Finite Group Databasebeta

← C11×#2780 #13065618

Subgroups — C11×#2780 #13065618

Order 1408.

464 conjugacy classes of subgroups.

The subgroup lattice has 396 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×#398C211yesmaximal, characteristic, complemented
4C11×#396C211yesmaximal, characteristic, complemented
5C11×#396C211yesmaximal, characteristic, complemented
6C11×#396C211yesmaximal, characteristic, complemented
7C11×#390C211yesmaximal, characteristic
8C11×#389C211yesmaximal, characteristic, complemented
9C11×#387C211yesmaximal, characteristic, complemented
10C11×#386C211yesmaximal, characteristic
11C11×#386C211yesmaximal, characteristic
12C11×#385C211yesmaximal, characteristic, complemented
13C11×#385C211yesmaximal, characteristic, complemented
14C11×#385C211yesmaximal, characteristic, complemented
15C11×#380C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C23×C4×C11C2211yescharacteristic
18C23×C4×C11C2211yescharacteristic
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×C4⋊C4C2211yescharacteristic
27C2×C11×C4⋊C4C2211yescharacteristic
28C2×C11×C4⋊C4C2211yescharacteristic
29C2×C11×C4⋊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×C11×C22⋊C4C2211yescharacteristic
39C2×C11×C22⋊C4C2211yescharacteristic
40C2×C42×C11C2211yescharacteristic
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—41no—
54C2×D4×C11—41no—
55C2×D4×C11Q814yes—
56C22×C4×C11—22no—
57C22×C4×C11—41no—
58C22×C4×C11—41no—
59C22×C4×C11—41no—
60C22×C4×C11—41no—
61C22×C4×C11—41no—
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
72C22×C4×C11C2311yescharacteristic
73C22×C4×C11C2311yescharacteristic
74C22×C4×C11C2311yescharacteristic
75C11×C4⋊C4—22no—
76C11×C4⋊C4—22no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
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—
96C42×C11—41no—
97#2780C1111yesmaximal, characteristic, direct product factor, Sylow
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—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11C2×Q812yes—
111C23×C11C2×Q812yes—
112C23×C11C2411yescharacteristic
113D4×C11—44no—
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—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—44no—
151C2×C4×C11—44no—
152C2×C4×C11C2×Q812yes—
153C2×C4×C11#4112yes—
154C2×C4×C11#4112yes—
155#400C2×C1111yescharacteristic, complemented
156#399C2×C1111yescharacteristic, complemented
157#398C2×C1111yescharacteristic, complemented
158#396C2×C1111yescharacteristic, complemented
159#396C2×C1111yescharacteristic, complemented
160#396C2×C1111yescharacteristic, complemented
161#390C2×C1111yescharacteristic
162#389C2×C1111yescharacteristic, complemented
163#387C2×C1111yescharacteristic, complemented
164#386C2×C1111yescharacteristic
165#386C2×C1111yescharacteristic
166#385C2×C1111yescharacteristic, complemented
167#385C2×C1111yescharacteristic, complemented
168#385C2×C1111yescharacteristic, complemented
169#380C2×C1111yescharacteristic, complemented
170C22×C11—22no—
171C22×C11—22no—
172C22×C11—22no—
173C22×C11—22no—
174C22×C11—22no—
175C22×C11—22no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11C22×Q811yescharacteristic
185C22×C11C2×#4111yescharacteristic
186C22×C11C2×#4111yescharacteristic
187C22×C11H(5,𝔽2)11yescharacteristic
188C22×C11H(5,𝔽2)11yescharacteristic
189C22×C11H(5,𝔽2)11yescharacteristic
190C22×C11H(5,𝔽2)11yescharacteristic
191C4×C11—22no—
192C4×C11—22no—
193C4×C11—22no—
194C4×C11—41no—
195C4×C11—41no—
196C4×C11—41no—
197C4×C11—41no—
198C4×C11—41no—
199C4×C11—41no—
200C4×C11—41no—
201C4×C11—41no—
202C4×C11—41no—
203C4×C11—41no—
204C22×D4C22×C1111yescharacteristic
205C23×C4C22×C1111yescharacteristic
206C23×C4C22×C1111yescharacteristic
207C2×C4⋊C4C22×C1111yescharacteristic
208C2×C4⋊C4C22×C1111yescharacteristic
209C2×C4⋊C4C22×C1111yescharacteristic
210C2×C4⋊C4C22×C1111yescharacteristic
211C2×C4⋊C4C22×C1111yescharacteristic
212C2×C4⋊C4C22×C1111yescharacteristic
