Finite Group Databasebeta

← C11×#24720 #14601913

Subgroups — C11×#24720 #14601913

Order 2816.

706 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3079C211yesmaximal, characteristic, complemented
2C2×C11×#474C211yesmaximal, characteristic, complemented
3C4×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic
4C11×#2925C211yesmaximal, characteristic, complemented
5C11×#2078C212yesmaximal, complemented
6C11×#2051C212yesmaximal
7C11×#1997C211yesmaximal, characteristic, complemented
8C11×#1952C212yesmaximal, complemented
9C11×#1950C211yesmaximal, characteristic, complemented
10C11×#1931C212yesmaximal, complemented
11C11×#1800C211yesmaximal, characteristic, complemented
12C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14C4×C11×#41C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C11×#477—21no—
17C11×#476—21no—
18C11×#475—21no—
19C11×#474—21no—
20C11×#474—21no—
21C11×#474—21no—
22C11×#474—22no—
23C11×#442—21no—
24C11×#440—21no—
25C4×C11×SD16—21no—
26C4×C11×D8—21no—
27C11×#433—22no—
28C11×#432—21no—
29C11×#431—21no—
30C2×C11×#108C2212yes—
31C11×#428C2211yescharacteristic
32C11×#428C2212yes—
33C2×C11×#107C2212yes—
34C11×#423C2211yescharacteristic
35C11×#423C2211yescharacteristic
36C2×C11×C4⋊C8C2211yescharacteristic
37C11×#418C2211yescharacteristic
38C11×#417C2211yescharacteristic
39C11×#417C2212yes—
40C2×C11×#102C2212yes—
41C2×C11×#100C2212yes—
42C11×#408C2212yes—
43C11×#405C2212yes—
44C4×C11×M16C2211yescharacteristic
45C11×#343C2212yes—
46C11×#343C2212yes—
47C11×#343C2212yes—
48C11×#341C2212yes—
49C2×C11×#41C2311yescharacteristic
50C22×Q8×C11—21no—
51C22×D4×C11C2311yescharacteristic
52C23×C4×C11—21no—
53C11×AGL(1,ℤ/8)—22no—
54C11×AGL(1,ℤ/8)—22no—
55C2×C11×SD16—21no—
56C2×C11×D8—21no—
57C2×C11×M16C2311yescharacteristic
58C2×C11×M16C2312yes—
59C2×C11×M16C2312yes—
60C2×C11×M16C2311yescharacteristic
61C22×C8×C11C2312yes—
62C11×C4⋊Q8—21no—
63C11×C4⋊Q8—21no—
64C11×C4⋊Q8—21no—
65C11×C4⋊Q8—21no—
66C4×Q8×C11D411yescharacteristic
67C4×Q8×C11D411yescharacteristic
68C4×D4×C11—21no—
69C4×D4×C11—21no—
70C4×D4×C11—21no—
71C4×D4×C11—21no—
72C4×D4×C11—21no—
73C4×D4×C11—21no—
74C4×D4×C11D411yescharacteristic
75C4×D4×C11D411yescharacteristic
76C11×#117—21no—
77C11×#117C2311yescharacteristic
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2312yes—
81C2×C11×C22⋊C4—21no—
82C2×C42×C11—21no—
83C2×C42×C11C2311yescharacteristic
84C11×#108—24no—
85C11×#107—22no—
86C11×#107—22no—
87C11×#107—21no—
88C11×#107—22no—
89C11×#106—21no—
90C11×#106—22no—
91C11×C4⋊C8—21no—
92C11×C4⋊C8—21no—
93C11×C4⋊C8—21no—
94C11×C4⋊C8—21no—
95C11×C4⋊C8D411yescharacteristic
96C11×C4⋊C8D411yescharacteristic
97C11×C4⋊C8D412yes—
98C11×#103—21no—
99C11×#103—22no—
100C11×#102—21no—
101C11×#102—22no—
102C11×#102—22no—
103C11×#102—22no—
104C11×#102—21no—
105C11×#102—21no—
106C11×#100—24no—
107C11×C22⋊C8—22no—
108C11×C22⋊C8—22no—
109C11×#97—22no—
110C11×#97—21no—
111C4×C8×C11—22no—
112C4×C8×C11—21no—
113#24720C1111yesmaximal, characteristic, direct product factor, Sylow
114C24×C11—21no—
115C11×#41—21no—
