Finite Group Databasebeta

← #13076313

Subgroups — #13076313

Order 1408.

472 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#380C211yesmaximal, characteristic, complemented
2#10622826C211yesmaximal, characteristic
3#10622823C211yesmaximal, characteristic, complemented
4#10622607C211yesmaximal, characteristic, complemented
5#10622602C211yesmaximal, characteristic, complemented
6#10622592C211yesmaximal, characteristic, complemented
7#10622591C211yesmaximal, characteristic, complemented
8#10622570C211yesmaximal, characteristic
9#10622569C211yesmaximal, characteristic
10#10622561C211yesmaximal, characteristic, complemented
11#10622560C211yesmaximal, characteristic, complemented
12#10622286C211yesmaximal, characteristic, complemented
13#10622280C211yesmaximal, characteristic, complemented
14#10622272C211yesmaximal, characteristic, complemented
15#10622265C211yesmaximal, characteristic, complemented
16C23×C4×C11C2211yescharacteristic
17C22×C22⋊D11C2211yescharacteristic
18C22×C4×D11C2211yescharacteristic
19C22×Dic22C2211yescharacteristic
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×C11×C4⋊C4C2211yescharacteristic
22C2×C11×C22⋊C4C2211yescharacteristic
23C2×C11×C22⋊C4C2211yescharacteristic
24C2×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊Dic11C2211yescharacteristic
26C2×C22⋊Dic11C2211yescharacteristic
27C2×(C2×D11)⋊C4C2211yescharacteristic
28C2×(C2×D11)⋊C4C2211yescharacteristic
29C2×(C2×D11)⋊C4C2211yescharacteristic
30C2×(C2×D11)⋊C4C2211yescharacteristic
31C2×(C2×D11)⋊C4C2211yescharacteristic
32C2×C4⋊Dic11C2211yescharacteristic
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
51C24×C11C2311yescharacteristic
52C23×D11C2311yescharacteristic
53C22×C4×C11—22no—
54C22×C4×C11—41no—
55C22×C4×C11—41no—
56C22×C4×C11C2311yescharacteristic
57C22×C4×C11C2311yescharacteristic
58C22×C4×C11C2311yescharacteristic
59C22×C4×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C2×C22⋊D11—41no—
63C2×C22⋊D11—41no—
64C2×C22⋊D11Q814yescomplemented
65C22×Dic11C2311yescharacteristic
66C22×Dic11C2311yescharacteristic
67C22×Dic11C2311yescharacteristic
68C22×Dic11C2311yescharacteristic
69C22×Dic11C2311yescharacteristic
70C22×Dic11C2311yescharacteristic
71C22×Dic11C2311yescharacteristic
72C2×C4×D11—22no—
73C2×C4×D11—41no—
74C2×C4×D11—41no—
75C2×Dic22—41no—
76C2×Dic22—41no—
77C2×Dic22—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C22⋊C4—41no—
81C11×C22⋊C4—41no—
82C22⋊Dic11—22no—
83C22⋊Dic11—41no—
84C22⋊Dic11—41no—
85(C2×D11)⋊C4—22no—
86(C2×D11)⋊C4—41no—
87(C2×D11)⋊C4—41no—
88(C2×D11)⋊C4—41no—
89(C2×D11)⋊C4—41no—
90C4⋊Dic11—41no—
91Dic11⋊C4—22no—
92Dic11⋊C4—22no—
93Dic11⋊C4—41no—
94Dic11⋊C4—41no—
95Dic11⋊C4—41no—
96C4×Dic11—41no—
97#2784—111nomaximal, Sylow
98C23×C11—21no—
99C23×C11—21no—
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—21no—
104C23×C11C2×Q812yes—
105C23×C11C2411yescharacteristic
106C22×D11—21no—
107C22×D11—21no—
108C22×D11—21no—
109C22×D11—21no—
110C22×D11—21no—
111C22×D11—21no—
112C22×D11C2×Q812yes—
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×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—44no—
131C2×C4×C11#4112yes—
132C22⋊D11—44no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—21no—
140C2×Dic11—21no—
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11—21no—
146C2×Dic11—21no—
147C2×Dic11—21no—
148C2×Dic11—21no—
149C2×Dic11—21no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11C2×Q812yes—
153C2×Dic11#4112yes—
154C4×D11—44no—
155Dic22—44no—
156#400—111no—
157#396—111no—
158#396—111no—
159#395—111no—
160#393—111no—
161#393—111no—
162#390—111no—
163#387—111no—
164#387—111no—
165#386—111no—
166#386—111no—
167#385—111no—
168#385—111no—
169#380—111no—
170#380D1111yescharacteristic, complemented
171C22×C11—22no—
172C22×C11—22no—
173C22×C11—22no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11C22×Q811yescharacteristic
179C22×C11C2×#4111yescharacteristic
180C22×C11C2×#4111yescharacteristic
181C22×C11H(5,𝔽2)11yescharacteristic
182C22×C11H(5,𝔽2)11yescharacteristic
183C22×C11H(5,𝔽2)11yescharacteristic
184C22×C11H(5,𝔽2)11yescharacteristic
185C2×D11—22no—
186C2×D11—22no—
187C2×D11—22no—
188C2×D11—41no—
189C2×D11—41no—
190C2×D11—41no—
191C2×D11—41no—
192C4×C11—22no—
193C4×C11—41no—
194C4×C11—41no—
195C4×C11—41no—
196C4×C11—41no—
197C4×C11—41no—
198Dic11—22no—
