Finite Group Databasebeta

← C11×#2461 #13065299

Subgroups — C11×#2461 #13065299

Order 1408.

646 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#124C211yesmaximal, characteristic, complemented
2C2×C11×#123C211yesmaximal, characteristic, complemented
3C2×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
4C2×C4×D4×C11C211yesmaximal, characteristic, complemented
5C11×#396C211yesmaximal, characteristic, complemented
6C11×#395C211yesmaximal, characteristic, complemented
7C11×#394C211yesmaximal, characteristic, complemented
8C11×#392C211yesmaximal, characteristic
9C11×#390C211yesmaximal, characteristic, complemented
10C11×#388C211yesmaximal, characteristic, complemented
11C11×#388C211yesmaximal, characteristic, complemented
12C11×#388C211yesmaximal, characteristic, complemented
13C11×#386C211yesmaximal, characteristic, complemented
14C11×#385C211yesmaximal, characteristic, complemented
15C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
16C22×Q8×C11C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C22×D4×C11C2211yescharacteristic
19C22×D4×C11C2211yescharacteristic
20C23×C4×C11C2211yescharacteristic
21C23×C4×C11C2211yescharacteristic
22C11×#124—24no—
23C11×#123—24no—
24C11×C22⋊Q8—24no—
25C4×D4×C11—24no—
26C2×C11×C4⋊C4C2211yescharacteristic
27C2×C11×C4⋊C4C2211yescharacteristic
28C2×C11×C4⋊C4C2211yescharacteristic
29C2×C11×C4⋊C4C2211yescharacteristic
30C2×C11×C4⋊C4C2211yescharacteristic
31C2×C11×C4⋊C4C2211yescharacteristic
32C2×C11×C4⋊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×C11×C22⋊C4C2211yescharacteristic
46C2×C42×C11C2211yescharacteristic
47C2×C42×C11C2211yescharacteristic
48C2×C42×C11C2211yescharacteristic
49C11×#95C2211yescharacteristic
50C11×#95C2211yescharacteristic
51C11×#95C2211yescharacteristic
52C11×#95C2211yescharacteristic
53C11×#95C2211yescharacteristic
54C11×#95C2211yescharacteristic
55C24×C11C2311yescharacteristic
56C24×C11C2311yescharacteristic
57C24×C11C2311yescharacteristic
58C2×Q8×C11—22no—
59C2×Q8×C11—22no—
60C2×Q8×C11—41no—
61C2×D4×C11—22no—
62C2×D4×C11—22no—
63C2×D4×C11—22no—
64C2×D4×C11—22no—
65C2×D4×C11—22no—
66C2×D4×C11—22no—
67C2×D4×C11—22no—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
70C22×C4×C11—22no—
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—22no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11C2311yescharacteristic
77C22×C4×C11C2311yescharacteristic
78C22×C4×C11C2311yescharacteristic
79C22×C4×C11C2311yescharacteristic
80C22×C4×C11C2311yescharacteristic
81C22×C4×C11C2311yescharacteristic
82C22×C4×C11C2311yescharacteristic
83C22×C4×C11C2311yescharacteristic
84C22×C4×C11C2311yescharacteristic
85C22×C4×C11C2311yescharacteristic
86C22×C4×C11C2311yescharacteristic
87C22×C4×C11C2311yescharacteristic
88C11×C4⋊C4—22no—
89C11×C4⋊C4—22no—
90C11×C4⋊C4—22no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—22no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4D414yescomplemented
95C11×C22⋊C4—22no—
96C11×C22⋊C4—22no—
97C11×C22⋊C4—22no—
98C11×C22⋊C4—22no—
99C11×C22⋊C4—22no—
100C11×C22⋊C4—22no—
101C11×C22⋊C4—22no—
102C11×C22⋊C4—22no—
103C11×C22⋊C4—22no—
104C11×C22⋊C4—22no—
105C11×C22⋊C4—22no—
106C11×C22⋊C4—22no—
107C11×C22⋊C4D414yescomplemented
108C42×C11—22no—
109C42×C11—22no—
110C42×C11—22no—
111#2461C1111yesmaximal, characteristic, direct product factor, Sylow
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—21no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11C2×D412yes—
132C23×C11#4112yes—
133C23×C11C2411yescharacteristic
134Q8×C11—44no—
135D4×C11—28no—
