Finite Group Databasebeta

← C11×#9931 #14587124

Subgroups — C11×#9931 #14587124

Order 2816.

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

normal subgroups only

This group has 792 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×#3193C211yesmaximal, characteristic, complemented
2C11×#3006C211yesmaximal, characteristic
3C11×#2616C211yesmaximal, characteristic, complemented
4C11×#1964C211yesmaximal, characteristic, complemented
5C11×#1789C211yesmaximal, characteristic, complemented
6C11×#1508C211yesmaximal, characteristic, complemented
7C11×#1305C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C2×C11×AGL(1,ℤ/8)—21no—
10C2×C11×C22⋊Q8—21no—
11C2×C11×C22⋊Q8C2211yescharacteristic
12C2×C11×#121C2211yescharacteristic
13C11×#484—21no—
14C11×#480—21no—
15C11×#468—22no—
16C11×#450—21no—
17C11×#449—22no—
18C11×#448—21no—
19C11×#448—21no—
20C11×#447—21no—
21C2×C11×#104—22no—
22C11×#417—21no—
23C2×C11×#99—22no—
24C11×#407C2211yescharacteristic
25C11×#407C2211yescharacteristic
26C11×#395—21no—
27C11×#394—21no—
28C11×#394—22no—
29C11×#380—21no—
30C11×#380C2211yescharacteristic
31C4×C11×C22⋊C4C2211yescharacteristic
32C11×#328—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×C11—21no—
42C22×D4×C11D411yescharacteristic
43C22×D4×C11D411yescharacteristic
44C23×C4×C11—21no—
45C23×C4×C11C2311yescharacteristic
46C11×AGL(1,ℤ/8)—44no—
47C2×C11×SD16—22no—
48C2×C11×SD16—22no—
49C2×C11×D8—22no—
50C2×C11×M16—21no—
51C2×C11×M16D412yes—
52C11×C22⋊Q8—21no—
53C11×C22⋊Q8—21no—
54C11×C22⋊Q8—21no—
55C11×C22⋊Q8—21no—
56C11×C22⋊Q8—44no—
57C11×#121—21no—
58C11×#121—21no—
59C11×#121—21no—
60C11×#121—21no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C4⋊C4D411yescharacteristic
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4D412yes—
72C2×C42×C11—21no—
73C11×#107—22no—
74C11×#104—44no—
75C11×#103—22no—
76C11×#103—22no—
77C11×#102—22no—
78C11×#102—22no—
79C11×#99—44no—
80C11×C22⋊C8—21no—
81C11×C22⋊C8—21no—
82C11×C22⋊C8—21no—
83C11×C22⋊C8D412yes—
84C11×#95—22no—
85C11×#95—21no—
86C11×#95—21no—
87#9931C1111yesmaximal, characteristic, direct product factor, Sylow
88C24×C11—21no—
89C24×C11—21no—
90C24×C11C2×D411yescharacteristic
91C11×#41—24no—
92C11×#41—24no—
93C11×#41—42no—
94C11×#41—42no—
95C11×#41—42no—
96C11×#41—42no—
97C11×#41—42no—
98C11×#41—42no—
99C2×Q8×C11—21no—
100C2×Q8×C11—21no—
101C2×Q8×C11—21no—
102C2×Q8×C11—21no—
103C2×Q8×C11—42no—
104C2×Q8×C11—42no—
105C2×D4×C11—21no—
106C2×D4×C11—21no—
107C2×D4×C11—21no—
108C2×D4×C11—21no—
109C2×D4×C11—42no—
110C2×D4×C11—42no—
111C2×D4×C11—42no—
112C2×D4×C11—42no—
113C2×D4×C11—41no—
114C2×D4×C11—41no—
115C2×D4×C11—42no—
116C2×D4×C11—42no—
117C2×D4×C11—41no—
118C2×D4×C11—41no—
119C22×C4×C11—24no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11—41no—
128C22×C4×C11—41no—
129C22×C4×C11—41no—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11#4111yescharacteristic
136C11×SD16—44no—
137C11×SD16—82no—
138C11×D8—44no—
139C11×M16—42no—
140C11×M16—42no—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—42no—
148C11×C4⋊C4—44no—
149C11×C4⋊C4—41no—
150C11×C4⋊C4—41no—
151C11×C22⋊C4—22no—
152C11×C22⋊C4—41no—
153C11×C22⋊C4—44no—
154C11×C22⋊C4—41no—
155C11×C22⋊C4—41no—
156C11×C22⋊C4—41no—
157C11×C22⋊C4—41no—
158C11×C22⋊C4—42no—
159C11×C22⋊C4—82no—
160C42×C11—42no—
161#3193C2×C1111yescharacteristic, complemented
162#3006C2×C1111yescharacteristic
163#2616C2×C1111yescharacteristic, complemented
