Finite Group Databasebeta

← C11×#11142 #14588335

Subgroups — C11×#11142 #14588335

Order 2816.

966 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#430C211yesmaximal, characteristic, complemented
2C2×C11×#418C211yesmaximal, characteristic
3C2×C11×#418C211yesmaximal, characteristic
4C22×C11×#100C211yesmaximal, characteristic
5C2×C11×#344C211yesmaximal, characteristic, complemented
6C11×#1742C211yesmaximal, characteristic, complemented
7C11×#1733C211yesmaximal, characteristic, complemented
8C23×D4×C11C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C11×#430—22no—
16C11×#430—22no—
17C2×C11×#108—22no—
18C11×#418—22no—
19C11×#418—22no—
20C11×#418—22no—
21C11×#418—22no—
22C2×C11×#102—22no—
23C2×C11×#102—22no—
24C2×C11×#100—22no—
25C2×C11×#100—22no—
26C2×C11×#100C414yescomplemented
27C11×#344—22no—
28C11×#343—22no—
29C11×#339—22no—
30C25×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C22×D4×C11—21no—
35C22×D4×C11—21no—
36C22×D4×C11—21no—
37C22×D4×C11—21no—
38C22×D4×C11—21no—
39C22×D4×C11—21no—
40C22×D4×C11—21no—
41C22×D4×C11—21no—
42C22×D4×C11C2×C412yes—
43C22×D4×C11D412yes—
44C22×D4×C11Q812yes—
45C23×C4×C11C2311yescharacteristic
46C2×C11×M16—21no—
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×M16—21no—
63C2×C11×M16—21no—
64C2×C11×M16C2×C412yes—
65C2×C11×M16C2×C412yes—
66C2×C11×M16D412yes—
67C2×C11×M16D412yes—
68C2×C11×M16D412yes—
69C2×C11×M16D412yes—
70C22×C8×C11—21no—
71C22×C8×C11—21no—
72C22×C8×C11—21no—
73C22×C8×C11—21no—
74C11×#117—21no—
75C11×#117—21no—
76C11×#117—21no—
77C11×#117—21no—
78C11×#117—21no—
79C11×#117—21no—
80C11×#117—21no—
81C11×#117D412yes—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4D412yes—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C42×C11—21no—
87C2×C42×C11—21no—
88C11×#108—28no—
89C11×#102—28no—
90C11×#102—28no—
91C11×#100—28no—
92#11142C1111yesmaximal, characteristic, direct product factor, Sylow
93C24×C11—22no—
94C24×C11—22no—
95C24×C11—22no—
96C24×C11—41no—
97C24×C11—41no—
98C24×C11—41no—
99C24×C11—41no—
100C24×C11—84no—
101C24×C11#4111yescharacteristic
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—41no—
118C2×D4×C11—41no—
119C2×D4×C11—41no—
120C2×D4×C11—41no—
121C2×D4×C11—41no—
122C2×D4×C11—41no—
123C2×D4×C11—41no—
124C2×D4×C11—41no—
125C2×D4×C11—41no—
126C2×D4×C11—41no—
127C2×D4×C11—41no—
128C2×D4×C11—41no—
129C2×D4×C11C4⋊C414yes—
130C22×C4×C11—22no—
131C22×C4×C11—41no—
132C22×C4×C11C22×C411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×Q811yescharacteristic
141C22×C4×C11#4111yescharacteristic
142C22×C4×C11#4111yescharacteristic
143C22×C4×C11#4111yescharacteristic
144C22×C4×C11#4111yescharacteristic
145C22×C4×C11#4111yescharacteristic
146C11×M16—22no—
147C11×M16—22no—
148C11×M16—22no—
149C11×M16—22no—
150C11×M16—22no—
151C11×M16—22no—
152C11×M16—22no—
153C11×M16—22no—
154C11×M16—22no—
155C11×M16—41no—
156C11×M16—41no—
157C11×M16—41no—
158C11×M16—41no—
159C11×M16—41no—
160C11×M16—41no—
161C11×M16C22⋊C414yes—
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—41no—
169C2×C8×C11—41no—
170C2×C8×C11—41no—
171C2×C8×C11—41no—
172C2×C8×C11—41no—
