Finite Group Databasebeta

← C2×C11×#2487 #14611957

Subgroups — C2×C11×#2487 #14611957

Order 2816.

3374 conjugacy classes of subgroups.

The subgroup lattice has 476 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×#2487C2116yesmaximal, direct product factor
4C2×C11×#400C212yesmaximal, complemented
5C2×C11×#399C212yesmaximal, complemented
6C2×C11×#389C212yesmaximal, complemented
7C2×C11×#386C212yesmaximal
8C2×C11×#385C212yesmaximal, complemented
9C2×C11×#380C211yesmaximal, characteristic, complemented
10C2×C11×#380C212yesmaximal, complemented
11C23×D4×C11C2211yescharacteristic
12C24×C4×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×C4×C11C2212yes—
15C2×C4×D4×C11—28no—
16C2×C4×D4×C11C2218yes—
17C22×C11×C4⋊C4—28no—
18C22×C11×C4⋊C4C2212yes—
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2212yes—
21C22×C11×C4⋊C4C2212yes—
22C22×C11×C4⋊C4C2214yes—
23C22×C11×C4⋊C4C2218yescomplemented
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2212yes—
27C22×C11×C22⋊C4C2214yes—
28C22×C42×C11C2211yescharacteristic
29C11×#400C22116yescomplemented
30C11×#399C22116yescomplemented
31C11×#389C22116yescomplemented
32C11×#386C22116yes—
33C11×#385C22116yescomplemented
34C11×#380C22116yescomplemented
35C11×#380C2218yescomplemented
36C2×C11×#95C2212yes—
37C2×C11×#95C2214yes—
38C2×C11×#95C2214yes—
39C25×C11C2311yescharacteristic
40C25×C11C2311yescharacteristic
41C22×D4×C11—24no—
42C22×D4×C11—24no—
43C22×D4×C11Q818yes—
44C22×D4×C11C2314yes—
45C23×C4×C11—28no—
46C23×C4×C11—28no—
47C23×C4×C11—24no—
48C23×C4×C11—28no—
49C23×C4×C11—48no—
50C23×C4×C11D418yes—
51C23×C4×C11C2314yes—
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2314yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2314yes—
56C23×C4×C11C2314yes—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2318yes—
60C23×C4×C11C2311yescharacteristic
61C4×D4×C11—232no—
62C2×C11×C4⋊C4—28no—
63C2×C11×C4⋊C4—28no—
64C2×C11×C4⋊C4—232no—
65C2×C11×C4⋊C4—24no—
66C2×C11×C4⋊C4—28no—
67C2×C11×C4⋊C4—48no—
68C2×C11×C4⋊C4C2318yes—
69C2×C11×C4⋊C4C2318yes—
70C2×C11×C4⋊C4C2314yes—
71C2×C11×C4⋊C4C2318yes—
72C2×C11×C4⋊C4C23116yes—
73C2×C11×C22⋊C4—24no—
74C2×C11×C22⋊C4—28no—
75C2×C11×C22⋊C4—24no—
76C2×C11×C22⋊C4—48no—
77C2×C11×C22⋊C4C2314yes—
78C2×C11×C22⋊C4C2314yes—
79C2×C11×C22⋊C4C2318yes—
80C2×C11×C22⋊C4C23116yes—
81C2×C42×C11—24no—
82C2×C42×C11C2314yes—
83C11×#95C23116yes—
84C11×#95C2318yes—
85C11×#95C23116yes—
86C2×#2487C1111yesmaximal, characteristic, direct product factor, Sylow
87C24×C11—24no—
88C24×C11—24no—
89C24×C11—22no—
90C24×C11—24no—
91C24×C11—22no—
92C24×C11—24no—
93C24×C11C2×D414yes—
94C24×C11C2×Q814yes—
95C24×C11C2×Q814yes—
96C24×C11#4114yes—
97C24×C11C2412yes—
98C24×C11C2412yes—
99C24×C11C2411yescharacteristic
100C2×D4×C11—232no—
101C2×D4×C11—28no—
102C2×D4×C11—28no—
103C2×D4×C11C2×Q8116yes—
104C22×C4×C11—22no—
105C22×C4×C11—24no—
106C22×C4×C11—22no—
107C22×C4×C11—232no—
108C22×C4×C11—216no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—216no—
112C22×C4×C11—28no—
113C22×C4×C11—28no—
