Finite Group Databasebeta

← C2×C11×#2564 #14612024

Subgroups — C2×C11×#2564 #14612024

Order 2816.

3374 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
2C22×C4×D4×C11C211yesmaximal, characteristic
3C11×#2564C2116yesmaximal, direct product factor
4C2×C11×#400C211yesmaximal, characteristic, complemented
5C2×C11×#399C211yesmaximal, characteristic, complemented
6C2×C11×#395C211yesmaximal, characteristic, complemented
7C2×C11×#393C211yesmaximal, characteristic, complemented
8C2×C11×#387C212yesmaximal, complemented
9C2×C11×#386C212yesmaximal
10C2×C11×#385C212yesmaximal, complemented
11C2×C11×#380C212yesmaximal, complemented
12C22×C11×#95C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C23×D4×C11C2211yescharacteristic
15C24×C4×C11C2212yes—
16C24×C4×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C2×C11×C22⋊Q8—28no—
19C2×C11×C22⋊Q8C2218yescomplemented
20C2×C4×D4×C11—28no—
21C2×C4×D4×C11C2218yes—
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2212yes—
25C22×C11×C4⋊C4C2212yes—
26C22×C11×C4⋊C4C2212yes—
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2212yes—
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2212yes—
31C22×C11×C22⋊C4C2212yes—
32C22×C42×C11C2211yescharacteristic
33C11×#400C2218yescomplemented
34C11×#399C2218yescomplemented
35C11×#395C2218yescomplemented
36C11×#393C2218yescomplemented
37C11×#387C22116yescomplemented
38C11×#386C22116yes—
39C11×#385C22116yescomplemented
40C11×#380C22116yescomplemented
41C2×C11×#95C2211yescharacteristic
42C2×C11×#95C2212yes—
43C2×C11×#95C2211yescharacteristic
44C2×C11×#95C2212yes—
45C2×C11×#95C2212yes—
46C2×C11×#95C2212yes—
47C2×C11×#95C2212yes—
48C2×C11×#95C2218yescomplemented
49C25×C11C2311yescharacteristic
50C25×C11C2311yescharacteristic
51C22×Q8×C11—24no—
52C22×Q8×C11—44no—
53C22×Q8×C11C2314yes—
54C22×D4×C11—24no—
55C22×D4×C11—24no—
56C22×D4×C11Q818yescomplemented
57C22×D4×C11C2314yes—
58C23×C4×C11—28no—
59C23×C4×C11—24no—
60C23×C4×C11—28no—
61C23×C4×C11—44no—
62C23×C4×C11—44no—
63C23×C4×C11—44no—
64C23×C4×C11D418yes—
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2312yes—
67C23×C4×C11C2312yes—
68C23×C4×C11C2312yes—
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2318yes—
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2312yes—
75C23×C4×C11C2314yes—
76C23×C4×C11C2314yes—
77C11×C22⋊Q8—232no—
78C4×D4×C11—232no—
79C2×C11×C4⋊C4—24no—
80C2×C11×C4⋊C4—24no—
81C2×C11×C4⋊C4—28no—
82C2×C11×C4⋊C4—28no—
83C2×C11×C4⋊C4—44no—
84C2×C11×C4⋊C4C2314yes—
85C2×C11×C4⋊C4C2318yes—
86C2×C11×C4⋊C4C2318yes—
87C2×C11×C4⋊C4C2314yes—
88C2×C11×C4⋊C4C2318yes—
89C2×C11×C22⋊C4—24no—
90C2×C11×C22⋊C4—28no—
91C2×C11×C22⋊C4—24no—
92C2×C11×C22⋊C4—28no—
93C2×C11×C22⋊C4—44no—
94C2×C11×C22⋊C4C2314yes—
95C2×C11×C22⋊C4C2314yes—
96C2×C11×C22⋊C4C2318yes—
97C2×C11×C22⋊C4C2318yes—
