Finite Group Databasebeta

← C11×#36577 #14613770

Subgroups — C11×#36577 #14613770

Order 2816.

2312 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#557C211yesmaximal, characteristic, complemented
2C22×C4×Q8×C11C211yesmaximal, characteristic
3C11×#2857C213yesmaximal
4C11×#2582C213yesmaximal, complemented
5C11×#2568C213yesmaximal, complemented
6C11×#2453C216yesmaximal, complemented
7C11×#2442C216yesmaximal
8C11×#2351C212yesmaximal, complemented
9Q8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
10Q8×C11×C22⋊C4C212yesmaximal
11C4×C11×C22⋊Q8C213yesmaximal
12C23×Q8×C11C2211yescharacteristic
13C11×#557—28no—
14C2×C11×C4⋊Q8C2213yes—
15C2×C11×#125C2216yes—
16C2×C11×C22⋊Q8C2213yes—
17C2×C4×Q8×C11—28no—
18C2×C4×Q8×C11C2213yes—
19C2×C4×Q8×C11C2213yes—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×Q8×C11C2213yes—
22C2×C4×Q8×C11C2212yes—
23C2×C4×Q8×C11C2212yes—
24C2×C4×Q8×C11C2211yescharacteristic
25C22×C11×C4⋊C4C2213yes—
26C22×C42×C11C2213yes—
27C11×#400C22112yes—
28C11×#398C22112yes—
29C11×#391C2216yes—
30C11×#391C2216yes—
31C11×#391C2213yes—
32C11×#391C2216yes—
33C11×#389C2216yes—
34C11×#389C2216yes—
35C11×#389C2216yes—
36C11×#389C2216yes—
37C11×#389C2213yes—
38C11×#387C2216yes—
39C11×#385C2216yes—
40C11×#384C2213yes—
41C11×#382C2216yes—
42C11×#380C2216yes—
43C11×#380C2216yes—
44C11×#380C2211yescharacteristic
45C4×C11×C4⋊C4C2216yes—
46C4×C11×C4⋊C4C2213yes—
47C4×C11×C22⋊C4C2216yes—
48C22×Q8×C11—24no—
49C22×Q8×C11—24no—
50C22×Q8×C11Q818yescomplemented
51C22×Q8×C11C2313yes—
52C22×Q8×C11C2313yes—
53C22×Q8×C11C2311yescharacteristic
54C23×C4×C11C2313yes—
55C23×C4×C11C2313yes—
56C23×C4×C11C2311yescharacteristic
57C11×C4⋊Q8—212no—
58C11×#125—224no—
59C11×C22⋊Q8—212no—
60C4×Q8×C11—24no—
61C4×Q8×C11—28no—
62C4×Q8×C11—28no—
63C4×Q8×C11—212no—
64C4×Q8×C11—212no—
65C4×Q8×C11—212no—
66C4×Q8×C11D418yes—
67C2×C11×C4⋊C4—212no—
68C2×C11×C4⋊C4C2313yes—
69C2×C11×C4⋊C4C2316yes—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2313yes—
72C2×C11×C4⋊C4C2316yes—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2316yes—
75C2×C11×C4⋊C4C2316yes—
76C2×C11×C4⋊C4C2316yes—
77C2×C11×C4⋊C4C2316yes—
78C2×C11×C4⋊C4C2316yes—
79C2×C11×C4⋊C4C2316yes—
80C2×C11×C4⋊C4C2313yes—
81C2×C11×C22⋊C4C2312yes—
82C2×C11×C22⋊C4C2316yes—
83C2×C42×C11—212no—
84C2×C42×C11C2313yes—
85C2×C42×C11C2313yes—
86C2×C42×C11C2313yes—
87C2×C42×C11C2316yes—
88C2×C42×C11C2316yes—
89C2×C42×C11C2313yes—
90C11×#95C2316yes—
91C11×#95C2316yes—
92C11×#95C2312yes—
93C11×#95C2316yes—
94C11×#95C2316yes—
95C11×#95C23112yes—
96C11×#95C23112yes—
97#36577C1111yesmaximal, characteristic, direct product factor, Sylow
98C24×C11C2411yescharacteristic
99C2×Q8×C11—232no—
100C2×Q8×C11—26no—
101C2×Q8×C11—26no—
102C2×Q8×C11—26no—
103C2×Q8×C11—26no—
104C2×Q8×C11—26no—
105C2×Q8×C11C2×D414yes—
106C2×Q8×C11C2×Q8112yes—
