Finite Group Databasebeta

← C11×#34281 #14611474

Subgroups — C11×#34281 #14611474

Order 2816.

2070 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#541C211yesmaximal, characteristic
2C11×#2373C214yesmaximal
3C11×#2373C214yesmaximal
4C11×#2371C214yesmaximal, complemented
5C11×#2370C214yesmaximal, complemented
6C11×#2330C211yesmaximal, characteristic, complemented
7C11×#2327C211yesmaximal, characteristic, complemented
8C11×#2323C212yesmaximal
9C11×#2314C211yesmaximal, characteristic
10C4×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
11C4×C11×#125C211yesmaximal, characteristic, complemented
12C4×C11×C22⋊Q8C212yesmaximal
13C11×#2295C212yesmaximal, complemented
14C11×#2276C212yesmaximal, complemented
15C4×C11×#117C211yesmaximal, characteristic
16C11×#541C4116yescomplemented
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×#126C2214yes—
19C2×C11×#125C2211yescharacteristic
20C2×C11×#125C2214yes—
21C2×C11×C22⋊Q8C2212yes—
22C2×C4×Q8×C11C2212yes—
23C2×C4×Q8×C11C2212yes—
24C2×C4×Q8×C11C2212yes—
25C2×C11×#117C2211yescharacteristic
26C2×C11×#117C2211yescharacteristic
27C22×C42×C11C2211yescharacteristic
28C11×#391C2212yes—
29C11×#391C2212yes—
30C11×#389C2212yes—
31C11×#389C2212yes—
32C11×#389C2214yes—
33C11×#389C2214yes—
34C11×#389C2214yes—
35C11×#388C2214yes—
36C11×#388C2214yes—
37C11×#388C2214yes—
38C11×#387C2214yes—
39C11×#387C2214yes—
40C11×#387C2214yes—
41C11×#387C2214yes—
42C11×#387C2214yes—
43C11×#387C2214yes—
44C11×#387C2214yes—
45C11×#387C2214yes—
46C11×#387C2214yes—
47C11×#385C2214yes—
48C11×#384C2211yescharacteristic
49C11×#382C2211yescharacteristic
50C11×#380C2212yes—
51C4×C11×C4⋊C4C2212yes—
52C4×C11×C4⋊C4C2212yes—
53C4×C11×C4⋊C4C2212yes—
54C4×C11×C4⋊C4C2212yes—
55C4×C11×C4⋊C4C2212yes—
56C4×C11×C4⋊C4C2214yes—
57C4×C11×C4⋊C4C2214yes—
58C4×C11×C4⋊C4C2214yes—
59C4×C11×C4⋊C4C2214yes—
60C4×C11×C4⋊C4C2214yes—
61C4×C11×C4⋊C4C2214yes—
62C4×C11×C4⋊C4C2214yes—
63C4×C11×C22⋊C4C2212yes—
64C4×C11×C22⋊C4C2212yes—
65C4×C11×C22⋊C4C2214yes—
66C11×#376C2211yescharacteristic
67C11×#376C2211yescharacteristic
68C11×#376C2214yes—
69C11×#376C2214yes—
70C43×C11C2211yescharacteristic
71C43×C11C2211yescharacteristic
72C22×Q8×C11C2312yes—
73C23×C4×C11C2312yes—
74C23×C4×C11C2311yescharacteristic
75C11×C4⋊Q8C2×C418yescomplemented
76C11×#126C2×C4132yes—
77C11×#125C2×C418yescomplemented
78C11×#125C2×C4132yescomplemented
79C11×C22⋊Q8C2×C4116yes—
80C4×Q8×C11—28no—
81C4×Q8×C11—28no—
82C4×Q8×C11C2×C4116yescomplemented
83C11×#117—24no—
84C11×#117C2×C418yes—
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2314yes—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C4⋊C4C2312yes—
90C2×C11×C4⋊C4C2314yes—
91C2×C11×C4⋊C4C2314yes—
92C2×C11×C4⋊C4C2314yes—
93C2×C11×C4⋊C4C2314yes—
94C2×C11×C4⋊C4C2312yes—
95C2×C11×C4⋊C4C2312yes—
96C2×C11×C4⋊C4C2314yes—
97C2×C11×C4⋊C4C2314yes—
