Finite Group Databasebeta

← C11×#14320 #14591513

Subgroups — C11×#14320 #14591513

Order 2816.

1318 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#395C211yesmaximal, characteristic
2C2×C11×#391C211yesmaximal, characteristic
3C2×C4×C11×C4⋊C4C211yesmaximal, characteristic
4C11×#1446C211yesmaximal, characteristic
5C11×#1445C212yesmaximal
6C11×#1442C212yesmaximal
7C11×#1442C211yesmaximal, characteristic
8C11×#1441C211yesmaximal, characteristic
9C11×#1436C212yesmaximal
10C11×#1434C212yesmaximal
11C11×#1434C211yesmaximal, characteristic
12C23×Q8×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2212yes—
17C22×C42×C11C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C11×#395C418yescomplemented
21C11×#391—24no—
22C4×C11×C4⋊C4—24no—
23C2×C11×#95C2212yes—
24C2×C11×#95C2212yes—
25C2×C11×#95C2212yes—
26C2×C11×#95C2211yescharacteristic
27C2×C11×#95C2212yes—
28C2×C11×#95C2212yes—
29C2×C11×#95C2211yescharacteristic
30C2×C11×#95C2211yescharacteristic
31C2×C11×#95C2212yes—
32C2×C11×#95C2212yes—
33C2×C11×#95C2212yes—
34C2×C11×#95C2212yes—
35C2×C11×#95C2212yes—
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2212yes—
38C22×Q8×C11—22no—
39C22×Q8×C11—22no—
40C22×Q8×C11—42no—
41C22×Q8×C11—42no—
42C22×Q8×C11C2×C414yes—
43C23×C4×C11C2312yes—
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2312yes—
47C23×C4×C11C2312yes—
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—42no—
61C2×C11×C4⋊C4—42no—
62C2×C11×C4⋊C4—42no—
63C2×C11×C4⋊C4C2×C414yes—
64C2×C11×C4⋊C4C2×C418yes—
65C2×C42×C11—22no—
66C2×C42×C11—22no—
67C2×C42×C11—22no—
68C2×C42×C11—42no—
69C2×C42×C11—42no—
70C2×C42×C11D414yes—
71C2×C42×C11Q814yescomplemented
72C11×#95—22no—
73C11×#95—22no—
74C11×#95—24no—
75C11×#95—24no—
76C11×#95—24no—
77C11×#95—24no—
78C11×#95—22no—
79C11×#95—24no—
80C11×#95—42no—
81C11×#95—42no—
82C11×#95—42no—
83C11×#95—42no—
84C11×#95—42no—
85C11×#95C2×C414yes—
86C11×#95C2×C418yes—
87#14320C1111yesmaximal, characteristic, direct product factor, Sylow
88C24×C11C2411yescharacteristic
89C2×Q8×C11—28no—
90C2×Q8×C11—48no—
91C2×Q8×C11—44no—
92C2×Q8×C11—44no—
93C2×Q8×C11—48no—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11C22×C414yes—
145C22×C4×C11C22×C414yes—
146C22×C4×C11C22×C412yes—
147C22×C4×C11C22×C412yes—
148C22×C4×C11C22×C412yes—
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×Q812yes—
153C22×C4×C11C2×Q812yes—
154C22×C4×C11C2×Q812yes—
155C22×C4×C11#4112yes—
156C22×C4×C11#4112yes—
157C22×C4×C11#4112yes—
158C22×C4×C11#4112yes—
159C11×C4⋊C4—28no—
160C11×C4⋊C4—28no—
161C11×C4⋊C4—48no—
162C11×C4⋊C4—44no—
163C42×C11—28no—
164C42×C11—44no—
165C42×C11—44no—
166C2×#395C2×C1111yescharacteristic
167C2×#391C2×C1111yescharacteristic
168C2×C4×C4⋊C4C2×C1111yescharacteristic
169#1446C2×C1111yescharacteristic
170#1445C2×C1112yes—
171#1442C2×C1112yes—
172#1442C2×C1111yescharacteristic
173#1441C2×C1111yescharacteristic
174#1436C2×C1112yes—
175#1434C2×C1111yescharacteristic
176#1434C2×C1112yes—
177C23×C11C23×C411yescharacteristic
178C23×C11C22×D411yescharacteristic
179C23×C11C22×Q811yescharacteristic
180C23×C11C2×#4111yescharacteristic
181C23×C11C2×#4111yescharacteristic
