Finite Group Databasebeta

← C11×#24632 #14601825

Subgroups — C11×#24632 #14601825

Order 2816.

830 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#462C211yesmaximal, characteristic
2C2×C4×C11×Q16C211yesmaximal, characteristic
3C11×#2546C211yesmaximal, characteristic
4C11×#2355C211yesmaximal, characteristic
5C11×#2056C212yesmaximal
6C11×#2016C212yesmaximal
7C11×#1981C212yesmaximal
8C11×#1956C211yesmaximal, characteristic
9C11×#1939C211yesmaximal, characteristic
10C11×#1928C212yesmaximal
11C11×#1803C211yesmaximal, characteristic
12C22×C11×Q16C2211yescharacteristic
13C22×C11×Q16C2212yes—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×C4⋊Q8C2212yes—
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C11×#462—24no—
19C4×C11×Q16—24no—
20C2×C11×#107C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C4⋊C8C2212yes—
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2212yes—
26C2×C11×#103C2212yes—
27C2×C11×#103C2212yes—
28C2×C11×#103C2212yes—
29C2×C4×C8×C11C2211yescharacteristic
30C11×#398—22no—
31C11×#391C2212yes—
32C11×#391C2212yes—
33C11×#389—21no—
34C11×#389—21no—
35C11×#387—22no—
36C11×#384C2211yescharacteristic
37C11×#382—21no—
38C4×C11×C4⋊C4—21no—
39C4×C11×C4⋊C4C2212yes—
40C4×C11×C4⋊C4C2211yescharacteristic
41C11×#340C2212yes—
42C11×#336C2212yes—
43C22×Q8×C11C2312yes—
44C22×Q8×C11C2311yescharacteristic
45C22×Q8×C11C2311yescharacteristic
46C2×C11×Q16—22no—
47C2×C11×Q16—22no—
48C2×C11×Q16—24no—
49C2×C11×Q16—22no—
50C2×C11×Q16—42no—
51C2×C11×Q16—42no—
52C22×C8×C11C2312yes—
53C22×C8×C11C2311yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C11×C4⋊Q8—24no—
56C11×C4⋊Q8—22no—
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8—42no—
59C4×Q8×C11—22no—
60C4×Q8×C11—22no—
61C4×Q8×C11—22no—
62C4×Q8×C11D414yes—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2312yes—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C42×C11—21no—
77C2×C42×C11—21no—
78C2×C42×C11—22no—
79C2×C42×C11C2312yes—
80C2×C42×C11C2311yescharacteristic
81C11×#107—22no—
82C11×C4⋊C8—22no—
83C11×C4⋊C8—42no—
84C11×#103—22no—
85C11×#103—24no—
86C11×#103—22no—
87C11×#103—24no—
88C11×#103—42no—
89C11×#103—42no—
90C4×C8×C11—22no—
91C11×#95—22no—
92C11×#95—22no—
93C11×#95—22no—
94C11×#95—22no—
95C11×#95—22no—
96C11×#95D412yes—
97#24632C1111yesmaximal, characteristic, direct product factor, Sylow
98C2×Q8×C11—21no—
99C2×Q8×C11—21no—
100C2×Q8×C11—21no—
101C2×Q8×C11—22no—
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—22no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11C2×D412yes—
115C2×Q8×C11#4112yes—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C11×Q16—28no—
128C11×Q16—48no—
129C2×C8×C11—21no—
130C2×C8×C11—21no—
131C2×C8×C11—22no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11—22no—
135C2×C8×C11—21no—
136C2×C8×C11—22no—
137C2×C8×C11#4112yes—
138C11×C4⋊C4—24no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—44no—
146C11×C4⋊C4—44no—
147C11×C4⋊C4—42no—
148C11×C4⋊C4—42no—
149C11×C4⋊C4—42no—
150C11×C4⋊C4—42no—
151C11×C4⋊C4—81no—
152C11×C4⋊C4Q1614yescomplemented
153C11×C4⋊C4C2×D412yes—
154C42×C11—24no—
155C42×C11—22no—
156C42×C11—22no—
157C42×C11—42no—
158C42×C11—82no—
159C42×C11C2×D412yes—
