Finite Group Databasebeta

← C11×#9981 #14587174

Subgroups — C11×#9981 #14587174

Order 2816.

764 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 764 conjugacy classes of subgroups — too many to draw. Only its 98 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, complemented
2C11×#3006C211yesmaximal, characteristic
3C11×#2816C211yesmaximal, characteristic, complemented
4C11×#1782C211yesmaximal, characteristic, complemented
5C11×#1511C211yesmaximal, characteristic, complemented
6C11×#1510C211yesmaximal, characteristic, complemented
7C11×#1306C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C2×C11×#137—21no—
10C2×C11×AGL(1,ℤ/8)—21no—
11C2×C11×C22⋊Q8C2211yescharacteristic
12C2×C11×#121C2211yescharacteristic
13C11×#452—22no—
14C11×#451—21no—
15C11×#450—21no—
16C11×#449—22no—
17C11×#448—21no—
18C11×#447—21no—
19C11×#417—21no—
20C11×#417—21no—
21C2×C11×#99—22no—
22C11×#407C2211yescharacteristic
23C11×#407C2211yescharacteristic
24C11×#399—21no—
25C11×#398—21no—
26C11×#394—21no—
27C11×#394—22no—
28C11×#393—21no—
29C11×#381C2211yescharacteristic
30C11×#381C2211yescharacteristic
31C11×#328—22no—
32C11×#327—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×#137—44no—
47C11×AGL(1,ℤ/8)—44no—
48C2×C11×Q16—22no—
49C2×C11×SD16—22no—
50C2×C11×SD16—22no—
51C2×C11×D8—22no—
52C2×C11×M16—21no—
53C2×C11×M16—21no—
54C11×C22⋊Q8—21no—
55C11×C22⋊Q8—21no—
56C11×C22⋊Q8—21no—
57C11×C22⋊Q8—21no—
58C11×#121—21no—
59C11×#121—21no—
60C11×#121—21no—
61C11×#121—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C4⋊C4D411yescharacteristic
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4D412yes—
72C11×#103—22no—
73C11×#103—22no—
74C11×#102—22no—
75C11×#102—22no—
76C11×#99—44no—
77C11×C22⋊C8—21no—
78C11×C22⋊C8—21no—
79C11×C22⋊C8D412yes—
80C11×C22⋊C8D412yes—
81C11×#95—22no—
82C11×#95—21no—
83C11×#95—21no—
84C11×#95—21no—
85C11×#95—21no—
86#9981C1111yesmaximal, characteristic, direct product factor, Sylow
87C24×C11—21no—
88C24×C11—21no—
89C24×C11C2×D411yescharacteristic
90C11×#41—24no—
91C11×#41—24no—
92C11×#41—42no—
93C11×#41—42no—
94C11×#41—42no—
95C11×#41—42no—
96C11×#41—42no—
97C11×#41—42no—
98C2×Q8×C11—21no—
99C2×Q8×C11—21no—
100C2×Q8×C11—21no—
101C2×Q8×C11—21no—
102C2×Q8×C11—42no—
103C2×Q8×C11—42no—
104C2×D4×C11—24no—
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—41no—
113C2×D4×C11—41no—
114C2×D4×C11—41no—
115C2×D4×C11—41no—
116C2×D4×C11—82no—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—42no—
123C22×C4×C11—42no—
124C22×C4×C11—42no—
125C22×C4×C11—41no—
126C22×C4×C11—41no—
127C22×C4×C11—41no—
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×SD16—44no—
137C11×D8—44no—
138C11×M16—42no—
139C11×M16—42no—
140C2×C8×C11—22no—
141C2×C8×C11—22no—
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—82no—
149C11×C22⋊C4—41no—
150C11×C22⋊C4—41no—
151C11×C22⋊C4—41no—
152C11×C22⋊C4—41no—
153C11×C22⋊C4—42no—
154C11×C22⋊C4—42no—
155C11×C22⋊C4—82no—
156C11×C22⋊C4—82no—
157#3007C2×C1111yescharacteristic, complemented
158#3006C2×C1111yescharacteristic
159#2816C2×C1111yescharacteristic, complemented
160#1782C2×C1111yescharacteristic, complemented