213C2×C4⋊C4C22×C1111yescharacteristic
214C2×C4⋊C4C22×C1111yescharacteristic
215C2×C4⋊C4C22×C1111yescharacteristic
216C2×C4⋊C4C22×C1111yescharacteristic
217C2×C4⋊C4C22×C1111yescharacteristic
218C2×C22⋊C4C22×C1111yescharacteristic
219C2×C22⋊C4C22×C1111yescharacteristic
220C2×C22⋊C4C22×C1111yescharacteristic
221C2×C22⋊C4C22×C1111yescharacteristic
222C2×C22⋊C4C22×C1111yescharacteristic
223C2×C22⋊C4C22×C1111yescharacteristic
224C2×C22⋊C4C22×C1111yescharacteristic
225C2×C22⋊C4C22×C1111yescharacteristic
226C2×C22⋊C4C22×C1111yescharacteristic
227C2×C22⋊C4C22×C1111yescharacteristic
228C2×C42C22×C1111yescharacteristic
229#95C22×C1111yescharacteristic
230#95C22×C1111yescharacteristic
231#95C22×C1111yescharacteristic
232#95C22×C1111yescharacteristic
233#95C22×C1111yescharacteristic
234#95C22×C1111yescharacteristic
235#95C22×C1111yescharacteristic
236#95C22×C1111yescharacteristic
237#95C22×C1111yescharacteristic
238#95C22×C1111yescharacteristic
239C2×C11—42no—
240C2×C11—42no—
241C2×C11#53811yescharacteristic
242C2×C11#54011yescharacteristic
243C2×C11#54311yescharacteristic
244C2×C11#55311yescharacteristic
245C2×C11#55411yescharacteristic
246C2×C11#55411yescharacteristic
247C2×C11#56011yescharacteristic
248C24C23×C1111yescharacteristic
249C24C23×C1111yescharacteristic
250C2×D4—41no—
251C2×D4—41no—
252C2×D4Q8×C1114yes—
253C22×C4—22no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4C23×C1111yescharacteristic
260C22×C4C23×C1111yescharacteristic
261C22×C4C23×C1111yescharacteristic
262C22×C4C23×C1111yescharacteristic
263C22×C4C23×C1111yescharacteristic
264C22×C4C23×C1111yescharacteristic
265C22×C4C23×C1111yescharacteristic
266C22×C4C23×C1111yescharacteristic
267C22×C4C23×C1111yescharacteristic
268C22×C4C23×C1111yescharacteristic
269C22×C4C23×C1111yescharacteristic
270C22×C4C23×C1111yescharacteristic
271C22×C4C23×C1111yescharacteristic
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C22⋊C4—22no—
284C22⋊C4—22no—
285C22⋊C4—22no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C42—41no—
294C11#278011yescharacteristic, direct product factor, Sylow
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23C2×Q8×C1112yes—
308C23C2×Q8×C1112yes—
309C23C24×C1111yescharacteristic
310D4—44no—
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—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—44no—
348C2×C4—44no—
349C2×C4C2×Q8×C1112yes—
350C2×C4C11×#4112yes—
351C2×C4C11×#4112yes—
352C22—22no—
353C22—22no—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—22no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22C22×Q8×C1111yescharacteristic
367C22C2×C11×#4111yescharacteristic
368C22C2×C11×#4111yescharacteristic
369C22C11×H(5,𝔽2)11yescharacteristic
370C22C11×H(5,𝔽2)11yescharacteristic
371C22C11×H(5,𝔽2)11yescharacteristic
372C22C11×H(5,𝔽2)11yescharacteristic
373C4—22no—
374C4—22no—
375C4—22no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—41no—
386C2—42no—
387C2—42no—
388C2C11×#53811yescharacteristic
389C2C11×#54011yescharacteristic
390C2C11×#54311yescharacteristic
391C2C11×#55311yescharacteristic
392C2C11×#55411yescharacteristic
393C2C11×#55411yescharacteristic
394C2C11×#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×#398C2semidirect
4. C11×#396C2semidirect
5. C11×#396C2semidirect
6. C11×#396C2semidirect
8. C11×#389C2semidirect
9. C11×#387C2semidirect
12. C11×#385C2semidirect
13. C11×#385C2semidirect
14. C11×#385C2semidirect
15. C11×#380C2semidirect
97. #2780C11direct (N × H)
155. #400C2×C11semidirect
156. #399C2×C11semidirect
157. #398C2×C11semidirect
158. #396C2×C11semidirect
159. #396C2×C11semidirect
160. #396C2×C11semidirect
162. #389C2×C11semidirect
163. #387C2×C11semidirect
166. #385C2×C11semidirect
167. #385C2×C11semidirect
168. #385C2×C11semidirect
169. #380C2×C11semidirect
294. C11#2780direct (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×#3982
C11×#3962
C11×#3902
C11×#3892
C11×#3872
C11×#3862
C11×#3852
C11×#3802
#278011