Finite Group Databasebeta

← C11×#36609 #14613802

Subgroups — C11×#36609 #14613802

Order 2816.

1938 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2862C211yesmaximal, characteristic, complemented
2C11×#2858C212yesmaximal
3C11×#2592C214yesmaximal, complemented
4C11×#2580C212yesmaximal, complemented
5C11×#2513C214yesmaximal, complemented
6C11×#2448C214yesmaximal, complemented
7C11×#2447C214yesmaximal, complemented
8C11×#2367C214yesmaximal, complemented
9C11×#2357C212yesmaximal, complemented
10C4×C11×C4⋊Q8C212yesmaximal, complemented
11C4×C11×#127C211yesmaximal, characteristic
12C42×Q8×C11C211yesmaximal, characteristic, complemented
13C2×C11×C4⋊Q8C2212yes—
14C2×C11×#127C2211yescharacteristic
15C2×C11×#124C2214yes—
16C2×C11×#124C2214yes—
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2212yes—
19C2×C4×Q8×C11C2214yes—
20C2×C4×D4×C11C2212yes—
21C2×C4×D4×C11C2214yes—
22C11×#399C2214yes—
23C11×#397C2218yes—
24C11×#397C2218yes—
25C11×#393C2214yes—
26C11×#391C2214yes—
27C11×#391C2214yes—
28C11×#391C2214yes—
29C11×#390C2214yes—
30C11×#390C2214yes—
31C11×#390C2214yes—
32C11×#390C2212yes—
33C11×#390C2214yes—
34C11×#390C2214yes—
35C11×#389C2214yes—
36C11×#389C2214yes—
37C11×#388C2218yes—
38C11×#388C2218yes—
39C11×#388C2218yes—
40C11×#385C2218yes—
41C11×#384C2211yescharacteristic
42C11×#382C2212yes—
43C11×#382C2212yes—
44C11×#381C2214yes—
45C4×C11×C4⋊C4C2212yes—
46C4×C11×C4⋊C4C2212yes—
47C4×C11×C4⋊C4C2212yes—
48C4×C11×C4⋊C4C2214yes—
49C4×C11×C4⋊C4C2211yescharacteristic
50C4×C11×C4⋊C4C2212yes—
51C4×C11×C4⋊C4C2214yes—
52C4×C11×C22⋊C4C2214yes—
53C43×C11C2211yescharacteristic
54C43×C11C2212yes—
55C22×Q8×C11C2311yescharacteristic
56C22×Q8×C11C2314yes—
57C22×D4×C11C2314yes—
58C22×D4×C11C2312yes—
59C23×C4×C11C2314yes—
60C11×C4⋊Q8—28no—
61C11×#127—24no—
62C11×#124—216no—
63C11×#124—48no—
64C4×Q8×C11—24no—
65C4×Q8×C11—28no—
66C4×Q8×C11—48no—
67C4×D4×C11—28no—
68C4×D4×C11—48no—
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C4⋊C4C2314yes—
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C4⋊C4C2312yes—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2314yes—
77C2×C11×C4⋊C4C2314yes—
78C2×C11×C4⋊C4C2318yes—
79C2×C11×C22⋊C4C2318yes—
80C2×C11×C22⋊C4C2314yes—
81C2×C11×C22⋊C4C2318yes—
82C2×C11×C22⋊C4C2318yes—
83C2×C11×C22⋊C4C2318yes—
84C2×C11×C22⋊C4C2318yes—
85C2×C42×C11C2312yes—
86C2×C42×C11C2312yes—
87C2×C42×C11C2312yes—
88C2×C42×C11C2311yescharacteristic
89C2×C42×C11C2312yes—
90C2×C42×C11C2312yes—
91C2×C42×C11C2312yes—
92C2×C42×C11C2312yes—
93C2×C42×C11C2318yes—
94C2×C42×C11C2311yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2312yes—
97C11×#95C2311yescharacteristic
98C11×#95C2314yes—
99C11×#95C2311yescharacteristic
100C11×#95C2312yes—
101C11×#95C2312yes—
102C11×#95C2318yes—