98C2×C11×C4⋊C4C2314yes—
99C2×C11×C4⋊C4C2314yes—
100C2×C11×C22⋊C4C2311yescharacteristic
101C2×C11×C22⋊C4C2311yescharacteristic
102C2×C11×C22⋊C4C2314yes—
103C2×C11×C22⋊C4C2312yes—
104C2×C11×C22⋊C4C2314yes—
105C2×C42×C11—24no—
106C2×C42×C11C2311yescharacteristic
107C2×C42×C11C2312yes—
108C2×C42×C11C2312yes—
109C2×C42×C11C2311yescharacteristic
110C2×C42×C11C2312yes—
111C2×C42×C11C2314yes—
112C2×C42×C11C2314yes—
113C2×C42×C11C2312yes—
114C2×C42×C11C2312yes—
115C2×C42×C11C2314yes—
116C2×C42×C11C2314yes—
117C2×C42×C11C2314yes—
118C2×C42×C11C2311yescharacteristic
119C2×C42×C11C2311yescharacteristic
120C2×C42×C11C2314yes—
121C2×C42×C11C2311yescharacteristic
122C2×C42×C11C2311yescharacteristic
123C11×#95C2312yes—
124C11×#95C2312yes—
125C11×#95C2312yes—
126C11×#95C2314yes—
127C11×#95C2312yes—
128C11×#95C2314yes—
129C11×#95C2314yes—
130C11×#95C2314yes—
131C11×#95C2314yes—
132C11×#95C2314yes—
133C11×#95C2314yes—
134C11×#95C2314yes—
135C11×#95C2314yes—
136C11×#95C2314yes—
137C11×#95C2314yes—
138#34281C1111yesmaximal, characteristic, direct product factor, Sylow
139C24×C11C2411yescharacteristic
140C2×Q8×C11—24no—
141C2×Q8×C11—24no—
142C2×Q8×C11C22×C418yes—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—42no—
148C22×C4×C11C22×C414yes—
149C22×C4×C11C2411yescharacteristic
150C22×C4×C11C2414yes—
151C22×C4×C11C2411yescharacteristic
152C22×C4×C11C2414yes—
153C22×C4×C11C2412yes—
154C22×C4×C11C2412yes—
155C22×C4×C11C2414yes—
156C22×C4×C11C2414yes—
157C22×C4×C11C2411yescharacteristic
158C22×C4×C11C2411yescharacteristic
159C22×C4×C11C2412yes—
160C22×C4×C11C2411yescharacteristic
161C22×C4×C11C2412yes—
162C22×C4×C11C2411yescharacteristic
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—28no—
166C11×C4⋊C4—28no—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—24no—
169C11×C4⋊C4—28no—
170C11×C4⋊C4—44no—
171C11×C4⋊C4—44no—
172C11×C4⋊C4C22×C418yes—
173C11×C4⋊C4C22×C418yes—
174C11×C4⋊C4C22×C4116yes—
175C11×C4⋊C4C22×C4116yes—
176C11×C4⋊C4C22×C4116yes—
177C11×C4⋊C4C22×C4116yes—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—44no—
181C11×C22⋊C4C22×C418yes—
182C11×C22⋊C4C22×C4116yes—
183C42×C11—24no—
184C42×C11—22no—
185C42×C11—22no—
186C42×C11—28no—
187C42×C11—28no—
188C42×C11—24no—
189C42×C11—24no—
190C42×C11—44no—
191C42×C11—42no—
192C42×C11—42no—
193C42×C11—44no—
194C42×C11—44no—
195C42×C11C22×C414yes—
196C42×C11C22×C414yes—
197C42×C11C22×C4116yes—
198C42×C11#4114yes—
199C42×C11#4114yes—
200C2×#541C2×C1111yescharacteristic
201#2373C2×C1114yes—
202#2373C2×C1114yes—
203#2371C2×C1114yescomplemented
204#2370C2×C1114yescomplemented
205#2330C2×C1111yescharacteristic, complemented
206#2327C2×C1111yescharacteristic, complemented
207#2323C2×C1112yes—
208#2314C2×C1111yescharacteristic
209C4×C4⋊Q8C2×C1111yescharacteristic, complemented