173C2×C8×C11—41no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—41no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—41no—
180C11×C22⋊C4—41no—
181C11×C22⋊C4—41no—
182C42×C11—22no—
183C42×C11—41no—
184C42×C11—41no—
185C42×C11—41no—
186C2×#430C2×C1111yescharacteristic, complemented
187C2×#418C2×C1111yescharacteristic
188C2×#418C2×C1111yescharacteristic
189C22×#100C2×C1111yescharacteristic
190C2×#344C2×C1111yescharacteristic, complemented
191#1742C2×C1111yescharacteristic, complemented
192#1733C2×C1111yescharacteristic, complemented
193C23×C11—24no—
194C23×C11—42no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—84no—
202C23×C11—84no—
203C23×C11—84no—
204C23×C11—84no—
205C23×C11—84no—
206C23×C11—84no—
207C23×C11—84no—
208C23×C11#11711yescharacteristic
209C23×C11#12111yescharacteristic
210C23×C11C22⋊Q811yescharacteristic
211C23×C11#12311yescharacteristic
212C23×C11#12311yescharacteristic
213C23×C11#12411yescharacteristic
214C23×C11#12411yescharacteristic
215D4×C11—24no—
216D4×C11—24no—
217D4×C11—42no—
218D4×C11—42no—
219D4×C11—42no—
220D4×C11—42no—
221D4×C11—42no—
222D4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—82no—
226C2×C4×C11—82no—
227C2×C4×C11C2×C22⋊C411yescharacteristic
228C2×C4×C11C2×C4⋊C411yescharacteristic
229C2×C4×C11C4×D411yescharacteristic
230C2×C4×C11C4×D411yescharacteristic
231C2×C4×C11C4×D411yescharacteristic
232C2×C4×C11C4×D411yescharacteristic
233C2×C4×C11#12011yescharacteristic
234C2×C4×C11#12011yescharacteristic
235C2×C4×C11#12011yescharacteristic
236C2×C4×C11#12111yescharacteristic
237C2×C4×C11#12111yescharacteristic
238C2×C4×C11#12111yescharacteristic
239C2×C4×C11#12111yescharacteristic
240C2×C4×C11#12111yescharacteristic
241C2×C4×C11#12111yescharacteristic
242C2×C4×C11#12111yescharacteristic
243C2×C4×C11C22⋊Q811yescharacteristic
244C2×C4×C11C22⋊Q811yescharacteristic
245C2×C4×C11C22⋊Q811yescharacteristic
246C2×C4×C11C22⋊Q811yescharacteristic
247C2×C4×C11C22⋊Q811yescharacteristic
248C2×C4×C11#12311yescharacteristic
249C2×C4×C11#12311yescharacteristic
250C2×C4×C11#12311yescharacteristic
251C2×C4×C11#12411yescharacteristic
252C2×C4×C11#12611yescharacteristic
253C2×C4×C11#12611yescharacteristic
254C2×C4×C11#12711yescharacteristic
255C8×C11—24no—
256C8×C11—42no—
257C8×C11—42no—
258C8×C11—42no—
259C23×D4C22×C1111yescharacteristic
260C22×M16C22×C1111yescharacteristic
261C22×M16C22×C1111yescharacteristic
262C22×M16C22×C1111yescharacteristic
263C22×M16C22×C1111yescharacteristic
264C2×#117C22×C1111yescharacteristic
265C2×#117C22×C1111yescharacteristic
266#430—22no—
267#430—22no—
268C2×#108—22no—
269#418—22no—
270#418—22no—
271#418—22no—
272#418—22no—
273C2×#102—22no—
274C2×#102—22no—
275C2×#100—22no—
276C2×#100—22no—
277C2×#100C4×C1114yescomplemented
278#344—22no—
279#343—22no—
280#339—22no—
281C22×C11—22no—
282C22×C11—22no—
283C22×C11—22no—
284C22×C11—41no—
285C22×C11—41no—
286C22×C11—41no—
287C22×C11—41no—
288C22×C11—44no—
289C22×C11—84no—
290C22×C11—84no—
291C22×C11—84no—
292C22×C11—84no—
293C22×C11—84no—
294C22×C11—84no—
295C22×C11—84no—
296C22×C11#38011yescharacteristic
