Finite Group Databasebeta

← C11×#19184 #14596377

Subgroups — C11×#19184 #14596377

Order 2816.

668 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3184C211yesmaximal, characteristic, complemented
2C11×#3106C211yesmaximal, characteristic, complemented
3C11×#3035C211yesmaximal, characteristic, complemented
4C11×#2971C211yesmaximal, characteristic, complemented
5C11×#1701C211yesmaximal, characteristic, complemented
6C11×#1697C211yesmaximal, characteristic, complemented
7C11×#1691C211yesmaximal, characteristic, complemented
8C11×#1687C211yesmaximal, characteristic, complemented
9C11×#1682C211yesmaximal, characteristic, complemented
10C11×#1678C211yesmaximal, characteristic, complemented
11C11×#1672C211yesmaximal, characteristic, complemented
12C11×#1668C211yesmaximal, characteristic, complemented
13C11×#1565C211yesmaximal, characteristic, complemented
14C11×#1553C211yesmaximal, characteristic, complemented
15C11×#1551C211yesmaximal, characteristic, complemented
16C2×C11×#135—21no—
17C11×#532C2211yescharacteristic
18C11×#532C2211yescharacteristic
19C4×C11×#41C2211yescharacteristic
20C11×#498C2211yescharacteristic
21C11×#493C2211yescharacteristic
22C11×#486C2211yescharacteristic
23C11×#486C2211yescharacteristic
24C11×#482—21no—
25C11×#477C2211yescharacteristic
26C11×#476C2211yescharacteristic
27C11×#469—21no—
28C11×#469—21no—
29C11×#464—21no—
30C11×#463—21no—
31C11×#462C2211yescharacteristic
32C11×#461C2211yescharacteristic
33C11×#460C2211yescharacteristic
34C11×#460C2211yescharacteristic
35C11×#459C2211yescharacteristic
36C11×#459C2211yescharacteristic
37C11×#449—21no—
38C8×Q8×C11C2211yescharacteristic
39C8×Q8×C11C2211yescharacteristic
40C11×#442—21no—
41C11×#442—21no—
42C4×C11×SD16—21no—
43C4×C11×D8—21no—
44C11×#436—21no—
45C11×#436—21no—
46C11×#436C2211yescharacteristic
47C11×#436C2211yescharacteristic
48C11×#432—21no—
49C11×#432C2211yescharacteristic
50C11×#431C2211yescharacteristic
51C2×C11×C4⋊C8C2211yescharacteristic
52C11×#416—21no—
53C4×C11×M16—21no—
54C4×C11×M16C2211yescharacteristic
55C11×#335C2211yescharacteristic
56C11×#335C2211yescharacteristic
57C11×#334C2211yescharacteristic
58C11×#334C2211yescharacteristic
59C11×#333C2211yescharacteristic
60C11×#333C2211yescharacteristic
61C11×#332C2211yescharacteristic
62C11×#332C2211yescharacteristic
63C11×#331C2211yescharacteristic
64C11×#331C2211yescharacteristic
65C11×#331C2211yescharacteristic
66C11×#331C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×#41—21no—
69C2×C11×#41D411yescharacteristic
70C11×#135—44no—
71C2×C11×Q16—21no—
72C2×C11×SD16—21no—
73C2×C11×SD16—21no—
74C2×C11×SD16—21no—
75C2×C11×D8—21no—
76C2×C11×D8—21no—
77C2×C11×D8—21no—
78C2×C11×D8—21no—
79C2×C11×M16—21no—
80C2×C11×M16—21no—
81C2×C11×M16D411yescharacteristic
82C2×C11×M16D411yescharacteristic
83C22×C8×C11—21no—
84C11×C4⋊Q8C2311yescharacteristic
85C11×C4⋊Q8C2311yescharacteristic
86C11×#127C2311yescharacteristic
87C11×#127C2311yescharacteristic
88C11×#124—21no—
89C11×#124—21no—
90C11×#121—21no—
91C11×#121—21no—
92C11×#121—21no—
93C11×#121—21no—
94C4×Q8×C11D411yescharacteristic
95C4×Q8×C11C2311yescharacteristic
96C4×D4×C11—21no—
97C4×D4×C11—21no—
98C4×D4×C11—21no—
99C4×D4×C11—21no—
100C4×D4×C11—21no—
101C4×D4×C11—21no—
102C4×D4×C11D411yescharacteristic
103C4×D4×C11C2311yescharacteristic
104C11×#117—21no—
105C11×#117D411yescharacteristic
106C2×C42×C11—21no—
107C2×C42×C11C2311yescharacteristic
108C11×#107—21no—
109C11×#106—21no—
110C11×#106—21no—
111C11×#106—21no—
112C11×C4⋊C8—21no—
113C11×C4⋊C8—21no—
114C11×C4⋊C8—21no—
115C11×C4⋊C8C2311yescharacteristic
116C11×C4⋊C8C2311yescharacteristic
117C11×C4⋊C8C2311yescharacteristic
118C11×C4⋊C8C2311yescharacteristic
