Finite Group Databasebeta

← #13073006

Subgroups — #13073006

Order 1408.

440 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#387C211yesmaximal, characteristic, complemented
2#10622602C211yesmaximal, characteristic
3#10622602C211yesmaximal, characteristic
4#10622595C211yesmaximal, characteristic, complemented
5#10622591C211yesmaximal, characteristic, complemented
6C4×(C2×D11)⋊C4C211yesmaximal, characteristic
7#10622546C211yesmaximal, characteristic, complemented
8#10622280C211yesmaximal, characteristic
9#10622277C211yesmaximal, characteristic
10#10622277C211yesmaximal, characteristic
11D11×#95C211yesmaximal, characteristic
12C11⋊#401C211yesmaximal, characteristic, complemented
13#10622271C211yesmaximal, characteristic, complemented
14#10622271C211yesmaximal, characteristic, complemented
15#10622264C211yesmaximal, characteristic, complemented
16C22×C4×D11C2211yescharacteristic
17C22×C4×D11C2211yescharacteristic
18C22×C4×D11C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×C42×C11C2211yescharacteristic
22C2×(C2×D11)⋊C4C2211yescharacteristic
23C2×(C2×D11)⋊C4C2211yescharacteristic
24C2×(C2×D11)⋊C4C2211yescharacteristic
25C2×(C2×D11)⋊C4C2211yescharacteristic
26C2×Dic11⋊C4C2211yescharacteristic
27C2×Dic11⋊C4C2211yescharacteristic
28C2×Dic11⋊C4C2211yescharacteristic
29C2×Dic11⋊C4C2211yescharacteristic
30C2×C4×Dic11C2211yescharacteristic
31C11×#95C2211yescharacteristic
32C11×#95C2211yescharacteristic
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
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—22no—
67C2×C4×D11—22no—
68C2×C4×D11—22no—
69C2×C4×D11—22no—
70C2×C4×D11—22no—
71C2×C4×D11—22no—
72C2×C4×D11—22no—
73C2×C4×D11—41no—
74C2×C4×D11—41no—
75C11×C4⋊C4—22no—
76C11×C4⋊C4—41no—
77C42×C11—41no—
78(C2×D11)⋊C4—22no—
79(C2×D11)⋊C4—22no—
80(C2×D11)⋊C4—22no—
81(C2×D11)⋊C4—22no—
82Dic11⋊C4—22no—
83Dic11⋊C4—22no—
84Dic11⋊C4—41no—
85Dic11⋊C4—41no—
86C4×Dic11—22no—
87#2493—111nomaximal, Sylow
88C23×C11C2411yescharacteristic
89C22×D11—21no—
90C22×D11—21no—
91C22×D11—21no—
92C22×D11—21no—
93C22×D11#4112yes—
94C22×D11#4112yes—
95C22×D11#4112yes—
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—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11#4112yes—
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—21no—
137C2×Dic11#4112yes—
138C4×D11—44no—
139C4×D11—44no—
140C4×D11—44no—
141#401—111no—
142#400—111no—
143#400—111no—
144#400—111no—
145#387—111no—
146#387—111no—
147#387D1111yescharacteristic, complemented
148#385—111no—
149#385—111no—
150#383—111no—
151#381—111no—
152#381—111no—
153#380—111no—
154C4×C22⋊C4—111no—
155C2×#95—111no—
156C22×C11C2×#4111yescharacteristic
157C22×C11C2×#4111yescharacteristic
158C22×C11C2×#4111yescharacteristic
159C22×C11C2×#4111yescharacteristic
160C22×C11C2×#4111yescharacteristic
161C22×C11H(5,𝔽2)11yescharacteristic
162C22×C112−1+411yescharacteristic
163C2×D11—22no—
164C2×D11—22no—
165C2×D11—22no—
166C2×D11—22no—
167C2×D11—22no—
168C2×D11—22no—
169C2×D11#12614yes—
170C4×C11—22no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11—41no—
176C4×C11—41no—
177Dic11—22no—
178Dic11—41no—
179Dic11—41no—
180Dic11—41no—
181Dic11—41no—
182Dic11—41no—
183Dic11—41no—
184C23×C4—111no—
185C23×C4—111no—
186C23×C4—111no—