98C2×C11×C22⋊C4C2318yes—
99C2×C42×C11—24no—
100C2×C42×C11C2314yes—
101C11×#95C2318yes—
102C11×#95C2314yes—
103C11×#95C2314yes—
104C11×#95C2318yes—
105C11×#95C2318yes—
106C11×#95C2318yes—
107C11×#95C2318yes—
108C2×#2564C1111yesmaximal, characteristic, direct product factor, Sylow
109C24×C11—24no—
110C24×C11—24no—
111C24×C11—22no—
112C24×C11—24no—
113C24×C11—22no—
114C24×C11—24no—
115C24×C11C2×D414yes—
116C24×C11C2×Q814yes—
117C24×C11C2×Q814yes—
118C24×C11#4114yes—
119C24×C11C2412yes—
120C24×C11C2412yes—
121C24×C11C2411yescharacteristic
122C2×Q8×C11—28no—
123C2×Q8×C11—48no—
124C2×Q8×C11—416no—
125C2×D4×C11—232no—
126C2×D4×C11—28no—
127C2×D4×C11—28no—
128C2×D4×C11C2×Q8116yescomplemented
129C22×C4×C11—22no—
130C22×C4×C11—24no—
131C22×C4×C11—22no—
132C22×C4×C11—24no—
133C22×C4×C11—24no—
134C22×C4×C11—24no—
135C22×C4×C11—22no—
136C22×C4×C11—24no—
137C22×C4×C11—22no—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—216no—
143C22×C4×C11—24no—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—24no—
148C22×C4×C11—24no—
149C22×C4×C11—28no—
150C22×C4×C11—216no—
151C22×C4×C11—416no—
152C22×C4×C11—48no—
153C22×C4×C11—48no—
154C22×C4×C11—48no—
155C22×C4×C11—432no—
156C22×C4×C11—416no—
157C22×C4×C11C2×D414yes—
158C22×C4×C11C2×D414yes—
159C22×C4×C11C2×D4116yes—
160C22×C4×C11C2×Q814yes—
161C22×C4×C11#4118yes—
162C22×C4×C11C2414yes—
163C22×C4×C11C2412yes—
164C22×C4×C11C2414yes—
165C22×C4×C11C2414yes—
166C22×C4×C11C2412yes—
167C22×C4×C11C2412yes—
168C22×C4×C11C2412yes—
169C22×C4×C11C2412yes—
170C22×C4×C11C2414yes—
171C11×C4⋊C4—28no—
172C11×C4⋊C4—28no—
173C11×C4⋊C4—216no—
174C11×C4⋊C4—216no—
175C11×C4⋊C4—48no—
176C11×C22⋊C4—28no—
177C11×C22⋊C4—216no—
178C11×C22⋊C4—28no—
179C11×C22⋊C4—216no—
180C11×C22⋊C4—48no—
181C42×C11—28no—
182C22×C22⋊Q8C2×C1111yescharacteristic, complemented
183C22×C4×D4C2×C1111yescharacteristic
184#2564C2×C11116yesdirect product factor
185C2×#400C2×C1111yescharacteristic, complemented
186C2×#399C2×C1111yescharacteristic, complemented
187C2×#395C2×C1111yescharacteristic, complemented
188C2×#393C2×C1111yescharacteristic, complemented
189C2×#387C2×C1112yescomplemented
190C2×#386C2×C1112yes—
191C2×#385C2×C1112yescomplemented
192C2×#380C2×C1112yescomplemented
193C22×#95C2×C1111yescharacteristic, complemented
194C23×C11—28no—
195C23×C11—28no—
196C23×C11—216no—
197C23×C11—216no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—28no—
201C23×C11—216no—
202C23×C11—22no—
203C23×C11—24no—
204C23×C11—22no—
205C23×C11—24no—
206C23×C11—44no—
207C23×C11—44no—
208C23×C11—48no—
209C23×C11C22⋊Q8116yes—
210C23×C11C22×D414yes—
211C23×C11C22×D412yes—
212C23×C11C22×Q814yes—
213C23×C11C22×Q814yes—
214C23×C11C22×Q812yes—
215C23×C11C2×#4114yes—
216C23×C11C2×#4112yes—
217C23×C11C2×#4114yes—
218C23×C11H(5,𝔽2)14yes—
219C23×C11C2511yescharacteristic
220Q8×C11—416no—
