Finite Group Databasebeta

← C11×#19201 #14596394

Subgroups — C11×#19201 #14596394

Order 2816.

660 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3246C211yesmaximal, characteristic, complemented
2C11×#3245C211yesmaximal, characteristic
3C11×#3131C211yesmaximal, characteristic, complemented
4C11×#2931C211yesmaximal, characteristic, complemented
5C11×#1699C212yesmaximal, complemented
6C11×#1697C212yesmaximal, complemented
7C11×#1683C212yesmaximal, complemented
8C11×#1681C212yesmaximal, complemented
9C2×C11×#335C211yesmaximal, characteristic, complemented
10C11×#1550C211yesmaximal, characteristic, complemented
11C11×#1547C211yesmaximal, characteristic, complemented
12C2×C11×#131—21no—
13C11×#533C2211yescharacteristic
14C11×#532C2211yescharacteristic
15C11×#532C2211yescharacteristic
16C11×#488—21no—
17C11×#488—21no—
18C11×#487C2211yescharacteristic
19C11×#487C2211yescharacteristic
20C11×#486C2211yescharacteristic
21C11×#486C2211yescharacteristic
22C11×#476C2212yes—
23C11×#475—21no—
24C11×#474—21no—
25C11×#474C2212yes—
26C11×#466—22no—
27C11×#465—22no—
28C11×#461C2212yes—
29C11×#460—21no—
30C11×#459—21no—
31C11×#459C2212yes—
32C11×#436—21no—
33C11×#436C2212yes—
34C8×D4×C11—21no—
35C8×D4×C11C2212yes—
36C11×#423C2211yescharacteristic
37C2×C11×C4⋊C8C2211yescharacteristic
38C2×C11×C4⋊C8C2211yescharacteristic
39C11×#416—21no—
40C11×#416—21no—
41C11×#408—21no—
42C2×C4×C8×C11C2211yescharacteristic
43C11×#335C2212yes—
44C11×#335C2212yes—
45C11×#333C2212yes—
46C11×#332C2212yes—
47C11×#332C2212yes—
48C11×#331C2212yes—
49C2×C11×#41—21no—
50C2×C11×#41—21no—
51C2×C11×SD16—22no—
52C2×C11×D8—22no—
53C11×#131—44no—
54C2×C11×M16—21no—
55C2×C11×M16—22no—
56C22×C8×C11—21no—
57C22×C8×C11—21no—
58C22×C8×C11—22no—
59C22×C8×C11D411yescharacteristic
60C22×C8×C11D411yescharacteristic
61C11×C4⋊Q8D411yescharacteristic
62C11×C4⋊Q8C2311yescharacteristic
63C11×C4⋊Q8C2311yescharacteristic
64C11×C4⋊Q8C2311yescharacteristic
65C11×#127D411yescharacteristic
66C11×#127C2311yescharacteristic
67C11×#125—21no—
68C11×#124—21no—
69C11×#124—21no—
70C11×C22⋊Q8—21no—
71C11×C22⋊Q8—21no—
72C11×#121—21no—
73C11×#121—21no—
74C11×#121—21no—
75C11×#121D412yes—
76C4×Q8×C11—21no—
77C4×Q8×C11—21no—
78C4×D4×C11—21no—
79C4×D4×C11—21no—
80C4×D4×C11—21no—
81C4×D4×C11C2312yes—
82C11×#117—21no—
83C2×C42×C11C2311yescharacteristic
84C11×#107—22no—
85C11×#106—22no—
86C11×C4⋊C8—21no—
87C11×C4⋊C8—21no—
88C11×C4⋊C8—21no—
89C11×C4⋊C8C2312yes—
90C11×C4⋊C8C2312yes—
91C11×C4⋊C8C2312yes—
92C11×#103—21no—
93C11×#103—21no—
94C11×#103—21no—
95C11×#103—21no—
96C11×#103—22no—
97C11×#102—22no—
98C11×#102—22no—
99C11×#102—21no—
100C11×#102—21no—
101C11×#102—21no—
102C11×#102—21no—
103C11×#102—22no—
104C11×C22⋊C8—22no—
105C11×C22⋊C8—22no—
106C4×C8×C11D411yescharacteristic
107C4×C8×C11D411yescharacteristic
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110#19201C1111yesmaximal, characteristic, direct product factor, Sylow
111C11×#41—42no—
112C11×#41—42no—
113C11×#41—42no—
114C11×#41—42no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×D4×C11—22no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—41no—
126C2×D4×C11C2×D412yes—
127C22×C4×C11—22no—
128C22×C4×C11—41no—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11#4111yescharacteristic
132C11×SD16—82no—
133C11×D8—82no—
134C11×M16—44no—
135C11×M16—42no—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C2×C8×C11—44no—
142C2×C8×C11—81no—
143C2×C8×C11—81no—
144C2×C8×C11C2×D411yescharacteristic
145C2×C8×C11C2×D411yescharacteristic
146C2×C8×C11C2×D411yescharacteristic
147C2×C8×C11C2×D411yescharacteristic
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—41no—
156C11×C4⋊C4—41no—
157C11×C4⋊C4C2×D412yes—
