Finite Group Databasebeta

← C11×#2796 #13065634

Subgroups — C11×#2796 #13065634

Order 1408.

434 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#400C211yesmaximal, characteristic, complemented
2C11×#399C211yesmaximal, characteristic, complemented
3C11×#397C211yesmaximal, characteristic, complemented
4C11×#397C211yesmaximal, characteristic, complemented
5C11×#397C211yesmaximal, characteristic, complemented
6C11×#394C211yesmaximal, characteristic
7C11×#390C211yesmaximal, characteristic
8C11×#389C211yesmaximal, characteristic, complemented
9C11×#388C211yesmaximal, characteristic, complemented
10C11×#388C211yesmaximal, characteristic, complemented
11C11×#387C211yesmaximal, characteristic, complemented
12C11×#387C211yesmaximal, characteristic, complemented
13C11×#386C211yesmaximal, characteristic
14C11×#385C211yesmaximal, characteristic, complemented
15C11×#385C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C23×C4×C11C2211yescharacteristic
18C2×C11×C4⋊C4C2211yescharacteristic
19C2×C11×C4⋊C4C2211yescharacteristic
20C2×C11×C4⋊C4C2211yescharacteristic
21C2×C11×C4⋊C4C2211yescharacteristic
22C2×C11×C4⋊C4C2211yescharacteristic
23C2×C11×C4⋊C4C2211yescharacteristic
24C2×C11×C4⋊C4C2211yescharacteristic
25C2×C11×C4⋊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×C42×C11C2211yescharacteristic
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
53C2×D4×C11—22no—
54C2×D4×C11—22no—
55C2×D4×C11—41no—
56C22×C4×C11—41no—
57C22×C4×C11—41no—
58C22×C4×C11—41no—
59C22×C4×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C22×C4×C11C2311yescharacteristic
68C22×C4×C11C2311yescharacteristic
69C22×C4×C11C2311yescharacteristic
70C22×C4×C11C2311yescharacteristic
71C22×C4×C11C2311yescharacteristic
72C11×C4⋊C4—22no—
73C11×C4⋊C4—22no—
74C11×C4⋊C4—22no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C22⋊C4—22no—
81C11×C22⋊C4—22no—
82C11×C22⋊C4—22no—
83C11×C22⋊C4—22no—
84C11×C22⋊C4—41no—
85C11×C22⋊C4—41no—
86C11×C22⋊C4—41no—
87C11×C22⋊C4—41no—
88C11×C22⋊C4—41no—
89C11×C22⋊C4—41no—
90C11×C22⋊C4—41no—
91C42×C11—41no—
92C42×C11—41no—
93#2796C1111yesmaximal, characteristic, direct product factor, Sylow
94C23×C11—21no—
95C23×C11—21no—
96C23×C11—21no—
97C23×C11—21no—
98C23×C11—21no—
99C23×C11—21no—
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11#4112yes—
108C23×C11C2411yescharacteristic
109D4×C11—44no—
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—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—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—44no—
148C2×C4×C11#4112yes—
149C2×C4×C11#4112yes—
150#400C2×C1111yescharacteristic, complemented
151#399C2×C1111yescharacteristic, complemented
152#397C2×C1111yescharacteristic, complemented
153#397C2×C1111yescharacteristic, complemented
154#397C2×C1111yescharacteristic, complemented
155#394C2×C1111yescharacteristic
156#390C2×C1111yescharacteristic
157#389C2×C1111yescharacteristic, complemented
158#388C2×C1111yescharacteristic, complemented
159#388C2×C1111yescharacteristic, complemented
160#387C2×C1111yescharacteristic, complemented
161#387C2×C1111yescharacteristic, complemented
162#386C2×C1111yescharacteristic
163#385C2×C1111yescharacteristic, complemented
164#385C2×C1111yescharacteristic, complemented
165C22×C11—22no—
166C22×C11—22no—
167C22×C11—22no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11—41no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11C2×#4111yescharacteristic
180C22×C11C2×#4111yescharacteristic
181C22×C11C2×#4111yescharacteristic
182C22×C11H(5,𝔽2)11yescharacteristic
183C22×C11H(5,𝔽2)11yescharacteristic
184C22×C11H(5,𝔽2)11yescharacteristic
185C22×C112−1+411yescharacteristic
186C4×C11—22no—
187C4×C11—22no—
188C4×C11—41no—
189C4×C11—41no—
190C4×C11—41no—
191C4×C11—41no—
192C4×C11—41no—
193C4×C11—41no—
194C4×C11—41no—
195C4×C11—41no—
196C4×C11—41no—
197C4×C11—41no—
198C4×C11—41no—
199C22×D4C22×C1111yescharacteristic
200C23×C4C22×C1111yescharacteristic
201C2×C4⋊C4C22×C1111yescharacteristic
202C2×C4⋊C4C22×C1111yescharacteristic
203C2×C4⋊C4C22×C1111yescharacteristic
204C2×C4⋊C4C22×C1111yescharacteristic
205C2×C4⋊C4C22×C1111yescharacteristic
206C2×C4⋊C4C22×C1111yescharacteristic
