Finite Group Databasebeta

← C2×C11×#2579 #14612023

Subgroups — C2×C11×#2579 #14612023

Order 2816.

3374 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C11C211yesmaximal, characteristic
2C23×C11×C4⋊C4C211yesmaximal, characteristic, complemented
3C11×#2579C2116yesmaximal, direct product factor
4C2×C11×#398C212yesmaximal, complemented
5C2×C11×#396C212yesmaximal, complemented
6C2×C11×#387C212yesmaximal, complemented
7C2×C11×#386C211yesmaximal, characteristic
8C2×C11×#386C211yesmaximal, characteristic
9C2×C11×#385C212yesmaximal, complemented
10C2×C11×#385C211yesmaximal, characteristic, complemented
11C2×C11×#385C211yesmaximal, characteristic, complemented
12C2×C11×#380C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C24×C4×C11C2211yescharacteristic
16C24×C4×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C2×C4×D4×C11—28no—
19C2×C4×D4×C11C2218yes—
20C22×C11×C4⋊C4—28no—
21C22×C11×C4⋊C4C2212yes—
22C22×C11×C4⋊C4C2212yes—
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2212yes—
25C22×C11×C4⋊C4C2212yes—
26C22×C11×C4⋊C4C2212yes—
27C22×C11×C4⋊C4C2218yescomplemented
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2212yes—
30C22×C11×C22⋊C4C2211yescharacteristic
31C22×C11×C22⋊C4C2211yescharacteristic
32C22×C11×C22⋊C4C2211yescharacteristic
33C22×C11×C22⋊C4C2212yes—
34C22×C42×C11C2211yescharacteristic
35C11×#398C22116yescomplemented
36C11×#396C22116yescomplemented
37C11×#387C22116yescomplemented
38C11×#386C2218yes—
39C11×#386C2218yes—
40C11×#385C22116yescomplemented
41C11×#385C2218yescomplemented
42C11×#385C2218yescomplemented
43C11×#380C2218yescomplemented
44C2×C11×#95C2212yes—
45C2×C11×#95C2212yes—
46C2×C11×#95C2212yes—
47C2×C11×#95C2212yes—
48C2×C11×#95C2212yes—
49C25×C11C2311yescharacteristic
50C25×C11C2311yescharacteristic
51C22×D4×C11—24no—
52C22×D4×C11—24no—
53C22×D4×C11Q818yes—
54C22×D4×C11C2314yes—
55C23×C4×C11—24no—
56C23×C4×C11—28no—
57C23×C4×C11—24no—
58C23×C4×C11—24no—
59C23×C4×C11—44no—
60C23×C4×C11—44no—
61C23×C4×C11—44no—
62C23×C4×C11D418yes—
63C23×C4×C11C2314yes—
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2312yes—
66C23×C4×C11C2312yes—
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2312yes—
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2312yes—
73C23×C4×C11C2314yes—
74C23×C4×C11C2314yes—
75C23×C4×C11C2314yes—
76C4×D4×C11—232no—
77C2×C11×C4⋊C4—28no—
78C2×C11×C4⋊C4—28no—
79C2×C11×C4⋊C4—232no—
80C2×C11×C4⋊C4—24no—
81C2×C11×C4⋊C4—28no—
82C2×C11×C4⋊C4—44no—
83C2×C11×C4⋊C4—44no—
84C2×C11×C4⋊C4C2318yes—
85C2×C11×C4⋊C4C2318yes—
86C2×C11×C4⋊C4C2314yes—
87C2×C11×C4⋊C4C2318yes—
88C2×C11×C4⋊C4C2318yes—
89C2×C11×C4⋊C4C2318yes—
90C2×C11×C22⋊C4—24no—
91C2×C11×C22⋊C4—24no—
