Finite Group Databasebeta

← C2×C11×#2447 #14611891

Subgroups — C2×C11×#2447 #14611891

Order 2816.

3070 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
1C22×C11×#124C211yesmaximal, characteristic
2C22×C4×D4×C11C211yesmaximal, characteristic
3C11×#2447C2116yesmaximal, direct product factor
4C2×C11×#397C212yesmaximal, complemented
5C2×C11×#397C212yesmaximal, complemented
6C2×C11×#391C211yesmaximal, characteristic, complemented
7C2×C11×#391C211yesmaximal, characteristic, complemented
8C2×C11×#390C211yesmaximal, characteristic
9C2×C11×#389C211yesmaximal, characteristic, complemented
10C2×C11×#385C212yesmaximal, complemented
11C2×C11×#381C212yesmaximal, complemented
12C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C23×D4×C11C2211yescharacteristic
15C24×C4×C11C2212yes—
16C2×C11×#124—28no—
17C2×C11×#124C2218yes—
18C2×C4×D4×C11—28no—
19C2×C4×D4×C11C2218yes—
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2212yes—
25C22×C11×C22⋊C4C2212yes—
26C22×C11×C22⋊C4C2212yes—
27C22×C11×C22⋊C4C2212yes—
28C22×C11×C22⋊C4C2212yes—
29C22×C11×C22⋊C4C2212yes—
30C22×C42×C11C2211yescharacteristic
31C22×C42×C11C2211yescharacteristic
32C22×C42×C11C2211yescharacteristic
33C11×#397C22116yescomplemented
34C11×#397C22116yescomplemented
35C11×#391C2218yescomplemented
36C11×#391C2218yescomplemented
37C11×#390C2218yes—
38C11×#389C2218yescomplemented
39C11×#385C22116yescomplemented
40C11×#381C22116yescomplemented
41C4×C11×C4⋊C4C2218yescomplemented
42C2×C11×#95C2211yescharacteristic
43C2×C11×#95C2212yes—
44C2×C11×#95C2212yes—
45C2×C11×#95C2212yes—
46C2×C11×#95C2212yes—
47C2×C11×#95C2211yescharacteristic
48C2×C11×#95C2212yes—
49C25×C11C2312yes—
50C22×Q8×C11—24no—
51C22×Q8×C11—24no—
52C22×Q8×C11—24no—
53C22×Q8×C11C2314yes—
54C22×D4×C11—24no—
55C22×D4×C11—24no—
56C22×D4×C11D418yes—
57C22×D4×C11C2314yes—
58C23×C4×C11—28no—
59C23×C4×C11—28no—
60C23×C4×C11—44no—
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2312yes—
66C23×C4×C11C2312yes—
67C23×C4×C11C2312yes—
68C23×C4×C11C2318yes—
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C11×#124—232no—
73C4×D4×C11—232no—
74C2×C11×C4⋊C4—24no—
75C2×C11×C4⋊C4—24no—
76C2×C11×C4⋊C4—24no—
77C2×C11×C4⋊C4—24no—
78C2×C11×C4⋊C4—44no—
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C4⋊C4C2314yes—
81C2×C11×C4⋊C4C2314yes—
82C2×C11×C4⋊C4C2314yes—
83C2×C11×C4⋊C4C2318yes—
84C2×C11×C22⋊C4—28no—
85C2×C11×C22⋊C4—28no—
86C2×C11×C22⋊C4—28no—
87C2×C11×C22⋊C4—28no—
88C2×C11×C22⋊C4—44no—
89C2×C11×C22⋊C4C2318yes—
90C2×C11×C22⋊C4C2318yes—
91C2×C11×C22⋊C4C2318yes—
92C2×C11×C22⋊C4C2318yes—
93C2×C11×C22⋊C4C2318yes—
94C2×C42×C11—24no—
95C2×C42×C11—24no—
96C2×C42×C11—24no—
97C2×C42×C11C2314yes—