207C2×C4⋊C4C22×C1111yescharacteristic
208C2×C4⋊C4C22×C1111yescharacteristic
209C2×C22⋊C4C22×C1111yescharacteristic
210C2×C22⋊C4C22×C1111yescharacteristic
211C2×C22⋊C4C22×C1111yescharacteristic
212C2×C22⋊C4C22×C1111yescharacteristic
213C2×C22⋊C4C22×C1111yescharacteristic
214C2×C22⋊C4C22×C1111yescharacteristic
215C2×C22⋊C4C22×C1111yescharacteristic
216C2×C22⋊C4C22×C1111yescharacteristic
217C2×C22⋊C4C22×C1111yescharacteristic
218C2×C22⋊C4C22×C1111yescharacteristic
219C2×C22⋊C4C22×C1111yescharacteristic
220C2×C42C22×C1111yescharacteristic
221C2×C42C22×C1111yescharacteristic
222#95C22×C1111yescharacteristic
223#95C22×C1111yescharacteristic
224#95C22×C1111yescharacteristic
225#95C22×C1111yescharacteristic
226#95C22×C1111yescharacteristic
227#95C22×C1111yescharacteristic
228#95C22×C1111yescharacteristic
229#95C22×C1111yescharacteristic
230#95C22×C1111yescharacteristic
231#95C22×C1111yescharacteristic
232#95C22×C1111yescharacteristic
233#95C22×C1111yescharacteristic
234C2×C11—42no—
235C2×C11—81no—
236C2×C11#53911yescharacteristic
237C2×C11#53911yescharacteristic
238C2×C11#54211yescharacteristic
239C2×C11#55111yescharacteristic
240C2×C11#55311yescharacteristic
241C2×C11#55911yescharacteristic
242C2×C11#56011yescharacteristic
243C24C23×C1111yescharacteristic
244C24C23×C1111yescharacteristic
245C2×D4—22no—
246C2×D4—22no—
247C2×D4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4C23×C1111yescharacteristic
252C22×C4C23×C1111yescharacteristic
253C22×C4C23×C1111yescharacteristic
254C22×C4C23×C1111yescharacteristic
255C22×C4C23×C1111yescharacteristic
256C22×C4C23×C1111yescharacteristic
257C22×C4C23×C1111yescharacteristic
258C22×C4C23×C1111yescharacteristic
259C22×C4C23×C1111yescharacteristic
260C22×C4C23×C1111yescharacteristic
261C22×C4C23×C1111yescharacteristic
262C22×C4C23×C1111yescharacteristic
263C22×C4C23×C1111yescharacteristic
264C4⋊C4—22no—
265C4⋊C4—22no—
266C4⋊C4—22no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C22⋊C4—22no—
273C22⋊C4—22no—
274C22⋊C4—22no—
275C22⋊C4—22no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C42—41no—
284C42—41no—
285C11#279611yescharacteristic, direct product factor, Sylow
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23C11×#4112yes—
300C23C24×C1111yescharacteristic
301D4—44no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
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—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—44no—
340C2×C4C11×#4112yes—
341C2×C4C11×#4112yes—
342C22—22no—
343C22—22no—
344C22—22no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22C2×C11×#4111yescharacteristic
357C22C2×C11×#4111yescharacteristic
358C22C2×C11×#4111yescharacteristic
359C22C11×H(5,𝔽2)11yescharacteristic
360C22C11×H(5,𝔽2)11yescharacteristic
361C22C11×H(5,𝔽2)11yescharacteristic
362C22C11×2−1+411yescharacteristic
363C4—22no—
364C4—22no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—41no—
376C2—42no—
377C2—81no—
378C2C11×#53911yescharacteristic
379C2C11×#53911yescharacteristic
380C2C11×#54211yescharacteristic
381C2C11×#55111yescharacteristic
382C2C11×#55311yescharacteristic
383C2C11×#55911yescharacteristic
384C2C11×#56011yescharacteristic
subgroupG/H
center, socleC23×C11C24
commutator, Frattini, cosocleC23C24×C11
prime radicalC22×D4×C11C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#400C2semidirect
2. C11×#399C2semidirect
3. C11×#397C2semidirect
4. C11×#397C2semidirect
5. C11×#397C2semidirect
8. C11×#389C2semidirect
9. C11×#388C2semidirect
10. C11×#388C2semidirect
11. C11×#387C2semidirect
12. C11×#387C2semidirect
14. C11×#385C2semidirect
15. C11×#385C2semidirect
93. #2796C11direct (N × H)
150. #400C2×C11semidirect
151. #399C2×C11semidirect
152. #397C2×C11semidirect
153. #397C2×C11semidirect
154. #397C2×C11semidirect
157. #389C2×C11semidirect
158. #388C2×C11semidirect
159. #388C2×C11semidirect
160. #387C2×C11semidirect
161. #387C2×C11semidirect
163. #385C2×C11semidirect
164. #385C2×C11semidirect
285. C11#2796direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#4002
C11×#3992
C11×#3972
C11×#3942
C11×#3902
C11×#3892
C11×#3882
C11×#3872
C11×#3862
C11×#3852
#279611