Finite Group Databasebeta

← C2×C11×#2455 #14611845

Subgroups — C2×C11×#2455 #14611845

Order 2816.

3894 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#123C212yesmaximal, complemented
2C22×C4×D4×C11C212yesmaximal, complemented
3C11×#2455C2116yesmaximal, direct product factor
4C2×C11×#399C211yesmaximal, characteristic, complemented
5C2×C11×#394C212yesmaximal, complemented
6C2×C11×#392C211yesmaximal, characteristic
7C2×C11×#389C212yesmaximal, complemented
8C2×C11×#388C212yesmaximal, complemented
9C2×C11×#385C212yesmaximal, complemented
10C2×C11×#385C211yesmaximal, characteristic, complemented
11C23×D4×C11C2212yes—
12C23×D4×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×C4×C11C2212yes—
15C2×C11×#123—216no—
16C2×C11×#123C22116yescomplemented
17C2×C4×D4×C11—216no—
18C2×C4×D4×C11C22116yescomplemented
19C22×C11×C4⋊C4C2212yes—
20C22×C11×C4⋊C4C2212yes—
21C22×C11×C4⋊C4C2212yes—
22C22×C11×C4⋊C4C2212yes—
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2212yes—
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2212yes—
27C22×C11×C22⋊C4C2212yes—
28C22×C11×C22⋊C4C2212yes—
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C11×C22⋊C4C2212yes—
31C22×C42×C11C2212yes—
32C11×#399C2218yescomplemented
33C11×#394C22116yescomplemented
34C11×#392C2218yes—
35C11×#389C22116yescomplemented
36C11×#388C22116yescomplemented
37C11×#385C2218yescomplemented
38C11×#385C22116yescomplemented
39C2×C11×#95C2211yescharacteristic
40C2×C11×#95C2212yes—
41C2×C11×#95C2211yescharacteristic
42C2×C11×#95C2212yes—
43C25×C11C2312yes—
44C25×C11C2311yescharacteristic
45C22×D4×C11—28no—
46C22×D4×C11—28no—
47C22×D4×C11—28no—
48C22×D4×C11—28no—
49C22×D4×C11—42no—
50C22×D4×C11C2318yes—
51C22×D4×C11C2314yes—
52C23×C4×C11—28no—
53C23×C4×C11—28no—
54C23×C4×C11—28no—
55C23×C4×C11—42no—
56C23×C4×C11—44no—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2312yes—
59C23×C4×C11C2312yes—
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2314yes—
62C23×C4×C11C2318yes—
63C23×C4×C11C2312yes—
64C23×C4×C11C2312yes—
65C23×C4×C11C2312yes—
66C11×#123—264no—
67C4×D4×C11—264no—
68C2×C11×C4⋊C4—28no—
69C2×C11×C4⋊C4—28no—
70C2×C11×C4⋊C4—28no—
71C2×C11×C4⋊C4—28no—
72C2×C11×C4⋊C4—42no—
73C2×C11×C4⋊C4C2318yes—
74C2×C11×C4⋊C4C2318yes—
75C2×C11×C4⋊C4C2318yes—
76C2×C11×C4⋊C4C2318yes—
77C2×C11×C4⋊C4C2314yes—
78C2×C11×C22⋊C4—28no—
79C2×C11×C22⋊C4—24no—
80C2×C11×C22⋊C4—28no—
81C2×C11×C22⋊C4—28no—
82C2×C11×C22⋊C4—28no—
83C2×C11×C22⋊C4—42no—
84C2×C11×C22⋊C4D4116yescomplemented
85C2×C11×C22⋊C4C2318yes—
86C2×C11×C22⋊C4C2318yes—
87C2×C11×C22⋊C4C2318yes—
88C2×C11×C22⋊C4C2314yes—
89C2×C11×C22⋊C4C2318yes—
90C2×C11×C22⋊C4C2314yes—
91C2×C11×C22⋊C4C2318yes—
92C2×C42×C11—28no—
93C2×C42×C11C2318yes—
94C11×#95C2318yes—
95C11×#95C2318yes—
96C11×#95C2314yes—
97C11×#95C2314yes—
98C2×#2455C1111yesmaximal, characteristic, direct product factor, Sylow
99C24×C11—24no—
100C24×C11—24no—
101C24×C11—24no—
102C24×C11—24no—
103C24×C11—24no—
104C24×C11—24no—
105C24×C11—22no—
106C24×C11—24no—
107C24×C11—22no—
108C24×C11—24no—
109C24×C11C2×D418yes—
110C24×C11#4114yes—
111C24×C11C2414yes—
112C24×C11C2412yes—
113C24×C11C2411yescharacteristic
114C2×D4×C11—264no—
115C2×D4×C11—216no—
