Finite Group Databasebeta

← C11×#24344 #14601537

Subgroups — C11×#24344 #14601537

Order 2816.

988 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#557C211yesmaximal, characteristic
2C2×C11×#477C211yesmaximal, characteristic
3C2×C11×#441C211yesmaximal, characteristic
4C11×#2581C211yesmaximal, characteristic
5C11×#2059C212yesmaximal
6C11×#2026C212yesmaximal
7C11×#1993C211yesmaximal, characteristic
8C11×#1985C211yesmaximal, characteristic
9C11×#1878C212yesmaximal
10C11×#1863C212yesmaximal
11C11×#1805C211yesmaximal, characteristic
12C22×C11×Q16C2211yescharacteristic
13C11×#557—24no—
14C11×#557—24no—
15C2×C11×C4⋊Q8—21no—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#125—22no—
18C2×C11×#125C2212yes—
19C2×C4×Q8×C11—21no—
20C2×C4×Q8×C11C2212yes—
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×Q8×C11C2211yescharacteristic
24C11×#477—24no—
25C11×#441—24no—
26C2×C11×#107C2212yes—
27C2×C11×#106C2211yescharacteristic
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×#103C2212yes—
30C2×C11×#103C2212yes—
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#97C2211yescharacteristic
34C11×#400—21no—
35C11×#395—21no—
36C11×#391C2212yes—
37C11×#389C2212yes—
38C11×#387—22no—
39C11×#382C2211yescharacteristic
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#336C2212yes—
44C11×#336C2212yes—
45C22×Q8×C11—21no—
46C22×Q8×C11D411yescharacteristic
47C22×Q8×C11C2311yescharacteristic
48C22×Q8×C11C2311yescharacteristic
49C2×C11×Q16—22no—
50C2×C11×Q16—22no—
51C2×C11×Q16Q814yescomplemented
52C22×C8×C11C2311yescharacteristic
53C22×C8×C11C2312yes—
54C22×C8×C11C2311yescharacteristic
55C11×C4⋊Q8—28no—
56C11×C4⋊Q8—22no—
57C11×C4⋊Q8D414yes—
58C11×#125—216no—
59C11×#125—24no—
60C11×#125—24no—
61C4×Q8×C11—28no—
62C4×Q8×C11—24no—
63C4×Q8×C11—24no—
64C4×Q8×C11—22no—
65C4×Q8×C11—22no—
66C4×Q8×C11—22no—
67C4×Q8×C11—22no—
68C4×Q8×C11—22no—
69C4×Q8×C11D414yes—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4D412yes—
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2312yes—
83C2×C42×C11—22no—
84C2×C42×C11—21no—
85C2×C42×C11—21no—
86C2×C42×C11C2312yes—
87C2×C42×C11C2311yescharacteristic
88C11×#107—24no—
89C11×#106—22no—
90C11×C4⋊C8—22no—
91C11×#103—22no—
92C11×#103—24no—
93C11×#103—22no—
94C11×#103—24no—
95C11×#97—22no—
96C11×#95—21no—
97C11×#95—21no—
98C11×#95—22no—
99C11×#95—22no—
100C11×#95—22no—
101#24344C1111yesmaximal, characteristic, direct product factor, Sylow
102C2×Q8×C11—22no—
103C2×Q8×C11—24no—
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11—21no—
107C2×Q8×C11—21no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—42no—
113C2×Q8×C11—44no—
114C2×Q8×C11C2×D412yes—
115C2×Q8×C11C2×Q812yes—
116C2×Q8×C11C2×Q812yes—
117C2×Q8×C11#4112yes—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—21no—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2411yescharacteristic
129C11×Q16—28no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11—22no—
133C2×C8×C11—21no—
134C2×C8×C11—22no—
135C2×C8×C11—21no—
136C2×C8×C11—22no—
137C2×C8×C11—21no—
138C2×C8×C11C2×Q812yes—
139C11×C4⋊C4—28no—
140C11×C4⋊C4—28no—
141C11×C4⋊C4—28no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—44no—
153C11×C4⋊C4—42no—
154C11×C4⋊C4C2×D412yes—
155C11×C4⋊C4C2×D414yes—
156C42×C11—28no—
157C42×C11—24no—
158C42×C11—22no—
159C42×C11—22no—
160C42×C11—42no—
