Finite Group Databasebeta

← C11×#11128 #14588321

Subgroups — C11×#11128 #14588321

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#108C211yesmaximal, characteristic
2C2×C11×#419C211yesmaximal, characteristic
3C22×C11×#103C211yesmaximal, characteristic
4C22×C11×#101C211yesmaximal, characteristic
5C2×C11×#343C211yesmaximal, characteristic
6C11×#1736C211yesmaximal, characteristic
7C11×#1729C211yesmaximal, characteristic
8C23×Q8×C11C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C2×C11×#108—22no—
16C2×C11×#108—22no—
17C2×C11×#108—22no—
18C11×#419—22no—
19C11×#419—22no—
20C2×C11×#103—22no—
21C2×C11×#103—22no—
22C2×C11×#103—22no—
23C2×C11×#103C414yescomplemented
24C2×C11×#101—22no—
25C2×C11×#101—22no—
26C2×C11×#101—22no—
27C11×#343—22no—
28C11×#340—22no—
29C11×#336—22no—
30C22×Q8×C11—21no—
31C22×Q8×C11—21no—
32C22×Q8×C11—21no—
33C22×Q8×C11—21no—
34C22×Q8×C11—21no—
35C22×Q8×C11—21no—
36C22×Q8×C11—21no—
37C22×Q8×C11—21no—
38C22×Q8×C11—21no—
39C22×Q8×C11—21no—
40C22×Q8×C11—21no—
41C22×Q8×C11C2×C412yes—
42C22×Q8×C11D412yes—
43C22×Q8×C11Q812yes—
44C23×C4×C11—21no—
45C23×C4×C11—21no—
46C23×C4×C11C2311yescharacteristic
47C2×C11×M16—21no—
48C2×C11×M16—21no—
49C2×C11×M16—21no—
50C2×C11×M16—21no—
51C2×C11×M16—21no—
52C2×C11×M16—21no—
53C2×C11×M16—21no—
54C2×C11×M16—21no—
55C2×C11×M16—21no—
56C2×C11×M16—21no—
57C2×C11×M16—21no—
58C2×C11×M16—21no—
59C2×C11×M16—21no—
60C2×C11×M16—21no—
61C2×C11×M16—21no—
62C2×C11×M16D412yes—
63C2×C11×M16D412yes—
64C2×C11×M16D412yes—
65C22×C8×C11—21no—
66C22×C8×C11—21no—
67C22×C8×C11—21no—
68C22×C8×C11—21no—
69C22×C8×C11—21no—
70C22×C8×C11—21no—
71C22×C8×C11—21no—
72C22×C8×C11C2×C412yes—
73C22×C8×C11D412yes—
74C22×C8×C11D412yes—
75C11×#117—21no—
76C11×#117—21no—
77C11×#117—21no—
78C11×#117—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4C2×C412yes—
85C2×C11×C4⋊C4D412yes—
86C2×C11×C22⋊C4—21no—
87C2×C42×C11—21no—
88C11×#108—28no—
89C11×#103—28no—
90C11×#103—28no—
91C11×#101—28no—
92#11128C1111yesmaximal, characteristic, direct product factor, Sylow
93C24×C11#4111yescharacteristic
94C2×Q8×C11—22no—
95C2×Q8×C11—22no—
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11—22no—
99C2×Q8×C11—22no—
100C2×Q8×C11—22no—
101C2×Q8×C11—22no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—41no—
110C2×Q8×C11—41no—
111C2×Q8×C11—41no—
112C2×Q8×C11—41no—
113C2×Q8×C11—41no—
114C2×Q8×C11—41no—
115C2×Q8×C11—41no—
116C2×Q8×C11—41no—
117C2×Q8×C11—41no—
118C2×Q8×C11—41no—
119C2×Q8×C11—41no—
120C2×Q8×C11—41no—
121C2×Q8×C11C4⋊C414yes—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—41no—
128C22×C4×C11—41no—
129C22×C4×C11—41no—
130C22×C4×C11—41no—
131C22×C4×C11—41no—
132C22×C4×C11—41no—
133C22×C4×C11—82no—
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×Q811yescharacteristic
143C22×C4×C11#4111yescharacteristic
144C22×C4×C11#4111yescharacteristic
145C22×C4×C11#4111yescharacteristic
146C22×C4×C11#4111yescharacteristic
147C22×C4×C11#4111yescharacteristic
148C11×M16—22no—
149C11×M16—22no—
150C11×M16—22no—
151C11×M16—22no—
152C11×M16—22no—
153C11×M16—22no—