98C2×C42×C11C2314yes—
99C2×C42×C11C2314yes—
100C11×#95C2314yes—
101C11×#95C2314yes—
102C11×#95C2318yes—
103C11×#95C2318yes—
104C11×#95C2318yes—
105C11×#95C2318yes—
106C11×#95C2318yes—
107C2×#2447C1111yesmaximal, characteristic, direct product factor, Sylow
108C24×C11—24no—
109C24×C11—24no—
110C24×C11—24no—
111C24×C11—24no—
112C24×C11—24no—
113C24×C11—24no—
114C24×C11C2×D418yes—
115C24×C11C2414yes—
116C24×C11C2411yescharacteristic
117C2×Q8×C11—28no—
118C2×Q8×C11—28no—
119C2×Q8×C11—28no—
120C2×Q8×C11—416no—
121C2×D4×C11—232no—
122C2×D4×C11—28no—
123C2×D4×C11—28no—
124C2×D4×C11C2×D4116yes—
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—24no—
133C22×C4×C11—24no—
134C22×C4×C11—216no—
135C22×C4×C11—22no—
136C22×C4×C11—24no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—22no—
145C22×C4×C11—24no—
146C22×C4×C11—22no—
147C22×C4×C11—24no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—216no—
152C22×C4×C11—48no—
153C22×C4×C11—432no—
154C22×C4×C11C2×D414yes—
155C22×C4×C11#4114yes—
156C22×C4×C11#4114yes—
157C22×C4×C11#4114yes—
158C22×C4×C11#4114yes—
159C22×C4×C11C2412yes—
160C22×C4×C11C2414yes—
161C22×C4×C11C2412yes—
162C22×C4×C11C2412yes—
163C22×C4×C11C2414yes—
164C22×C4×C11C2414yes—
165C22×C4×C11C2412yes—
166C22×C4×C11C2412yes—
167C22×C4×C11C2412yes—
168C22×C4×C11C2412yes—
169C11×C4⋊C4—28no—
170C11×C4⋊C4—28no—
171C11×C4⋊C4—28no—
172C11×C4⋊C4—28no—
173C11×C4⋊C4—48no—
174C11×C22⋊C4—216no—
175C11×C22⋊C4—216no—
176C11×C22⋊C4—216no—
177C11×C22⋊C4—216no—
178C11×C22⋊C4—48no—
179C42×C11—28no—
180C42×C11—28no—
181C42×C11—28no—
182C22×#124C2×C1111yescharacteristic
183C22×C4×D4C2×C1111yescharacteristic
184#2447C2×C11116yesdirect product factor
185C2×#397C2×C1112yescomplemented
186C2×#397C2×C1112yescomplemented
187C2×#391C2×C1111yescharacteristic, complemented
188C2×#391C2×C1111yescharacteristic, complemented
189C2×#390C2×C1111yescharacteristic
190C2×#389C2×C1111yescharacteristic, complemented
191C2×#385C2×C1112yescomplemented
192C2×#381C2×C1112yescomplemented
193C2×C4×C4⋊C4C2×C1111yescharacteristic, complemented
194C23×C11—216no—
195C23×C11—216no—
196C23×C11—216no—
197C23×C11—24no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—24no—
201C23×C11—24no—
202C23×C11—24no—
203C23×C11—48no—
204C23×C11—48no—
205C23×C11—48no—
206C23×C11—48no—
207C23×C11C22×D418yes—
208C23×C11C22×D412yes—
209C23×C11C2×#4112yes—
210C23×C11C2×#4112yes—
211C23×C11C2×#4112yes—
212C23×C11C2×#4112yes—
213C23×C11H(5,𝔽2)12yes—
214C23×C112−1+412yes—
215C23×C11C2511yescharacteristic
216Q8×C11—416no—
217D4×C11—232no—
218C2×C4×C11—28no—
219C2×C4×C11—28no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