114C22×C4×C11—28no—
115C22×C4×C11—24no—
116C22×C4×C11—28no—
117C22×C4×C11—28no—
118C22×C4×C11—24no—
119C22×C4×C11—28no—
120C22×C4×C11—28no—
121C22×C4×C11—216no—
122C22×C4×C11—416no—
123C22×C4×C11—432no—
124C22×C4×C11—416no—
125C22×C4×C11C2×D414yes—
126C22×C4×C11C2×D4116yes—
127C22×C4×C11C2×D414yes—
128C22×C4×C11C2×Q814yes—
129C22×C4×C11#4118yes—
130C22×C4×C11C2412yes—
131C22×C4×C11C2418yes—
132C22×C4×C11C2418yes—
133C22×C4×C11C2412yes—
134C22×C4×C11C2412yes—
135C22×C4×C11C2412yes—
136C22×C4×C11C2412yes—
137C11×C4⋊C4—216no—
138C11×C4⋊C4—216no—
139C11×C4⋊C4—28no—
140C11×C4⋊C4—216no—
141C11×C4⋊C4—416no—
142C11×C22⋊C4—28no—
143C11×C22⋊C4—216no—
144C11×C22⋊C4—28no—
145C11×C22⋊C4—416no—
146C42×C11—28no—
147C22×C4×D4C2×C1111yescharacteristic
148C23×C4⋊C4C2×C1111yescharacteristic, complemented
149#2487C2×C11116yesdirect product factor
150C2×#400C2×C1112yescomplemented
151C2×#399C2×C1112yescomplemented
152C2×#389C2×C1112yescomplemented
153C2×#386C2×C1112yes—
154C2×#385C2×C1112yescomplemented
155C2×#380C2×C1111yescharacteristic, complemented
156C2×#380C2×C1112yescomplemented
157C23×C11—28no—
158C23×C11—28no—
159C23×C11—216no—
160C23×C11—216no—
161C23×C11—24no—
162C23×C11—24no—
163C23×C11—28no—
164C23×C11—216no—
165C23×C11—22no—
166C23×C11—24no—
167C23×C11—22no—
168C23×C11—24no—
169C23×C11—44no—
170C23×C11—44no—
171C23×C11—48no—
172C23×C11C22⋊Q8116yes—
173C23×C11C22×D414yes—
174C23×C11C22×D412yes—
175C23×C11C22×Q814yes—
176C23×C11C22×Q814yes—
177C23×C11C22×Q812yes—
178C23×C11C2×#4114yes—
179C23×C11C2×#4112yes—
180C23×C11C2×#4114yes—
181C23×C11H(5,𝔽2)14yes—
182C23×C11C2511yescharacteristic
183D4×C11—232no—
184C2×C4×C11—28no—
185C2×C4×C11—28no—
186C2×C4×C11—22no—
187C2×C4×C11—24no—
188C2×C4×C11—22no—
189C2×C4×C11—232no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—28no—
193C2×C4×C11—28no—
194C2×C4×C11—28no—
195C2×C4×C11—24no—
196C2×C4×C11—28no—
197C2×C4×C11—28no—
198C2×C4×C11—24no—
199C2×C4×C11—28no—
200C2×C4×C11—432no—
201C2×C4×C11—44no—
202C2×C4×C11—44no—
203C2×C4×C11—416no—
204C2×C4×C11—416no—
205C2×C4×C11—416no—
206C2×C4×C11#123116yes—
207C2×C4×C11C22×D414yes—
208C2×C4×C11C22×D414yes—
209C2×C4×C11C22×Q814yes—
210C2×C4×C11C2×#4118yes—
211C23×D4C22×C1111yescharacteristic
212C24×C4C22×C1111yescharacteristic
213C24×C4C22×C1111yescharacteristic
214C24×C4C22×C1112yes—
215C2×C4×D4—28no—
216C2×C4×D4C22×C1118yes—
217C22×C4⋊C4—28no—
218C22×C4⋊C4C22×C1112yes—
219C22×C4⋊C4C22×C1111yescharacteristic
220C22×C4⋊C4C22×C1112yes—
221C22×C4⋊C4C22×C1112yes—
222C22×C4⋊C4C22×C1114yes—
223C22×C4⋊C4C22×C1118yescomplemented
224C22×C22⋊C4C22×C1111yescharacteristic
225C22×C22⋊C4C22×C1111yescharacteristic
226C22×C22⋊C4C22×C1112yes—
227C22×C22⋊C4C22×C1114yes—
228C22×C42C22×C1111yescharacteristic
229#400C22×C11116yescomplemented
230#399C22×C11116yescomplemented
231#389C22×C11116yescomplemented
232#386C22×C11116yes—
233#385C22×C11116yescomplemented
234#380C22×C11116yescomplemented
235#380C22×C1118yescomplemented
236C2×#95C22×C1112yes—
237C2×#95C22×C1114yes—
