Finite Group Databasebeta

← C11×#34967 #14612160

Subgroups — C11×#34967 #14612160

Order 2816.

2164 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2522C214yesmaximal, complemented
2C11×#2516C214yesmaximal, complemented
3C11×#2464C214yesmaximal, complemented
4C11×#2457C214yesmaximal, complemented
5C11×#2402C211yesmaximal, characteristic, complemented
6C11×#2397C211yesmaximal, characteristic, complemented
7C11×#2392C212yesmaximal, complemented
8C4×C11×#123C214yesmaximal, complemented
9C4×C11×#121C214yesmaximal, complemented
10C11×#2298C211yesmaximal, characteristic, complemented
11C42×D4×C11C212yesmaximal, complemented
12C2×C11×#123C2214yes—
13C2×C11×#121C2214yes—
14C2×C4×D4×C11C2212yes—
15C2×C4×D4×C11C2214yes—
16C2×C4×D4×C11C2214yes—
17C2×C4×D4×C11C2214yes—
18C2×C11×#117C2211yescharacteristic
19C22×C42×C11C2214yes—
20C11×#400C2214yes—
21C11×#399C2214yes—
22C11×#398C2212yes—
23C11×#398C2214yes—
24C11×#397C2212yes—
25C11×#396C2214yes—
26C11×#394C2212yes—
27C11×#394C2214yes—
28C11×#392C2212yes—
29C11×#392C2214yes—
30C11×#390C2214yes—
31C11×#389C2214yes—
32C11×#388C2214yes—
33C11×#388C2214yes—
34C11×#388C2214yes—
35C11×#388C2214yes—
36C11×#388C2214yes—
37C11×#387C2214yes—
38C11×#387C2214yes—
39C11×#387C2214yes—
40C11×#386C2214yes—
41C11×#386C2214yes—
42C11×#386C2214yes—
43C11×#385C2214yes—
44C11×#381C2214yes—
45C11×#380C2214yes—
46C4×C11×C4⋊C4C2212yes—
47C4×C11×C4⋊C4C2214yes—
48C4×C11×C4⋊C4C2214yes—
49C4×C11×C4⋊C4C2212yes—
50C4×C11×C22⋊C4C2214yes—
51C4×C11×C22⋊C4C2214yes—
52C4×C11×C22⋊C4C2214yes—
53C4×C11×C22⋊C4C2214yes—
54C4×C11×C22⋊C4C2212yes—
55C11×#376C2211yescharacteristic
56C43×C11C2211yescharacteristic
57C22×D4×C11C2312yes—
58C22×D4×C11C2314yes—
59C22×D4×C11C2314yes—
60C23×C4×C11C2314yes—
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2314yes—
63C23×C4×C11C2314yes—
64C11×#123—216no—
65C11×#121—216no—
66C4×D4×C11—216no—
67C4×D4×C11—28no—
68C4×D4×C11—48no—
69C4×D4×C11—48no—
70C11×#117—24no—
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C4⋊C4C2314yes—
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C4⋊C4C2314yes—
75C2×C11×C4⋊C4C2314yes—
76C2×C11×C4⋊C4C2314yes—
77C2×C11×C4⋊C4C2314yes—
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C22⋊C4C2312yes—
80C2×C11×C22⋊C4C2314yes—
81C2×C11×C22⋊C4C2314yes—
82C2×C11×C22⋊C4C2314yes—
83C2×C11×C22⋊C4C2314yes—
84C2×C11×C22⋊C4C2314yes—
85C2×C11×C22⋊C4C2314yes—
86C2×C11×C22⋊C4C2314yes—
87C2×C11×C22⋊C4C2314yes—
88C2×C11×C22⋊C4C2314yes—
89C2×C11×C22⋊C4C2314yes—
90C2×C42×C11—48no—
91C2×C42×C11C2314yes—
92C2×C42×C11C2312yes—
93C2×C42×C11C2314yes—
94C2×C42×C11C2312yes—
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2314yes—
97C2×C42×C11C2314yes—
98C2×C42×C11C2311yescharacteristic
99C11×#95C2314yes—
100C11×#95C2314yes—
101C11×#95C2314yes—
102C11×#95C2312yes—
103C11×#95C2312yes—
