Finite Group Databasebeta

← C11×#33745 #14610938

Subgroups — C11×#33745 #14610938

Order 2816.

496 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3177C211yesmaximal, characteristic, complemented
2C11×#3175C211yesmaximal, characteristic
3C11×#2255C211yesmaximal, characteristic, complemented
4C11×#2251C211yesmaximal, characteristic, complemented
5C11×#2242C211yesmaximal, characteristic, complemented
6C11×#2241C211yesmaximal, characteristic, complemented
7C11×#2220C211yesmaximal, characteristic
8C11×#2219C211yesmaximal, characteristic, complemented
9C11×#2217C211yesmaximal, characteristic
10C11×#2216C211yesmaximal, characteristic, complemented
11C11×#2176C211yesmaximal, characteristic, complemented
12C11×#2175C211yesmaximal, characteristic, complemented
13C4×C11×Q32C211yesmaximal, characteristic, complemented
14C4×C11×SD32C211yesmaximal, characteristic, complemented
15C11×#2108C211yesmaximal, characteristic, complemented
16C11×#542—21no—
17C11×#541—21no—
18C2×C11×Q32C2211yescharacteristic
19C2×C11×Q32C2211yescharacteristic
20C2×C11×SD32C2211yescharacteristic
21C2×C11×SD32C2211yescharacteristic
22C2×C11×M32C2211yescharacteristic
23C22×C11×C16C2211yescharacteristic
24C11×#500C2211yescharacteristic
25C11×#499C2211yescharacteristic
26C11×#495C2211yescharacteristic
27C11×#494C2211yescharacteristic
28C11×#491—21no—
29C11×#489—21no—
30C11×#470—21no—
31C11×#468—21no—
32C11×#467C2211yescharacteristic
33C11×#467C2211yescharacteristic
34C11×#467C2211yescharacteristic
35C11×#466C2211yescharacteristic
36C11×#441—21no—
37C11×#440—21no—
38C4×C11×Q16C2211yescharacteristic
39C4×C11×Q16C2211yescharacteristic
40C4×C11×Q16C2211yescharacteristic
41C4×C11×D8C2211yescharacteristic
42C11×#405C2211yescharacteristic
43C11×#367C2211yescharacteristic
44C11×#367C2211yescharacteristic
45C11×#366C2211yescharacteristic
46C11×#366C2211yescharacteristic
47C11×#358C2211yescharacteristic
48C11×#358C2211yescharacteristic
49C11×#358C2211yescharacteristic
50C11×#358C2211yescharacteristic
51C11×#358C2211yescharacteristic
52C11×#358C2211yescharacteristic
53C11×#357C2211yescharacteristic
54C11×#357C2211yescharacteristic
55C11×#346C2211yescharacteristic
56C11×#346C2211yescharacteristic
57C4×C11×C16C2211yescharacteristic
58C4×C11×C16C2211yescharacteristic
59C2×C11×Q16—21no—
60C2×C11×Q16C2311yescharacteristic
61C2×C11×Q16C2311yescharacteristic
62C2×C11×Q16C2311yescharacteristic
63C2×C11×SD16—21no—
64C2×C11×D8C2311yescharacteristic
65C2×C11×M16D411yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×C4⋊Q8—21no—
68C11×C4⋊Q8—21no—
69C11×#126—41no—
70C11×#126—41no—
71C11×#126—41no—
72C11×#125—21no—
73C11×#125—41no—
74C11×#125—41no—
75C11×#124—21no—
76C11×#124—41no—
77C11×#123—41no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—21no—
81C11×C22⋊Q8—41no—
82C11×#121—21no—
83C4×Q8×C11—21no—
84C4×Q8×C11—21no—
85C4×Q8×C11—21no—
86C4×D4×C11—21no—
87C11×#117D411yescharacteristic
88C11×Q32—22no—
89C11×Q32—22no—
90C11×SD32—22no—
91C11×SD32—22no—
92C11×M32—22no—
93C2×C11×C16—22no—
94C2×C11×C16C2311yescharacteristic
95C2×C11×C16C2311yescharacteristic
96C2×C11×C16C2311yescharacteristic
