Finite Group Databasebeta

← C11×#36603 #14613796

Subgroups — C11×#36603 #14613796

Order 2816.

1686 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2860C213yesmaximal, complemented
2C11×#2595C213yesmaximal, complemented
3C11×#2594C213yesmaximal, complemented
4C11×#2585C213yesmaximal, complemented
5C11×#2554C213yesmaximal
6C11×#2469C213yesmaximal, complemented
7C11×#2458C213yesmaximal, complemented
8C11×#2374C213yesmaximal, complemented
9C11×#2373C213yesmaximal, complemented
10C4×C11×#126C213yesmaximal, complemented
11C42×Q8×C11C211yesmaximal, characteristic, complemented
12C2×C11×#126C2213yes—
13C2×C11×#126C2213yes—
14C2×C11×#123C2213yes—
15C2×C4×Q8×C11C2213yes—
16C11×#401C2211yescharacteristic
17C11×#400C2213yes—
18C11×#398C2213yes—
19C11×#398C2213yes—
20C11×#397C2213yes—
21C11×#396C2213yes—
22C11×#395C2211yescharacteristic
23C11×#394C2213yes—
24C11×#393C2213yes—
25C11×#392C2211yescharacteristic
26C11×#390C2213yes—
27C11×#390C2213yes—
28C11×#390C2213yes—
29C11×#389C2213yes—
30C11×#389C2213yes—
31C11×#389C2213yes—
32C11×#388C2213yes—
33C11×#388C2213yes—
34C11×#388C2213yes—
35C11×#388C2213yes—
36C11×#388C2213yes—
37C11×#388C2213yes—
38C11×#388C2213yes—
39C11×#388C2213yes—
40C11×#388C2213yes—
41C11×#388C2213yes—
42C11×#388C2213yes—
43C11×#388C2213yes—
44C11×#387C2213yes—
45C11×#387C2213yes—
46C11×#387C2213yes—
47C11×#387C2213yes—
48C11×#387C2213yes—
49C11×#387C2213yes—
50C11×#387C2213yes—
51C11×#387C2213yes—
52C11×#386C2213yes—
53C11×#385C2213yes—
54C11×#383C2211yescharacteristic
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×C22⋊C4C2213yes—
62C4×C11×C22⋊C4C2213yes—
63C4×C11×C22⋊C4C2213yes—
64C4×C11×C22⋊C4C2213yes—
65C11×#376C2211yescharacteristic
66C43×C11C2213yes—
67C22×Q8×C11C2311yescharacteristic
68C22×D4×C11C2313yes—
69C23×C4×C11C2313yes—
70C11×#126—212no—
71C11×#126—212no—
72C11×#123—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×C22⋊C4C2313yes—
87C2×C11×C22⋊C4C2313yes—
88C2×C11×C22⋊C4C2313yes—
89C2×C11×C22⋊C4C2313yes—
90C2×C11×C22⋊C4C2313yes—
91C2×C11×C22⋊C4C2313yes—
92C2×C11×C22⋊C4C2313yes—
93C2×C11×C22⋊C4C2313yes—
94C2×C11×C22⋊C4C2313yes—
95C2×C11×C22⋊C4C2313yes—
96C2×C11×C22⋊C4C2313yes—
97C2×C11×C22⋊C4C2313yes—
98C2×C42×C11C2313yes—
99C2×C42×C11C2313yes—
100C2×C42×C11C2313yes—
101C2×C42×C11C2313yes—
102C2×C42×C11C2313yes—
103C2×C42×C11C2313yes—
104C2×C42×C11C2313yes—
105C2×C42×C11C2313yes—
106C2×C42×C11C2313yes—
107C2×C42×C11C2311yescharacteristic
108C11×#95C2311yescharacteristic
109C11×#95C2313yes—
110C11×#95C2313yes—
111C11×#95C2313yes—
112C11×#95C2313yes—
113C11×#95C2313yes—
114C11×#95C2313yes—
115C11×#95C2313yes—
