Finite Group Databasebeta

← C11×#24523 #14601716

Subgroups — C11×#24523 #14601716

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3094C211yesmaximal, characteristic
2C2×C11×#448C211yesmaximal, characteristic
3C11×#2924C211yesmaximal, characteristic, complemented
4C2×C11×#419C211yesmaximal, characteristic, complemented
5C11×#2064C212yesmaximal, complemented
6C11×#2046C212yesmaximal, complemented
7C11×#1977C212yesmaximal, complemented
8C11×#1930C212yesmaximal, complemented
9C11×#1900C211yesmaximal, characteristic
10C11×#1855C211yesmaximal, characteristic, complemented
11C11×#1784C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C22×C11×SD16C2212yes—
14C22×C11×M16C2211yescharacteristic
15C2×C11×#121C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17C11×#482—21no—
18C11×#482—21no—
19C11×#481—21no—
20C11×#480—21no—
21C11×#448—21no—
22C11×#448—21no—
23C11×#448—22no—
24C11×#433—22no—
25C11×#432—21no—
26C11×#431—21no—
27C2×C11×#108C2212yes—
28C11×#428C2211yescharacteristic
29C11×#428C2211yescharacteristic
30C11×#424C2212yes—
31C11×#419—21no—
32C11×#419—21no—
33C11×#419C2212yes—
34C11×#419C2212yes—
35C11×#418C2211yescharacteristic
36C11×#418C2211yescharacteristic
37C2×C11×#103—21no—
38C2×C11×#103—21no—
39C2×C11×#103C2212yes—
40C2×C11×#101C2212yes—
41C2×C11×#101C2212yes—
42C2×C11×#100C2212yes—
43C11×#407C2211yescharacteristic
44C11×#407C2211yescharacteristic
45C2×C11×C22⋊C8C2211yescharacteristic
46C11×#405C2212yes—
47C11×#343C2212yes—
48C11×#341C2212yes—
49C22×Q8×C11—21no—
50C22×Q8×C11—24no—
51C22×Q8×C11—21no—
52C22×Q8×C11—21no—
53C22×Q8×C11—21no—
54C22×Q8×C11—21no—
55C22×Q8×C11—42no—
56C22×Q8×C11C2312yes—
57C22×D4×C11—21no—
58C22×D4×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11C2311yescharacteristic
61C2×C11×SD16—24no—
62C2×C11×SD16—22no—
63C2×C11×SD16—22no—
64C2×C11×SD16—42no—
65C2×C11×M16—21no—
66C2×C11×M16—42no—
67C2×C11×M16C2311yescharacteristic
68C2×C11×M16C2312yes—
69C2×C11×M16C2312yes—
70C2×C11×M16C2311yescharacteristic
71C22×C8×C11—21no—
72C22×C8×C11C2312yes—
73C11×#121—21no—
74C11×#121—21no—
75C11×#121—21no—
76C11×#121—21no—
77C11×#117—21no—
78C11×#117—21no—
79C11×#117D411yescharacteristic
80C11×#117D411yescharacteristic
81C11×#117C2311yescharacteristic
82C11×#117C2311yescharacteristic
83C2×C11×C4⋊C4D411yescharacteristic
84C2×C11×C4⋊C4D411yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C42×C11—21no—
89C11×#108—42no—
90C11×#107—21no—
91C11×#107—21no—
92C11×#106—21no—
93C11×#106—21no—
94C11×C4⋊C8—22no—
95C11×C4⋊C8—22no—
96C11×#103—22no—
97C11×#103—22no—
98C11×#103—22no—
99C11×#103—22no—
100C11×#103—22no—
101C11×#103—22no—
102C11×#102—21no—
103C11×#102—21no—
104C11×#102—21no—
105C11×#102—21no—
106C11×#101—24no—
107C11×#101—42no—
108C11×#100—42no—
109C11×C22⋊C8—21no—
110C11×C22⋊C8—21no—
111C11×C22⋊C8—21no—
112C11×C22⋊C8—21no—
113C11×C22⋊C8D411yescharacteristic
114C11×C22⋊C8D411yescharacteristic
115C11×C22⋊C8D412yes—
116C11×#97—22no—
117C4×C8×C11—22no—
