Finite Group Databasebeta

← C11×#24673 #14601866

Subgroups — C11×#24673 #14601866

Order 2816.

806 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3038C211yesmaximal, characteristic
2C2×C11×#460C211yesmaximal, characteristic, complemented
3C4×C11×#137C211yesmaximal, characteristic, complemented
4C11×#2925C211yesmaximal, characteristic, complemented
5C11×#2051C212yesmaximal, complemented
6C11×#2019C212yesmaximal, complemented
7C11×#1977C212yesmaximal, complemented
8C11×#1965C211yesmaximal, characteristic, complemented
9C11×#1950C211yesmaximal, characteristic, complemented
10C11×#1931C212yesmaximal, complemented
11C11×#1801C211yesmaximal, characteristic, complemented
12C2×C11×#137C2211yescharacteristic
13C2×C11×AGL(1,ℤ/8)C2212yes—
14C22×C11×SD16C2212yes—
15C2×C11×#127C2211yescharacteristic
16C4×C11×#41C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C11×#460—21no—
19C11×#460—21no—
20C11×#460—21no—
21C11×#460—21no—
22C11×#460—22no—
23C11×#459—21no—
24C11×#459—21no—
25C11×#441—21no—
26C11×#440—21no—
27C4×C11×Q16—21no—
28C4×C11×SD16—21no—
29C11×#433—22no—
30C11×#432—21no—
31C11×#431—21no—
32C2×C11×#108C2212yes—
33C11×#428C2211yescharacteristic
34C11×#423C2211yescharacteristic
35C11×#423C2211yescharacteristic
36C2×C11×C4⋊C8C2211yescharacteristic
37C11×#419C2211yescharacteristic
38C11×#418C2212yes—
39C11×#417C2211yescharacteristic
40C2×C11×#102C2212yes—
41C2×C11×#101C2212yes—
42C2×C11×#100C2212yes—
43C2×C11×#100C2212yes—
44C11×#408C2212yes—
45C11×#405C2212yes—
46C4×C11×M16C2211yescharacteristic
47C11×#343C2212yes—
48C11×#341C2212yes—
49C2×C11×#41C2311yescharacteristic
50C22×Q8×C11C2311yescharacteristic
51C22×D4×C11—21no—
52C22×D4×C11—21no—
53C22×D4×C11C2312yes—
54C11×#137—22no—
55C11×#137—22no—
56C11×AGL(1,ℤ/8)—42no—
57C11×AGL(1,ℤ/8)—42no—
58C2×C11×Q16—21no—
59C2×C11×SD16—21no—
60C2×C11×SD16—22no—
61C2×C11×SD16—24no—
62C2×C11×SD16—22no—
63C2×C11×SD16—22no—
64C2×C11×SD16—42no—
65C2×C11×D8—22no—
66C2×C11×M16C2312yes—
67C2×C11×M16C2312yes—
68C2×C11×M16C2311yescharacteristic
69C2×C11×M16C2311yescharacteristic
70C22×C8×C11C2312yes—
71C11×#127—21no—
72C11×#127—21no—
73C11×#127—21no—
74C11×#127—21no—
75C4×Q8×C11—21no—
76C4×Q8×C11—21no—
77C4×Q8×C11—21no—
78C4×Q8×C11—21no—
79C4×Q8×C11D411yescharacteristic
80C4×Q8×C11D411yescharacteristic
81C4×D4×C11—21no—
82C4×D4×C11—21no—
83C4×D4×C11D411yescharacteristic
84C4×D4×C11D411yescharacteristic
85C11×#117—21no—
86C11×#117C2311yescharacteristic
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C42×C11—21no—
90C2×C42×C11—21no—
91C2×C42×C11C2311yescharacteristic
92C11×#108—42no—
93C11×#107—21no—
94C11×#106—21no—
95C11×C4⋊C8—21no—
96C11×C4⋊C8—21no—
97C11×C4⋊C8—21no—
98C11×C4⋊C8—21no—
99C11×C4⋊C8D411yescharacteristic
100C11×C4⋊C8D411yescharacteristic
101C11×C4⋊C8D412yes—
102C11×#103—21no—
103C11×#103—21no—
104C11×#103—21no—
105C11×#102—21no—
106C11×#102—22no—
107C11×#102—22no—
108C11×#102—22no—
109C11×#102—22no—
110C11×#101—42no—
111C11×#100—24no—
112C11×#100—42no—
113C11×C22⋊C8—22no—
114C11×C22⋊C8—22no—
115C11×#97—22no—
116C11×#97—21no—
117C4×C8×C11—22no—
118C4×C8×C11—21no—
119#24673C1111yesmaximal, characteristic, direct product factor, Sylow