97C2×C11×C16C2311yescharacteristic
98C11×#107—21no—
99C11×#107C2311yescharacteristic
100C11×#107C2311yescharacteristic
101C11×#107C2311yescharacteristic
102C11×#107C2311yescharacteristic
103C11×#106—21no—
104C11×#103—21no—
105C11×#103—21no—
106C11×#103—21no—
107C11×#103—21no—
108C11×#103—21no—
109C11×#103—21no—
110C11×#102—21no—
111C11×#102—21no—
112C11×#97D411yescharacteristic
113C11×#97D411yescharacteristic
114C4×C8×C11C2311yescharacteristic
115C4×C8×C11C2311yescharacteristic
116#33745C1111yesmaximal, characteristic, direct product factor, Sylow
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×Q8×C11—21no—
120C2×Q8×C11—41no—
121C2×D4×C11—21no—
122C2×D4×C11—41no—
123C22×C4×C11—41no—
124C22×C4×C11C2×D411yescharacteristic
125C11×Q16—21no—
126C11×Q16—21no—
127C11×Q16—21no—
128C11×Q16—21no—
129C11×Q16—21no—
130C11×Q16—21no—
131C11×Q16—42no—
132C11×SD16—42no—
133C11×D8—21no—
134C11×D8—21no—
135C11×M16—22no—
136C2×C8×C11—21no—
137C2×C8×C11—21no—
138C2×C8×C11C2×D411yescharacteristic
139C2×C8×C11C2×D411yescharacteristic
140C2×C8×C11C2×D411yescharacteristic
141C2×C8×C11C2411yescharacteristic
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—41no—
147C11×C4⋊C4—41no—
148C11×C4⋊C4—41no—
149C11×C4⋊C4—41no—
150C11×C4⋊C4—41no—
151C11×C4⋊C4—41no—
152C11×C4⋊C4—41no—
153C11×C4⋊C4—41no—
154C11×C4⋊C4—41no—
155C11×C4⋊C4—41no—
156C11×C4⋊C4—41no—
157C11×C4⋊C4D811yescharacteristic
158C11×C4⋊C4D811yescharacteristic
159C11×C22⋊C4—41no—
160C11×C22⋊C4—41no—
161C11×C22⋊C4—41no—
162C11×C22⋊C4—41no—
163C11×C22⋊C4—41no—
164C11×C22⋊C4—41no—
165C11×C22⋊C4—41no—
166C11×C22⋊C4D811yescharacteristic
167C11×C22⋊C4D811yescharacteristic
168C42×C11—41no—
169C42×C11—41no—
170C42×C11—41no—
171C42×C11C2×D411yescharacteristic
172C42×C11C2×D411yescharacteristic
173C11×C16—21no—
174C11×C16—21no—
175C11×C16#4112yes—
176C11×C16#4112yes—
177#3177C2×C1111yescharacteristic, complemented
178#3175C2×C1111yescharacteristic
179#2255C2×C1111yescharacteristic, complemented
180#2251C2×C1111yescharacteristic, complemented
181#2242C2×C1111yescharacteristic, complemented
182#2241C2×C1111yescharacteristic, complemented
183#2220C2×C1111yescharacteristic
184#2219C2×C1111yescharacteristic, complemented
185#2217C2×C1111yescharacteristic
186#2216C2×C1111yescharacteristic, complemented
187#2176C2×C1111yescharacteristic, complemented
188#2175C2×C1111yescharacteristic, complemented
189C4×Q32C2×C1111yescharacteristic, complemented
190C4×SD32C2×C1111yescharacteristic, complemented
191#2108C2×C1111yescharacteristic, complemented
192C23×C11—41no—
193C23×C11C2×D811yescharacteristic
194Q8×C11—41no—
195Q8×C11—41no—
196Q8×C11—41no—
197Q8×C11—41no—
198Q8×C11—41no—
199Q8×C11—41no—
200Q8×C11—161no—
201D4×C11—41no—
202D4×C11—41no—
203D4×C11—161no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—161no—
214C2×C4×C11C2×D811yescharacteristic
215C2×C4×C11C2×D811yescharacteristic
216C2×C4×C11C2×D811yescharacteristic
217C2×C4×C11C2×D811yescharacteristic
218C2×C4×C11C2×D811yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C8×C11—21no—
221C8×C11—21no—
222C8×C11#13512yes—
223C8×C11C2×#4111yescharacteristic