182C23×C11C2×#4111yescharacteristic
183C23×C11C2×#4111yescharacteristic
184C23×C11H(5,𝔽2)12yes—
185C23×C11H(5,𝔽2)12yes—
186C23×C112−1+412yes—
187C23×C112−1+412yes—
188Q8×C11—416no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—24no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—24no—
203C2×C4×C11—22no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—42no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—42no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—42no—
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—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11C4×D414yes—
252C2×C4×C11C4×Q814yes—
253C2×C4×C11C22⋊Q814yes—
254C23×Q8C22×C1111yescharacteristic
255C22×C4⋊C4C22×C1111yescharacteristic
256C22×C4⋊C4C22×C1111yescharacteristic
257C22×C4⋊C4C22×C1111yescharacteristic
258C22×C4⋊C4C22×C1112yes—
259C22×C42C22×C1111yescharacteristic
260C22×C42C22×C1111yescharacteristic
261C22×C42C22×C1111yescharacteristic
262#395C4×C1118yescomplemented
263#391—24no—
264C4×C4⋊C4—24no—
265C2×#95C22×C1112yes—
266C2×#95C22×C1112yes—
267C2×#95C22×C1112yes—
268C2×#95C22×C1111yescharacteristic
269C2×#95C22×C1112yes—
270C2×#95C22×C1112yes—
271C2×#95C22×C1111yescharacteristic
272C2×#95C22×C1111yescharacteristic
273C2×#95C22×C1112yes—
274C2×#95C22×C1112yes—
275C2×#95C22×C1112yes—
276C2×#95C22×C1112yes—
277C2×#95C22×C1112yes—
278C2×#95C22×C1112yes—
279C2×#95C22×C1111yescharacteristic
280C22×C11C2×C4×D411yescharacteristic
281C22×C11C2×C4×Q811yescharacteristic
282C22×C11C4×#4111yescharacteristic
283C22×C11#51812yes—
284C22×C11#51912yes—
285C22×C11C2×C22⋊Q811yescharacteristic
286C22×C11#52511yescharacteristic
287C22×C11#52911yescharacteristic
288C22×C11#53311yescharacteristic
289C22×C11#53411yescharacteristic
290C22×C11#53511yescharacteristic
291C22×C11#53611yescharacteristic
292C22×C11#53611yescharacteristic
293C22×C11#53812yes—
294C22×C11#53912yes—
295C22×C11#53912yes—
296C22×C11#54112yes—
297C22×C11#54212yes—
298C22×C11#54212yes—
299C22×C11#54212yes—
300C22×C11#54212yes—
301C22×C11#54412yes—
302C22×C11#54412yes—
303C4×C11—24no—
304C4×C11—24no—
305C4×C11—24no—
306C4×C11—42no—
307C4×C11—44no—
308C4×C11—44no—
309C4×C11—42no—
310C4×C11—42no—
311C4×C11—42no—
312C4×C11—82no—
313C4×C11—82no—
314C22×Q8—22no—
315C22×Q8—22no—
316C22×Q8—42no—
317C22×Q8—42no—
318C22×Q8C2×C4×C1114yes—
319C23×C4C23×C1112yes—
320C23×C4C23×C1112yes—
321C23×C4C23×C1111yescharacteristic
322C23×C4C23×C1112yes—
323C23×C4C23×C1112yes—
324C23×C4C23×C1111yescharacteristic
325C23×C4C23×C1111yescharacteristic
326C23×C4C23×C1111yescharacteristic
327C23×C4C23×C1111yescharacteristic
328C23×C4C23×C1111yescharacteristic
329C23×C4C23×C1111yescharacteristic
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4C2×C4×C1114yes—
340C2×C4⋊C4C2×C4×C1118yes—
341C2×C42—22no—
342C2×C42—22no—
343C2×C42—22no—
344C2×C42—42no—
345C2×C42—42no—
346C2×C42D4×C1114yes—
347C2×C42Q8×C1114yescomplemented
348#95—22no—
349#95—22no—
350#95—24no—
351#95—24no—
352#95—24no—
353#95—24no—
354#95—22no—
355#95—24no—
356#95—42no—
357#95—42no—
358#95—42no—
359#95—42no—
360#95—42no—
361#95C2×C4×C1114yes—
362#95C2×C4×C1118yes—
