Finite Group Databasebeta

← C11×#36695 #14613888

Subgroups — C11×#36695 #14613888

Order 2816.

1664 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2845C211yesmaximal, characteristic, complemented
2C11×#2837C214yesmaximal, complemented
3C11×#2831C214yesmaximal, complemented
4C11×#2829C214yesmaximal, complemented
5C11×#2820C212yesmaximal, complemented
6C11×#2819C211yesmaximal, characteristic
7C11×#2396C214yesmaximal, complemented
8C11×#2395C214yesmaximal, complemented
9C11×#2392C214yesmaximal, complemented
10C4×C11×#125C211yesmaximal, characteristic, complemented
11C4×C11×#124C212yesmaximal, complemented
12C2×C11×#125C2211yescharacteristic
13C2×C11×#124C2212yes—
14C2×C4×Q8×C11C2212yes—
15C2×C4×D4×C11C2214yes—
16C2×C4×D4×C11C2212yes—
17C2×C11×#117C2214yes—
18C11×#400C2214yes—
19C11×#400C2214yes—
20C11×#399C2214yes—
21C11×#399C2214yes—
22C11×#398C2214yes—
23C11×#398C2214yes—
24C11×#398C2214yes—
25C11×#398C2214yes—
26C11×#397C2214yes—
27C11×#397C2214yes—
28C11×#397C2214yes—
29C11×#397C2214yes—
30C11×#396C2214yes—
31C11×#396C2214yes—
32C11×#396C2214yes—
33C11×#396C2214yes—
34C11×#395C2214yes—
35C11×#394C2214yes—
36C11×#394C2214yes—
37C11×#394C2214yes—
38C11×#394C2214yes—
39C11×#394C2214yes—
40C11×#393C2214yes—
41C11×#392C2214yes—
42C11×#391C2212yes—
43C11×#390C2212yes—
44C11×#389C2212yes—
45C11×#388C2214yes—
46C11×#388C2214yes—
47C11×#387C2214yes—
48C11×#382C2212yes—
49C11×#382C2211yescharacteristic
50C4×C11×C4⋊C4C2214yes—
51C4×C11×C4⋊C4C2212yes—
52C4×C11×C4⋊C4C2214yes—
53C4×C11×C22⋊C4C2214yes—
54C4×C11×C22⋊C4C2214yes—
55C4×C11×C22⋊C4C2214yes—
56C43×C11C2211yescharacteristic
57C22×Q8×C11C2312yes—
58C22×D4×C11C2312yes—
59C22×D4×C11C2314yes—
60C23×C4×C11C2314yes—
61C11×#125—24no—
62C11×#124—28no—
63C4×Q8×C11—44no—
64C4×D4×C11—48no—
65C4×D4×C11—44no—
66C11×#117—48no—
67C2×C11×C4⋊C4C2314yes—
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C4⋊C4C2314yes—
70C2×C11×C4⋊C4C2314yes—
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⋊C4C2312yes—
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C22⋊C4C2314yes—
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×C11C2311yescharacteristic
91C2×C42×C11C2312yes—
92C2×C42×C11C2314yes—
93C2×C42×C11C2314yes—
94C2×C42×C11C2312yes—
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C11×#95C2314yes—
98C11×#95C2314yes—
99C11×#95C2314yes—
100C11×#95C2314yes—
101C11×#95C2314yes—
102C11×#95C2314yes—
103C11×#95C2314yes—
104C11×#95C2314yes—
105C11×#95C2314yes—
106C11×#95C2314yes—
107C11×#95C2314yes—
108#36695C1111yesmaximal, characteristic, direct product factor, Sylow
109C24×C11C2414yes—
110C2×Q8×C11—24no—
111C2×Q8×C11—42no—
112C2×Q8×C11—42no—