164#1964C2×C1111yescharacteristic, complemented
165#1789C2×C1111yescharacteristic, complemented
166#1508C2×C1111yescharacteristic, complemented
167#1305C2×C1111yescharacteristic, complemented
168C23×C11—21no—
169C23×C11—21no—
170C23×C11—22no—
171C23×C11—41no—
172C23×C11—41no—
173C23×C11—41no—
174C23×C11—41no—
175C23×C11—41no—
176C23×C11—42no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—41no—
181C23×C11—81no—
182C23×C11—81no—
183C23×C11#12011yescharacteristic
184C23×C11#12111yescharacteristic
185C23×C11#12711yescharacteristic
186Q8×C11—22no—
187Q8×C11—22no—
188Q8×C11—41no—
189Q8×C11—41no—
190Q8×C11—42no—
191Q8×C11—81no—
192D4×C11—22no—
193D4×C11—22no—
194D4×C11—41no—
195D4×C11—41no—
196D4×C11—42no—
197D4×C11—44no—
198D4×C11—44no—
199D4×C11—42no—
200D4×C11—82no—
201D4×C11—81no—
202D4×C11—81no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—44no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—44no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—42no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—81no—
226C2×C4×C11—81no—
227C2×C4×C11#12011yescharacteristic
228C2×C4×C11#12011yescharacteristic
229C2×C4×C11#12111yescharacteristic
230C2×C4×C11#12111yescharacteristic
231C8×C11—42no—
232C8×C11—42no—
233C22×#41C22×C1111yescharacteristic
234C2×AGL(1,ℤ/8)—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8C22×C1111yescharacteristic
237C2×#121C22×C1111yescharacteristic
238#484—21no—
239#480—21no—
240#468—22no—
241#450—21no—
242#449—22no—
243#448—21no—
244#448—21no—
245#447—21no—
246C2×#104—22no—
247#417—21no—
248C2×#99—22no—
249#407C22×C1111yescharacteristic
250#407C22×C1111yescharacteristic
251#395—21no—
252#394—21no—
253#394—22no—
254#380—21no—
255#380C22×C1111yescharacteristic
256C4×C22⋊C4C22×C1111yescharacteristic
257#328—22no—
258C22×C11—21no—
259C22×C11—21no—
260C22×C11—21no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11—81no—
270C22×C11—81no—
271C22×C11—81no—
272C22×C11—81no—
273C22×C11—81no—
274C22×C11—81no—
275C22×C11—81no—
276C22×C11—81no—
277C22×C11—81no—
278C22×C11—162no—
279C22×C11#39211yescharacteristic
280C22×C11#45311yescharacteristic
281C22×C11#45411yescharacteristic
282C4×C11—21no—
283C4×C11—21no—
284C4×C11—21no—
285C4×C11—42no—
286C4×C11—82no—
287C4×C11—82no—
288C4×C11—81no—
289C4×C11—81no—
290C4×C11—81no—
291C4×C11B(4,𝔽2)12yes—
292C2×#41—21no—
293C2×#41—21no—
294C2×#41—21no—
295C2×#41—21no—
296C2×#41—44no—
297C22×Q8D4×C1111yescharacteristic
298C22×Q8D4×C1111yescharacteristic
299C22×D4—21no—
300C22×D4—21no—
301C22×D4D4×C1111yescharacteristic
302C22×D4D4×C1111yescharacteristic
303C23×C4—21no—
304C23×C4C23×C1111yescharacteristic
305AGL(1,ℤ/8)—44no—
306C2×SD16—22no—
307C2×SD16—22no—
308C2×D8—22no—
309C2×M16—21no—
310C2×M16D4×C1112yes—
311C22⋊Q8—21no—
312C22⋊Q8—21no—
313C22⋊Q8—21no—
314C22⋊Q8—21no—
315C22⋊Q8—44no—
316#121—21no—
317#121—21no—
318#121—21no—
319#121—21no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4D4×C1111yescharacteristic
324C2×C4⋊C4D4×C1111yescharacteristic
325C2×C22⋊C4—21no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4D4×C1112yes—
331C2×C42—21no—
332#107—22no—
333#104—44no—
334#103—22no—
335#103—22no—
336#102—22no—
337#102—22no—
338#99—44no—
339C22⋊C8—21no—
340C22⋊C8—21no—
341C22⋊C8—21no—
342C22⋊C8D4×C1112yes—
343#95—22no—
344#95—21no—
345#95—21no—
346C2×C11—21no—
347C2×C11—21no—
348C2×C11—41no—
349C2×C11—41no—
350C2×C11—82no—
351C2×C11—161no—
