Finite Group Databasebeta

← C11×#22663 #14599856

Subgroups — C11×#22663 #14599856

Order 2816.

1022 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
1C2×C11×#436C211yesmaximal, characteristic
2C2×C11×#428C212yesmaximal, complemented
3C11×#2354C211yesmaximal, characteristic
4D4×C11×C4⋊C4C211yesmaximal, characteristic
5C11×#1948C211yesmaximal, characteristic, complemented
6C11×#1947C211yesmaximal, characteristic, complemented
7C11×#1854C212yesmaximal, complemented
8C11×#1853C212yesmaximal, complemented
9C11×#1844C211yesmaximal, characteristic, complemented
10C11×#1809C212yesmaximal, complemented
11C4×C11×#107C211yesmaximal, characteristic, complemented
12C22×C11×M16C2212yes—
13C2×C4×D4×C11—21no—
14C2×C4×D4×C11C2211yescharacteristic
15C2×C11×#117C2212yes—
16C22×C11×C4⋊C4C2212yes—
17C11×#436C418yescomplemented
18C11×#428—28no—
19C2×C11×#107C2212yes—
20C2×C11×#107C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22C2×C11×#106C2212yes—
23C2×C11×#106C2212yes—
24C2×C11×#106C2212yes—
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2212yes—
27C2×C4×C8×C11C2211yescharacteristic
28C11×#390—21no—
29C11×#389—21no—
30C11×#388—22no—
31C11×#385—22no—
32C11×#384C2211yescharacteristic
33C11×#384C2211yescharacteristic
34C11×#380C2212yes—
35C11×#380C2212yes—
36C4×C11×C4⋊C4—21no—
37C4×C11×C4⋊C4C2211yescharacteristic
38C4×C11×C4⋊C4C2211yescharacteristic
39C11×#340C2212yes—
40C11×#340C2212yes—
41C11×#340C2211yescharacteristic
42C11×#340C2211yescharacteristic
43C22×D4×C11D411yescharacteristic
44C23×C4×C11—22no—
45C23×C4×C11C2312yes—
46C2×C11×M16—24no—
47C2×C11×M16—24no—
48C2×C11×M16C2×C418yescomplemented
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2312yes—
51C22×C8×C11C2311yescharacteristic
52C4×D4×C11—44no—
53C4×D4×C11C2×C414yes—
54C4×D4×C11Q814yes—
55C11×#117—24no—
56C11×#117—42no—
57C2×C11×C4⋊C4—24no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—42no—
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4D412yes—
75C2×C42×C11—22no—
76C2×C42×C11—21no—
77C2×C42×C11—21no—
78C2×C42×C11C2311yescharacteristic
79C11×#107—22no—
80C11×#107—24no—
81C11×#107D414yescomplemented
82C11×#106—24no—
83C11×#106—24no—
84C11×#106—42no—
85C11×C4⋊C8C2×C414yescomplemented
86C11×C22⋊C8C2×C418yescomplemented
87C4×C8×C11C2×C414yescomplemented
88C11×#95—22no—
89C11×#95—21no—
90C11×#95—21no—
91C11×#95—22no—
92#22663C1111yesmaximal, characteristic, direct product factor, Sylow
93C24×C11C2×D412yes—
94C2×D4×C11—22no—
95C2×D4×C11—22no—
96C2×D4×C11C4⋊C414yes—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—44no—
108C22×C4×C11—44no—
109C22×C4×C11—82no—
110C22×C4×C11C22×C414yes—
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×Q814yes—
115C22×C4×C11C2411yescharacteristic
116C11×M16—216no—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11—21no—