113C2×D4×C11—24no—
114C2×D4×C11—42no—
115C2×D4×C11—44no—
116C2×D4×C11—42no—
117C2×D4×C11—44no—
118C2×D4×C11—44no—
119C22×C4×C11—28no—
120C22×C4×C11—28no—
121C22×C4×C11—28no—
122C22×C4×C11C2411yescharacteristic
123C22×C4×C11C2414yes—
124C22×C4×C11C2414yes—
125C22×C4×C11C2414yes—
126C22×C4×C11C2412yes—
127C22×C4×C11C2414yes—
128C22×C4×C11C2414yes—
129C22×C4×C11C2411yescharacteristic
130C22×C4×C11C2412yes—
131C22×C4×C11C2411yescharacteristic
132C11×C4⋊C4—24no—
133C11×C4⋊C4—28no—
134C11×C4⋊C4—42no—
135C11×C4⋊C4—44no—
136C11×C4⋊C4—44no—
137C11×C4⋊C4—44no—
138C11×C4⋊C4—44no—
139C11×C4⋊C4—44no—
140C11×C4⋊C4—42no—
141C11×C4⋊C4—44no—
142C11×C4⋊C4—42no—
143C11×C4⋊C4—44no—
144C11×C22⋊C4—28no—
145C11×C22⋊C4—28no—
146C11×C22⋊C4—44no—
147C11×C22⋊C4—44no—
148C11×C22⋊C4—44no—
149C11×C22⋊C4—44no—
150C11×C22⋊C4—44no—
151C11×C22⋊C4—44no—
152C11×C22⋊C4—44no—
153C11×C22⋊C4—44no—
154C11×C22⋊C4—44no—
155C42×C11—28no—
156C42×C11—28no—
157C42×C11—24no—
158C42×C11—22no—
159C42×C11—41no—
160C42×C11—42no—
161C42×C11#4114yes—
162#2845C2×C1111yescharacteristic, complemented
163#2837C2×C1114yescomplemented
164#2831C2×C1114yescomplemented
165#2829C2×C1114yescomplemented
166#2820C2×C1112yescomplemented
167#2819C2×C1111yescharacteristic
168#2396C2×C1114yescomplemented
169#2395C2×C1114yescomplemented
170#2392C2×C1114yescomplemented
171C4×#125C2×C1111yescharacteristic, complemented
172C4×#124C2×C1112yescomplemented
173C23×C11—24no—
174C23×C11—24no—
175C23×C11—24no—
176C23×C11—24no—
177C23×C11—24no—
178C23×C11—24no—
179C23×C11—24no—
180C23×C11C2511yescharacteristic
181Q8×C11—48no—
182D4×C11—48no—
183D4×C11—416no—
184C2×C4×C11—22no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—22no—
188C2×C4×C11—24no—
189C2×C4×C11—24no—
190C2×C4×C11—24no—
191C2×C4×C11—22no—
192C2×C4×C11—24no—
193C2×C4×C11—24no—
194C2×C4×C11—24no—
195C2×C4×C11—24no—
196C2×C4×C11—24no—
197C2×C4×C11—21no—
198C2×C4×C11—24no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—416no—
209C2×C4×C11C2×#4112yes—
210C2×C4×C11C2×#4114yes—
211C2×C4×C11H(5,𝔽2)14yes—
212C2×C4×C112−1+412yes—
213C2×#125C22×C1111yescharacteristic
214C2×#124C22×C1112yes—
215C2×C4×Q8C22×C1112yes—
216C2×C4×D4C22×C1114yes—
217C2×C4×D4C22×C1112yes—
218C2×#117C22×C1114yes—
219#400C22×C1114yes—
220#400C22×C1114yes—
221#399C22×C1114yes—
222#399C22×C1114yes—
223#398C22×C1114yes—
224#398C22×C1114yes—
225#398C22×C1114yes—
226#398C22×C1114yes—
227#397C22×C1114yes—
228#397C22×C1114yes—
229#397C22×C1114yes—
230#397C22×C1114yes—
231#396C22×C1114yes—
232#396C22×C1114yes—
233#396C22×C1114yes—
234#396C22×C1114yes—
235#395C22×C1114yes—
236#394C22×C1114yes—
237#394C22×C1114yes—
238#394C22×C1114yes—