107C2×Q8×C11C2×Q814yes—
108C2×Q8×C11#4114yes—
109C22×C4×C11—22no—
110C22×C4×C11—26no—
111C22×C4×C11—26no—
112C22×C4×C11—22no—
113C22×C4×C11—26no—
114C22×C4×C11—26no—
115C22×C4×C11—43no—
116C22×C4×C11C2×Q8112yes—
117C22×C4×C11#4114yes—
118C22×C4×C11C2412yes—
119C22×C4×C11C2413yes—
120C22×C4×C11C2416yes—
121C22×C4×C11C2416yes—
122C22×C4×C11C2412yes—
123C22×C4×C11C2413yes—
124C22×C4×C11C2413yes—
125C22×C4×C11C2411yescharacteristic
126C22×C4×C11C2413yes—
127C22×C4×C11C2411yescharacteristic
128C11×C4⋊C4—212no—
129C11×C4⋊C4—26no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—212no—
132C11×C4⋊C4—212no—
133C11×C4⋊C4—212no—
134C11×C4⋊C4—212no—
135C11×C4⋊C4—26no—
136C11×C4⋊C4—212no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—46no—
139C11×C4⋊C4—46no—
140C11×C4⋊C4C2×D4112yes—
141C11×C22⋊C4—212no—
142C11×C22⋊C4—24no—
143C42×C11—26no—
144C42×C11—26no—
145C42×C11—26no—
146C42×C11—212no—
147C42×C11—212no—
148C42×C11C2×D4112yes—
149C2×#557C2×C1111yescharacteristic, complemented
150C22×C4×Q8C2×C1111yescharacteristic
151#2857C2×C1113yes—
152#2582C2×C1113yescomplemented
153#2568C2×C1113yescomplemented
154#2453C2×C1116yescomplemented
155#2442C2×C1116yes—
156#2351C2×C1112yescomplemented
157Q8×C4⋊C4C2×C1111yescharacteristic, complemented
158Q8×C22⋊C4C2×C1112yes—
159C4×C22⋊Q8C2×C1113yes—
160C23×C11—21no—
161C23×C11—21no—
162C23×C11—21no—
163C23×C11—21no—
164C23×C11C22×Q812yes—
165C23×C11C2×#4112yes—
166C23×C112−1+412yes—
167C23×C11C2511yescharacteristic
168Q8×C11—224no—
169Q8×C11—412no—
170Q8×C11C22⋊Q8116yescomplemented
171C2×C4×C11—21no—
172C2×C4×C11—23no—
173C2×C4×C11—23no—
174C2×C4×C11—21no—
175C2×C4×C11—23no—
176C2×C4×C11—23no—
177C2×C4×C11—224no—
178C2×C4×C11—28no—
179C2×C4×C11—22no—
180C2×C4×C11—23no—
181C2×C4×C11—26no—
182C2×C4×C11—22no—
183C2×C4×C11—26no—
184C2×C4×C11—26no—
185C2×C4×C11—26no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—23no—
190C2×C4×C11—26no—
191C2×C4×C11—26no—
192C2×C4×C11—22no—
193C2×C4×C11—23no—
194C2×C4×C11—412no—
195C2×C4×C11C22×D416yes—
196C2×C4×C11C22×D416yes—
197C2×C4×C11C22×D412yes—
198C2×C4×C11C22×Q816yes—
199C2×C4×C11C22×Q816yes—
200C2×C4×C11C2×#4112yes—
201C2×C4×C11C2×#4116yes—
202C2×C4×C11C2×#4112yes—
203C2×C4×C112−1+412yes—
204C23×Q8C22×C1111yescharacteristic
205#557—28no—
206C2×C4⋊Q8C22×C1113yes—
207C2×#125C22×C1116yes—
208C2×C22⋊Q8C22×C1113yes—
209C2×C4×Q8—28no—
210C2×C4×Q8C22×C1113yes—
211C2×C4×Q8C22×C1113yes—
212C2×C4×Q8C22×C1112yes—
213C2×C4×Q8C22×C1112yes—
214C2×C4×Q8C22×C1111yescharacteristic
215C2×C4×Q8C22×C1113yes—
216C2×C4×Q8C22×C1111yescharacteristic
217C22×C4⋊C4C22×C1113yes—
218C22×C42C22×C1113yes—
219#400C22×C11112yes—
220#398C22×C11112yes—
221#391C22×C1113yes—
222#391C22×C1116yes—
223#391C22×C1116yes—
224#391C22×C1116yes—
225#389C22×C1113yes—
226#389C22×C1116yes—
227#389C22×C1116yes—