92C2×C11×C22⋊C4—24no—
93C2×C11×C22⋊C4—24no—
94C2×C11×C22⋊C4—28no—
95C2×C11×C22⋊C4—44no—
96C2×C11×C22⋊C4C2314yes—
97C2×C11×C22⋊C4C2314yes—
98C2×C11×C22⋊C4C2314yes—
99C2×C11×C22⋊C4C2314yes—
100C2×C11×C22⋊C4C2318yes—
101C2×C11×C22⋊C4C2318yes—
102C2×C42×C11—24no—
103C2×C42×C11C2314yes—
104C11×#95C2318yes—
105C11×#95C2318yes—
106C11×#95C2318yes—
107C11×#95C2318yes—
108C11×#95C2318yes—
109C2×#2579C1111yesmaximal, characteristic, direct product factor, Sylow
110C24×C11—24no—
111C24×C11—24no—
112C24×C11—22no—
113C24×C11—24no—
114C24×C11—22no—
115C24×C11—24no—
116C24×C11C2×D414yes—
117C24×C11C2×Q814yes—
118C24×C11C2×Q814yes—
119C24×C11#4114yes—
120C24×C11C2412yes—
121C24×C11C2412yes—
122C24×C11C2411yescharacteristic
123C2×D4×C11—232no—
124C2×D4×C11—28no—
125C2×D4×C11—28no—
126C2×D4×C11C2×Q8116yes—
127C22×C4×C11—232no—
128C22×C4×C11—22no—
129C22×C4×C11—28no—
130C22×C4×C11—24no—
131C22×C4×C11—24no—
132C22×C4×C11—22no—
133C22×C4×C11—24no—
134C22×C4×C11—24no—
135C22×C4×C11—216no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—28no—
139C22×C4×C11—24no—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—24no—
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—24no—
150C22×C4×C11—28no—
151C22×C4×C11—416no—
152C22×C4×C11—48no—
153C22×C4×C11—48no—
154C22×C4×C11—48no—
155C22×C4×C11—416no—
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×C11C2414yes—
164C22×C4×C11C2412yes—
165C22×C4×C11C2412yes—
166C22×C4×C11C2414yes—
167C22×C4×C11C2412yes—
168C22×C4×C11C2412yes—
169C22×C4×C11C2412yes—
170C22×C4×C11C2414yes—
171C11×C4⋊C4—216no—
172C11×C4⋊C4—216no—
173C11×C4⋊C4—28no—
174C11×C4⋊C4—216no—
175C11×C4⋊C4—48no—
176C11×C4⋊C4—48no—
177C11×C22⋊C4—28no—
178C11×C22⋊C4—28no—
179C11×C22⋊C4—28no—
180C11×C22⋊C4—28no—
181C11×C22⋊C4—216no—
182C11×C22⋊C4—48no—
183C42×C11—28no—
184C22×C4×D4C2×C1111yescharacteristic
185C23×C4⋊C4C2×C1111yescharacteristic, complemented
186#2579C2×C11116yesdirect product factor
187C2×#398C2×C1112yescomplemented
188C2×#396C2×C1112yescomplemented
189C2×#387C2×C1112yescomplemented
190C2×#386C2×C1111yescharacteristic
191C2×#386C2×C1111yescharacteristic
192C2×#385C2×C1112yescomplemented
193C2×#385C2×C1111yescharacteristic, complemented
194C2×#385C2×C1111yescharacteristic, complemented
195C2×#380C2×C1111yescharacteristic, complemented
196C23×C11—28no—
197C23×C11—28no—
198C23×C11—216no—
199C23×C11—216no—
200C23×C11—24no—
201C23×C11—24no—
202C23×C11—28no—
203C23×C11—216no—
204C23×C11—22no—
205C23×C11—24no—
206C23×C11—22no—
207C23×C11—24no—
208C23×C11—44no—
209C23×C11—44no—
210C23×C11—48no—
211C23×C11C22⋊Q8116yes—
212C23×C11C22×D414yes—
213C23×C11C22×D412yes—
214C23×C11C22×Q814yes—
215C23×C11C22×Q814yes—
