Finite Group Databasebeta

← C2×C11×#2442 #14611886

Subgroups — C2×C11×#2442 #14611886

Order 2816.

2942 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#125C211yesmaximal, characteristic, complemented
2C23×C11×C4⋊C4C211yesmaximal, characteristic
3C11×#2442C2116yesmaximal, direct product factor
4C2×C11×#400C212yesmaximal, complemented
5C2×C11×#398C212yesmaximal, complemented
6C2×C11×#389C211yesmaximal, characteristic, complemented
7C2×C11×#389C211yesmaximal, characteristic, complemented
8C2×C11×#385C212yesmaximal
9C2×C11×#382C211yesmaximal, characteristic, complemented
10C2×C11×#380C212yesmaximal
11C2×C11×#380C211yesmaximal, characteristic
12C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
13C24×C4×C11C2212yes—
14C24×C4×C11C2211yescharacteristic
15C2×C11×#125—28no—
16C2×C11×#125C2218yescomplemented
17C22×C11×C4⋊C4—28no—
18C22×C11×C4⋊C4C2212yes—
19C22×C11×C4⋊C4C2212yes—
20C22×C11×C4⋊C4C2212yes—
21C22×C11×C4⋊C4C2218yes—
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C4⋊C4C2212yes—
26C22×C11×C4⋊C4C2212yes—
27C22×C11×C4⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2212yes—
31C22×C42×C11C2211yescharacteristic
32C22×C42×C11C2211yescharacteristic
33C11×#400C22116yescomplemented
34C11×#398C22116yescomplemented
35C11×#389C2218yescomplemented
36C11×#389C2218yescomplemented
37C11×#385C22116yes—
38C11×#382C2218yescomplemented
39C11×#380C22116yes—
40C11×#380C2218yes—
41C4×C11×C22⋊C4C2218yes—
42C2×C11×#95C2211yescharacteristic
43C2×C11×#95C2212yes—
44C2×C11×#95C2212yes—
45C2×C11×#95C2211yescharacteristic
46C2×C11×#95C2212yes—
47C2×C11×#95C2212yes—
48C2×C11×#95C2212yes—
49C25×C11C2311yescharacteristic
50C23×C4×C11—24no—
51C23×C4×C11—24no—
52C23×C4×C11—28no—
53C23×C4×C11—28no—
54C23×C4×C11—44no—
55C23×C4×C11Q818yes—
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2312yes—
61C23×C4×C11C2312yes—
62C23×C4×C11C2312yes—
63C23×C4×C11C2318yes—
64C23×C4×C11C2312yes—
65C23×C4×C11C2314yes—
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C11×#125—232no—
69C2×C11×C4⋊C4—28no—
70C2×C11×C4⋊C4—24no—
71C2×C11×C4⋊C4—28no—
72C2×C11×C4⋊C4—28no—
73C2×C11×C4⋊C4—24no—
74C2×C11×C4⋊C4—24no—
75C2×C11×C4⋊C4—232no—
76C2×C11×C4⋊C4—44no—
77C2×C11×C4⋊C4—44no—
78C2×C11×C4⋊C4D418yes—
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C4⋊C4C2318yes—
81C2×C11×C4⋊C4C2314yes—
82C2×C11×C4⋊C4C2314yes—
83C2×C11×C4⋊C4C2318yes—
84C2×C11×C4⋊C4C2318yes—
85C2×C11×C4⋊C4C2318yes—
86C2×C11×C4⋊C4C2318yes—
87C2×C11×C4⋊C4C2314yes—
88C2×C11×C22⋊C4—24no—
89C2×C11×C22⋊C4—28no—
90C2×C11×C22⋊C4—24no—
91C2×C11×C22⋊C4C2314yes—
92C2×C11×C22⋊C4C2314yes—
93C2×C11×C22⋊C4C2318yes—
94C2×C42×C11—24no—
95C2×C42×C11—24no—
96C2×C42×C11C2314yes—
97C2×C42×C11C2314yes—
98C11×#95C2314yes—
99C11×#95C2314yes—
