Finite Group Databasebeta

← C11×#24987 #14602180

Subgroups — C11×#24987 #14602180

Order 2816.

638 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#471C211yesmaximal, characteristic
2C11×#2949C211yesmaximal, characteristic, complemented
3C11×#2082C211yesmaximal, characteristic, complemented
4C11×#2081C211yesmaximal, characteristic, complemented
5C11×#2049C211yesmaximal, characteristic, complemented
6C11×#2048C211yesmaximal, characteristic
7C11×#1977C211yesmaximal, characteristic, complemented
8C11×#1953C211yesmaximal, characteristic, complemented
9C11×#1905C211yesmaximal, characteristic, complemented
10C11×#1904C211yesmaximal, characteristic
11C11×#1833C211yesmaximal, characteristic, complemented
12C11×#1830C211yesmaximal, characteristic, complemented
13C11×#1829C211yesmaximal, characteristic, complemented
14C11×#1814C211yesmaximal, characteristic, complemented
15C11×#1757C211yesmaximal, characteristic, complemented
16C2×C11×#137C2211yescharacteristic
17C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C2×C11×#131C2211yescharacteristic
20C11×#519C2211yescharacteristic
21C11×#518C2211yescharacteristic
22C11×#471—22no—
23C11×#471—22no—
24C11×#440—22no—
25C4×C11×SD16—22no—
26C11×#430C2211yescharacteristic
27C11×#430C2211yescharacteristic
28C2×C11×#108C2211yescharacteristic
29C2×C11×#108C2211yescharacteristic
30C11×#427C2211yescharacteristic
31C11×#421C2211yescharacteristic
32C11×#421C2211yescharacteristic
33C11×#419C2211yescharacteristic
34C11×#419C2211yescharacteristic
35C11×#418C2211yescharacteristic
36C11×#418C2211yescharacteristic
37C11×#413C2211yescharacteristic
38C2×C11×#101C2211yescharacteristic
39C2×C11×#101C2211yescharacteristic
40C2×C11×#100C2211yescharacteristic
41C2×C11×#100C2211yescharacteristic
42C11×#410C2211yescharacteristic
43C11×#405C2211yescharacteristic
44C11×#405C2211yescharacteristic
45C11×#344C2211yescharacteristic
46C11×#344C2211yescharacteristic
47C11×#344C2211yescharacteristic
48C11×#344C2211yescharacteristic
49C11×#344C2211yescharacteristic
50C11×#344C2211yescharacteristic
51C11×#344C2211yescharacteristic
52C11×#344C2211yescharacteristic
53C11×H(3,ℤ/4)C2211yescharacteristic
54C11×H(3,ℤ/4)C2211yescharacteristic
55C2×C11×#41C2311yescharacteristic
56C22×Q8×C11C2311yescharacteristic
57C22×D4×C11C2311yescharacteristic
58C11×#137—22no—
59C11×#137—41no—
60C11×AGL(1,ℤ/8)—22no—
61C11×AGL(1,ℤ/8)—41no—
62C2×C11×Q16—21no—
63C2×C11×SD16—21no—
64C2×C11×SD16—21no—
65C2×C11×SD16—21no—
66C2×C11×SD16—21no—
67C2×C11×SD16—21no—
68C2×C11×SD16—21no—
69C2×C11×SD16D412yes—
70C2×C11×SD16D412yes—
71C2×C11×D8—21no—
72C11×#131—21no—
73C11×#131—21no—
74C11×#131—21no—
75C11×#131—21no—
76C2×C11×M16—21no—
77C2×C11×M16C2311yescharacteristic
78C2×C11×M16C2311yescharacteristic
79C2×C11×M16C2311yescharacteristic
80C2×C11×M16C2311yescharacteristic
81C2×C11×M16C2311yescharacteristic
82C2×C11×M16C2311yescharacteristic
83C2×C11×M16C2311yescharacteristic
84C22×C8×C11—21no—
85C22×C8×C11C2311yescharacteristic
86C4×Q8×C11—22no—
87C4×Q8×C11—41no—
88C4×D4×C11—22no—
89C4×D4×C11—41no—
90C11×#117—22no—
91C11×#117C2311yescharacteristic
92C11×#117C2311yescharacteristic
93C11×#117C2311yescharacteristic
94C11×#117C2311yescharacteristic
95C2×C11×C22⋊C4—22no—
96C11×#108—21no—
97C11×#108—21no—
98C11×#108—21no—
99C11×#108—21no—
100C11×#108—41no—
101C11×#108—41no—
102C11×#107—21no—