154C11×M16—41no—
155C11×M16—41no—
156C11×M16—41no—
157C11×M16—41no—
158C11×M16—41no—
159C11×M16—41no—
160C2×C8×C11—22no—
161C2×C8×C11—22no—
162C2×C8×C11—22no—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—41no—
170C2×C8×C11—41no—
171C2×C8×C11—41no—
172C2×C8×C11—41no—
173C2×C8×C11—41no—
174C2×C8×C11—41no—
175C2×C8×C11C22⋊C414yes—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—41no—
181C11×C4⋊C4—41no—
182C11×C22⋊C4—41no—
183C11×C22⋊C4—41no—
184C42×C11—41no—
185C42×C11—41no—
186C22×#108C2×C1111yescharacteristic
187C2×#419C2×C1111yescharacteristic
188C22×#103C2×C1111yescharacteristic
189C22×#101C2×C1111yescharacteristic
190C2×#343C2×C1111yescharacteristic
191#1736C2×C1111yescharacteristic
192#1729C2×C1111yescharacteristic
193C23×C11—22no—
194C23×C11—22no—
195C23×C11C4×D411yescharacteristic
196C23×C11#12111yescharacteristic
197C23×C11C22⋊Q811yescharacteristic
198C23×C11#12311yescharacteristic
199C23×C11#12411yescharacteristic
200C23×C11#12411yescharacteristic
201C23×C11#12611yescharacteristic
202Q8×C11—24no—
203Q8×C11—24no—
204Q8×C11—42no—
205Q8×C11—42no—
206Q8×C11—42no—
207Q8×C11—42no—
208Q8×C11—42no—
209Q8×C11—42no—
210C2×C4×C11—24no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—82no—
222C2×C4×C11—82no—
223C2×C4×C11—82no—
224C2×C4×C11C2×C22⋊C411yescharacteristic
225C2×C4×C11C2×C4⋊C411yescharacteristic
226C2×C4×C11#11711yescharacteristic
227C2×C4×C11C4×D411yescharacteristic
228C2×C4×C11C4×D411yescharacteristic
229C2×C4×C11C4×D411yescharacteristic
230C2×C4×C11#12011yescharacteristic
231C2×C4×C11#12011yescharacteristic
232C2×C4×C11#12011yescharacteristic
233C2×C4×C11#12111yescharacteristic
234C2×C4×C11#12111yescharacteristic
235C2×C4×C11#12111yescharacteristic
236C2×C4×C11#12111yescharacteristic
237C2×C4×C11#12111yescharacteristic
238C2×C4×C11#12111yescharacteristic
239C2×C4×C11#12111yescharacteristic
240C2×C4×C11C22⋊Q811yescharacteristic
241C2×C4×C11C22⋊Q811yescharacteristic
242C2×C4×C11C22⋊Q811yescharacteristic
243C2×C4×C11C22⋊Q811yescharacteristic
244C2×C4×C11C22⋊Q811yescharacteristic
245C2×C4×C11#12311yescharacteristic
246C2×C4×C11#12311yescharacteristic
247C2×C4×C11#12311yescharacteristic
248C2×C4×C11#12311yescharacteristic
249C2×C4×C11#12411yescharacteristic
250C2×C4×C11#12611yescharacteristic
251C2×C4×C11#12711yescharacteristic
252C8×C11—24no—
253C8×C11—42no—
254C8×C11—42no—
255C8×C11—42no—
256C23×Q8C22×C1111yescharacteristic
257C22×M16C22×C1111yescharacteristic
258C22×M16C22×C1111yescharacteristic
259C22×M16C22×C1111yescharacteristic
260C23×C8C22×C1111yescharacteristic
261C2×#117C22×C1111yescharacteristic
262C22×C4⋊C4C22×C1111yescharacteristic
263C2×#108—22no—
264C2×#108—22no—
265C2×#108—22no—
266#419—22no—
267#419—22no—
268C2×#103—22no—
269C2×#103—22no—
270C2×#103—22no—
271C2×#103C4×C1114yescomplemented
272C2×#101—22no—
273C2×#101—22no—
274C2×#101—22no—
275#343—22no—
276#340—22no—
277#336—22no—
278C22×C11—22no—
279C22×C11—22no—
280C22×C11—22no—
281C22×C11—22no—
282C22×C11—21no—
283C22×C11—21no—
284C22×C11—21no—
285C22×C11—21no—
286C22×C11#38511yescharacteristic