221D4×C11—232no—
222C2×C4×C11—28no—
223C2×C4×C11—28no—
224C2×C4×C11—28no—
225C2×C4×C11—216no—
226C2×C4×C11—22no—
227C2×C4×C11—24no—
228C2×C4×C11—22no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
245C2×C4×C11—416no—
246C2×C4×C11—432no—
247C2×C4×C11—416no—
248C2×C4×C11—44no—
249C2×C4×C11—48no—
250C2×C4×C11—44no—
251C2×C4×C11—48no—
252C2×C4×C11—48no—
253C2×C4×C11C22×D414yes—
254C2×C4×C11C22×D414yes—
255C2×C4×C11C22×Q814yes—
256C2×C4×C11C2×#4118yes—
257C23×Q8C22×C1111yescharacteristic
258C23×D4C22×C1111yescharacteristic
259C24×C4C22×C1112yes—
260C24×C4C22×C1111yescharacteristic
261C24×C4C22×C1111yescharacteristic
262C2×C22⋊Q8—28no—
263C2×C22⋊Q8C22×C1118yescomplemented
264C2×C4×D4—28no—
265C2×C4×D4C22×C1118yes—
266C22×C4⋊C4C22×C1111yescharacteristic
267C22×C4⋊C4C22×C1111yescharacteristic
268C22×C4⋊C4C22×C1112yes—
269C22×C4⋊C4C22×C1112yes—
270C22×C4⋊C4C22×C1112yes—
271C22×C22⋊C4C22×C1111yescharacteristic
272C22×C22⋊C4C22×C1112yes—
273C22×C22⋊C4C22×C1111yescharacteristic
274C22×C22⋊C4C22×C1112yes—
275C22×C22⋊C4C22×C1112yes—
276C22×C42C22×C1111yescharacteristic
277#400C22×C1118yescomplemented
278#399C22×C1118yescomplemented
279#395C22×C1118yescomplemented
280#393C22×C1118yescomplemented
281#387C22×C11116yescomplemented
282#386C22×C11116yes—
283#385C22×C11116yescomplemented
284#380C22×C11116yescomplemented
285C2×#95C22×C1111yescharacteristic
286C2×#95C22×C1112yes—
287C2×#95C22×C1111yescharacteristic
288C2×#95C22×C1112yes—
289C2×#95C22×C1112yes—
290C2×#95C22×C1112yes—
291C2×#95C22×C1112yes—
292C2×#95C22×C1118yescomplemented
293C22×C11—232no—
294C22×C11—24no—
295C22×C11—24no—
296C22×C11—28no—
297C22×C11—28no—
298C22×C11—24no—
299C22×C11—28no—
300C22×C11—416no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—44no—
304C22×C11C2×C22⋊Q818yes—
305C22×C11C2×C22⋊Q814yes—
306C22×C11#53214yes—
307C22×C11#53414yes—
308C22×C11#55118yes—
309C22×C11#55418yes—
310C22×C11C23×D411yescharacteristic
311C22×C11C23×Q811yescharacteristic
312C22×C11C22×#4111yescharacteristic
313C22×C11C22×#4112yes—
314C22×C11C2×H(5,𝔽2)12yes—
315C4×C11—24no—
316C4×C11—24no—
317C4×C11—24no—
318C4×C11—28no—
319C4×C11—42no—
320C4×C11—44no—
321C4×C11—42no—
322C4×C11—44no—
323C4×C11—44no—
324C25C23×C1111yescharacteristic
325C25C23×C1111yescharacteristic
326C22×Q8—24no—
327C22×Q8—44no—
328C22×Q8C23×C1114yes—
329C22×D4—24no—
330C22×D4—24no—
331C22×D4Q8×C1118yescomplemented
332C22×D4C23×C1114yes—
333C23×C4—28no—
334C23×C4—24no—
335C23×C4—28no—
336C23×C4—44no—
337C23×C4—44no—
338C23×C4—44no—
339C23×C4D4×C1118yes—
340C23×C4C23×C1112yes—
341C23×C4C23×C1112yes—
342C23×C4C23×C1111yescharacteristic
343C23×C4C23×C1111yescharacteristic
344C23×C4C23×C1112yes—
345C23×C4C23×C1118yes—
346C23×C4C23×C1111yescharacteristic
347C23×C4C23×C1111yescharacteristic
348C23×C4C23×C1111yescharacteristic