158C11×C22⋊C4—22no—
159C11×C22⋊C4—22no—
160C11×C22⋊C4—41no—
161C11×C22⋊C4—41no—
162C11×C22⋊C4—41no—
163C42×C11—41no—
164C42×C11C2×D411yescharacteristic
165C42×C11C2×D411yescharacteristic
166C42×C11#4111yescharacteristic
167C42×C11C2411yescharacteristic
168#3246C2×C1111yescharacteristic, complemented
169#3245C2×C1111yescharacteristic
170#3131C2×C1111yescharacteristic, complemented
171#2931C2×C1111yescharacteristic, complemented
172#1699C2×C1112yescomplemented
173#1697C2×C1112yescomplemented
174#1683C2×C1112yescomplemented
175#1681C2×C1112yescomplemented
176C2×#335C2×C1111yescharacteristic, complemented
177#1550C2×C1111yescharacteristic, complemented
178#1547C2×C1111yescharacteristic, complemented
179C23×C11—22no—
180C23×C11—41no—
181C23×C11#12111yescharacteristic
182Q8×C11—42no—
183Q8×C11—41no—
184Q8×C11—41no—
185Q8×C11—41no—
186Q8×C11—41no—
187Q8×C11—81no—
188D4×C11—22no—
189D4×C11—22no—
190D4×C11—42no—
191D4×C11—44no—
192D4×C11—41no—
193D4×C11—41no—
194D4×C11—41no—
195D4×C11—41no—
196D4×C11—42no—
197D4×C11—81no—
198D4×C11—82no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—22no—
202C2×C4×C11—41no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—82no—
209C2×C4×C11#12111yescharacteristic
210C2×C4×C11#12111yescharacteristic
211C2×C4×C11#12111yescharacteristic
212C2×C4×C11#13512yes—
213C2×C4×C11AGL(1,ℤ/8)12yes—
214C2×C4×C11C22×D411yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C8×C11—21no—
218C8×C11—21no—
219C8×C11—21no—
220C8×C11—21no—
221C8×C11—42no—
222C8×C11—42no—
223C8×C11—42no—
224C2×#131—21no—
225#533C22×C1111yescharacteristic
226#532C22×C1111yescharacteristic
227#532C22×C1111yescharacteristic
228#488—21no—
229#488—21no—
230#487C22×C1111yescharacteristic
231#487C22×C1111yescharacteristic
232#486C22×C1111yescharacteristic
233#486C22×C1111yescharacteristic
234#476C22×C1112yes—
235#475—21no—
236#474—21no—
237#474C22×C1112yes—
238#466—22no—
239#465—22no—
240#461C22×C1112yes—
241#460—21no—
242#459—21no—
243#459C22×C1112yes—
244#436—21no—
245#436C22×C1112yes—
246C8×D4—21no—
247C8×D4C22×C1112yes—
248#423C22×C1111yescharacteristic
249C2×C4⋊C8C22×C1111yescharacteristic
250C2×C4⋊C8C22×C1111yescharacteristic
251#416—21no—
252#416—21no—
253#408—21no—
254C2×C4×C8C22×C1111yescharacteristic
255#335C22×C1112yes—
256#335C22×C1112yes—
257#333C22×C1112yes—
258#332C22×C1112yes—
259#332C22×C1112yes—
260#331C22×C1112yes—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11—42no—
266C22×C11—81no—
267C22×C11—81no—
268C22×C11—81no—
269C22×C11#46312yes—
270C22×C11C2×#12111yescharacteristic
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—21no—
274C4×C11—42no—
275C4×C11—81no—
276C4×C11—81no—
277C4×C11—81no—
278C4×C11#46312yes—
279C4×C11C2×#13511yescharacteristic
280C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
281C4×C11#57611yescharacteristic
282C4×C11#57811yescharacteristic
283C2×#41—21no—
284C2×#41—21no—
285C2×SD16—22no—
286C2×D8—22no—
287#131—44no—
288C2×M16—21no—
289C2×M16—22no—
290C22×C8—21no—
291C22×C8—21no—
292C22×C8—22no—
293C22×C8D4×C1111yescharacteristic
294C22×C8D4×C1111yescharacteristic
295C4⋊Q8D4×C1111yescharacteristic
296C4⋊Q8C23×C1111yescharacteristic
297C4⋊Q8C23×C1111yescharacteristic
298C4⋊Q8C23×C1111yescharacteristic
299#127D4×C1111yescharacteristic
300#127C23×C1111yescharacteristic
301#125—21no—
302#124—21no—
303#124—21no—
304C22⋊Q8—21no—
305C22⋊Q8—21no—
306#121—21no—
307#121—21no—
308#121—21no—
309#121D4×C1112yes—
310C4×Q8—21no—
311C4×Q8—21no—
312C4×D4—21no—
313C4×D4—21no—
314C4×D4—21no—
315C4×D4C23×C1112yes—
316#117—21no—
317C2×C42C23×C1111yescharacteristic
318#107—22no—
319#106—22no—
320C4⋊C8—21no—
321C4⋊C8—21no—
322C4⋊C8—21no—
323C4⋊C8C23×C1112yes—
324C4⋊C8C23×C1112yes—
