Finite Group Databasebeta

← C11×#11118 #14588311

Subgroups — C11×#11118 #14588311

Order 2816.

852 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#430C211yesmaximal, characteristic, complemented
2C2×C11×#421C211yesmaximal, characteristic
3C2×C11×#421C211yesmaximal, characteristic
4C11×#2879C211yesmaximal, characteristic
5C2×C11×#344C211yesmaximal, characteristic, complemented
6C11×#1742C211yesmaximal, characteristic, complemented
7C11×#1733C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
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×#421—22no—
19C11×#421—22no—
20C11×#421—22no—
21C11×#421C414yescomplemented
22C2×C11×#104—22no—
23C2×C11×#104—22no—
24C11×#408—22no—
25C11×#408—22no—
26C11×#407—22no—
27C11×#344—22no—
28C11×#343—22no—
29C11×#339—22no—
30C2×C11×#41—21no—
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×#41C2×C412yes—
41C2×C11×#41D412yes—
42C22×Q8×C11Q811yescharacteristic
43C22×D4×C11—21no—
44C22×D4×C11Q811yescharacteristic
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×M16—21no—
63C2×C11×M16—21no—
64C2×C11×M16—21no—
65C2×C11×M16C2×C412yes—
66C2×C11×M16D412yes—
67C2×C11×M16D412yes—
68C2×C11×M16D412yes—
69C2×C11×M16D412yes—
70C2×C11×M16D412yes—
71C22×C8×C11—21no—
72C22×C8×C11—21no—
73C22×C8×C11—21no—
74C22×C8×C11—21no—
75C11×#117—21no—
76C11×#117—21no—
77C11×#117—21no—
78C11×#117—21no—
79C11×#117—21no—
80C11×#117—21no—
81C11×#117—21no—
82C11×#117C2×C412yes—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C42×C11—21no—
88C2×C42×C11D412yes—
89C11×#108—28no—
90C11×#104—28no—
91C11×#104—28no—
92C11×C22⋊C8—28no—
93#11118C1111yesmaximal, characteristic, direct product factor, Sylow
94C24×C11—21no—
95C24×C11#4111yescharacteristic
96C11×#41—22no—
97C11×#41—22no—
98C11×#41—22no—
99C11×#41—22no—
100C11×#41—22no—
101C11×#41—22no—
102C11×#41—22no—
103C11×#41—22no—
104C11×#41—41no—
105C11×#41—41no—
106C11×#41—41no—
107C11×#41—41no—
108C11×#41—41no—
109C11×#41—41no—
110C11×#41—41no—
111C11×#41—41no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11C4⋊C412yes—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—41no—
126C2×D4×C11—41no—
127C2×D4×C11—41no—
128C2×D4×C11—41no—
129C2×D4×C11C4⋊C412yes—
130C22×C4×C11—21no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—41no—
135C22×C4×C11—41no—
136C22×C4×C11—41no—
137C22×C4×C11—41no—
138C22×C4×C11—41no—
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×C11C2×Q811yescharacteristic
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—41no—
163C11×M16—41no—
164C11×M16—41no—
165C11×M16—41no—
166C11×M16—41no—
167C11×M16—41no—
168C11×M16C22⋊C414yes—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C2×C8×C11—22no—
175C2×C8×C11—41no—
176C2×C8×C11—41no—
177C2×C8×C11—41no—
178C2×C8×C11—41no—
179C2×C8×C11—41no—
180C2×C8×C11—41no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—41no—
183C11×C4⋊C4—41no—
184C11×C4⋊C4—41no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—41no—
187C11×C22⋊C4—41no—
188C11×C22⋊C4—41no—
189C42×C11—22no—
190C42×C11—22no—
191C42×C11—22no—
192C42×C11—41no—
193C2×#430C2×C1111yescharacteristic, complemented
194C2×#421C2×C1111yescharacteristic
195C2×#421C2×C1111yescharacteristic
196#2879C2×C1111yescharacteristic
197C2×#344C2×C1111yescharacteristic, complemented
198#1742C2×C1111yescharacteristic, complemented
199#1733C2×C1111yescharacteristic, complemented
200C23×C11—22no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—81no—
204C23×C11—82no—
205C23×C11C4×D411yescharacteristic
206C23×C11#12111yescharacteristic
207C23×C11C22⋊Q811yescharacteristic
208C23×C11#12311yescharacteristic
209C23×C11#12411yescharacteristic
210C23×C11#12411yescharacteristic
211C23×C11#12611yescharacteristic
212Q8×C11—22no—
213Q8×C11—22no—
214Q8×C11—41no—
215Q8×C11—41no—
216D4×C11—22no—
217D4×C11—22no—
218D4×C11—42no—
219D4×C11—42no—