116C11×#41—21no—
117C11×#41—21no—
118C11×#41—21no—
119C2×Q8×C11—41no—
120C2×Q8×C11—41no—
121C2×Q8×C11—82no—
122C2×Q8×C11C2×D411yescharacteristic
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11C2×D411yescharacteristic
130C2×D4×C11#4112yes—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
136C22×C4×C11—41no—
137C22×C4×C11—41no—
138C22×C4×C11—82no—
139C22×C4×C11#4111yescharacteristic
140C22×C4×C11#4111yescharacteristic
141C22×C4×C11C2411yescharacteristic
142C11×SD16—24no—
143C11×D8—24no—
144C11×M16—21no—
145C11×M16—22no—
146C11×M16—22no—
147C11×M16—22no—
148C11×M16—21no—
149C11×M16—21no—
150C11×M16—22no—
151C11×M16#4112yes—
152C2×C8×C11—21no—
153C2×C8×C11—22no—
154C2×C8×C11—21no—
155C2×C8×C11—22no—
156C2×C8×C11—22no—
157C2×C8×C11—22no—
158C2×C8×C11C2×D412yes—
159C2×C8×C11C2×D412yes—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—41no—
167C11×C4⋊C4—41no—
168C11×C4⋊C4C2×D411yescharacteristic
169C11×C4⋊C4C2×D411yescharacteristic
170C11×C22⋊C4—21no—
171C11×C22⋊C4—21no—
172C11×C22⋊C4—21no—
173C11×C22⋊C4—41no—
174C11×C22⋊C4—41no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11C2×D411yescharacteristic
179C42×C11C2×D411yescharacteristic
180C42×C11C2×D411yescharacteristic
181C42×C11C2×D411yescharacteristic
182#3079C2×C1111yescharacteristic, complemented
183C2×#474C2×C1111yescharacteristic, complemented
184C4×AGL(1,ℤ/8)C2×C1111yescharacteristic
185#2925C2×C1111yescharacteristic, complemented
186#2078C2×C1112yescomplemented
187#2051C2×C1112yes—
188#1997C2×C1111yescharacteristic, complemented
189#1952C2×C1112yescomplemented
190#1950C2×C1111yescharacteristic, complemented
191#1931C2×C1112yescomplemented
192#1800C2×C1111yescharacteristic, complemented
193C23×C11—21no—
194C23×C11—22no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—81no—
198C23×C11—81no—
199C23×C11C2×#4111yescharacteristic
200Q8×C11—21no—
201Q8×C11—21no—
202Q8×C11—82no—
203Q8×C11—82no—
204D4×C11—21no—
205D4×C11—22no—
206D4×C11—21no—
207D4×C11—22no—
208D4×C11—41no—
209D4×C11—41no—
210D4×C11—41no—
211D4×C11—41no—
212C2×C4×C11—22no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—42no—
220C2×C4×C11—41no—
221C2×C4×C11—42no—
222C2×C4×C11—81no—
223C2×C4×C11—82no—
224C2×C4×C11—82no—
225C2×C4×C11—81no—
226C2×C4×C11—82no—
227C2×C4×C11#12111yescharacteristic
228C2×C4×C11#12111yescharacteristic
229C2×C4×C11#12111yescharacteristic
230C2×C4×C11#12111yescharacteristic
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C2×#4111yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C2×C4×C112−1+411yescharacteristic
236C2×C4×C112−1+411yescharacteristic
237C8×C11—22no—
238C8×C11—22no—
239C8×C11—22no—
240C8×C11—42no—
241C8×C11—41no—
242C8×C11—42no—
243C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
244C2×C4⋊Q8C22×C1111yescharacteristic
245C4×#41C22×C1111yescharacteristic
246C2×C4×D4C22×C1111yescharacteristic
247#477—21no—
248#476—21no—
249#475—21no—
250#474—21no—
251#474—21no—
252#474—21no—
253#474—22no—
254#442—21no—
255#440—21no—
256C4×SD16—21no—
257C4×D8—21no—
258#433—22no—
259#432—21no—
260#431—21no—