216C23×C11C22×Q812yes—
217C23×C11C2×#4114yes—
218C23×C11C2×#4112yes—
219C23×C11C2×#4114yes—
220C23×C11H(5,𝔽2)14yes—
221C23×C11C2511yescharacteristic
222D4×C11—232no—
223C2×C4×C11—232no—
224C2×C4×C11—28no—
225C2×C4×C11—216no—
226C2×C4×C11—28no—
227C2×C4×C11—28no—
228C2×C4×C11—22no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
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—24no—
246C2×C4×C11—24no—
247C2×C4×C11—416no—
248C2×C4×C11—416no—
249C2×C4×C11—416no—
250C2×C4×C11—44no—
251C2×C4×C11—44no—
252C2×C4×C11—48no—
253C2×C4×C11—48no—
254C2×C4×C11—48no—
255C2×C4×C11C22×D414yes—
256C2×C4×C11C22×D414yes—
257C2×C4×C11C22×Q814yes—
258C2×C4×C11C2×#4118yes—
259C23×D4C22×C1111yescharacteristic
260C24×C4C22×C1111yescharacteristic
261C24×C4C22×C1111yescharacteristic
262C24×C4C22×C1111yescharacteristic
263C24×C4C22×C1111yescharacteristic
264C2×C4×D4—28no—
265C2×C4×D4C22×C1118yes—
266C22×C4⋊C4—28no—
267C22×C4⋊C4C22×C1112yes—
268C22×C4⋊C4C22×C1112yes—
269C22×C4⋊C4C22×C1111yescharacteristic
270C22×C4⋊C4C22×C1112yes—
271C22×C4⋊C4C22×C1112yes—
272C22×C4⋊C4C22×C1112yes—
273C22×C4⋊C4C22×C1118yescomplemented
274C22×C22⋊C4C22×C1111yescharacteristic
275C22×C22⋊C4C22×C1112yes—
276C22×C22⋊C4C22×C1111yescharacteristic
277C22×C22⋊C4C22×C1111yescharacteristic
278C22×C22⋊C4C22×C1111yescharacteristic
279C22×C22⋊C4C22×C1112yes—
280C22×C42C22×C1111yescharacteristic
281#398C22×C11116yescomplemented
282#396C22×C11116yescomplemented
283#387C22×C11116yescomplemented
284#386C22×C1118yes—
285#386C22×C1118yes—
286#385C22×C11116yescomplemented
287#385C22×C1118yescomplemented
288#385C22×C1118yescomplemented
289#380C22×C1118yescomplemented
290C2×#95C22×C1112yes—
291C2×#95C22×C1112yes—
292C2×#95C22×C1112yes—
293C2×#95C22×C1112yes—
294C2×#95C22×C1112yes—
295C22×C11—232no—
296C22×C11—24no—
297C22×C11—24no—
298C22×C11—28no—
299C22×C11—28no—
300C22×C11—24no—
301C22×C11—28no—
302C22×C11—416no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—44no—
306C22×C11C2×C22⋊Q818yes—
307C22×C11C2×C22⋊Q814yes—
308C22×C11#52514yes—
309C22×C11#53414yes—
310C22×C11#55318yes—
311C22×C11#55418yes—
312C22×C11C23×D411yescharacteristic
313C22×C11C23×Q811yescharacteristic
314C22×C11C22×#4111yescharacteristic
315C22×C11C22×#4112yes—
316C22×C11C2×H(5,𝔽2)12yes—
317C4×C11—24no—
318C4×C11—28no—
319C4×C11—24no—
320C4×C11—24no—
321C4×C11—42no—
322C4×C11—42no—
323C4×C11—44no—
324C4×C11—44no—
325C4×C11—44no—
326C25C23×C1111yescharacteristic
327C25C23×C1111yescharacteristic
328C22×D4—24no—
329C22×D4—24no—
330C22×D4Q8×C1118yes—
331C22×D4C23×C1114yes—
332C23×C4—24no—
333C23×C4—28no—
334C23×C4—24no—
335C23×C4—24no—
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×C1114yes—