220D4×C11—42no—
221D4×C11—42no—
222D4×C11—41no—
223D4×C11—41no—
224C2×C4×C11—22no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—82no—
234C2×C4×C11—82no—
235C2×C4×C11C2×C22⋊C411yescharacteristic
236C2×C4×C11C2×C4⋊C411yescharacteristic
237C2×C4×C11#11711yescharacteristic
238C2×C4×C11C4×D411yescharacteristic
239C2×C4×C11C4×D411yescharacteristic
240C2×C4×C11C4×D411yescharacteristic
241C2×C4×C11#12011yescharacteristic
242C2×C4×C11#12011yescharacteristic
243C2×C4×C11#12011yescharacteristic
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#12111yescharacteristic
251C2×C4×C11C22⋊Q811yescharacteristic
252C2×C4×C11C22⋊Q811yescharacteristic
253C2×C4×C11C22⋊Q811yescharacteristic
254C2×C4×C11C22⋊Q811yescharacteristic
255C2×C4×C11C22⋊Q811yescharacteristic
256C2×C4×C11#12311yescharacteristic
257C2×C4×C11#12311yescharacteristic
258C2×C4×C11#12311yescharacteristic
259C2×C4×C11#12311yescharacteristic
260C2×C4×C11#12411yescharacteristic
261C2×C4×C11#12611yescharacteristic
262C2×C4×C11#12711yescharacteristic
263C8×C11—24no—
264C8×C11—42no—
265C8×C11—42no—
266C8×C11—42no—
267C22×#41C22×C1111yescharacteristic
268C22×M16C22×C1111yescharacteristic
269C22×M16C22×C1111yescharacteristic
270C22×M16C22×C1111yescharacteristic
271C22×M16C22×C1111yescharacteristic
272C2×#117C22×C1111yescharacteristic
273C2×#117C22×C1111yescharacteristic
274#430—22no—
275#430—22no—
276C2×#108—22no—
277#421—22no—
278#421—22no—
279#421—22no—
280#421C4×C1114yescomplemented
281C2×#104—22no—
282C2×#104—22no—
283#408—22no—
284#408—22no—
285#407—22no—
286#344—22no—
287#343—22no—
288#339—22no—
289C22×C11—41no—
290C22×C11—41no—
291C22×C11—41no—
292C22×C11—41no—
293C22×C11—41no—
294C22×C11—41no—
295C22×C11—41no—
296C22×C11—44no—
297C22×C11—42no—
298C22×C11—82no—
299C22×C11—82no—
300C22×C11#38511yescharacteristic
301C22×C11#38811yescharacteristic
302C22×C11#39011yescharacteristic
303C22×C11#39311yescharacteristic
304C22×C11#39411yescharacteristic
305C22×C11#39611yescharacteristic
306C22×C11#39711yescharacteristic
307C4×C11—42no—
308C4×C11—82no—
309C4×C11—82no—
310C4×C11#38011yescharacteristic
311C4×C11#38511yescharacteristic
312C4×C11#38611yescharacteristic
313C4×C11#38811yescharacteristic
314C4×C11#39211yescharacteristic
315C4×C11#39411yescharacteristic
316C4×C11#39611yescharacteristic
317C4×C11#39911yescharacteristic
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×#41C2×C4×C1112yes—
329C2×#41D4×C1112yes—
330C22×Q8Q8×C1111yescharacteristic
331C22×D4—21no—
332C22×D4Q8×C1111yescharacteristic
333C23×C4—21no—
334C23×C4C23×C1111yescharacteristic
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×M16C2×C4×C1112yes—
354C2×M16D4×C1112yes—
355C2×M16D4×C1112yes—
356C2×M16D4×C1112yes—
357C2×M16D4×C1112yes—
358C2×M16D4×C1112yes—
359C22×C8—21no—
360C22×C8—21no—
361C22×C8—21no—
362C22×C8—21no—
363#117—21no—
364#117—21no—
365#117—21no—
366#117—21no—
367#117—21no—
368#117—21no—
369#117—21no—
370#117C2×C4×C1112yes—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C42—21no—
376C2×C42D4×C1112yes—
377#108—28no—
378#104—28no—
379#104—28no—
380C22⋊C8—28no—
381C2×C11—21no—
382C2×C11—21no—
383C2×C11—21no—
384C2×C11—21no—
385C2×C11—21no—
386C2×C11—21no—
387C2×C11—21no—
388C2×C11—82no—
389C2×C11#143911yescharacteristic
390C24—21no—
391C24C11×#4111yescharacteristic
392#41—22no—
393#41—22no—
394#41—22no—
395#41—22no—
396#41—22no—
397#41—22no—
398#41—22no—
399#41—22no—
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×Q8C11×C4⋊C412yes—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4C11×C4⋊C412yes—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4C22×C4×C1111yescharacteristic
436C22×C4C2×D4×C1111yescharacteristic
437C22×C4C2×D4×C1111yescharacteristic
438C22×C4C2×D4×C1111yescharacteristic
439C22×C4C2×D4×C1111yescharacteristic
440C22×C4C2×D4×C1111yescharacteristic
