Finite Group Databasebeta

← C11×#19053 #14596246

Subgroups — C11×#19053 #14596246

Order 2816.

994 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3548C211yesmaximal, characteristic, complemented
2C11×#3235C211yesmaximal, characteristic, complemented
3C11×#3214C211yesmaximal, characteristic, complemented
4C11×#3150C211yesmaximal, characteristic, complemented
5C11×#1661C214yesmaximal, complemented
6C11×#1656C214yesmaximal, complemented
7C11×#1536C211yesmaximal, characteristic, complemented
8C11×#1531C211yesmaximal, characteristic, complemented
9C11×#1530C211yesmaximal, characteristic, complemented
10C2×C11×#135—22no—
11C11×#562C2214yes—
12C11×#554—21no—
13C11×#554—21no—
14C11×#550—21no—
15C11×#550—21no—
16C11×#547—21no—
17C11×#547—21no—
18C11×#540—22no—
19C11×#537—22no—
20C11×#537—22no—
21C11×#533C2211yescharacteristic
22C11×#532C2211yescharacteristic
23C11×#532C2211yescharacteristic
24C11×#532C2211yescharacteristic
25C11×#501C2212yes—
26C11×#497—21no—
27C11×#497C2212yes—
28C11×#496—21no—
29C11×#496C2212yes—
30C11×#496C2212yes—
31C11×#490C2212yes—
32C11×#489C2212yes—
33C11×#482—22no—
34C11×#476—21no—
35C11×#474—21no—
36C11×#461—21no—
37C11×#459—21no—
38C11×#449—22no—
39C11×#432C2211yescharacteristic
40C11×#432C2211yescharacteristic
41C2×C11×#97C2211yescharacteristic
42C11×#330C2214yes—
43C11×#329C2214yes—
44C11×#329C2214yes—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41—21no—
48C2×C11×#41D412yes—
49C2×C11×#41D412yes—
50C11×#135—48no—
51C2×C11×Q16—22no—
52C2×C11×SD16—22no—
53C2×C11×SD16—22no—
54C2×C11×SD16—22no—
55C2×C11×D8—22no—
56C2×C11×D8—22no—
57C22×C8×C11—21no—
58C11×C4⋊Q8D411yescharacteristic
59C11×C4⋊Q8D411yescharacteristic
60C11×C4⋊Q8D411yescharacteristic
61C11×C4⋊Q8D411yescharacteristic
62C11×C4⋊Q8C2311yescharacteristic
63C11×#127—22no—
64C11×#127D411yescharacteristic
65C11×#127D411yescharacteristic
66C11×#127C2311yescharacteristic
67C11×#125—22no—
68C11×#125C2312yes—
69C11×#124—21no—
70C11×#124C2312yes—
71C11×#124C2312yes—
72C11×#123—24no—
73C11×#123—24no—
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8—24no—
77C11×C22⋊Q8—24no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—21no—
80C11×#121—24no—
81C11×#121—24no—
82C11×#121—22no—
83C11×#121—22no—
84C11×#121—24no—
85C11×#121—24no—
86C11×#121—21no—
87C11×#121—21no—
88C11×#121—21no—
89C11×#121—21no—
90C11×#121—21no—
91C11×#121—21no—
92C4×Q8×C11—21no—
93C4×Q8×C11—21no—
94C4×D4×C11—22no—
95C4×D4×C11—22no—
96C4×D4×C11—21no—
97C4×D4×C11—21no—
98C4×D4×C11—21no—
99C4×D4×C11—21no—
100C4×D4×C11—21no—
101C4×D4×C11—21no—
102C11×#117D412yes—
103C2×C11×C4⋊C4—22no—
104C2×C11×C4⋊C4—22no—
105C2×C42×C11C2311yescharacteristic
106C11×#107—22no—
107C11×#106—22no—
108C11×C4⋊C8—21no—
109C11×C4⋊C8—21no—
110C11×#103—22no—
111C11×#102—22no—
112C11×#102—22no—
113C11×#102—22no—
114C11×C22⋊C8—21no—
115C11×C22⋊C8—21no—
116C11×#97—21no—
117C11×#97C2312yes—
118C11×#97C2312yes—
119C11×#97C2312yes—
120#19053C1111yesmaximal, characteristic, direct product factor, Sylow
121C11×#41—44no—
122C11×#41—44no—
123C11×#41—82no—
124C11×#41—84no—
125C11×#41—84no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11C2×D412yes—
130C2×Q8×C11C2×D412yes—
131C2×D4×C11—24no—
132C2×D4×C11—24no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—41no—
143C2×D4×C11C2×D412yes—
144C2×D4×C11C2×D412yes—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—41no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C11×Q16—44no—
154C11×SD16—44no—
155C11×SD16—44no—
156C11×SD16—82no—
157C11×D8—44no—
158C11×D8—82no—
159C2×C8×C11—24no—
160C2×C8×C11—22no—
161C2×C8×C11—22no—
162C2×C8×C11—22no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4C2×D412yes—