103C11×#95C2318yes—
104C11×#95C2314yes—
105C11×#95C2318yes—
106#36609C1111yesmaximal, characteristic, direct product factor, Sylow
107C24×C11C2414yes—
108C2×Q8×C11—22no—
109C2×Q8×C11—24no—
110C2×Q8×C11—28no—
111C2×Q8×C11—28no—
112C2×Q8×C11—28no—
113C2×D4×C11—24no—
114C2×D4×C11—28no—
115C2×D4×C11—24no—
116C2×D4×C11—28no—
117C2×D4×C11—28no—
118C2×D4×C11—24no—
119C22×C4×C11—28no—
120C22×C4×C11—48no—
121C22×C4×C11C2412yes—
122C22×C4×C11C2412yes—
123C22×C4×C11C2418yes—
124C22×C4×C11C2414yes—
125C22×C4×C11C2412yes—
126C22×C4×C11C2411yescharacteristic
127C22×C4×C11C2412yes—
128C22×C4×C11C2411yescharacteristic
129C22×C4×C11C2412yes—
130C22×C4×C11C2412yes—
131C22×C4×C11C2411yescharacteristic
132C11×C4⋊C4—24no—
133C11×C4⋊C4—24no—
134C11×C4⋊C4—24no—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—28no—
139C11×C4⋊C4—28no—
140C11×C4⋊C4—28no—
141C11×C4⋊C4—48no—
142C11×C22⋊C4—28no—
143C11×C22⋊C4—216no—
144C11×C22⋊C4—216no—
145C11×C22⋊C4—48no—
146C11×C22⋊C4—48no—
147C11×C22⋊C4—48no—
148C42×C11—24no—
149C42×C11—24no—
150C42×C11—24no—
151C42×C11—24no—
152C42×C11—24no—
153C42×C11—24no—
154C42×C11—24no—
155C42×C11—22no—
156C42×C11—48no—
157C42×C11#4114yes—
158C42×C11#4118yes—
159C42×C11#4114yes—
160#2862C2×C1111yescharacteristic, complemented
161#2858C2×C1112yes—
162#2592C2×C1114yescomplemented
163#2580C2×C1112yescomplemented
164#2513C2×C1114yescomplemented
165#2448C2×C1114yescomplemented
166#2447C2×C1114yescomplemented
167#2367C2×C1114yescomplemented
168#2357C2×C1112yescomplemented
169C4×C4⋊Q8C2×C1112yescomplemented
170C4×#127C2×C1111yescharacteristic
171C42×Q8C2×C1111yescharacteristic, complemented
172C23×C11—28no—
173C23×C11—24no—
174C23×C11—24no—
175C23×C11—28no—
176C23×C11—24no—
177C23×C11C2511yescharacteristic
178Q8×C11—28no—
179Q8×C11—416no—
180D4×C11—48no—
181D4×C11—416no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—28no—
192C2×C4×C11—24no—
193C2×C4×C11—28no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—28no—
199C2×C4×C11—28no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—88no—
203C2×C4×C11C2×#4114yes—
204C2×C4×C11C2×#4112yes—
205C2×C4×C11C2×#4114yes—
206C2×C4×C11C2×#4112yes—
207C2×C4×C11C2×#4112yes—
208C2×C4×C11C2×#4112yes—
209C2×C4×C11C2×#4114yes—
210C2×C4×C11C2×#4114yes—
211C2×C4×C11H(5,𝔽2)14yes—
212C2×C4×C112−1+412yes—
213C2×C4⋊Q8C22×C1112yes—
214C2×#127C22×C1111yescharacteristic
215C2×#124C22×C1114yes—
216C2×#124C22×C1114yes—
217C2×C4×Q8C22×C1111yescharacteristic
218C2×C4×Q8C22×C1112yes—
219C2×C4×Q8C22×C1114yes—
220C2×C4×D4C22×C1112yes—
221C2×C4×D4C22×C1114yes—
222#399C22×C1114yes—
223#397C22×C1118yes—
224#397C22×C1118yes—
225#393C22×C1114yes—
226#391C22×C1114yes—
227#391C22×C1114yes—
228#391C22×C1114yes—
229#390C22×C1114yes—
230#390C22×C1112yes—
