Finite Group Databasebeta

← C11×#11137 #14588330

Subgroups — C11×#11137 #14588330

Order 2816.

854 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#430C211yesmaximal, characteristic, complemented
2C2×C11×#413C211yesmaximal, characteristic
3C11×#2879C211yesmaximal, characteristic
4C2×C11×#408C211yesmaximal, characteristic
5C11×#1738C211yesmaximal, characteristic, complemented
6C2×C11×#341C211yesmaximal, characteristic, complemented
7C2×C11×#341C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C23×C8×C11C2211yescharacteristic
15C11×#430—22no—
16C11×#430—22no—
17C2×C11×#108—22no—
18C11×#413—22no—
19C11×#413—22no—
20C2×C11×#101C412yes—
21C2×C11×#100C412yes—
22C11×#408—22no—
23C11×#408—22no—
24C11×#408—22no—
25C11×#408—22no—
26C11×#407—22no—
27C2×C11×C22⋊C8—22no—
28C11×#341—22no—
29C11×#341—22no—
30C11×#341—22no—
31C2×C11×#41—21no—
32C2×C11×#41—21no—
33C2×C11×#41—21no—
34C2×C11×#41—21no—
35C2×C11×#41—21no—
36C2×C11×#41—21no—
37C2×C11×#41—21no—
38C2×C11×#41—21no—
39C2×C11×#41—21no—
40C2×C11×#41—21no—
41C2×C11×#41—21no—
42C2×C11×#41—21no—
43C22×Q8×C11C2×C411yescharacteristic
44C22×D4×C11C2×C411yescharacteristic
45C22×D4×C11Q812yes—
46C23×C4×C11D412yes—
47C23×C4×C11C2311yescharacteristic
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×M16—21no—
63C2×C11×M16—21no—
64C2×C11×M16—21no—
65C2×C11×M16—21no—
66C2×C11×M16—21no—
67C2×C11×M16—21no—
68C2×C11×M16—21no—
69C2×C11×M16—21no—
70C2×C11×M16—21no—
71C2×C11×M16C2×C412yes—
72C2×C11×M16C2×C412yes—
73C2×C11×M16D412yes—
74C2×C11×M16D412yes—
75C2×C11×M16D412yes—
76C2×C11×M16D412yes—
77C2×C11×M16D412yes—
78C22×C8×C11—21no—
79C22×C8×C11—21no—
80C22×C8×C11—21no—
81C22×C8×C11—21no—
82C22×C8×C11—21no—
83C22×C8×C11—21no—
84C22×C8×C11—21no—
85C22×C8×C11—21no—
86C22×C8×C11—21no—
87C22×C8×C11—21no—
88C22×C8×C11—21no—
89C22×C8×C11D412yes—
90C11×#108—28no—
91C11×#101—24no—
92C11×#100—24no—
93C11×C22⋊C8—28no—
94C11×C22⋊C8—28no—
95#11137C1111yesmaximal, characteristic, direct product factor, Sylow
96C24×C11C4⋊C412yes—
97C24×C11C2×Q811yescharacteristic
98C11×#41—41no—
99C11×#41—41no—
100C11×#41—41no—
101C11×#41—41no—
102C11×#41—41no—
103C11×#41—41no—
104C11×#41—41no—
105C11×#41—41no—
106C11×#41—41no—
107C11×#41—41no—
108C11×#41—41no—
109C11×#41—41no—
110C11×#41—41no—
111C11×#41—41no—
112C11×#41—41no—
113C11×#41—41no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×Q8×C11—21no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11C4⋊C412yes—
139C22×C4×C11C22×C411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11#4111yescharacteristic
148C22×C4×C11#4111yescharacteristic
149C22×C4×C11#4111yescharacteristic
150C22×C4×C11#4111yescharacteristic
151C22×C4×C11#4111yescharacteristic
152C22×C4×C11#4111yescharacteristic
153C11×M16—22no—
154C11×M16—22no—
155C11×M16—22no—
156C11×M16—22no—
157C11×M16—22no—
158C11×M16—22no—
159C11×M16—22no—
160C11×M16—22no—
161C11×M16—22no—
162C11×M16—22no—
163C11×M16—22no—
164C11×M16—41no—
165C11×M16—41no—
166C11×M16—41no—
167C11×M16—41no—
168C11×M16—41no—
169C11×M16—41no—
170C11×M16—41no—