346C23×C4C23×C1111yescharacteristic
347C23×C4C23×C1111yescharacteristic
348C23×C4C23×C1111yescharacteristic
349C23×C4C23×C1112yes—
350C23×C4C23×C1114yes—
351C23×C4C23×C1114yes—
352C23×C4C23×C1114yes—
353C4×D4—232no—
354C2×C4⋊C4—28no—
355C2×C4⋊C4—28no—
356C2×C4⋊C4—232no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—28no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4C23×C1118yes—
362C2×C4⋊C4C23×C1118yes—
363C2×C4⋊C4C23×C1114yes—
364C2×C4⋊C4C23×C1118yes—
365C2×C4⋊C4C23×C1118yes—
366C2×C4⋊C4C23×C1118yes—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—28no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4C23×C1114yes—
374C2×C22⋊C4C23×C1114yes—
375C2×C22⋊C4C23×C1114yes—
376C2×C22⋊C4C23×C1114yes—
377C2×C22⋊C4C23×C1118yes—
378C2×C22⋊C4C23×C1118yes—
379C2×C42—24no—
380C2×C42C23×C1114yes—
381#95C23×C1118yes—
382#95C23×C1118yes—
383#95C23×C1118yes—
384#95C23×C1118yes—
385#95C23×C1118yes—
386C2×C11—28no—
387C2×C11—44no—
388C2×C11#257918yesdirect product factor
389C2×C11C22×C22⋊Q811yescharacteristic
390C2×C11C2×#52511yescharacteristic
391C2×C11C2×#53411yescharacteristic
392C2×C11C2×#55312yes—
393C2×C11C2×#55412yes—
394C24—24no—
395C24—24no—
396C24—22no—
397C24—24no—
398C24—22no—
399C24—24no—
400C24C2×D4×C1114yes—
401C24C2×Q8×C1114yes—
402C24C2×Q8×C1114yes—
403C24C11×#4114yes—
404C24C24×C1112yes—
405C24C24×C1112yes—
406C24C24×C1111yescharacteristic
407C2×D4—232no—
408C2×D4—28no—
409C2×D4—28no—
410C2×D4C2×Q8×C11116yes—
411C22×C4—232no—
412C22×C4—22no—
413C22×C4—28no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—22no—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—216no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—28no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—28no—
435C22×C4—416no—
436C22×C4—48no—
437C22×C4—48no—
438C22×C4—48no—
439C22×C4—416no—
440C22×C4—416no—
441C22×C4C2×D4×C1114yes—
442C22×C4C2×D4×C1114yes—
443C22×C4C2×D4×C11116yes—
444C22×C4C2×Q8×C1114yes—
445C22×C4C11×#4118yes—
446C22×C4C24×C1114yes—
447C22×C4C24×C1114yes—
448C22×C4C24×C1112yes—
449C22×C4C24×C1112yes—
450C22×C4C24×C1114yes—
451C22×C4C24×C1112yes—
452C22×C4C24×C1112yes—
453C22×C4C24×C1112yes—
454C22×C4C24×C1114yes—
455C4⋊C4—216no—
456C4⋊C4—216no—
457C4⋊C4—28no—
458C4⋊C4—216no—
459C4⋊C4—48no—
460C4⋊C4—48no—
461C22⋊C4—28no—
462C22⋊C4—28no—
463C22⋊C4—28no—
464C22⋊C4—28no—
465C22⋊C4—216no—
466C22⋊C4—48no—
467C42—28no—
468C11C2×#257911yescharacteristic, direct product factor, Sylow
469C23—28no—
470C23—28no—
471C23—216no—
472C23—216no—
473C23—24no—
474C23—24no—
475C23—28no—
476C23—216no—
477C23—22no—
478C23—24no—
479C23—22no—
480C23—24no—
481C23—44no—
482C23—44no—
483C23—48no—
484C23C11×C22⋊Q8116yes—
