Finite Group Databasebeta

← C11×#23024 #14600217

Subgroups — C11×#23024 #14600217

Order 2816.

982 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#467C211yesmaximal, characteristic
2C2×C4×C11×Q16C211yesmaximal, characteristic, complemented
3C22×C11×#107C211yesmaximal, characteristic
4C11×#2360C212yesmaximal
5C11×#1969C211yesmaximal, characteristic, complemented
6C11×#1942C211yesmaximal, characteristic, complemented
7C11×#1928C212yesmaximal, complemented
8C11×#1872C212yesmaximal
9C11×#1863C212yesmaximal, complemented
10C4×C11×#107C211yesmaximal, characteristic, complemented
11C8×C11×C22⋊C4C211yesmaximal, characteristic
12C22×C11×Q16C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C11×C22⋊Q8C2212yes—
15C2×C4×Q8×C11C2212yes—
16C22×C11×C4⋊C4C2212yes—
17C11×#467C418yescomplemented
18C4×C11×Q16—24no—
19C2×C11×#107—24no—
20C2×C11×#107C2212yes—
21C2×C11×#107C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#103C2212yes—
25C2×C11×#103C2212yes—
26C2×C11×#103C2212yes—
27C2×C11×C22⋊C8C2211yescharacteristic
28C2×C4×C8×C11C2211yescharacteristic
29C2×C4×C8×C11C2211yescharacteristic
30C11×#391C2212yes—
31C11×#389—22no—
32C11×#389C2212yes—
33C11×#387—22no—
34C11×#385—22no—
35C4×C11×C4⋊C4C2212yes—
36C4×C11×C22⋊C4—22no—
37C4×C11×C22⋊C4C2211yescharacteristic
38C11×#340C2212yes—
39C11×#340C2212yes—
40C11×#336C2211yescharacteristic
41C11×#336C2211yescharacteristic
42C22×Q8×C11C2312yes—
43C23×C4×C11—22no—
44C23×C4×C11C2311yescharacteristic
45C2×C11×Q16—22no—
46C2×C11×Q16—22no—
47C2×C11×Q16C2×C414yescomplemented
48C22×C8×C11—22no—
49C22×C8×C11—22no—
50C22×C8×C11C2×C414yes—
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2311yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C11×C22⋊Q8—24no—
56C11×C22⋊Q8C2×C418yes—
57C4×Q8×C11—24no—
58C4×Q8×C11—42no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—24no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—42no—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4D411yescharacteristic
70C2×C11×C22⋊C4D411yescharacteristic
71C2×C42×C11—22no—
72C2×C42×C11—22no—
73C2×C42×C11C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C11×#107—22no—
76C11×#107—24no—
77C11×#107C2×C414yescomplemented
78C11×#107D414yes—
79C11×#103—24no—
80C11×#103—42no—
81C11×#103C2×C418yescomplemented
82C11×C22⋊C8—22no—
83C4×C8×C11—22no—
84C4×C8×C11—22no—
85C11×#95—22no—
86C11×#95—22no—
87C11×#95—22no—
88C11×#95—22no—
89C11×#95D411yescharacteristic
90C11×#95D411yescharacteristic
91#23024C1111yesmaximal, characteristic, direct product factor, Sylow
92C24×C11C2×D411yescharacteristic
93C2×Q8×C11—22no—
94C2×Q8×C11—22no—
95C2×Q8×C11—22no—
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11C22×C414yes—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—44no—
108C22×C4×C11—44no—
109C22×C4×C11—82no—
110C22×C4×C11C22×C412yes—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11#4112yes—
117C22×C4×C11C2411yescharacteristic
118C11×Q16—28no—
119C2×C8×C11—28no—
120C2×C8×C11—21no—
121C2×C8×C11—21no—
122C2×C8×C11—21no—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11—21no—
128C2×C8×C11C22×C412yes—
129C2×C8×C11C22×C412yes—
130C2×C8×C11C2×D412yes—
131C2×C8×C11#4112yes—
132C11×C4⋊C4—28no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—44no—
138C11×C4⋊C4—44no—
139C11×C4⋊C4—82no—
140C11×C4⋊C4C22×C414yes—
141C11×C4⋊C4C2×D414yes—
142C11×C22⋊C4—28no—
143C11×C22⋊C4—22no—
144C11×C22⋊C4Q1614yescomplemented
145C42×C11—21no—
146C42×C11—21no—
147C42×C11—21no—
148C42×C11—21no—
149C42×C11—44no—
150C42×C11—82no—
151C2×#467C2×C1111yescharacteristic
152C2×C4×Q16C2×C1111yescharacteristic, complemented
153C22×#107C2×C1111yescharacteristic
154#2360C2×C1112yes—