171C11×M16—41no—
172C11×M16C22⋊C414yes—
173C2×C8×C11—22no—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C2×C8×C11—22no—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C2×C8×C11—22no—
181C2×C8×C11—22no—
182C2×C8×C11—22no—
183C2×C8×C11—41no—
184C2×C8×C11—41no—
185C2×C8×C11—41no—
186C2×C8×C11—41no—
187C2×C8×C11—41no—
188C2×C8×C11—41no—
189C2×C8×C11—41no—
190C2×C8×C11—41no—
191C2×C8×C11—41no—
192C2×C8×C11—41no—
193C2×C8×C11—41no—
194C2×C8×C11—41no—
195C2×#430C2×C1111yescharacteristic, complemented
196C2×#413C2×C1111yescharacteristic
197#2879C2×C1111yescharacteristic
198C2×#408C2×C1111yescharacteristic
199#1738C2×C1111yescharacteristic, complemented
200C2×#341C2×C1111yescharacteristic, complemented
201C2×#341C2×C1111yescharacteristic, complemented
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—42no—
206C23×C11—44no—
207C23×C11C2×C4⋊C411yescharacteristic
208C23×C11C22⋊Q811yescharacteristic
209C23×C11C22⋊Q811yescharacteristic
210C23×C11C22⋊Q811yescharacteristic
211C23×C11C22⋊Q811yescharacteristic
212C23×C11C22⋊Q811yescharacteristic
213C23×C11C22⋊Q811yescharacteristic
214Q8×C11—41no—
215Q8×C11—41no—
216Q8×C11—41no—
217Q8×C11—41no—
218D4×C11—42no—
219D4×C11—42no—
220D4×C11—42no—
221D4×C11—42no—
222D4×C11—41no—
223D4×C11—41no—
224D4×C11—41no—
225D4×C11—41no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11C2×C22⋊C411yescharacteristic
234C2×C4×C11#11711yescharacteristic
235C2×C4×C11C4×D411yescharacteristic
236C2×C4×C11C4×D411yescharacteristic
237C2×C4×C11C4×D411yescharacteristic
238C2×C4×C11C4×D411yescharacteristic
239C2×C4×C11#12011yescharacteristic
240C2×C4×C11#12011yescharacteristic
241C2×C4×C11#12011yescharacteristic
242C2×C4×C11#12111yescharacteristic
243C2×C4×C11#12111yescharacteristic
244C2×C4×C11#12111yescharacteristic
245C2×C4×C11#12111yescharacteristic
246C2×C4×C11#12111yescharacteristic
247C2×C4×C11#12111yescharacteristic
248C2×C4×C11#12111yescharacteristic
249C2×C4×C11#12111yescharacteristic
250C2×C4×C11#12311yescharacteristic
251C2×C4×C11#12311yescharacteristic
252C2×C4×C11#12311yescharacteristic
253C2×C4×C11#12311yescharacteristic
254C2×C4×C11#12311yescharacteristic
255C2×C4×C11#12411yescharacteristic
256C2×C4×C11#12411yescharacteristic
257C2×C4×C11#12411yescharacteristic
258C2×C4×C11#12611yescharacteristic
259C2×C4×C11#12611yescharacteristic
260C2×C4×C11#12711yescharacteristic
261C8×C11—24no—
262C8×C11—42no—
263C8×C11—42no—
264C8×C11—42no—
265C8×C11—42no—
266C8×C11—42no—
267C22×#41C22×C1111yescharacteristic
268C22×M16C22×C1111yescharacteristic
269C22×M16C22×C1111yescharacteristic
270C22×M16C22×C1111yescharacteristic
271C22×M16C22×C1111yescharacteristic
272C22×M16C22×C1111yescharacteristic
273C23×C8C22×C1111yescharacteristic
274#430—22no—
275#430—22no—
276C2×#108—22no—
277#413—22no—
278#413—22no—
279C2×#101C4×C1112yes—
280C2×#100C4×C1112yes—
281#408—22no—
282#408—22no—
283#408—22no—
284#408—22no—
285#407—22no—
286C2×C22⋊C8—22no—
287#341—22no—
288#341—22no—
289#341—22no—
290C22×C11—22no—
291C22×C11—22no—
292C22×C11—22no—