228#389C22×C1116yes—
229#389C22×C1116yes—
230#387C22×C1116yes—
231#385C22×C1116yes—
232#384C22×C1113yes—
233#382C22×C1116yes—
234#380C22×C1116yes—
235#380C22×C1116yes—
236#380C22×C1111yescharacteristic
237C4×C4⋊C4C22×C1113yes—
238C4×C4⋊C4C22×C1116yes—
239C4×C22⋊C4C22×C1116yes—
240C22×C11—22no—
241C22×C11—22no—
242C22×C11—22no—
243C22×C11—22no—
244C22×C11—22no—
245C22×C11—22no—
246C22×C11#55714yescomplemented
247C22×C11C23×D411yescharacteristic
248C22×C11C23×Q811yescharacteristic
249C22×C11C22×#4111yescharacteristic
250C22×C11C22×#4111yescharacteristic
251C22×C11C2×2−1+411yescharacteristic
252C22×C11C2×2−1+411yescharacteristic
253C22×C11#58511yescharacteristic
254C4×C11—26no—
255C4×C11—22no—
256C4×C11—26no—
257C4×C11—46no—
258C4×C11—46no—
259C4×C11—42no—
260C4×C11—43no—
261C4×C11—42no—
262C4×C11C2×C22⋊Q8112yes—
263C4×C11#54814yes—
264C22×Q8—24no—
265C22×Q8—24no—
266C22×Q8Q8×C1118yescomplemented
267C22×Q8C23×C1113yes—
268C22×Q8C23×C1113yes—
269C22×Q8C23×C1111yescharacteristic
270C23×C4C23×C1113yes—
271C23×C4C23×C1113yes—
272C23×C4C23×C1111yescharacteristic
273C4⋊Q8—212no—
274#125—224no—
275C22⋊Q8—212no—
276C4×Q8—24no—
277C4×Q8—28no—
278C4×Q8—28no—
279C4×Q8—212no—
280C4×Q8—212no—
281C4×Q8—212no—
282C4×Q8D4×C1118yes—
283C2×C4⋊C4—212no—
284C2×C4⋊C4C23×C1113yes—
285C2×C4⋊C4C23×C1116yes—
286C2×C4⋊C4C23×C1111yescharacteristic
287C2×C4⋊C4C23×C1116yes—
288C2×C4⋊C4C23×C1116yes—
289C2×C4⋊C4C23×C1116yes—
290C2×C4⋊C4C23×C1113yes—
291C2×C4⋊C4C23×C1116yes—
292C2×C4⋊C4C23×C1116yes—
293C2×C4⋊C4C23×C1111yescharacteristic
294C2×C4⋊C4C23×C1116yes—
295C2×C4⋊C4C23×C1116yes—
296C2×C4⋊C4C23×C1113yes—
297C2×C22⋊C4C23×C1116yes—
298C2×C22⋊C4C23×C1112yes—
299C2×C42—212no—
300C2×C42C23×C1116yes—
301C2×C42C23×C1113yes—
302C2×C42C23×C1113yes—
303C2×C42C23×C1113yes—
304C2×C42C23×C1116yes—
305C2×C42C23×C1113yes—
306#95C23×C1116yes—
307#95C23×C1116yes—
308#95C23×C1112yes—
309#95C23×C1116yes—
310#95C23×C1116yes—
311#95C23×C11112yes—
312#95C23×C11112yes—
313C2×C11—24no—
314C2×C11C22×C22⋊Q811yescharacteristic
315C2×C11C2×#54811yescharacteristic
316C2×C11C2×#55711yescharacteristic
317C2×C11#348011yescharacteristic
318C2×C11#348911yescharacteristic
319C2×C11#350211yescharacteristic
320C2×C11#352311yescharacteristic
321C24C24×C1111yescharacteristic
322C2×Q8—232no—
323C2×Q8—26no—
324C2×Q8—26no—
325C2×Q8—26no—
326C2×Q8—26no—
327C2×Q8—26no—
328C2×Q8C2×D4×C1114yes—
329C2×Q8C2×Q8×C11112yes—
330C2×Q8C2×Q8×C1114yes—
331C2×Q8C11×#4114yes—
332C22×C4—22no—
333C22×C4—26no—
334C22×C4—26no—
335C22×C4—22no—
336C22×C4—26no—
337C22×C4—26no—
338C22×C4—43no—
339C22×C4C2×Q8×C11112yes—
340C22×C4C11×#4114yes—
341C22×C4C24×C1112yes—
342C22×C4C24×C1113yes—
343C22×C4C24×C1116yes—
344C22×C4C24×C1116yes—
345C22×C4C24×C1112yes—
346C22×C4C24×C1113yes—
347C22×C4C24×C1113yes—
348C22×C4C24×C1111yescharacteristic