155#1969C2×C1111yescharacteristic, complemented
156#1942C2×C1111yescharacteristic, complemented
157#1928C2×C1112yescomplemented
158#1872C2×C1112yes—
159#1863C2×C1112yescomplemented
160C4×#107C2×C1111yescharacteristic, complemented
161C8×C22⋊C4C2×C1111yescharacteristic
162C23×C11—21no—
163C23×C11—21no—
164C23×C11—21no—
165C23×C11—21no—
166C23×C11C4×D412yes—
167C23×C11C2×Q1612yes—
168C23×C11#13512yes—
169C23×C11C22×D411yescharacteristic
170Q8×C11—24no—
171Q8×C11—24no—
172Q8×C11—42no—
173Q8×C11—42no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—24no—
185C2×C4×C11—24no—
186C2×C4×C11—21no—
187C2×C4×C11—24no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—88no—
203C2×C4×C11C4×D412yes—
204C2×C4×C11C2×Q1612yes—
205C2×C4×C11C2×Q1612yes—
206C2×C4×C11C23×C411yescharacteristic
207C2×C4×C11C22×D411yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C2×C4×C11H(5,𝔽2)11yescharacteristic
211C2×C4×C112−1+411yescharacteristic
212C8×C11—22no—
213C8×C11—41no—
214C8×C11—41no—
215C8×C11C4×D414yes—
216C22×Q16C22×C1111yescharacteristic
217C23×C8C22×C1111yescharacteristic
218C2×C22⋊Q8C22×C1112yes—
219C2×C4×Q8C22×C1112yes—
220C22×C4⋊C4C22×C1112yes—
221#467C4×C1118yescomplemented
222C4×Q16—24no—
223C2×#107—24no—
224C2×#107C22×C1112yes—
225C2×#107C22×C1111yescharacteristic
226C2×#107C22×C1111yescharacteristic
227C2×#107C22×C1111yescharacteristic
228C2×#103C22×C1112yes—
229C2×#103C22×C1112yes—
230C2×#103C22×C1112yes—
231C2×C22⋊C8C22×C1111yescharacteristic
232C2×C4×C8C22×C1111yescharacteristic
233C2×C4×C8C22×C1111yescharacteristic
234#391C22×C1112yes—
235#389—22no—
236#389C22×C1112yes—
237#387—22no—
238#385—22no—
239C4×C4⋊C4C22×C1112yes—
240C4×C22⋊C4—22no—
241C4×C22⋊C4C22×C1111yescharacteristic
242#340C22×C1112yes—
243#340C22×C1112yes—
244#336C22×C1111yescharacteristic
245#336C22×C1111yescharacteristic
246C22×C11—22no—
247C22×C11—22no—
248C22×C11—22no—
249C22×C11—22no—
250C22×C11—22no—
251C22×C11—22no—
252C22×C11C4×Q1614yescomplemented
253C22×C11C2×C4×D411yescharacteristic
254C22×C11D4211yescharacteristic
255C22×C11#54711yescharacteristic
256C22×C11C22×Q1611yescharacteristic
257C22×C11C2×#13511yescharacteristic
258C22×C11#57611yescharacteristic
259C22×C11#57811yescharacteristic
260C4×C11—22no—
261C4×C11—22no—
262C4×C11—22no—
263C4×C11—41no—
264C4×C11—44no—
265C4×C11—44no—
266C4×C11—41no—
267C4×C11—44no—
268C4×C11—82no—
269C4×C11C2×C4×D411yescharacteristic
270C4×C11#52011yescharacteristic
271C4×C11#54811yescharacteristic
272C4×C11#55311yescharacteristic
273C22×Q8C23×C1112yes—
274C23×C4—22no—
275C23×C4C23×C1111yescharacteristic
276C2×Q16—22no—
277C2×Q16—22no—
278C2×Q16C2×C4×C1114yescomplemented
279C22×C8—22no—
280C22×C8—22no—
281C22×C8C2×C4×C1114yes—
282C22×C8C23×C1111yescharacteristic
283C22×C8C23×C1111yescharacteristic
284C22×C8C23×C1111yescharacteristic
285C22×C8C23×C1111yescharacteristic
286C22⋊Q8—24no—
287C22⋊Q8C2×C4×C1118yes—
288C4×Q8—24no—
289C4×Q8—42no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4C23×C1112yes—
297C2×C4⋊C4C23×C1112yes—
298C2×C4⋊C4C23×C1112yes—
299C2×C22⋊C4—22no—
300C2×C22⋊C4D4×C1111yescharacteristic
301C2×C22⋊C4D4×C1111yescharacteristic
302C2×C42—22no—
303C2×C42—22no—
304C2×C42C23×C1111yescharacteristic
305C2×C42C23×C1111yescharacteristic
306#107—22no—
307#107—24no—
308#107C2×C4×C1114yescomplemented
309#107D4×C1114yes—
310#103—24no—
311#103—42no—
312#103C2×C4×C1118yescomplemented
313C22⋊C8—22no—
314C4×C8—22no—
315C4×C8—22no—
316#95—22no—
317#95—22no—
318#95—22no—
319#95—22no—
320#95D4×C1111yescharacteristic
321#95D4×C1111yescharacteristic
322C2×C11—24no—
323C2×C11#236111yescharacteristic
324C2×C11C2×C4×Q1611yescharacteristic
325C2×C11#295111yescharacteristic
326C2×C11#328011yescharacteristic
