Finite Group Databasebeta

← C2×C11×#2405 #14611849

Subgroups — C2×C11×#2405 #14611849

Order 2816.

7822 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
1C24×D4×C11C211yesmaximal, characteristic
2C22×C11×#123C212yesmaximal, complemented
3C23×C11×C22⋊C4C211yesmaximal, characteristic, complemented
4C11×#2405C2116yesmaximal, direct product factor
5C2×C11×#394C214yesmaximal, complemented
6C2×C11×#386C212yesmaximal, complemented
7C2×C11×#385C212yesmaximal, complemented
8C2×C11×#379C212yesmaximal, complemented
9C2×C11×#379C211yesmaximal, characteristic, complemented
10C26×C11C2211yescharacteristic
11C26×C11C2211yescharacteristic
12C23×D4×C11—28no—
13C23×D4×C11—216no—
14C23×D4×C11C2212yes—
15C23×D4×C11C2218yes—
16C23×D4×C11C2212yes—
17C24×C4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic, complemented
19C24×C4×C11C2211yescharacteristic, complemented
20C2×C11×#123—216no—
21C2×C11×#123C22116yescomplemented
22C22×C11×C4⋊C4C2214yescomplemented
23C22×C11×C22⋊C4—28no—
24C22×C11×C22⋊C4C2212yes—
25C22×C11×C22⋊C4C2212yes—
26C22×C11×C22⋊C4C2218yescomplemented
27C22×C11×C22⋊C4C2212yescomplemented
28C22×C11×C22⋊C4C2214yescomplemented
29C22×C11×C22⋊C4C2212yescomplemented
30C22×C11×C22⋊C4C2212yescomplemented
31C22×C11×C22⋊C4C2214yescomplemented
32C11×#394C22132yescomplemented
33C11×#386C22116yescomplemented
34C11×#385C22116yescomplemented
35C11×#379C22116yescomplemented
36C11×#379C2218yescomplemented
37C2×C11×#95C2214yescomplemented
38C25×C11—28no—
39C25×C11—28no—
40C25×C11—24no—
41C25×C11—28no—
42C25×C11—28no—
43C25×C11—44no—
44C25×C11—44no—
45C25×C11D418yes—
46C25×C11C2311yescharacteristic
47C25×C11C2312yes—
48C25×C11C2314yes—
49C25×C11C2314yes—
50C25×C11C2311yescharacteristic
51C25×C11C2311yescharacteristic
52C22×D4×C11—2128no—
53C22×D4×C11—28no—
54C22×D4×C11—28no—
55C22×D4×C11—232no—
56C22×D4×C11—28no—
57C22×D4×C11—28no—
58C22×D4×C11—264no—
59C22×D4×C11—28no—
60C22×D4×C11D4116yes—
61C22×D4×C11C2318yes—
62C22×D4×C11C2318yes—
63C23×C4×C11—24no—
64C23×C4×C11—28no—
65C23×C4×C11—24no—
66C23×C4×C11—24no—
67C23×C4×C11—28no—
68C23×C4×C11—44no—
69C23×C4×C11C2314yes—
70C23×C4×C11C2314yes—
71C23×C4×C11C2312yes—
72C23×C4×C11C2312yes—
73C23×C4×C11C2312yes—
74C23×C4×C11C2314yescomplemented
75C23×C4×C11C2314yescomplemented
76C11×#123—264no—
77C2×C11×C4⋊C4—216no—
78C2×C11×C4⋊C4C23116yescomplemented
79C2×C11×C22⋊C4—28no—
80C2×C11×C22⋊C4—232no—
81C2×C11×C22⋊C4—28no—
82C2×C11×C22⋊C4—28no—
83C2×C11×C22⋊C4—216no—
84C2×C11×C22⋊C4—28no—
85C2×C11×C22⋊C4—44no—
86C2×C11×C22⋊C4—48no—
87C2×C11×C22⋊C4C2318yes—
88C2×C11×C22⋊C4C2318yes—
89C2×C11×C22⋊C4C2318yescomplemented
90C2×C11×C22⋊C4C2318yescomplemented
91C2×C11×C22⋊C4C23116yescomplemented
92C2×C11×C22⋊C4C23116yescomplemented
93C2×C11×C22⋊C4C2318yescomplemented
94C11×#95C23116yescomplemented
95C2×#2405C1111yesmaximal, characteristic, direct product factor, Sylow
96C24×C11—24no—
97C24×C11—24no—
98C24×C11—24no—
99C24×C11—24no—
100C24×C11—232no—
101C24×C11—232no—
102C24×C11—232no—
103C24×C11—216no—
104C24×C11—216no—