120C2×C8×C11—21no—
121C2×C8×C11C22×C412yes—
122C2×C8×C11C22×C414yes—
123C2×C8×C11C22×C412yes—
124C2×C8×C11C2×D412yes—
125C2×C8×C11#4112yes—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—44no—
137C11×C4⋊C4—42no—
138C11×C4⋊C4—42no—
139C11×C4⋊C4—81no—
140C11×C4⋊C4—81no—
141C11×C4⋊C4C4⋊C414yes—
142C11×C4⋊C4C2×D412yes—
143C11×C4⋊C4C2×D412yes—
144C11×C22⋊C4—44no—
145C11×C22⋊C4—44no—
146C11×C22⋊C4—82no—
147C11×C22⋊C4C4⋊C418yes—
148C42×C11—44no—
149C42×C11—42no—
150C42×C11—42no—
151C42×C11C22×C412yes—
152C42×C11C2×Q812yes—
153C2×#436C2×C1111yescharacteristic
154C2×#428C2×C1112yescomplemented
155#2354C2×C1111yescharacteristic
156D4×C4⋊C4C2×C1111yescharacteristic
157#1948C2×C1111yescharacteristic, complemented
158#1947C2×C1111yescharacteristic, complemented
159#1854C2×C1112yescomplemented
160#1853C2×C1112yescomplemented
161#1844C2×C1111yescharacteristic, complemented
162#1809C2×C1112yescomplemented
163C4×#107C2×C1111yescharacteristic, complemented
164C23×C11—22no—
165C23×C11—22no—
166C23×C11—22no—
167C23×C11—22no—
168C23×C11—22no—
169C23×C11—22no—
170C23×C11C2×C4⋊C414yes—
171C23×C11C22×D411yescharacteristic
172D4×C11—28no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—24no—
178C2×C4×C11—24no—
179C2×C4×C11—24no—
180C2×C4×C11—24no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—41no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—41no—
199C2×C4×C11—88no—
200C2×C4×C11C2×C4⋊C412yes—
201C2×C4×C11C2×C4⋊C414yes—
202C2×C4×C11C2×C4⋊C412yes—
203C2×C4×C11AGL(1,ℤ/8)12yes—
204C2×C4×C11#13712yes—
205C2×C4×C11C23×C411yescharacteristic
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C22×Q811yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11H(5,𝔽2)11yescharacteristic
210C2×C4×C112−1+411yescharacteristic
211C8×C11—24no—
212C8×C11—22no—
213C8×C11C4×D414yescomplemented
214C22×M16C22×C1112yes—
215C2×C4×D4—21no—
216C2×C4×D4C22×C1111yescharacteristic
217C2×#117C22×C1112yes—
218C22×C4⋊C4C22×C1112yes—
219#436C4×C1118yescomplemented
220#428—28no—
221C2×#107C22×C1111yescharacteristic
222C2×#107C22×C1112yes—
223C2×#107C22×C1111yescharacteristic
224C2×#106C22×C1112yes—
225C2×#106C22×C1112yes—
226C2×#106C22×C1112yes—
227C2×C4⋊C8C22×C1111yescharacteristic
228C2×C22⋊C8C22×C1112yes—
229C2×C4×C8C22×C1111yescharacteristic
230#390—21no—
231#389—21no—
232#388—22no—
233#385—22no—
234#384C22×C1111yescharacteristic
235#384C22×C1111yescharacteristic
236#380C22×C1112yes—
237#380C22×C1112yes—
238C4×C4⋊C4—21no—
239C4×C4⋊C4C22×C1111yescharacteristic
240C4×C4⋊C4C22×C1111yescharacteristic
241#340C22×C1112yes—
242#340C22×C1112yes—
243#340C22×C1111yescharacteristic
244#340C22×C1111yescharacteristic
245C22×C11—24no—
246C22×C11—24no—
247C22×C11—24no—
248C22×C11—42no—
249C22×C11—42no—
250C22×C11—42no—
251C22×C11—42no—
252C22×C11C22×C4⋊C411yescharacteristic