349C23×C4C23×C1112yes—
350C23×C4C23×C1114yes—
351C23×C4C23×C1114yes—
352C22⋊Q8—232no—
353C4×D4—232no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—28no—
357C2×C4⋊C4—28no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4C23×C1114yes—
360C2×C4⋊C4C23×C1118yes—
361C2×C4⋊C4C23×C1114yes—
362C2×C4⋊C4C23×C1118yes—
363C2×C4⋊C4C23×C1118yes—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4C23×C1114yes—
370C2×C22⋊C4C23×C1114yes—
371C2×C22⋊C4C23×C1118yes—
372C2×C22⋊C4C23×C1118yes—
373C2×C22⋊C4C23×C1118yes—
374C2×C42—24no—
375C2×C42C23×C1114yes—
376#95C23×C1118yes—
377#95C23×C1114yes—
378#95C23×C1114yes—
379#95C23×C1118yes—
380#95C23×C1118yes—
381#95C23×C1118yes—
382#95C23×C1118yes—
383C2×C11—28no—
384C2×C11—44no—
385C2×C11#256418yesdirect product factor
386C2×C11C22×C22⋊Q811yescharacteristic
387C2×C11C2×#53211yescharacteristic
388C2×C11C2×#53411yescharacteristic
389C2×C11C2×#55112yes—
390C2×C11C2×#55412yes—
391C24—24no—
392C24—24no—
393C24—22no—
394C24—24no—
395C24—22no—
396C24—24no—
397C24C2×D4×C1114yes—
398C24C2×Q8×C1114yes—
399C24C2×Q8×C1114yes—
400C24C11×#4114yes—
401C24C24×C1112yes—
402C24C24×C1112yes—
403C24C24×C1111yescharacteristic
404C2×Q8—28no—
405C2×Q8—48no—
406C2×Q8—416no—
407C2×D4—232no—
408C2×D4—28no—
409C2×D4—28no—
410C2×D4C2×Q8×C11116yescomplemented
411C22×C4—22no—
412C22×C4—24no—
413C22×C4—22no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—22no—
418C22×C4—24no—
419C22×C4—22no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—216no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—28no—
432C22×C4—216no—
433C22×C4—416no—
434C22×C4—48no—
435C22×C4—48no—
436C22×C4—48no—
437C22×C4—432no—
438C22×C4—416no—
439C22×C4C2×D4×C1114yes—
440C22×C4C2×D4×C1114yes—
441C22×C4C2×D4×C11116yes—
442C22×C4C2×Q8×C1114yes—
443C22×C4C11×#4118yes—
444C22×C4C24×C1114yes—
445C22×C4C24×C1112yes—
446C22×C4C24×C1114yes—
447C22×C4C24×C1114yes—
448C22×C4C24×C1112yes—
449C22×C4C24×C1112yes—
450C22×C4C24×C1112yes—
451C22×C4C24×C1112yes—
452C22×C4C24×C1114yes—
453C4⋊C4—28no—
454C4⋊C4—28no—
455C4⋊C4—216no—
456C4⋊C4—216no—
457C4⋊C4—48no—
458C22⋊C4—28no—
459C22⋊C4—216no—
460C22⋊C4—28no—
461C22⋊C4—216no—
462C22⋊C4—48no—
463C42—28no—
464C11C2×#256411yescharacteristic, direct product factor, Sylow
465C23—28no—
466C23—28no—
467C23—216no—
468C23—216no—
469C23—24no—
470C23—24no—
471C23—28no—
472C23—216no—
473C23—22no—
474C23—24no—
475C23—22no—
476C23—24no—
477C23—44no—
478C23—44no—
479C23—48no—
480C23C11×C22⋊Q8116yes—
481C23C22×D4×C1114yes—
482C23C22×D4×C1112yes—
483C23C22×Q8×C1114yes—
484C23C22×Q8×C1114yes—
485C23C22×Q8×C1112yes—
486C23C2×C11×#4114yes—
487C23C2×C11×#4112yes—
488C23C2×C11×#4114yes—
489C23C11×H(5,𝔽2)14yes—
490C23C25×C1111yescharacteristic
491Q8—416no—
492D4—232no—
493C2×C4—28no—
494C2×C4—28no—
495C2×C4—28no—
496C2×C4—216no—