105C24×C11—28no—
106C24×C11—24no—
107C24×C11—24no—
108C24×C11—24no—
109C24×C11—216no—
110C24×C11—24no—
111C24×C11—28no—
112C24×C11—24no—
113C24×C11—28no—
114C24×C11—216no—
115C24×C11—416no—
116C24×C11—48no—
117C24×C11—48no—
118C24×C11—464no—
119C24×C11—464no—
120C24×C11—416no—
121C24×C11—416no—
122C24×C11C2×D414yes—
123C24×C11C2×D418yes—
124C24×C11C2×D4116yes—
125C24×C11C2×D418yes—
126C24×C11C2×D414yes—
127C24×C11C2×D414yes—
128C24×C11#4118yes—
129C24×C11C2412yes—
130C24×C11C2414yes—
131C24×C11C2412yes—
132C24×C11C2412yes—
133C24×C11C2411yescharacteristic
134C2×D4×C11—2256no—
135C2×D4×C11—264no—
136C2×D4×C11—264no—
137C2×D4×C11—216no—
138C2×D4×C11—216no—
139C2×D4×C11—216no—
140C2×D4×C11—216no—
141C2×D4×C11—216no—
142C2×D4×C11C2×D4132yes—
143C22×C4×C11—232no—
144C22×C4×C11—28no—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—216no—
148C22×C4×C11—28no—
149C22×C4×C11—24no—
150C22×C4×C11—24no—
151C22×C4×C11—28no—
152C22×C4×C11—28no—
153C22×C4×C11—28no—
154C22×C4×C11—216no—
155C22×C4×C11—28no—
156C22×C4×C11—28no—
157C22×C4×C11—28no—
158C22×C4×C11—48no—
159C22×C4×C11—416no—
160C22×C4×C11—416no—
161C22×C4×C11C2×D418yes—
162C22×C4×C11C2414yes—
163C22×C4×C11C2418yes—
164C22×C4×C11C2414yes—
165C22×C4×C11C2414yes—
166C11×C4⋊C4—232no—
167C11×C22⋊C4—216no—
168C11×C22⋊C4—216no—
169C11×C22⋊C4—216no—
170C11×C22⋊C4—232no—
171C11×C22⋊C4—216no—
172C11×C22⋊C4—48no—
173C11×C22⋊C4—416no—
174C24×D4C2×C1111yescharacteristic
175C22×#123C2×C1112yescomplemented
176C23×C22⋊C4C2×C1111yescharacteristic, complemented
177#2405C2×C11116yesdirect product factor
178C2×#394C2×C1114yescomplemented
179C2×#386C2×C1112yescomplemented
180C2×#385C2×C1112yescomplemented
181C2×#379C2×C1112yescomplemented
182C2×#379C2×C1111yescharacteristic, complemented
183C23×C11—28no—
184C23×C11—28no—
185C23×C11—28no—
186C23×C11—28no—
187C23×C11—232no—
188C23×C11—232no—
189C23×C11—24no—
190C23×C11—24no—
191C23×C11—24no—
192C23×C11—24no—
193C23×C11—232no—
194C23×C11—232no—
195C23×C11—28no—
196C23×C11—216no—
197C23×C11—28no—
198C23×C11—232no—
199C23×C11—28no—
200C23×C11—232no—
201C23×C11—24no—
202C23×C11—24no—
203C23×C11—24no—
204C23×C11—24no—
205C23×C11—28no—
206C23×C11—24no—
207C23×C11—28no—
208C23×C11—416no—
209C23×C11—4128no—
210C23×C11—464no—
211C23×C11—464no—
212C23×C11—4128no—
213C23×C11—416no—
214C23×C11—48no—
215C23×C11—416no—
216C23×C11—48no—
217C23×C11—416no—
218C23×C11—416no—
219C23×C11#120116yes—
220C23×C11#123116yescomplemented
221C23×C11C22×D414yes—
222C23×C11C22×D418yes—
223C23×C11C22×D418yes—
224C23×C11C22×D414yes—
225C23×C11C22×D414yes—
226C23×C11C22×D412yes—
227C23×C11C22×D414yes—
228C23×C11C2×#4118yes—
229C23×C11C2×#4114yes—
230C23×C11H(5,𝔽2)14yes—
231C23×C11C2511yescharacteristic
232D4×C11—264no—
233D4×C11—264no—
234C2×C4×C11—232no—
235C2×C4×C11—216no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—28no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—28no—
242C2×C4×C11—28no—
243C2×C4×C11—28no—
244C2×C4×C11—28no—
245C2×C4×C11—416no—
246C2×C4×C11—416no—
247C2×C4×C11—48no—