116C2×D4×C11—216no—
117C2×D4×C11—216no—
118C2×D4×C11—216no—
119C2×D4×C11—44no—
120C2×D4×C11—416no—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—24no—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—24no—
131C22×C4×C11—216no—
132C22×C4×C11—24no—
133C22×C4×C11—24no—
134C22×C4×C11—24no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—24no—
138C22×C4×C11—216no—
139C22×C4×C11—216no—
140C22×C4×C11—44no—
141C22×C4×C11—48no—
142C22×C4×C11—416no—
143C22×C4×C11—432no—
144C22×C4×C11C2×D418yes—
145C22×C4×C11C2×D418yes—
146C22×C4×C11#4118yes—
147C22×C4×C11C2412yes—
148C22×C4×C11C2414yes—
149C22×C4×C11C2414yes—
150C22×C4×C11C2412yes—
151C22×C4×C11C2414yes—
152C22×C4×C11C2414yes—
153C22×C4×C11C2414yes—
154C11×C4⋊C4—216no—
155C11×C4⋊C4—216no—
156C11×C4⋊C4—216no—
157C11×C4⋊C4—216no—
158C11×C4⋊C4—44no—
159C11×C22⋊C4—216no—
160C11×C22⋊C4—28no—
161C11×C22⋊C4—216no—
162C11×C22⋊C4—216no—
163C11×C22⋊C4—216no—
164C11×C22⋊C4—44no—
165C11×C22⋊C4C2×D4132yescomplemented
166C42×C11—216no—
167C22×#123C2×C1112yescomplemented
168C22×C4×D4C2×C1112yescomplemented
169#2455C2×C11116yesdirect product factor
170C2×#399C2×C1111yescharacteristic, complemented
171C2×#394C2×C1112yescomplemented
172C2×#392C2×C1111yescharacteristic
173C2×#389C2×C1112yescomplemented
174C2×#388C2×C1112yescomplemented
175C2×#385C2×C1112yescomplemented
176C2×#385C2×C1111yescharacteristic, complemented
177C23×C11—216no—
178C23×C11—216no—
179C23×C11—28no—
180C23×C11—216no—
181C23×C11—216no—
182C23×C11—24no—
183C23×C11—24no—
184C23×C11—24no—
185C23×C11—24no—
186C23×C11—24no—
187C23×C11—24no—
188C23×C11—22no—
189C23×C11—24no—
190C23×C11—22no—
191C23×C11—24no—
192C23×C11—48no—
193C23×C11—48no—
194C23×C11—44no—
195C23×C11—48no—
196C23×C11—48no—
197C23×C11—48no—
198C23×C11—44no—
199C23×C11C22×D418yes—
200C23×C11C22×D414yes—
201C23×C11C2×#4114yes—
202C23×C11C2×#4112yes—
203C23×C11C2×#4114yes—
204C23×C11H(5,𝔽2)12yes—
205C23×C112−1+412yes—
206C23×C11C2511yescharacteristic
207D4×C11—264no—
208D4×C11—416no—
209C2×C4×C11—216no—
210C2×C4×C11—216no—
211C2×C4×C11—216no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—24no—
228C2×C4×C11—416no—
229C2×C4×C11—432no—
230C2×C4×C11—48no—
231C2×C4×C11—48no—
232C2×C4×C11—44no—
233C2×C4×C11—44no—
234C2×C4×C11C22×D418yes—
235C2×C4×C11C22×D418yes—
236C2×C4×C11C2×#4118yes—
237C23×D4C22×C1112yes—
238C23×D4C22×C1111yescharacteristic
239C24×C4C22×C1111yescharacteristic
240C24×C4C22×C1112yes—
241C2×#123—216no—
242C2×#123C22×C11116yescomplemented
243C2×C4×D4—216no—
244C2×C4×D4C22×C11116yescomplemented
245C22×C4⋊C4C22×C1112yes—
246C22×C4⋊C4C22×C1112yes—
247C22×C4⋊C4C22×C1112yes—
248C22×C4⋊C4C22×C1112yes—
249C22×C4⋊C4C22×C1111yescharacteristic
250C22×C22⋊C4C22×C1112yes—
251C22×C22⋊C4C22×C1111yescharacteristic
252C22×C22⋊C4C22×C1112yes—
253C22×C22⋊C4C22×C1112yes—
254C22×C22⋊C4C22×C1112yes—
255C22×C22⋊C4C22×C1111yescharacteristic
256C22×C22⋊C4C22×C1112yes—
257C22×C42C22×C1112yes—
258#399C22×C1118yescomplemented
259#394C22×C11116yescomplemented
260#392C22×C1118yes—
261#389C22×C11116yescomplemented
262#388C22×C11116yescomplemented
263#385C22×C1118yescomplemented
264#385C22×C11116yescomplemented
265C2×#95C22×C1111yescharacteristic