441C22×C4C2×D4×C1111yescharacteristic
442C22×C4C2×D4×C1111yescharacteristic
443C22×C4C2×Q8×C1111yescharacteristic
444C22×C4C11×#4111yescharacteristic
445C22×C4C11×#4111yescharacteristic
446C22×C4C11×#4111yescharacteristic
447C22×C4C11×#4111yescharacteristic
448C22×C4C11×#4111yescharacteristic
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—
464M16C11×C22⋊C414yes—
465C2×C8—22no—
466C2×C8—22no—
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—41no—
472C2×C8—41no—
473C2×C8—41no—
474C2×C8—41no—
475C2×C8—41no—
476C2×C8—41no—
477C4⋊C4—22no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C22⋊C4—22no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C42—22no—
486C42—22no—
487C42—22no—
488C42—41no—
489C11#1111811yescharacteristic, direct product factor, Sylow
490C23—22no—
491C23—41no—
492C23—41no—
493C23—81no—
494C23—82no—
495C23C4×D4×C1111yescharacteristic
496C23C11×#12111yescharacteristic
497C23C11×C22⋊Q811yescharacteristic
498C23C11×#12311yescharacteristic
499C23C11×#12411yescharacteristic
500C23C11×#12411yescharacteristic
501C23C11×#12611yescharacteristic
502Q8—22no—
503Q8—22no—
504Q8—41no—
505Q8—41no—
506D4—22no—
507D4—22no—
508D4—42no—
509D4—42no—
510D4—42no—
511D4—42no—
512D4—41no—
513D4—41no—
514C2×C4—22no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—82no—
524C2×C4—82no—
525C2×C4C2×C11×C22⋊C411yescharacteristic
526C2×C4C2×C11×C4⋊C411yescharacteristic
527C2×C4C11×#11711yescharacteristic
528C2×C4C4×D4×C1111yescharacteristic
529C2×C4C4×D4×C1111yescharacteristic
530C2×C4C4×D4×C1111yescharacteristic
531C2×C4C11×#12011yescharacteristic
532C2×C4C11×#12011yescharacteristic
533C2×C4C11×#12011yescharacteristic
534C2×C4C11×#12111yescharacteristic
535C2×C4C11×#12111yescharacteristic
536C2×C4C11×#12111yescharacteristic
537C2×C4C11×#12111yescharacteristic
538C2×C4C11×#12111yescharacteristic
539C2×C4C11×#12111yescharacteristic
540C2×C4C11×#12111yescharacteristic
541C2×C4C11×C22⋊Q811yescharacteristic
542C2×C4C11×C22⋊Q811yescharacteristic
543C2×C4C11×C22⋊Q811yescharacteristic
544C2×C4C11×C22⋊Q811yescharacteristic
545C2×C4C11×C22⋊Q811yescharacteristic
546C2×C4C11×#12311yescharacteristic
547C2×C4C11×#12311yescharacteristic
548C2×C4C11×#12311yescharacteristic
549C2×C4C11×#12311yescharacteristic
550C2×C4C11×#12411yescharacteristic
551C2×C4C11×#12611yescharacteristic
552C2×C4C11×#12711yescharacteristic
553C8—24no—
554C8—42no—
555C8—42no—
556C8—42no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—44no—
565C22—42no—
566C22—82no—
567C22—82no—
568C22C11×#38511yescharacteristic
569C22C11×#38811yescharacteristic
570C22C11×#39011yescharacteristic
571C22C11×#39311yescharacteristic
572C22C11×#39411yescharacteristic
573C22C11×#39611yescharacteristic
574C22C11×#39711yescharacteristic
575C4—42no—
576C4—82no—
577C4—82no—
578C4C11×#38011yescharacteristic
579C4C11×#38511yescharacteristic
580C4C11×#38611yescharacteristic
581C4C11×#38811yescharacteristic
582C4C11×#39211yescharacteristic
583C4C11×#39411yescharacteristic
584C4C11×#39611yescharacteristic
585C4C11×#39911yescharacteristic
586C2—21no—
587C2—21no—
588C2—21no—
589C2—21no—
590C2—21no—
591C2—21no—
592C2—21no—
593C2—82no—
594C2C11×#143911yescharacteristic
subgroupG/H
centerC4×C11#392
commutatorC22×C4C22×C4×C11
Frattini, cosocleC23×C4C23×C11
socleC2×C11#1439
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ 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. C2×C11×#344C2semidirect
6. C11×#1742C2semidirect
7. C11×#1733C2semidirect
21. C11×#421C4semidirect
93. #11118C11direct (N × H)
193. C2×#430C2×C11semidirect
197. C2×#344C2×C11semidirect
198. #1742C2×C11semidirect
199. #1733C2×C11semidirect
280. #421C4×C11semidirect
489. C11#11118direct (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×#4212
C11×#28792
C2×C11×#3442
C11×#17422
C11×#17332
#1111811