119C11×C4⋊C8C2311yescharacteristic
120C11×C4⋊C8C2311yescharacteristic
121C11×#103—21no—
122C11×#103—21no—
123C11×#103—21no—
124C11×#102—21no—
125C11×#102—21no—
126C11×#102—21no—
127C11×#102—21no—
128C11×#102—21no—
129C11×#102—21no—
130C11×#102—21no—
131C11×#102—21no—
132C11×#102—21no—
133C11×C22⋊C8—21no—
134C11×C22⋊C8—21no—
135C11×C22⋊C8—21no—
136C11×C22⋊C8—21no—
137C11×#97—21no—
138C11×#97D411yescharacteristic
139C11×#97D411yescharacteristic
140C4×C8×C11—21no—
141C4×C8×C11—21no—
142C4×C8×C11—21no—
143C4×C8×C11C2311yescharacteristic
144C4×C8×C11C2311yescharacteristic
145#19184C1111yesmaximal, characteristic, direct product factor, Sylow
146C11×#41—22no—
147C11×#41—41no—
148C11×#41—42no—
149C11×#41—42no—
150C11×#41—82no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11C2×D411yescharacteristic
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—41no—
162C2×D4×C11—41no—
163C2×D4×C11C2×D411yescharacteristic
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—41no—
168C22×C4×C11—41no—
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11#4111yescharacteristic
172C11×Q16—42no—
173C11×SD16—42no—
174C11×SD16—42no—
175C11×SD16—42no—
176C11×D8—42no—
177C11×D8—42no—
178C11×D8—42no—
179C11×D8—42no—
180C11×M16—22no—
181C11×M16—41no—
182C11×M16—42no—
183C11×M16—42no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—42no—
191C2×C8×C11C2×D411yescharacteristic
192C2×C8×C11C2×D411yescharacteristic
193C2×C8×C11C2×D411yescharacteristic
194C2×C8×C11C2×D411yescharacteristic
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4C2×D411yescharacteristic
202C11×C4⋊C4C2×D411yescharacteristic
203C11×C22⋊C4—21no—
204C11×C22⋊C4—21no—
205C11×C22⋊C4—21no—
206C11×C22⋊C4—41no—
207C11×C22⋊C4—41no—
208C11×C22⋊C4—41no—
209C11×C22⋊C4—41no—
210C42×C11—21no—
211C42×C11—21no—
212C42×C11—21no—
213C42×C11C2×D411yescharacteristic
214C42×C11C2×D411yescharacteristic
215C42×C11#4111yescharacteristic
216C42×C11C2411yescharacteristic
217#3184C2×C1111yescharacteristic, complemented
218#3106C2×C1111yescharacteristic, complemented
219#3035C2×C1111yescharacteristic, complemented
220#2971C2×C1111yescharacteristic, complemented
221#1701C2×C1111yescharacteristic, complemented
222#1697C2×C1111yescharacteristic, complemented
223#1691C2×C1111yescharacteristic, complemented
224#1687C2×C1111yescharacteristic, complemented
225#1682C2×C1111yescharacteristic, complemented
226#1678C2×C1111yescharacteristic, complemented
227#1672C2×C1111yescharacteristic, complemented
228#1668C2×C1111yescharacteristic, complemented
229#1565C2×C1111yescharacteristic, complemented
230#1553C2×C1111yescharacteristic, complemented
231#1551C2×C1111yescharacteristic, complemented
232C23×C11—21no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11#12111yescharacteristic
236Q8×C11—21no—
237Q8×C11—41no—
238Q8×C11—41no—
239Q8×C11—81no—
240Q8×C11AGL(1,ℤ/8)12yes—
241D4×C11—21no—
242D4×C11—21no—
243D4×C11—42no—
244D4×C11—41no—
245D4×C11—41no—
246D4×C11—41no—
247D4×C11—41no—
248D4×C11—41no—
249D4×C11—41no—
250D4×C11—41no—
251D4×C11—41no—
252D4×C11—81no—
253D4×C11—81no—
254D4×C11—82no—
255D4×C11—82no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—41no—
264C2×C4×C11—42no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—81no—
270C2×C4×C11—82no—
271C2×C4×C11—82no—
272C2×C4×C11#12111yescharacteristic
273C2×C4×C11#12111yescharacteristic
274C2×C4×C11#12111yescharacteristic
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C8×C11—21no—
279C8×C11—21no—
280C8×C11—21no—
281C8×C11—41no—
282C8×C11—41no—
283C8×C11—41no—
284C8×C11—41no—
285C8×C11—41no—
286C8×C11—41no—
287C8×C11#13512yescomplemented
288C2×#135—21no—
289#532C22×C1111yescharacteristic
