Finite Group Databasebeta

← #13076233

Subgroups — #13076233

Order 1408.

498 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#397C211yesmaximal, characteristic, complemented
2#10622603C211yesmaximal, characteristic, complemented
3#10622602C211yesmaximal, characteristic, complemented
4#10622574C211yesmaximal, characteristic, complemented
5#10622573C211yesmaximal, characteristic
6#10622572C211yesmaximal, characteristic, complemented
7#10622569C211yesmaximal, characteristic, complemented
8#10622569C211yesmaximal, characteristic, complemented
9#10622558C211yesmaximal, characteristic, complemented
10#10622283C211yesmaximal, characteristic, complemented
11#10622280C211yesmaximal, characteristic, complemented
12#10622278C211yesmaximal, characteristic, complemented
13#10622278C211yesmaximal, characteristic, complemented
14C11⋊#401C211yesmaximal, characteristic, complemented
15#10622272C211yesmaximal, characteristic, complemented
16C22×C22⋊D11C2211yescharacteristic
17C22×C22⋊D11C2211yescharacteristic
18C22×D44C2211yescharacteristic
19C22×C4×D11C2211yescharacteristic
20C22×C4×D11C2211yescharacteristic
21C2×C11×C4⋊C4C2211yescharacteristic
22C2×C11×C22⋊C4C2211yescharacteristic
23C2×C11×C22⋊C4C2211yescharacteristic
24C2×C11×C22⋊C4C2211yescharacteristic
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×(C2×D11)⋊C4C2211yescharacteristic
33C2×(C2×D11)⋊C4C2211yescharacteristic
34C2×(C2×D11)⋊C4C2211yescharacteristic
35C2×C4⋊Dic11C2211yescharacteristic
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
53C23×D11C2311yescharacteristic
54C22×C4×C11C2311yescharacteristic
55C22×C4×C11C2311yescharacteristic
56C22×C4×C11C2311yescharacteristic
57C22×C4×C11C2311yescharacteristic
58C22×C4×C11C2311yescharacteristic
59C22×C4×C11C2311yescharacteristic
60C2×C22⋊D11—22no—
61C2×C22⋊D11—22no—
62C2×C22⋊D11—41no—
63C2×C22⋊D11—41no—
64C2×C22⋊D11—41no—
65C2×C22⋊D11—41no—
66C22×Dic11C2311yescharacteristic
67C22×Dic11C2311yescharacteristic
68C22×Dic11C2311yescharacteristic
69C22×Dic11C2311yescharacteristic
70C22×Dic11C2311yescharacteristic
71C22×Dic11C2311yescharacteristic
72C2×D44—22no—
73C2×D44—22no—
74C2×D44—41no—
75C2×C4×D11—22no—
76C2×C4×D11—41no—
77C2×C4×D11—41no—
78C2×C4×D11—41no—
79C2×C4×D11—41no—
80C2×C4×D11—41no—
81C11×C4⋊C4—41no—
82C11×C22⋊C4—41no—
83C11×C22⋊C4—41no—
84C11×C22⋊C4—41no—
85C22⋊Dic11—22no—
86C22⋊Dic11—41no—
87(C2×D11)⋊C4—22no—
88(C2×D11)⋊C4—22no—
89(C2×D11)⋊C4—22no—
90(C2×D11)⋊C4—41no—
91(C2×D11)⋊C4—41no—
92(C2×D11)⋊C4—41no—
93(C2×D11)⋊C4—41no—
94(C2×D11)⋊C4—41no—
95C4⋊Dic11—41no—
96Dic11⋊C4—41no—
97Dic11⋊C4—41no—
98C4×Dic11—41no—
99#2778—111nomaximal, Sylow
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11C2411yescharacteristic
108C22×D11—21no—
109C22×D11—21no—
110C22×D11—21no—
111C22×D11—21no—
112C22×D11—21no—
113C22×D11—21no—
114C22×D11—21no—
115C22×D11—21no—
116C22×D11—21no—
117C22×D11—21no—
