Finite Group Databasebeta

← C11×#2705 #13065543

Subgroups — C11×#2705 #13065543

Order 1408.

540 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#126C211yesmaximal, characteristic, complemented
2C2×C11×#123C211yesmaximal, characteristic, complemented
3C11×#399C211yesmaximal, characteristic, complemented
4C11×#396C211yesmaximal, characteristic, complemented
5C11×#396C211yesmaximal, characteristic, complemented
6C11×#394C211yesmaximal, characteristic, complemented
7C11×#394C211yesmaximal, characteristic, complemented
8C11×#392C211yesmaximal, characteristic
9C11×#390C211yesmaximal, characteristic, complemented
10C11×#390C211yesmaximal, characteristic, complemented
11C11×#389C211yesmaximal, characteristic, complemented
12C11×#388C211yesmaximal, characteristic, complemented
13C11×#387C211yesmaximal, characteristic, complemented
14C11×#386C211yesmaximal, characteristic, complemented
15C11×#380C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C22×D4×C11C2211yescharacteristic
19C23×C4×C11C2211yescharacteristic
20C11×#126—24no—
21C11×#123—24no—
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×C4⋊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×C11×C22⋊C4C2211yescharacteristic
41C2×C11×C22⋊C4C2211yescharacteristic
42C2×C11×C22⋊C4C2211yescharacteristic
43C2×C11×C22⋊C4C2211yescharacteristic
44C2×C11×C22⋊C4C2211yescharacteristic
45C2×C42×C11C2211yescharacteristic
46C2×C42×C11C2211yescharacteristic
47C11×#95C2211yescharacteristic
48C11×#95C2211yescharacteristic
49C11×#95C2211yescharacteristic
50C11×#95C2211yescharacteristic
51C11×#95C2211yescharacteristic
52C11×#95C2211yescharacteristic
53C24×C11C2311yescharacteristic
54C24×C11C2311yescharacteristic
55C24×C11C2311yescharacteristic
56C2×D4×C11—22no—
57C2×D4×C11—22no—
58C2×D4×C11—22no—
59C2×D4×C11—22no—
60C2×D4×C11—41no—
61C2×D4×C11—41no—
62C2×D4×C11—41no—
63C2×D4×C11—41no—
64C2×D4×C11—41no—
65C22×C4×C11—22no—
66C22×C4×C11—22no—
67C22×C4×C11—41no—
68C22×C4×C11C2311yescharacteristic
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
80C11×C4⋊C4—22no—
81C11×C4⋊C4—22no—
82C11×C4⋊C4—22no—
83C11×C4⋊C4—22no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4D414yescomplemented
89C11×C22⋊C4—22no—
90C11×C22⋊C4—22no—
91C11×C22⋊C4—22no—
92C11×C22⋊C4—22no—
93C11×C22⋊C4—22no—
94C11×C22⋊C4—22no—
95C11×C22⋊C4—22no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—41no—
103C42×C11—22no—
104C42×C11—41no—
105#2705C1111yesmaximal, characteristic, direct product factor, Sylow
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—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11#4112yes—
127C23×C11C2411yescharacteristic
128D4×C11—44no—
129D4×C11—44no—
130D4×C11—44no—
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—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—44no—
164C2×C4×C11C2×D412yes—
165C2×C4×C11C2×D412yes—
166C2×C4×C11C2×D412yes—
167C2×C4×C11#4112yes—
168C2×#126C2×C1111yescharacteristic, complemented
169C2×#123C2×C1111yescharacteristic, complemented
170#399C2×C1111yescharacteristic, complemented