136D4×C11—44no—
137D4×C11—44no—
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—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—44no—
168C2×C4×C11—44no—
169C2×C4×C11C2×D412yes—
170C2×C4×C11C2×D412yes—
171C2×C4×C11C2×D412yes—
172C2×C4×C11C2×D412yes—
173C2×C4×C11C2×D412yes—
174C2×C4×C11#4112yes—
175C2×C4×C11#4112yes—
176C2×#124C2×C1111yescharacteristic, complemented
177C2×#123C2×C1111yescharacteristic, complemented
178C2×C22⋊Q8C2×C1111yescharacteristic, complemented
179C2×C4×D4C2×C1111yescharacteristic, complemented
180#396C2×C1111yescharacteristic, complemented
181#395C2×C1111yescharacteristic, complemented
182#394C2×C1111yescharacteristic, complemented
183#392C2×C1111yescharacteristic
184#390C2×C1111yescharacteristic, complemented
185#388C2×C1111yescharacteristic, complemented
186#388C2×C1111yescharacteristic, complemented
187#388C2×C1111yescharacteristic, complemented
188#386C2×C1111yescharacteristic, complemented
189#385C2×C1111yescharacteristic, complemented
190C4×C4⋊C4C2×C1111yescharacteristic, complemented
191C22×C11—22no—
192C22×C11—22no—
193C22×C11—22no—
194C22×C11—22no—
195C22×C11—22no—
196C22×C11—22no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11—41no—
200C22×C11—41no—
201C22×C11—41no—
202C22×C11—41no—
203C22×C11—41no—
204C22×C11—41no—
205C22×C11—41no—
206C22×C11—41no—
207C22×C11—41no—
208C22×C11—41no—
209C22×C11—41no—
210C22×C11—41no—
211C22×C11—41no—
212C22×C11C22×D411yescharacteristic
213C22×C11C22×D411yescharacteristic
214C22×C11C2×#4111yescharacteristic
215C22×C11C2×#4111yescharacteristic
216C22×C11C2×#4111yescharacteristic
217C22×C11H(5,𝔽2)11yescharacteristic
218C22×C112−1+411yescharacteristic
219C4×C11—22no—
220C4×C11—22no—
221C4×C11—22no—
222C4×C11—22no—
223C4×C11—22no—
224C4×C11—22no—
225C4×C11—22no—
226C4×C11—41no—
227C4×C11—41no—
228C4×C11—41no—
229C4×C11—41no—
230C4×C11—41no—
231C22×Q8C22×C1111yescharacteristic
232C22×D4C22×C1111yescharacteristic
233C22×D4C22×C1111yescharacteristic
234C22×D4C22×C1111yescharacteristic
235C23×C4C22×C1111yescharacteristic
236C23×C4C22×C1111yescharacteristic
237#124—24no—
238#123—24no—
239C22⋊Q8—24no—
240C4×D4—24no—
241C2×C4⋊C4C22×C1111yescharacteristic
242C2×C4⋊C4C22×C1111yescharacteristic
243C2×C4⋊C4C22×C1111yescharacteristic
244C2×C4⋊C4C22×C1111yescharacteristic
245C2×C4⋊C4C22×C1111yescharacteristic
246C2×C4⋊C4C22×C1111yescharacteristic
247C2×C4⋊C4C22×C1111yescharacteristic
248C2×C22⋊C4C22×C1111yescharacteristic
249C2×C22⋊C4C22×C1111yescharacteristic
250C2×C22⋊C4C22×C1111yescharacteristic
251C2×C22⋊C4C22×C1111yescharacteristic
252C2×C22⋊C4C22×C1111yescharacteristic
253C2×C22⋊C4C22×C1111yescharacteristic
254C2×C22⋊C4C22×C1111yescharacteristic
255C2×C22⋊C4C22×C1111yescharacteristic
256C2×C22⋊C4C22×C1111yescharacteristic
257C2×C22⋊C4C22×C1111yescharacteristic
258C2×C22⋊C4C22×C1111yescharacteristic
259C2×C22⋊C4C22×C1111yescharacteristic
260C2×C22⋊C4C22×C1111yescharacteristic
261C2×C42C22×C1111yescharacteristic
262C2×C42C22×C1111yescharacteristic
263C2×C42C22×C1111yescharacteristic
264#95C22×C1111yescharacteristic
265#95C22×C1111yescharacteristic
266#95C22×C1111yescharacteristic
267#95C22×C1111yescharacteristic
268#95C22×C1111yescharacteristic
269#95C22×C1111yescharacteristic
270C2×C11—42no—
271C2×C11—42no—
272C2×C11—81no—
273C2×C11#52511yescharacteristic
274C2×C11#53211yescharacteristic
275C2×C11#54211yescharacteristic
276C2×C11D4211yescharacteristic
277C2×C11#54711yescharacteristic
278C2×C11#54811yescharacteristic
279C2×C11#55111yescharacteristic