104C11×#95C2314yes—
105C11×#95C2314yes—
106C11×#95C2314yes—
107C11×#95C2314yes—
108C11×#95C2314yes—
109C11×#95C2314yes—
110#34967C1111yesmaximal, characteristic, direct product factor, Sylow
111C24×C11C2411yescharacteristic
112C24×C11C2414yes—
113C2×D4×C11—28no—
114C2×D4×C11—28no—
115C2×D4×C11—28no—
116C2×D4×C11—28no—
117C2×D4×C11—24no—
118C2×D4×C11—28no—
119C2×D4×C11—44no—
120C2×D4×C11—44no—
121C22×C4×C11—28no—
122C22×C4×C11—22no—
123C22×C4×C11—28no—
124C22×C4×C11—28no—
125C22×C4×C11—28no—
126C22×C4×C11—28no—
127C22×C4×C11—28no—
128C22×C4×C11—28no—
129C22×C4×C11—24no—
130C22×C4×C11—44no—
131C22×C4×C11—44no—
132C22×C4×C11C2414yes—
133C22×C4×C11C2412yes—
134C22×C4×C11C2414yes—
135C22×C4×C11C2414yes—
136C22×C4×C11C2411yescharacteristic
137C22×C4×C11C2414yes—
138C22×C4×C11C2412yes—
139C22×C4×C11C2414yes—
140C22×C4×C11C2411yescharacteristic
141C11×C4⋊C4—24no—
142C11×C4⋊C4—28no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—28no—
145C11×C4⋊C4—28no—
146C11×C4⋊C4—28no—
147C11×C4⋊C4—44no—
148C11×C4⋊C4—44no—
149C11×C22⋊C4—28no—
150C11×C22⋊C4—24no—
151C11×C22⋊C4—28no—
152C11×C22⋊C4—28no—
153C11×C22⋊C4—28no—
154C11×C22⋊C4—28no—
155C11×C22⋊C4—44no—
156C11×C22⋊C4—44no—
157C11×C22⋊C4—44no—
158C11×C22⋊C4—44no—
159C11×C22⋊C4#41116yes—
160C42×C11—22no—
161C42×C11—28no—
162C42×C11—24no—
163C42×C11—28no—
164C42×C11—24no—
165C42×C11—44no—
166C42×C11—44no—
167C42×C11#4114yes—
168#2522C2×C1114yescomplemented
169#2516C2×C1114yescomplemented
170#2464C2×C1114yescomplemented
171#2457C2×C1114yescomplemented
172#2402C2×C1111yescharacteristic, complemented
173#2397C2×C1111yescharacteristic, complemented
174#2392C2×C1112yescomplemented
175C4×#123C2×C1114yescomplemented
176C4×#121C2×C1114yescomplemented
177#2298C2×C1111yescharacteristic, complemented
178C42×D4C2×C1112yescomplemented
179C23×C11—24no—
180C23×C11—24no—
181C23×C11—24no—
182C23×C11—24no—
183C23×C11—24no—
184C23×C11—24no—
185C23×C11—21no—
186C23×C11—24no—
187C23×C11—22no—
188C23×C11C2×#4118yes—
189C23×C11C2511yescharacteristic
190D4×C11—216no—
191D4×C11—416no—
192D4×C11—416no—
193C2×C4×C11—24no—
194C2×C4×C11—24no—
195C2×C4×C11—24no—
196C2×C4×C11—24no—
197C2×C4×C11—24no—
198C2×C4×C11—22no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—21no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—22no—
211C2×C4×C11—416no—
212C2×C4×C11—416no—
213C2×C4×C11—416no—
214C2×C4×C11—44no—
215C2×C4×C11C2×#4118yes—
216C2×C4×C11C2×#4114yes—
217C2×C4×C11C2×#4118yes—
218C2×C4×C11C2×#4112yes—
219C2×C4×C11H(5,𝔽2)14yes—
220C2×#123C22×C1114yes—
221C2×#121C22×C1114yes—
222C2×C4×D4C22×C1112yes—
223C2×C4×D4C22×C1114yes—
224C2×C4×D4C22×C1114yes—
225C2×C4×D4C22×C1114yes—
226C2×#117C22×C1111yescharacteristic
227C22×C42C22×C1114yes—
228#400C22×C1114yes—
229#399C22×C1114yes—
230#398C22×C1112yes—
231#398C22×C1114yes—