239#394C22×C1114yes—
240#394C22×C1114yes—
241#393C22×C1114yes—
242#392C22×C1114yes—
243#391C22×C1112yes—
244#390C22×C1112yes—
245#389C22×C1112yes—
246#388C22×C1114yes—
247#388C22×C1114yes—
248#387C22×C1114yes—
249#382C22×C1111yescharacteristic
250#382C22×C1112yes—
251C4×C4⋊C4C22×C1114yes—
252C4×C4⋊C4C22×C1112yes—
253C4×C4⋊C4C22×C1114yes—
254C4×C22⋊C4C22×C1114yes—
255C4×C22⋊C4C22×C1114yes—
256C4×C22⋊C4C22×C1114yes—
257C43C22×C1111yescharacteristic
258C22×C11—44no—
259C22×C11—44no—
260C22×C11—44no—
261C22×C11—44no—
262C22×C11—44no—
263C22×C11—44no—
264C22×C11—44no—
265C22×C11C22×#4111yescharacteristic
266C22×C11C2×H(5,𝔽2)12yes—
267C22×C11C2×2−1+411yescharacteristic
268C22×C11#58512yes—
269C22×C11#58511yescharacteristic
270C4×C11—24no—
271C4×C11—22no—
272C4×C11—44no—
273C4×C11—44no—
274C4×C11—44no—
275C4×C11—42no—
276C4×C11—44no—
277C4×C11—44no—
278C4×C11—41no—
279C4×C11#56214yes—
280C22×Q8C23×C1112yes—
281C22×D4C23×C1112yes—
282C22×D4C23×C1114yes—
283C23×C4C23×C1114yes—
284#125—24no—
285#124—28no—
286C4×Q8—44no—
287C4×D4—48no—
288C4×D4—44no—
289#117—48no—
290C2×C4⋊C4C23×C1114yes—
291C2×C4⋊C4C23×C1112yes—
292C2×C4⋊C4C23×C1114yes—
293C2×C4⋊C4C23×C1114yes—
294C2×C4⋊C4C23×C1112yes—
295C2×C4⋊C4C23×C1114yes—
296C2×C4⋊C4C23×C1112yes—
297C2×C4⋊C4C23×C1114yes—
298C2×C4⋊C4C23×C1112yes—
299C2×C4⋊C4C23×C1114yes—
300C2×C4⋊C4C23×C1114yes—
301C2×C4⋊C4C23×C1114yes—
302C2×C22⋊C4C23×C1114yes—
303C2×C22⋊C4C23×C1114yes—
304C2×C22⋊C4C23×C1114yes—
305C2×C22⋊C4C23×C1114yes—
306C2×C22⋊C4C23×C1114yes—
307C2×C22⋊C4C23×C1114yes—
308C2×C22⋊C4C23×C1114yes—
309C2×C22⋊C4C23×C1114yes—
310C2×C22⋊C4C23×C1114yes—
311C2×C22⋊C4C23×C1114yes—
312C2×C22⋊C4C23×C1114yes—
313C2×C42C23×C1114yes—
314C2×C42C23×C1114yes—
315C2×C42C23×C1112yes—
316C2×C42C23×C1111yescharacteristic
317C2×C42C23×C1112yes—
318C2×C42C23×C1111yescharacteristic
319C2×C42C23×C1111yescharacteristic
320#95C23×C1114yes—
321#95C23×C1114yes—
322#95C23×C1114yes—
323#95C23×C1114yes—
324#95C23×C1114yes—
325#95C23×C1114yes—
326#95C23×C1114yes—
327#95C23×C1114yes—
328#95C23×C1114yes—
329#95C23×C1114yes—
330#95C23×C1114yes—
331C2×C11—84no—
332C2×C11#346012yes—
333C2×C11#346111yescharacteristic
334C2×C11C2×#56211yescharacteristic
335C2×C11#352912yes—
336C2×C11#353111yescharacteristic
337C24C24×C1114yes—
338C2×Q8—24no—
339C2×Q8—42no—
340C2×Q8—42no—
341C2×D4—24no—
342C2×D4—42no—
343C2×D4—44no—
344C2×D4—42no—
345C2×D4—44no—
346C2×D4—44no—
347C22×C4—28no—
348C22×C4—28no—
349C22×C4—28no—
350C22×C4C24×C1111yescharacteristic
351C22×C4C24×C1114yes—
352C22×C4C24×C1114yes—
353C22×C4C24×C1114yes—
354C22×C4C24×C1112yes—
355C22×C4C24×C1114yes—
356C22×C4C24×C1114yes—
357C22×C4C24×C1111yescharacteristic