210C4×#125C2×C1111yescharacteristic, complemented
211C4×C22⋊Q8C2×C1112yes—
212#2295C2×C1112yescomplemented
213#2276C2×C1112yescomplemented
214C4×#117C2×C1111yescharacteristic
215C23×C11—21no—
216C23×C11—21no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11C23×C412yes—
220C23×C11C2511yescharacteristic
221Q8×C11—216no—
222C2×C4×C11—21no—
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—21no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—24no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—28no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—22no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—22no—
248C2×C4×C11—24no—
249C2×C4×C11—48no—
250C2×C4×C11C23×C414yes—
251C2×C4×C11C23×C414yes—
252C2×C4×C11C23×C418yes—
253C2×C4×C11C23×C418yes—
254C2×C4×C11C23×C412yes—
255C2×C4×C11C23×C412yes—
256C2×C4×C11C2×#4112yes—
257C2×C4×C11C2×#4114yes—
258C2×C4×C11C2×#4112yes—
259C2×C4×C11C2×#4112yes—
260C2×C4×C11C2×#4112yes—
261C2×C4×C112−1+414yes—
262#541C4×C11116yescomplemented
263C2×C4⋊Q8C22×C1111yescharacteristic
264C2×#126C22×C1114yes—
265C2×#125C22×C1111yescharacteristic
266C2×#125C22×C1114yes—
267C2×C22⋊Q8C22×C1112yes—
268C2×C4×Q8C22×C1112yes—
269C2×C4×Q8C22×C1112yes—
270C2×C4×Q8C22×C1112yes—
271C2×#117C22×C1111yescharacteristic
272C2×#117C22×C1111yescharacteristic
273C22×C42C22×C1111yescharacteristic
274#391C22×C1112yes—
275#391C22×C1112yes—
276#389C22×C1112yes—
277#389C22×C1114yes—
278#389C22×C1112yes—
279#389C22×C1114yes—
280#389C22×C1114yes—
281#388C22×C1114yes—
282#388C22×C1114yes—
283#388C22×C1114yes—
284#387C22×C1114yes—
285#387C22×C1114yes—
286#387C22×C1114yes—
287#387C22×C1114yes—
288#387C22×C1114yes—
289#387C22×C1114yes—
290#387C22×C1114yes—
291#387C22×C1114yes—
292#387C22×C1114yes—
293#385C22×C1114yes—
294#384C22×C1111yescharacteristic
295#382C22×C1111yescharacteristic
296#380C22×C1112yes—
297C4×C4⋊C4C22×C1112yes—
298C4×C4⋊C4C22×C1114yes—
299C4×C4⋊C4C22×C1114yes—
300C4×C4⋊C4C22×C1112yes—
301C4×C4⋊C4C22×C1112yes—
302C4×C4⋊C4C22×C1112yes—
303C4×C4⋊C4C22×C1114yes—
304C4×C4⋊C4C22×C1114yes—
305C4×C4⋊C4C22×C1114yes—
306C4×C4⋊C4C22×C1114yes—
307C4×C4⋊C4C22×C1112yes—
308C4×C4⋊C4C22×C1114yes—
309C4×C22⋊C4C22×C1112yes—
310C4×C22⋊C4C22×C1112yes—
311C4×C22⋊C4C22×C1114yes—
312#376C22×C1111yescharacteristic
313#376C22×C1114yes—
314#376C22×C1114yes—
315#376C22×C1111yescharacteristic
316C43C22×C1111yescharacteristic
317C43C22×C1111yescharacteristic
318C22×C11—22no—
319C22×C11—24no—
320C22×C11—42no—
321C22×C11—41no—
322C22×C11—41no—
323C22×C11C24×C411yescharacteristic
324C22×C11C22×#4111yescharacteristic
325C22×C11C22×#4111yescharacteristic
326C22×C11C2×2−1+412yes—
327C22×C11#58512yes—
328C4×C11—22no—
329C4×C11—28no—
330C4×C11—24no—
331C4×C11—24no—
332C4×C11—28no—
333C4×C11—24no—
334C4×C11—24no—
335C4×C11—22no—
336C4×C11—22no—