266C2×#95C22×C1112yes—
267C2×#95C22×C1111yescharacteristic
268C2×#95C22×C1112yes—
269C22×C11—28no—
270C22×C11—28no—
271C22×C11—24no—
272C22×C11—28no—
273C22×C11—28no—
274C22×C11—44no—
275C22×C11—44no—
276C22×C11—42no—
277C22×C11—44no—
278C22×C11—44no—
279C22×C11—432no—
280C22×C11—416no—
281C22×C11—44no—
282C22×C11—42no—
283C22×C11#52518yes—
284C22×C11#53914yes—
285C22×C11D4214yes—
286C22×C11#54718yes—
287C22×C11#55914yes—
288C22×C11C23×D412yes—
289C22×C11C22×#4111yescharacteristic
290C22×C11C22×#4112yes—
291C22×C11C2×H(5,𝔽2)11yescharacteristic
292C22×C11C2×2−1+411yescharacteristic
293C4×C11—28no—
294C4×C11—28no—
295C4×C11—28no—
296C4×C11—44no—
297C4×C11—44no—
298C4×C11—42no—
299C4×C11—42no—
300C25C23×C1112yes—
301C25C23×C1111yescharacteristic
302C22×D4—28no—
303C22×D4—28no—
304C22×D4—28no—
305C22×D4—28no—
306C22×D4—42no—
307C22×D4C23×C1118yes—
308C22×D4C23×C1114yes—
309C23×C4—28no—
310C23×C4—28no—
311C23×C4—28no—
312C23×C4—42no—
313C23×C4—44no—
314C23×C4C23×C1112yes—
315C23×C4C23×C1111yescharacteristic
316C23×C4C23×C1112yes—
317C23×C4C23×C1111yescharacteristic
318C23×C4C23×C1114yes—
319C23×C4C23×C1118yes—
320C23×C4C23×C1112yes—
321C23×C4C23×C1112yes—
322C23×C4C23×C1112yes—
323#123—264no—
324C4×D4—264no—
325C2×C4⋊C4—28no—
326C2×C4⋊C4—28no—
327C2×C4⋊C4—28no—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4C23×C1118yes—
331C2×C4⋊C4C23×C1118yes—
332C2×C4⋊C4C23×C1118yes—
333C2×C4⋊C4C23×C1118yes—
334C2×C4⋊C4C23×C1114yes—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4D4×C11116yescomplemented
342C2×C22⋊C4C23×C1118yes—
343C2×C22⋊C4C23×C1118yes—
344C2×C22⋊C4C23×C1118yes—
345C2×C22⋊C4C23×C1118yes—
346C2×C22⋊C4C23×C1114yes—
347C2×C22⋊C4C23×C1114yes—
348C2×C22⋊C4C23×C1118yes—
349C2×C42—28no—
350C2×C42C23×C1118yes—
351#95C23×C1118yes—
352#95C23×C1118yes—
353#95C23×C1114yes—
354#95C23×C1114yes—
355C2×C11—48no—
356C2×C11—44no—
357C2×C11#245518yesdirect product factor
358C2×C11C2×#52512yes—
359C2×C11C2×#53911yescharacteristic
360C2×C11C2×D4211yescharacteristic
361C2×C11C2×#54712yes—
362C2×C11C2×#55911yescharacteristic
363C24—24no—
364C24—24no—
365C24—24no—
366C24—24no—
367C24—24no—
368C24—24no—
369C24—22no—
370C24—24no—
371C24—22no—
372C24—24no—
373C24C2×D4×C1118yes—
374C24C11×#4114yes—
375C24C24×C1114yes—
376C24C24×C1112yes—
377C24C24×C1111yescharacteristic
378C2×D4—264no—
379C2×D4—216no—
380C2×D4—216no—
381C2×D4—216no—
382C2×D4—216no—
383C2×D4—44no—
384C2×D4—416no—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—24no—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—24no—
395C22×C4—216no—
396C22×C4—24no—
397C22×C4—24no—
398C22×C4—24no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—24no—
402C22×C4—216no—
403C22×C4—216no—
404C22×C4—44no—
405C22×C4—48no—
406C22×C4—416no—
407C22×C4—432no—
408C22×C4C2×D4×C1118yes—
409C22×C4C2×D4×C1118yes—
410C22×C4C11×#4118yes—
411C22×C4C24×C1112yes—
412C22×C4C24×C1114yes—
413C22×C4C24×C1114yes—
414C22×C4C24×C1112yes—
415C22×C4C24×C1114yes—
416C22×C4C24×C1114yes—
417C22×C4C24×C1114yes—
418C4⋊C4—216no—
419C4⋊C4—216no—
420C4⋊C4—216no—
421C4⋊C4—216no—
422C4⋊C4—44no—
423C22⋊C4—216no—
424C22⋊C4—28no—
425C22⋊C4—216no—
426C22⋊C4—216no—
427C22⋊C4—216no—
428C22⋊C4—44no—