280C24C23×C1111yescharacteristic
281C24C23×C1111yescharacteristic
282C24C23×C1111yescharacteristic
283C2×Q8—22no—
284C2×Q8—22no—
285C2×Q8—41no—
286C2×D4—22no—
287C2×D4—22no—
288C2×D4—22no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—22no—
292C2×D4—22no—
293C2×D4—41no—
294C2×D4—41no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4C23×C1111yescharacteristic
302C22×C4C23×C1111yescharacteristic
303C22×C4C23×C1111yescharacteristic
304C22×C4C23×C1111yescharacteristic
305C22×C4C23×C1111yescharacteristic
306C22×C4C23×C1111yescharacteristic
307C22×C4C23×C1111yescharacteristic
308C22×C4C23×C1111yescharacteristic
309C22×C4C23×C1111yescharacteristic
310C22×C4C23×C1111yescharacteristic
311C22×C4C23×C1111yescharacteristic
312C22×C4C23×C1111yescharacteristic
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—22no—
318C4⋊C4—41no—
319C4⋊C4D4×C1114yescomplemented
320C22⋊C4—22no—
321C22⋊C4—22no—
322C22⋊C4—22no—
323C22⋊C4—22no—
324C22⋊C4—22no—
325C22⋊C4—22no—
326C22⋊C4—22no—
327C22⋊C4—22no—
328C22⋊C4—22no—
329C22⋊C4—22no—
330C22⋊C4—22no—
331C22⋊C4—22no—
332C22⋊C4D4×C1114yescomplemented
333C42—22no—
334C42—22no—
335C42—22no—
336C11#246111yescharacteristic, direct product factor, Sylow
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23C2×D4×C1112yes—
357C23C11×#4112yes—
358C23C24×C1111yescharacteristic
359Q8—44no—
360D4—28no—
361D4—44no—
362D4—44no—
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—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—44no—
393C2×C4—44no—
394C2×C4C2×D4×C1112yes—
395C2×C4C2×D4×C1112yes—
396C2×C4C2×D4×C1112yes—
397C2×C4C2×D4×C1112yes—
398C2×C4C2×D4×C1112yes—
399C2×C4C11×#4112yes—
400C2×C4C11×#4112yes—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22C22×D4×C1111yescharacteristic
423C22C22×D4×C1111yescharacteristic
424C22C2×C11×#4111yescharacteristic
425C22C2×C11×#4111yescharacteristic
426C22C2×C11×#4111yescharacteristic
427C22C11×H(5,𝔽2)11yescharacteristic
428C22C11×2−1+411yescharacteristic
429C4—22no—
430C4—22no—
431C4—22no—
432C4—22no—
433C4—22no—
434C4—22no—
435C4—22no—
436C4—41no—
437C4—41no—
438C4—41no—
439C4—41no—
440C4—41no—
441C2—42no—
442C2—42no—
443C2—81no—
444C2C11×#52511yescharacteristic
445C2C11×#53211yescharacteristic
446C2C11×#54211yescharacteristic
447C2D42×C1111yescharacteristic
448C2C11×#54711yescharacteristic
449C2C11×#54811yescharacteristic
450C2C11×#55111yescharacteristic
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×#124C2semidirect
2. C2×C11×#123C2semidirect
3. C2×C11×C22⋊Q8C2semidirect
4. C2×C4×D4×C11C2semidirect
5. C11×#396C2semidirect
6. C11×#395C2semidirect
7. C11×#394C2semidirect
9. C11×#390C2semidirect
10. C11×#388C2semidirect
11. C11×#388C2semidirect
12. C11×#388C2semidirect
13. C11×#386C2semidirect
14. C11×#385C2semidirect
15. C4×C11×C4⋊C4C2semidirect
94. C11×C4⋊C4D4semidirect
107. C11×C22⋊C4D4semidirect
111. #2461C11direct (N × H)
176. C2×#124C2×C11semidirect
177. C2×#123C2×C11semidirect
178. C2×C22⋊Q8C2×C11semidirect
179. C2×C4×D4C2×C11semidirect
180. #396C2×C11semidirect
181. #395C2×C11semidirect
182. #394C2×C11semidirect
184. #390C2×C11semidirect
185. #388C2×C11semidirect
186. #388C2×C11semidirect
187. #388C2×C11semidirect
188. #386C2×C11semidirect
189. #385C2×C11semidirect
190. C4×C4⋊C4C2×C11semidirect
319. C4⋊C4D4×C11semidirect
332. C22⋊C4D4×C11semidirect
336. C11#2461direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#1242
C2×C11×#1232
C2×C11×C22⋊Q82
C2×C4×D4×C112
C11×#3962
C11×#3952
C11×#3942
C11×#3922
C11×#3902
C11×#3882
C11×#3862
C11×#3852
C4×C11×C4⋊C42
#246111