120C24×C11—22no—
121C11×#41—21no—
122C11×#41—21no—
123C11×#41—21no—
124C11×#41—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11C2×D411yescharacteristic
131C2×Q8×C11#4112yes—
132C2×D4×C11—21no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—41no—
140C2×D4×C11—41no—
141C2×D4×C11—41no—
142C2×D4×C11—41no—
143C2×D4×C11—82no—
144C2×D4×C11—82no—
145C2×D4×C11C2×D411yescharacteristic
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11#4111yescharacteristic
152C22×C4×C11#4111yescharacteristic
153C22×C4×C11C2411yescharacteristic
154C11×Q16—24no—
155C11×SD16—24no—
156C11×SD16—44no—
157C11×SD16—44no—
158C11×SD16—44no—
159C11×D8—44no—
160C11×M16—21no—
161C11×M16—22no—
162C11×M16—21no—
163C11×M16—22no—
164C11×M16—22no—
165C11×M16—21no—
166C11×M16—22no—
167C11×M16#4112yes—
168C2×C8×C11—21no—
169C2×C8×C11—22no—
170C2×C8×C11—21no—
171C2×C8×C11—22no—
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C2×C8×C11C2×D412yes—
175C2×C8×C11C2×D412yes—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—41no—
181C11×C4⋊C4—41no—
182C11×C4⋊C4C2×D411yescharacteristic
183C11×C4⋊C4C2×D411yescharacteristic
184C11×C22⋊C4—21no—
185C11×C22⋊C4—21no—
186C11×C22⋊C4—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—41no—
191C42×C11—41no—
192C42×C11C2×D411yescharacteristic
193C42×C11C2×D411yescharacteristic
194C42×C11C2×D411yescharacteristic
195C42×C11C2×D411yescharacteristic
196#3038C2×C1111yescharacteristic
197C2×#460C2×C1111yescharacteristic, complemented
198C4×#137C2×C1111yescharacteristic, complemented
199#2925C2×C1111yescharacteristic, complemented
200#2051C2×C1112yescomplemented
201#2019C2×C1112yescomplemented
202#1977C2×C1112yescomplemented
203#1965C2×C1111yescharacteristic, complemented
204#1950C2×C1111yescharacteristic, complemented
205#1931C2×C1112yescomplemented
206#1801C2×C1111yescharacteristic, complemented
207C23×C11—21no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—82no—
212C23×C11—82no—
213C23×C11C2×#4111yescharacteristic
214Q8×C11—22no—
215Q8×C11—21no—
216Q8×C11—21no—
217Q8×C11—22no—
218Q8×C11—41no—
219Q8×C11—41no—
220D4×C11—21no—
221D4×C11—21no—
222D4×C11—41no—
223D4×C11—41no—
224D4×C11—42no—
225D4×C11—42no—
226D4×C11—42no—
227D4×C11—42no—
228D4×C11—82no—
229D4×C11—82no—
230D4×C11—82no—
231D4×C11—82no—
232C2×C4×C11—22no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—22no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—42no—
243C2×C4×C11—41no—
244C2×C4×C11—81no—
245C2×C4×C11—81no—
246C2×C4×C11#12111yescharacteristic
247C2×C4×C11#12111yescharacteristic
248C2×C4×C11#12111yescharacteristic
249C2×C4×C11#12111yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11H(5,𝔽2)11yescharacteristic
255C2×C4×C11H(5,𝔽2)11yescharacteristic
256C8×C11—22no—
257C8×C11—22no—
258C8×C11—22no—
259C8×C11—41no—
260C8×C11—42no—
261C8×C11—42no—
262C2×#137C22×C1111yescharacteristic
263C2×AGL(1,ℤ/8)C22×C1112yes—
264C22×SD16C22×C1112yes—
265C2×#127C22×C1111yescharacteristic
266C4×#41C22×C1111yescharacteristic
267C2×C4×Q8C22×C1111yescharacteristic
268#460—21no—
269#460—21no—
270#460—21no—
271#460—21no—
272#460—22no—
273#459—21no—