100C11×#95C2318yes—
101C11×#95C2318yes—
102C11×#95C2318yes—
103C11×#95C2318yes—
104C11×#95C2318yes—
105C2×#2442C1111yesmaximal, characteristic, direct product factor, Sylow
106C24×C11—22no—
107C24×C11—22no—
108C24×C11—22no—
109C24×C11—22no—
110C24×C11C2×Q814yes—
111C24×C11#4114yes—
112C24×C11#4114yes—
113C24×C11C2412yes—
114C24×C11C2411yescharacteristic
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—24no—
118C22×C4×C11—24no—
119C22×C4×C11—232no—
120C22×C4×C11—28no—
121C22×C4×C11—28no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—24no—
125C22×C4×C11—24no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—24no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—24no—
134C22×C4×C11—24no—
135C22×C4×C11—216no—
136C22×C4×C11—24no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—24no—
140C22×C4×C11—24no—
141C22×C4×C11—22no—
142C22×C4×C11—24no—
143C22×C4×C11—22no—
144C22×C4×C11—216no—
145C22×C4×C11—48no—
146C22×C4×C11—432no—
147C22×C4×C11C2×D418yes—
148C22×C4×C11C2×D414yes—
149C22×C4×C11C2×Q814yes—
150C22×C4×C11C2×Q8116yes—
151C22×C4×C11C2×Q814yes—
152C22×C4×C11#4114yes—
153C22×C4×C11C2412yes—
154C22×C4×C11C2412yes—
155C22×C4×C11C2412yes—
156C22×C4×C11C2414yes—
157C22×C4×C11C2414yes—
158C22×C4×C11C2414yes—
159C22×C4×C11C2412yes—
160C22×C4×C11C2414yes—
161C22×C4×C11C2412yes—
162C22×C4×C11C2412yes—
163C11×C4⋊C4—216no—
164C11×C4⋊C4—28no—
165C11×C4⋊C4—216no—
166C11×C4⋊C4—216no—
167C11×C4⋊C4—28no—
168C11×C4⋊C4—28no—
169C11×C4⋊C4—48no—
170C11×C4⋊C4—48no—
171C11×C4⋊C4C2×D4116yes—
172C11×C22⋊C4—28no—
173C11×C22⋊C4—216no—
174C11×C22⋊C4—28no—
175C42×C11—28no—
176C42×C11—28no—
177C22×#125C2×C1111yescharacteristic, complemented
178C23×C4⋊C4C2×C1111yescharacteristic
179#2442C2×C11116yesdirect product factor
180C2×#400C2×C1112yescomplemented
181C2×#398C2×C1112yescomplemented
182C2×#389C2×C1111yescharacteristic, complemented
183C2×#389C2×C1111yescharacteristic, complemented
184C2×#385C2×C1112yes—
185C2×#382C2×C1111yescharacteristic, complemented
186C2×#380C2×C1112yes—
187C2×#380C2×C1111yescharacteristic
188C2×C4×C22⋊C4C2×C1111yescharacteristic
189C23×C11—28no—
190C23×C11—28no—
191C23×C11—28no—
192C23×C11—28no—
193C23×C11—28no—
194C23×C11—28no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11#125116yescomplemented
200C23×C11C22×D412yes—
201C23×C11C22×Q814yes—
202C23×C11C22×Q812yes—
203C23×C11C2×#4114yes—
204C23×C11C2×#4114yes—
205C23×C11C2×#4112yes—
206C23×C11C2×#4112yes—
207C23×C11C2×#4112yes—
208C23×C11H(5,𝔽2)12yes—
209C23×C112−1+412yes—
210C23×C11C2511yescharacteristic
211C2×C4×C11—28no—
212C2×C4×C11—216no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—232no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—24no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—22no—
