Finite Group Databasebeta

← C11×#9943 #14587136

Subgroups — C11×#9943 #14587136

Order 2816.

798 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 798 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3007C211yesmaximal, characteristic
2C11×#2583C211yesmaximal, characteristic, complemented
3C11×#2406C211yesmaximal, characteristic
4C11×#1789C211yesmaximal, characteristic
5C11×#1511C211yesmaximal, characteristic, complemented
6C11×#1463C211yesmaximal, characteristic, complemented
7C11×#1284C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C2×C11×#137—21no—
10C2×C11×#123—21no—
11C2×C11×C22⋊Q8C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C11×#452—22no—
14C11×#451—21no—
15C11×#450—21no—
16C2×C11×#104—22no—
17C11×#417—21no—
18C11×#407C2211yescharacteristic
19C11×#407C2211yescharacteristic
20C11×#398—21no—
21C11×#395—21no—
22C11×#395—21no—
23C11×#394—21no—
24C11×#389—22no—
25C11×#386—21no—
26C11×#385—21no—
27C11×#385—21no—
28C11×#385—22no—
29C11×#381C2211yescharacteristic
30C4×C11×C22⋊C4C2211yescharacteristic
31C11×#328—22no—
32C11×#324—22no—
33C2×C11×#41—21no—
34C2×C11×#41—21no—
35C2×C11×#41—21no—
36C2×C11×#41—21no—
37C2×C11×#41—44no—
38C22×Q8×C11D411yescharacteristic
39C22×Q8×C11D411yescharacteristic
40C22×D4×C11—21no—
41C22×D4×C11D411yescharacteristic
42C23×C4×C11—21no—
43C23×C4×C11D411yescharacteristic
44C23×C4×C11D411yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C11×#137—44no—
47C2×C11×Q16—22no—
48C2×C11×SD16—22no—
49C2×C11×M16—21no—
50C2×C11×M16—21no—
51C11×#123—44no—
52C11×C22⋊Q8—21no—
53C11×C22⋊Q8—21no—
54C11×C22⋊Q8—21no—
55C11×C22⋊Q8—21no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—21no—
71C2×C11×C22⋊C4—21no—
72C2×C42×C11D412yes—
73C11×#104—44no—
74C11×#103—22no—
75C11×#102—22no—
76C11×C22⋊C8—21no—
77C11×C22⋊C8—21no—
78C11×C22⋊C8—21no—
79C11×C22⋊C8D412yes—
80C11×#95—22no—
81C11×#95—22no—
82C11×#95—22no—
83C11×#95—21no—
84C11×#95—21no—
85C11×#95D412yes—
86#9943C1111yesmaximal, characteristic, direct product factor, Sylow
87C24×C11—21no—
88C24×C11C2×D411yescharacteristic
89C11×#41—24no—
90C11×#41—24no—
91C11×#41—42no—
92C11×#41—42no—
93C11×#41—42no—
94C11×#41—42no—
95C11×#41—42no—
96C11×#41—42no—
97C2×Q8×C11—21no—
98C2×Q8×C11—21no—
99C2×Q8×C11—21no—
100C2×Q8×C11—21no—
101C2×Q8×C11—42no—
102C2×Q8×C11—42no—
103C2×D4×C11—24no—
104C2×D4×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11—42no—
107C2×D4×C11—42no—
108C2×D4×C11—41no—
109C2×D4×C11—41no—
110C22×C4×C11—22no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—42no—
122C22×C4×C11—42no—
123C22×C4×C11—42no—
124C22×C4×C11—42no—
125C22×C4×C11—41no—
126C22×C4×C11—41no—
127C22×C4×C11—42no—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11#4111yescharacteristic
134C11×Q16—44no—
135C11×SD16—44no—
136C11×M16—42no—
137C11×M16—42no—
138C2×C8×C11—22no—
139C2×C8×C11—41no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—44no—
143C11×C4⋊C4—44no—
144C11×C4⋊C4—41no—
145C11×C4⋊C4—41no—
146C11×C4⋊C4—41no—
147C11×C4⋊C4—41no—
148C11×C4⋊C4—41no—
149C11×C4⋊C4—41no—
150C11×C4⋊C4—82no—
151C11×C22⋊C4—24no—