118C22×D11—21no—
119C22×D11—21no—
120C22×D11#4112yes—
121C22×D11#4112yes—
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—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C22⋊D11—44no—
141C22⋊D11—44no—
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×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—21no—
159C2×Dic11#4112yes—
160D44—44no—
161C4×D11—44no—
162C4×D11—44no—
163#401—111no—
164#400—111no—
165#397D1111yescharacteristic, complemented
166#394—111no—
167#394—111no—
168#392—111no—
169#388—111no—
170#388—111no—
171#388—111no—
172#386—111no—
173#386—111no—
174#386—111no—
175#386—111no—
176#385—111no—
177#380—111no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11C2×#4111yescharacteristic
186C22×C11C2×#4111yescharacteristic
187C22×C11C2×#4111yescharacteristic
188C22×C11H(5,𝔽2)11yescharacteristic
189C22×C11H(5,𝔽2)11yescharacteristic
190C22×C11H(5,𝔽2)11yescharacteristic
191C22×C11H(5,𝔽2)11yescharacteristic
192C2×D11—22no—
193C2×D11—22no—
194C2×D11—22no—
195C2×D11—22no—
196C2×D11—22no—
197C2×D11—22no—
198C2×D11—41no—
199C2×D11—41no—
200C2×D11—41no—
201C2×D11—41no—
202C2×D11—41no—
203C2×D11—41no—
204C2×D11—41no—
205C2×D11—41no—
206C4×C11—41no—
207C4×C11—41no—
208C4×C11—41no—
209C4×C11—41no—
210C4×C11—41no—
211C4×C11—41no—
212Dic11—22no—
213Dic11—41no—
214Dic11—41no—
215Dic11—41no—
216Dic11—41no—
217Dic11—41no—
218C22×D4—111no—
219C22×D4—111no—
220C22×D4—111no—
221C23×C4—111no—
222C23×C4—111no—
223C2×C4⋊C4—111no—
224C2×C4⋊C4—111no—
225C2×C4⋊C4—111no—
226C2×C4⋊C4C2×D1111yescharacteristic
227C2×C22⋊C4—111no—
228C2×C22⋊C4—111no—
229C2×C22⋊C4—111no—
230C2×C22⋊C4—111no—
231C2×C22⋊C4—111no—
232C2×C22⋊C4—111no—
233C2×C22⋊C4—111no—
234C2×C22⋊C4—111no—
235C2×C22⋊C4—111no—
236C2×C22⋊C4—111no—
237C2×C22⋊C4C2×D1111yescharacteristic
238C2×C22⋊C4C2×D1111yescharacteristic
239C2×C22⋊C4C2×D1111yescharacteristic
240C2×C42—111no—
241#95—111no—
242#95—111no—
243#95—111no—
244#95—111no—
245#95—111no—
246#95—111no—
247#95—111no—
248#95—111no—
249#95—111no—
250#95C2×D1111yescharacteristic
251#95C2×D1111yescharacteristic
252#95C2×D1111yescharacteristic
253C2×C11—81no—
254C2×C11#53811yescharacteristic
255C2×C11#53811yescharacteristic
256C2×C11#53811yescharacteristic
257C2×C11#55111yescharacteristic
258C2×C11#55311yescharacteristic
259C2×C11#55311yescharacteristic
260C2×C11#56011yescharacteristic
261D11—42no—
262D11—42no—
263C24—111no—
264C24—111no—
265C24C22×D1111yescharacteristic
266C2×D4—222no—
267C2×D4—222no—
268C2×D4—222no—
269C2×D4—222no—
270C2×D4—441no—
271C2×D4—441no—
272C2×D4—441no—
273C2×D4—441no—
274C2×D4—441no—
275C22×C4—111no—
276C22×C4—111no—
277C22×C4—111no—
278C22×C4—111no—
279C22×C4—111no—
280C22×C4—111no—
281C22×C4—222no—
282C22×C4—441no—
283C22×C4—441no—
284C22×C4—441no—
285C22×C4—441no—
286C22×C4—441no—
287C22×C4C22×D1111yescharacteristic
288C22×C4C22×D1111yescharacteristic