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—24no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—22no—
239C2×C4×C11—24no—
240C2×C4×C11—22no—
241C2×C4×C11—24no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—432no—
246C2×C4×C11—48no—
247C2×C4×C11—44no—
248C2×C4×C11—44no—
249C2×C4×C11—48no—
250C2×C4×C11—44no—
251C2×C4×C11—44no—
252C2×C4×C11—48no—
253C2×C4×C11#123116yes—
254C2×C4×C11C22×D414yes—
255C2×C4×C11C2×#4114yes—
256C2×C4×C11C2×#4114yes—
257C2×C4×C11C2×#4114yes—
258C2×C4×C11C2×#4114yes—
259C23×Q8C22×C1111yescharacteristic
260C23×D4C22×C1111yescharacteristic
261C24×C4C22×C1112yes—
262C2×#124—28no—
263C2×#124C22×C1118yes—
264C2×C4×D4—28no—
265C2×C4×D4C22×C1118yes—
266C22×C4⋊C4C22×C1111yescharacteristic
267C22×C4⋊C4C22×C1111yescharacteristic
268C22×C4⋊C4C22×C1111yescharacteristic
269C22×C4⋊C4C22×C1111yescharacteristic
270C22×C4⋊C4C22×C1112yes—
271C22×C22⋊C4C22×C1112yes—
272C22×C22⋊C4C22×C1112yes—
273C22×C22⋊C4C22×C1112yes—
274C22×C22⋊C4C22×C1112yes—
275C22×C22⋊C4C22×C1112yes—
276C22×C42C22×C1111yescharacteristic
277C22×C42C22×C1111yescharacteristic
278C22×C42C22×C1111yescharacteristic
279#397C22×C11116yescomplemented
280#397C22×C11116yescomplemented
281#391C22×C1118yescomplemented
282#391C22×C1118yescomplemented
283#390C22×C1118yes—
284#389C22×C1118yescomplemented
285#385C22×C11116yescomplemented
286#381C22×C11116yescomplemented
287C4×C4⋊C4C22×C1118yescomplemented
288C2×#95C22×C1111yescharacteristic
289C2×#95C22×C1112yes—
290C2×#95C22×C1112yes—
291C2×#95C22×C1112yes—
292C2×#95C22×C1112yes—
293C2×#95C22×C1111yescharacteristic
294C2×#95C22×C1112yes—
295C22×C11—28no—
296C22×C11—28no—
297C22×C11—28no—
298C22×C11—44no—
299C22×C11—44no—
300C22×C11—432no—
301C22×C11—44no—
302C22×C11—44no—
303C22×C11C2×#12314yes—
304C22×C11#52914yes—
305C22×C11#54214yes—
306C22×C11#54614yes—
307C22×C11#54714yes—
308C22×C11#55614yes—
309C22×C11#55914yes—
310C22×C11C23×D411yescharacteristic
311C22×C11C22×#4111yescharacteristic
312C22×C11C22×#4111yescharacteristic
313C22×C11C22×#4111yescharacteristic
314C22×C11C22×#4111yescharacteristic
315C22×C11C2×H(5,𝔽2)11yescharacteristic
316C22×C11C2×2−1+411yescharacteristic
317C4×C11—24no—
318C4×C11—24no—
319C4×C11—44no—
320C4×C11—42no—
321C4×C11—42no—
322C4×C11—44no—
323C4×C11—42no—
324C4×C11—42no—
325C4×C11—44no—
326C4×C11C2×#12318yes—
327C25C23×C1112yes—
328C22×Q8—24no—
329C22×Q8—24no—
330C22×Q8—24no—
331C22×Q8C23×C1114yes—
332C22×D4—24no—
333C22×D4—24no—
334C22×D4D4×C1118yes—
335C22×D4C23×C1114yes—
336C23×C4—28no—
337C23×C4—28no—
338C23×C4—44no—
339C23×C4C23×C1111yescharacteristic
340C23×C4C23×C1112yes—
341C23×C4C23×C1111yescharacteristic
342C23×C4C23×C1111yescharacteristic
343C23×C4C23×C1112yes—
