Finite Group Databasebeta

← C11×#24773 #14601966

Subgroups — C11×#24773 #14601966

Order 2816.

892 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#471C212yesmaximal, complemented
2C11×#3038C211yesmaximal, characteristic
3C2×C11×#460C211yesmaximal, characteristic, complemented
4C4×C11×#137C211yesmaximal, characteristic, complemented
5C11×#2906C211yesmaximal, characteristic, complemented
6C11×#2063C212yesmaximal, complemented
7C11×#2046C212yesmaximal, complemented
8C11×#1965C211yesmaximal, characteristic, complemented
9C11×#1950C211yesmaximal, characteristic, complemented
10C11×#1907C212yesmaximal, complemented
11C11×#1801C211yesmaximal, characteristic, complemented
12C2×C11×#137C2211yescharacteristic
13C2×C11×AGL(1,ℤ/8)C2212yes—
14C22×C11×SD16C2212yes—
15C2×C11×#131C2212yes—
16C2×C11×#127C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C11×#471—28no—
20C11×#460—21no—
21C11×#460—21no—
22C11×#460—21no—
23C11×#460—21no—
24C11×#460—22no—
25C11×#459—21no—
26C11×#459—21no—
27C11×#441—21no—
28C11×#440—21no—
29C4×C11×Q16—21no—
30C4×C11×SD16—21no—
31C2×C11×#108C2212yes—
32C11×#428C2211yescharacteristic
33C11×#424—22no—
34C11×#424C2212yes—
35C11×#423—21no—
36C11×#423C2211yescharacteristic
37C11×#423C2211yescharacteristic
38C2×C11×C4⋊C8—21no—
39C2×C11×C4⋊C8C2211yescharacteristic
40C11×#419C2211yescharacteristic
41C11×#418C2212yes—
42C11×#417C2211yescharacteristic
43C2×C11×#102C2212yes—
44C2×C11×#101C2212yes—
45C2×C11×#100C2212yes—
46C2×C11×#100C2212yes—
47C4×C11×M16C2211yescharacteristic
48C11×#343C2212yes—
49C11×#341C2212yes—
50C2×C11×#41C2311yescharacteristic
51C22×Q8×C11C2311yescharacteristic
52C22×D4×C11—21no—
53C22×D4×C11—21no—
54C22×D4×C11C2312yes—
55C11×#137—22no—
56C11×#137D414yescomplemented
57C11×AGL(1,ℤ/8)—24no—
58C11×AGL(1,ℤ/8)—24no—
59C2×C11×Q16—21no—
60C2×C11×SD16—21no—
61C2×C11×SD16—24no—
62C2×C11×SD16—22no—
63C2×C11×SD16—22no—
64C2×C11×SD16—22no—
65C2×C11×SD16—42no—
66C2×C11×D8—22no—
67C11×#131—24no—
68C11×#131—42no—
69C2×C11×M16—22no—
70C2×C11×M16C2311yescharacteristic
71C2×C11×M16C2312yes—
72C2×C11×M16C2312yes—
73C2×C11×M16C2311yescharacteristic
74C22×C8×C11—22no—
75C22×C8×C11C2312yes—
76C11×#127—21no—
77C11×#127—21no—
78C11×#127—21no—
79C11×#127—21no—
80C4×Q8×C11—21no—
81C4×Q8×C11—21no—
82C4×Q8×C11—21no—
83C4×Q8×C11—21no—
84C4×Q8×C11D411yescharacteristic
85C4×Q8×C11D411yescharacteristic
86C4×D4×C11—21no—
87C4×D4×C11—21no—
88C4×D4×C11D411yescharacteristic
89C4×D4×C11D411yescharacteristic
90C11×#117—21no—
91C11×#117C2311yescharacteristic
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C42×C11—21no—
95C2×C42×C11—21no—
96C2×C42×C11C2311yescharacteristic
97C11×#108—24no—
98C11×#107—21no—
99C11×#106—21no—
100C11×C4⋊C8—22no—
101C11×C4⋊C8—22no—
102C11×C4⋊C8—21no—
103C11×C4⋊C8—21no—
104C11×C4⋊C8—21no—
105C11×C4⋊C8—21no—
106C11×C4⋊C8D411yescharacteristic
107C11×C4⋊C8D411yescharacteristic
108C11×C4⋊C8D412yes—
109C11×#103—21no—
110C11×#103—21no—
111C11×#103—21no—
112C11×#102—21no—
113C11×#102—22no—
114C11×#102—22no—
115C11×#102—22no—
116C11×#102—22no—
117C11×#101—24no—
118C11×#100—24no—
119C11×#100—42no—
120C11×#97—21no—
121C4×C8×C11—21no—
122#24773C1111yesmaximal, characteristic, direct product factor, Sylow
123C24×C11—22no—