287C22×C11#38811yescharacteristic
288C22×C11#39011yescharacteristic
289C22×C11#39311yescharacteristic
290C22×C11#39411yescharacteristic
291C22×C11#39611yescharacteristic
292C22×C11#39711yescharacteristic
293C22×C11#47112yes—
294C22×C11#47312yes—
295C4×C11—44no—
296C4×C11—82no—
297C4×C11—82no—
298C4×C11#38011yescharacteristic
299C4×C11#38511yescharacteristic
300C4×C11#38611yescharacteristic
301C4×C11#38811yescharacteristic
302C4×C11#39211yescharacteristic
303C4×C11#39411yescharacteristic
304C4×C11#39611yescharacteristic
305C4×C11#39911yescharacteristic
306C22×Q8—21no—
307C22×Q8—21no—
308C22×Q8—21no—
309C22×Q8—21no—
310C22×Q8—21no—
311C22×Q8—21no—
312C22×Q8—21no—
313C22×Q8—21no—
314C22×Q8—21no—
315C22×Q8—21no—
316C22×Q8—21no—
317C22×Q8C2×C4×C1112yes—
318C22×Q8D4×C1112yes—
319C22×Q8Q8×C1112yes—
320C23×C4—21no—
321C23×C4—21no—
322C23×C4C23×C1111yescharacteristic
323C2×M16—21no—
324C2×M16—21no—
325C2×M16—21no—
326C2×M16—21no—
327C2×M16—21no—
328C2×M16—21no—
329C2×M16—21no—
330C2×M16—21no—
331C2×M16—21no—
332C2×M16—21no—
333C2×M16—21no—
334C2×M16—21no—
335C2×M16—21no—
336C2×M16—21no—
337C2×M16—21no—
338C2×M16D4×C1112yes—
339C2×M16D4×C1112yes—
340C2×M16D4×C1112yes—
341C22×C8—21no—
342C22×C8—21no—
343C22×C8—21no—
344C22×C8—21no—
345C22×C8—21no—
346C22×C8—21no—
347C22×C8—21no—
348C22×C8C2×C4×C1112yes—
349C22×C8D4×C1112yes—
350C22×C8D4×C1112yes—
351#117—21no—
352#117—21no—
353#117—21no—
354#117—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4C2×C4×C1112yes—
361C2×C4⋊C4D4×C1112yes—
362C2×C22⋊C4—21no—
363C2×C42—21no—
364#108—28no—
365#103—28no—
366#103—28no—
367#101—28no—
368C2×C11—21no—
369C2×C11—21no—
370C2×C11—21no—
371C2×C11—21no—
372C2×C11#143911yescharacteristic
373C2×C11#197711yescharacteristic
374C2×C11#197911yescharacteristic
375C2×C11#205212yes—
376C2×C11#206412yes—
377C24C11×#4111yescharacteristic
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—41no—
394C2×Q8—41no—
395C2×Q8—41no—
396C2×Q8—41no—
397C2×Q8—41no—
398C2×Q8—41no—
399C2×Q8—41no—
400C2×Q8—41no—
401C2×Q8—41no—
402C2×Q8—41no—
403C2×Q8—41no—
404C2×Q8—41no—
405C2×Q8C11×C4⋊C414yes—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—82no—
418C22×C4C22×C4×C1111yescharacteristic
419C22×C4C2×D4×C1111yescharacteristic
420C22×C4C2×D4×C1111yescharacteristic
421C22×C4C2×D4×C1111yescharacteristic
422C22×C4C2×D4×C1111yescharacteristic
423C22×C4C2×D4×C1111yescharacteristic
424C22×C4C2×D4×C1111yescharacteristic
425C22×C4C2×D4×C1111yescharacteristic
426C22×C4C2×Q8×C1111yescharacteristic
427C22×C4C11×#4111yescharacteristic
428C22×C4C11×#4111yescharacteristic
429C22×C4C11×#4111yescharacteristic
430C22×C4C11×#4111yescharacteristic
431C22×C4C11×#4111yescharacteristic
432M16—22no—
433M16—22no—
434M16—22no—
435M16—22no—
436M16—22no—
437M16—22no—
438M16—41no—
439M16—41no—
440M16—41no—
441M16—41no—
442M16—41no—
443M16—41no—
444C2×C8—22no—
445C2×C8—22no—
446C2×C8—22no—
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—22no—
451C2×C8—22no—
452C2×C8—22no—
453C2×C8—41no—
454C2×C8—41no—
455C2×C8—41no—
456C2×C8—41no—
