Finite Group Databasebeta

← C11×#36568 #14613761

Subgroups — C11×#36568 #14613761

Order 2816.

1632 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2863C213yesmaximal, complemented
2C11×#2588C213yesmaximal, complemented
3C11×#2587C213yesmaximal
4C11×#2586C213yesmaximal, complemented
5C11×#2556C213yesmaximal
6C11×#2465C213yesmaximal
7C11×#2462C213yesmaximal, complemented
8C11×#2370C213yesmaximal, complemented
9C11×#2368C213yesmaximal
10C4×C11×#126C213yesmaximal
11C42×Q8×C11C211yesmaximal, characteristic, complemented
12C2×C11×#126C2211yescharacteristic
13C2×C11×#125C2213yes—
14C2×C11×C22⋊Q8C2213yes—
15C2×C4×Q8×C11C2213yes—
16C11×#400C2213yes—
17C11×#399C2211yescharacteristic
18C11×#398C2213yes—
19C11×#398C2213yes—
20C11×#396C2213yes—
21C11×#396C2211yescharacteristic
22C11×#395C2213yes—
23C11×#395C2213yes—
24C11×#395C2213yes—
25C11×#393C2211yescharacteristic
26C11×#391C2213yes—
27C11×#391C2213yes—
28C11×#391C2213yes—
29C11×#391C2213yes—
30C11×#389C2213yes—
31C11×#389C2213yes—
32C11×#389C2213yes—
33C11×#389C2213yes—
34C11×#389C2213yes—
35C11×#389C2213yes—
36C11×#388C2213yes—
37C11×#388C2213yes—
38C11×#388C2213yes—
39C11×#387C2213yes—
40C11×#387C2213yes—
41C11×#387C2213yes—
42C11×#387C2213yes—
43C11×#387C2213yes—
44C11×#387C2213yes—
45C11×#387C2213yes—
46C11×#387C2213yes—
47C11×#387C2213yes—
48C11×#387C2213yes—
49C11×#387C2213yes—
50C11×#387C2213yes—
51C11×#387C2213yes—
52C11×#385C2213yes—
53C11×#385C2213yes—
54C11×#383C2213yes—
55C4×C11×C4⋊C4C2213yes—
56C4×C11×C4⋊C4C2213yes—
57C4×C11×C4⋊C4C2213yes—
58C4×C11×C4⋊C4C2213yes—
59C4×C11×C4⋊C4C2213yes—
60C4×C11×C4⋊C4C2213yes—
61C4×C11×C4⋊C4C2213yes—
62C4×C11×C22⋊C4C2213yes—
63C4×C11×C22⋊C4C2213yes—
64C4×C11×C22⋊C4C2213yes—
65C2×C11×#95C2211yescharacteristic
66C43×C11C2213yes—
67C22×Q8×C11C2311yescharacteristic
68C22×Q8×C11C2313yes—
69C23×C4×C11C2313yes—
70C11×#126Q818yescomplemented
71C11×#125—212no—
72C11×C22⋊Q8—212no—
73C4×Q8×C11—212no—
74C2×C11×C4⋊C4C2313yes—
75C2×C11×C4⋊C4C2313yes—
76C2×C11×C4⋊C4C2313yes—
77C2×C11×C4⋊C4C2313yes—
78C2×C11×C4⋊C4C2313yes—
79C2×C11×C4⋊C4C2313yes—
80C2×C11×C4⋊C4C2313yes—
81C2×C11×C4⋊C4C2313yes—
82C2×C11×C4⋊C4C2313yes—
83C2×C11×C4⋊C4C2313yes—
84C2×C11×C4⋊C4C2313yes—
85C2×C11×C4⋊C4C2313yes—
86C2×C11×C4⋊C4C2313yes—
87C2×C11×C4⋊C4C2313yes—
88C2×C11×C4⋊C4C2313yes—
89C2×C11×C4⋊C4C2313yes—
90C2×C11×C22⋊C4C2313yes—
91C2×C11×C22⋊C4C2313yes—
92C2×C11×C22⋊C4C2313yes—
93C2×C11×C22⋊C4C2313yes—
94C2×C42×C11C2313yes—
95C2×C42×C11C2313yes—
96C2×C42×C11C2313yes—
97C2×C42×C11C2313yes—
98C2×C42×C11C2313yes—
99C2×C42×C11C2313yes—
100C2×C42×C11C2313yes—
101C2×C42×C11C2313yes—
102C2×C42×C11C2313yes—
103C2×C42×C11C2311yescharacteristic
104C11×#95C2311yescharacteristic
105C11×#95C2313yes—
106C11×#95C2313yes—