289C22×C4C22×D1111yescharacteristic
290C22×C4C22×D1111yescharacteristic
291C22×C4C22×D1111yescharacteristic
292C22×C4C22×D1111yescharacteristic
293C4⋊C4—41no—
294C4⋊C4—441no—
295C4⋊C4—441no—
296C4⋊C4—441no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—222no—
301C22⋊C4—222no—
302C22⋊C4—222no—
303C22⋊C4—222no—
304C22⋊C4—441no—
305C22⋊C4—441no—
306C22⋊C4—441no—
307C22⋊C4—441no—
308C22⋊C4—441no—
309C22⋊C4—441no—
310C42—441no—
311C11#277811yescharacteristic, complemented, Sylow
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—112no—
320C23—112no—
321C23—221no—
322C23—221no—
323C23—221no—
324C23—221no—
325C23—221no—
326C23—221no—
327C23—221no—
328C23—221no—
329C23—221no—
330C23—221no—
331C23—221no—
332C23—221no—
333C23C23×D1111yescharacteristic
334D4—444no—
335D4—444no—
336D4—444no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—112no—
356C2×C4—221no—
357C2×C4—221no—
358C2×C4—221no—
359C2×C4—221no—
360C2×C4—221no—
361C2×C4—221no—
362C2×C4—221no—
363C2×C4—221no—
364C2×C4—221no—
365C2×C4—221no—
366C2×C4—221no—
367C2×C4—221no—
368C2×C4—221no—
369C2×C4—221no—
370C2×C4—221no—
371C2×C4—221no—
372C2×C4—221no—
373C2×C4—444no—
374C2×C4—444no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—222no—
383C22—222no—
384C22—222no—
385C22—222no—
386C22—222no—
387C22—222no—
388C22—441no—
389C22—441no—
390C22—441no—
391C22—441no—
392C22—441no—
393C22—441no—
394C22—441no—
395C22—441no—
396C22#6703711yescharacteristic
397C22#6703711yescharacteristic
398C22#41×D1111yescharacteristic
399C22#41×D1111yescharacteristic
400C22#41×D1111yescharacteristic
401C22#6704211yescharacteristic
402C22#6704211yescharacteristic
403C4—41no—
404C4—41no—
405C4—41no—
406C4—41no—
407C4—41no—
408C4—41no—
409C4—222no—
410C4—441no—
411C4—441no—
412C4—441no—
413C4—441no—
414C4—441no—
415C2—81no—
416C2—442no—
417C2—442no—
418C2#1062315111yescharacteristic
419C2#1062318811yescharacteristic
420C2#1062319011yescharacteristic
421C2#1062319211yescharacteristic
422C2#1062320911yescharacteristic
423C2#1062323511yescharacteristic
424C2#1062324011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#397C2
prime radical#10622573C2
hypercenter#397D11
hypocenterC11#2778
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C11×#397C2semidirect
2. #10622603C2semidirect
3. #10622602C2semidirect
4. #10622574C2semidirect
6. #10622572C2semidirect
7. #10622569C2semidirect
8. #10622569C2semidirect
9. #10622558C2semidirect
10. #10622283C2semidirect
11. #10622280C2semidirect
12. #10622278C2semidirect
13. #10622278C2semidirect
14. C11⋊#401C2semidirect
15. #10622272C2semidirect
165. #397D11semidirect
311. C11#2778semidirect

Maximal subgroups

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

subgroupindex
C11×#3972
#106226032
#106226022
#106225742
#106225732
#106225722
#106225692
#106225582
#106222832
#106222802
#106222782
C11⋊#4012
#106222722
#277811