116C11×#95C2313yes—
117C11×#95C2311yescharacteristic
118C11×#95C2311yescharacteristic
119C11×#95C2313yes—
120C11×#95C2313yes—
121C11×#95C2313yes—
122C11×#95C2313yes—
123C11×#95C2313yes—
124C11×#95C2313yes—
125C11×#95C2313yes—
126#36603C1111yesmaximal, characteristic, direct product factor, Sylow
127C24×C11C2413yes—
128C2×Q8×C11—26no—
129C2×D4×C11—26no—
130C2×D4×C11—43no—
131C2×D4×C11—43no—
132C22×C4×C11—26no—
133C22×C4×C11—43no—
134C22×C4×C11—43no—
135C22×C4×C11C2413yes—
136C22×C4×C11C2411yescharacteristic
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—43no—
154C11×C4⋊C4—43no—
155C11×C4⋊C4—43no—
156C11×C4⋊C4#41112yes—
157C11×C22⋊C4—26no—
158C11×C22⋊C4—26no—
159C11×C22⋊C4—26no—
160C11×C22⋊C4—26no—
161C11×C22⋊C4—26no—
162C11×C22⋊C4—26no—
163C11×C22⋊C4—26no—
164C11×C22⋊C4—26no—
165C11×C22⋊C4—26no—
166C11×C22⋊C4—43no—
167C11×C22⋊C4—43no—
168C11×C22⋊C4—43no—
169C42×C11—26no—
170C42×C11—26no—
171C42×C11—26no—
172C42×C11—26no—
173C42×C11—43no—
174C42×C11—43no—
175C42×C11—43no—
176C42×C11—43no—
177C42×C11—43no—
178C42×C11#4114yes—
179#2860C2×C1113yescomplemented
180#2595C2×C1113yescomplemented
181#2594C2×C1113yescomplemented
182#2585C2×C1113yescomplemented
183#2554C2×C1113yes—
184#2469C2×C1113yescomplemented
185#2458C2×C1113yescomplemented
186#2374C2×C1113yescomplemented
187#2373C2×C1113yescomplemented
188C4×#126C2×C1113yescomplemented
189C42×Q8C2×C1111yescharacteristic, complemented
190C23×C11—23no—
191C23×C11—23no—
192C23×C11—23no—
193C23×C11—23no—
194C23×C11—23no—
195C23×C11—23no—
196C23×C11—23no—
197C23×C11C2511yescharacteristic
198Q8×C11—28no—
199D4×C11—86no—
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—23no—
218C2×C4×C11—23no—
219C2×C4×C11—23no—
220C2×C4×C11—23no—
221C2×C4×C11—23no—
222C2×C4×C11—23no—
223C2×C4×C11—23no—
224C2×C4×C11—86no—
225C2×C4×C11C2×#4116yes—
226C2×C4×C11C2×#4116yes—
227C2×C4×C11C2×#4116yes—
228C2×C4×C11C2×#4116yes—
229C2×#126C22×C1113yes—
230C2×#126C22×C1113yes—
231C2×#123C22×C1113yes—
232C2×C4×Q8C22×C1113yes—
233#401C22×C1111yescharacteristic
234#400C22×C1113yes—
235#398C22×C1113yes—
236#398C22×C1113yes—
237#397C22×C1113yes—
238#396C22×C1113yes—
239#395C22×C1111yescharacteristic
240#394C22×C1113yes—
241#393C22×C1113yes—
242#392C22×C1111yescharacteristic
243#390C22×C1113yes—
244#390C22×C1113yes—
245#390C22×C1113yes—
246#389C22×C1113yes—
247#389C22×C1113yes—
248#389C22×C1113yes—
249#388C22×C1113yes—
250#388C22×C1113yes—
251#388C22×C1113yes—
252#388C22×C1113yes—
253#388C22×C1113yes—
254#388C22×C1113yes—
255#388C22×C1113yes—
256#388C22×C1113yes—
257#388C22×C1113yes—
258#388C22×C1113yes—
259#388C22×C1113yes—