161#1511C2×C1111yescharacteristic, complemented
162#1510C2×C1111yescharacteristic, complemented
163#1306C2×C1111yescharacteristic, complemented
164C23×C11—22no—
165C23×C11—22no—
166C23×C11—41no—
167C23×C11—41no—
168C23×C11—41no—
169C23×C11—42no—
170C23×C11—42no—
171C23×C11—41no—
172C23×C11—41no—
173C23×C11—42no—
174C23×C11—81no—
175C23×C11—81no—
176C23×C11#12011yescharacteristic
177C23×C11#12111yescharacteristic
178C23×C11#12711yescharacteristic
179Q8×C11—22no—
180Q8×C11—22no—
181Q8×C11—41no—
182Q8×C11—41no—
183Q8×C11—42no—
184Q8×C11—81no—
185D4×C11—22no—
186D4×C11—22no—
187D4×C11—41no—
188D4×C11—41no—
189D4×C11—42no—
190D4×C11—44no—
191D4×C11—44no—
192D4×C11—81no—
193D4×C11—82no—
194D4×C11—82no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—44no—
203C2×C4×C11—44no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—42no—
208C2×C4×C11—41no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—81no—
217C2×C4×C11—81no—
218C2×C4×C11—81no—
219C2×C4×C11#12011yescharacteristic
220C2×C4×C11#12011yescharacteristic
221C2×C4×C11#12111yescharacteristic
222C2×C4×C11#12111yescharacteristic
223C8×C11—42no—
224C8×C11—42no—
225C22×#41C22×C1111yescharacteristic
226C2×#137—21no—
227C2×AGL(1,ℤ/8)—21no—
228C2×C22⋊Q8C22×C1111yescharacteristic
229C2×#121C22×C1111yescharacteristic
230#452—22no—
231#451—21no—
232#450—21no—
233#449—22no—
234#448—21no—
235#447—21no—
236#417—21no—
237#417—21no—
238C2×#99—22no—
239#407C22×C1111yescharacteristic
240#407C22×C1111yescharacteristic
241#399—21no—
242#398—21no—
243#394—21no—
244#394—22no—
245#393—21no—
246#381C22×C1111yescharacteristic
247#381C22×C1111yescharacteristic
248#328—22no—
249#327—22no—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—21no—
258C22×C11—42no—
259C22×C11—82no—
260C22×C11—84no—
261C22×C11—82no—
262C22×C11—82no—
263C22×C11—81no—
264C22×C11—81no—
265C22×C11—81no—
266C22×C11—81no—
267C22×C11—81no—
268C22×C11#39211yescharacteristic
269C22×C11B(4,𝔽2)12yes—
270C4×C11—21no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—21no—
274C4×C11—42no—
275C4×C11—82no—
276C4×C11—81no—
277C4×C11—81no—
278C4×C11—81no—
279C4×C11—161no—
280C2×#41—21no—
281C2×#41—21no—
282C2×#41—21no—
283C2×#41—21no—
284C2×#41—44no—
285C22×Q8D4×C1111yescharacteristic
286C22×Q8D4×C1111yescharacteristic
287C22×D4—21no—
288C22×D4—21no—
289C22×D4D4×C1111yescharacteristic
290C22×D4D4×C1111yescharacteristic
291C23×C4—21no—
292C23×C4C23×C1111yescharacteristic
293#137—44no—
294AGL(1,ℤ/8)—44no—
295C2×Q16—22no—
296C2×SD16—22no—
297C2×SD16—22no—
298C2×D8—22no—
299C2×M16—21no—
300C2×M16—21no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304C22⋊Q8—21no—
305#121—21no—
306#121—21no—
307#121—21no—
308#121—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4D4×C1111yescharacteristic
312C2×C4⋊C4D4×C1111yescharacteristic
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4D4×C1112yes—
319#103—22no—
320#103—22no—
321#102—22no—
322#102—22no—
323#99—44no—
324C22⋊C8—21no—
325C22⋊C8—21no—
326C22⋊C8D4×C1112yes—
327C22⋊C8D4×C1112yes—
328#95—22no—
329#95—21no—
330#95—21no—
331#95—21no—
332#95—21no—
333C2×C11—22no—
334C2×C11—41no—