103C11×#106—21no—
104C11×#104—41no—
105C11×#104—41no—
106C11×#103—22no—
107C11×#103—41no—
108C11×#102—22no—
109C11×#102—41no—
110C11×#101—22no—
111C11×#101—21no—
112C11×#101—41no—
113C11×#100—22no—
114C11×#100—21no—
115C11×#100—41no—
116C11×#99—22no—
117C11×#97—21no—
118C11×#97—21no—
119C4×C8×C11—21no—
120C4×C8×C11—21no—
121#24987C1111yesmaximal, characteristic, direct product factor, Sylow
122C24×C11—21no—
123C11×#41—21no—
124C11×#41—21no—
125C11×#41—21no—
126C11×#41—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11C2×D412yes—
133C2×Q8×C11#4111yescharacteristic
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11C2×D412yes—
141C2×D4×C11#4111yescharacteristic
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—42no—
145C22×C4×C11C2411yescharacteristic
146C11×Q16—42no—
147C11×SD16—22no—
148C11×SD16—22no—
149C11×SD16—22no—
150C11×SD16—22no—
151C11×SD16—42no—
152C11×SD16—42no—
153C11×D8—42no—
154C11×M16—21no—
155C11×M16—21no—
156C11×M16—21no—
157C11×M16—21no—
158C11×M16—21no—
159C11×M16—21no—
160C11×M16—21no—
161C11×M16—21no—
162C11×M16—21no—
163C11×M16—21no—
164C11×M16—21no—
165C11×M16—21no—
166C11×M16—21no—
167C11×M16—21no—
168C11×M16—41no—
169C11×M16—41no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—41no—
178C2×C8×C11—41no—
179C2×C8×C11C2×D411yescharacteristic
180C2×C8×C11C2×D411yescharacteristic
181C2×C8×C11#4111yescharacteristic
182C2×C8×C11#4111yescharacteristic
183C2×C8×C11#4111yescharacteristic
184C2×C8×C11#4111yescharacteristic
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—42no—
190C11×C22⋊C4—21no—
191C11×C22⋊C4—21no—
192C11×C22⋊C4—21no—
193C11×C22⋊C4—42no—
194C11×C22⋊C4#4112yes—
195C42×C11—21no—
196C42×C11—21no—
197C42×C11—21no—
198C42×C11—21no—
199C42×C11—42no—
200C2×#471C2×C1111yescharacteristic
201#2949C2×C1111yescharacteristic, complemented
202#2082C2×C1111yescharacteristic, complemented
203#2081C2×C1111yescharacteristic, complemented
204#2049C2×C1111yescharacteristic, complemented
205#2048C2×C1111yescharacteristic
206#1977C2×C1111yescharacteristic, complemented
207#1953C2×C1111yescharacteristic, complemented
208#1905C2×C1111yescharacteristic, complemented
209#1904C2×C1111yescharacteristic
210#1833C2×C1111yescharacteristic, complemented
211#1830C2×C1111yescharacteristic, complemented
212#1829C2×C1111yescharacteristic, complemented
213#1814C2×C1111yescharacteristic, complemented
214#1757C2×C1111yescharacteristic, complemented
215C23×C11—21no—
216C23×C11—22no—
217C23×C11—41no—
218C23×C11—41no—
219C23×C11—161no—
220C23×C11C2×#4111yescharacteristic
221Q8×C11—22no—
222Q8×C11—21no—
223Q8×C11—22no—
224Q8×C11—21no—
225Q8×C11—41no—
226Q8×C11—41no—
227D4×C11—22no—
228D4×C11—21no—
229D4×C11—22no—
230D4×C11—21no—
231D4×C11—41no—
232D4×C11—41no—
233D4×C11—41no—
234D4×C11—41no—
235C2×C4×C11—21no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—162no—
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11H(5,𝔽2)11yescharacteristic
251C2×C4×C11H(5,𝔽2)11yescharacteristic
252C8×C11—41no—
253C8×C11—41no—
254C8×C11—41no—
255C8×C11—41no—
256C8×C11—41no—
257C8×C11—41no—
258C8×C11—41no—
259C8×C11#12311yescharacteristic
260C8×C11#12311yescharacteristic
261C8×C11#12311yescharacteristic
262C8×C11#12311yescharacteristic
263C2×#137C22×C1111yescharacteristic
264C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
265C22×SD16C22×C1111yescharacteristic