260#388C22×C1113yes—
261#387C22×C1113yes—
262#387C22×C1113yes—
263#387C22×C1113yes—
264#387C22×C1113yes—
265#387C22×C1113yes—
266#387C22×C1113yes—
267#387C22×C1113yes—
268#387C22×C1113yes—
269#386C22×C1113yes—
270#385C22×C1113yes—
271#383C22×C1111yescharacteristic
272C4×C4⋊C4C22×C1113yes—
273C4×C4⋊C4C22×C1113yes—
274C4×C4⋊C4C22×C1113yes—
275C4×C4⋊C4C22×C1113yes—
276C4×C4⋊C4C22×C1113yes—
277C4×C4⋊C4C22×C1113yes—
278C4×C22⋊C4C22×C1113yes—
279C4×C22⋊C4C22×C1113yes—
280C4×C22⋊C4C22×C1113yes—
281C4×C22⋊C4C22×C1113yes—
282#376C22×C1111yescharacteristic
283C43C22×C1113yes—
284C22×C11—43no—
285C22×C11—43no—
286C22×C11—43no—
287C22×C11—43no—
288C22×C11—43no—
289C22×C11—43no—
290C22×C11—43no—
291C22×C11C22×#4113yes—
292C22×C11C22×#4111yescharacteristic
293C22×C11#58513yes—
294C4×C11—26no—
295C4×C11—26no—
296C4×C11—26no—
297C4×C11—26no—
298C4×C11—41no—
299C4×C11—43no—
300C4×C11—43no—
301C4×C11—43no—
302C4×C11—43no—
303C4×C11—43no—
304C22×Q8C23×C1111yescharacteristic
305C22×D4C23×C1113yes—
306C23×C4C23×C1113yes—
307#126—212no—
308#126—212no—
309#123—212no—
310C4×Q8—212no—
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×C4⋊C4C23×C1113yes—
318C2×C4⋊C4C23×C1113yes—
319C2×C4⋊C4C23×C1113yes—
320C2×C4⋊C4C23×C1113yes—
321C2×C4⋊C4C23×C1113yes—
322C2×C4⋊C4C23×C1113yes—
323C2×C22⋊C4C23×C1113yes—
324C2×C22⋊C4C23×C1113yes—
325C2×C22⋊C4C23×C1113yes—
326C2×C22⋊C4C23×C1113yes—
327C2×C22⋊C4C23×C1113yes—
328C2×C22⋊C4C23×C1113yes—
329C2×C22⋊C4C23×C1113yes—
330C2×C22⋊C4C23×C1113yes—
331C2×C22⋊C4C23×C1113yes—
332C2×C22⋊C4C23×C1113yes—
333C2×C22⋊C4C23×C1113yes—
334C2×C22⋊C4C23×C1113yes—
335C2×C42C23×C1113yes—
336C2×C42C23×C1113yes—
337C2×C42C23×C1113yes—
338C2×C42C23×C1113yes—
339C2×C42C23×C1113yes—
340C2×C42C23×C1113yes—
341C2×C42C23×C1113yes—
342C2×C42C23×C1113yes—
343C2×C42C23×C1113yes—
344C2×C42C23×C1111yescharacteristic
345#95C23×C1111yescharacteristic
346#95C23×C1113yes—
347#95C23×C1113yes—
348#95C23×C1113yes—
349#95C23×C1113yes—
350#95C23×C1113yes—
351#95C23×C1113yes—
352#95C23×C1113yes—
353#95C23×C1113yes—
354#95C23×C1111yescharacteristic
355#95C23×C1111yescharacteristic
356#95C23×C1113yes—
357#95C23×C1113yes—
358#95C23×C1113yes—
359#95C23×C1113yes—
360#95C23×C1113yes—
361#95C23×C1113yes—
362#95C23×C1113yes—
363C2×C11—83no—
364C2×C11#344411yescharacteristic
365C2×C11#348013yes—
366C2×C11#352113yes—
367C24C24×C1113yes—
368C2×Q8—26no—
369C2×D4—26no—
370C2×D4—43no—
371C2×D4—43no—
372C22×C4—26no—
373C22×C4—43no—
374C22×C4—43no—
375C22×C4C24×C1113yes—
376C22×C4C24×C1111yescharacteristic
377C22×C4C24×C1113yes—
378C22×C4C24×C1113yes—
379C22×C4C24×C1113yes—