429C22⋊C4C2×D4×C11132yescomplemented
430C42—216no—
431C11C2×#245511yescharacteristic, direct product factor, Sylow
432C23—216no—
433C23—216no—
434C23—28no—
435C23—216no—
436C23—216no—
437C23—24no—
438C23—24no—
439C23—24no—
440C23—24no—
441C23—24no—
442C23—24no—
443C23—22no—
444C23—24no—
445C23—22no—
446C23—24no—
447C23—48no—
448C23—48no—
449C23—44no—
450C23—48no—
451C23—48no—
452C23—48no—
453C23—44no—
454C23C22×D4×C1118yes—
455C23C22×D4×C1114yes—
456C23C2×C11×#4114yes—
457C23C2×C11×#4112yes—
458C23C2×C11×#4114yes—
459C23C11×H(5,𝔽2)12yes—
460C23C11×2−1+412yes—
461C23C25×C1111yescharacteristic
462D4—264no—
463D4—416no—
464C2×C4—216no—
465C2×C4—216no—
466C2×C4—216no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—24no—
483C2×C4—416no—
484C2×C4—432no—
485C2×C4—48no—
486C2×C4—48no—
487C2×C4—44no—
488C2×C4—44no—
489C2×C4C22×D4×C1118yes—
490C2×C4C22×D4×C1118yes—
491C2×C4C2×C11×#4118yes—
492C22—28no—
493C22—28no—
494C22—24no—
495C22—28no—
496C22—28no—
497C22—44no—
498C22—44no—
499C22—42no—
500C22—44no—
501C22—44no—
502C22—432no—
503C22—416no—
504C22—44no—
505C22—42no—
506C22C11×#52518yes—
507C22C11×#53914yes—
508C22D42×C1114yes—
509C22C11×#54718yes—
510C22C11×#55914yes—
511C22C23×D4×C1112yes—
512C22C22×C11×#4111yescharacteristic
513C22C22×C11×#4112yes—
514C22C2×C11×H(5,𝔽2)11yescharacteristic
515C22C2×C11×2−1+411yescharacteristic
516C4—28no—
517C4—28no—
518C4—28no—
519C4—44no—
520C4—44no—
521C4—42no—
522C4—42no—
523C2—48no—
524C2—44no—
525C2C11×#245518yesdirect product factor
526C2C2×C11×#52512yes—
527C2C2×C11×#53911yescharacteristic
528C2C2×D42×C1111yescharacteristic
529C2C2×C11×#54712yes—
530C2C2×C11×#55911yescharacteristic
subgroupG/H
center, socleC24×C11C24
commutator, Frattini, cosocleC23C25×C11
prime radicalC2×C11×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#123C2semidirect
2. C22×C4×D4×C11C2semidirect
3. C11×#2455C2direct (N × H)
4. C2×C11×#399C2semidirect
5. C2×C11×#394C2semidirect
7. C2×C11×#389C2semidirect
8. C2×C11×#388C2semidirect
9. C2×C11×#385C2semidirect
10. C2×C11×#385C2semidirect
16. C2×C11×#123C22semidirect
18. C2×C4×D4×C11C22semidirect
32. C11×#399C22semidirect
33. C11×#394C22semidirect
35. C11×#389C22semidirect
36. C11×#388C22semidirect
37. C11×#385C22semidirect
38. C11×#385C22semidirect
84. C2×C11×C22⋊C4D4semidirect
98. C2×#2455C11direct (N × H)
165. C11×C22⋊C4C2×D4semidirect
167. C22×#123C2×C11semidirect
168. C22×C4×D4C2×C11semidirect
169. #2455C2×C11direct (N × H)
170. C2×#399C2×C11semidirect
171. C2×#394C2×C11semidirect
173. C2×#389C2×C11semidirect
174. C2×#388C2×C11semidirect
175. C2×#385C2×C11semidirect
176. C2×#385C2×C11semidirect
242. C2×#123C22×C11semidirect
244. C2×C4×D4C22×C11semidirect
258. #399C22×C11semidirect
259. #394C22×C11semidirect
261. #389C22×C11semidirect
262. #388C22×C11semidirect
263. #385C22×C11semidirect
264. #385C22×C11semidirect
341. C2×C22⋊C4D4×C11semidirect
357. C2×C11#2455direct (N × H)
429. C22⋊C4C2×D4×C11semidirect
431. C11C2×#2455direct (N × H)
525. C2C11×#2455direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1232
C22×C4×D4×C112
C11×#24552
C2×C11×#3992
C2×C11×#3942
C2×C11×#3922
C2×C11×#3892
C2×C11×#3882
C2×C11×#3852
C2×#245511