237C2×C4×C11—24no—
238C2×C4×C11—22no—
239C2×C4×C11—432no—
240C2×C4×C11—44no—
241C2×C4×C11—48no—
242C2×C4×C11—44no—
243C2×C4×C11—48no—
244C2×C4×C11—44no—
245C2×C4×C11—44no—
246C2×C4×C11—48no—
247C2×C4×C11C22⋊Q8116yes—
248C2×C4×C11C22×D418yes—
249C2×C4×C11C22×D414yes—
250C2×C4×C11C22×Q814yes—
251C2×C4×C11C22×Q814yes—
252C2×C4×C11C2×#4114yes—
253C24×C4C22×C1112yes—
254C24×C4C22×C1111yescharacteristic
255C2×#125—28no—
256C2×#125C22×C1118yescomplemented
257C22×C4⋊C4—28no—
258C22×C4⋊C4C22×C1112yes—
259C22×C4⋊C4C22×C1112yes—
260C22×C4⋊C4C22×C1112yes—
261C22×C4⋊C4C22×C1118yes—
262C22×C4⋊C4C22×C1111yescharacteristic
263C22×C4⋊C4C22×C1111yescharacteristic
264C22×C4⋊C4C22×C1111yescharacteristic
265C22×C4⋊C4C22×C1112yes—
266C22×C4⋊C4C22×C1112yes—
267C22×C4⋊C4C22×C1111yescharacteristic
268C22×C22⋊C4C22×C1111yescharacteristic
269C22×C22⋊C4C22×C1111yescharacteristic
270C22×C22⋊C4C22×C1112yes—
271C22×C42C22×C1111yescharacteristic
272C22×C42C22×C1111yescharacteristic
273#400C22×C11116yescomplemented
274#398C22×C11116yescomplemented
275#389C22×C1118yescomplemented
276#389C22×C1118yescomplemented
277#385C22×C11116yes—
278#382C22×C1118yescomplemented
279#380C22×C11116yes—
280#380C22×C1118yes—
281C4×C22⋊C4C22×C1118yes—
282C2×#95C22×C1111yescharacteristic
283C2×#95C22×C1112yes—
284C2×#95C22×C1112yes—
285C2×#95C22×C1111yescharacteristic
286C2×#95C22×C1112yes—
287C2×#95C22×C1112yes—
288C2×#95C22×C1112yes—
289C22×C11—24no—
290C22×C11—24no—
291C22×C11—24no—
292C22×C11—24no—
293C22×C11—232no—
294C22×C11—24no—
295C22×C11—24no—
296C22×C11C2×C22⋊Q814yes—
297C22×C11C2×#12514yes—
298C22×C11C2×#12518yescomplemented
299C22×C11#54414yes—
300C22×C11#54614yes—
301C22×C11#54814yes—
302C22×C11#55214yes—
303C22×C11#55314yes—
304C22×C11C23×D411yescharacteristic
305C22×C11C23×Q811yescharacteristic
306C22×C11C22×#4111yescharacteristic
307C22×C11C22×#4111yescharacteristic
308C22×C11C22×#4111yescharacteristic
309C22×C11C2×H(5,𝔽2)11yescharacteristic
310C22×C11C2×2−1+411yescharacteristic
311C4×C11—24no—
312C4×C11—28no—
313C4×C11—42no—
314C4×C11—44no—
315C4×C11—42no—
316C4×C11—44no—
317C4×C11—42no—
318C4×C11—42no—
319C4×C11—44no—
320C4×C11C2×C22⋊Q818yes—
321C25C23×C1111yescharacteristic
322C23×C4—24no—
323C23×C4—24no—
324C23×C4—28no—
325C23×C4—28no—
326C23×C4—44no—
327C23×C4Q8×C1118yes—
328C23×C4C23×C1111yescharacteristic
329C23×C4C23×C1112yes—
330C23×C4C23×C1112yes—
331C23×C4C23×C1111yescharacteristic
332C23×C4C23×C1111yescharacteristic
333C23×C4C23×C1111yescharacteristic
334C23×C4C23×C1112yes—
335C23×C4C23×C1118yes—
336C23×C4C23×C1112yes—
337C23×C4C23×C1111yescharacteristic
338C23×C4C23×C1114yes—
339C23×C4C23×C1111yescharacteristic
340#125—232no—