231#390C22×C1114yes—
232#390C22×C1114yes—
233#390C22×C1114yes—
234#390C22×C1114yes—
235#389C22×C1114yes—
236#389C22×C1114yes—
237#388C22×C1118yes—
238#388C22×C1118yes—
239#388C22×C1118yes—
240#385C22×C1118yes—
241#384C22×C1111yescharacteristic
242#382C22×C1112yes—
243#382C22×C1112yes—
244#381C22×C1114yes—
245C4×C4⋊C4C22×C1114yes—
246C4×C4⋊C4C22×C1114yes—
247C4×C4⋊C4C22×C1111yescharacteristic
248C4×C4⋊C4C22×C1112yes—
249C4×C4⋊C4C22×C1112yes—
250C4×C4⋊C4C22×C1112yes—
251C4×C4⋊C4C22×C1112yes—
252C4×C22⋊C4C22×C1114yes—
253C43C22×C1111yescharacteristic
254C43C22×C1112yes—
255C22×C11—44no—
256C22×C11—44no—
257C22×C11—48no—
258C22×C11—44no—
259C22×C11—48no—
260C22×C11C22×#4111yescharacteristic
261C22×C11C22×#4112yes—
262C22×C11C22×#4111yescharacteristic
263C22×C11C2×H(5,𝔽2)12yes—
264C22×C11C2×2−1+411yescharacteristic
265C4×C11—24no—
266C4×C11—22no—
267C4×C11—22no—
268C4×C11—24no—
269C4×C11—48no—
270C4×C11—42no—
271C4×C11—44no—
272C4×C11—42no—
273C4×C11—42no—
274C4×C11#55614yes—
275C4×C11#55918yes—
276C22×Q8C23×C1111yescharacteristic
277C22×Q8C23×C1114yes—
278C22×D4C23×C1114yes—
279C22×D4C23×C1112yes—
280C23×C4C23×C1114yes—
281C4⋊Q8—28no—
282#127—24no—
283#124—216no—
284#124—48no—
285C4×Q8—24no—
286C4×Q8—28no—
287C4×Q8—48no—
288C4×D4—28no—
289C4×D4—48no—
290C2×C4⋊C4C23×C1114yes—
291C2×C4⋊C4C23×C1112yes—
292C2×C4⋊C4C23×C1112yes—
293C2×C4⋊C4C23×C1112yes—
294C2×C4⋊C4C23×C1112yes—
295C2×C4⋊C4C23×C1112yes—
296C2×C4⋊C4C23×C1111yescharacteristic
297C2×C4⋊C4C23×C1114yes—
298C2×C4⋊C4C23×C1114yes—
299C2×C4⋊C4C23×C1118yes—
300C2×C22⋊C4C23×C1114yes—
301C2×C22⋊C4C23×C1118yes—
302C2×C22⋊C4C23×C1118yes—
303C2×C22⋊C4C23×C1118yes—
304C2×C22⋊C4C23×C1118yes—
305C2×C22⋊C4C23×C1118yes—
306C2×C42C23×C1112yes—
307C2×C42C23×C1112yes—
308C2×C42C23×C1112yes—
309C2×C42C23×C1112yes—
310C2×C42C23×C1112yes—
311C2×C42C23×C1112yes—
312C2×C42C23×C1112yes—
313C2×C42C23×C1111yescharacteristic
314C2×C42C23×C1118yes—
315C2×C42C23×C1111yescharacteristic
316C2×C42C23×C1112yes—
317C2×C42C23×C1111yescharacteristic
318#95C23×C1111yescharacteristic
319#95C23×C1114yes—
320#95C23×C1111yescharacteristic
321#95C23×C1112yes—
322#95C23×C1112yes—
323#95C23×C1118yes—
324#95C23×C1118yes—
325#95C23×C1114yes—
326#95C23×C1118yes—
327C2×C11—84no—
328C2×C11#344411yescharacteristic
329C2×C11C2×#55611yescharacteristic
330C2×C11C2×#55912yes—
331C2×C11#350811yescharacteristic
332C2×C11#351112yes—
333C24C24×C1114yes—
334C2×Q8—22no—
335C2×Q8—24no—
336C2×Q8—28no—
337C2×Q8—28no—
338C2×Q8—28no—
339C2×D4—24no—
340C2×D4—28no—
341C2×D4—24no—
342C2×D4—28no—
343C2×D4—28no—
344C2×D4—24no—
345C22×C4—28no—
346C22×C4—48no—
347C22×C4C24×C1112yes—
348C22×C4C24×C1112yes—
349C22×C4C24×C1118yes—
350C22×C4C24×C1114yes—
351C22×C4C24×C1112yes—