457C2×C8—41no—
458C2×C8—41no—
459C2×C8C11×C22⋊C414yes—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C22⋊C4—41no—
467C22⋊C4—41no—
468C42—41no—
469C42—41no—
470C11#1112811yescharacteristic, direct product factor, Sylow
471C23—22no—
472C23—22no—
473C23C4×D4×C1111yescharacteristic
474C23C11×#12111yescharacteristic
475C23C11×C22⋊Q811yescharacteristic
476C23C11×#12311yescharacteristic
477C23C11×#12411yescharacteristic
478C23C11×#12411yescharacteristic
479C23C11×#12611yescharacteristic
480Q8—24no—
481Q8—24no—
482Q8—42no—
483Q8—42no—
484Q8—42no—
485Q8—42no—
486Q8—42no—
487Q8—42no—
488C2×C4—24no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—82no—
500C2×C4—82no—
501C2×C4—82no—
502C2×C4C2×C11×C22⋊C411yescharacteristic
503C2×C4C2×C11×C4⋊C411yescharacteristic
504C2×C4C11×#11711yescharacteristic
505C2×C4C4×D4×C1111yescharacteristic
506C2×C4C4×D4×C1111yescharacteristic
507C2×C4C4×D4×C1111yescharacteristic
508C2×C4C11×#12011yescharacteristic
509C2×C4C11×#12011yescharacteristic
510C2×C4C11×#12011yescharacteristic
511C2×C4C11×#12111yescharacteristic
512C2×C4C11×#12111yescharacteristic
513C2×C4C11×#12111yescharacteristic
514C2×C4C11×#12111yescharacteristic
515C2×C4C11×#12111yescharacteristic
516C2×C4C11×#12111yescharacteristic
517C2×C4C11×#12111yescharacteristic
518C2×C4C11×C22⋊Q811yescharacteristic
519C2×C4C11×C22⋊Q811yescharacteristic
520C2×C4C11×C22⋊Q811yescharacteristic
521C2×C4C11×C22⋊Q811yescharacteristic
522C2×C4C11×C22⋊Q811yescharacteristic
523C2×C4C11×#12311yescharacteristic
524C2×C4C11×#12311yescharacteristic
525C2×C4C11×#12311yescharacteristic
526C2×C4C11×#12311yescharacteristic
527C2×C4C11×#12411yescharacteristic
528C2×C4C11×#12611yescharacteristic
529C2×C4C11×#12711yescharacteristic
530C8—24no—
531C8—42no—
532C8—42no—
533C8—42no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—22no—
539C22—22no—
540C22—22no—
541C22—22no—
542C22C11×#38511yescharacteristic
543C22C11×#38811yescharacteristic
544C22C11×#39011yescharacteristic
545C22C11×#39311yescharacteristic
546C22C11×#39411yescharacteristic
547C22C11×#39611yescharacteristic
548C22C11×#39711yescharacteristic
549C22C11×#47112yes—
550C22C11×#47312yes—
551C4—44no—
552C4—82no—
553C4—82no—
554C4C11×#38011yescharacteristic
555C4C11×#38511yescharacteristic
556C4C11×#38611yescharacteristic
557C4C11×#38811yescharacteristic
558C4C11×#39211yescharacteristic
559C4C11×#39411yescharacteristic
560C4C11×#39611yescharacteristic
561C4C11×#39911yescharacteristic
562C2—21no—
563C2—21no—
564C2—21no—
565C2—21no—
566C2C11×#143911yescharacteristic
567C2C11×#197711yescharacteristic
568C2C11×#197911yescharacteristic
569C2C11×#205212yes—
570C2C11×#206412yes—
subgroupG/H
center, socleC23×C11#121
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC24×C11#41
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
23. C2×C11×#103C4semidirect
92. #11128C11direct (N × H)
271. C2×#103C4×C11semidirect
470. C11#11128direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1082
C2×C11×#4192
C22×C11×#1032
C22×C11×#1012
C2×C11×#3432
C11×#17362
C11×#17292
#1112811