124C11×#41—21no—
125C11×#41—21no—
126C11×#41C2×D412yes—
127C11×#41#4112yes—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11C2×D412yes—
134C2×Q8×C11C2×D411yescharacteristic
135C2×D4×C11—21no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—41no—
143C2×D4×C11—41no—
144C2×D4×C11—41no—
145C2×D4×C11—41no—
146C2×D4×C11—82no—
147C2×D4×C11—82no—
148C2×D4×C11C2×D411yescharacteristic
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11#4111yescharacteristic
155C22×C4×C11#4111yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C11×Q16—24no—
158C11×SD16—24no—
159C11×SD16—44no—
160C11×SD16—44no—
161C11×SD16—44no—
162C11×D8—44no—
163C11×M16—22no—
164C11×M16—22no—
165C11×M16—21no—
166C11×M16—22no—
167C11×M16—21no—
168C11×M16—22no—
169C11×M16—21no—
170C11×M16—44no—
171C11×M16C2×D412yes—
172C2×C8×C11—21no—
173C2×C8×C11—22no—
174C2×C8×C11—21no—
175C2×C8×C11—22no—
176C2×C8×C11—22no—
177C2×C8×C11—22no—
178C2×C8×C11—44no—
179C2×C8×C11C2×D412yes—
180C2×C8×C11C2×D412yes—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—41no—
186C11×C4⋊C4—41no—
187C11×C4⋊C4C2×D411yescharacteristic
188C11×C4⋊C4C2×D411yescharacteristic
189C11×C22⋊C4—21no—
190C11×C22⋊C4—21no—
191C11×C22⋊C4—21no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—41no—
196C42×C11—41no—
197C42×C11C2×D411yescharacteristic
198C42×C11C2×D411yescharacteristic
199C42×C11C2×D411yescharacteristic
200C42×C11C2×D411yescharacteristic
201C2×#471C2×C1112yescomplemented
202#3038C2×C1111yescharacteristic
203C2×#460C2×C1111yescharacteristic, complemented
204C4×#137C2×C1111yescharacteristic, complemented
205#2906C2×C1111yescharacteristic, complemented
206#2063C2×C1112yescomplemented
207#2046C2×C1112yescomplemented
208#1965C2×C1111yescharacteristic, complemented
209#1950C2×C1111yescharacteristic, complemented
210#1907C2×C1112yescomplemented
211#1801C2×C1111yescharacteristic, complemented
212C23×C11—21no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—82no—
217C23×C11—82no—
218C23×C11C2×#4111yescharacteristic
219Q8×C11—21no—
220Q8×C11—22no—
221Q8×C11—22no—
222Q8×C11—41no—
223Q8×C11—41no—
224Q8×C11#12112yes—
225D4×C11—22no—
226D4×C11—22no—
227D4×C11—21no—
228D4×C11—42no—
229D4×C11—42no—
230D4×C11—42no—
231D4×C11—42no—
232D4×C11—82no—
233D4×C11—82no—
234D4×C11—82no—
235D4×C11—82no—
236D4×C11#12112yes—
237C2×C4×C11—21no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—22no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—42no—
248C2×C4×C11—41no—
249C2×C4×C11—81no—
250C2×C4×C11—81no—
251C2×C4×C11#12111yescharacteristic
252C2×C4×C11#12111yescharacteristic
253C2×C4×C11#12111yescharacteristic
254C2×C4×C11#12111yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11H(5,𝔽2)11yescharacteristic
260C2×C4×C112−1+411yescharacteristic
261C8×C11—22no—
262C8×C11—22no—
263C8×C11—22no—
264C8×C11—42no—
265C8×C11—41no—
266C8×C11—42no—
267C2×#137C22×C1111yescharacteristic
268C2×AGL(1,ℤ/8)C22×C1112yes—
269C22×SD16C22×C1112yes—
270C2×#131C22×C1112yes—
271C2×#127C22×C1111yescharacteristic
272C4×#41C22×C1111yescharacteristic
273C2×C4×Q8C22×C1111yescharacteristic
274#471—28no—
275#460—21no—
276#460—21no—
277#460—21no—
278#460—21no—
279#460—22no—
280#459—21no—
281#459—21no—
282#441—21no—
283#440—21no—
284C4×Q16—21no—