238C2×#95C22×C1114yes—
239C22×C11—24no—
240C22×C11—24no—
241C22×C11—28no—
242C22×C11—28no—
243C22×C11—232no—
244C22×C11—24no—
245C22×C11—28no—
246C22×C11—42no—
247C22×C11—42no—
248C22×C11—44no—
249C22×C11—416no—
250C22×C11C2×C22⋊Q818yes—
251C22×C11C2×C22⋊Q814yes—
252C22×C11C2×#12314yes—
253C22×C11#53514yes—
254C22×C11#55318yes—
255C22×C11#55418yes—
256C22×C11C23×D411yescharacteristic
257C22×C11C23×Q811yescharacteristic
258C22×C11C22×#4111yescharacteristic
259C22×C11C22×#4112yes—
260C22×C11C2×H(5,𝔽2)12yes—
261C4×C11—24no—
262C4×C11—24no—
263C4×C11—42no—
264C4×C11—42no—
265C4×C11—48no—
266C4×C11—48no—
267C4×C11C2×#12318yes—
268C25C23×C1111yescharacteristic
269C25C23×C1111yescharacteristic
270C22×D4—24no—
271C22×D4—24no—
272C22×D4Q8×C1118yes—
273C22×D4C23×C1114yes—
274C23×C4—28no—
275C23×C4—28no—
276C23×C4—24no—
277C23×C4—28no—
278C23×C4—48no—
279C23×C4D4×C1118yes—
280C23×C4C23×C1111yescharacteristic
281C23×C4C23×C1114yes—
282C23×C4C23×C1114yes—
283C23×C4C23×C1111yescharacteristic
284C23×C4C23×C1114yes—
285C23×C4C23×C1111yescharacteristic
286C23×C4C23×C1114yes—
287C23×C4C23×C1111yescharacteristic
288C23×C4C23×C1118yes—
289C23×C4C23×C1111yescharacteristic
290C4×D4—232no—
291C2×C4⋊C4—28no—
292C2×C4⋊C4—28no—
293C2×C4⋊C4—232no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—28no—
296C2×C4⋊C4—48no—
297C2×C4⋊C4C23×C1118yes—
298C2×C4⋊C4C23×C1118yes—
299C2×C4⋊C4C23×C1114yes—
300C2×C4⋊C4C23×C1118yes—
301C2×C4⋊C4C23×C11116yes—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—28no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—48no—
306C2×C22⋊C4C23×C1114yes—
307C2×C22⋊C4C23×C1114yes—
308C2×C22⋊C4C23×C1118yes—
309C2×C22⋊C4C23×C11116yes—
310C2×C42—24no—
311C2×C42C23×C1114yes—
312#95C23×C11116yes—
313#95C23×C1118yes—
314#95C23×C11116yes—
315C2×C11—28no—
316C2×C11—44no—
317C2×C11#248718yesdirect product factor
318C2×C11C22×C22⋊Q811yescharacteristic
319C2×C11C22×#12311yescharacteristic
320C2×C11C2×#53511yescharacteristic
321C2×C11C2×#55312yes—
322C2×C11C2×#55412yes—
323C24—24no—
324C24—24no—
325C24—22no—
326C24—24no—
327C24—22no—
328C24—24no—
329C24C2×D4×C1114yes—
330C24C2×Q8×C1114yes—
331C24C2×Q8×C1114yes—
332C24C11×#4114yes—
333C24C24×C1112yes—
334C24C24×C1112yes—
335C24C24×C1111yescharacteristic
336C2×D4—232no—
337C2×D4—28no—
338C2×D4—28no—
339C2×D4C2×Q8×C11116yes—
340C22×C4—22no—
341C22×C4—24no—
342C22×C4—22no—
343C22×C4—232no—
344C22×C4—216no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—216no—
348C22×C4—28no—
349C22×C4—28no—
350C22×C4—28no—
351C22×C4—24no—
352C22×C4—28no—
353C22×C4—28no—
354C22×C4—24no—
355C22×C4—28no—
356C22×C4—28no—
357C22×C4—216no—
358C22×C4—416no—
359C22×C4—432no—
360C22×C4—416no—
361C22×C4C2×D4×C1114yes—
362C22×C4C2×D4×C11116yes—
363C22×C4C2×D4×C1114yes—
364C22×C4C2×Q8×C1114yes—
365C22×C4C11×#4118yes—
366C22×C4C24×C1112yes—
367C22×C4C24×C1118yes—
368C22×C4C24×C1118yes—
369C22×C4C24×C1112yes—
370C22×C4C24×C1112yes—
371C22×C4C24×C1112yes—
372C22×C4C24×C1112yes—
373C4⋊C4—216no—
374C4⋊C4—216no—
375C4⋊C4—28no—