485C23C22×D4×C1114yes—
486C23C22×D4×C1112yes—
487C23C22×Q8×C1114yes—
488C23C22×Q8×C1114yes—
489C23C22×Q8×C1112yes—
490C23C2×C11×#4114yes—
491C23C2×C11×#4112yes—
492C23C2×C11×#4114yes—
493C23C11×H(5,𝔽2)14yes—
494C23C25×C1111yescharacteristic
495D4—232no—
496C2×C4—232no—
497C2×C4—28no—
498C2×C4—216no—
499C2×C4—28no—
500C2×C4—28no—
501C2×C4—22no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—416no—
521C2×C4—416no—
522C2×C4—416no—
523C2×C4—44no—
524C2×C4—44no—
525C2×C4—48no—
526C2×C4—48no—
527C2×C4—48no—
528C2×C4C22×D4×C1114yes—
529C2×C4C22×D4×C1114yes—
530C2×C4C22×Q8×C1114yes—
531C2×C4C2×C11×#4118yes—
532C22—24no—
533C22—24no—
534C22—28no—
535C22—28no—
536C22—232no—
537C22—24no—
538C22—28no—
539C22—42no—
540C22—42no—
541C22—44no—
542C22—416no—
543C22C2×C11×C22⋊Q818yes—
544C22C2×C11×C22⋊Q814yes—
545C22C11×#52514yes—
546C22C11×#53414yes—
547C22C11×#55318yes—
548C22C11×#55418yes—
549C22C23×D4×C1111yescharacteristic
550C22C23×Q8×C1111yescharacteristic
551C22C22×C11×#4111yescharacteristic
552C22C22×C11×#4112yes—
553C22C2×C11×H(5,𝔽2)12yes—
554C4—24no—
555C4—28no—
556C4—24no—
557C4—24no—
558C4—42no—
559C4—42no—
560C4—44no—
561C4—44no—
562C4—44no—
563C2—28no—
564C2—44no—
565C2C11×#257918yesdirect product factor
566C2C22×C11×C22⋊Q811yescharacteristic
567C2C2×C11×#52511yescharacteristic
568C2C2×C11×#53411yescharacteristic
569C2C2×C11×#55312yes—
570C2C2×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
2. C23×C11×C4⋊C4C2semidirect
3. C11×#2579C2direct (N × H)
4. C2×C11×#398C2semidirect
5. C2×C11×#396C2semidirect
6. C2×C11×#387C2semidirect
9. C2×C11×#385C2semidirect
10. C2×C11×#385C2semidirect
11. C2×C11×#385C2semidirect
12. C2×C11×#380C2semidirect
27. C22×C11×C4⋊C4C22semidirect
35. C11×#398C22semidirect
36. C11×#396C22semidirect
37. C11×#387C22semidirect
40. C11×#385C22semidirect
41. C11×#385C22semidirect
42. C11×#385C22semidirect
43. C11×#380C22semidirect
109. C2×#2579C11direct (N × H)
185. C23×C4⋊C4C2×C11semidirect
186. #2579C2×C11direct (N × H)
187. C2×#398C2×C11semidirect
188. C2×#396C2×C11semidirect
189. C2×#387C2×C11semidirect
192. C2×#385C2×C11semidirect
193. C2×#385C2×C11semidirect
194. C2×#385C2×C11semidirect
195. C2×#380C2×C11semidirect
273. C22×C4⋊C4C22×C11semidirect
281. #398C22×C11semidirect
282. #396C22×C11semidirect
283. #387C22×C11semidirect
286. #385C22×C11semidirect
287. #385C22×C11semidirect
288. #385C22×C11semidirect
289. #380C22×C11semidirect
388. C2×C11#2579direct (N × H)
468. C11C2×#2579direct (N × H)
565. C2C11×#2579direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D4×C112
C23×C11×C4⋊C42
C11×#25792
C2×C11×#3982
C2×C11×#3962
C2×C11×#3872
C2×C11×#3862
C2×C11×#3852
C2×C11×#3802
C2×#257911