Finite Group Databasebeta

← #13076549

Subgroups — #13076549

Order 1408.

470 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#388C211yesmaximal, characteristic, complemented
2#10622604C211yesmaximal, characteristic, complemented
3#10622598C211yesmaximal, characteristic, complemented
4#10622574C211yesmaximal, characteristic, complemented
5#10622574C211yesmaximal, characteristic, complemented
6#10622573C211yesmaximal, characteristic
7#10622572C211yesmaximal, characteristic, complemented
8#10622570C211yesmaximal, characteristic, complemented
9#10622564C211yesmaximal, characteristic, complemented
10#10622552C211yesmaximal, characteristic, complemented
11#10622546C211yesmaximal, characteristic, complemented
12#10622287C211yesmaximal, characteristic, complemented
13#10622283C211yesmaximal, characteristic, complemented
14#10622282C211yesmaximal, characteristic, complemented
15#10622282C211yesmaximal, characteristic, complemented
16C22×C22⋊D11C2211yescharacteristic
17C22×C22⋊D11C2211yescharacteristic
18C22×D44C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20C2×C11×C22⋊C4C2211yescharacteristic
21C2×C11×C22⋊C4C2211yescharacteristic
22C2×C11×C22⋊C4C2211yescharacteristic
23C2×C42×C11C2211yescharacteristic
24C2×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊Dic11C2211yescharacteristic
26C2×(C2×D11)⋊C4C2211yescharacteristic
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×(C2×D11)⋊C4C2211yescharacteristic
36C2×C4⋊Dic11C2211yescharacteristic
37C2×C4⋊Dic11C2211yescharacteristic
38C2×C4⋊Dic11C2211yescharacteristic
39C2×Dic11⋊C4C2211yescharacteristic
40C2×Dic11⋊C4C2211yescharacteristic
41C2×C4×Dic11C2211yescharacteristic
42C2×C4×Dic11C2211yescharacteristic
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—41no—
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—41no—
74C2×D44—41no—
75C11×C4⋊C4—22no—
76C11×C22⋊C4—22no—
77C11×C22⋊C4—22no—
78C11×C22⋊C4—41no—
79C42×C11—41no—
80C22⋊Dic11—41no—
81C22⋊Dic11—41no—
82(C2×D11)⋊C4—22no—
83(C2×D11)⋊C4—22no—
84(C2×D11)⋊C4—22no—
85(C2×D11)⋊C4—41no—
86(C2×D11)⋊C4—41no—
87(C2×D11)⋊C4—41no—
88(C2×D11)⋊C4—41no—
89(C2×D11)⋊C4—41no—
90(C2×D11)⋊C4—41no—
91(C2×D11)⋊C4—41no—
92C4⋊Dic11—41no—
93C4⋊Dic11—41no—
94C4⋊Dic11—41no—
95Dic11⋊C4—22no—
96Dic11⋊C4—41no—
97C4×Dic11—41no—
98C4×Dic11—41no—
99#2803—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—21no—
121C22×D11—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—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#4112yes—
139C2×C4×C11#4112yes—
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—
161#397—111no—
162#394—111no—
163#394—111no—
164#394—111no—
165#394—111no—
166#392—111no—
167#390—111no—
168#390—111no—
169#389—111no—
170#388—111no—
171#388—111no—
172#388—111no—
173#388—111no—
174#388D1111yescharacteristic, complemented
175#387—111no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11C2×#4111yescharacteristic
184C22×C11C2×#4111yescharacteristic
185C22×C11C2×#4111yescharacteristic
186C22×C11H(5,𝔽2)11yescharacteristic
187C22×C11H(5,𝔽2)11yescharacteristic
188C22×C11H(5,𝔽2)11yescharacteristic
189C22×C11H(5,𝔽2)11yescharacteristic
190C2×D11—41no—
191C2×D11—41no—
192C2×D11—41no—
193C2×D11—41no—
194C2×D11—41no—
195C2×D11—41no—
196C2×D11—41no—
197C2×D11—41no—
198C2×D11—41no—
199C2×D11—41no—
200C2×D11—41no—
201C2×D11—41no—
202C2×D11—41no—
203C2×D11—41no—
204C4×C11—22no—
205C4×C11—22no—
206C4×C11—41no—
207C4×C11—41no—
208C4×C11—41no—
209C4×C11—41no—
210Dic11—22no—
211Dic11—41no—
212Dic11—41no—
213Dic11—41no—
214Dic11—41no—
215Dic11—41no—
216C22×D4—111no—
217C22×D4—111no—
218C22×D4—111no—
219C2×C4⋊C4—111no—
220C2×C4⋊C4—111no—
221C2×C4⋊C4—111no—
222C2×C4⋊C4—111no—
223C2×C4⋊C4—111no—
224C2×C4⋊C4C2×D1111yescharacteristic
225C2×C22⋊C4—111no—
226C2×C22⋊C4—111no—