327C2×C11D4×Q1611yescharacteristic
328C2×C11#333611yescharacteristic
329C2×C11#333811yescharacteristic
330C24C2×D4×C1111yescharacteristic
331C2×Q8—22no—
332C2×Q8—22no—
333C2×Q8—22no—
334C2×Q8—22no—
335C2×Q8—22no—
336C2×Q8C22×C4×C1114yes—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—44no—
346C22×C4—44no—
347C22×C4—82no—
348C22×C4C22×C4×C1112yes—
349C22×C4C2×D4×C1111yescharacteristic
350C22×C4C2×D4×C1111yescharacteristic
351C22×C4C2×D4×C1111yescharacteristic
352C22×C4C2×D4×C1111yescharacteristic
353C22×C4C2×D4×C1111yescharacteristic
354C22×C4C11×#4112yes—
355C22×C4C24×C1111yescharacteristic
356Q16—28no—
357C2×C8—21no—
358C2×C8—21no—
359C2×C8—28no—
360C2×C8—21no—
361C2×C8—21no—
362C2×C8—21no—
363C2×C8—21no—
364C2×C8—21no—
365C2×C8—21no—
366C2×C8C22×C4×C1112yes—
367C2×C8C22×C4×C1112yes—
368C2×C8C2×D4×C1112yes—
369C2×C8C11×#4112yes—
370C4⋊C4—28no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—44no—
376C4⋊C4—44no—
377C4⋊C4—82no—
378C4⋊C4C22×C4×C1114yes—
379C4⋊C4C2×D4×C1114yes—
380C22⋊C4—28no—
381C22⋊C4—22no—
382C22⋊C4C11×Q1614yescomplemented
383C42—21no—
384C42—21no—
385C42—21no—
386C42—21no—
387C42—44no—
388C42—82no—
389C11#2302411yescharacteristic, direct product factor, Sylow
390C23—21no—
391C23—21no—
392C23—21no—
393C23—21no—
394C23C4×D4×C1112yes—
395C23C2×C11×Q1612yes—
396C23C11×#13512yes—
397C23C22×D4×C1111yescharacteristic
398Q8—24no—
399Q8—24no—
400Q8—42no—
401Q8—42no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—21no—
415C2×C4—24no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—88no—
431C2×C4C4×D4×C1112yes—
432C2×C4C2×C11×Q1612yes—
433C2×C4C2×C11×Q1612yes—
434C2×C4C23×C4×C1111yescharacteristic
435C2×C4C22×D4×C1111yescharacteristic
436C2×C4C2×C11×#4111yescharacteristic
437C2×C4C2×C11×#4111yescharacteristic
438C2×C4C11×H(5,𝔽2)11yescharacteristic
439C2×C4C11×2−1+411yescharacteristic
440C8—22no—
441C8—41no—
442C8—41no—
443C8C4×D4×C1114yes—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22C4×C11×Q1614yescomplemented
451C22C2×C4×D4×C1111yescharacteristic
452C22D42×C1111yescharacteristic
453C22C11×#54711yescharacteristic
454C22C22×C11×Q1611yescharacteristic
455C22C2×C11×#13511yescharacteristic
456C22C11×#57611yescharacteristic
457C22C11×#57811yescharacteristic
458C4—22no—
459C4—22no—
460C4—22no—
461C4—44no—
462C4—41no—
463C4—44no—
464C4—41no—
465C4—44no—
466C4—82no—
467C4C2×C4×D4×C1111yescharacteristic
468C4C11×#52011yescharacteristic
469C4C11×#54811yescharacteristic
470C4C11×#55311yescharacteristic
471C2—24no—
472C2C11×#236111yescharacteristic
473C2C2×C4×C11×Q1611yescharacteristic
474C2C11×#295111yescharacteristic
475C2C11×#328011yescharacteristic
476C2D4×C11×Q1611yescharacteristic
477C2C11×#333611yescharacteristic
478C2C11×#333811yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×C11×Q16C2semidirect
5. C11×#1969C2semidirect
6. C11×#1942C2semidirect
7. C11×#1928C2semidirect
9. C11×#1863C2semidirect
10. C4×C11×#107C2semidirect
17. C11×#467C4semidirect
47. C2×C11×Q16C2×C4semidirect
77. C11×#107C2×C4semidirect
81. C11×#103C2×C4semidirect
91. #23024C11direct (N × H)
144. C11×C22⋊C4Q16semidirect
152. C2×C4×Q16C2×C11semidirect
155. #1969C2×C11semidirect
156. #1942C2×C11semidirect
157. #1928C2×C11semidirect
159. #1863C2×C11semidirect
160. C4×#107C2×C11semidirect
221. #467C4×C11semidirect
252. C22×C11C4×Q16semidirect
278. C2×Q16C2×C4×C11semidirect
308. #107C2×C4×C11semidirect
312. #103C2×C4×C11semidirect
382. C22⋊C4C11×Q16semidirect
389. C11#23024direct (N × H)
450. C22C4×C11×Q16semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4672
C2×C4×C11×Q162
C22×C11×#1072
C11×#23602
C11×#19692
C11×#19422
C11×#19282
C11×#18722
C11×#18632
C4×C11×#1072
C8×C11×C22⋊C42
#2302411