293C22×C11—41no—
294C22×C11—41no—
295C22×C11—41no—
296C22×C11—41no—
297C22×C11—44no—
298C22×C11—44no—
299C22×C11—42no—
300C22×C11—82no—
301C22×C11#38011yescharacteristic
302C22×C11#38511yescharacteristic
303C22×C11#38511yescharacteristic
304C22×C11#39311yescharacteristic
305C22×C11#39611yescharacteristic
306C22×C11#39611yescharacteristic
307C22×C11#39911yescharacteristic
308C4×C11—42no—
309C4×C11#38611yescharacteristic
310C4×C11#38811yescharacteristic
311C4×C11#38811yescharacteristic
312C4×C11#39011yescharacteristic
313C4×C11#39211yescharacteristic
314C4×C11#39411yescharacteristic
315C4×C11#39411yescharacteristic
316C4×C11#39711yescharacteristic
317C2×#41—21no—
318C2×#41—21no—
319C2×#41—21no—
320C2×#41—21no—
321C2×#41—21no—
322C2×#41—21no—
323C2×#41—21no—
324C2×#41—21no—
325C2×#41—21no—
326C2×#41—21no—
327C2×#41—21no—
328C2×#41—21no—
329C22×Q8C2×C4×C1111yescharacteristic
330C22×D4C2×C4×C1111yescharacteristic
331C22×D4Q8×C1112yes—
332C23×C4D4×C1112yes—
333C23×C4C23×C1111yescharacteristic
334C2×M16—21no—
335C2×M16—21no—
336C2×M16—21no—
337C2×M16—21no—
338C2×M16—21no—
339C2×M16—21no—
340C2×M16—21no—
341C2×M16—21no—
342C2×M16—21no—
343C2×M16—21no—
344C2×M16—21no—
345C2×M16—21no—
346C2×M16—21no—
347C2×M16—21no—
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16C2×C4×C1112yes—
358C2×M16C2×C4×C1112yes—
359C2×M16D4×C1112yes—
360C2×M16D4×C1112yes—
361C2×M16D4×C1112yes—
362C2×M16D4×C1112yes—
363C2×M16D4×C1112yes—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—21no—
370C22×C8—21no—
371C22×C8—21no—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—21no—
375C22×C8D4×C1112yes—
376#108—28no—
377#101—24no—
378#100—24no—
379C22⋊C8—28no—
380C22⋊C8—28no—
381C2×C11—21no—
382C2×C11—21no—
383C2×C11—21no—
384C2×C11—21no—
385C2×C11—21no—
386C2×C11—21no—
387C2×C11—82no—
388C2×C11#143911yescharacteristic
389C2×C11#185812yes—
390C24C11×C4⋊C412yes—
391C24C2×Q8×C1111yescharacteristic
392#41—41no—
393#41—41no—
394#41—41no—
395#41—41no—
396#41—41no—
397#41—41no—
398#41—41no—
399#41—41no—
400#41—41no—
401#41—41no—
402#41—41no—
403#41—41no—
404#41—41no—
405#41—41no—
406#41—41no—
407#41—41no—
408C2×Q8—21no—
409C2×Q8—21no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4C11×C4⋊C412yes—
433C22×C4C22×C4×C1111yescharacteristic
434C22×C4C2×D4×C1111yescharacteristic
435C22×C4C2×D4×C1111yescharacteristic
436C22×C4C2×D4×C1111yescharacteristic
437C22×C4C2×D4×C1111yescharacteristic
438C22×C4C2×D4×C1111yescharacteristic
439C22×C4C2×D4×C1111yescharacteristic
440C22×C4C2×D4×C1111yescharacteristic
441C22×C4C11×#4111yescharacteristic
442C22×C4C11×#4111yescharacteristic
443C22×C4C11×#4111yescharacteristic
444C22×C4C11×#4111yescharacteristic
445C22×C4C11×#4111yescharacteristic
446C22×C4C11×#4111yescharacteristic
447M16—22no—
448M16—22no—
449M16—22no—
450M16—22no—
451M16—22no—
452M16—22no—
453M16—22no—
454M16—22no—
455M16—22no—
456M16—22no—
457M16—22no—
458M16—41no—
459M16—41no—
460M16—41no—
461M16—41no—
462M16—41no—
463M16—41no—
464M16—41no—
465M16—41no—
466M16C11×C22⋊C414yes—