253C22×C11D4211yescharacteristic
254C22×C11#54711yescharacteristic
255C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
256C22×C11C2×#13711yescharacteristic
257C22×C11#57711yescharacteristic
258C22×C11#57711yescharacteristic
259C4×C11—24no—
260C4×C11—22no—
261C4×C11—42no—
262C4×C11—42no—
263C4×C11—81no—
264C4×C11—81no—
265C4×C11—82no—
266C4×C11—82no—
267C4×C11#42814yescomplemented
268C4×C11C2×C4×D411yescharacteristic
269C4×C11#52011yescharacteristic
270C4×C11D4×Q811yescharacteristic
271C4×C11#55411yescharacteristic
272C22×D4D4×C1111yescharacteristic
273C23×C4—22no—
274C23×C4C23×C1112yes—
275C2×M16—24no—
276C2×M16—24no—
277C2×M16C2×C4×C1118yescomplemented
278C22×C8C23×C1112yes—
279C22×C8C23×C1111yescharacteristic
280C22×C8C23×C1111yescharacteristic
281C4×D4—44no—
282C4×D4C2×C4×C1114yes—
283C4×D4Q8×C1114yes—
284#117—24no—
285#117—42no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4D4×C1111yescharacteristic
294C2×C4⋊C4C23×C1112yes—
295C2×C4⋊C4C23×C1112yes—
296C2×C4⋊C4C23×C1111yescharacteristic
297C2×C4⋊C4C23×C1111yescharacteristic
298C2×C4⋊C4C23×C1111yescharacteristic
299C2×C4⋊C4C23×C1111yescharacteristic
300C2×C22⋊C4—22no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4D4×C1112yes—
304C2×C42—22no—
305C2×C42—21no—
306C2×C42—21no—
307C2×C42C23×C1111yescharacteristic
308#107—22no—
309#107—24no—
310#107D4×C1114yescomplemented
311#106—24no—
312#106—24no—
313#106—42no—
314C4⋊C8C2×C4×C1114yescomplemented
315C22⋊C8C2×C4×C1118yescomplemented
316C4×C8C2×C4×C1114yescomplemented
317#95—22no—
318#95—21no—
319#95—21no—
320#95—22no—
321C2×C11—44no—
322C2×C11D4×C4⋊C411yescharacteristic
323C2×C11C2×#42811yescharacteristic
324C2×C11#291211yescharacteristic
325C2×C11#327211yescharacteristic
326C2×C11#327811yescharacteristic
327C2×C11#335411yescharacteristic
328C2×C11#335611yescharacteristic
329C24C2×D4×C1112yes—
330C2×D4—22no—
331C2×D4—22no—
332C2×D4C11×C4⋊C414yes—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—44no—
344C22×C4—44no—
345C22×C4—82no—
346C22×C4C22×C4×C1114yes—
347C22×C4C2×D4×C1112yes—
348C22×C4C2×D4×C1111yescharacteristic
349C22×C4C2×D4×C1111yescharacteristic
350C22×C4C2×Q8×C1114yes—
351C22×C4C24×C1111yescharacteristic
352M16—216no—
353C2×C8—22no—
354C2×C8—22no—
355C2×C8—21no—
356C2×C8—21no—
357C2×C8C22×C4×C1112yes—
358C2×C8C22×C4×C1114yes—
359C2×C8C22×C4×C1112yes—
360C2×C8C2×D4×C1112yes—
361C2×C8C11×#4112yes—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—44no—
373C4⋊C4—42no—
374C4⋊C4—42no—
375C4⋊C4—81no—
376C4⋊C4—81no—
377C4⋊C4C11×C4⋊C414yes—
378C4⋊C4C2×D4×C1112yes—
379C4⋊C4C2×D4×C1112yes—
380C22⋊C4—44no—
381C22⋊C4—44no—
382C22⋊C4—82no—
383C22⋊C4C11×C4⋊C418yes—
384C42—44no—
385C42—42no—
386C42—42no—
387C42C22×C4×C1112yes—
388C42C2×Q8×C1112yes—
389C11#2266311yescharacteristic, direct product factor, Sylow
