Finite Group Databasebeta

← C11×#19414 #14596607

Subgroups — C11×#19414 #14596607

Order 2816.

662 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3227C211yesmaximal, characteristic, complemented
2C11×#3079C211yesmaximal, characteristic, complemented
3C11×#3035C211yesmaximal, characteristic
4C11×#2988C211yesmaximal, characteristic, complemented
5C11×#1678C212yesmaximal, complemented
6C11×#1677C212yesmaximal, complemented
7C11×#1672C212yesmaximal, complemented
8C11×#1671C212yesmaximal, complemented
9C11×#1570C211yesmaximal, characteristic, complemented
10C11×#1547C211yesmaximal, characteristic, complemented
11C2×C11×#333C211yesmaximal, characteristic, complemented
12C2×C11×#135—21no—
13C11×#532C2211yescharacteristic
14C2×C11×C4⋊Q8C2211yescharacteristic
15C4×C11×#41C2211yescharacteristic
16C11×#498C2212yes—
17C11×#486C2212yes—
18C11×#481—22no—
19C11×#477C2212yes—
20C11×#476—21no—
21C11×#476—21no—
22C11×#476C2212yes—
23C11×#475—21no—
24C11×#474—21no—
25C11×#464—21no—
26C11×#463—21no—
27C11×#462C2211yescharacteristic
28C11×#461C2211yescharacteristic
29C11×#460C2211yescharacteristic
30C11×#459C2211yescharacteristic
31C8×Q8×C11C2212yes—
32C8×D4×C11—22no—
33C8×D4×C11C2212yes—
34C11×#431—21no—
35C11×#431C2211yescharacteristic
36C11×#428—21no—
37C11×#423C2211yescharacteristic
38C2×C11×C4⋊C8—21no—
39C2×C11×C4⋊C8C2211yescharacteristic
40C2×C11×C4⋊C8C2211yescharacteristic
41C11×#417—21no—
42C11×#416—21no—
43C11×#334C2212yes—
44C11×#334C2212yes—
45C11×#333C2212yes—
46C11×#333C2212yes—
47C11×#332C2212yes—
48C11×#331C2212yes—
49C2×C11×#41—21no—
50C2×C11×#41D411yescharacteristic
51C22×Q8×C11—21no—
52C11×#135—44no—
53C2×C11×Q16—21no—
54C2×C11×SD16—21no—
55C2×C11×SD16—21no—
56C2×C11×D8—21no—
57C2×C11×M16—21no—
58C22×C8×C11—21no—
59C22×C8×C11—21no—
60C22×C8×C11—22no—
61C11×C4⋊Q8—21no—
62C11×C4⋊Q8—21no—
63C11×C4⋊Q8—21no—
64C11×C4⋊Q8C2311yescharacteristic
65C11×C4⋊Q8C2312yes—
66C11×#127C2311yescharacteristic
67C11×#124—21no—
68C11×#121—21no—
69C11×#121—21no—
70C4×Q8×C11D411yescharacteristic
71C4×Q8×C11C2311yescharacteristic
72C4×D4×C11—21no—
73C4×D4×C11—21no—
74C4×D4×C11—21no—
75C4×D4×C11—21no—
76C4×D4×C11D411yescharacteristic
77C4×D4×C11C2311yescharacteristic
78C11×#117—21no—
79C11×#117D411yescharacteristic
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C42×C11—21no—
83C2×C42×C11C2311yescharacteristic
84C11×#107—22no—
85C11×#106—22no—
86C11×#106—22no—
87C11×#106—22no—
88C11×C4⋊C8—22no—
89C11×C4⋊C8—21no—
90C11×C4⋊C8—21no—
91C11×C4⋊C8—21no—
92C11×C4⋊C8D411yescharacteristic
93C11×C4⋊C8D411yescharacteristic
94C11×C4⋊C8C2312yes—
95C11×C4⋊C8C2312yes—
96C11×C4⋊C8C2311yescharacteristic
97C11×C4⋊C8C2311yescharacteristic
98C11×#103—22no—
99C11×#103—21no—
100C11×#103—21no—
101C11×#102—22no—
102C11×#102—22no—
103C11×#102—22no—
104C11×#102—21no—
105C11×#102—21no—
106C11×C22⋊C8—22no—