232#397C22×C1112yes—
233#396C22×C1114yes—
234#394C22×C1112yes—
235#394C22×C1114yes—
236#392C22×C1112yes—
237#392C22×C1114yes—
238#390C22×C1114yes—
239#389C22×C1114yes—
240#388C22×C1114yes—
241#388C22×C1114yes—
242#388C22×C1114yes—
243#388C22×C1114yes—
244#388C22×C1114yes—
245#387C22×C1114yes—
246#387C22×C1114yes—
247#387C22×C1114yes—
248#386C22×C1114yes—
249#386C22×C1114yes—
250#386C22×C1114yes—
251#385C22×C1114yes—
252#381C22×C1114yes—
253#380C22×C1114yes—
254C4×C4⋊C4C22×C1112yes—
255C4×C4⋊C4C22×C1114yes—
256C4×C4⋊C4C22×C1114yes—
257C4×C4⋊C4C22×C1112yes—
258C4×C22⋊C4C22×C1114yes—
259C4×C22⋊C4C22×C1114yes—
260C4×C22⋊C4C22×C1114yes—
261C4×C22⋊C4C22×C1114yes—
262C4×C22⋊C4C22×C1112yes—
263#376C22×C1111yescharacteristic
264C43C22×C1111yescharacteristic
265C22×C11—28no—
266C22×C11—28no—
267C22×C11—28no—
268C22×C11—44no—
269C22×C11—44no—
270C22×C11—44no—
271C22×C11—44no—
272C22×C11—42no—
273C22×C11—41no—
274C22×C11—44no—
275C22×C11C22×#4111yescharacteristic
276C22×C11C22×#4114yes—
277C22×C11C2×H(5,𝔽2)12yes—
278C4×C11—24no—
279C4×C11—28no—
280C4×C11—28no—
281C4×C11—42no—
282C4×C11—44no—
283C4×C11—41no—
284C4×C11—44no—
285C4×C11—44no—
286C4×C11#54014yes—
287C22×D4C23×C1112yes—
288C22×D4C23×C1114yes—
289C22×D4C23×C1114yes—
290C23×C4C23×C1111yescharacteristic
291C23×C4C23×C1114yes—
292C23×C4C23×C1114yes—
293C23×C4C23×C1114yes—
294#123—216no—
295#121—216no—
296C4×D4—216no—
297C4×D4—28no—
298C4×D4—48no—
299C4×D4—48no—
300#117—24no—
301C2×C4⋊C4C23×C1112yes—
302C2×C4⋊C4C23×C1114yes—
303C2×C4⋊C4C23×C1112yes—
304C2×C4⋊C4C23×C1114yes—
305C2×C4⋊C4C23×C1114yes—
306C2×C4⋊C4C23×C1114yes—
307C2×C4⋊C4C23×C1114yes—
308C2×C4⋊C4C23×C1114yes—
309C2×C22⋊C4C23×C1112yes—
310C2×C22⋊C4C23×C1114yes—
311C2×C22⋊C4C23×C1114yes—
312C2×C22⋊C4C23×C1114yes—
313C2×C22⋊C4C23×C1114yes—
314C2×C22⋊C4C23×C1114yes—
315C2×C22⋊C4C23×C1114yes—
316C2×C22⋊C4C23×C1114yes—
317C2×C22⋊C4C23×C1114yes—
318C2×C22⋊C4C23×C1114yes—
319C2×C22⋊C4C23×C1114yes—
320C2×C42—48no—
321C2×C42C23×C1111yescharacteristic
322C2×C42C23×C1112yes—
323C2×C42C23×C1114yes—
324C2×C42C23×C1114yes—
325C2×C42C23×C1112yes—
326C2×C42C23×C1114yes—
327C2×C42C23×C1114yes—
328C2×C42C23×C1111yescharacteristic
329#95C23×C1114yes—
330#95C23×C1114yes—
331#95C23×C1114yes—
332#95C23×C1112yes—
333#95C23×C1112yes—
334#95C23×C1114yes—
335#95C23×C1114yes—
336#95C23×C1114yes—
337#95C23×C1114yes—
338#95C23×C1114yes—
339#95C23×C1114yes—
340C2×C11—48no—
341C2×C11—81no—
342C2×C11#344412yes—
343C2×C11C2×#54011yescharacteristic
344C2×C11#348114yes—
345C24C24×C1111yescharacteristic
346C24C24×C1114yes—
347C2×D4—28no—
348C2×D4—28no—
349C2×D4—28no—
350C2×D4—28no—
351C2×D4—24no—
352C2×D4—28no—
353C2×D4—44no—
354C2×D4—44no—
355C22×C4—28no—
356C22×C4—22no—
357C22×C4—28no—
358C22×C4—28no—
359C22×C4—28no—
360C22×C4—28no—
361C22×C4—28no—