187C2×C4⋊C4—111no—
188C2×C4⋊C4—111no—
189C2×C4⋊C4—111no—
190C2×C4⋊C4—111no—
191C2×C4⋊C4C2×D1111yescharacteristic
192C2×C4⋊C4C2×D1111yescharacteristic
193C2×C22⋊C4—111no—
194C2×C22⋊C4—111no—
195C2×C22⋊C4—111no—
196C2×C22⋊C4—111no—
197C2×C42—111no—
198C2×C42C2×D1111yescharacteristic
199#95—111no—
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#95C2×D1111yescharacteristic
216#95C2×D1111yescharacteristic
217#95C2×D1111yescharacteristic
218#95C2×D1111yescharacteristic
219C2×C11C2×#12611yescharacteristic
220C2×C11#52911yescharacteristic
221C2×C11#53911yescharacteristic
222C2×C11#55111yescharacteristic
223C2×C11#55111yescharacteristic
224C2×C11#55211yescharacteristic
225C2×C11#55211yescharacteristic
226D11—24no—
227C24—111no—
228C22×C4—111no—
229C22×C4—111no—
230C22×C4—111no—
231C22×C4—111no—
232C22×C4—111no—
233C22×C4—111no—
234C22×C4—111no—
235C22×C4—222no—
236C22×C4—222no—
237C22×C4—222no—
238C22×C4—222no—
239C22×C4—222no—
240C22×C4—222no—
241C22×C4—222no—
242C22×C4—441no—
243C22×C4—441no—
244C22×C4C22×D1111yescharacteristic
245C22×C4C22×D1111yescharacteristic
246C22×C4C22×D1111yescharacteristic
247C22×C4C22×D1111yescharacteristic
248C22×C4C22×D1111yescharacteristic
249C22×C4C22×D1111yescharacteristic
250C22×C4C22×D1111yescharacteristic
251C4⋊C4—22no—
252C4⋊C4—41no—
253C4⋊C4—222no—
254C4⋊C4—222no—
255C4⋊C4—441no—
256C4⋊C4—441no—
257C22⋊C4—222no—
258C22⋊C4—222no—
259C22⋊C4—222no—
260C22⋊C4—222no—
261C42—41no—
262C42—222no—
263C11#249311yescharacteristic, complemented, Sylow
264C23—112no—
265C23—112no—
266C23—112no—
267C23—221no—
268C23—221no—
269C23—221no—
270C23—221no—
271C23C23×D1111yescharacteristic
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—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—112no—
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—221no—
313C2×C4—444no—
314C2×C4—444no—
315C2×C4—444no—
316C2×C4#433912yes—
317C22—114no—
318C22—222no—
319C22—222no—
320C22—222no—
321C22—222no—
322C22—222no—
323C22—222no—
324C22C2×#433911yescharacteristic
325C22#6703711yescharacteristic
326C22#6704011yescharacteristic
327C22#41×D1111yescharacteristic
328C22#41×D1111yescharacteristic
329C22#41×D1111yescharacteristic
330C22#41×D1111yescharacteristic
331C4—22no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—222no—
339C4—441no—
340C4—441no—
341C4—441no—
342C4—441no—
343C4—441no—
344C4—441no—
345C2—224no—
346C2#1062305911yescharacteristic
347C2#1062308711yescharacteristic
348C2#1062311211yescharacteristic
349C2#1062316911yescharacteristic
350C2#1062319011yescharacteristic
351C2#1062322411yescharacteristic
352C2D11×#12611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#387C2
prime radicalC23×D11C23
hypercenter#387D11
hypocenterC11#2493
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. #10622595C2semidirect
5. #10622591C2semidirect
7. #10622546C2semidirect
12. C11⋊#401C2semidirect
13. #10622271C2semidirect
14. #10622271C2semidirect
15. #10622264C2semidirect
147. #387D11semidirect
263. C11#2493semidirect

Maximal subgroups

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

subgroupindex
C11×#3872
#106226022
#106225952
#106225912
C4×(C2×D11)⋊C42
#106225462
#106222802
#106222772
D11×#952
C11⋊#4012
#106222712
#106222642
#249311