261C2×#108C22×C1112yes—
262#428C22×C1112yes—
263#428C22×C1111yescharacteristic
264C2×#107C22×C1112yes—
265#423C22×C1111yescharacteristic
266#423C22×C1111yescharacteristic
267C2×C4⋊C8C22×C1111yescharacteristic
268#418C22×C1111yescharacteristic
269#417C22×C1112yes—
270#417C22×C1111yescharacteristic
271C2×#102C22×C1112yes—
272C2×#100C22×C1112yes—
273#408C22×C1112yes—
274#405C22×C1112yes—
275C4×M16C22×C1111yescharacteristic
276#343C22×C1112yes—
277#343C22×C1112yes—
278#343C22×C1112yes—
279#341C22×C1112yes—
280C22×C11—21no—
281C22×C11—21no—
282C22×C11—41no—
283C22×C11—42no—
284C22×C11—41no—
285C22×C11—41no—
286C22×C11—82no—
287C22×C11—82no—
288C22×C11—81no—
289C22×C11—81no—
290C22×C11C2×#12111yescharacteristic
291C22×C11#55211yescharacteristic
292C22×C11#55611yescharacteristic
293C4×C11—21no—
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—41no—
297C4×C11—41no—
298C4×C11—41no—
299C4×C11—81no—
300C4×C11—82no—
301C4×C11#47212yes—
302C4×C11#52511yescharacteristic
303C4×C11#53611yescharacteristic
304C4×C11#54711yescharacteristic
305C4×C11#54811yescharacteristic
306C2×#41C23×C1111yescharacteristic
307C22×Q8—21no—
308C22×D4C23×C1111yescharacteristic
309C23×C4—21no—
310AGL(1,ℤ/8)—22no—
311AGL(1,ℤ/8)—22no—
312C2×SD16—21no—
313C2×D8—21no—
314C2×M16C23×C1111yescharacteristic
315C2×M16C23×C1112yes—
316C2×M16C23×C1112yes—
317C2×M16C23×C1111yescharacteristic
318C22×C8C23×C1112yes—
319C4⋊Q8—21no—
320C4⋊Q8—21no—
321C4⋊Q8—21no—
322C4⋊Q8—21no—
323C4×Q8D4×C1111yescharacteristic
324C4×Q8D4×C1111yescharacteristic
325C4×D4—21no—
326C4×D4—21no—
327C4×D4—21no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—21no—
331C4×D4D4×C1111yescharacteristic
332C4×D4D4×C1111yescharacteristic
333#117—21no—
334#117C23×C1111yescharacteristic
335C2×C4⋊C4—21no—
336C2×C4⋊C4C23×C1111yescharacteristic
337C2×C4⋊C4C23×C1112yes—
338C2×C22⋊C4—21no—
339C2×C42—21no—
340C2×C42C23×C1111yescharacteristic
341#108—24no—
342#107—22no—
343#107—22no—
344#107—21no—
345#107—22no—
346#106—21no—
347#106—22no—
348C4⋊C8—21no—
349C4⋊C8—21no—
350C4⋊C8—21no—
351C4⋊C8—21no—
352C4⋊C8D4×C1111yescharacteristic
353C4⋊C8D4×C1111yescharacteristic
354C4⋊C8D4×C1112yes—
355#103—21no—
356#103—22no—
357#102—21no—
358#102—22no—
359#102—22no—
360#102—22no—
361#102—21no—
362#102—21no—
363#100—24no—
364C22⋊C8—22no—
365C22⋊C8—22no—
366#97—22no—
367#97—21no—
368C4×C8—22no—
369C4×C8—21no—
370C2×C11—21no—
371C2×C11—21no—
372C2×C11—81no—
373C2×C11—82no—
374C2×C11#241511yescharacteristic
375C2×C11C2×#47211yescharacteristic
376C2×C11#306911yescharacteristic
377C24—21no—
378#41—21no—
379#41—21no—
380#41—21no—
381#41—21no—
382C2×Q8—41no—
383C2×Q8—41no—
384C2×Q8—82no—
385C2×Q8C2×D4×C1111yescharacteristic
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4C2×D4×C1111yescharacteristic
393C2×D4C11×#4112yes—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—82no—
402C22×C4C11×#4111yescharacteristic
403C22×C4C11×#4111yescharacteristic
404C22×C4C24×C1111yescharacteristic
405SD16—24no—
406D8—24no—
407M16—21no—
408M16—22no—
409M16—22no—
410M16—22no—