358C22×C4C24×C1112yes—
359C22×C4C24×C1111yescharacteristic
360C4⋊C4—24no—
361C4⋊C4—28no—
362C4⋊C4—44no—
363C4⋊C4—44no—
364C4⋊C4—42no—
365C4⋊C4—44no—
366C4⋊C4—42no—
367C4⋊C4—44no—
368C4⋊C4—42no—
369C4⋊C4—44no—
370C4⋊C4—44no—
371C4⋊C4—44no—
372C22⋊C4—28no—
373C22⋊C4—28no—
374C22⋊C4—44no—
375C22⋊C4—44no—
376C22⋊C4—44no—
377C22⋊C4—44no—
378C22⋊C4—44no—
379C22⋊C4—44no—
380C22⋊C4—44no—
381C22⋊C4—44no—
382C22⋊C4—44no—
383C42—28no—
384C42—28no—
385C42—24no—
386C42—22no—
387C42—41no—
388C42—42no—
389C42C11×#4114yes—
390C11#3669511yescharacteristic, direct product factor, Sylow
391C23—24no—
392C23—24no—
393C23—24no—
394C23—24no—
395C23—24no—
396C23—24no—
397C23—24no—
398C23C25×C1111yescharacteristic
399Q8—48no—
400D4—48no—
401D4—416no—
402C2×C4—22no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—22no—
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—24no—
409C2×C4—22no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—21no—
416C2×C4—24no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—24no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—416no—
427C2×C4C2×C11×#4112yes—
428C2×C4C2×C11×#4114yes—
429C2×C4C11×H(5,𝔽2)14yes—
430C2×C4C11×2−1+412yes—
431C22—44no—
432C22—44no—
433C22—44no—
434C22—44no—
435C22—44no—
436C22—44no—
437C22—44no—
438C22C22×C11×#4111yescharacteristic
439C22C2×C11×H(5,𝔽2)12yes—
440C22C2×C11×2−1+411yescharacteristic
441C22C11×#58512yes—
442C22C11×#58511yescharacteristic
443C4—24no—
444C4—22no—
445C4—44no—
446C4—44no—
447C4—44no—
448C4—44no—
449C4—42no—
450C4—44no—
451C4—41no—
452C4C11×#56214yes—
453C2—84no—
454C2C11×#346012yes—
455C2C11×#346111yescharacteristic
456C2C2×C11×#56211yescharacteristic
457C2C11×#352912yes—
458C2C11×#353111yescharacteristic
subgroupG/H
centerC22×C4×C11C24
commutator, Frattini, cosocleC23C25×C11
socleC23×C11C25
prime radicalC11×#2819C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2845C2semidirect
2. C11×#2837C2semidirect
3. C11×#2831C2semidirect
4. C11×#2829C2semidirect
5. C11×#2820C2semidirect
7. C11×#2396C2semidirect
8. C11×#2395C2semidirect
9. C11×#2392C2semidirect
10. C4×C11×#125C2semidirect
11. C4×C11×#124C2semidirect
108. #36695C11direct (N × H)
162. #2845C2×C11semidirect
163. #2837C2×C11semidirect
164. #2831C2×C11semidirect
165. #2829C2×C11semidirect
166. #2820C2×C11semidirect
168. #2396C2×C11semidirect
169. #2395C2×C11semidirect
170. #2392C2×C11semidirect
171. C4×#125C2×C11semidirect
172. C4×#124C2×C11semidirect
390. C11#36695direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28452
C11×#28372
C11×#28312
C11×#28292
C11×#28202
C11×#28192
C11×#23962
C11×#23952
C11×#23922
C4×C11×#1252
C4×C11×#1242
#3669511