Finite Group Databasebeta

← C11×#2778 #13065616

Subgroups — C11×#2778 #13065616

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×#401C211yesmaximal, characteristic, complemented
2C11×#400C211yesmaximal, characteristic, complemented
3C11×#397C211yesmaximal, characteristic, complemented
4C11×#394C211yesmaximal, characteristic, complemented
5C11×#394C211yesmaximal, characteristic, complemented
6C11×#392C211yesmaximal, characteristic
7C11×#388C211yesmaximal, characteristic, complemented
8C11×#388C211yesmaximal, characteristic, complemented
9C11×#388C211yesmaximal, characteristic, complemented
10C11×#386C211yesmaximal, characteristic, complemented
11C11×#386C211yesmaximal, characteristic, complemented
12C11×#386C211yesmaximal, characteristic, complemented
13C11×#386C211yesmaximal, characteristic, complemented
14C11×#385C211yesmaximal, characteristic, complemented
15C11×#380C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C22×D4×C11C2211yescharacteristic
19C23×C4×C11C2211yescharacteristic
20C23×C4×C11C2211yescharacteristic
21C2×C11×C4⋊C4C2211yescharacteristic
22C2×C11×C4⋊C4C2211yescharacteristic
23C2×C11×C4⋊C4C2211yescharacteristic
24C2×C11×C4⋊C4C2211yescharacteristic
25C2×C11×C22⋊C4C2211yescharacteristic
26C2×C11×C22⋊C4C2211yescharacteristic
27C2×C11×C22⋊C4C2211yescharacteristic
28C2×C11×C22⋊C4C2211yescharacteristic
29C2×C11×C22⋊C4C2211yescharacteristic
30C2×C11×C22⋊C4C2211yescharacteristic
31C2×C11×C22⋊C4C2211yescharacteristic
32C2×C11×C22⋊C4C2211yescharacteristic
33C2×C11×C22⋊C4C2211yescharacteristic
34C2×C11×C22⋊C4C2211yescharacteristic
35C2×C11×C22⋊C4C2211yescharacteristic
36C2×C11×C22⋊C4C2211yescharacteristic
37C2×C11×C22⋊C4C2211yescharacteristic
38C2×C42×C11C2211yescharacteristic
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
52C24×C11C2311yescharacteristic
53C24×C11C2311yescharacteristic
54C2×D4×C11—22no—
55C2×D4×C11—22no—
56C2×D4×C11—22no—
57C2×D4×C11—22no—
58C2×D4×C11—41no—
59C2×D4×C11—41no—
60C2×D4×C11—41no—
61C2×D4×C11—41no—
62C2×D4×C11—41no—
63C22×C4×C11—22no—
64C22×C4×C11—41no—
65C22×C4×C11—41no—
66C22×C4×C11—41no—
67C22×C4×C11—41no—
68C22×C4×C11—41no—
69C22×C4×C11C2311yescharacteristic
70C22×C4×C11C2311yescharacteristic
71C22×C4×C11C2311yescharacteristic
72C22×C4×C11C2311yescharacteristic
73C22×C4×C11C2311yescharacteristic
74C22×C4×C11C2311yescharacteristic
75C22×C4×C11C2311yescharacteristic
76C22×C4×C11C2311yescharacteristic
77C22×C4×C11C2311yescharacteristic
78C22×C4×C11C2311yescharacteristic
79C22×C4×C11C2311yescharacteristic
80C22×C4×C11C2311yescharacteristic
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C22⋊C4—22no—
86C11×C22⋊C4—22no—
87C11×C22⋊C4—22no—
88C11×C22⋊C4—22no—
89C11×C22⋊C4—41no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—41no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—41no—
98C42×C11—41no—
99#2778C1111yesmaximal, characteristic, direct product factor, Sylow
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—21no—
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11#4112yes—
120C23×C11#4112yes—
121C23×C11C2411yescharacteristic
122D4×C11—44no—
123D4×C11—44no—
124D4×C11—44no—