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—
241C2×C42—111no—
242C2×C42C2×D1111yescharacteristic
243#95—111no—
244#95—111no—
245#95—111no—
246#95—111no—
247#95—111no—
248#95—111no—
249#95C2×D1111yescharacteristic
250#95C2×D1111yescharacteristic
251C2×C11—81no—
252C2×C11#53811yescharacteristic
253C2×C11#53811yescharacteristic
254C2×C11#54011yescharacteristic
255C2×C11#55311yescharacteristic
256C2×C11#55511yescharacteristic
257C2×C11#55911yescharacteristic
258C2×C11#56011yescharacteristic
259D11—81no—
260D11—81no—
261C24—111no—
262C24—111no—
263C24C22×D1111yescharacteristic
264C2×D4—222no—
265C2×D4—222no—
266C2×D4—441no—
267C2×D4—441no—
268C2×D4—441no—
269C2×D4—441no—
270C2×D4—441no—
271C2×D4—441no—
272C2×D4—441no—
273C22×C4—111no—
274C22×C4—111no—
275C22×C4—111no—
276C22×C4—111no—
277C22×C4—111no—
278C22×C4—111no—
279C22×C4C22×D1111yescharacteristic
280C22×C4C22×D1111yescharacteristic
281C22×C4C22×D1111yescharacteristic
282C22×C4C22×D1111yescharacteristic
283C22×C4C22×D1111yescharacteristic
284C22×C4C22×D1111yescharacteristic
285C4⋊C4—22no—
286C4⋊C4—222no—
287C4⋊C4—441no—
288C4⋊C4—441no—
289C4⋊C4—441no—
290C4⋊C4—441no—
291C22⋊C4—22no—
292C22⋊C4—22no—
293C22⋊C4—41no—
294C22⋊C4—222no—
295C22⋊C4—222no—
296C22⋊C4—222no—
297C22⋊C4—441no—
298C22⋊C4—441no—
299C22⋊C4—441no—
300C22⋊C4—441no—
301C22⋊C4—441no—
302C22⋊C4—441no—
303C22⋊C4—441no—
304C22⋊C4—441no—
305C22⋊C4—441no—
306C42—41no—
307C42—441no—
308C42—441no—
309C11#280311yescharacteristic, complemented, Sylow
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—221no—
318C23—221no—
319C23—221no—
320C23—221no—
321C23—221no—
322C23—221no—
323C23—221no—
324C23—221no—
325C23—221no—
326C23—221no—
327C23—221no—
328C23—221no—
329C23—221no—
330C23—221no—
331C23C23×D1111yescharacteristic
332D4—444no—
333D4—444no—
334D4—444no—
335C2×C4—21no—
336C2×C4—21no—
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—112no—
352C2×C4—221no—
353C2×C4—221no—
354C2×C4—221no—
355C2×C4—221no—
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#433912yes—
370C2×C4#434112yes—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—441no—
379C22—441no—
380C22—441no—
381C22—441no—
382C22—441no—
383C22—441no—
384C22—441no—
385C22—441no—
386C22—441no—
387C22—441no—
388C22—441no—
389C22—441no—
390C22—441no—
391C22—441no—
392C22C2×#433911yescharacteristic
393C22C2×#434111yescharacteristic
394C22#6703711yescharacteristic
395C22#41×D1111yescharacteristic
396C22#6704211yescharacteristic
397C22#6704211yescharacteristic
398C22#6704211yescharacteristic
399C4—22no—
400C4—22no—
401C4—41no—
402C4—41no—
403C4—41no—
404C4—41no—
405C4—222no—
406C4—441no—
407C4—441no—
408C4—441no—
409C4—441no—
410C4—441no—
411C2—81no—
412C2—881no—
413C2—881no—
414C2#1062306311yescharacteristic
415C2#1062309311yescharacteristic
416C2#1062309611yescharacteristic
417C2#1062314811yescharacteristic
418C2#1062318811yescharacteristic
419C2#1062321211yescharacteristic
420C2#1062324211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#388C2
prime radical#10622573C2
hypercenter#388D11
hypocenterC11#2803
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C11×#388C2semidirect
2. #10622604C2semidirect
3. #10622598C2semidirect
4. #10622574C2semidirect
5. #10622574C2semidirect
7. #10622572C2semidirect
8. #10622570C2semidirect
9. #10622564C2semidirect
10. #10622552C2semidirect
11. #10622546C2semidirect
12. #10622287C2semidirect
13. #10622283C2semidirect
14. #10622282C2semidirect
15. #10622282C2semidirect
174. #388D11semidirect
309. C11#2803semidirect

Maximal subgroups

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

subgroupindex
C11×#3882
#106226042
#106225982
#106225742
#106225732
#106225722
#106225702
#106225642
#106225522
#106225462
#106222872
#106222832
#106222822
#280311