248C2×C4×C11—48no—
249C2×C4×C11—416no—
250C2×C4×C11C22×D418yes—
251C26C22×C1111yescharacteristic
252C26C22×C1111yescharacteristic
253C23×D4—28no—
254C23×D4—216no—
255C23×D4C22×C1112yes—
256C23×D4C22×C1118yes—
257C23×D4C22×C1112yes—
258C24×C4C22×C1111yescharacteristic
259C24×C4C22×C1111yescharacteristic, complemented
260C24×C4C22×C1111yescharacteristic, complemented
261C2×#123—216no—
262C2×#123C22×C11116yescomplemented
263C22×C4⋊C4C22×C1114yescomplemented
264C22×C22⋊C4—28no—
265C22×C22⋊C4C22×C1112yes—
266C22×C22⋊C4C22×C1112yes—
267C22×C22⋊C4C22×C1118yescomplemented
268C22×C22⋊C4C22×C1112yescomplemented
269C22×C22⋊C4C22×C1114yescomplemented
270C22×C22⋊C4C22×C1112yescomplemented
271C22×C22⋊C4C22×C1112yescomplemented
272C22×C22⋊C4C22×C1114yescomplemented
273#394C22×C11132yescomplemented
274#386C22×C11116yescomplemented
275#385C22×C11116yescomplemented
276#379C22×C11116yescomplemented
277#379C22×C1118yescomplemented
278C2×#95C22×C1114yescomplemented
279C22×C11—232no—
280C22×C11—232no—
281C22×C11—24no—
282C22×C11—24no—
283C22×C11—24no—
284C22×C11—24no—
285C22×C11—216no—
286C22×C11—216no—
287C22×C11—24no—
288C22×C11—28no—
289C22×C11—24no—
290C22×C11—24no—
291C22×C11—216no—
292C22×C11—464no—
293C22×C11—464no—
294C22×C11—416no—
295C22×C11—432no—
296C22×C11—44no—
297C22×C11—44no—
298C22×C11—48no—
299C22×C11—48no—
300C22×C11C2×#12018yes—
301C22×C11C2×#12014yes—
302C22×C11C2×#12314yes—
303C22×C11C2×#12318yescomplemented
304C22×C11#53414yes—
305C22×C11#546116yes—
306C22×C11C23×D411yescharacteristic
307C22×C11C23×D412yes—
308C22×C11C22×#4112yes—
309C22×C11C2×H(5,𝔽2)12yes—
310C4×C11—28no—
311C4×C11—44no—
312C4×C11—44no—
313C4×C11—48no—
314C25—28no—
315C25—28no—
316C25—24no—
317C25—28no—
318C25—28no—
319C25—44no—
320C25—44no—
321C25D4×C1118yes—
322C25C23×C1111yescharacteristic
323C25C23×C1112yes—
324C25C23×C1114yes—
325C25C23×C1114yes—
326C25C23×C1111yescharacteristic
327C25C23×C1111yescharacteristic
328C22×D4—2128no—
329C22×D4—28no—
330C22×D4—28no—
331C22×D4—232no—
332C22×D4—28no—
333C22×D4—28no—
334C22×D4—264no—
335C22×D4—28no—
336C22×D4D4×C11116yes—
337C22×D4C23×C1118yes—
338C22×D4C23×C1118yes—
339C23×C4—24no—
340C23×C4—28no—
341C23×C4—24no—
342C23×C4—24no—
343C23×C4—28no—
344C23×C4—44no—
345C23×C4C23×C1114yes—
346C23×C4C23×C1112yes—
347C23×C4C23×C1112yes—
348C23×C4C23×C1114yes—
349C23×C4C23×C1112yes—
350C23×C4C23×C1114yescomplemented
351C23×C4C23×C1114yescomplemented
352#123—264no—
353C2×C4⋊C4—216no—
354C2×C4⋊C4C23×C11116yescomplemented
355C2×C22⋊C4—28no—
356C2×C22⋊C4—232no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—216no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—48no—
363C2×C22⋊C4C23×C1118yes—
364C2×C22⋊C4C23×C1118yes—
365C2×C22⋊C4C23×C1118yescomplemented
366C2×C22⋊C4C23×C1118yescomplemented
367C2×C22⋊C4C23×C11116yescomplemented
368C2×C22⋊C4C23×C11116yescomplemented
369C2×C22⋊C4C23×C1118yescomplemented
370#95C23×C11116yescomplemented
371C2×C11—28no—
372C2×C11—28no—
373C2×C11—44no—
374C2×C11—48no—
375C2×C11#240518yesdirect product factor