176C11×C4⋊C4C2×D412yes—
177C11×C22⋊C4—24no—
178C11×C22⋊C4—24no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—41no—
185C11×C22⋊C4—41no—
186C42×C11—22no—
187C42×C11C2×D411yescharacteristic
188C42×C11C2×D411yescharacteristic
189C42×C11C2×D411yescharacteristic
190C42×C11C2411yescharacteristic
191#3548C2×C1111yescharacteristic, complemented
192#3235C2×C1111yescharacteristic, complemented
193#3214C2×C1111yescharacteristic, complemented
194#3150C2×C1111yescharacteristic, complemented
195#1661C2×C1114yescomplemented
196#1656C2×C1114yescomplemented
197#1536C2×C1111yescharacteristic, complemented
198#1531C2×C1111yescharacteristic, complemented
199#1530C2×C1111yescharacteristic, complemented
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—41no—
203C23×C11#12011yescharacteristic
204Q8×C11—42no—
205Q8×C11—42no—
206Q8×C11—42no—
207Q8×C11—42no—
208Q8×C11—42no—
209D4×C11—42no—
210D4×C11—42no—
211D4×C11—42no—
212D4×C11—42no—
213D4×C11—42no—
214D4×C11—42no—
215D4×C11—41no—
216D4×C11—41no—
217D4×C11—42no—
218D4×C11—42no—
219D4×C11—82no—
220D4×C11—82no—
221D4×C11—84no—
222D4×C11—84no—
223D4×C11—82no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—44no—
232C2×C4×C11—44no—
233C2×C4×C11—41no—
234C2×C4×C11—84no—
235C2×C4×C11—84no—
236C2×C4×C11—82no—
237C2×C4×C11#12011yescharacteristic
238C2×C4×C11#12011yescharacteristic
239C2×C4×C11#12011yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C8×C11—24no—
244C8×C11—42no—
245C8×C11—42no—
246C2×#135—22no—
247#562C22×C1114yes—
248#554—21no—
249#554—21no—
250#550—21no—
251#550—21no—
252#547—21no—
253#547—21no—
254#540—22no—
255#537—22no—
256#537—22no—
257#533C22×C1111yescharacteristic
258#532C22×C1111yescharacteristic
259#532C22×C1111yescharacteristic
260#532C22×C1111yescharacteristic
261#501C22×C1112yes—
262#497—21no—
263#497C22×C1112yes—
264#496—21no—
265#496C22×C1112yes—
266#496C22×C1112yes—
267#490C22×C1112yes—
268#489C22×C1112yes—
269#482—22no—
270#476—21no—
271#474—21no—
272#461—21no—
273#459—21no—
274#449—22no—
275#432C22×C1111yescharacteristic
276#432C22×C1111yescharacteristic
277C2×#97C22×C1111yescharacteristic
278#330C22×C1114yes—
279#329C22×C1114yes—
280#329C22×C1114yes—
281C22×C11—21no—
282C22×C11—21no—
283C22×C11—21no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—81no—
291C22×C11—81no—
292C22×C11—81no—
293C22×C11C2×#12011yescharacteristic
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—21no—
297C4×C11—21no—
298C4×C11—21no—
299C4×C11—42no—
300C4×C11—42no—
301C4×C11—42no—
302C4×C11—42no—
303C4×C11—81no—
304C4×C11#45312yes—
305C2×#41—22no—
306C2×#41—22no—
307C2×#41—21no—
308C2×#41D4×C1112yes—
309C2×#41D4×C1112yes—
310#135—48no—
311C2×Q16—22no—
312C2×SD16—22no—
313C2×SD16—22no—
314C2×SD16—22no—
315C2×D8—22no—
316C2×D8—22no—
317C22×C8—21no—
318C4⋊Q8D4×C1111yescharacteristic
319C4⋊Q8D4×C1111yescharacteristic
320C4⋊Q8D4×C1111yescharacteristic
321C4⋊Q8D4×C1111yescharacteristic
322C4⋊Q8C23×C1111yescharacteristic
323#127—22no—
324#127D4×C1111yescharacteristic
325#127D4×C1111yescharacteristic
326#127C23×C1111yescharacteristic
327#125—22no—
328#125C23×C1112yes—
329#124—21no—
330#124C23×C1112yes—
331#124C23×C1112yes—
332#123—24no—
333#123—24no—
334C22⋊Q8—22no—
335C22⋊Q8—22no—
336C22⋊Q8—24no—
337C22⋊Q8—24no—
338C22⋊Q8—21no—
339C22⋊Q8—21no—
340#121—24no—
341#121—24no—
342#121—22no—
343#121—22no—
344#121—24no—
345#121—24no—
346#121—21no—
347#121—21no—
348#121—21no—
349#121—21no—
350#121—21no—
351#121—21no—
352C4×Q8—21no—
353C4×Q8—21no—
354C4×D4—22no—
355C4×D4—22no—
356C4×D4—21no—
357C4×D4—21no—
358C4×D4—21no—
359C4×D4—21no—
360C4×D4—21no—
361C4×D4—21no—