160C42×C11#4112yes—
161C2×#462C2×C1111yescharacteristic
162C2×C4×Q16C2×C1111yescharacteristic
163#2546C2×C1111yescharacteristic
164#2355C2×C1111yescharacteristic
165#2056C2×C1112yes—
166#2016C2×C1112yes—
167#1981C2×C1112yes—
168#1956C2×C1111yescharacteristic
169#1939C2×C1111yescharacteristic
170#1928C2×C1112yes—
171#1803C2×C1111yescharacteristic
172C23×C11C22×D411yescharacteristic
173Q8×C11—22no—
174Q8×C11—22no—
175Q8×C11—22no—
176Q8×C11—22no—
177Q8×C11—41no—
178Q8×C11—41no—
179Q8×C11—41no—
180Q8×C11—41no—
181Q8×C11—42no—
182Q8×C11—42no—
183Q8×C11—42no—
184Q8×C11—42no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11#12112yes—
211C2×C4×C11#12112yes—
212C2×C4×C11C2×Q1614yes—
213C2×C4×C11C2×Q1612yes—
214C2×C4×C11#13712yes—
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C11C2×#4111yescharacteristic
218C2×C4×C11C2×#4111yescharacteristic
219C2×C4×C11H(5,𝔽2)11yescharacteristic
220C2×C4×C11H(5,𝔽2)11yescharacteristic
221C8×C11—22no—
222C8×C11—41no—
223C8×C11—42no—
224C22×Q16C22×C1111yescharacteristic
225C22×Q16C22×C1112yes—
226C2×C4⋊Q8C22×C1111yescharacteristic
227C2×C4⋊Q8C22×C1112yes—
228C2×C4×Q8C22×C1111yescharacteristic
229C2×C4×Q8C22×C1111yescharacteristic
230#462—24no—
231C4×Q16—24no—
232C2×#107C22×C1111yescharacteristic
233C2×C4⋊C8C22×C1111yescharacteristic
234C2×C4⋊C8C22×C1112yes—
235C2×#103C22×C1111yescharacteristic
236C2×#103C22×C1111yescharacteristic
237C2×#103C22×C1112yes—
238C2×#103C22×C1112yes—
239C2×#103C22×C1112yes—
240C2×#103C22×C1112yes—
241C2×C4×C8C22×C1111yescharacteristic
242#398—22no—
243#391C22×C1112yes—
244#391C22×C1112yes—
245#389—21no—
246#389—21no—
247#387—22no—
248#384C22×C1111yescharacteristic
249#382—21no—
250C4×C4⋊C4—21no—
251C4×C4⋊C4C22×C1112yes—
252C4×C4⋊C4C22×C1111yescharacteristic
253#340C22×C1112yes—
254#336C22×C1112yes—
255C22×C11C2×#12111yescharacteristic
256C22×C11#54611yescharacteristic
257C22×C11#55011yescharacteristic
258C22×C11C22×Q1611yescharacteristic
259C22×C11C2×#13711yescharacteristic
260C22×C11#57711yescharacteristic
261C22×C11#57811yescharacteristic
262C4×C11—24no—
263C4×C11—22no—
264C4×C11—42no—
265C4×C11—42no—
266C4×C11—42no—
267C4×C11—42no—
268C4×C11—82no—
269C4×C11—82no—
270C4×C11—81no—
271C4×C11#46214yes—
272C4×C11#52511yescharacteristic
273C4×C11#53511yescharacteristic
274C4×C11#55311yescharacteristic
275C4×C11#55511yescharacteristic
276C22×Q8C23×C1112yes—
277C22×Q8C23×C1111yescharacteristic
278C22×Q8C23×C1111yescharacteristic
279C2×Q16—22no—
280C2×Q16—22no—
281C2×Q16—24no—
282C2×Q16—22no—
283C2×Q16—42no—
284C2×Q16—42no—
285C22×C8C23×C1112yes—
286C22×C8C23×C1111yescharacteristic
287C22×C8C23×C1111yescharacteristic
288C4⋊Q8—24no—
289C4⋊Q8—22no—
290C4⋊Q8—22no—
291C4⋊Q8—42no—
292C4×Q8—22no—
293C4×Q8—22no—
294C4×Q8—22no—
295C4×Q8D4×C1114yes—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4D4×C1111yescharacteristic
305C2×C4⋊C4D4×C1111yescharacteristic
306C2×C4⋊C4C23×C1111yescharacteristic
307C2×C4⋊C4C23×C1112yes—
308C2×C4⋊C4C23×C1111yescharacteristic
309C2×C42—21no—
310C2×C42—21no—
311C2×C42—22no—
312C2×C42C23×C1112yes—
313C2×C42C23×C1111yescharacteristic
314#107—22no—
315C4⋊C8—22no—
316C4⋊C8—42no—
317#103—22no—
318#103—24no—
319#103—22no—
320#103—24no—