297C22×C11#38811yescharacteristic
298C22×C11#38811yescharacteristic
299C22×C11#39311yescharacteristic
300C22×C11#39411yescharacteristic
301C22×C11#39411yescharacteristic
302C22×C11#39911yescharacteristic
303C4×C11—82no—
304C4×C11—82no—
305C4×C11#38511yescharacteristic
306C4×C11#38511yescharacteristic
307C4×C11#38611yescharacteristic
308C4×C11#39011yescharacteristic
309C4×C11#39211yescharacteristic
310C4×C11#39611yescharacteristic
311C4×C11#39611yescharacteristic
312C4×C11#39711yescharacteristic
313C25—21no—
314C22×D4—21no—
315C22×D4—21no—
316C22×D4—21no—
317C22×D4—21no—
318C22×D4—21no—
319C22×D4—21no—
320C22×D4—21no—
321C22×D4—21no—
322C22×D4—21no—
323C22×D4—21no—
324C22×D4—21no—
325C22×D4C2×C4×C1112yes—
326C22×D4D4×C1112yes—
327C22×D4Q8×C1112yes—
328C23×C4C23×C1111yescharacteristic
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×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×M16C2×C4×C1112yes—
348C2×M16C2×C4×C1112yes—
349C2×M16D4×C1112yes—
350C2×M16D4×C1112yes—
351C2×M16D4×C1112yes—
352C2×M16D4×C1112yes—
353C22×C8—21no—
354C22×C8—21no—
355C22×C8—21no—
356C22×C8—21no—
357#117—21no—
358#117—21no—
359#117—21no—
360#117—21no—
361#117—21no—
362#117—21no—
363#117—21no—
364#117D4×C1112yes—
365C2×C4⋊C4—21no—
366C2×C4⋊C4D4×C1112yes—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C42—21no—
370C2×C42—21no—
371#108—28no—
372#102—28no—
373#102—28no—
374#100—28no—
375C2×C11—21no—
376C2×C11—21no—
377C2×C11—21no—
378C2×C11—21no—
379C2×C11—21no—
380C2×C11—21no—
381C2×C11—84no—
382C2×C11#143911yescharacteristic
383C2×C11#204812yes—
384C24—22no—
385C24—22no—
386C24—22no—
387C24—41no—
388C24—41no—
389C24—41no—
390C24—41no—
391C24—84no—
392C24C11×#4111yescharacteristic
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—41no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—41no—
414C2×D4—41no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4C11×C4⋊C414yes—
421C22×C4—22no—
422C22×C4—41no—
423C22×C4C22×C4×C1111yescharacteristic
424C22×C4C2×D4×C1111yescharacteristic
425C22×C4C2×D4×C1111yescharacteristic
426C22×C4C2×D4×C1111yescharacteristic
427C22×C4C2×D4×C1111yescharacteristic
428C22×C4C2×D4×C1111yescharacteristic
429C22×C4C2×D4×C1111yescharacteristic
430C22×C4C2×D4×C1111yescharacteristic
431C22×C4C2×Q8×C1111yescharacteristic
432C22×C4C11×#4111yescharacteristic
433C22×C4C11×#4111yescharacteristic
434C22×C4C11×#4111yescharacteristic
435C22×C4C11×#4111yescharacteristic
436C22×C4C11×#4111yescharacteristic
437M16—22no—
438M16—22no—
439M16—22no—
440M16—22no—
441M16—22no—
442M16—22no—
443M16—22no—
444M16—22no—
445M16—22no—
446M16—41no—
447M16—41no—
448M16—41no—
449M16—41no—
450M16—41no—
451M16—41no—
452M16C11×C22⋊C414yes—
453C2×C8—22no—
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—41no—
460C2×C8—41no—
461C2×C8—41no—
462C2×C8—41no—
463C2×C8—41no—
464C2×C8—41no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—41no—
469C22⋊C4—22no—
470C22⋊C4—41no—
471C22⋊C4—41no—
472C22⋊C4—41no—
473C42—22no—
474C42—41no—
475C42—41no—
476C42—41no—
477C11#1114211yescharacteristic, direct product factor, Sylow
478C23—24no—
479C23—42no—
