Finite Group Databasebeta

← C11×#24732 #14601925

Subgroups — C11×#24732 #14601925

Order 2816.

914 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#462C212yesmaximal
2C2×C11×#462C211yesmaximal, characteristic
3C2×C4×C11×Q16C211yesmaximal, characteristic
4C11×#2546C211yesmaximal, characteristic
5Q8×C11×C4⋊C4C211yesmaximal, characteristic
6C11×#2068C212yesmaximal
7C11×#2043C212yesmaximal
8C11×#1956C211yesmaximal, characteristic
9C11×#1939C211yesmaximal, characteristic
10C11×#1878C212yesmaximal
11C11×#1803C211yesmaximal, characteristic
12C22×C11×Q16C2212yes—
13C22×C11×Q16C2211yescharacteristic
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×C4⋊Q8C2212yes—
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×Q8×C11C2212yes—
18C2×C4×Q8×C11C2211yescharacteristic
19C11×#462—28no—
20C11×#462—24no—
21C4×C11×Q16—24no—
22C2×C11×#107C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2212yes—
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2212yes—
28C2×C11×#103C2212yes—
29C2×C11×#103C2212yes—
30C2×C11×#103C2212yes—
31C2×C4×C8×C11C2211yescharacteristic
32C11×#398—22no—
33C11×#391C2212yes—
34C11×#389—21no—
35C11×#389—21no—
36C11×#389—22no—
37C11×#389C2212yes—
38C11×#384—21no—
39C11×#384C2211yescharacteristic
40C4×C11×C4⋊C4—21no—
41C4×C11×C4⋊C4C2211yescharacteristic
42C11×#340C2212yes—
43C11×#336C2212yes—
44C22×Q8×C11C2312yes—
45C22×Q8×C11C2311yescharacteristic
46C22×Q8×C11C2311yescharacteristic
47C2×C11×Q16—22no—
48C2×C11×Q16—22no—
49C2×C11×Q16—24no—
50C2×C11×Q16—24no—
51C2×C11×Q16—24no—
52C2×C11×Q16D414yes—
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2312yes—
55C22×C8×C11C2311yescharacteristic
56C11×C4⋊Q8—24no—
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8—22no—
59C11×C4⋊Q8—42no—
60C4×Q8×C11—22no—
61C4×Q8×C11—24no—
62C4×Q8×C11—22no—
63C4×Q8×C11—22no—
64C4×Q8×C11—42no—
65C4×Q8×C11D414yes—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C42×C11—21no—
82C2×C42×C11—22no—
83C2×C42×C11—21no—
84C2×C42×C11C2312yes—
85C2×C42×C11C2311yescharacteristic
86C11×#107—22no—
87C11×C4⋊C8—24no—
88C11×C4⋊C8—22no—
89C11×#103—22no—
90C11×#103—24no—
91C11×#103—24no—
92C11×#103—22no—
93C11×#103—24no—
94C11×#103—42no—
95C4×C8×C11—22no—
96C11×#95—22no—
97C11×#95—22no—
98C11×#95—22no—
99C11×#95D412yes—
100#24732C1111yesmaximal, characteristic, direct product factor, Sylow
101C2×Q8×C11—21no—
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—21no—
114C2×Q8×C11—22no—
115C2×Q8×C11C2×D412yes—
116C2×Q8×C11C2×D412yes—
117C2×Q8×C11C2×D412yes—
118C2×Q8×C11#4112yes—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2411yescharacteristic
130C11×Q16—28no—
131C11×Q16—48no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C2×C8×C11—21no—
137C2×C8×C11—22no—
138C2×C8×C11—21no—
139C2×C8×C11—21no—
140C2×C8×C11C2×D412yes—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—44no—
149C11×C4⋊C4—44no—
150C11×C4⋊C4—44no—
151C11×C4⋊C4—42no—
152C11×C4⋊C4—42no—
153C11×C4⋊C4—42no—
154C11×C4⋊C4—42no—
155C11×C4⋊C4—81no—
156C11×C4⋊C4—82no—
157C11×C4⋊C4Q1614yescomplemented
158C11×C4⋊C4C2×D412yes—
159C42×C11—24no—
160C42×C11—22no—
161C42×C11—22no—
162C42×C11—44no—
163C42×C11—42no—
164C42×C11C2×D412yes—
165C42×C11#4112yes—
166C2×#462C2×C1112yes—
167C2×#462C2×C1111yescharacteristic
168C2×C4×Q16C2×C1111yescharacteristic
169#2546C2×C1111yescharacteristic