341C2×C4⋊C4—28no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—28no—
344C2×C4⋊C4—28no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—232no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4D4×C1118yes—
351C2×C4⋊C4C23×C1114yes—
352C2×C4⋊C4C23×C1118yes—
353C2×C4⋊C4C23×C1114yes—
354C2×C4⋊C4C23×C1118yes—
355C2×C4⋊C4C23×C1118yes—
356C2×C4⋊C4C23×C1114yes—
357C2×C4⋊C4C23×C1118yes—
358C2×C4⋊C4C23×C1118yes—
359C2×C4⋊C4C23×C1114yes—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4C23×C1114yes—
364C2×C22⋊C4C23×C1114yes—
365C2×C22⋊C4C23×C1118yes—
366C2×C42—24no—
367C2×C42—24no—
368C2×C42C23×C1114yes—
369C2×C42C23×C1114yes—
370#95C23×C1114yes—
371#95C23×C1114yes—
372#95C23×C1118yes—
373#95C23×C1118yes—
374#95C23×C1118yes—
375#95C23×C1118yes—
376#95C23×C1118yes—
377C2×C11—28no—
378C2×C11#244218yesdirect product factor
379C2×C11C22×C22⋊Q811yescharacteristic
380C2×C11C22×#12511yescharacteristic
381C2×C11C2×#54411yescharacteristic
382C2×C11C2×#54611yescharacteristic
383C2×C11C2×#54811yescharacteristic
384C2×C11C2×#55211yescharacteristic
385C2×C11C2×#55311yescharacteristic
386C24—22no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24C2×Q8×C1114yes—
391C24C11×#4114yes—
392C24C11×#4114yes—
393C24C24×C1112yes—
394C24C24×C1111yescharacteristic
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—24no—
398C22×C4—24no—
399C22×C4—232no—
400C22×C4—28no—
401C22×C4—28no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—24no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—24no—
413C22×C4—22no—
414C22×C4—24no—
415C22×C4—216no—
416C22×C4—24no—
417C22×C4—22no—
418C22×C4—24no—
419C22×C4—22no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—216no—
425C22×C4—48no—
426C22×C4—432no—
427C22×C4C2×D4×C1118yes—
428C22×C4C2×D4×C1114yes—
429C22×C4C2×Q8×C1114yes—
430C22×C4C2×Q8×C11116yes—
431C22×C4C2×Q8×C1114yes—
432C22×C4C11×#4114yes—
433C22×C4C24×C1112yes—
434C22×C4C24×C1112yes—
435C22×C4C24×C1112yes—
436C22×C4C24×C1114yes—
437C22×C4C24×C1114yes—
438C22×C4C24×C1114yes—
439C22×C4C24×C1112yes—
440C22×C4C24×C1114yes—
441C22×C4C24×C1112yes—
442C22×C4C24×C1112yes—
443C4⋊C4—216no—
444C4⋊C4—28no—
445C4⋊C4—216no—
446C4⋊C4—216no—
447C4⋊C4—28no—
448C4⋊C4—28no—
449C4⋊C4—48no—
450C4⋊C4—48no—
451C4⋊C4C2×D4×C11116yes—
452C22⋊C4—28no—
453C22⋊C4—216no—
454C22⋊C4—28no—
455C42—28no—
456C42—28no—
457C11C2×#244211yescharacteristic, direct product factor, Sylow
458C23—28no—
459C23—28no—
460C23—28no—
461C23—28no—
462C23—28no—
463C23—28no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23C11×#125116yescomplemented
469C23C22×D4×C1112yes—
470C23C22×Q8×C1114yes—
471C23C22×Q8×C1112yes—
472C23C2×C11×#4114yes—
473C23C2×C11×#4114yes—
474C23C2×C11×#4112yes—
475C23C2×C11×#4112yes—
476C23C2×C11×#4112yes—
477C23C11×H(5,𝔽2)12yes—