171#396C2×C1111yescharacteristic, complemented
172#396C2×C1111yescharacteristic, complemented
173#394C2×C1111yescharacteristic, complemented
174#394C2×C1111yescharacteristic, complemented
175#392C2×C1111yescharacteristic
176#390C2×C1111yescharacteristic, complemented
177#390C2×C1111yescharacteristic, complemented
178#389C2×C1111yescharacteristic, complemented
179#388C2×C1111yescharacteristic, complemented
180#387C2×C1111yescharacteristic, complemented
181#386C2×C1111yescharacteristic, complemented
182#380C2×C1111yescharacteristic, complemented
183C22×C11—22no—
184C22×C11—22no—
185C22×C11—22no—
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×C11—41no—
200C22×C11—41no—
201C22×C11—41no—
202C22×C11—41no—
203C22×C11—41no—
204C22×C11C22×D411yescharacteristic
205C22×C11C2×#4111yescharacteristic
206C22×C11C2×#4111yescharacteristic
207C22×C11H(5,𝔽2)11yescharacteristic
208C22×C11H(5,𝔽2)11yescharacteristic
209C22×C11H(5,𝔽2)11yescharacteristic
210C22×C112−1+411yescharacteristic
211C4×C11—22no—
212C4×C11—22no—
213C4×C11—22no—
214C4×C11—22no—
215C4×C11—41no—
216C4×C11—41no—
217C4×C11—41no—
218C4×C11—41no—
219C4×C11—41no—
220C4×C11—41no—
221C4×C11—41no—
222C4×C11—41no—
223C22×D4C22×C1111yescharacteristic
224C22×D4C22×C1111yescharacteristic
225C22×D4C22×C1111yescharacteristic
226C23×C4C22×C1111yescharacteristic
227#126—24no—
228#123—24no—
229C2×C4⋊C4C22×C1111yescharacteristic
230C2×C4⋊C4C22×C1111yescharacteristic
231C2×C4⋊C4C22×C1111yescharacteristic
232C2×C4⋊C4C22×C1111yescharacteristic
233C2×C4⋊C4C22×C1111yescharacteristic
234C2×C4⋊C4C22×C1111yescharacteristic
235C2×C4⋊C4C22×C1111yescharacteristic
236C2×C4⋊C4C22×C1111yescharacteristic
237C2×C4⋊C4C22×C1111yescharacteristic
238C2×C22⋊C4C22×C1111yescharacteristic
239C2×C22⋊C4C22×C1111yescharacteristic
240C2×C22⋊C4C22×C1111yescharacteristic
241C2×C22⋊C4C22×C1111yescharacteristic
242C2×C22⋊C4C22×C1111yescharacteristic
243C2×C22⋊C4C22×C1111yescharacteristic
244C2×C22⋊C4C22×C1111yescharacteristic
245C2×C22⋊C4C22×C1111yescharacteristic
246C2×C22⋊C4C22×C1111yescharacteristic
247C2×C22⋊C4C22×C1111yescharacteristic
248C2×C22⋊C4C22×C1111yescharacteristic
249C2×C22⋊C4C22×C1111yescharacteristic
250C2×C22⋊C4C22×C1111yescharacteristic
251C2×C22⋊C4C22×C1111yescharacteristic
252C2×C42C22×C1111yescharacteristic
253C2×C42C22×C1111yescharacteristic
254#95C22×C1111yescharacteristic
255#95C22×C1111yescharacteristic
256#95C22×C1111yescharacteristic
257#95C22×C1111yescharacteristic
258#95C22×C1111yescharacteristic
259#95C22×C1111yescharacteristic
260C2×C11—42no—
261C2×C11—81no—
262C2×C11—81no—
263C2×C11#53711yescharacteristic
264C2×C11#53911yescharacteristic
265C2×C11#54211yescharacteristic
266C2×C11#54611yescharacteristic
267C2×C11#55011yescharacteristic
268C2×C11#55111yescharacteristic
269C2×C11#56011yescharacteristic
270C24C23×C1111yescharacteristic
271C24C23×C1111yescharacteristic
272C24C23×C1111yescharacteristic
273C2×D4—22no—
274C2×D4—22no—
275C2×D4—22no—
276C2×D4—22no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—41no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—41no—