290#532C22×C1111yescharacteristic
291C4×#41C22×C1111yescharacteristic
292#498C22×C1111yescharacteristic
293#493C22×C1111yescharacteristic
294#486C22×C1111yescharacteristic
295#486C22×C1111yescharacteristic
296#482—21no—
297#477C22×C1111yescharacteristic
298#476C22×C1111yescharacteristic
299#469—21no—
300#469—21no—
301#464—21no—
302#463—21no—
303#462C22×C1111yescharacteristic
304#461C22×C1111yescharacteristic
305#460C22×C1111yescharacteristic
306#460C22×C1111yescharacteristic
307#459C22×C1111yescharacteristic
308#459C22×C1111yescharacteristic
309#449—21no—
310C8×Q8C22×C1111yescharacteristic
311C8×Q8C22×C1111yescharacteristic
312#442—21no—
313#442—21no—
314C4×SD16—21no—
315C4×D8—21no—
316#436—21no—
317#436—21no—
318#436C22×C1111yescharacteristic
319#436C22×C1111yescharacteristic
320#432—21no—
321#432C22×C1111yescharacteristic
322#431C22×C1111yescharacteristic
323C2×C4⋊C8C22×C1111yescharacteristic
324#416—21no—
325C4×M16—21no—
326C4×M16C22×C1111yescharacteristic
327#335C22×C1111yescharacteristic
328#335C22×C1111yescharacteristic
329#334C22×C1111yescharacteristic
330#334C22×C1111yescharacteristic
331#333C22×C1111yescharacteristic
332#333C22×C1111yescharacteristic
333#332C22×C1111yescharacteristic
334#332C22×C1111yescharacteristic
335#331C22×C1111yescharacteristic
336#331C22×C1111yescharacteristic
337#331C22×C1111yescharacteristic
338#331C22×C1111yescharacteristic
339C22×C11—21no—
340C22×C11—21no—
341C22×C11—21no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11—81no—
346C22×C11—81no—
347C22×C11—81no—
348C22×C11—81no—
349C22×C11—81no—
350C22×C11—81no—
351C22×C11C2×#12111yescharacteristic
352C4×C11—21no—
353C4×C11—21no—
354C4×C11—22no—
355C4×C11—21no—
356C4×C11—21no—
357C4×C11—41no—
358C4×C11—41no—
359C4×C11—81no—
360C4×C11—81no—
361C4×C11C2×#13511yescharacteristic
362C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
363C4×C11#57511yescharacteristic
364C4×C11#57511yescharacteristic
365C2×#41—21no—
366C2×#41—21no—
367C2×#41D4×C1111yescharacteristic
368#135—44no—
369C2×Q16—21no—
370C2×SD16—21no—
371C2×SD16—21no—
372C2×SD16—21no—
373C2×D8—21no—
374C2×D8—21no—
375C2×D8—21no—
376C2×D8—21no—
377C2×M16—21no—
378C2×M16—21no—
379C2×M16D4×C1111yescharacteristic
380C2×M16D4×C1111yescharacteristic
381C22×C8—21no—
382C4⋊Q8C23×C1111yescharacteristic
383C4⋊Q8C23×C1111yescharacteristic
384#127C23×C1111yescharacteristic
385#127C23×C1111yescharacteristic
386#124—21no—
387#124—21no—
388#121—21no—
389#121—21no—
390#121—21no—
391#121—21no—
392C4×Q8D4×C1111yescharacteristic
393C4×Q8C23×C1111yescharacteristic
394C4×D4—21no—
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—21no—
399C4×D4—21no—
400C4×D4D4×C1111yescharacteristic
401C4×D4C23×C1111yescharacteristic
402#117—21no—
403#117D4×C1111yescharacteristic
404C2×C42—21no—
405C2×C42C23×C1111yescharacteristic
406#107—21no—
407#106—21no—
408#106—21no—
409#106—21no—
410C4⋊C8—21no—
411C4⋊C8—21no—
412C4⋊C8—21no—
413C4⋊C8C23×C1111yescharacteristic
414C4⋊C8C23×C1111yescharacteristic
415C4⋊C8C23×C1111yescharacteristic
416C4⋊C8C23×C1111yescharacteristic
417C4⋊C8C23×C1111yescharacteristic
418C4⋊C8C23×C1111yescharacteristic
419#103—21no—
420#103—21no—
421#103—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431C22⋊C8—21no—
432C22⋊C8—21no—
433C22⋊C8—21no—
434C22⋊C8—21no—
435#97—21no—
436#97D4×C1111yescharacteristic
437#97D4×C1111yescharacteristic
438C4×C8—21no—
439C4×C8—21no—
440C4×C8—21no—
441C4×C8C23×C1111yescharacteristic
442C4×C8C23×C1111yescharacteristic
443C2×C11—41no—
444C2×C11—81no—
445C2×C11—161no—
446C2×C11—161no—
447C2×C11#303511yescharacteristic
448C2×C11#305511yescharacteristic
449C2×C11#306811yescharacteristic
450#41—22no—
451#41—41no—
452#41—42no—
453#41—42no—