480C23—42no—
481C23—42no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—84no—
487C23—84no—
488C23—84no—
489C23—84no—
490C23—84no—
491C23—84no—
492C23—84no—
493C23C11×#11711yescharacteristic
494C23C11×#12111yescharacteristic
495C23C11×C22⋊Q811yescharacteristic
496C23C11×#12311yescharacteristic
497C23C11×#12311yescharacteristic
498C23C11×#12411yescharacteristic
499C23C11×#12411yescharacteristic
500D4—24no—
501D4—24no—
502D4—42no—
503D4—42no—
504D4—42no—
505D4—42no—
506D4—42no—
507D4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—82no—
511C2×C4—82no—
512C2×C4C2×C11×C22⋊C411yescharacteristic
513C2×C4C2×C11×C4⋊C411yescharacteristic
514C2×C4C4×D4×C1111yescharacteristic
515C2×C4C4×D4×C1111yescharacteristic
516C2×C4C4×D4×C1111yescharacteristic
517C2×C4C4×D4×C1111yescharacteristic
518C2×C4C11×#12011yescharacteristic
519C2×C4C11×#12011yescharacteristic
520C2×C4C11×#12011yescharacteristic
521C2×C4C11×#12111yescharacteristic
522C2×C4C11×#12111yescharacteristic
523C2×C4C11×#12111yescharacteristic
524C2×C4C11×#12111yescharacteristic
525C2×C4C11×#12111yescharacteristic
526C2×C4C11×#12111yescharacteristic
527C2×C4C11×#12111yescharacteristic
528C2×C4C11×C22⋊Q811yescharacteristic
529C2×C4C11×C22⋊Q811yescharacteristic
530C2×C4C11×C22⋊Q811yescharacteristic
531C2×C4C11×C22⋊Q811yescharacteristic
532C2×C4C11×C22⋊Q811yescharacteristic
533C2×C4C11×#12311yescharacteristic
534C2×C4C11×#12311yescharacteristic
535C2×C4C11×#12311yescharacteristic
536C2×C4C11×#12411yescharacteristic
537C2×C4C11×#12611yescharacteristic
538C2×C4C11×#12611yescharacteristic
539C2×C4C11×#12711yescharacteristic
540C8—24no—
541C8—42no—
542C8—42no—
543C8—42no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—44no—
552C22—84no—
553C22—84no—
554C22—84no—
555C22—84no—
556C22—84no—
557C22—84no—
558C22—84no—
559C22C11×#38011yescharacteristic
560C22C11×#38811yescharacteristic
561C22C11×#38811yescharacteristic
562C22C11×#39311yescharacteristic
563C22C11×#39411yescharacteristic
564C22C11×#39411yescharacteristic
565C22C11×#39911yescharacteristic
566C4—82no—
567C4—82no—
568C4C11×#38511yescharacteristic
569C4C11×#38511yescharacteristic
570C4C11×#38611yescharacteristic
571C4C11×#39011yescharacteristic
572C4C11×#39211yescharacteristic
573C4C11×#39611yescharacteristic
574C4C11×#39611yescharacteristic
575C4C11×#39711yescharacteristic
576C2—21no—
577C2—21no—
578C2—21no—
579C2—21no—
580C2—21no—
581C2—21no—
582C2—84no—
583C2C11×#143911yescharacteristic
584C2C11×#204812yes—
subgroupG/H
center, socleC22×C11#394
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
prime radicalC23×D4×C11C22
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
1. C2×C11×#430C2semidirect
5. C2×C11×#344C2semidirect
6. C11×#1742C2semidirect
7. C11×#1733C2semidirect
26. C2×C11×#100C4semidirect
92. #11142C11direct (N × H)
186. C2×#430C2×C11semidirect
190. C2×#344C2×C11semidirect
191. #1742C2×C11semidirect
192. #1733C2×C11semidirect
277. C2×#100C4×C11semidirect
477. C11#11142direct (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×#4182
C22×C11×#1002
C2×C11×#3442
C11×#17422
C11×#17332
#1114211