376C4⋊C4—216no—
377C4⋊C4—416no—
378C22⋊C4—28no—
379C22⋊C4—216no—
380C22⋊C4—28no—
381C22⋊C4—416no—
382C42—28no—
383C11C2×#248711yescharacteristic, direct product factor, Sylow
384C23—28no—
385C23—28no—
386C23—216no—
387C23—216no—
388C23—24no—
389C23—24no—
390C23—28no—
391C23—216no—
392C23—22no—
393C23—24no—
394C23—22no—
395C23—24no—
396C23—44no—
397C23—44no—
398C23—48no—
399C23C11×C22⋊Q8116yes—
400C23C22×D4×C1114yes—
401C23C22×D4×C1112yes—
402C23C22×Q8×C1114yes—
403C23C22×Q8×C1114yes—
404C23C22×Q8×C1112yes—
405C23C2×C11×#4114yes—
406C23C2×C11×#4112yes—
407C23C2×C11×#4114yes—
408C23C11×H(5,𝔽2)14yes—
409C23C25×C1111yescharacteristic
410D4—232no—
411C2×C4—28no—
412C2×C4—28no—
413C2×C4—22no—
414C2×C4—24no—
415C2×C4—22no—
416C2×C4—232no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—28no—
420C2×C4—28no—
421C2×C4—28no—
422C2×C4—24no—
423C2×C4—28no—
424C2×C4—28no—
425C2×C4—24no—
426C2×C4—28no—
427C2×C4—432no—
428C2×C4—44no—
429C2×C4—44no—
430C2×C4—416no—
431C2×C4—416no—
432C2×C4—416no—
433C2×C4C11×#123116yes—
434C2×C4C22×D4×C1114yes—
435C2×C4C22×D4×C1114yes—
436C2×C4C22×Q8×C1114yes—
437C2×C4C2×C11×#4118yes—
438C22—24no—
439C22—24no—
440C22—28no—
441C22—28no—
442C22—232no—
443C22—24no—
444C22—28no—
445C22—42no—
446C22—42no—
447C22—44no—
448C22—416no—
449C22C2×C11×C22⋊Q818yes—
450C22C2×C11×C22⋊Q814yes—
451C22C2×C11×#12314yes—
452C22C11×#53514yes—
453C22C11×#55318yes—
454C22C11×#55418yes—
455C22C23×D4×C1111yescharacteristic
456C22C23×Q8×C1111yescharacteristic
457C22C22×C11×#4111yescharacteristic
458C22C22×C11×#4112yes—
459C22C2×C11×H(5,𝔽2)12yes—
460C4—24no—
461C4—24no—
462C4—42no—
463C4—48no—
464C4—42no—
465C4—48no—
466C4C2×C11×#12318yes—
467C2—28no—
468C2—44no—
469C2C11×#248718yesdirect product factor
470C2C22×C11×C22⋊Q811yescharacteristic
471C2C22×C11×#12311yescharacteristic
472C2C2×C11×#53511yescharacteristic
473C2C2×C11×#55312yes—
474C2C2×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×#2487C2direct (N × H)
4. C2×C11×#400C2semidirect
5. C2×C11×#399C2semidirect
6. C2×C11×#389C2semidirect
8. C2×C11×#385C2semidirect
9. C2×C11×#380C2semidirect
10. C2×C11×#380C2semidirect
23. C22×C11×C4⋊C4C22semidirect
29. C11×#400C22semidirect
30. C11×#399C22semidirect
31. C11×#389C22semidirect
33. C11×#385C22semidirect
34. C11×#380C22semidirect
35. C11×#380C22semidirect
86. C2×#2487C11direct (N × H)
148. C23×C4⋊C4C2×C11semidirect
149. #2487C2×C11direct (N × H)
150. C2×#400C2×C11semidirect
151. C2×#399C2×C11semidirect
152. C2×#389C2×C11semidirect
154. C2×#385C2×C11semidirect
155. C2×#380C2×C11semidirect
156. C2×#380C2×C11semidirect
223. C22×C4⋊C4C22×C11semidirect
229. #400C22×C11semidirect
230. #399C22×C11semidirect
231. #389C22×C11semidirect
233. #385C22×C11semidirect
234. #380C22×C11semidirect
235. #380C22×C11semidirect
317. C2×C11#2487direct (N × H)
383. C11C2×#2487direct (N × H)
469. C2C11×#2487direct (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×#24872
C2×C11×#4002
C2×C11×#3992
C2×C11×#3892
C2×C11×#3862
C2×C11×#3852
C2×C11×#3802
C2×#248711