118#24523C1111yesmaximal, characteristic, direct product factor, Sylow
119C24×C11—21no—
120C24×C11#4111yescharacteristic
121C2×Q8×C11—22no—
122C2×Q8×C11—24no—
123C2×Q8×C11—24no—
124C2×Q8×C11—22no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11—22no—
128C2×Q8×C11—44no—
129C2×Q8×C11—44no—
130C2×Q8×C11—44no—
131C2×Q8×C11—42no—
132C2×Q8×C11—42no—
133C2×Q8×C11—41no—
134C2×Q8×C11—41no—
135C2×Q8×C11#4114yes—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—41no—
141C2×D4×C11—41no—
142C2×D4×C11—82no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—21no—
146C22×C4×C11—22no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—44no—
150C22×C4×C11—41no—
151C22×C4×C11—41no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11#4111yescharacteristic
157C22×C4×C11C2411yescharacteristic
158C11×SD16—44no—
159C11×SD16—44no—
160C11×M16—22no—
161C11×M16—22no—
162C11×M16—22no—
163C11×M16—22no—
164C11×M16—22no—
165C11×M16—22no—
166C11×M16—42no—
167C2×C8×C11—22no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11—22no—
173C2×C8×C11—42no—
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⋊C4C2×D411yescharacteristic
181C11×C4⋊C4C2×D411yescharacteristic
182C11×C4⋊C4C2×D411yescharacteristic
183C11×C4⋊C4C2×D411yescharacteristic
184C11×C22⋊C4—21no—
185C11×C22⋊C4—21no—
186C11×C22⋊C4—21no—
187C11×C22⋊C4—21no—
188C11×C22⋊C4—41no—
189C11×C22⋊C4—41no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11—21no—
194#3094C2×C1111yescharacteristic
195C2×#448C2×C1111yescharacteristic
196#2924C2×C1111yescharacteristic, complemented
197C2×#419C2×C1111yescharacteristic, complemented
198#2064C2×C1112yescomplemented
199#2046C2×C1112yescomplemented
200#1977C2×C1112yescomplemented
201#1930C2×C1112yescomplemented
202#1900C2×C1111yescharacteristic
203#1855C2×C1111yescharacteristic, complemented
204#1784C2×C1111yescharacteristic, complemented
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11—42no—
210C23×C11—81no—
211C23×C11—81no—
212C23×C11#12111yescharacteristic
213C23×C11#12111yescharacteristic
214C23×C11C2×#4111yescharacteristic
215Q8×C11—24no—
216Q8×C11—24no—
217Q8×C11—44no—
218Q8×C11—44no—
219Q8×C11—42no—
220Q8×C11—42no—
221D4×C11—41no—
222D4×C11—41no—
223D4×C11—42no—
224D4×C11—82no—
225D4×C11—82no—
226C2×C4×C11—22no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—24no—
238C2×C4×C11—44no—
239C2×C4×C11—44no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
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×C11C22×D411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C2×#4112yes—
251C2×C4×C11H(5,𝔽2)12yes—
252C8×C11—22no—
253C8×C11—22no—
254C8×C11—41no—
255C8×C11—42no—
256C8×C11—41no—
257C8×C11—42no—
258C23×Q8C22×C1111yescharacteristic
259C22×SD16C22×C1112yes—
260C22×M16C22×C1111yescharacteristic
261C2×#121C22×C1111yescharacteristic
262C2×#117C22×C1111yescharacteristic
263#482—21no—
264#482—21no—
265#481—21no—
266#480—21no—
267#448—21no—
268#448—21no—
269#448—22no—
270#433—22no—
271#432—21no—
272#431—21no—
273C2×#108C22×C1112yes—