337C4×C11—44no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11—44no—
341C4×C11C4×#4114yes—
342C22×Q8C23×C1112yes—
343C23×C4C23×C1112yes—
344C23×C4C23×C1111yescharacteristic
345C4⋊Q8C2×C4×C1118yescomplemented
346#126C2×C4×C11132yes—
347#125C2×C4×C1118yescomplemented
348#125C2×C4×C11132yescomplemented
349C22⋊Q8C2×C4×C11116yes—
350C4×Q8—28no—
351C4×Q8—28no—
352C4×Q8C2×C4×C11116yescomplemented
353#117—24no—
354#117C2×C4×C1118yes—
355C2×C4⋊C4C23×C1111yescharacteristic
356C2×C4⋊C4C23×C1111yescharacteristic
357C2×C4⋊C4C23×C1112yes—
358C2×C4⋊C4C23×C1112yes—
359C2×C4⋊C4C23×C1114yes—
360C2×C4⋊C4C23×C1114yes—
361C2×C4⋊C4C23×C1114yes—
362C2×C4⋊C4C23×C1114yes—
363C2×C4⋊C4C23×C1114yes—
364C2×C4⋊C4C23×C1112yes—
365C2×C4⋊C4C23×C1112yes—
366C2×C4⋊C4C23×C1114yes—
367C2×C4⋊C4C23×C1114yes—
368C2×C4⋊C4C23×C1114yes—
369C2×C4⋊C4C23×C1114yes—
370C2×C22⋊C4C23×C1111yescharacteristic
371C2×C22⋊C4C23×C1111yescharacteristic
372C2×C22⋊C4C23×C1114yes—
373C2×C22⋊C4C23×C1112yes—
374C2×C22⋊C4C23×C1114yes—
375C2×C42—24no—
376C2×C42C23×C1111yescharacteristic
377C2×C42C23×C1114yes—
378C2×C42C23×C1114yes—
379C2×C42C23×C1111yescharacteristic
380C2×C42C23×C1112yes—
381C2×C42C23×C1112yes—
382C2×C42C23×C1112yes—
383C2×C42C23×C1112yes—
384C2×C42C23×C1112yes—
385C2×C42C23×C1114yes—
386C2×C42C23×C1114yes—
387C2×C42C23×C1114yes—
388C2×C42C23×C1111yescharacteristic
389C2×C42C23×C1111yescharacteristic
390C2×C42C23×C1114yes—
391C2×C42C23×C1111yescharacteristic
392C2×C42C23×C1111yescharacteristic
393#95C23×C1112yes—
394#95C23×C1112yes—
395#95C23×C1112yes—
396#95C23×C1114yes—
397#95C23×C1112yes—
398#95C23×C1114yes—
399#95C23×C1114yes—
400#95C23×C1114yes—
401#95C23×C1114yes—
402#95C23×C1114yes—
403#95C23×C1114yes—
404#95C23×C1114yes—
405#95C23×C1114yes—
406#95C23×C1114yes—
407#95C23×C1114yes—
408C2×C11—42no—
409C2×C11C2×C4×#4111yescharacteristic
410C2×C11C4×2−1+412yes—
411C2×C11#349512yes—
412C2×C11#350911yescharacteristic
413C2×C11#351211yescharacteristic
414C24C24×C1111yescharacteristic
415C2×Q8—24no—
416C2×Q8—24no—
417C2×Q8C22×C4×C1118yes—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—42no—
423C22×C4C22×C4×C1114yes—
424C22×C4C24×C1111yescharacteristic
425C22×C4C24×C1114yes—
426C22×C4C24×C1111yescharacteristic
427C22×C4C24×C1114yes—
428C22×C4C24×C1112yes—
429C22×C4C24×C1112yes—
430C22×C4C24×C1114yes—
431C22×C4C24×C1114yes—
432C22×C4C24×C1111yescharacteristic
433C22×C4C24×C1111yescharacteristic
434C22×C4C24×C1112yes—
435C22×C4C24×C1111yescharacteristic
436C22×C4C24×C1112yes—
437C22×C4C24×C1111yescharacteristic
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—28no—
441C4⋊C4—28no—
442C4⋊C4—24no—
443C4⋊C4—24no—
444C4⋊C4—28no—
445C4⋊C4—44no—
446C4⋊C4—44no—
447C4⋊C4C22×C4×C1118yes—
448C4⋊C4C22×C4×C1118yes—
449C4⋊C4C22×C4×C11116yes—
450C4⋊C4C22×C4×C11116yes—
451C4⋊C4C22×C4×C11116yes—
452C4⋊C4C22×C4×C11116yes—