107C11×C22⋊C8D412yes—
108C4×C8×C11—22no—
109C4×C8×C11C2312yes—
110#19414C1111yesmaximal, characteristic, direct product factor, Sylow
111C11×#41—22no—
112C11×#41—42no—
113C11×#41—42no—
114C11×#41SD1614yes—
115C2×Q8×C11—21no—
116C2×Q8×C11—22no—
117C2×Q8×C11—41no—
118C2×Q8×C11—82no—
119C2×Q8×C11C2×D411yescharacteristic
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—41no—
125C2×D4×C11C2×D411yescharacteristic
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—41no—
130C22×C4×C11—41no—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11#4111yescharacteristic
134C11×Q16—42no—
135C11×SD16—42no—
136C11×SD16—42no—
137C11×D8—42no—
138C11×M16—42no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11—42no—
144C2×C8×C11—81no—
145C2×C8×C11—82no—
146C2×C8×C11C2×D412yes—
147C2×C8×C11C2×D412yes—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—41no—
155C11×C4⋊C4—41no—
156C11×C4⋊C4C2×D411yescharacteristic
157C11×C4⋊C4C2×D411yescharacteristic
158C11×C22⋊C4—21no—
159C11×C22⋊C4—21no—
160C11×C22⋊C4—21no—
161C11×C22⋊C4—41no—
162C11×C22⋊C4—41no—
163C42×C11—21no—
164C42×C11—21no—
165C42×C11—21no—
166C42×C11C2×D411yescharacteristic
167C42×C11C2×D411yescharacteristic
168C42×C11#4111yescharacteristic
169C42×C11C2411yescharacteristic
170#3227C2×C1111yescharacteristic, complemented
171#3079C2×C1111yescharacteristic, complemented
172#3035C2×C1111yescharacteristic
173#2988C2×C1111yescharacteristic, complemented
174#1678C2×C1112yescomplemented
175#1677C2×C1112yescomplemented
176#1672C2×C1112yescomplemented
177#1671C2×C1112yescomplemented
178#1570C2×C1111yescharacteristic, complemented
179#1547C2×C1111yescharacteristic, complemented
180C2×#333C2×C1111yescharacteristic, complemented
181C23×C11—21no—
182C23×C11—41no—
183C23×C11#12111yescharacteristic
184Q8×C11—21no—
185Q8×C11—41no—
186Q8×C11—41no—
187Q8×C11—82no—
188Q8×C11—82no—
189Q8×C11C2×SD1612yes—
190D4×C11—24no—
191D4×C11—21no—
192D4×C11—41no—
193D4×C11—41no—
194D4×C11—41no—
195D4×C11—41no—
196D4×C11—81no—
197D4×C11—82no—
198D4×C11C2×SD1612yes—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—24no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—42no—
210C2×C4×C11—81no—
211C2×C4×C11—82no—
212C2×C4×C11—82no—
213C2×C4×C11#12111yescharacteristic
214C2×C4×C11#12111yescharacteristic
215C2×C4×C11#12111yescharacteristic
216C2×C4×C11C2×SD1612yes—
217C2×C4×C11#13512yes—
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C8×C11—22no—
222C8×C11—22no—
223C8×C11—41no—
224C8×C11—41no—
225C8×C11—42no—
226C8×C11—42no—
227C2×#135—21no—
228#532C22×C1111yescharacteristic
229C2×C4⋊Q8C22×C1111yescharacteristic
230C4×#41C22×C1111yescharacteristic
231#498C22×C1112yes—
232#486C22×C1112yes—
233#481—22no—
234#477C22×C1112yes—
235#476—21no—
236#476—21no—
237#476C22×C1112yes—
238#475—21no—
239#474—21no—
240#464—21no—
241#463—21no—
242#462C22×C1111yescharacteristic