321#103—42no—
322#103—42no—
323C4×C8—22no—
324#95—22no—
325#95—22no—
326#95—22no—
327#95—22no—
328#95—22no—
329#95D4×C1112yes—
330C2×C11#241411yescharacteristic
331C2×C11C2×#46211yescharacteristic
332C2×C11#304611yescharacteristic
333C2×C11#329911yescharacteristic
334C2×C11#332811yescharacteristic
335C2×C11#339511yescharacteristic
336C2×C11#340011yescharacteristic
337C2×Q8—21no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—22no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8—21no—
344C2×Q8—21no—
345C2×Q8—22no—
346C2×Q8—22no—
347C2×Q8—22no—
348C2×Q8—21no—
349C2×Q8—21no—
350C2×Q8—21no—
351C2×Q8—22no—
352C2×Q8—22no—
353C2×Q8C2×D4×C1112yes—
354C2×Q8C11×#4112yes—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4C2×D4×C1112yes—
362C22×C4C2×D4×C1111yescharacteristic
363C22×C4C2×D4×C1112yes—
364C22×C4C2×D4×C1111yescharacteristic
365C22×C4C24×C1111yescharacteristic
366Q16—28no—
367Q16—48no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—22no—
372C2×C8—21no—
373C2×C8—22no—
374C2×C8—21no—
375C2×C8—22no—
376C2×C8C11×#4112yes—
377C4⋊C4—24no—
378C4⋊C4—22no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—21no—
383C4⋊C4—22no—
384C4⋊C4—44no—
385C4⋊C4—44no—
386C4⋊C4—42no—
387C4⋊C4—42no—
388C4⋊C4—42no—
389C4⋊C4—42no—
390C4⋊C4—81no—
391C4⋊C4C11×Q1614yescomplemented
392C4⋊C4C2×D4×C1112yes—
393C42—24no—
394C42—22no—
395C42—22no—
396C42—42no—
397C42—82no—
398C42C2×D4×C1112yes—
399C42C11×#4112yes—
400C11#2463211yescharacteristic, direct product factor, Sylow
401C23C22×D4×C1111yescharacteristic
402Q8—22no—
403Q8—22no—
404Q8—22no—
405Q8—22no—
406Q8—41no—
407Q8—41no—
408Q8—41no—
409Q8—41no—
410Q8—42no—
411Q8—42no—
412Q8—42no—
413Q8—42no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4C11×#12112yes—
440C2×C4C11×#12112yes—
441C2×C4C2×C11×Q1614yes—
442C2×C4C2×C11×Q1612yes—
443C2×C4C11×#13712yes—
444C2×C4C22×D4×C1111yescharacteristic
445C2×C4C2×C11×#4111yescharacteristic
446C2×C4C2×C11×#4111yescharacteristic
447C2×C4C2×C11×#4111yescharacteristic
448C2×C4C11×H(5,𝔽2)11yescharacteristic
449C2×C4C11×H(5,𝔽2)11yescharacteristic
450C8—22no—
451C8—42no—
452C8—41no—
453C22C2×C11×#12111yescharacteristic
454C22C11×#54611yescharacteristic
455C22C11×#55011yescharacteristic
456C22C22×C11×Q1611yescharacteristic
457C22C2×C11×#13711yescharacteristic
458C22C11×#57711yescharacteristic
459C22C11×#57811yescharacteristic
460C4—24no—
461C4—22no—
462C4—42no—
463C4—42no—
464C4—42no—
465C4—42no—
466C4—82no—
467C4—81no—
468C4—82no—
469C4C11×#46214yes—
470C4C11×#52511yescharacteristic
471C4C11×#53511yescharacteristic
472C4C11×#55311yescharacteristic
473C4C11×#55511yescharacteristic
474C2C11×#241411yescharacteristic
475C2C2×C11×#46211yescharacteristic
476C2C11×#304611yescharacteristic
477C2C11×#329911yescharacteristic
478C2C11×#332811yescharacteristic
479C2C11×#339511yescharacteristic
480C2C11×#340011yescharacteristic
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
97. #24632C11direct (N × H)
152. C11×C4⋊C4Q16semidirect
391. C4⋊C4C11×Q16semidirect
400. C11#24632direct (N × H)

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
C11×#23552
C11×#20562
C11×#20162
C11×#19812
C11×#19562
C11×#19392
C11×#19282
C11×#18032
#2463211