170Q8×C4⋊C4C2×C1111yescharacteristic
171#2068C2×C1112yes—
172#2043C2×C1112yes—
173#1956C2×C1111yescharacteristic
174#1939C2×C1111yescharacteristic
175#1878C2×C1112yes—
176#1803C2×C1111yescharacteristic
177C23×C11C22×D411yescharacteristic
178Q8×C11—22no—
179Q8×C11—22no—
180Q8×C11—22no—
181Q8×C11—22no—
182Q8×C11—22no—
183Q8×C11—41no—
184Q8×C11—41no—
185Q8×C11—42no—
186Q8×C11—42no—
187Q8×C11—42no—
188Q8×C11—42no—
189Q8×C11#12114yes—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—21no—
195C2×C4×C11—22no—
196C2×C4×C11—21no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11#12112yes—
216C2×C4×C11#12112yes—
217C2×C4×C11C2×Q1614yes—
218C2×C4×C11C2×Q1612yes—
219C2×C4×C11#13712yes—
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C2×#4111yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C2×C4×C11H(5,𝔽2)11yescharacteristic
225C2×C4×C112−1+411yescharacteristic
226C8×C11—22no—
227C8×C11—42no—
228C8×C11—41no—
229C22×Q16C22×C1112yes—
230C22×Q16C22×C1111yescharacteristic
231C2×C4⋊Q8C22×C1111yescharacteristic
232C2×C4⋊Q8C22×C1112yes—
233C2×C4×Q8C22×C1111yescharacteristic
234C2×C4×Q8C22×C1112yes—
235C2×C4×Q8C22×C1111yescharacteristic
236#462—28no—
237#462—24no—
238C4×Q16—24no—
239C2×#107C22×C1111yescharacteristic
240C2×C4⋊C8C22×C1111yescharacteristic
241C2×C4⋊C8C22×C1112yes—
242C2×#103C22×C1112yes—
243C2×#103C22×C1112yes—
244C2×#103C22×C1112yes—
245C2×#103C22×C1111yescharacteristic
246C2×#103C22×C1111yescharacteristic
247C2×#103C22×C1112yes—
248C2×C4×C8C22×C1111yescharacteristic
249#398—22no—
250#391C22×C1112yes—
251#389—21no—
252#389—21no—
253#389—22no—
254#389C22×C1112yes—
255#384—21no—
256#384C22×C1111yescharacteristic
257C4×C4⋊C4—21no—
258C4×C4⋊C4C22×C1111yescharacteristic
259#340C22×C1112yes—
260#336C22×C1112yes—
261C22×C11C2×#12111yescharacteristic
262C22×C11D4211yescharacteristic
263C22×C11#54811yescharacteristic
264C22×C11C22×Q1611yescharacteristic
265C22×C11C2×#13711yescharacteristic
266C22×C11#57711yescharacteristic
267C22×C11#57811yescharacteristic
268C4×C11—24no—
269C4×C11—24no—
270C4×C11—22no—
271C4×C11—42no—
272C4×C11—42no—
273C4×C11—42no—
274C4×C11—82no—
275C4×C11—82no—
276C4×C11—81no—
277C4×C11#46214yescomplemented
278C4×C11C2×#12111yescharacteristic
279C4×C11#53711yescharacteristic
280C4×C11#54711yescharacteristic
281C4×C11#55311yescharacteristic
282C22×Q8C23×C1112yes—
283C22×Q8C23×C1111yescharacteristic
284C22×Q8C23×C1111yescharacteristic
285C2×Q16—22no—
286C2×Q16—22no—
287C2×Q16—24no—
288C2×Q16—24no—
289C2×Q16—24no—
290C2×Q16D4×C1114yes—
291C22×C8C23×C1112yes—
292C22×C8C23×C1111yescharacteristic
293C22×C8C23×C1111yescharacteristic
294C4⋊Q8—24no—
295C4⋊Q8—22no—
296C4⋊Q8—22no—
297C4⋊Q8—42no—
298C4×Q8—22no—
299C4×Q8—24no—
300C4×Q8—22no—
301C4×Q8—22no—
302C4×Q8—42no—
303C4×Q8D4×C1114yes—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4D4×C1111yescharacteristic
315C2×C4⋊C4D4×C1111yescharacteristic
316C2×C4⋊C4C23×C1111yescharacteristic
317C2×C4⋊C4C23×C1112yes—
318C2×C4⋊C4C23×C1111yescharacteristic
319C2×C42—21no—
320C2×C42—22no—
321C2×C42—21no—
322C2×C42C23×C1112yes—
323C2×C42C23×C1111yescharacteristic
324#107—22no—
325C4⋊C8—24no—
326C4⋊C8—22no—
327#103—22no—
328#103—24no—
329#103—24no—
330#103—22no—
331#103—24no—
332#103—42no—
333C4×C8—22no—
334#95—22no—
335#95—22no—
336#95—22no—
337#95D4×C1112yes—
338C2×C11#241611yescharacteristic