152C11×C22⋊C4—44no—
153C11×C22⋊C4—42no—
154C11×C22⋊C4—44no—
155C11×C22⋊C4—41no—
156C11×C22⋊C4—41no—
157C42×C11—42no—
158#3007C2×C1111yescharacteristic
159#2583C2×C1111yescharacteristic, complemented
160#2406C2×C1111yescharacteristic
161#1789C2×C1111yescharacteristic
162#1511C2×C1111yescharacteristic, complemented
163#1463C2×C1111yescharacteristic, complemented
164#1284C2×C1111yescharacteristic, complemented
165C23×C11—22no—
166C23×C11—22no—
167C23×C11—22no—
168C23×C11—41no—
169C23×C11—42no—
170C23×C11—41no—
171C23×C11—41no—
172C23×C11—42no—
173C23×C11#12011yescharacteristic
174C23×C11#12011yescharacteristic
175C23×C11#12111yescharacteristic
176Q8×C11—22no—
177Q8×C11—22no—
178Q8×C11—41no—
179Q8×C11—41no—
180Q8×C11—42no—
181Q8×C11—81no—
182D4×C11—22no—
183D4×C11—22no—
184D4×C11—41no—
185D4×C11—41no—
186D4×C11—44no—
187D4×C11—44no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—24no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—44no—
200C2×C4×C11—44no—
201C2×C4×C11—42no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—81no—
220C2×C4×C11#12011yescharacteristic
221C2×C4×C11#12111yescharacteristic
222C2×C4×C11#12111yescharacteristic
223C2×C4×C11#12711yescharacteristic
224C8×C11—42no—
225C8×C11—81no—
226C22×#41C22×C1111yescharacteristic
227C2×#137—21no—
228C2×#123—21no—
229C2×C22⋊Q8C22×C1111yescharacteristic
230C22×C4⋊C4C22×C1111yescharacteristic
231#452—22no—
232#451—21no—
233#450—21no—
234C2×#104—22no—
235#417—21no—
236#407C22×C1111yescharacteristic
237#407C22×C1111yescharacteristic
238#398—21no—
239#395—21no—
240#395—21no—
241#394—21no—
242#389—22no—
243#386—21no—
244#385—21no—
245#385—21no—
246#385—22no—
247#381C22×C1111yescharacteristic
248C4×C22⋊C4C22×C1111yescharacteristic
249#328—22no—
250#324—22no—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—21no—
258C22×C11—44no—
259C22×C11—44no—
260C22×C11—42no—
261C22×C11—82no—
262C22×C11—81no—
263C22×C11—81no—
264C22×C11#39211yescharacteristic
265C22×C11#45612yes—
266C22×C11B(4,𝔽2)12yes—
267C4×C11—21no—
268C4×C11—21no—
269C4×C11—21no—
270C4×C11—21no—
271C4×C11—44no—
272C4×C11—42no—
273C4×C11—42no—
274C4×C11—82no—
275C4×C11—81no—
276C4×C11—81no—
277C4×C11—81no—
278C2×#41—21no—
279C2×#41—21no—
280C2×#41—21no—
281C2×#41—21no—
282C2×#41—44no—
283C22×Q8D4×C1111yescharacteristic
284C22×Q8D4×C1111yescharacteristic
285C22×D4—21no—
286C22×D4D4×C1111yescharacteristic
287C23×C4—21no—
288C23×C4D4×C1111yescharacteristic
289C23×C4D4×C1111yescharacteristic
290C23×C4C23×C1111yescharacteristic
291#137—44no—
292C2×Q16—22no—
293C2×SD16—22no—
294C2×M16—21no—
295C2×M16—21no—
296#123—44no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4D4×C1111yescharacteristic
312C2×C22⋊C4—21no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C42D4×C1112yes—
318#104—44no—
319#103—22no—
320#102—22no—
321C22⋊C8—21no—
322C22⋊C8—21no—
323C22⋊C8—21no—
324C22⋊C8D4×C1112yes—
325#95—22no—
326#95—22no—
327#95—22no—
328#95—21no—
329#95—21no—
330#95D4×C1112yes—
331C2×C11—22no—
332C2×C11—22no—
333C2×C11—41no—
334C2×C11—82no—
335C2×C11#200511yescharacteristic