363C2×C11C4×C22⋊Q811yescharacteristic
364C2×C11#232111yescharacteristic
365C2×C11#232711yescharacteristic
366C2×C11#233112yes—
367C2×C11#233212yes—
368C2×C11#262711yescharacteristic
369C2×C11#262811yescharacteristic
370C2×C11#263211yescharacteristic
371C2×C11#263811yescharacteristic
372C2×C11#265012yes—
373C2×C11#266612yes—
374C24C24×C1111yescharacteristic
375C2×Q8—28no—
376C2×Q8—48no—
377C2×Q8—44no—
378C2×Q8—44no—
379C2×Q8—48no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4C22×C4×C1114yes—
431C22×C4C22×C4×C1114yes—
432C22×C4C22×C4×C1112yes—
433C22×C4C22×C4×C1112yes—
434C22×C4C22×C4×C1112yes—
435C22×C4C2×D4×C1112yes—
436C22×C4C2×D4×C1112yes—
437C22×C4C2×D4×C1112yes—
438C22×C4C2×Q8×C1112yes—
439C22×C4C2×Q8×C1112yes—
440C22×C4C2×Q8×C1112yes—
441C22×C4C11×#4112yes—
442C22×C4C11×#4112yes—
443C22×C4C11×#4112yes—
444C22×C4C11×#4112yes—
445C4⋊C4—28no—
446C4⋊C4—28no—
447C4⋊C4—48no—
448C4⋊C4—44no—
449C42—28no—
450C42—44no—
451C42—44no—
452C11#1432011yescharacteristic, direct product factor, Sylow
453C23C23×C4×C1111yescharacteristic
454C23C22×D4×C1111yescharacteristic
455C23C22×Q8×C1111yescharacteristic
456C23C2×C11×#4111yescharacteristic
457C23C2×C11×#4111yescharacteristic
458C23C2×C11×#4111yescharacteristic
459C23C2×C11×#4111yescharacteristic
460C23C11×H(5,𝔽2)12yes—
461C23C11×H(5,𝔽2)12yes—
462C23C11×2−1+412yes—
463C23C11×2−1+412yes—
464Q8—416no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—24no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—42no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4C4×D4×C1114yes—
528C2×C4C4×Q8×C1114yes—
529C2×C4C11×C22⋊Q814yes—
530C22C2×C4×D4×C1111yescharacteristic
531C22C2×C4×Q8×C1111yescharacteristic
532C22C4×C11×#4111yescharacteristic
533C22C11×#51812yes—
534C22C11×#51912yes—
535C22C2×C11×C22⋊Q811yescharacteristic
536C22C11×#52511yescharacteristic
537C22C11×#52911yescharacteristic
538C22C11×#53311yescharacteristic
539C22C11×#53411yescharacteristic
540C22C11×#53511yescharacteristic
541C22C11×#53611yescharacteristic
542C22C11×#53611yescharacteristic
543C22C11×#53812yes—
544C22C11×#53912yes—
545C22C11×#53912yes—
546C22C11×#54112yes—
547C22C11×#54212yes—
548C22C11×#54212yes—
549C22C11×#54212yes—
550C22C11×#54212yes—
551C22C11×#54412yes—
552C22C11×#54412yes—
553C4—24no—
554C4—24no—
555C4—24no—
556C4—42no—
557C4—42no—
558C4—44no—
559C4—42no—
560C4—44no—
561C4—42no—
562C4—82no—
563C4—82no—
564C2C4×C11×C22⋊Q811yescharacteristic
565C2C11×#232111yescharacteristic
566C2C11×#232711yescharacteristic
567C2C11×#233112yes—
568C2C11×#233212yes—
569C2C11×#262711yescharacteristic
570C2C11×#262811yescharacteristic
571C2C11×#263211yescharacteristic
572C2C11×#263811yescharacteristic
573C2C11×#265012yes—
574C2C11×#266612yes—
subgroupG/H
center, socle, prime radicalC24×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
20. C11×#395C4semidirect
71. C2×C42×C11Q8semidirect
87. #14320C11direct (N × H)
262. #395C4×C11semidirect
347. C2×C42Q8×C11semidirect
452. C11#14320direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3952
C2×C11×#3912
C2×C4×C11×C4⋊C42
C11×#14462
C11×#14452
C11×#14422
C11×#14412
C11×#14362
C11×#14342
#1432011