376C2×C11C22×#12011yescharacteristic
377C2×C11C22×#12311yescharacteristic
378C2×C11C2×#53411yescharacteristic
379C2×C11C2×#54614yes—
380C24—24no—
381C24—24no—
382C24—24no—
383C24—24no—
384C24—232no—
385C24—232no—
386C24—232no—
387C24—216no—
388C24—216no—
389C24—28no—
390C24—24no—
391C24—24no—
392C24—24no—
393C24—216no—
394C24—24no—
395C24—28no—
396C24—24no—
397C24—28no—
398C24—216no—
399C24—416no—
400C24—48no—
401C24—48no—
402C24—464no—
403C24—464no—
404C24—416no—
405C24—416no—
406C24C2×D4×C1114yes—
407C24C2×D4×C1118yes—
408C24C2×D4×C11116yes—
409C24C2×D4×C1118yes—
410C24C2×D4×C1114yes—
411C24C2×D4×C1114yes—
412C24C11×#4118yes—
413C24C24×C1112yes—
414C24C24×C1114yes—
415C24C24×C1112yes—
416C24C24×C1112yes—
417C24C24×C1111yescharacteristic
418C2×D4—2256no—
419C2×D4—264no—
420C2×D4—264no—
421C2×D4—216no—
422C2×D4—216no—
423C2×D4—216no—
424C2×D4—216no—
425C2×D4—216no—
426C2×D4C2×D4×C11132yes—
427C22×C4—232no—
428C22×C4—28no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—216no—
432C22×C4—28no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—28no—
436C22×C4—28no—
437C22×C4—28no—
438C22×C4—216no—
439C22×C4—28no—
440C22×C4—28no—
441C22×C4—28no—
442C22×C4—48no—
443C22×C4—416no—
444C22×C4—416no—
445C22×C4C2×D4×C1118yes—
446C22×C4C24×C1114yes—
447C22×C4C24×C1118yes—
448C22×C4C24×C1114yes—
449C22×C4C24×C1114yes—
450C4⋊C4—232no—
451C22⋊C4—216no—
452C22⋊C4—216no—
453C22⋊C4—216no—
454C22⋊C4—232no—
455C22⋊C4—216no—
456C22⋊C4—48no—
457C22⋊C4—416no—
458C11C2×#240511yescharacteristic, direct product factor, Sylow
459C23—28no—
460C23—28no—
461C23—28no—
462C23—28no—
463C23—232no—
464C23—232no—
465C23—24no—
466C23—24no—
467C23—24no—
468C23—24no—
469C23—232no—
470C23—232no—
471C23—28no—
472C23—216no—
473C23—28no—
474C23—232no—
475C23—28no—
476C23—232no—
477C23—24no—
478C23—24no—
479C23—24no—
480C23—24no—
481C23—28no—
482C23—24no—
483C23—28no—
484C23—416no—
485C23—4128no—
486C23—464no—
487C23—464no—
488C23—4128no—
489C23—416no—
490C23—48no—
491C23—416no—
492C23—48no—
493C23—416no—
494C23—416no—
495C23C11×#120116yes—
496C23C11×#123116yescomplemented
497C23C22×D4×C1114yes—
498C23C22×D4×C1118yes—
499C23C22×D4×C1118yes—
500C23C22×D4×C1114yes—
501C23C22×D4×C1114yes—
502C23C22×D4×C1112yes—
503C23C22×D4×C1114yes—
504C23C2×C11×#4118yes—
505C23C2×C11×#4114yes—
506C23C11×H(5,𝔽2)14yes—
507C23C25×C1111yescharacteristic
508D4—264no—
509D4—264no—
510C2×C4—232no—
511C2×C4—216no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—28no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—28no—
518C2×C4—28no—
519C2×C4—28no—
520C2×C4—28no—
521C2×C4—416no—
522C2×C4—416no—
523C2×C4—48no—
524C2×C4—48no—
525C2×C4—416no—
526C2×C4C22×D4×C1118yes—
527C22—232no—
528C22—232no—
529C22—24no—
530C22—24no—
531C22—24no—
532C22—24no—
533C22—216no—
534C22—216no—
535C22—24no—
536C22—28no—
537C22—24no—
538C22—24no—
539C22—216no—
540C22—464no—
541C22—464no—
542C22—416no—
543C22—432no—
544C22—44no—
545C22—44no—
546C22—48no—
547C22—48no—
548C22C2×C11×#12018yes—
549C22C2×C11×#12014yes—