325C4⋊C8C23×C1112yes—
326#103—21no—
327#103—21no—
328#103—21no—
329#103—21no—
330#103—22no—
331#102—22no—
332#102—22no—
333#102—21no—
334#102—21no—
335#102—21no—
336#102—21no—
337#102—22no—
338C22⋊C8—22no—
339C22⋊C8—22no—
340C4×C8D4×C1111yescharacteristic
341C4×C8D4×C1111yescharacteristic
342C4×C8C23×C1111yescharacteristic
343C4×C8C23×C1111yescharacteristic
344C2×C11—22no—
345C2×C11—82no—
346C2×C11—161no—
347C2×C11C2×#46311yescharacteristic
348C2×C11#306111yescharacteristic
349C2×C11#306711yescharacteristic
350#41—42no—
351#41—42no—
352#41—42no—
353#41—42no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×D4—22no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—41no—
365C2×D4C2×D4×C1112yes—
366C22×C4—22no—
367C22×C4—41no—
368C22×C4C2×D4×C1111yescharacteristic
369C22×C4C2×D4×C1111yescharacteristic
370C22×C4C11×#4111yescharacteristic
371SD16—82no—
372D8—82no—
373M16—44no—
374M16—42no—
375C2×C8—22no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—44no—
381C2×C8—81no—
382C2×C8—81no—
383C2×C8C2×D4×C1111yescharacteristic
384C2×C8C2×D4×C1111yescharacteristic
385C2×C8C2×D4×C1111yescharacteristic
386C2×C8C2×D4×C1111yescharacteristic
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4C2×D4×C1112yes—
397C22⋊C4—22no—
398C22⋊C4—22no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—41no—
402C42—41no—
403C42C2×D4×C1111yescharacteristic
404C42C2×D4×C1111yescharacteristic
405C42C11×#4111yescharacteristic
406C42C24×C1111yescharacteristic
407C11#1920111yescharacteristic, direct product factor, Sylow
408C23—22no—
409C23—41no—
410C23C11×#12111yescharacteristic
411Q8—42no—
412Q8—41no—
413Q8—41no—
414Q8—41no—
415Q8—41no—
416Q8—81no—
417D4—22no—
418D4—22no—
419D4—42no—
420D4—44no—
421D4—41no—
422D4—41no—
423D4—41no—
424D4—41no—
425D4—42no—
426D4—81no—
427D4—82no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—22no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—82no—
438C2×C4C11×#12111yescharacteristic
439C2×C4C11×#12111yescharacteristic
440C2×C4C11×#12111yescharacteristic
441C2×C4C11×#13512yes—
442C2×C4C11×AGL(1,ℤ/8)12yes—
443C2×C4C22×D4×C1111yescharacteristic
444C2×C4C22×D4×C1111yescharacteristic
445C2×C4C2×C11×#4111yescharacteristic
446C8—21no—
447C8—21no—
448C8—21no—
449C8—21no—
450C8—42no—
451C8—42no—
452C8—42no—
453C22—21no—
454C22—21no—
455C22—42no—
456C22—42no—
457C22—42no—
458C22—81no—
459C22—81no—
460C22—81no—
461C22C11×#46312yes—
462C22C2×C11×#12111yescharacteristic
463C4—21no—
464C4—21no—
465C4—21no—
466C4—42no—
467C4—81no—
468C4—81no—
469C4—81no—
470C4C11×#46312yes—
471C4C2×C11×#13511yescharacteristic
472C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
473C4C11×#57611yescharacteristic
474C4C11×#57811yescharacteristic
475C2—22no—
476C2—82no—
477C2—161no—
478C2C2×C11×#46311yescharacteristic
479C2C11×#306111yescharacteristic
480C2C11×#306711yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3245C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3246C2semidirect
3. C11×#3131C2semidirect
4. C11×#2931C2semidirect
5. C11×#1699C2semidirect
6. C11×#1697C2semidirect
7. C11×#1683C2semidirect
8. C11×#1681C2semidirect
9. C2×C11×#335C2semidirect
10. C11×#1550C2semidirect
11. C11×#1547C2semidirect
110. #19201C11direct (N × H)
168. #3246C2×C11semidirect
170. #3131C2×C11semidirect
171. #2931C2×C11semidirect
172. #1699C2×C11semidirect
173. #1697C2×C11semidirect
174. #1683C2×C11semidirect
175. #1681C2×C11semidirect
176. C2×#335C2×C11semidirect
177. #1550C2×C11semidirect
178. #1547C2×C11semidirect
407. C11#19201direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32462
C11×#32452
C11×#31312
C11×#29312
C11×#16992
C11×#16972
C11×#16832
C11×#16812
C2×C11×#3352
C11×#15502
C11×#15472
#1920111