274#428C22×C1111yescharacteristic
275#428C22×C1111yescharacteristic
276#424C22×C1112yes—
277#419—21no—
278#419—21no—
279#419C22×C1112yes—
280#419C22×C1112yes—
281#418C22×C1111yescharacteristic
282#418C22×C1111yescharacteristic
283C2×#103—21no—
284C2×#103—21no—
285C2×#103C22×C1112yes—
286C2×#101C22×C1112yes—
287C2×#101C22×C1112yes—
288C2×#100C22×C1112yes—
289#407C22×C1111yescharacteristic
290#407C22×C1111yescharacteristic
291C2×C22⋊C8C22×C1111yescharacteristic
292#405C22×C1112yes—
293#343C22×C1112yes—
294#341C22×C1112yes—
295C22×C11—21no—
296C22×C11—21no—
297C22×C11—21no—
298C22×C11—21no—
299C22×C11—21no—
300C22×C11—21no—
301C22×C11—21no—
302C22×C11—44no—
303C22×C11—81no—
304C22×C11—81no—
305C22×C11—81no—
306C22×C11—162no—
307C22×C11#47112yes—
308C22×C11C2×#12111yescharacteristic
309C22×C11#55112yes—
310C4×C11—21no—
311C4×C11—21no—
312C4×C11—44no—
313C4×C11—41no—
314C4×C11—41no—
315C4×C11—41no—
316C4×C11—41no—
317C4×C11—81no—
318C4×C11#52511yescharacteristic
319C4×C11#53511yescharacteristic
320C4×C11#54612yes—
321C22×Q8—21no—
322C22×Q8—24no—
323C22×Q8—21no—
324C22×Q8—21no—
325C22×Q8—21no—
326C22×Q8—21no—
327C22×Q8—42no—
328C22×Q8C23×C1112yes—
329C22×D4—21no—
330C22×D4C23×C1111yescharacteristic
331C23×C4—21no—
332C23×C4C23×C1111yescharacteristic
333C2×SD16—24no—
334C2×SD16—22no—
335C2×SD16—22no—
336C2×SD16—42no—
337C2×M16—21no—
338C2×M16—42no—
339C2×M16C23×C1112yes—
340C2×M16C23×C1111yescharacteristic
341C2×M16C23×C1112yes—
342C2×M16C23×C1111yescharacteristic
343C22×C8—21no—
344C22×C8C23×C1112yes—
345#121—21no—
346#121—21no—
347#121—21no—
348#121—21no—
349#117—21no—
350#117—21no—
351#117D4×C1111yescharacteristic
352#117D4×C1111yescharacteristic
353#117C23×C1111yescharacteristic
354#117C23×C1111yescharacteristic
355C2×C4⋊C4D4×C1111yescharacteristic
356C2×C4⋊C4D4×C1111yescharacteristic
357C2×C4⋊C4C23×C1111yescharacteristic
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C42—21no—
361#108—42no—
362#107—21no—
363#107—21no—
364#106—21no—
365#106—21no—
366C4⋊C8—22no—
367C4⋊C8—22no—
368#103—22no—
369#103—22no—
370#103—22no—
371#103—22no—
372#103—22no—
373#103—22no—
374#102—21no—
375#102—21no—
376#102—21no—
377#102—21no—
378#101—24no—
379#101—42no—
380#100—42no—
381C22⋊C8—21no—
382C22⋊C8—21no—
383C22⋊C8—21no—
384C22⋊C8—21no—
385C22⋊C8D4×C1111yescharacteristic
386C22⋊C8D4×C1111yescharacteristic
387C22⋊C8D4×C1112yes—
388#97—22no—
389C4×C8—22no—
390C2×C11—22no—
391C2×C11—22no—
392C2×C11—41no—
393C2×C11—161no—
394C2×C11#241111yescharacteristic
395C2×C11C2×#47111yescharacteristic
396C2×C11#306911yescharacteristic
397C24—21no—
398C24C11×#4111yescharacteristic
399C2×Q8—22no—
400C2×Q8—24no—
401C2×Q8—24no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—44no—
407C2×Q8—44no—
408C2×Q8—44no—
409C2×Q8—42no—
410C2×Q8—42no—
411C2×Q8—41no—
412C2×Q8—41no—
413C2×Q8C11×#4114yes—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—82no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—44no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4C2×D4×C1111yescharacteristic