349C22×C4C24×C1113yes—
350C22×C4C24×C1111yescharacteristic
351C4⋊C4—212no—
352C4⋊C4—26no—
353C4⋊C4—22no—
354C4⋊C4—212no—
355C4⋊C4—212no—
356C4⋊C4—212no—
357C4⋊C4—212no—
358C4⋊C4—26no—
359C4⋊C4—212no—
360C4⋊C4—22no—
361C4⋊C4—46no—
362C4⋊C4—46no—
363C4⋊C4C2×D4×C11112yes—
364C22⋊C4—212no—
365C22⋊C4—24no—
366C42—26no—
367C42—26no—
368C42—26no—
369C42—212no—
370C42—212no—
371C42C2×D4×C11112yes—
372C11#3657711yescharacteristic, direct product factor, Sylow
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23C22×Q8×C1112yes—
378C23C2×C11×#4112yes—
379C23C11×2−1+412yes—
380C23C25×C1111yescharacteristic
381Q8—224no—
382Q8—412no—
383Q8C11×C22⋊Q8116yescomplemented
384C2×C4—21no—
385C2×C4—23no—
386C2×C4—23no—
387C2×C4—21no—
388C2×C4—23no—
389C2×C4—23no—
390C2×C4—224no—
391C2×C4—28no—
392C2×C4—22no—
393C2×C4—23no—
394C2×C4—26no—
395C2×C4—22no—
396C2×C4—26no—
397C2×C4—26no—
398C2×C4—26no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—23no—
403C2×C4—26no—
404C2×C4—26no—
405C2×C4—22no—
406C2×C4—23no—
407C2×C4—412no—
408C2×C4C22×D4×C1116yes—
409C2×C4C22×D4×C1116yes—
410C2×C4C22×D4×C1112yes—
411C2×C4C22×Q8×C1116yes—
412C2×C4C22×Q8×C1116yes—
413C2×C4C2×C11×#4112yes—
414C2×C4C2×C11×#4116yes—
415C2×C4C2×C11×#4112yes—
416C2×C4C11×2−1+412yes—
417C22—22no—
418C22—22no—
419C22—22no—
420C22—22no—
421C22—22no—
422C22—22no—
423C22C11×#55714yescomplemented
424C22C23×D4×C1111yescharacteristic
425C22C23×Q8×C1111yescharacteristic
426C22C22×C11×#4111yescharacteristic
427C22C22×C11×#4111yescharacteristic
428C22C2×C11×2−1+411yescharacteristic
429C22C2×C11×2−1+411yescharacteristic
430C22C11×#58511yescharacteristic
431C4—26no—
432C4—22no—
433C4—26no—
434C4—46no—
435C4—46no—
436C4—43no—
437C4—42no—
438C4—42no—
439C4C2×C11×C22⋊Q8112yes—
440C4C11×#54814yes—
441C2—24no—
442C2C22×C11×C22⋊Q811yescharacteristic
443C2C2×C11×#54811yescharacteristic
444C2C2×C11×#55711yescharacteristic
445C2C11×#348011yescharacteristic
446C2C11×#348911yescharacteristic
447C2C11×#350211yescharacteristic
448C2C11×#352311yescharacteristic
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. C2×C11×#557C2semidirect
4. C11×#2582C2semidirect
5. C11×#2568C2semidirect
6. C11×#2453C2semidirect
8. C11×#2351C2semidirect
9. Q8×C11×C4⋊C4C2semidirect
50. C22×Q8×C11Q8semidirect
97. #36577C11direct (N × H)
149. C2×#557C2×C11semidirect
152. #2582C2×C11semidirect
153. #2568C2×C11semidirect
154. #2453C2×C11semidirect
156. #2351C2×C11semidirect
157. Q8×C4⋊C4C2×C11semidirect
170. Q8×C11C22⋊Q8semidirect
246. C22×C11#557semidirect
266. C22×Q8Q8×C11semidirect
372. C11#36577direct (N × H)
383. Q8C11×C22⋊Q8semidirect
423. C22C11×#557semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#5572
C22×C4×Q8×C112
C11×#28572
C11×#25822
C11×#25682
C11×#24532
C11×#24422
C11×#23512
Q8×C11×C4⋊C42
Q8×C11×C22⋊C42
C4×C11×C22⋊Q82
#3657711