243#461C22×C1111yescharacteristic
244#460C22×C1111yescharacteristic
245#459C22×C1111yescharacteristic
246C8×Q8C22×C1112yes—
247C8×D4—22no—
248C8×D4C22×C1112yes—
249#431—21no—
250#431C22×C1111yescharacteristic
251#428—21no—
252#423C22×C1111yescharacteristic
253C2×C4⋊C8—21no—
254C2×C4⋊C8C22×C1111yescharacteristic
255C2×C4⋊C8C22×C1111yescharacteristic
256#417—21no—
257#416—21no—
258#334C22×C1112yes—
259#334C22×C1112yes—
260#333C22×C1112yes—
261#333C22×C1112yes—
262#332C22×C1112yes—
263#331C22×C1112yes—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—22no—
267C22×C11—41no—
268C22×C11—41no—
269C22×C11—81no—
270C22×C11—81no—
271C22×C11—81no—
272C22×C11#46512yes—
273C22×C11C2×#12111yescharacteristic
274C4×C11—21no—
275C4×C11—22no—
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—41no—
279C4×C11—41no—
280C4×C11—81no—
281C4×C11—82no—
282C4×C11#46512yes—
283C4×C11C22×SD1611yescharacteristic
284C4×C11C2×#13511yescharacteristic
285C4×C11#57711yescharacteristic
286C4×C11#57811yescharacteristic
287C2×#41—21no—
288C2×#41D4×C1111yescharacteristic
289C22×Q8—21no—
290#135—44no—
291C2×Q16—21no—
292C2×SD16—21no—
293C2×SD16—21no—
294C2×D8—21no—
295C2×M16—21no—
296C22×C8—21no—
297C22×C8—21no—
298C22×C8—22no—
299C4⋊Q8—21no—
300C4⋊Q8—21no—
301C4⋊Q8—21no—
302C4⋊Q8C23×C1112yes—
303C4⋊Q8C23×C1111yescharacteristic
304#127C23×C1111yescharacteristic
305#124—21no—
306#121—21no—
307#121—21no—
308C4×Q8D4×C1111yescharacteristic
309C4×Q8C23×C1111yescharacteristic
310C4×D4—21no—
311C4×D4—21no—
312C4×D4—21no—
313C4×D4—21no—
314C4×D4D4×C1111yescharacteristic
315C4×D4C23×C1111yescharacteristic
316#117—21no—
317#117D4×C1111yescharacteristic
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C42—21no—
321C2×C42C23×C1111yescharacteristic
322#107—22no—
323#106—22no—
324#106—22no—
325#106—22no—
326C4⋊C8—22no—
327C4⋊C8—21no—
328C4⋊C8—21no—
329C4⋊C8—21no—
330C4⋊C8D4×C1111yescharacteristic
331C4⋊C8D4×C1111yescharacteristic
332C4⋊C8C23×C1112yes—
333C4⋊C8C23×C1112yes—
334C4⋊C8C23×C1111yescharacteristic
335C4⋊C8C23×C1111yescharacteristic
336#103—22no—
337#103—21no—
338#103—21no—
339#102—22no—
340#102—22no—
341#102—22no—
342#102—21no—
343#102—21no—
344C22⋊C8—22no—
345C22⋊C8D4×C1112yes—
346C4×C8—22no—
347C4×C8C23×C1112yes—
348C2×C11—22no—
349C2×C11—42no—
350C2×C11—161no—
351C2×C11#304611yescharacteristic
352C2×C11C2×#46511yescharacteristic
353C2×C11#306811yescharacteristic
354#41—22no—
355#41—42no—
356#41—42no—
357#41C11×SD1614yes—
358C2×Q8—21no—
359C2×Q8—22no—
360C2×Q8—41no—
361C2×Q8—82no—
362C2×Q8C2×D4×C1111yescharacteristic
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—41no—
368C2×D4C2×D4×C1111yescharacteristic
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4C2×D4×C1111yescharacteristic
375C22×C4C2×D4×C1111yescharacteristic
376C22×C4C11×#4111yescharacteristic
377Q16—42no—
378SD16—42no—