107C11×#95C2313yes—
108C11×#95C2313yes—
109C11×#95C2313yes—
110C11×#95C2313yes—
111C11×#95C2313yes—
112C11×#95C2313yes—
113C11×#95C2311yescharacteristic
114C11×#95C2311yescharacteristic
115C11×#95C2313yes—
116C11×#95C2313yes—
117C11×#95C2313yes—
118C11×#95C2313yes—
119C11×#95C2313yes—
120C11×#95C2313yes—
121C11×#95C2313yes—
122C11×#95C2313yes—
123C11×#95C2313yes—
124C11×#95C2313yes—
125C11×#95C2313yes—
126#36568C1111yesmaximal, characteristic, direct product factor, Sylow
127C24×C11C2411yescharacteristic
128C2×Q8×C11—26no—
129C2×Q8×C11—26no—
130C2×Q8×C11—43no—
131C2×Q8×C11—43no—
132C22×C4×C11—26no—
133C22×C4×C11—43no—
134C22×C4×C11—43no—
135C22×C4×C11C2413yes—
136C22×C4×C11C2413yes—
137C22×C4×C11C2413yes—
138C22×C4×C11C2413yes—
139C22×C4×C11C2413yes—
140C22×C4×C11C2413yes—
141C22×C4×C11C2413yes—
142C22×C4×C11C2413yes—
143C22×C4×C11C2413yes—
144C22×C4×C11C2413yes—
145C11×C4⋊C4—26no—
146C11×C4⋊C4—26no—
147C11×C4⋊C4—26no—
148C11×C4⋊C4—26no—
149C11×C4⋊C4—26no—
150C11×C4⋊C4—26no—
151C11×C4⋊C4—26no—
152C11×C4⋊C4—26no—
153C11×C4⋊C4—26no—
154C11×C4⋊C4—43no—
155C11×C4⋊C4—43no—
156C11×C4⋊C4—43no—
157C11×C4⋊C4—43no—
158C11×C4⋊C4—43no—
159C11×C4⋊C4C2×Q8112yes—
160C11×C4⋊C4#41112yes—
161C11×C22⋊C4—26no—
162C11×C22⋊C4—26no—
163C11×C22⋊C4—43no—
164C11×C22⋊C4C2×Q8112yes—
165C42×C11—26no—
166C42×C11—26no—
167C42×C11—26no—
168C42×C11—26no—
169C42×C11—43no—
170C42×C11—43no—
171C42×C11—43no—
172C42×C11—43no—
173C42×C11—43no—
174C42×C11C2×Q814yes—
175#2863C2×C1113yescomplemented
176#2588C2×C1113yescomplemented
177#2587C2×C1113yes—
178#2586C2×C1113yescomplemented
179#2556C2×C1113yes—
180#2465C2×C1113yes—
181#2462C2×C1113yescomplemented
182#2370C2×C1113yescomplemented
183#2368C2×C1113yes—
184C4×#126C2×C1113yes—
185C42×Q8C2×C1111yescharacteristic, complemented
186C23×C11—23no—
187C23×C11—23no—
188C23×C11C22×Q812yes—
189C23×C11C2511yescharacteristic
190Q8×C11—28no—
191Q8×C11—86no—
192C2×C4×C11—23no—
193C2×C4×C11—23no—
194C2×C4×C11—23no—
195C2×C4×C11—23no—
196C2×C4×C11—23no—
197C2×C4×C11—23no—
198C2×C4×C11—23no—
199C2×C4×C11—23no—
200C2×C4×C11—23no—
201C2×C4×C11—23no—
202C2×C4×C11—23no—
203C2×C4×C11—23no—
204C2×C4×C11—23no—
205C2×C4×C11—23no—
206C2×C4×C11—23no—
207C2×C4×C11—23no—
208C2×C4×C11—23no—
209C2×C4×C11—23no—
210C2×C4×C11—23no—
211C2×C4×C11—23no—
212C2×C4×C11—23no—
213C2×C4×C11—23no—
214C2×C4×C11—23no—
215C2×C4×C11—23no—
216C2×C4×C11—23no—
217C2×C4×C11—86no—
218C2×C4×C11C22×Q816yes—
219C2×C4×C11C22×Q816yes—
220C2×C4×C11C2×#4116yes—
221C2×C4×C11C2×#4116yes—
222C2×C4×C11C2×#4116yes—
223C2×#126C22×C1111yescharacteristic
224C2×#125C22×C1113yes—
225C2×C22⋊Q8C22×C1113yes—
226C2×C4×Q8C22×C1113yes—
227#400C22×C1113yes—
228#399C22×C1111yescharacteristic
229#398C22×C1113yes—
230#398C22×C1113yes—