550C22C2×C11×#12314yes—
551C22C2×C11×#12318yescomplemented
552C22C11×#53414yes—
553C22C11×#546116yes—
554C22C23×D4×C1111yescharacteristic
555C22C23×D4×C1112yes—
556C22C22×C11×#4112yes—
557C22C2×C11×H(5,𝔽2)12yes—
558C4—28no—
559C4—44no—
560C4—44no—
561C4—48no—
562C2—28no—
563C2—28no—
564C2—44no—
565C2—48no—
566C2C11×#240518yesdirect product factor
567C2C22×C11×#12011yescharacteristic
568C2C22×C11×#12311yescharacteristic
569C2C2×C11×#53411yescharacteristic
570C2C2×C11×#54614yes—
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC23C25×C11
prime radicalC24×D4×C11C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C11×#123C2semidirect
3. C23×C11×C22⋊C4C2semidirect
4. C11×#2405C2direct (N × H)
5. C2×C11×#394C2semidirect
6. C2×C11×#386C2semidirect
7. C2×C11×#385C2semidirect
8. C2×C11×#379C2semidirect
9. C2×C11×#379C2semidirect
18. C24×C4×C11C22semidirect
19. C24×C4×C11C22semidirect
21. C2×C11×#123C22semidirect
22. C22×C11×C4⋊C4C22semidirect
26. C22×C11×C22⋊C4C22semidirect
27. C22×C11×C22⋊C4C22semidirect
28. C22×C11×C22⋊C4C22semidirect
29. C22×C11×C22⋊C4C22semidirect
30. C22×C11×C22⋊C4C22semidirect
31. C22×C11×C22⋊C4C22semidirect
32. C11×#394C22semidirect
33. C11×#386C22semidirect
34. C11×#385C22semidirect
35. C11×#379C22semidirect
36. C11×#379C22semidirect
37. C2×C11×#95C22semidirect
74. C23×C4×C11C23semidirect
75. C23×C4×C11C23semidirect
78. C2×C11×C4⋊C4C23semidirect
89. C2×C11×C22⋊C4C23semidirect
90. C2×C11×C22⋊C4C23semidirect
91. C2×C11×C22⋊C4C23semidirect
92. C2×C11×C22⋊C4C23semidirect
93. C2×C11×C22⋊C4C23semidirect
94. C11×#95C23semidirect
95. C2×#2405C11direct (N × H)
175. C22×#123C2×C11semidirect
176. C23×C22⋊C4C2×C11semidirect
177. #2405C2×C11direct (N × H)
178. C2×#394C2×C11semidirect
179. C2×#386C2×C11semidirect
180. C2×#385C2×C11semidirect
181. C2×#379C2×C11semidirect
182. C2×#379C2×C11semidirect
220. C23×C11#123semidirect
259. C24×C4C22×C11semidirect
260. C24×C4C22×C11semidirect
262. C2×#123C22×C11semidirect
263. C22×C4⋊C4C22×C11semidirect
267. C22×C22⋊C4C22×C11semidirect
268. C22×C22⋊C4C22×C11semidirect
269. C22×C22⋊C4C22×C11semidirect
270. C22×C22⋊C4C22×C11semidirect
271. C22×C22⋊C4C22×C11semidirect
272. C22×C22⋊C4C22×C11semidirect
273. #394C22×C11semidirect
274. #386C22×C11semidirect
275. #385C22×C11semidirect
276. #379C22×C11semidirect
277. #379C22×C11semidirect
278. C2×#95C22×C11semidirect
303. C22×C11C2×#123semidirect
350. C23×C4C23×C11semidirect
351. C23×C4C23×C11semidirect
354. C2×C4⋊C4C23×C11semidirect
365. C2×C22⋊C4C23×C11semidirect
366. C2×C22⋊C4C23×C11semidirect
367. C2×C22⋊C4C23×C11semidirect
368. C2×C22⋊C4C23×C11semidirect
369. C2×C22⋊C4C23×C11semidirect
370. #95C23×C11semidirect
375. C2×C11#2405direct (N × H)
458. C11C2×#2405direct (N × H)
496. C23C11×#123semidirect
551. C22C2×C11×#123semidirect
566. C2C11×#2405direct (N × H)

Maximal subgroups

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

subgroupindex
C24×D4×C112
C22×C11×#1232
C23×C11×C22⋊C42
C11×#24052
C2×C11×#3942
C2×C11×#3862
C2×C11×#3852
C2×C11×#3792
C2×#240511