453C22⋊C4—22no—
454C22⋊C4—22no—
455C22⋊C4—44no—
456C22⋊C4C22×C4×C1118yes—
457C22⋊C4C22×C4×C11116yes—
458C42—24no—
459C42—22no—
460C42—22no—
461C42—28no—
462C42—28no—
463C42—24no—
464C42—24no—
465C42—44no—
466C42—42no—
467C42—42no—
468C42—44no—
469C42—44no—
470C42C22×C4×C1114yes—
471C42C22×C4×C1114yes—
472C42C22×C4×C11116yes—
473C42C11×#4114yes—
474C42C11×#4114yes—
475C11#3428111yescharacteristic, direct product factor, Sylow
476C23—21no—
477C23—21no—
478C23—22no—
479C23—22no—
480C23C23×C4×C1112yes—
481C23C25×C1111yescharacteristic
482Q8—216no—
483C2×C4—21no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—21no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—24no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—28no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—48no—
511C2×C4C23×C4×C1114yes—
512C2×C4C23×C4×C1114yes—
513C2×C4C23×C4×C1118yes—
514C2×C4C23×C4×C1118yes—
515C2×C4C23×C4×C1112yes—
516C2×C4C23×C4×C1112yes—
517C2×C4C2×C11×#4112yes—
518C2×C4C2×C11×#4114yes—
519C2×C4C2×C11×#4112yes—
520C2×C4C2×C11×#4112yes—
521C2×C4C2×C11×#4112yes—
522C2×C4C11×2−1+414yes—
523C22—22no—
524C22—24no—
525C22—42no—
526C22—41no—
527C22—41no—
528C22C24×C4×C1111yescharacteristic
529C22C22×C11×#4111yescharacteristic
530C22C22×C11×#4111yescharacteristic
531C22C2×C11×2−1+412yes—
532C22C11×#58512yes—
533C4—22no—
534C4—28no—
535C4—24no—
536C4—24no—
537C4—28no—
538C4—24no—
539C4—24no—
540C4—22no—
541C4—22no—
542C4—44no—
543C4—41no—
544C4—41no—
545C4—44no—
546C4C4×C11×#4114yes—
547C2—42no—
548C2C2×C4×C11×#4111yescharacteristic
549C2C4×C11×2−1+412yes—
550C2C11×#349512yes—
551C2C11×#350911yescharacteristic
552C2C11×#351211yescharacteristic
subgroupG/H
center, socleC23×C11C25
commutatorC22C24×C4×C11
Frattini, cosocleC23C25×C11
prime radicalC24×C11C24
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#2371C2semidirect
5. C11×#2370C2semidirect
6. C11×#2330C2semidirect
7. C11×#2327C2semidirect
10. C4×C11×C4⋊Q8C2semidirect
11. C4×C11×#125C2semidirect
13. C11×#2295C2semidirect
14. C11×#2276C2semidirect
16. C11×#541C4semidirect
75. C11×C4⋊Q8C2×C4semidirect
77. C11×#125C2×C4semidirect
78. C11×#125C2×C4semidirect
82. C4×Q8×C11C2×C4semidirect
138. #34281C11direct (N × H)
203. #2371C2×C11semidirect
204. #2370C2×C11semidirect
205. #2330C2×C11semidirect
206. #2327C2×C11semidirect
209. C4×C4⋊Q8C2×C11semidirect
210. C4×#125C2×C11semidirect
212. #2295C2×C11semidirect
213. #2276C2×C11semidirect
262. #541C4×C11semidirect
345. C4⋊Q8C2×C4×C11semidirect
347. #125C2×C4×C11semidirect
348. #125C2×C4×C11semidirect
352. C4×Q8C2×C4×C11semidirect
475. C11#34281direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5412
C11×#23732
C11×#23712
C11×#23702
C11×#23302
C11×#23272
C11×#23232
C11×#23142
C4×C11×C4⋊Q82
C4×C11×#1252
C4×C11×C22⋊Q82
C11×#22952
C11×#22762
C4×C11×#1172
#3428111