274#459—21no—
275#441—21no—
276#440—21no—
277C4×Q16—21no—
278C4×SD16—21no—
279#433—22no—
280#432—21no—
281#431—21no—
282C2×#108C22×C1112yes—
283#428C22×C1111yescharacteristic
284#423C22×C1111yescharacteristic
285#423C22×C1111yescharacteristic
286C2×C4⋊C8C22×C1111yescharacteristic
287#419C22×C1111yescharacteristic
288#418C22×C1112yes—
289#417C22×C1111yescharacteristic
290C2×#102C22×C1112yes—
291C2×#101C22×C1112yes—
292C2×#100C22×C1112yes—
293C2×#100C22×C1112yes—
294#408C22×C1112yes—
295#405C22×C1112yes—
296C4×M16C22×C1111yescharacteristic
297#343C22×C1112yes—
298#341C22×C1112yes—
299C22×C11—21no—
300C22×C11—21no—
301C22×C11—41no—
302C22×C11—41no—
303C22×C11—41no—
304C22×C11—82no—
305C22×C11—82no—
306C22×C11—82no—
307C22×C11—162no—
308C22×C11—162no—
309C22×C11C2×#12111yescharacteristic
310C22×C11#55311yescharacteristic
311C22×C11#55511yescharacteristic
312C4×C11—21no—
313C4×C11—21no—
314C4×C11—21no—
315C4×C11—41no—
316C4×C11—42no—
317C4×C11—41no—
318C4×C11—41no—
319C4×C11—81no—
320C4×C11#47112yes—
321C4×C11#52511yescharacteristic
322C4×C11#53511yescharacteristic
323C4×C11#54611yescharacteristic
324C4×C11#55011yescharacteristic
325C2×#41C23×C1111yescharacteristic
326C22×Q8C23×C1111yescharacteristic
327C22×D4—21no—
328C22×D4—21no—
329C22×D4C23×C1112yes—
330#137—22no—
331#137—22no—
332AGL(1,ℤ/8)—42no—
333AGL(1,ℤ/8)—42no—
334C2×Q16—21no—
335C2×SD16—21no—
336C2×SD16—22no—
337C2×SD16—24no—
338C2×SD16—22no—
339C2×SD16—22no—
340C2×SD16—42no—
341C2×D8—22no—
342C2×M16C23×C1112yes—
343C2×M16C23×C1112yes—
344C2×M16C23×C1111yescharacteristic
345C2×M16C23×C1111yescharacteristic
346C22×C8C23×C1112yes—
347#127—21no—
348#127—21no—
349#127—21no—
350#127—21no—
351C4×Q8—21no—
352C4×Q8—21no—
353C4×Q8—21no—
354C4×Q8—21no—
355C4×Q8D4×C1111yescharacteristic
356C4×Q8D4×C1111yescharacteristic
357C4×D4—21no—
358C4×D4—21no—
359C4×D4D4×C1111yescharacteristic
360C4×D4D4×C1111yescharacteristic
361#117—21no—
362#117C23×C1111yescharacteristic
363C2×C4⋊C4—21no—
364C2×C4⋊C4C23×C1111yescharacteristic
365C2×C42—21no—
366C2×C42—21no—
367C2×C42C23×C1111yescharacteristic
368#108—42no—
369#107—21no—
370#106—21no—
371C4⋊C8—21no—
372C4⋊C8—21no—
373C4⋊C8—21no—
374C4⋊C8—21no—
375C4⋊C8D4×C1111yescharacteristic
376C4⋊C8D4×C1111yescharacteristic
377C4⋊C8D4×C1112yes—
378#103—21no—
379#103—21no—
380#103—21no—
381#102—21no—
382#102—22no—
383#102—22no—
384#102—22no—
385#102—22no—
386#101—42no—
387#100—24no—
388#100—42no—
389C22⋊C8—22no—
390C22⋊C8—22no—
391#97—22no—
392#97—21no—
393C4×C8—22no—
394C4×C8—21no—
395C2×C11—21no—
396C2×C11—21no—
397C2×C11—81no—
398C2×C11—162no—
399C2×C11#241411yescharacteristic
400C2×C11C2×#47111yescharacteristic
401C2×C11#306811yescharacteristic
402C24—22no—
403#41—21no—
404#41—21no—
405#41—21no—
406#41—21no—
407C2×Q8—21no—
408C2×Q8—21no—
409C2×Q8—21no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8C2×D4×C1111yescharacteristic
413C2×Q8C11×#4112yes—
414C2×D4—21no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—82no—
426C2×D4—82no—
427C2×D4C2×D4×C1111yescharacteristic
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4C11×#4111yescharacteristic
434C22×C4C11×#4111yescharacteristic