335C2×C11—41no—
336C2×C11—82no—
337C2×C11—161no—
338C2×C11#200811yescharacteristic
339C2×C11#200911yescharacteristic
340C2×C11#202111yescharacteristic
341C24—21no—
342C24—21no—
343C24C2×D4×C1111yescharacteristic
344#41—24no—
345#41—24no—
346#41—42no—
347#41—42no—
348#41—42no—
349#41—42no—
350#41—42no—
351#41—42no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—42no—
357C2×Q8—42no—
358C2×D4—24no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—42no—
364C2×D4—42no—
365C2×D4—42no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—82no—
371C22×C4—21no—
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—42no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4C2×D4×C1111yescharacteristic
383C22×C4C2×D4×C1111yescharacteristic
384C22×C4C2×D4×C1111yescharacteristic
385C22×C4C2×D4×C1111yescharacteristic
386C22×C4C2×D4×C1111yescharacteristic
387C22×C4C11×#4111yescharacteristic
388Q16—44no—
389SD16—44no—
390SD16—44no—
391D8—44no—
392M16—42no—
393M16—42no—
394C2×C8—22no—
395C2×C8—22no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—41no—
401C4⋊C4—41no—
402C4⋊C4—82no—
403C22⋊C4—41no—
404C22⋊C4—41no—
405C22⋊C4—41no—
406C22⋊C4—41no—
407C22⋊C4—42no—
408C22⋊C4—42no—
409C22⋊C4—82no—
410C22⋊C4—82no—
411C11#998111yescharacteristic, direct product factor, Sylow
412C23—22no—
413C23—22no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23—42no—
418C23—42no—
419C23—41no—
420C23—41no—
421C23—42no—
422C23—81no—
423C23—81no—
424C23C11×#12011yescharacteristic
425C23C11×#12111yescharacteristic
426C23C11×#12711yescharacteristic
427Q8—22no—
428Q8—22no—
429Q8—41no—
430Q8—41no—
431Q8—42no—
432Q8—81no—
433D4—22no—
434D4—22no—
435D4—41no—
436D4—41no—
437D4—42no—
438D4—44no—
439D4—44no—
440D4—81no—
441D4—82no—
442D4—82no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—44no—
451C2×C4—44no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—81no—
465C2×C4—81no—
466C2×C4—81no—
467C2×C4C11×#12011yescharacteristic
468C2×C4C11×#12011yescharacteristic
469C2×C4C11×#12111yescharacteristic
470C2×C4C11×#12111yescharacteristic
471C8—42no—
472C8—42no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—42no—
482C22—82no—
483C22—84no—
484C22—82no—
485C22—82no—
486C22—81no—
487C22—81no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22C11×#39211yescharacteristic
492C22C11×B(4,𝔽2)12yes—
493C4—21no—
494C4—21no—
495C4—21no—
496C4—21no—
497C4—42no—
498C4—82no—
499C4—81no—
500C4—81no—
501C4—81no—
502C4—161no—
503C2—22no—
504C2—41no—
505C2—41no—
506C2—82no—
507C2—161no—
508C2C11×#200811yescharacteristic
509C2C11×#200911yescharacteristic
510C2C11×#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×#3007C2semidirect
3. C11×#2816C2semidirect
4. C11×#1782C2semidirect
5. C11×#1511C2semidirect
6. C11×#1510C2semidirect
7. C11×#1306C2semidirect
86. #9981C11direct (N × H)
157. #3007C2×C11semidirect
159. #2816C2×C11semidirect
160. #1782C2×C11semidirect
161. #1511C2×C11semidirect
162. #1510C2×C11semidirect
163. #1306C2×C11semidirect
411. C11#9981direct (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×#30062
C11×#28162
C11×#17822
C11×#15112
C11×#15102
C11×#13062
#998111