352C2×C11#200611yescharacteristic
353C2×C11#200911yescharacteristic
354C2×C11#202111yescharacteristic
355C24—21no—
356C24—21no—
357C24C2×D4×C1111yescharacteristic
358#41—24no—
359#41—24no—
360#41—42no—
361#41—42no—
362#41—42no—
363#41—42no—
364#41—42no—
365#41—42no—
366C2×Q8—21no—
367C2×Q8—21no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—42no—
371C2×Q8—42no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4—42no—
377C2×D4—42no—
378C2×D4—42no—
379C2×D4—42no—
380C2×D4—41no—
381C2×D4—41no—
382C2×D4—42no—
383C2×D4—42no—
384C2×D4—41no—
385C2×D4—41no—
386C22×C4—24no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—42no—
393C22×C4—42no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4C2×D4×C1111yescharacteristic
398C22×C4C2×D4×C1111yescharacteristic
399C22×C4C2×D4×C1111yescharacteristic
400C22×C4C2×D4×C1111yescharacteristic
401C22×C4C2×D4×C1111yescharacteristic
402C22×C4C11×#4111yescharacteristic
403SD16—44no—
404SD16—82no—
405D8—44no—
406M16—42no—
407M16—42no—
408C2×C8—22no—
409C2×C8—22no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—42no—
415C4⋊C4—44no—
416C4⋊C4—41no—
417C4⋊C4—41no—
418C22⋊C4—22no—
419C22⋊C4—44no—
420C22⋊C4—41no—
421C22⋊C4—41no—
422C22⋊C4—41no—
423C22⋊C4—41no—
424C22⋊C4—41no—
425C22⋊C4—42no—
426C22⋊C4—82no—
427C42—42no—
428C11#993111yescharacteristic, direct product factor, Sylow
429C23—21no—
430C23—21no—
431C23—22no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—42no—
438C23—41no—
439C23—41no—
440C23—41no—
441C23—41no—
442C23—81no—
443C23—81no—
444C23C11×#12011yescharacteristic
445C23C11×#12111yescharacteristic
446C23C11×#12711yescharacteristic
447Q8—22no—
448Q8—22no—
449Q8—41no—
450Q8—41no—
451Q8—42no—
452Q8—81no—
453D4—22no—
454D4—22no—
455D4—41no—
456D4—41no—
457D4—42no—
458D4—44no—
459D4—44no—
460D4—42no—
461D4—82no—
462D4—81no—
463D4—81no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—44no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—44no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—81no—
487C2×C4—81no—
488C2×C4C11×#12011yescharacteristic
489C2×C4C11×#12011yescharacteristic
490C2×C4C11×#12111yescharacteristic
491C2×C4C11×#12111yescharacteristic
492C8—42no—
493C8—42no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—42no—
503C22—42no—
504C22—42no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22—81no—
514C22—162no—
515C22C11×#39211yescharacteristic
516C22C11×#45311yescharacteristic
517C22C11×#45411yescharacteristic
518C4—21no—
519C4—21no—
520C4—21no—
521C4—42no—
522C4—82no—
523C4—82no—
524C4—81no—
525C4—81no—
526C4—81no—
527C4C11×B(4,𝔽2)12yes—
528C2—21no—
529C2—21no—
530C2—41no—
531C2—41no—
532C2—82no—
533C2—161no—
534C2C11×#200611yescharacteristic
535C2C11×#200911yescharacteristic
536C2C11×#202111yescharacteristic
subgroupG/H
center, socleC22×C11#392
commutator, Frattini, cosocleC23×C4C23×C11
prime radicalC11×#3006C2
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
1. C11×#3193C2semidirect
3. C11×#2616C2semidirect
4. C11×#1964C2semidirect
5. C11×#1789C2semidirect
6. C11×#1508C2semidirect
7. C11×#1305C2semidirect
87. #9931C11direct (N × H)
161. #3193C2×C11semidirect
163. #2616C2×C11semidirect
164. #1964C2×C11semidirect
165. #1789C2×C11semidirect
166. #1508C2×C11semidirect
167. #1305C2×C11semidirect
428. C11#9931direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31932
C11×#30062
C11×#26162
C11×#19642
C11×#17892
C11×#15082
C11×#13052
#993111