224C8×C11C2×#4111yescharacteristic
225#542—21no—
226#541—21no—
227C2×Q32C22×C1111yescharacteristic
228C2×Q32C22×C1111yescharacteristic
229C2×SD32C22×C1111yescharacteristic
230C2×SD32C22×C1111yescharacteristic
231C2×M32C22×C1111yescharacteristic
232C22×C16C22×C1111yescharacteristic
233#500C22×C1111yescharacteristic
234#499C22×C1111yescharacteristic
235#495C22×C1111yescharacteristic
236#494C22×C1111yescharacteristic
237#491—21no—
238#489—21no—
239#470—21no—
240#468—21no—
241#467C22×C1111yescharacteristic
242#467C22×C1111yescharacteristic
243#467C22×C1111yescharacteristic
244#466C22×C1111yescharacteristic
245#441—21no—
246#440—21no—
247C4×Q16C22×C1111yescharacteristic
248C4×Q16C22×C1111yescharacteristic
249C4×Q16C22×C1111yescharacteristic
250C4×D8C22×C1111yescharacteristic
251#405C22×C1111yescharacteristic
252#367C22×C1111yescharacteristic
253#367C22×C1111yescharacteristic
254#366C22×C1111yescharacteristic
255#366C22×C1111yescharacteristic
256#358C22×C1111yescharacteristic
257#358C22×C1111yescharacteristic
258#358C22×C1111yescharacteristic
259#358C22×C1111yescharacteristic
260#358C22×C1111yescharacteristic
261#358C22×C1111yescharacteristic
262#357C22×C1111yescharacteristic
263#357C22×C1111yescharacteristic
264#346C22×C1111yescharacteristic
265#346C22×C1111yescharacteristic
266C4×C16C22×C1111yescharacteristic
267C4×C16C22×C1111yescharacteristic
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—21no—
271C22×C11—81no—
272C22×C11—81no—
273C22×C11—81no—
274C22×C11C22×D811yescharacteristic
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—81no—
281C4×C11—81no—
282C4×C11—81no—
283C4×C11—81no—
284C4×C11—81no—
285C4×C11—81no—
286C4×C11—81no—
287C4×C11#53211yescharacteristic
288C4×C11C2×#13511yescharacteristic
289C2×Q16—21no—
290C2×Q16C23×C1111yescharacteristic
291C2×Q16C23×C1111yescharacteristic
292C2×Q16C23×C1111yescharacteristic
293C2×SD16—21no—
294C2×D8C23×C1111yescharacteristic
295C2×M16D4×C1111yescharacteristic
296C22×C8C23×C1111yescharacteristic
297C4⋊Q8—21no—
298C4⋊Q8—21no—
299#126—41no—
300#126—41no—
301#126—41no—
302#125—21no—
303#125—41no—
304#125—41no—
305#124—21no—
306#124—41no—
307#123—41no—
308C22⋊Q8—21no—
309C22⋊Q8—21no—
310C22⋊Q8—21no—
311C22⋊Q8—41no—
312#121—21no—
313C4×Q8—21no—
314C4×Q8—21no—
315C4×Q8—21no—
316C4×D4—21no—
317#117D4×C1111yescharacteristic
318Q32—22no—
319Q32—22no—
320SD32—22no—
321SD32—22no—
322M32—22no—
323C2×C16—22no—
324C2×C16C23×C1111yescharacteristic
325C2×C16C23×C1111yescharacteristic
326C2×C16C23×C1111yescharacteristic
327C2×C16C23×C1111yescharacteristic
328#107—21no—
329#107C23×C1111yescharacteristic
330#107C23×C1111yescharacteristic
331#107C23×C1111yescharacteristic
332#107C23×C1111yescharacteristic
333#106—21no—
334#103—21no—
335#103—21no—
336#103—21no—
337#103—21no—
338#103—21no—
339#103—21no—
340#102—21no—
341#102—21no—
342#97D4×C1111yescharacteristic
343#97D4×C1111yescharacteristic
344C4×C8C23×C1111yescharacteristic
345C4×C8C23×C1111yescharacteristic
346C2×C11—41no—
347C2×C11—161no—
348C2×C11#316911yescharacteristic
349C2×C11#341611yescharacteristic
350C2×C11#341711yescharacteristic