231#396C22×C1111yescharacteristic
232#396C22×C1113yes—
233#395C22×C1113yes—
234#395C22×C1113yes—
235#395C22×C1113yes—
236#393C22×C1111yescharacteristic
237#391C22×C1113yes—
238#391C22×C1113yes—
239#391C22×C1113yes—
240#391C22×C1113yes—
241#389C22×C1113yes—
242#389C22×C1113yes—
243#389C22×C1113yes—
244#389C22×C1113yes—
245#389C22×C1113yes—
246#389C22×C1113yes—
247#388C22×C1113yes—
248#388C22×C1113yes—
249#388C22×C1113yes—
250#387C22×C1113yes—
251#387C22×C1113yes—
252#387C22×C1113yes—
253#387C22×C1113yes—
254#387C22×C1113yes—
255#387C22×C1113yes—
256#387C22×C1113yes—
257#387C22×C1113yes—
258#387C22×C1113yes—
259#387C22×C1113yes—
260#387C22×C1113yes—
261#387C22×C1113yes—
262#387C22×C1113yes—
263#385C22×C1113yes—
264#385C22×C1113yes—
265#383C22×C1113yes—
266C4×C4⋊C4C22×C1113yes—
267C4×C4⋊C4C22×C1113yes—
268C4×C4⋊C4C22×C1113yes—
269C4×C4⋊C4C22×C1113yes—
270C4×C4⋊C4C22×C1113yes—
271C4×C4⋊C4C22×C1113yes—
272C4×C4⋊C4C22×C1113yes—
273C4×C22⋊C4C22×C1113yes—
274C4×C22⋊C4C22×C1113yes—
275C4×C22⋊C4C22×C1113yes—
276C2×#95C22×C1111yescharacteristic
277C43C22×C1113yes—
278C22×C11—26no—
279C22×C11—41no—
280C22×C11—43no—
281C22×C11C23×Q811yescharacteristic
282C22×C11C22×#4113yes—
283C22×C11#58513yes—
284C4×C11—26no—
285C4×C11—26no—
286C4×C11—26no—
287C4×C11—26no—
288C4×C11—26no—
289C4×C11—43no—
290C4×C11—43no—
291C4×C11—43no—
292C4×C11—43no—
293C4×C11—43no—
294C22×Q8C23×C1111yescharacteristic
295C22×Q8C23×C1113yes—
296C23×C4C23×C1113yes—
297#126Q8×C1118yescomplemented
298#125—212no—
299C22⋊Q8—212no—
300C4×Q8—212no—
301C2×C4⋊C4C23×C1113yes—
302C2×C4⋊C4C23×C1113yes—
303C2×C4⋊C4C23×C1113yes—
304C2×C4⋊C4C23×C1113yes—
305C2×C4⋊C4C23×C1113yes—
306C2×C4⋊C4C23×C1113yes—
307C2×C4⋊C4C23×C1113yes—
308C2×C4⋊C4C23×C1113yes—
309C2×C4⋊C4C23×C1113yes—
310C2×C4⋊C4C23×C1113yes—
311C2×C4⋊C4C23×C1113yes—
312C2×C4⋊C4C23×C1113yes—
313C2×C4⋊C4C23×C1113yes—
314C2×C4⋊C4C23×C1113yes—
315C2×C4⋊C4C23×C1113yes—
316C2×C4⋊C4C23×C1113yes—
317C2×C22⋊C4C23×C1113yes—
318C2×C22⋊C4C23×C1113yes—
319C2×C22⋊C4C23×C1113yes—
320C2×C22⋊C4C23×C1113yes—
321C2×C42C23×C1113yes—
322C2×C42C23×C1113yes—
323C2×C42C23×C1113yes—
324C2×C42C23×C1113yes—
325C2×C42C23×C1113yes—
326C2×C42C23×C1113yes—
327C2×C42C23×C1113yes—
328C2×C42C23×C1113yes—
329C2×C42C23×C1113yes—
330C2×C42C23×C1111yescharacteristic
331#95C23×C1111yescharacteristic
332#95C23×C1113yes—
333#95C23×C1113yes—
334#95C23×C1113yes—
335#95C23×C1113yes—
336#95C23×C1113yes—
337#95C23×C1113yes—
338#95C23×C1113yes—
339#95C23×C1113yes—
340#95C23×C1111yescharacteristic
341#95C23×C1111yescharacteristic
342#95C23×C1113yes—
343#95C23×C1113yes—
344#95C23×C1113yes—
345#95C23×C1113yes—
346#95C23×C1113yes—
347#95C23×C1113yes—
348#95C23×C1113yes—
349#95C23×C1113yes—
350#95C23×C1113yes—