379SD16—42no—
380D8—42no—
381M16—42no—
382C2×C8—22no—
383C2×C8—22no—
384C2×C8—21no—
385C2×C8—21no—
386C2×C8—42no—
387C2×C8—82no—
388C2×C8—81no—
389C2×C8C2×D4×C1112yes—
390C2×C8C2×D4×C1112yes—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—41no—
398C4⋊C4—41no—
399C4⋊C4C2×D4×C1111yescharacteristic
400C4⋊C4C2×D4×C1111yescharacteristic
401C22⋊C4—21no—
402C22⋊C4—21no—
403C22⋊C4—21no—
404C22⋊C4—41no—
405C22⋊C4—41no—
406C42—21no—
407C42—21no—
408C42—21no—
409C42C2×D4×C1111yescharacteristic
410C42C2×D4×C1111yescharacteristic
411C42C11×#4111yescharacteristic
412C42C24×C1111yescharacteristic
413C11#1941411yescharacteristic, direct product factor, Sylow
414C23—21no—
415C23—41no—
416C23C11×#12111yescharacteristic
417Q8—21no—
418Q8—41no—
419Q8—41no—
420Q8—82no—
421Q8—82no—
422Q8C2×C11×SD1612yes—
423D4—24no—
424D4—21no—
425D4—41no—
426D4—41no—
427D4—41no—
428D4—41no—
429D4—81no—
430D4—82no—
431D4C2×C11×SD1612yes—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—24no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—42no—
443C2×C4—81no—
444C2×C4—82no—
445C2×C4—82no—
446C2×C4C11×#12111yescharacteristic
447C2×C4C11×#12111yescharacteristic
448C2×C4C11×#12111yescharacteristic
449C2×C4C2×C11×SD1612yes—
450C2×C4C11×#13512yes—
451C2×C4C22×D4×C1111yescharacteristic
452C2×C4C22×D4×C1111yescharacteristic
453C2×C4C2×C11×#4111yescharacteristic
454C8—22no—
455C8—22no—
456C8—41no—
457C8—41no—
458C8—42no—
459C8—42no—
460C22—21no—
461C22—21no—
462C22—22no—
463C22—41no—
464C22—41no—
465C22—81no—
466C22—81no—
467C22—81no—
468C22C11×#46512yes—
469C22C2×C11×#12111yescharacteristic
470C4—21no—
471C4—22no—
472C4—21no—
473C4—21no—
474C4—41no—
475C4—41no—
476C4—81no—
477C4—82no—
478C4C11×#46512yes—
479C4C22×C11×SD1611yescharacteristic
480C4C2×C11×#13511yescharacteristic
481C4C11×#57711yescharacteristic
482C4C11×#57811yescharacteristic
483C2—22no—
484C2—42no—
485C2—161no—
486C2C11×#304611yescharacteristic
487C2C2×C11×#46511yescharacteristic
488C2C11×#306811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3035C2
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×#3227C2semidirect
2. C11×#3079C2semidirect
4. C11×#2988C2semidirect
5. C11×#1678C2semidirect
6. C11×#1677C2semidirect
7. C11×#1672C2semidirect
8. C11×#1671C2semidirect
9. C11×#1570C2semidirect
10. C11×#1547C2semidirect
11. C2×C11×#333C2semidirect
110. #19414C11direct (N × H)
170. #3227C2×C11semidirect
171. #3079C2×C11semidirect
173. #2988C2×C11semidirect
174. #1678C2×C11semidirect
175. #1677C2×C11semidirect
176. #1672C2×C11semidirect
177. #1671C2×C11semidirect
178. #1570C2×C11semidirect
179. #1547C2×C11semidirect
180. C2×#333C2×C11semidirect
413. C11#19414direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32272
C11×#30792
C11×#30352
C11×#29882
C11×#16782
C11×#16772
C11×#16722
C11×#16712
C11×#15702
C11×#15472
C2×C11×#3332
#1941411