351C2×Q8—21no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8—41no—
355C2×D4—21no—
356C2×D4—41no—
357C22×C4—41no—
358C22×C4C2×D4×C1111yescharacteristic
359Q16—21no—
360Q16—21no—
361Q16—21no—
362Q16—21no—
363Q16—21no—
364Q16—21no—
365Q16—42no—
366SD16—42no—
367D8—21no—
368D8—21no—
369M16—22no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8C2×D4×C1111yescharacteristic
373C2×C8C2×D4×C1111yescharacteristic
374C2×C8C2×D4×C1111yescharacteristic
375C2×C8C24×C1111yescharacteristic
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4C11×D811yescharacteristic
392C4⋊C4C11×D811yescharacteristic
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4C11×D811yescharacteristic
401C22⋊C4C11×D811yescharacteristic
402C42—41no—
403C42—41no—
404C42—41no—
405C42C2×D4×C1111yescharacteristic
406C42C2×D4×C1111yescharacteristic
407C16—21no—
408C16—21no—
409C16C11×#4112yes—
410C16C11×#4112yes—
411C11#3374511yescharacteristic, direct product factor, Sylow
412C23—41no—
413C23C2×C11×D811yescharacteristic
414Q8—41no—
415Q8—41no—
416Q8—41no—
417Q8—41no—
418Q8—41no—
419Q8—41no—
420Q8—161no—
421D4—41no—
422D4—41no—
423D4—161no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—161no—
434C2×C4C2×C11×D811yescharacteristic
435C2×C4C2×C11×D811yescharacteristic
436C2×C4C2×C11×D811yescharacteristic
437C2×C4C2×C11×D811yescharacteristic
438C2×C4C2×C11×D811yescharacteristic
439C2×C4C22×D4×C1111yescharacteristic
440C8—21no—
441C8—21no—
442C8C11×#13512yes—
443C8C2×C11×#4111yescharacteristic
444C8C2×C11×#4111yescharacteristic
445C22—21no—
446C22—21no—
447C22—21no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22C22×C11×D811yescharacteristic
452C4—21no—
453C4—21no—
454C4—21no—
455C4—21no—
456C4—21no—
457C4—81no—
458C4—81no—
459C4—81no—
460C4—81no—
461C4—81no—
462C4—81no—
463C4—81no—
464C4C11×#53211yescharacteristic
465C4C2×C11×#13511yescharacteristic
466C2—41no—
467C2—161no—
468C2C11×#316911yescharacteristic
469C2C11×#341611yescharacteristic
470C2C11×#341711yescharacteristic
subgroupG/H
center, socleC22×C11C22×D8
commutator, Frattini, cosocleC2×C8C24×C11
prime radicalC11×#466C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C11×#117 ◁ C11×#405 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3177C2semidirect
3. C11×#2255C2semidirect
4. C11×#2251C2semidirect
5. C11×#2242C2semidirect
6. C11×#2241C2semidirect
8. C11×#2219C2semidirect
10. C11×#2216C2semidirect
11. C11×#2176C2semidirect
12. C11×#2175C2semidirect
13. C4×C11×Q32C2semidirect
14. C4×C11×SD32C2semidirect
15. C11×#2108C2semidirect
116. #33745C11direct (N × H)
177. #3177C2×C11semidirect
179. #2255C2×C11semidirect
180. #2251C2×C11semidirect
181. #2242C2×C11semidirect
182. #2241C2×C11semidirect
184. #2219C2×C11semidirect
186. #2216C2×C11semidirect
187. #2176C2×C11semidirect
188. #2175C2×C11semidirect
189. C4×Q32C2×C11semidirect
190. C4×SD32C2×C11semidirect
191. #2108C2×C11semidirect
411. C11#33745direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31772
C11×#31752
C11×#22552
C11×#22512
C11×#22422
C11×#22412
C11×#22202
C11×#22192
C11×#22172
C11×#22162
C11×#21762
C11×#21752
C4×C11×Q322
C4×C11×SD322
C11×#21082
#3374511