336C2×C11#201011yescharacteristic
337C2×C11#202111yescharacteristic
338C24—21no—
339C24C2×D4×C1111yescharacteristic
340#41—24no—
341#41—24no—
342#41—42no—
343#41—42no—
344#41—42no—
345#41—42no—
346#41—42no—
347#41—42no—
348C2×Q8—21no—
349C2×Q8—21no—
350C2×Q8—21no—
351C2×Q8—21no—
352C2×Q8—42no—
353C2×Q8—42no—
354C2×D4—24no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—42no—
358C2×D4—42no—
359C2×D4—41no—
360C2×D4—41no—
361C22×C4—22no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—22no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—42no—
373C22×C4—42no—
374C22×C4—42no—
375C22×C4—42no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—42no—
379C22×C4C2×D4×C1111yescharacteristic
380C22×C4C2×D4×C1111yescharacteristic
381C22×C4C2×D4×C1111yescharacteristic
382C22×C4C2×D4×C1111yescharacteristic
383C22×C4C2×D4×C1111yescharacteristic
384C22×C4C11×#4111yescharacteristic
385Q16—44no—
386SD16—44no—
387M16—42no—
388M16—42no—
389C2×C8—22no—
390C2×C8—41no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—44no—
394C4⋊C4—44no—
395C4⋊C4—41no—
396C4⋊C4—41no—
397C4⋊C4—41no—
398C4⋊C4—41no—
399C4⋊C4—41no—
400C4⋊C4—41no—
401C4⋊C4—82no—
402C22⋊C4—24no—
403C22⋊C4—44no—
404C22⋊C4—42no—
405C22⋊C4—44no—
406C22⋊C4—41no—
407C22⋊C4—41no—
408C42—42no—
409C11#994311yescharacteristic, direct product factor, Sylow
410C23—22no—
411C23—22no—
412C23—22no—
413C23—41no—
414C23—42no—
415C23—41no—
416C23—41no—
417C23—42no—
418C23C11×#12011yescharacteristic
419C23C11×#12011yescharacteristic
420C23C11×#12111yescharacteristic
421Q8—22no—
422Q8—22no—
423Q8—41no—
424Q8—41no—
425Q8—42no—
426Q8—81no—
427D4—22no—
428D4—22no—
429D4—41no—
430D4—41no—
431D4—44no—
432D4—44no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—24no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—44no—
445C2×C4—44no—
446C2×C4—42no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—81no—
465C2×C4C11×#12011yescharacteristic
466C2×C4C11×#12111yescharacteristic
467C2×C4C11×#12111yescharacteristic
468C2×C4C11×#12711yescharacteristic
469C8—42no—
470C8—81no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—44no—
479C22—44no—
480C22—42no—
481C22—82no—
482C22—81no—
483C22—81no—
484C22C11×#39211yescharacteristic
485C22C11×#45612yes—
486C22C11×B(4,𝔽2)12yes—
487C4—21no—
488C4—21no—
489C4—21no—
490C4—21no—
491C4—44no—
492C4—42no—
493C4—42no—
494C4—82no—
495C4—81no—
496C4—81no—
497C4—81no—
498C2—22no—
499C2—22no—
500C2—41no—
501C2—82no—
502C2C11×#200511yescharacteristic
503C2C11×#201011yescharacteristic
504C2C11×#202111yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC23×C4C23×C11
prime radicalC22×C11×#41C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2583C2semidirect
5. C11×#1511C2semidirect
6. C11×#1463C2semidirect
7. C11×#1284C2semidirect
86. #9943C11direct (N × H)
159. #2583C2×C11semidirect
162. #1511C2×C11semidirect
163. #1463C2×C11semidirect
164. #1284C2×C11semidirect
409. C11#9943direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30072
C11×#25832
C11×#24062
C11×#17892
C11×#15112
C11×#14632
C11×#12842
#994311