285C22×C4C23×C1111yescharacteristic
286C22×C4C23×C1111yescharacteristic
287C22×C4C23×C1111yescharacteristic
288C22×C4C23×C1111yescharacteristic
289C22×C4C23×C1111yescharacteristic
290C22×C4C23×C1111yescharacteristic
291C22×C4C23×C1111yescharacteristic
292C22×C4C23×C1111yescharacteristic
293C22×C4C23×C1111yescharacteristic
294C22×C4C23×C1111yescharacteristic
295C22×C4C23×C1111yescharacteristic
296C22×C4C23×C1111yescharacteristic
297C4⋊C4—22no—
298C4⋊C4—22no—
299C4⋊C4—22no—
300C4⋊C4—22no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4D4×C1114yescomplemented
306C22⋊C4—22no—
307C22⋊C4—22no—
308C22⋊C4—22no—
309C22⋊C4—22no—
310C22⋊C4—22no—
311C22⋊C4—22no—
312C22⋊C4—22no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C22⋊C4—41no—
320C42—22no—
321C42—41no—
322C11#270511yescharacteristic, direct product factor, Sylow
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23C11×#4112yes—
344C23C24×C1111yescharacteristic
345D4—44no—
346D4—44no—
347D4—44no—
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—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—44no—
381C2×C4C2×D4×C1112yes—
382C2×C4C2×D4×C1112yes—
383C2×C4C2×D4×C1112yes—
384C2×C4C11×#4112yes—
385C22—22no—
386C22—22no—
387C22—22no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22C22×D4×C1111yescharacteristic
407C22C2×C11×#4111yescharacteristic
408C22C2×C11×#4111yescharacteristic
409C22C11×H(5,𝔽2)11yescharacteristic
410C22C11×H(5,𝔽2)11yescharacteristic
411C22C11×H(5,𝔽2)11yescharacteristic
412C22C11×2−1+411yescharacteristic
413C4—22no—
414C4—22no—
415C4—22no—
416C4—22no—
417C4—41no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—41no—
422C4—41no—
423C4—41no—
424C4—41no—
425C2—42no—
426C2—81no—
427C2—81no—
428C2C11×#53711yescharacteristic
429C2C11×#53911yescharacteristic
430C2C11×#54211yescharacteristic
431C2C11×#54611yescharacteristic
432C2C11×#55011yescharacteristic
433C2C11×#55111yescharacteristic
434C2C11×#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. C2×C11×#126C2semidirect
2. C2×C11×#123C2semidirect
3. C11×#399C2semidirect
4. C11×#396C2semidirect
5. C11×#396C2semidirect
6. C11×#394C2semidirect
7. C11×#394C2semidirect
9. C11×#390C2semidirect
10. C11×#390C2semidirect
11. C11×#389C2semidirect
12. C11×#388C2semidirect
13. C11×#387C2semidirect
14. C11×#386C2semidirect
15. C11×#380C2semidirect
88. C11×C4⋊C4D4semidirect
105. #2705C11direct (N × H)
168. C2×#126C2×C11semidirect
169. C2×#123C2×C11semidirect
170. #399C2×C11semidirect
171. #396C2×C11semidirect
172. #396C2×C11semidirect
173. #394C2×C11semidirect
174. #394C2×C11semidirect
176. #390C2×C11semidirect
177. #390C2×C11semidirect
178. #389C2×C11semidirect
179. #388C2×C11semidirect
180. #387C2×C11semidirect
181. #386C2×C11semidirect
182. #380C2×C11semidirect
305. C4⋊C4D4×C11semidirect
322. C11#2705direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#1262
C2×C11×#1232
C11×#3992
C11×#3962
C11×#3942
C11×#3922
C11×#3902
C11×#3892
C11×#3882
C11×#3872
C11×#3862
C11×#3802
#270511