351#95C23×C1113yes—
352#95C23×C1113yes—
353C2×C11—42no—
354C2×C11#344411yescharacteristic
355C2×C11Q8×#4113yes—
356C2×C11#352113yes—
357C24C24×C1111yescharacteristic
358C2×Q8—26no—
359C2×Q8—26no—
360C2×Q8—43no—
361C2×Q8—43no—
362C22×C4—26no—
363C22×C4—43no—
364C22×C4—43no—
365C22×C4C24×C1113yes—
366C22×C4C24×C1113yes—
367C22×C4C24×C1113yes—
368C22×C4C24×C1113yes—
369C22×C4C24×C1113yes—
370C22×C4C24×C1113yes—
371C22×C4C24×C1113yes—
372C22×C4C24×C1113yes—
373C22×C4C24×C1113yes—
374C22×C4C24×C1113yes—
375C4⋊C4—26no—
376C4⋊C4—26no—
377C4⋊C4—26no—
378C4⋊C4—26no—
379C4⋊C4—26no—
380C4⋊C4—26no—
381C4⋊C4—26no—
382C4⋊C4—26no—
383C4⋊C4—26no—
384C4⋊C4—43no—
385C4⋊C4—43no—
386C4⋊C4—43no—
387C4⋊C4—43no—
388C4⋊C4—43no—
389C4⋊C4C2×Q8×C11112yes—
390C4⋊C4C11×#41112yes—
391C22⋊C4—26no—
392C22⋊C4—26no—
393C22⋊C4—43no—
394C22⋊C4C2×Q8×C11112yes—
395C42—26no—
396C42—26no—
397C42—26no—
398C42—26no—
399C42—43no—
400C42—43no—
401C42—43no—
402C42—43no—
403C42—43no—
404C42C2×Q8×C1114yes—
405C11#3656811yescharacteristic, direct product factor, Sylow
406C23—23no—
407C23—23no—
408C23C22×Q8×C1112yes—
409C23C25×C1111yescharacteristic
410Q8—28no—
411Q8—86no—
412C2×C4—23no—
413C2×C4—23no—
414C2×C4—23no—
415C2×C4—23no—
416C2×C4—23no—
417C2×C4—23no—
418C2×C4—23no—
419C2×C4—23no—
420C2×C4—23no—
421C2×C4—23no—
422C2×C4—23no—
423C2×C4—23no—
424C2×C4—23no—
425C2×C4—23no—
426C2×C4—23no—
427C2×C4—23no—
428C2×C4—23no—
429C2×C4—23no—
430C2×C4—23no—
431C2×C4—23no—
432C2×C4—23no—
433C2×C4—23no—
434C2×C4—23no—
435C2×C4—23no—
436C2×C4—23no—
437C2×C4—86no—
438C2×C4C22×Q8×C1116yes—
439C2×C4C22×Q8×C1116yes—
440C2×C4C2×C11×#4116yes—
441C2×C4C2×C11×#4116yes—
442C2×C4C2×C11×#4116yes—
443C22—26no—
444C22—41no—
445C22—43no—
446C22C23×Q8×C1111yescharacteristic
447C22C22×C11×#4113yes—
448C22C11×#58513yes—
449C4—26no—
450C4—26no—
451C4—26no—
452C4—26no—
453C4—26no—
454C4—43no—
455C4—43no—
456C4—43no—
457C4—43no—
458C4—43no—
459C2—42no—
460C2C11×#344411yescharacteristic
461C2Q8×C11×#4113yes—
462C2C11×#352113yes—
subgroupG/H
center, socleC23×C11C25
commutator, Frattini, cosocleC23C25×C11
prime radicalC24×C11C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2863C2semidirect
2. C11×#2588C2semidirect
4. C11×#2586C2semidirect
7. C11×#2462C2semidirect
8. C11×#2370C2semidirect
11. C42×Q8×C11C2semidirect
70. C11×#126Q8semidirect
126. #36568C11direct (N × H)
175. #2863C2×C11semidirect
176. #2588C2×C11semidirect
178. #2586C2×C11semidirect
181. #2462C2×C11semidirect
182. #2370C2×C11semidirect
185. C42×Q8C2×C11semidirect
297. #126Q8×C11semidirect
405. C11#36568direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28632
C11×#25882
C11×#25872
C11×#25862
C11×#25562
C11×#24652
C11×#24622
C11×#23702
C11×#23682
C4×C11×#1262
C42×Q8×C112
#3656811