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—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—44no—
161C2×C4×C11—44no—
162C2×C4×C11#4112yes—
163#401C2×C1111yescharacteristic, complemented
164#400C2×C1111yescharacteristic, complemented
165#397C2×C1111yescharacteristic, complemented
166#394C2×C1111yescharacteristic, complemented
167#394C2×C1111yescharacteristic, complemented
168#392C2×C1111yescharacteristic
169#388C2×C1111yescharacteristic, complemented
170#388C2×C1111yescharacteristic, complemented
171#388C2×C1111yescharacteristic, complemented
172#386C2×C1111yescharacteristic, complemented
173#386C2×C1111yescharacteristic, complemented
174#386C2×C1111yescharacteristic, complemented
175#386C2×C1111yescharacteristic, complemented
176#385C2×C1111yescharacteristic, complemented
177#380C2×C1111yescharacteristic, complemented
178C22×C11—22no—
179C22×C11—22no—
180C22×C11—22no—
181C22×C11—22no—
182C22×C11—22no—
183C22×C11—22no—
184C22×C11—41no—
185C22×C11—41no—
186C22×C11—41no—
187C22×C11—41no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11—41no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11C2×#4111yescharacteristic
200C22×C11C2×#4111yescharacteristic
201C22×C11C2×#4111yescharacteristic
202C22×C11H(5,𝔽2)11yescharacteristic
203C22×C11H(5,𝔽2)11yescharacteristic
204C22×C11H(5,𝔽2)11yescharacteristic
205C22×C11H(5,𝔽2)11yescharacteristic
206C4×C11—22no—
207C4×C11—41no—
208C4×C11—41no—
209C4×C11—41no—
210C4×C11—41no—
211C4×C11—41no—
212C4×C11—41no—
213C4×C11—41no—
214C4×C11—41no—
215C4×C11—41no—
216C4×C11—41no—
217C4×C11—41no—
218C22×D4C22×C1111yescharacteristic
219C22×D4C22×C1111yescharacteristic
220C22×D4C22×C1111yescharacteristic
221C23×C4C22×C1111yescharacteristic
222C23×C4C22×C1111yescharacteristic
223C2×C4⋊C4C22×C1111yescharacteristic
224C2×C4⋊C4C22×C1111yescharacteristic
225C2×C4⋊C4C22×C1111yescharacteristic
226C2×C4⋊C4C22×C1111yescharacteristic
227C2×C22⋊C4C22×C1111yescharacteristic
228C2×C22⋊C4C22×C1111yescharacteristic
229C2×C22⋊C4C22×C1111yescharacteristic
230C2×C22⋊C4C22×C1111yescharacteristic
231C2×C22⋊C4C22×C1111yescharacteristic
232C2×C22⋊C4C22×C1111yescharacteristic
233C2×C22⋊C4C22×C1111yescharacteristic
234C2×C22⋊C4C22×C1111yescharacteristic
235C2×C22⋊C4C22×C1111yescharacteristic
236C2×C22⋊C4C22×C1111yescharacteristic
237C2×C22⋊C4C22×C1111yescharacteristic
238C2×C22⋊C4C22×C1111yescharacteristic
239C2×C22⋊C4C22×C1111yescharacteristic
240C2×C42C22×C1111yescharacteristic
241#95C22×C1111yescharacteristic
242#95C22×C1111yescharacteristic
243#95C22×C1111yescharacteristic
244#95C22×C1111yescharacteristic
245#95C22×C1111yescharacteristic
246#95C22×C1111yescharacteristic
247#95C22×C1111yescharacteristic
248#95C22×C1111yescharacteristic
249#95C22×C1111yescharacteristic
250#95C22×C1111yescharacteristic
251#95C22×C1111yescharacteristic
252#95C22×C1111yescharacteristic
253C2×C11—42no—
254C2×C11—42no—
255C2×C11—81no—
256C2×C11#53811yescharacteristic
257C2×C11#53811yescharacteristic
258C2×C11#53811yescharacteristic
259C2×C11#55111yescharacteristic
260C2×C11#55311yescharacteristic
261C2×C11#55311yescharacteristic
262C2×C11#56011yescharacteristic