390C23—22no—
391C23—22no—
392C23—22no—
393C23—22no—
394C23—22no—
395C23—22no—
396C23C2×C11×C4⋊C414yes—
397C23C22×D4×C1111yescharacteristic
398D4—28no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—24no—
404C2×C4—24no—
405C2×C4—24no—
406C2×C4—24no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—41no—
425C2×C4—88no—
426C2×C4C2×C11×C4⋊C412yes—
427C2×C4C2×C11×C4⋊C414yes—
428C2×C4C2×C11×C4⋊C412yes—
429C2×C4C11×AGL(1,ℤ/8)12yes—
430C2×C4C11×#13712yes—
431C2×C4C23×C4×C1111yescharacteristic
432C2×C4C22×D4×C1111yescharacteristic
433C2×C4C22×Q8×C1111yescharacteristic
434C2×C4C2×C11×#4111yescharacteristic
435C2×C4C11×H(5,𝔽2)11yescharacteristic
436C2×C4C11×2−1+411yescharacteristic
437C8—24no—
438C8—22no—
439C8C4×D4×C1114yescomplemented
440C22—24no—
441C22—24no—
442C22—24no—
443C22—42no—
444C22—42no—
445C22—42no—
446C22—42no—
447C22C22×C11×C4⋊C411yescharacteristic
448C22D42×C1111yescharacteristic
449C22C11×#54711yescharacteristic
450C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
451C22C2×C11×#13711yescharacteristic
452C22C11×#57711yescharacteristic
453C22C11×#57711yescharacteristic
454C4—22no—
455C4—24no—
456C4—42no—
457C4—42no—
458C4—82no—
459C4—82no—
460C4—81no—
461C4—81no—
462C4C11×#42814yescomplemented
463C4C2×C4×D4×C1111yescharacteristic
464C4C11×#52011yescharacteristic
465C4D4×Q8×C1111yescharacteristic
466C4C11×#55411yescharacteristic
467C2—44no—
468C2D4×C11×C4⋊C411yescharacteristic
469C2C2×C11×#42811yescharacteristic
470C2C11×#291211yescharacteristic
471C2C11×#327211yescharacteristic
472C2C11×#327811yescharacteristic
473C2C11×#335411yescharacteristic
474C2C11×#335611yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#428C2semidirect
5. C11×#1948C2semidirect
6. C11×#1947C2semidirect
7. C11×#1854C2semidirect
8. C11×#1853C2semidirect
9. C11×#1844C2semidirect
10. C11×#1809C2semidirect
11. C4×C11×#107C2semidirect
17. C11×#436C4semidirect
48. C2×C11×M16C2×C4semidirect
81. C11×#107D4semidirect
85. C11×C4⋊C8C2×C4semidirect
86. C11×C22⋊C8C2×C4semidirect
87. C4×C8×C11C2×C4semidirect
92. #22663C11direct (N × H)
154. C2×#428C2×C11semidirect
157. #1948C2×C11semidirect
158. #1947C2×C11semidirect
159. #1854C2×C11semidirect
160. #1853C2×C11semidirect
161. #1844C2×C11semidirect
162. #1809C2×C11semidirect
163. C4×#107C2×C11semidirect
213. C8×C11C4×D4semidirect
219. #436C4×C11semidirect
267. C4×C11#428semidirect
277. C2×M16C2×C4×C11semidirect
310. #107D4×C11semidirect
314. C4⋊C8C2×C4×C11semidirect
315. C22⋊C8C2×C4×C11semidirect
316. C4×C8C2×C4×C11semidirect
389. C11#22663direct (N × H)
439. C8C4×D4×C11semidirect
462. C4C11×#428semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4362
C2×C11×#4282
C11×#23542
D4×C11×C4⋊C42
C11×#19482
C11×#19472
C11×#18542
C11×#18532
C11×#18442
C11×#18092
C4×C11×#1072
#2266311