285C4×SD16—21no—
286C2×#108C22×C1112yes—
287#428C22×C1111yescharacteristic
288#424—22no—
289#424C22×C1112yes—
290#423—21no—
291#423C22×C1111yescharacteristic
292#423C22×C1111yescharacteristic
293C2×C4⋊C8—21no—
294C2×C4⋊C8C22×C1111yescharacteristic
295#419C22×C1111yescharacteristic
296#418C22×C1112yes—
297#417C22×C1111yescharacteristic
298C2×#102C22×C1112yes—
299C2×#101C22×C1112yes—
300C2×#100C22×C1112yes—
301C2×#100C22×C1112yes—
302C4×M16C22×C1111yescharacteristic
303#343C22×C1112yes—
304#341C22×C1112yes—
305C22×C11—21no—
306C22×C11—21no—
307C22×C11—22no—
308C22×C11—41no—
309C22×C11—41no—
310C22×C11—82no—
311C22×C11—82no—
312C22×C11—82no—
313C22×C11—162no—
314C22×C11—162no—
315C22×C11C2×#12111yescharacteristic
316C22×C11#54711yescharacteristic
317C22×C11#55311yescharacteristic
318C4×C11—22no—
319C4×C11—21no—
320C4×C11—21no—
321C4×C11—21no—
322C4×C11—42no—
323C4×C11—41no—
324C4×C11—41no—
325C4×C11—81no—
326C4×C11#47112yescomplemented
327C4×C11C2×#12111yescharacteristic
328C4×C11#53711yescharacteristic
329C4×C11D4211yescharacteristic
330C4×C11#54811yescharacteristic
331C2×#41C23×C1111yescharacteristic
332C22×Q8C23×C1111yescharacteristic
333C22×D4—21no—
334C22×D4—21no—
335C22×D4C23×C1112yes—
336#137—22no—
337#137D4×C1114yescomplemented
338AGL(1,ℤ/8)—24no—
339AGL(1,ℤ/8)—24no—
340C2×Q16—21no—
341C2×SD16—21no—
342C2×SD16—24no—
343C2×SD16—22no—
344C2×SD16—22no—
345C2×SD16—22no—
346C2×SD16—42no—
347C2×D8—22no—
348#131—24no—
349#131—42no—
350C2×M16—22no—
351C2×M16C23×C1112yes—
352C2×M16C23×C1112yes—
353C2×M16C23×C1111yescharacteristic
354C2×M16C23×C1111yescharacteristic
355C22×C8—22no—
356C22×C8C23×C1112yes—
357#127—21no—
358#127—21no—
359#127—21no—
360#127—21no—
361C4×Q8—21no—
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8D4×C1111yescharacteristic
366C4×Q8D4×C1111yescharacteristic
367C4×D4—21no—
368C4×D4—21no—
369C4×D4D4×C1111yescharacteristic
370C4×D4D4×C1111yescharacteristic
371#117—21no—
372#117C23×C1111yescharacteristic
373C2×C4⋊C4—21no—
374C2×C4⋊C4C23×C1111yescharacteristic
375C2×C42—21no—
376C2×C42—21no—
377C2×C42C23×C1111yescharacteristic
378#108—24no—
379#107—21no—
380#106—21no—
381C4⋊C8—22no—
382C4⋊C8—22no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8D4×C1111yescharacteristic
388C4⋊C8D4×C1111yescharacteristic
389C4⋊C8D4×C1112yes—
390#103—21no—
391#103—21no—
392#103—21no—
393#102—21no—
394#102—22no—
395#102—22no—
396#102—22no—
397#102—22no—
398#101—24no—
399#100—24no—
400#100—42no—
401#97—21no—
402C4×C8—21no—
403C2×C11—21no—
404C2×C11—21no—
405C2×C11—42no—
406C2×C11—162no—
407C2×C11#241611yescharacteristic
408C2×C11C2×#47111yescharacteristic
409C2×C11#306811yescharacteristic
410C24—22no—
411#41—21no—
412#41—21no—
413#41C2×D4×C1112yes—
414#41C11×#4112yes—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8C2×D4×C1112yes—
421C2×Q8C2×D4×C1111yescharacteristic
422C2×D4—21no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—41no—
433C2×D4—82no—
434C2×D4—82no—
435C2×D4C2×D4×C1111yescharacteristic
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4C11×#4111yescharacteristic
442C22×C4C11×#4111yescharacteristic
443C22×C4C24×C1111yescharacteristic
444Q16—24no—
445SD16—24no—
446SD16—44no—
447SD16—44no—
448SD16—44no—