266C2×#131C22×C1111yescharacteristic
267#519C22×C1111yescharacteristic
268#518C22×C1111yescharacteristic
269#471—22no—
270#471—22no—
271#440—22no—
272C4×SD16—22no—
273#430C22×C1111yescharacteristic
274#430C22×C1111yescharacteristic
275C2×#108C22×C1111yescharacteristic
276C2×#108C22×C1111yescharacteristic
277#427C22×C1111yescharacteristic
278#421C22×C1111yescharacteristic
279#421C22×C1111yescharacteristic
280#419C22×C1111yescharacteristic
281#419C22×C1111yescharacteristic
282#418C22×C1111yescharacteristic
283#418C22×C1111yescharacteristic
284#413C22×C1111yescharacteristic
285C2×#101C22×C1111yescharacteristic
286C2×#101C22×C1111yescharacteristic
287C2×#100C22×C1111yescharacteristic
288C2×#100C22×C1111yescharacteristic
289#410C22×C1111yescharacteristic
290#405C22×C1111yescharacteristic
291#405C22×C1111yescharacteristic
292#344C22×C1111yescharacteristic
293#344C22×C1111yescharacteristic
294#344C22×C1111yescharacteristic
295#344C22×C1111yescharacteristic
296#344C22×C1111yescharacteristic
297#344C22×C1111yescharacteristic
298#344C22×C1111yescharacteristic
299#344C22×C1111yescharacteristic
300H(3,ℤ/4)C22×C1111yescharacteristic
301H(3,ℤ/4)C22×C1111yescharacteristic
302C22×C11—41no—
303C22×C11—41no—
304C22×C11—42no—
305C22×C11—82no—
306C22×C11—81no—
307C22×C11—161no—
308C22×C11—161no—
309C22×C11#52911yescharacteristic
310C22×C11#54611yescharacteristic
311C22×C11#55511yescharacteristic
312C4×C11—42no—
313C4×C11—41no—
314C4×C11—42no—
315C4×C11—81no—
316C4×C11—81no—
317C4×C11—81no—
318C4×C11C2×#12311yescharacteristic
319C4×C11#54011yescharacteristic
320C4×C11#54611yescharacteristic
321C4×C11#55311yescharacteristic
322C2×#41C23×C1111yescharacteristic
323C22×Q8C23×C1111yescharacteristic
324C22×D4C23×C1111yescharacteristic
325#137—22no—
326#137—41no—
327AGL(1,ℤ/8)—22no—
328AGL(1,ℤ/8)—41no—
329C2×Q16—21no—
330C2×SD16—21no—
331C2×SD16—21no—
332C2×SD16—21no—
333C2×SD16—21no—
334C2×SD16—21no—
335C2×SD16—21no—
336C2×SD16D4×C1112yes—
337C2×SD16D4×C1112yes—
338C2×D8—21no—
339#131—21no—
340#131—21no—
341#131—21no—
342#131—21no—
343C2×M16—21no—
344C2×M16C23×C1111yescharacteristic
345C2×M16C23×C1111yescharacteristic
346C2×M16C23×C1111yescharacteristic
347C2×M16C23×C1111yescharacteristic
348C2×M16C23×C1111yescharacteristic
349C2×M16C23×C1111yescharacteristic
350C2×M16C23×C1111yescharacteristic
351C22×C8—21no—
352C22×C8C23×C1111yescharacteristic
353C4×Q8—22no—
354C4×Q8—41no—
355C4×D4—22no—
356C4×D4—41no—
357#117—22no—
358#117C23×C1111yescharacteristic
359#117C23×C1111yescharacteristic
360#117C23×C1111yescharacteristic
361#117C23×C1111yescharacteristic
362C2×C22⋊C4—22no—
363#108—21no—
364#108—21no—
365#108—21no—
366#108—21no—
367#108—41no—
368#108—41no—
369#107—21no—
370#106—21no—
371#104—41no—
372#104—41no—
373#103—22no—
374#103—41no—
375#102—22no—
376#102—41no—
377#101—22no—
378#101—21no—
379#101—41no—
380#100—22no—
381#100—21no—
382#100—41no—
383#99—22no—
384#97—21no—
385#97—21no—
386C4×C8—21no—
387C4×C8—21no—
388C2×C11—21no—
389C2×C11—21no—
390C2×C11—21no—
391C2×C11—81no—
392C2×C11—82no—
393C2×C11#242011yescharacteristic
394C24—21no—
395#41—21no—
396#41—21no—
397#41—21no—
398#41—21no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8C2×D4×C1112yes—
405C2×Q8C11×#4111yescharacteristic
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4C2×D4×C1112yes—
413C2×D4C11×#4111yescharacteristic