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—41no—
489C11#1113711yescharacteristic, direct product factor, Sylow
490C23—22no—
491C23—22no—
492C23—22no—
493C23—42no—
494C23—44no—
495C23C2×C11×C4⋊C411yescharacteristic
496C23C11×C22⋊Q811yescharacteristic
497C23C11×C22⋊Q811yescharacteristic
498C23C11×C22⋊Q811yescharacteristic
499C23C11×C22⋊Q811yescharacteristic
500C23C11×C22⋊Q811yescharacteristic
501C23C11×C22⋊Q811yescharacteristic
502Q8—41no—
503Q8—41no—
504Q8—41no—
505Q8—41no—
506D4—42no—
507D4—42no—
508D4—42no—
509D4—42no—
510D4—41no—
511D4—41no—
512D4—41no—
513D4—41no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4C2×C11×C22⋊C411yescharacteristic
522C2×C4C11×#11711yescharacteristic
523C2×C4C4×D4×C1111yescharacteristic
524C2×C4C4×D4×C1111yescharacteristic
525C2×C4C4×D4×C1111yescharacteristic
526C2×C4C4×D4×C1111yescharacteristic
527C2×C4C11×#12011yescharacteristic
528C2×C4C11×#12011yescharacteristic
529C2×C4C11×#12011yescharacteristic
530C2×C4C11×#12111yescharacteristic
531C2×C4C11×#12111yescharacteristic
532C2×C4C11×#12111yescharacteristic
533C2×C4C11×#12111yescharacteristic
534C2×C4C11×#12111yescharacteristic
535C2×C4C11×#12111yescharacteristic
536C2×C4C11×#12111yescharacteristic
537C2×C4C11×#12111yescharacteristic
538C2×C4C11×#12311yescharacteristic
539C2×C4C11×#12311yescharacteristic
540C2×C4C11×#12311yescharacteristic
541C2×C4C11×#12311yescharacteristic
542C2×C4C11×#12311yescharacteristic
543C2×C4C11×#12411yescharacteristic
544C2×C4C11×#12411yescharacteristic
545C2×C4C11×#12411yescharacteristic
546C2×C4C11×#12611yescharacteristic
547C2×C4C11×#12611yescharacteristic
548C2×C4C11×#12711yescharacteristic
549C8—24no—
550C8—42no—
551C8—42no—
552C8—42no—
553C8—42no—
554C8—42no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—44no—
563C22—42no—
564C22—44no—
565C22—82no—
566C22C11×#38011yescharacteristic
567C22C11×#38511yescharacteristic
568C22C11×#38511yescharacteristic
569C22C11×#39311yescharacteristic
570C22C11×#39611yescharacteristic
571C22C11×#39611yescharacteristic
572C22C11×#39911yescharacteristic
573C4—42no—
574C4C11×#38611yescharacteristic
575C4C11×#38811yescharacteristic
576C4C11×#38811yescharacteristic
577C4C11×#39011yescharacteristic
578C4C11×#39211yescharacteristic
579C4C11×#39411yescharacteristic
580C4C11×#39411yescharacteristic
581C4C11×#39711yescharacteristic
582C2—21no—
583C2—21no—
584C2—21no—
585C2—21no—
586C2—21no—
587C2—21no—
588C2—82no—
589C2C11×#143911yescharacteristic
590C2C11×#185812yes—
subgroupG/H
centerC2×C4×C11#120
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
socleC22×C11#385
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#430C2semidirect
5. C11×#1738C2semidirect
6. C2×C11×#341C2semidirect
7. C2×C11×#341C2semidirect
95. #11137C11direct (N × H)
195. C2×#430C2×C11semidirect
199. #1738C2×C11semidirect
200. C2×#341C2×C11semidirect
201. C2×#341C2×C11semidirect
489. C11#11137direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4302
C2×C11×#4132
C11×#28792
C2×C11×#4082
C11×#17382
C2×C11×#3412
#1113711