435C22×C4C24×C1111yescharacteristic
436Q16—24no—
437SD16—24no—
438SD16—44no—
439SD16—44no—
440SD16—44no—
441D8—44no—
442M16—21no—
443M16—22no—
444M16—21no—
445M16—22no—
446M16—22no—
447M16—21no—
448M16—22no—
449M16C11×#4112yes—
450C2×C8—21no—
451C2×C8—22no—
452C2×C8—22no—
453C2×C8—22no—
454C2×C8—21no—
455C2×C8—22no—
456C2×C8C2×D4×C1112yes—
457C2×C8C2×D4×C1112yes—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4C2×D4×C1111yescharacteristic
465C4⋊C4C2×D4×C1111yescharacteristic
466C22⋊C4—21no—
467C22⋊C4—21no—
468C22⋊C4—21no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—41no—
473C42—41no—
474C42C2×D4×C1111yescharacteristic
475C42C2×D4×C1111yescharacteristic
476C42C2×D4×C1111yescharacteristic
477C42C2×D4×C1111yescharacteristic
478C11#2467311yescharacteristic, direct product factor, Sylow
479C23—21no—
480C23—42no—
481C23—42no—
482C23—42no—
483C23—82no—
484C23—82no—
485C23C2×C11×#4111yescharacteristic
486Q8—22no—
487Q8—21no—
488Q8—21no—
489Q8—22no—
490Q8—41no—
491Q8—41no—
492D4—21no—
493D4—21no—
494D4—41no—
495D4—41no—
496D4—42no—
497D4—42no—
498D4—42no—
499D4—42no—
500D4—82no—
501D4—82no—
502D4—82no—
503D4—82no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—41no—
516C2×C4—81no—
517C2×C4—81no—
518C2×C4C11×#12111yescharacteristic
519C2×C4C11×#12111yescharacteristic
520C2×C4C11×#12111yescharacteristic
521C2×C4C11×#12111yescharacteristic
522C2×C4C22×D4×C1111yescharacteristic
523C2×C4C22×D4×C1111yescharacteristic
524C2×C4C2×C11×#4111yescharacteristic
525C2×C4C2×C11×#4111yescharacteristic
526C2×C4C11×H(5,𝔽2)11yescharacteristic
527C2×C4C11×H(5,𝔽2)11yescharacteristic
528C8—22no—
529C8—22no—
530C8—22no—
531C8—42no—
532C8—41no—
533C8—42no—
534C22—21no—
535C22—21no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—82no—
540C22—82no—
541C22—82no—
542C22—162no—
543C22—162no—
544C22C2×C11×#12111yescharacteristic
545C22C11×#55311yescharacteristic
546C22C11×#55511yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—41no—
551C4—42no—
552C4—41no—
553C4—41no—
554C4—81no—
555C4C11×#47112yes—
556C4C11×#52511yescharacteristic
557C4C11×#53511yescharacteristic
558C4C11×#54611yescharacteristic
559C4C11×#55011yescharacteristic
560C2—21no—
561C2—21no—
562C2—81no—
563C2—162no—
564C2C11×#241411yescharacteristic
565C2C2×C11×#47111yescharacteristic
566C2C11×#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
2. C2×C11×#460C2semidirect
3. C4×C11×#137C2semidirect
4. C11×#2925C2semidirect
5. C11×#2051C2semidirect
6. C11×#2019C2semidirect
7. C11×#1977C2semidirect
8. C11×#1965C2semidirect
9. C11×#1950C2semidirect
10. C11×#1931C2semidirect
11. C11×#1801C2semidirect
119. #24673C11direct (N × H)
197. C2×#460C2×C11semidirect
198. C4×#137C2×C11semidirect
199. #2925C2×C11semidirect
200. #2051C2×C11semidirect
201. #2019C2×C11semidirect
202. #1977C2×C11semidirect
203. #1965C2×C11semidirect
204. #1950C2×C11semidirect
205. #1931C2×C11semidirect
206. #1801C2×C11semidirect
478. C11#24673direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30382
C2×C11×#4602
C4×C11×#1372
C11×#29252
C11×#20512
C11×#20192
C11×#19772
C11×#19652
C11×#19502
C11×#19312
C11×#18012
#2467311