380C22×C4C24×C1113yes—
381C22×C4C24×C1113yes—
382C22×C4C24×C1113yes—
383C22×C4C24×C1113yes—
384C22×C4C24×C1113yes—
385C4⋊C4—26no—
386C4⋊C4—26no—
387C4⋊C4—26no—
388C4⋊C4—26no—
389C4⋊C4—26no—
390C4⋊C4—26no—
391C4⋊C4—26no—
392C4⋊C4—26no—
393C4⋊C4—43no—
394C4⋊C4—43no—
395C4⋊C4—43no—
396C4⋊C4C11×#41112yes—
397C22⋊C4—26no—
398C22⋊C4—26no—
399C22⋊C4—26no—
400C22⋊C4—26no—
401C22⋊C4—26no—
402C22⋊C4—26no—
403C22⋊C4—26no—
404C22⋊C4—26no—
405C22⋊C4—26no—
406C22⋊C4—43no—
407C22⋊C4—43no—
408C22⋊C4—43no—
409C42—26no—
410C42—26no—
411C42—26no—
412C42—26no—
413C42—43no—
414C42—43no—
415C42—43no—
416C42—43no—
417C42—43no—
418C42C11×#4114yes—
419C11#3660311yescharacteristic, direct product factor, Sylow
420C23—23no—
421C23—23no—
422C23—23no—
423C23—23no—
424C23—23no—
425C23—23no—
426C23—23no—
427C23C25×C1111yescharacteristic
428Q8—28no—
429D4—86no—
430C2×C4—23no—
431C2×C4—23no—
432C2×C4—23no—
433C2×C4—23no—
434C2×C4—23no—
435C2×C4—23no—
436C2×C4—23no—
437C2×C4—23no—
438C2×C4—23no—
439C2×C4—23no—
440C2×C4—23no—
441C2×C4—23no—
442C2×C4—23no—
443C2×C4—23no—
444C2×C4—23no—
445C2×C4—23no—
446C2×C4—23no—
447C2×C4—23no—
448C2×C4—23no—
449C2×C4—23no—
450C2×C4—23no—
451C2×C4—23no—
452C2×C4—23no—
453C2×C4—23no—
454C2×C4—86no—
455C2×C4C2×C11×#4116yes—
456C2×C4C2×C11×#4116yes—
457C2×C4C2×C11×#4116yes—
458C2×C4C2×C11×#4116yes—
459C22—43no—
460C22—43no—
461C22—43no—
462C22—43no—
463C22—43no—
464C22—43no—
465C22—43no—
466C22C22×C11×#4113yes—
467C22C22×C11×#4111yescharacteristic
468C22C11×#58513yes—
469C4—26no—
470C4—26no—
471C4—26no—
472C4—26no—
473C4—41no—
474C4—43no—
475C4—43no—
476C4—43no—
477C4—43no—
478C4—43no—
479C2—83no—
480C2C11×#344411yescharacteristic
481C2C11×#348013yes—
482C2C11×#352113yes—
subgroupG/H
center, socleC23×C11C25
commutator, Frattini, cosocleC23C25×C11
prime radicalC11×#392C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2860C2semidirect
2. C11×#2595C2semidirect
3. C11×#2594C2semidirect
4. C11×#2585C2semidirect
6. C11×#2469C2semidirect
7. C11×#2458C2semidirect
8. C11×#2374C2semidirect
9. C11×#2373C2semidirect
10. C4×C11×#126C2semidirect
11. C42×Q8×C11C2semidirect
126. #36603C11direct (N × H)
179. #2860C2×C11semidirect
180. #2595C2×C11semidirect
181. #2594C2×C11semidirect
182. #2585C2×C11semidirect
184. #2469C2×C11semidirect
185. #2458C2×C11semidirect
186. #2374C2×C11semidirect
187. #2373C2×C11semidirect
188. C4×#126C2×C11semidirect
189. C42×Q8C2×C11semidirect
419. C11#36603direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28602
C11×#25952
C11×#25942
C11×#25852
C11×#25542
C11×#24692
C11×#24582
C11×#23742
C11×#23732
C4×C11×#1262
C42×Q8×C112
#3660311