352C22×C4C24×C1111yescharacteristic
353C22×C4C24×C1112yes—
354C22×C4C24×C1111yescharacteristic
355C22×C4C24×C1112yes—
356C22×C4C24×C1112yes—
357C22×C4C24×C1111yescharacteristic
358C4⋊C4—24no—
359C4⋊C4—24no—
360C4⋊C4—24no—
361C4⋊C4—24no—
362C4⋊C4—24no—
363C4⋊C4—22no—
364C4⋊C4—28no—
365C4⋊C4—28no—
366C4⋊C4—28no—
367C4⋊C4—48no—
368C22⋊C4—28no—
369C22⋊C4—216no—
370C22⋊C4—216no—
371C22⋊C4—48no—
372C22⋊C4—48no—
373C22⋊C4—48no—
374C42—24no—
375C42—24no—
376C42—24no—
377C42—24no—
378C42—24no—
379C42—24no—
380C42—24no—
381C42—22no—
382C42—48no—
383C42C11×#4114yes—
384C42C11×#4118yes—
385C42C11×#4114yes—
386C11#3660911yescharacteristic, direct product factor, Sylow
387C23—28no—
388C23—24no—
389C23—24no—
390C23—28no—
391C23—24no—
392C23C25×C1111yescharacteristic
393Q8—28no—
394Q8—416no—
395D4—48no—
396D4—416no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—28no—
407C2×C4—24no—
408C2×C4—28no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—28no—
414C2×C4—28no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—88no—
418C2×C4C2×C11×#4114yes—
419C2×C4C2×C11×#4112yes—
420C2×C4C2×C11×#4114yes—
421C2×C4C2×C11×#4112yes—
422C2×C4C2×C11×#4112yes—
423C2×C4C2×C11×#4112yes—
424C2×C4C2×C11×#4114yes—
425C2×C4C2×C11×#4114yes—
426C2×C4C11×H(5,𝔽2)14yes—
427C2×C4C11×2−1+412yes—
428C22—44no—
429C22—44no—
430C22—48no—
431C22—44no—
432C22—48no—
433C22C22×C11×#4111yescharacteristic
434C22C22×C11×#4112yes—
435C22C22×C11×#4111yescharacteristic
436C22C2×C11×H(5,𝔽2)12yes—
437C22C2×C11×2−1+411yescharacteristic
438C4—24no—
439C4—22no—
440C4—22no—
441C4—24no—
442C4—48no—
443C4—44no—
444C4—42no—
445C4—42no—
446C4—42no—
447C4C11×#55614yes—
448C4C11×#55918yes—
449C2—84no—
450C2C11×#344411yescharacteristic
451C2C2×C11×#55611yescharacteristic
452C2C2×C11×#55912yes—
453C2C11×#350811yescharacteristic
454C2C11×#351112yes—
subgroupG/H
center, socleC23×C11C25
commutator, Frattini, cosocleC23C25×C11
prime radicalC2×C11×#127C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2862C2semidirect
3. C11×#2592C2semidirect
4. C11×#2580C2semidirect
5. C11×#2513C2semidirect
6. C11×#2448C2semidirect
7. C11×#2447C2semidirect
8. C11×#2367C2semidirect
9. C11×#2357C2semidirect
10. C4×C11×C4⋊Q8C2semidirect
12. C42×Q8×C11C2semidirect
106. #36609C11direct (N × H)
160. #2862C2×C11semidirect
162. #2592C2×C11semidirect
163. #2580C2×C11semidirect
164. #2513C2×C11semidirect
165. #2448C2×C11semidirect
166. #2447C2×C11semidirect
167. #2367C2×C11semidirect
168. #2357C2×C11semidirect
169. C4×C4⋊Q8C2×C11semidirect
171. C42×Q8C2×C11semidirect
386. C11#36609direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28622
C11×#28582
C11×#25922
C11×#25802
C11×#25132
C11×#24482
C11×#24472
C11×#23672
C11×#23572
C4×C11×C4⋊Q82
C4×C11×#1272
C42×Q8×C112
#3660911