199Dic11—22no—
200Dic11—41no—
201Dic11—41no—
202Dic11—41no—
203Dic11—41no—
204Dic11—41no—
205C22×Q8—111no—
206C22×D4—111no—
207C23×C4—111no—
208C23×C4C2×D1111yescharacteristic
209C2×C4⋊C4—111no—
210C2×C4⋊C4—111no—
211C2×C4⋊C4—111no—
212C2×C4⋊C4—111no—
213C2×C4⋊C4—111no—
214C2×C4⋊C4—111no—
215C2×C4⋊C4C2×D1111yescharacteristic
216C2×C4⋊C4C2×D1111yescharacteristic
217C2×C22⋊C4—111no—
218C2×C22⋊C4—111no—
219C2×C22⋊C4—111no—
220C2×C22⋊C4—111no—
221C2×C22⋊C4—111no—
222C2×C22⋊C4—111no—
223C2×C22⋊C4—111no—
224C2×C22⋊C4—111no—
225C2×C22⋊C4C2×D1111yescharacteristic
226C2×C22⋊C4C2×D1111yescharacteristic
227C2×C42—111no—
228#95—111no—
229#95—111no—
230#95—111no—
231#95—111no—
232#95—111no—
233#95—111no—
234#95—111no—
235#95—111no—
236#95—111no—
237#95—111no—
238#95C2×D1111yescharacteristic
239#95C2×D1111yescharacteristic
240C2×C11—42no—
241C2×C11#53811yescharacteristic
242C2×C11#53811yescharacteristic
243C2×C11#54311yescharacteristic
244C2×C11#55411yescharacteristic
245C2×C11#55411yescharacteristic
246C2×C11#55511yescharacteristic
247C2×C11#56011yescharacteristic
248D11—42no—
249C24—111no—
250C24C22×D1111yescharacteristic
251C2×Q8—441no—
252C2×Q8—441no—
253C2×Q8—441no—
254C2×D4—114no—
255C2×D4—441no—
256C2×D4—441no—
257C22×C4—22no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—111no—
261C22×C4—111no—
262C22×C4—111no—
263C22×C4—111no—
264C22×C4—111no—
265C22×C4—111no—
266C22×C4—111no—
267C22×C4—222no—
268C22×C4—441no—
269C22×C4—441no—
270C22×C4C22×D1111yescharacteristic
271C22×C4C22×D1111yescharacteristic
272C22×C4C22×D1111yescharacteristic
273C22×C4C22×D1111yescharacteristic
274C22×C4C22×D1111yescharacteristic
275C22×C4C22×D1111yescharacteristic
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—222no—
279C4⋊C4—222no—
280C4⋊C4—441no—
281C4⋊C4—441no—
282C4⋊C4—441no—
283C4⋊C4—441no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—222no—
287C22⋊C4—222no—
288C22⋊C4—441no—
289C22⋊C4—441no—
290C22⋊C4—441no—
291C22⋊C4—441no—
292C22⋊C4—441no—
293C22⋊C4—441no—
294C42—441no—
295C11#278411yescharacteristic, complemented, Sylow
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—112no—
303C23—221no—
304C23—221no—
305C23—221no—
306C23—221no—
307C23—221no—
308C23—221no—
309C23Q8×D1112yes—
310C23C23×D1111yescharacteristic
311Q8—444no—
312D4—444no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—44no—
331C2×C4—112no—
332C2×C4—112no—
333C2×C4—221no—
334C2×C4—221no—
335C2×C4—221no—
336C2×C4—221no—
337C2×C4—221no—
338C2×C4—221no—
339C2×C4—221no—
340C2×C4—221no—
341C2×C4—221no—
342C2×C4—221no—
343C2×C4—221no—
344C2×C4—221no—
345C2×C4—221no—
346C2×C4—221no—
347C2×C4—221no—
348C2×C4—221no—
349C2×C4—221no—
350C2×C4—221no—
351C2×C4—221no—
352C2×C4—444no—
353C2×C4#433912yes—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—222no—
362C22—222no—
363C22—222no—
364C22—441no—
365C22—441no—
366C22—441no—
367C22—441no—
368C22C2×#433911yescharacteristic
369C22#6703711yescharacteristic
370C22#6703711yescharacteristic
371C22#6703711yescharacteristic
372C22C2×Q8×D1111yescharacteristic
373C22#41×D1111yescharacteristic
374C22#6704211yescharacteristic
375C4—22no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—222no—
382C4—222no—
383C4—441no—
384C4—441no—
385C4—441no—
386C4—441no—
387C4—441no—
388C2—42no—
389C2—442no—
390C2#1062302511yescharacteristic
391C2#1062304211yescharacteristic
392C2#1062306311yescharacteristic
393C2#1062314411yescharacteristic
394C2#1062315111yescharacteristic
395C2#1062316511yescharacteristic
396C2#1062316711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#380C2
prime radicalC22×C22⋊D11C22
hypercenter#380D11
hypocenterC11#2784
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C11×#380C2semidirect
3. #10622823C2semidirect
4. #10622607C2semidirect
5. #10622602C2semidirect
6. #10622592C2semidirect
7. #10622591C2semidirect
10. #10622561C2semidirect
11. #10622560C2semidirect
12. #10622286C2semidirect
13. #10622280C2semidirect
14. #10622272C2semidirect
15. #10622265C2semidirect
64. C2×C22⋊D11Q8semidirect
170. #380D11semidirect
295. C11#2784semidirect

Maximal subgroups

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

subgroupindex
C11×#3802
#106228262
#106228232
#106226072
#106226022
#106225922
#106225912
#106225702
#106225692
#106225612
#106225602
#106222862
#106222802
#106222722
#106222652
#278411