449D8—44no—
450M16—21no—
451M16—22no—
452M16—22no—
453M16—22no—
454M16—21no—
455M16—22no—
456M16—21no—
457M16—44no—
458M16C2×D4×C1112yes—
459C2×C8—21no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—21no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—44no—
466C2×C8C2×D4×C1112yes—
467C2×C8C2×D4×C1112yes—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4C2×D4×C1111yescharacteristic
475C4⋊C4C2×D4×C1111yescharacteristic
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—41no—
483C42—41no—
484C42C2×D4×C1111yescharacteristic
485C42C2×D4×C1111yescharacteristic
486C42C2×D4×C1111yescharacteristic
487C42C2×D4×C1111yescharacteristic
488C11#2477311yescharacteristic, direct product factor, Sylow
489C23—21no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—82no—
494C23—82no—
495C23C2×C11×#4111yescharacteristic
496Q8—21no—
497Q8—22no—
498Q8—22no—
499Q8—41no—
500Q8—41no—
501Q8C11×#12112yes—
502D4—22no—
503D4—22no—
504D4—21no—
505D4—42no—
506D4—42no—
507D4—42no—
508D4—42no—
509D4—82no—
510D4—82no—
511D4—82no—
512D4—82no—
513D4C11×#12112yes—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—81no—
527C2×C4—81no—
528C2×C4C11×#12111yescharacteristic
529C2×C4C11×#12111yescharacteristic
530C2×C4C11×#12111yescharacteristic
531C2×C4C11×#12111yescharacteristic
532C2×C4C22×D4×C1111yescharacteristic
533C2×C4C22×D4×C1111yescharacteristic
534C2×C4C22×D4×C1111yescharacteristic
535C2×C4C2×C11×#4111yescharacteristic
536C2×C4C11×H(5,𝔽2)11yescharacteristic
537C2×C4C11×2−1+411yescharacteristic
538C8—22no—
539C8—22no—
540C8—22no—
541C8—42no—
542C8—41no—
543C8—42no—
544C22—21no—
545C22—21no—
546C22—22no—
547C22—41no—
548C22—41no—
549C22—82no—
550C22—82no—
551C22—82no—
552C22—162no—
553C22—162no—
554C22C2×C11×#12111yescharacteristic
555C22C11×#54711yescharacteristic
556C22C11×#55311yescharacteristic
557C4—22no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—42no—
562C4—41no—
563C4—41no—
564C4—81no—
565C4C11×#47112yescomplemented
566C4C2×C11×#12111yescharacteristic
567C4C11×#53711yescharacteristic
568C4D42×C1111yescharacteristic
569C4C11×#54811yescharacteristic
570C2—21no—
571C2—21no—
572C2—42no—
573C2—162no—
574C2C11×#241611yescharacteristic
575C2C2×C11×#47111yescharacteristic
576C2C11×#306811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3038C2
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. C2×C11×#471C2semidirect
3. C2×C11×#460C2semidirect
4. C4×C11×#137C2semidirect
5. C11×#2906C2semidirect
6. C11×#2063C2semidirect
7. C11×#2046C2semidirect
8. C11×#1965C2semidirect
9. C11×#1950C2semidirect
10. C11×#1907C2semidirect
11. C11×#1801C2semidirect
56. C11×#137D4semidirect
122. #24773C11direct (N × H)
201. C2×#471C2×C11semidirect
203. C2×#460C2×C11semidirect
204. C4×#137C2×C11semidirect
205. #2906C2×C11semidirect
206. #2063C2×C11semidirect
207. #2046C2×C11semidirect
208. #1965C2×C11semidirect
209. #1950C2×C11semidirect
210. #1907C2×C11semidirect
211. #1801C2×C11semidirect
326. C4×C11#471semidirect
337. #137D4×C11semidirect
488. C11#24773direct (N × H)
565. C4C11×#471semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4712
C11×#30382
C2×C11×#4602
C4×C11×#1372
C11×#29062
C11×#20632
C11×#20462
C11×#19652
C11×#19502
C11×#19072
C11×#18012
#2477311