431C22×C4C2×D4×C1111yescharacteristic
432C22×C4C2×D4×C1111yescharacteristic
433C22×C4C2×D4×C1111yescharacteristic
434C22×C4C11×#4111yescharacteristic
435C22×C4C24×C1111yescharacteristic
436SD16—44no—
437SD16—44no—
438M16—22no—
439M16—22no—
440M16—22no—
441M16—22no—
442M16—22no—
443M16—22no—
444M16—42no—
445C2×C8—22no—
446C2×C8—22no—
447C2×C8—22no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—22no—
451C2×C8—42no—
452C2×C8C2×D4×C1112yes—
453C2×C8C2×D4×C1112yes—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4C2×D4×C1111yescharacteristic
459C4⋊C4C2×D4×C1111yescharacteristic
460C4⋊C4C2×D4×C1111yescharacteristic
461C4⋊C4C2×D4×C1111yescharacteristic
462C22⋊C4—21no—
463C22⋊C4—21no—
464C22⋊C4—21no—
465C22⋊C4—21no—
466C22⋊C4—41no—
467C22⋊C4—41no—
468C42—21no—
469C42—21no—
470C42—21no—
471C42—21no—
472C11#2452311yescharacteristic, direct product factor, Sylow
473C23—22no—
474C23—22no—
475C23—41no—
476C23—41no—
477C23—42no—
478C23—81no—
479C23—81no—
480C23C11×#12111yescharacteristic
481C23C11×#12111yescharacteristic
482C23C2×C11×#4111yescharacteristic
483Q8—24no—
484Q8—24no—
485Q8—44no—
486Q8—44no—
487Q8—42no—
488Q8—42no—
489D4—41no—
490D4—41no—
491D4—42no—
492D4—82no—
493D4—82no—
494C2×C4—22no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—24no—
506C2×C4—44no—
507C2×C4—44no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—41no—
512C2×C4—81no—
513C2×C4—81no—
514C2×C4C11×#12111yescharacteristic
515C2×C4C11×#12111yescharacteristic
516C2×C4C22×D4×C1111yescharacteristic
517C2×C4C22×D4×C1111yescharacteristic
518C2×C4C2×C11×#4112yes—
519C2×C4C11×H(5,𝔽2)12yes—
520C8—22no—
521C8—22no—
522C8—41no—
523C8—42no—
524C8—41no—
525C8—42no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—21no—
532C22—21no—
533C22—44no—
534C22—81no—
535C22—81no—
536C22—81no—
537C22—162no—
538C22C11×#47112yes—
539C22C2×C11×#12111yescharacteristic
540C22C11×#55112yes—
541C4—21no—
542C4—21no—
543C4—44no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—81no—
549C4C11×#52511yescharacteristic
550C4C11×#53511yescharacteristic
551C4C11×#54612yes—
552C2—22no—
553C2—22no—
554C2—41no—
555C2—161no—
556C2C11×#241111yescharacteristic
557C2C2×C11×#47111yescharacteristic
558C2C11×#306911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#2924C2semidirect
4. C2×C11×#419C2semidirect
5. C11×#2064C2semidirect
6. C11×#2046C2semidirect
7. C11×#1977C2semidirect
8. C11×#1930C2semidirect
10. C11×#1855C2semidirect
11. C11×#1784C2semidirect
118. #24523C11direct (N × H)
196. #2924C2×C11semidirect
197. C2×#419C2×C11semidirect
198. #2064C2×C11semidirect
199. #2046C2×C11semidirect
200. #1977C2×C11semidirect
201. #1930C2×C11semidirect
203. #1855C2×C11semidirect
204. #1784C2×C11semidirect
472. C11#24523direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#30942
C2×C11×#4482
C11×#29242
C2×C11×#4192
C11×#20642
C11×#20462
C11×#19772
C11×#19302
C11×#19002
C11×#18552
C11×#17842
#2452311