344C23×C4C23×C1111yescharacteristic
345C23×C4C23×C1112yes—
346C23×C4C23×C1118yes—
347C23×C4C23×C1111yescharacteristic
348C23×C4C23×C1111yescharacteristic
349C23×C4C23×C1111yescharacteristic
350#124—232no—
351C4×D4—232no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4C23×C1114yes—
358C2×C4⋊C4C23×C1114yes—
359C2×C4⋊C4C23×C1114yes—
360C2×C4⋊C4C23×C1114yes—
361C2×C4⋊C4C23×C1118yes—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4C23×C1118yes—
368C2×C22⋊C4C23×C1118yes—
369C2×C22⋊C4C23×C1118yes—
370C2×C22⋊C4C23×C1118yes—
371C2×C22⋊C4C23×C1118yes—
372C2×C42—24no—
373C2×C42—24no—
374C2×C42—24no—
375C2×C42C23×C1114yes—
376C2×C42C23×C1114yes—
377C2×C42C23×C1114yes—
378#95C23×C1114yes—
379#95C23×C1114yes—
380#95C23×C1118yes—
381#95C23×C1118yes—
382#95C23×C1118yes—
383#95C23×C1118yes—
384#95C23×C1118yes—
385C2×C11—48no—
386C2×C11#244718yesdirect product factor
387C2×C11C22×#12311yescharacteristic
388C2×C11C2×#52911yescharacteristic
389C2×C11C2×#54211yescharacteristic
390C2×C11C2×#54611yescharacteristic
391C2×C11C2×#54711yescharacteristic
392C2×C11C2×#55611yescharacteristic
393C2×C11C2×#55911yescharacteristic
394C24—24no—
395C24—24no—
396C24—24no—
397C24—24no—
398C24—24no—
399C24—24no—
400C24C2×D4×C1118yes—
401C24C24×C1114yes—
402C24C24×C1111yescharacteristic
403C2×Q8—28no—
404C2×Q8—28no—
405C2×Q8—28no—
406C2×Q8—416no—
407C2×D4—232no—
408C2×D4—28no—
409C2×D4—28no—
410C2×D4C2×D4×C11116yes—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—216no—
421C22×C4—22no—
422C22×C4—24no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—216no—
438C22×C4—48no—
439C22×C4—432no—
440C22×C4C2×D4×C1114yes—
441C22×C4C11×#4114yes—
442C22×C4C11×#4114yes—
443C22×C4C11×#4114yes—
444C22×C4C11×#4114yes—
445C22×C4C24×C1112yes—
446C22×C4C24×C1114yes—
447C22×C4C24×C1112yes—
448C22×C4C24×C1112yes—
449C22×C4C24×C1114yes—
450C22×C4C24×C1114yes—
451C22×C4C24×C1112yes—
452C22×C4C24×C1112yes—
453C22×C4C24×C1112yes—
454C22×C4C24×C1112yes—
455C4⋊C4—28no—
456C4⋊C4—28no—
457C4⋊C4—28no—
458C4⋊C4—28no—
459C4⋊C4—48no—
460C22⋊C4—216no—
461C22⋊C4—216no—
462C22⋊C4—216no—
463C22⋊C4—216no—
464C22⋊C4—48no—
465C42—28no—
466C42—28no—
467C42—28no—
468C11C2×#244711yescharacteristic, direct product factor, Sylow
469C23—216no—
470C23—216no—
471C23—216no—
472C23—24no—
473C23—24no—
474C23—24no—
475C23—24no—
476C23—24no—
477C23—24no—
478C23—48no—
479C23—48no—
480C23—48no—
481C23—48no—
482C23C22×D4×C1118yes—
483C23C22×D4×C1112yes—
484C23C2×C11×#4112yes—
485C23C2×C11×#4112yes—
486C23C2×C11×#4112yes—
487C23C2×C11×#4112yes—
488C23C11×H(5,𝔽2)12yes—
489C23C11×2−1+412yes—
490C23C25×C1111yescharacteristic
491Q8—416no—
492D4—232no—
493C2×C4—28no—