362C22×C4—28no—
363C22×C4—24no—
364C22×C4—44no—
365C22×C4—44no—
366C22×C4C24×C1114yes—
367C22×C4C24×C1112yes—
368C22×C4C24×C1114yes—
369C22×C4C24×C1114yes—
370C22×C4C24×C1111yescharacteristic
371C22×C4C24×C1114yes—
372C22×C4C24×C1112yes—
373C22×C4C24×C1114yes—
374C22×C4C24×C1111yescharacteristic
375C4⋊C4—24no—
376C4⋊C4—28no—
377C4⋊C4—24no—
378C4⋊C4—28no—
379C4⋊C4—28no—
380C4⋊C4—28no—
381C4⋊C4—44no—
382C4⋊C4—44no—
383C22⋊C4—28no—
384C22⋊C4—24no—
385C22⋊C4—28no—
386C22⋊C4—28no—
387C22⋊C4—28no—
388C22⋊C4—28no—
389C22⋊C4—44no—
390C22⋊C4—44no—
391C22⋊C4—44no—
392C22⋊C4—44no—
393C22⋊C4C11×#41116yes—
394C42—22no—
395C42—28no—
396C42—24no—
397C42—28no—
398C42—24no—
399C42—44no—
400C42—44no—
401C42C11×#4114yes—
402C11#3496711yescharacteristic, direct product factor, Sylow
403C23—24no—
404C23—24no—
405C23—24no—
406C23—24no—
407C23—24no—
408C23—24no—
409C23—21no—
410C23—24no—
411C23—22no—
412C23C2×C11×#4118yes—
413C23C25×C1111yescharacteristic
414D4—216no—
415D4—416no—
416D4—416no—
417C2×C4—24no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—24no—
421C2×C4—24no—
422C2×C4—22no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—24no—
428C2×C4—21no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—22no—
435C2×C4—416no—
436C2×C4—416no—
437C2×C4—416no—
438C2×C4—44no—
439C2×C4C2×C11×#4118yes—
440C2×C4C2×C11×#4114yes—
441C2×C4C2×C11×#4118yes—
442C2×C4C2×C11×#4112yes—
443C2×C4C11×H(5,𝔽2)14yes—
444C22—28no—
445C22—28no—
446C22—28no—
447C22—44no—
448C22—44no—
449C22—44no—
450C22—44no—
451C22—42no—
452C22—41no—
453C22—44no—
454C22C22×C11×#4111yescharacteristic
455C22C22×C11×#4114yes—
456C22C2×C11×H(5,𝔽2)12yes—
457C4—24no—
458C4—28no—
459C4—28no—
460C4—42no—
461C4—44no—
462C4—41no—
463C4—44no—
464C4—44no—
465C4C11×#54014yes—
466C2—48no—
467C2—81no—
468C2C11×#344412yes—
469C2C2×C11×#54011yescharacteristic
470C2C11×#348114yes—
subgroupG/H
centerC22×C4×C11C24
commutator, Frattini, cosocleC23C25×C11
socleC23×C11C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2522C2semidirect
2. C11×#2516C2semidirect
3. C11×#2464C2semidirect
4. C11×#2457C2semidirect
5. C11×#2402C2semidirect
6. C11×#2397C2semidirect
7. C11×#2392C2semidirect
8. C4×C11×#123C2semidirect
9. C4×C11×#121C2semidirect
10. C11×#2298C2semidirect
11. C42×D4×C11C2semidirect
110. #34967C11direct (N × H)
168. #2522C2×C11semidirect
169. #2516C2×C11semidirect
170. #2464C2×C11semidirect
171. #2457C2×C11semidirect
172. #2402C2×C11semidirect
173. #2397C2×C11semidirect
174. #2392C2×C11semidirect
175. C4×#123C2×C11semidirect
176. C4×#121C2×C11semidirect
177. #2298C2×C11semidirect
178. C42×D4C2×C11semidirect
402. C11#34967direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#25222
C11×#25162
C11×#24642
C11×#24572
C11×#24022
C11×#23972
C11×#23922
C4×C11×#1232
C4×C11×#1212
C11×#22982
C42×D4×C112
#3496711