263C24C23×C1111yescharacteristic
264C24C23×C1111yescharacteristic
265C24C23×C1111yescharacteristic
266C2×D4—22no—
267C2×D4—22no—
268C2×D4—22no—
269C2×D4—22no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C22×C4—22no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4C23×C1111yescharacteristic
282C22×C4C23×C1111yescharacteristic
283C22×C4C23×C1111yescharacteristic
284C22×C4C23×C1111yescharacteristic
285C22×C4C23×C1111yescharacteristic
286C22×C4C23×C1111yescharacteristic
287C22×C4C23×C1111yescharacteristic
288C22×C4C23×C1111yescharacteristic
289C22×C4C23×C1111yescharacteristic
290C22×C4C23×C1111yescharacteristic
291C22×C4C23×C1111yescharacteristic
292C22×C4C23×C1111yescharacteristic
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C22⋊C4—22no—
298C22⋊C4—22no—
299C22⋊C4—22no—
300C22⋊C4—22no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C42—41no—
311C11#277811yescharacteristic, direct product factor, Sylow
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23C11×#4112yes—
332C23C11×#4112yes—
333C23C24×C1111yescharacteristic
334D4—44no—
335D4—44no—
336D4—44no—
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—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—44no—
373C2×C4—44no—
374C2×C4C11×#4112yes—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—22no—
379C22—22no—
380C22—22no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22C2×C11×#4111yescharacteristic
397C22C2×C11×#4111yescharacteristic
398C22C2×C11×#4111yescharacteristic
399C22C11×H(5,𝔽2)11yescharacteristic
400C22C11×H(5,𝔽2)11yescharacteristic
401C22C11×H(5,𝔽2)11yescharacteristic
402C22C11×H(5,𝔽2)11yescharacteristic
403C4—22no—
404C4—41no—
405C4—41no—
406C4—41no—
407C4—41no—
408C4—41no—
409C4—41no—
410C4—41no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—41no—
415C2—42no—
416C2—42no—
417C2—81no—
418C2C11×#53811yescharacteristic
419C2C11×#53811yescharacteristic
420C2C11×#53811yescharacteristic
421C2C11×#55111yescharacteristic
422C2C11×#55311yescharacteristic
423C2C11×#55311yescharacteristic
424C2C11×#56011yescharacteristic
subgroupG/H
center, socleC23×C11C24
commutator, Frattini, cosocleC23C24×C11
prime radicalC11×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#401C2semidirect
2. C11×#400C2semidirect
3. C11×#397C2semidirect
4. C11×#394C2semidirect
5. C11×#394C2semidirect
7. C11×#388C2semidirect
8. C11×#388C2semidirect
9. C11×#388C2semidirect
10. C11×#386C2semidirect
11. C11×#386C2semidirect
12. C11×#386C2semidirect
13. C11×#386C2semidirect
14. C11×#385C2semidirect
15. C11×#380C2semidirect
99. #2778C11direct (N × H)
163. #401C2×C11semidirect
164. #400C2×C11semidirect
165. #397C2×C11semidirect
166. #394C2×C11semidirect
167. #394C2×C11semidirect
169. #388C2×C11semidirect
170. #388C2×C11semidirect
171. #388C2×C11semidirect
172. #386C2×C11semidirect
173. #386C2×C11semidirect
174. #386C2×C11semidirect
175. #386C2×C11semidirect
176. #385C2×C11semidirect
177. #380C2×C11semidirect
311. C11#2778direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#4012
C11×#4002
C11×#3972
C11×#3942
C11×#3922
C11×#3882
C11×#3862
C11×#3852
C11×#3802
#277811