411M16—21no—
412M16—21no—
413M16—22no—
414M16C11×#4112yes—
415C2×C8—21no—
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—22no—
419C2×C8—21no—
420C2×C8—22no—
421C2×C8C2×D4×C1112yes—
422C2×C8C2×D4×C1112yes—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—22no—
426C4⋊C4—21no—
427C4⋊C4—22no—
428C4⋊C4—21no—
429C4⋊C4—41no—
430C4⋊C4—41no—
431C4⋊C4C2×D4×C1111yescharacteristic
432C4⋊C4C2×D4×C1111yescharacteristic
433C22⋊C4—21no—
434C22⋊C4—21no—
435C22⋊C4—21no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C42—21no—
439C42—21no—
440C42—21no—
441C42C2×D4×C1111yescharacteristic
442C42C2×D4×C1111yescharacteristic
443C42C2×D4×C1111yescharacteristic
444C42C2×D4×C1111yescharacteristic
445C11#2472011yescharacteristic, direct product factor, Sylow
446C23—21no—
447C23—22no—
448C23—41no—
449C23—41no—
450C23—81no—
451C23—81no—
452C23C2×C11×#4111yescharacteristic
453Q8—21no—
454Q8—21no—
455Q8—82no—
456Q8—82no—
457D4—21no—
458D4—22no—
459D4—21no—
460D4—22no—
461D4—41no—
462D4—41no—
463D4—41no—
464D4—41no—
465C2×C4—22no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—81no—
476C2×C4—82no—
477C2×C4—82no—
478C2×C4—81no—
479C2×C4—82no—
480C2×C4C11×#12111yescharacteristic
481C2×C4C11×#12111yescharacteristic
482C2×C4C11×#12111yescharacteristic
483C2×C4C11×#12111yescharacteristic
484C2×C4C22×D4×C1111yescharacteristic
485C2×C4C22×D4×C1111yescharacteristic
486C2×C4C2×C11×#4111yescharacteristic
487C2×C4C2×C11×#4111yescharacteristic
488C2×C4C11×2−1+411yescharacteristic
489C2×C4C11×2−1+411yescharacteristic
490C8—22no—
491C8—22no—
492C8—22no—
493C8—42no—
494C8—41no—
495C8—42no—
496C22—21no—
497C22—21no—
498C22—41no—
499C22—42no—
500C22—41no—
501C22—41no—
502C22—82no—
503C22—82no—
504C22—81no—
505C22—81no—
506C22C2×C11×#12111yescharacteristic
507C22C11×#55211yescharacteristic
508C22C11×#55611yescharacteristic
509C4—21no—
510C4—21no—
511C4—21no—
512C4—41no—
513C4—41no—
514C4—41no—
515C4—81no—
516C4—82no—
517C4C11×#47212yes—
518C4C11×#52511yescharacteristic
519C4C11×#53611yescharacteristic
520C4C11×#54711yescharacteristic
521C4C11×#54811yescharacteristic
522C2—21no—
523C2—21no—
524C2—81no—
525C2—82no—
526C2C11×#241511yescharacteristic
527C2C2×C11×#47211yescharacteristic
528C2C11×#306911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×AGL(1,ℤ/8)C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3079C2semidirect
2. C2×C11×#474C2semidirect
4. C11×#2925C2semidirect
5. C11×#2078C2semidirect
7. C11×#1997C2semidirect
8. C11×#1952C2semidirect
9. C11×#1950C2semidirect
10. C11×#1931C2semidirect
11. C11×#1800C2semidirect
113. #24720C11direct (N × H)
182. #3079C2×C11semidirect
183. C2×#474C2×C11semidirect
185. #2925C2×C11semidirect
186. #2078C2×C11semidirect
188. #1997C2×C11semidirect
189. #1952C2×C11semidirect
190. #1950C2×C11semidirect
191. #1931C2×C11semidirect
192. #1800C2×C11semidirect
445. C11#24720direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30792
C2×C11×#4742
C4×C11×AGL(1,ℤ/8)2
C11×#29252
C11×#20782
C11×#20512
C11×#19972
C11×#19522
C11×#19502
C11×#19312
C11×#18002
#2472011