494C2×C4—28no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—22no—
516C2×C4—24no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—432no—
521C2×C4—48no—
522C2×C4—44no—
523C2×C4—44no—
524C2×C4—48no—
525C2×C4—44no—
526C2×C4—44no—
527C2×C4—48no—
528C2×C4C11×#123116yes—
529C2×C4C22×D4×C1114yes—
530C2×C4C2×C11×#4114yes—
531C2×C4C2×C11×#4114yes—
532C2×C4C2×C11×#4114yes—
533C2×C4C2×C11×#4114yes—
534C22—28no—
535C22—28no—
536C22—28no—
537C22—44no—
538C22—44no—
539C22—432no—
540C22—44no—
541C22—44no—
542C22C2×C11×#12314yes—
543C22C11×#52914yes—
544C22C11×#54214yes—
545C22C11×#54614yes—
546C22C11×#54714yes—
547C22C11×#55614yes—
548C22C11×#55914yes—
549C22C23×D4×C1111yescharacteristic
550C22C22×C11×#4111yescharacteristic
551C22C22×C11×#4111yescharacteristic
552C22C22×C11×#4111yescharacteristic
553C22C22×C11×#4111yescharacteristic
554C22C2×C11×H(5,𝔽2)11yescharacteristic
555C22C2×C11×2−1+411yescharacteristic
556C4—24no—
557C4—24no—
558C4—44no—
559C4—42no—
560C4—44no—
561C4—42no—
562C4—42no—
563C4—42no—
564C4—44no—
565C4C2×C11×#12318yes—
566C2—48no—
567C2C11×#244718yesdirect product factor
568C2C22×C11×#12311yescharacteristic
569C2C2×C11×#52911yescharacteristic
570C2C2×C11×#54211yescharacteristic
571C2C2×C11×#54611yescharacteristic
572C2C2×C11×#54711yescharacteristic
573C2C2×C11×#55611yescharacteristic
574C2C2×C11×#55911yescharacteristic
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
3. C11×#2447C2direct (N × H)
4. C2×C11×#397C2semidirect
5. C2×C11×#397C2semidirect
6. C2×C11×#391C2semidirect
7. C2×C11×#391C2semidirect
9. C2×C11×#389C2semidirect
10. C2×C11×#385C2semidirect
11. C2×C11×#381C2semidirect
12. C2×C4×C11×C4⋊C4C2semidirect
33. C11×#397C22semidirect
34. C11×#397C22semidirect
35. C11×#391C22semidirect
36. C11×#391C22semidirect
38. C11×#389C22semidirect
39. C11×#385C22semidirect
40. C11×#381C22semidirect
41. C4×C11×C4⋊C4C22semidirect
107. C2×#2447C11direct (N × H)
184. #2447C2×C11direct (N × H)
185. C2×#397C2×C11semidirect
186. C2×#397C2×C11semidirect
187. C2×#391C2×C11semidirect
188. C2×#391C2×C11semidirect
190. C2×#389C2×C11semidirect
191. C2×#385C2×C11semidirect
192. C2×#381C2×C11semidirect
193. C2×C4×C4⋊C4C2×C11semidirect
279. #397C22×C11semidirect
280. #397C22×C11semidirect
281. #391C22×C11semidirect
282. #391C22×C11semidirect
284. #389C22×C11semidirect
285. #385C22×C11semidirect
286. #381C22×C11semidirect
287. C4×C4⋊C4C22×C11semidirect
386. C2×C11#2447direct (N × H)
468. C11C2×#2447direct (N × H)
567. C2C11×#2447direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1242
C22×C4×D4×C112
C11×#24472
C2×C11×#3972
C2×C11×#3912
C2×C11×#3902
C2×C11×#3892
C2×C11×#3852
C2×C11×#3812
C2×C4×C11×C4⋊C42
C2×#244711