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—42no—
417C22×C4C24×C1111yescharacteristic
418Q16—42no—
419SD16—22no—
420SD16—22no—
421SD16—22no—
422SD16—22no—
423SD16—42no—
424SD16—42no—
425D8—42no—
426M16—21no—
427M16—21no—
428M16—21no—
429M16—21no—
430M16—21no—
431M16—21no—
432M16—21no—
433M16—21no—
434M16—21no—
435M16—21no—
436M16—21no—
437M16—21no—
438M16—21no—
439M16—21no—
440M16—41no—
441M16—41no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—41no—
450C2×C8—41no—
451C2×C8C2×D4×C1111yescharacteristic
452C2×C8C2×D4×C1111yescharacteristic
453C2×C8C11×#4111yescharacteristic
454C2×C8C11×#4111yescharacteristic
455C2×C8C11×#4111yescharacteristic
456C2×C8C11×#4111yescharacteristic
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—42no—
462C22⋊C4—21no—
463C22⋊C4—21no—
464C22⋊C4—21no—
465C22⋊C4—42no—
466C22⋊C4C11×#4112yes—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—21no—
471C42—42no—
472C11#2498711yescharacteristic, direct product factor, Sylow
473C23—21no—
474C23—22no—
475C23—41no—
476C23—41no—
477C23—161no—
478C23C2×C11×#4111yescharacteristic
479Q8—22no—
480Q8—21no—
481Q8—22no—
482Q8—21no—
483Q8—41no—
484Q8—41no—
485D4—22no—
486D4—21no—
487D4—22no—
488D4—21no—
489D4—41no—
490D4—41no—
491D4—41no—
492D4—41no—
493C2×C4—21no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—162no—
504C2×C4C22×D4×C1111yescharacteristic
505C2×C4C2×C11×#4111yescharacteristic
506C2×C4C2×C11×#4111yescharacteristic
507C2×C4C2×C11×#4111yescharacteristic
508C2×C4C11×H(5,𝔽2)11yescharacteristic
509C2×C4C11×H(5,𝔽2)11yescharacteristic
510C8—41no—
511C8—41no—
512C8—41no—
513C8—41no—
514C8—41no—
515C8—41no—
516C8—41no—
517C8C11×#12311yescharacteristic
518C8C11×#12311yescharacteristic
519C8C11×#12311yescharacteristic
520C8C11×#12311yescharacteristic
521C22—41no—
522C22—41no—
523C22—42no—
524C22—82no—
525C22—81no—
526C22—161no—
527C22—161no—
528C22C11×#52911yescharacteristic
529C22C11×#54611yescharacteristic
530C22C11×#55511yescharacteristic
531C4—42no—
532C4—41no—
533C4—42no—
534C4—81no—
535C4—81no—
536C4—81no—
537C4C2×C11×#12311yescharacteristic
538C4C11×#54011yescharacteristic
539C4C11×#54611yescharacteristic
540C4C11×#55311yescharacteristic
541C2—21no—
542C2—21no—
543C2—21no—
544C2—82no—
545C2—81no—
546C2C11×#242011yescharacteristic
subgroupG/H
center, socleC2×C11#2420
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×AGL(1,ℤ/8)C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2949C2semidirect
3. C11×#2082C2semidirect
4. C11×#2081C2semidirect
5. C11×#2049C2semidirect
7. C11×#1977C2semidirect
8. C11×#1953C2semidirect
9. C11×#1905C2semidirect
11. C11×#1833C2semidirect
12. C11×#1830C2semidirect
13. C11×#1829C2semidirect
14. C11×#1814C2semidirect
15. C11×#1757C2semidirect
121. #24987C11direct (N × H)
201. #2949C2×C11semidirect
202. #2082C2×C11semidirect
203. #2081C2×C11semidirect
204. #2049C2×C11semidirect
206. #1977C2×C11semidirect
207. #1953C2×C11semidirect
208. #1905C2×C11semidirect
210. #1833C2×C11semidirect
211. #1830C2×C11semidirect
212. #1829C2×C11semidirect
213. #1814C2×C11semidirect
214. #1757C2×C11semidirect
472. C11#24987direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4712
C11×#29492
C11×#20822
C11×#20812
C11×#20492
C11×#20482
C11×#19772
C11×#19532
C11×#19052
C11×#19042
C11×#18332
C11×#18302
C11×#18292
C11×#18142
C11×#17572
#2498711