362#117D4×C1112yes—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C42C23×C1111yescharacteristic
366#107—22no—
367#106—22no—
368C4⋊C8—21no—
369C4⋊C8—21no—
370#103—22no—
371#102—22no—
372#102—22no—
373#102—22no—
374C22⋊C8—21no—
375C22⋊C8—21no—
376#97—21no—
377#97C23×C1112yes—
378#97C23×C1112yes—
379#97C23×C1112yes—
380C2×C11—41no—
381C2×C11—82no—
382C2×C11—82no—
383C2×C11—161no—
384C2×C11C2×#45311yescharacteristic
385C2×C11#301911yescharacteristic
386C2×C11#302011yescharacteristic
387#41—44no—
388#41—44no—
389#41—82no—
390#41—84no—
391#41—84no—
392C2×Q8—21no—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×Q8C2×D4×C1112yes—
396C2×Q8C2×D4×C1112yes—
397C2×D4—24no—
398C2×D4—24no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—21no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—41no—
409C2×D4C2×D4×C1112yes—
410C2×D4C2×D4×C1112yes—
411C22×C4—24no—
412C22×C4—24no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—41no—
416C22×C4C2×D4×C1111yescharacteristic
417C22×C4C2×D4×C1111yescharacteristic
418C22×C4C2×D4×C1111yescharacteristic
419Q16—44no—
420SD16—44no—
421SD16—44no—
422SD16—82no—
423D8—44no—
424D8—82no—
425C2×C8—24no—
426C2×C8—22no—
427C2×C8—22no—
428C2×C8—22no—
429C4⋊C4—24no—
430C4⋊C4—24no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4C2×D4×C1112yes—
442C4⋊C4C2×D4×C1112yes—
443C22⋊C4—24no—
444C22⋊C4—24no—
445C22⋊C4—22no—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—41no—
451C22⋊C4—41no—
452C42—22no—
453C42C2×D4×C1111yescharacteristic
454C42C2×D4×C1111yescharacteristic
455C42C2×D4×C1111yescharacteristic
456C42C24×C1111yescharacteristic
457C11#1905311yescharacteristic, direct product factor, Sylow
458C23—22no—
459C23—22no—
460C23—41no—
461C23C11×#12011yescharacteristic
462Q8—42no—
463Q8—42no—
464Q8—42no—
465Q8—42no—
466Q8—42no—
467D4—42no—
468D4—42no—
469D4—42no—
470D4—42no—
471D4—42no—
472D4—42no—
473D4—41no—
474D4—41no—
475D4—42no—
476D4—42no—
477D4—82no—
478D4—82no—
479D4—84no—
480D4—84no—
481D4—82no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—44no—
490C2×C4—44no—
491C2×C4—41no—
492C2×C4—84no—
493C2×C4—84no—
494C2×C4—82no—
495C2×C4C11×#12011yescharacteristic
496C2×C4C11×#12011yescharacteristic
497C2×C4C11×#12011yescharacteristic
498C2×C4C22×D4×C1111yescharacteristic
499C2×C4C22×D4×C1111yescharacteristic
500C2×C4C22×D4×C1111yescharacteristic
501C8—24no—
502C8—42no—
503C8—42no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—42no—
508C22—42no—
509C22—42no—
510C22—42no—
511C22—42no—
512C22—42no—
513C22—81no—
514C22—81no—
515C22—81no—
516C22C2×C11×#12011yescharacteristic
517C4—21no—
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—42no—
523C4—42no—
524C4—42no—
525C4—42no—
526C4—81no—
527C4C11×#45312yes—
528C2—41no—
529C2—82no—
530C2—82no—
531C2—161no—
532C2C2×C11×#45311yescharacteristic
533C2C11×#301911yescharacteristic
534C2C11×#302011yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
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×#3548C2semidirect
2. C11×#3235C2semidirect
3. C11×#3214C2semidirect
4. C11×#3150C2semidirect
5. C11×#1661C2semidirect
6. C11×#1656C2semidirect
7. C11×#1536C2semidirect
8. C11×#1531C2semidirect
9. C11×#1530C2semidirect
120. #19053C11direct (N × H)
191. #3548C2×C11semidirect
192. #3235C2×C11semidirect
193. #3214C2×C11semidirect
194. #3150C2×C11semidirect
195. #1661C2×C11semidirect
196. #1656C2×C11semidirect
197. #1536C2×C11semidirect
198. #1531C2×C11semidirect
199. #1530C2×C11semidirect
457. C11#19053direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35482
C11×#32352
C11×#32142
C11×#31502
C11×#16612
C11×#16562
C11×#15362
C11×#15312
C11×#15302
#1905311