339C2×C11C2×#46211yescharacteristic
340C2×C11#304611yescharacteristic
341C2×C11#327811yescharacteristic
342C2×C11D4×Q1611yescharacteristic
343C2×C11#336311yescharacteristic
344C2×C11#337411yescharacteristic
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—21no—
348C2×Q8—21no—
349C2×Q8—21no—
350C2×Q8—22no—
351C2×Q8—22no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8—22no—
355C2×Q8—22no—
356C2×Q8—22no—
357C2×Q8—21no—
358C2×Q8—22no—
359C2×Q8C2×D4×C1112yes—
360C2×Q8C2×D4×C1112yes—
361C2×Q8C2×D4×C1112yes—
362C2×Q8C11×#4112yes—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4C2×D4×C1112yes—
370C22×C4C2×D4×C1111yescharacteristic
371C22×C4C2×D4×C1112yes—
372C22×C4C2×D4×C1111yescharacteristic
373C22×C4C24×C1111yescharacteristic
374Q16—28no—
375Q16—48no—
376C2×C8—21no—
377C2×C8—21no—
378C2×C8—21no—
379C2×C8—22no—
380C2×C8—22no—
381C2×C8—22no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8C2×D4×C1112yes—
385C4⋊C4—24no—
386C4⋊C4—22no—
387C4⋊C4—21no—
388C4⋊C4—22no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—22no—
392C4⋊C4—44no—
393C4⋊C4—44no—
394C4⋊C4—44no—
395C4⋊C4—42no—
396C4⋊C4—42no—
397C4⋊C4—42no—
398C4⋊C4—42no—
399C4⋊C4—81no—
400C4⋊C4—82no—
401C4⋊C4C11×Q1614yescomplemented
402C4⋊C4C2×D4×C1112yes—
403C42—24no—
404C42—22no—
405C42—22no—
406C42—44no—
407C42—42no—
408C42C2×D4×C1112yes—
409C42C11×#4112yes—
410C11#2473211yescharacteristic, direct product factor, Sylow
411C23C22×D4×C1111yescharacteristic
412Q8—22no—
413Q8—22no—
414Q8—22no—
415Q8—22no—
416Q8—22no—
417Q8—41no—
418Q8—41no—
419Q8—42no—
420Q8—42no—
421Q8—42no—
422Q8—42no—
423Q8C11×#12114yes—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—21no—
429C2×C4—22no—
430C2×C4—21no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4C11×#12112yes—
450C2×C4C11×#12112yes—
451C2×C4C2×C11×Q1614yes—
452C2×C4C2×C11×Q1612yes—
453C2×C4C11×#13712yes—
454C2×C4C22×D4×C1111yescharacteristic
455C2×C4C22×D4×C1111yescharacteristic
456C2×C4C2×C11×#4111yescharacteristic
457C2×C4C2×C11×#4111yescharacteristic
458C2×C4C11×H(5,𝔽2)11yescharacteristic
459C2×C4C11×2−1+411yescharacteristic
460C8—22no—
461C8—42no—
462C8—41no—
463C22C2×C11×#12111yescharacteristic
464C22D42×C1111yescharacteristic
465C22C11×#54811yescharacteristic
466C22C22×C11×Q1611yescharacteristic
467C22C2×C11×#13711yescharacteristic
468C22C11×#57711yescharacteristic
469C22C11×#57811yescharacteristic
470C4—24no—
471C4—24no—
472C4—22no—
473C4—42no—
474C4—42no—
475C4—42no—
476C4—82no—
477C4—82no—
478C4—81no—
479C4C11×#46214yescomplemented
480C4C2×C11×#12111yescharacteristic
481C4C11×#53711yescharacteristic
482C4C11×#54711yescharacteristic
483C4C11×#55311yescharacteristic
484C2C11×#241611yescharacteristic
485C2C2×C11×#46211yescharacteristic
486C2C11×#304611yescharacteristic
487C2C11×#327811yescharacteristic
488C2D4×C11×Q1611yescharacteristic
489C2C11×#336311yescharacteristic
490C2C11×#337411yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C4×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
100. #24732C11direct (N × H)
157. C11×C4⋊C4Q16semidirect
277. C4×C11#462semidirect
401. C4⋊C4C11×Q16semidirect
410. C11#24732direct (N × H)
479. C4C11×#462semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#4622
C2×C4×C11×Q162
C11×#25462
Q8×C11×C4⋊C42
C11×#20682
C11×#20432
C11×#19562
C11×#19392
C11×#18782
C11×#18032
#2473211