—111no—
155C22×C11—22no—
156C22×C11—22no—
157C22×C11—22no—
158C22×C11—41no—
159C22×C11—41no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11C2×#4111yescharacteristic
163C22×C11C2×#4111yescharacteristic
164C22×C11C2×#4111yescharacteristic
165C22×C11C2×#4111yescharacteristic
166C22×C11C2×#4111yescharacteristic
167C22×C11H(5,𝔽2)11yescharacteristic
168C22×C112−1+411yescharacteristic
169C4×C11—22no—
170C4×C11—22no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11—41no—
174C4×C11—41no—
175Dic11—22no—
176Dic11—22no—
177Dic11—41no—
178Dic11—41no—
179Dic11—41no—
180Dic11—41no—
181Dic11—41no—
182Dic11—41no—
183C22×Q8—111no—
184C23×C4—111no—
185C2×C4⋊C4—111no—
186C2×C4⋊C4—111no—
187C2×C4⋊C4—111no—
188C2×C4⋊C4—111no—
189C2×C4⋊C4C2×D1111yescharacteristic
190C2×C22⋊C4—111no—
191C2×C22⋊C4—111no—
192C2×C22⋊C4—111no—
193C2×C22⋊C4C2×D1111yescharacteristic
194C2×C22⋊C4C2×D1111yescharacteristic
195C2×C22⋊C4C2×D1111yescharacteristic
196C2×C42—111no—
197C2×C42—111no—
198C2×C42—111no—
199C2×C42C2×D1111yescharacteristic
200#95—111no—
201#95—111no—
202#95—111no—
203#95—111no—
204#95—111no—
205#95—111no—
206#95—111no—
207#95—111no—
208#95—111no—
209#95—111no—
210#95—111no—
211#95—111no—
212#95—111no—
213#95—111no—
214#95—111no—
215#95—111no—
216#95C2×D1111yescharacteristic
217#95C2×D1111yescharacteristic
218C2×C11—42no—
219C2×C11#52911yescharacteristic
220C2×C11#52911yescharacteristic
221C2×C11#54211yescharacteristic
222C2×C11#55111yescharacteristic
223C2×C11#55111yescharacteristic
224C2×C11#55211yescharacteristic
225C2×C11#55611yescharacteristic
226C24C22×D1111yescharacteristic
227C2×Q8—222no—
228C2×Q8—222no—
229C2×Q8—441no—
230C22×C4—111no—
231C22×C4—111no—
232C22×C4—111no—
233C22×C4—111no—
234C22×C4—111no—
235C22×C4—111no—
236C22×C4—111no—
237C22×C4—111no—
238C22×C4—222no—
239C22×C4—222no—
240C22×C4—441no—
241C22×C4C22×D1111yescharacteristic
242C22×C4C22×D1111yescharacteristic
243C22×C4C22×D1111yescharacteristic
244C22×C4C22×D1111yescharacteristic
245C22×C4C22×D1111yescharacteristic
246C22×C4C22×D1111yescharacteristic
247C4⋊C4—22no—
248C4⋊C4—222no—
249C4⋊C4—222no—
250C4⋊C4—441no—
251C4⋊C4—441no—
252C22⋊C4—22no—
253C22⋊C4—22no—
254C22⋊C4—22no—
255C22⋊C4—222no—
256C22⋊C4—222no—
257C22⋊C4—441no—
258C42—22no—
259C42—222no—
260C42—222no—
261C42—441no—
262C11#252711yescharacteristic, complemented, Sylow
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23—21no—
269C23#433912yes—
270C23C23×D1111yescharacteristic
271Q8—444no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
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—112no—
289C2×C4—112no—
290C2×C4—221no—
291C2×C4—221no—
292C2×C4—221no—
293C2×C4—221no—
294C2×C4—221no—
295C2×C4—221no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—221no—
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—444no—
313C2×C4#434112yes—
314C2×C4#434112yes—
315C22—22no—
316C22—22no—
317C22—22no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22C2×#433911yescharacteristic
323C22C2×#434111yescharacteristic
324C22C2×#434111yescharacteristic
325C22#41×D1111yescharacteristic
326C22#41×D1111yescharacteristic
327C22#6704211yescharacteristic
328C22#6704311yescharacteristic
329C4—22no—
330C4—22no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—222no—
336C4—222no—
337C4—441no—
338C4—441no—
339C4—441no—
340C4—441no—
341C4—441no—
342C4—441no—
343C2—42no—
344C2#1062305811yescharacteristic
345C2#1062306911yescharacteristic
346C2#1062307211yescharacteristic
347C2#1062313111yescharacteristic
348C2#1062318911yescharacteristic
349C2#1062321311yescharacteristic
350C2#1062323311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#388C2
prime radicalC24×C11C23
hypercenter#388D11
hypocenterC11#2527
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #10622594C2semidirect
3. #10622591C2semidirect
10. #10622545C2semidirect
11. #10622542C2semidirect
12. C11⋊#401C2semidirect
13. #10622273C2semidirect
14. #10622266C2semidirect
15. #10622259C2semidirect
262. C11#2527semidirect

Maximal subgroups

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

subgroupindex
C11×#3882
#106225942
#106225912
#106225652
#106225632
#106225602
#106225572
#106225562
C22⋊C4×Dic112
#106225452
#106225422
C11⋊#4012
#106222732
#106222662
#106222592
#252711