497C2×C4—22no—
498C2×C4—24no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—22no—
504C2×C4—24no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—416no—
517C2×C4—432no—
518C2×C4—416no—
519C2×C4—44no—
520C2×C4—48no—
521C2×C4—44no—
522C2×C4—48no—
523C2×C4—48no—
524C2×C4C22×D4×C1114yes—
525C2×C4C22×D4×C1114yes—
526C2×C4C22×Q8×C1114yes—
527C2×C4C2×C11×#4118yes—
528C22—24no—
529C22—24no—
530C22—28no—
531C22—28no—
532C22—232no—
533C22—24no—
534C22—28no—
535C22—42no—
536C22—42no—
537C22—44no—
538C22—416no—
539C22C2×C11×C22⋊Q818yes—
540C22C2×C11×C22⋊Q814yes—
541C22C11×#53214yes—
542C22C11×#53414yes—
543C22C11×#55118yes—
544C22C11×#55418yes—
545C22C23×D4×C1111yescharacteristic
546C22C23×Q8×C1111yescharacteristic
547C22C22×C11×#4111yescharacteristic
548C22C22×C11×#4112yes—
549C22C2×C11×H(5,𝔽2)12yes—
550C4—24no—
551C4—24no—
552C4—24no—
553C4—28no—
554C4—42no—
555C4—44no—
556C4—42no—
557C4—44no—
558C4—44no—
559C2—28no—
560C2—44no—
561C2C11×#256418yesdirect product factor
562C2C22×C11×C22⋊Q811yescharacteristic
563C2C2×C11×#53211yescharacteristic
564C2C2×C11×#53411yescharacteristic
565C2C2×C11×#55112yes—
566C2C2×C11×#55412yes—
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC23C25×C11
prime radicalC23×D4×C11C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×C22⋊Q8C2semidirect
3. C11×#2564C2direct (N × H)
4. C2×C11×#400C2semidirect
5. C2×C11×#399C2semidirect
6. C2×C11×#395C2semidirect
7. C2×C11×#393C2semidirect
8. C2×C11×#387C2semidirect
10. C2×C11×#385C2semidirect
11. C2×C11×#380C2semidirect
12. C22×C11×#95C2semidirect
19. C2×C11×C22⋊Q8C22semidirect
33. C11×#400C22semidirect
34. C11×#399C22semidirect
35. C11×#395C22semidirect
36. C11×#393C22semidirect
37. C11×#387C22semidirect
39. C11×#385C22semidirect
40. C11×#380C22semidirect
48. C2×C11×#95C22semidirect
56. C22×D4×C11Q8semidirect
108. C2×#2564C11direct (N × H)
128. C2×D4×C11C2×Q8semidirect
182. C22×C22⋊Q8C2×C11semidirect
184. #2564C2×C11direct (N × H)
185. C2×#400C2×C11semidirect
186. C2×#399C2×C11semidirect
187. C2×#395C2×C11semidirect
188. C2×#393C2×C11semidirect
189. C2×#387C2×C11semidirect
191. C2×#385C2×C11semidirect
192. C2×#380C2×C11semidirect
193. C22×#95C2×C11semidirect
263. C2×C22⋊Q8C22×C11semidirect
277. #400C22×C11semidirect
278. #399C22×C11semidirect
279. #395C22×C11semidirect
280. #393C22×C11semidirect
281. #387C22×C11semidirect
283. #385C22×C11semidirect
284. #380C22×C11semidirect
292. C2×#95C22×C11semidirect
331. C22×D4Q8×C11semidirect
385. C2×C11#2564direct (N × H)
410. C2×D4C2×Q8×C11semidirect
464. C11C2×#2564direct (N × H)
561. C2C11×#2564direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×C22⋊Q82
C22×C4×D4×C112
C11×#25642
C2×C11×#4002
C2×C11×#3992
C2×C11×#3952
C2×C11×#3932
C2×C11×#3872
C2×C11×#3862
C2×C11×#3852
C2×C11×#3802
C22×C11×#952
C2×#256411