478C23C11×2−1+412yes—
479C23C25×C1111yescharacteristic
480C2×C4—28no—
481C2×C4—216no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—232no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—22no—
508C2×C4—432no—
509C2×C4—44no—
510C2×C4—48no—
511C2×C4—44no—
512C2×C4—48no—
513C2×C4—44no—
514C2×C4—44no—
515C2×C4—48no—
516C2×C4C11×C22⋊Q8116yes—
517C2×C4C22×D4×C1118yes—
518C2×C4C22×D4×C1114yes—
519C2×C4C22×Q8×C1114yes—
520C2×C4C22×Q8×C1114yes—
521C2×C4C2×C11×#4114yes—
522C22—24no—
523C22—24no—
524C22—24no—
525C22—24no—
526C22—232no—
527C22—24no—
528C22—24no—
529C22C2×C11×C22⋊Q814yes—
530C22C2×C11×#12514yes—
531C22C2×C11×#12518yescomplemented
532C22C11×#54414yes—
533C22C11×#54614yes—
534C22C11×#54814yes—
535C22C11×#55214yes—
536C22C11×#55314yes—
537C22C23×D4×C1111yescharacteristic
538C22C23×Q8×C1111yescharacteristic
539C22C22×C11×#4111yescharacteristic
540C22C22×C11×#4111yescharacteristic
541C22C22×C11×#4111yescharacteristic
542C22C2×C11×H(5,𝔽2)11yescharacteristic
543C22C2×C11×2−1+411yescharacteristic
544C4—24no—
545C4—28no—
546C4—44no—
547C4—42no—
548C4—42no—
549C4—44no—
550C4—42no—
551C4—42no—
552C4—44no—
553C4C2×C11×C22⋊Q818yes—
554C2—28no—
555C2C11×#244218yesdirect product factor
556C2C22×C11×C22⋊Q811yescharacteristic
557C2C22×C11×#12511yescharacteristic
558C2C2×C11×#54411yescharacteristic
559C2C2×C11×#54611yescharacteristic
560C2C2×C11×#54811yescharacteristic
561C2C2×C11×#55211yescharacteristic
562C2C2×C11×#55311yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC23C25×C11
prime radicalC25×C11C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#125C2semidirect
3. C11×#2442C2direct (N × H)
4. C2×C11×#400C2semidirect
5. C2×C11×#398C2semidirect
6. C2×C11×#389C2semidirect
7. C2×C11×#389C2semidirect
9. C2×C11×#382C2semidirect
16. C2×C11×#125C22semidirect
33. C11×#400C22semidirect
34. C11×#398C22semidirect
35. C11×#389C22semidirect
36. C11×#389C22semidirect
38. C11×#382C22semidirect
105. C2×#2442C11direct (N × H)
177. C22×#125C2×C11semidirect
179. #2442C2×C11direct (N × H)
180. C2×#400C2×C11semidirect
181. C2×#398C2×C11semidirect
182. C2×#389C2×C11semidirect
183. C2×#389C2×C11semidirect
185. C2×#382C2×C11semidirect
199. C23×C11#125semidirect
256. C2×#125C22×C11semidirect
273. #400C22×C11semidirect
274. #398C22×C11semidirect
275. #389C22×C11semidirect
276. #389C22×C11semidirect
278. #382C22×C11semidirect
298. C22×C11C2×#125semidirect
378. C2×C11#2442direct (N × H)
457. C11C2×#2442direct (N × H)
468. C23C11×#125semidirect
531. C22C2×C11×#125semidirect
555. C2C11×#2442direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1252
C23×C11×C4⋊C42
C11×#24422
C2×C11×#4002
C2×C11×#3982
C2×C11×#3892
C2×C11×#3852
C2×C11×#3822
C2×C11×#3802
C2×C4×C11×C22⋊C42
C2×#244211