454#41—82no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8C2×D4×C1111yescharacteristic
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4C2×D4×C1111yescharacteristic
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4C2×D4×C1111yescharacteristic
474C22×C4C2×D4×C1111yescharacteristic
475C22×C4C11×#4111yescharacteristic
476Q16—42no—
477SD16—42no—
478SD16—42no—
479SD16—42no—
480D8—42no—
481D8—42no—
482D8—42no—
483D8—42no—
484M16—22no—
485M16—41no—
486M16—42no—
487M16—42no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—42no—
495C2×C8C2×D4×C1111yescharacteristic
496C2×C8C2×D4×C1111yescharacteristic
497C2×C8C2×D4×C1111yescharacteristic
498C2×C8C2×D4×C1111yescharacteristic
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4C2×D4×C1111yescharacteristic
506C4⋊C4C2×D4×C1111yescharacteristic
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C42—21no—
515C42—21no—
516C42—21no—
517C42C2×D4×C1111yescharacteristic
518C42C2×D4×C1111yescharacteristic
519C42C11×#4111yescharacteristic
520C42C24×C1111yescharacteristic
521C11#1918411yescharacteristic, direct product factor, Sylow
522C23—21no—
523C23—41no—
524C23—41no—
525C23C11×#12111yescharacteristic
526Q8—21no—
527Q8—41no—
528Q8—41no—
529Q8—81no—
530Q8C11×AGL(1,ℤ/8)12yes—
531D4—21no—
532D4—21no—
533D4—42no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—81no—
543D4—81no—
544D4—82no—
545D4—82no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—81no—
560C2×C4—82no—
561C2×C4—82no—
562C2×C4C11×#12111yescharacteristic
563C2×C4C11×#12111yescharacteristic
564C2×C4C11×#12111yescharacteristic
565C2×C4C22×D4×C1111yescharacteristic
566C2×C4C22×D4×C1111yescharacteristic
567C2×C4C2×C11×#4111yescharacteristic
568C8—21no—
569C8—21no—
570C8—21no—
571C8—41no—
572C8—41no—
573C8—41no—
574C8—41no—
575C8—41no—
576C8—41no—
577C8C11×#13512yescomplemented
578C22—21no—
579C22—21no—
580C22—21no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22C2×C11×#12111yescharacteristic
591C4—21no—
592C4—21no—
593C4—22no—
594C4—21no—
595C4—21no—
596C4—41no—
597C4—41no—
598C4—81no—
599C4—81no—
600C4C2×C11×#13511yescharacteristic
601C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
602C4C11×#57511yescharacteristic
603C4C11×#57511yescharacteristic
604C2—41no—
605C2—81no—
606C2—161no—
607C2—161no—
608C2C11×#303511yescharacteristic
609C2C11×#305511yescharacteristic
610C2C11×#306811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
commutator, Frattini, cosocleC42C24×C11
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3184C2semidirect
2. C11×#3106C2semidirect
3. C11×#3035C2semidirect
4. C11×#2971C2semidirect
5. C11×#1701C2semidirect
6. C11×#1697C2semidirect
7. C11×#1691C2semidirect
8. C11×#1687C2semidirect
9. C11×#1682C2semidirect
10. C11×#1678C2semidirect
11. C11×#1672C2semidirect
12. C11×#1668C2semidirect
13. C11×#1565C2semidirect
14. C11×#1553C2semidirect
15. C11×#1551C2semidirect
145. #19184C11direct (N × H)
217. #3184C2×C11semidirect
218. #3106C2×C11semidirect
219. #3035C2×C11semidirect
220. #2971C2×C11semidirect
221. #1701C2×C11semidirect
222. #1697C2×C11semidirect
223. #1691C2×C11semidirect
224. #1687C2×C11semidirect
225. #1682C2×C11semidirect
226. #1678C2×C11semidirect
227. #1672C2×C11semidirect
228. #1668C2×C11semidirect
229. #1565C2×C11semidirect
230. #1553C2×C11semidirect
231. #1551C2×C11semidirect
287. C8×C11#135semidirect
521. C11#19184direct (N × H)
577. C8C11×#135semidirect

Maximal subgroups

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

subgroupindex
C11×#31842
C11×#31062
C11×#30352
C11×#29712
C11×#17012
C11×#16972
C11×#16912
C11×#16872
C11×#16822
C11×#16782
C11×#16722
C11×#16682
C11×#15652
C11×#15532
C11×#15512
#1918411