161C42×C11C2×D412yes—
162C42×C11C2×D412yes—
163C2×#557C2×C1111yescharacteristic
164C2×#477C2×C1111yescharacteristic
165C2×#441C2×C1111yescharacteristic
166#2581C2×C1111yescharacteristic
167#2059C2×C1112yes—
168#2026C2×C1112yes—
169#1993C2×C1111yescharacteristic
170#1985C2×C1111yescharacteristic
171#1878C2×C1112yes—
172#1863C2×C1112yes—
173#1805C2×C1111yescharacteristic
174C23×C11C22×D411yescharacteristic
175Q8×C11—22no—
176Q8×C11—22no—
177Q8×C11—22no—
178Q8×C11—22no—
179Q8×C11—22no—
180Q8×C11—44no—
181Q8×C11—48no—
182Q8×C11—41no—
183Q8×C11—41no—
184Q8×C11C22⋊Q814yes—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—24no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—24no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—44no—
201C2×C4×C11—42no—
202C2×C4×C11—41no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11#12012yes—
208C2×C4×C11#12012yes—
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C22×Q811yescharacteristic
212C2×C4×C11C2×#4111yescharacteristic
213C2×C4×C112−1+411yescharacteristic
214C2×C4×C112−1+411yescharacteristic
215C8×C11—22no—
216C8×C11—41no—
217C8×C11—42no—
218C22×Q16C22×C1111yescharacteristic
219#557—24no—
220#557—24no—
221C2×C4⋊Q8—21no—
222C2×C4⋊Q8C22×C1111yescharacteristic
223C2×#125—22no—
224C2×#125C22×C1112yes—
225C2×C4×Q8—21no—
226C2×C4×Q8C22×C1111yescharacteristic
227C2×C4×Q8C22×C1112yes—
228C2×C4×Q8C22×C1111yescharacteristic
229C2×C4×Q8C22×C1111yescharacteristic
230#477—24no—
231#441—24no—
232C2×#107C22×C1112yes—
233C2×#106C22×C1111yescharacteristic
234C2×C4⋊C8C22×C1111yescharacteristic
235C2×#103C22×C1112yes—
236C2×#103C22×C1112yes—
237C2×#103C22×C1111yescharacteristic
238C2×#103C22×C1111yescharacteristic
239C2×#97C22×C1111yescharacteristic
240#400—21no—
241#395—21no—
242#391C22×C1112yes—
243#389C22×C1112yes—
244#387—22no—
245#382C22×C1111yescharacteristic
246#340C22×C1112yes—
247#340C22×C1112yes—
248#340C22×C1112yes—
249#336C22×C1112yes—
250#336C22×C1112yes—
251C22×C11C2×#12011yescharacteristic
252C22×C11#54811yescharacteristic
253C22×C11D4×Q811yescharacteristic
254C22×C11#57512yes—
255C22×C11#57812yes—
256C4×C11—24no—
257C4×C11—22no—
258C4×C11—22no—
259C4×C11—42no—
260C4×C11—42no—
261C4×C11—44no—
262C4×C11—42no—
263C4×C11—42no—
264C4×C11—82no—
265C4×C11—81no—
266C4×C11C2×C22⋊Q811yescharacteristic
267C4×C11#53611yescharacteristic
268C4×C11#54811yescharacteristic
269C4×C11D4×Q811yescharacteristic
270C22×Q8—21no—
271C22×Q8D4×C1111yescharacteristic
272C22×Q8C23×C1111yescharacteristic
273C22×Q8C23×C1111yescharacteristic
274C2×Q16—22no—
275C2×Q16—22no—
276C2×Q16Q8×C1114yescomplemented
277C22×C8C23×C1111yescharacteristic
278C22×C8C23×C1112yes—
279C22×C8C23×C1111yescharacteristic
280C4⋊Q8—28no—
281C4⋊Q8—22no—
282C4⋊Q8D4×C1114yes—
283#125—216no—
284#125—24no—
285#125—24no—
286C4×Q8—28no—
287C4×Q8—24no—
288C4×Q8—24no—
289C4×Q8—22no—
290C4×Q8—22no—
291C4×Q8—22no—
292C4×Q8—22no—
293C4×Q8—22no—
294C4×Q8D4×C1114yes—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4D4×C1111yescharacteristic
303C2×C4⋊C4D4×C1112yes—
304C2×C4⋊C4C23×C1111yescharacteristic
305C2×C4⋊C4C23×C1112yes—
306C2×C4⋊C4C23×C1111yescharacteristic
307C2×C4⋊C4C23×C1112yes—
308C2×C42—22no—
309C2×C42—21no—
310C2×C42—21no—
311C2×C42C23×C1112yes—
312C2×C42C23×C1111yescharacteristic
313#107—24no—
314#106—22no—
315C4⋊C8—22no—
316#103—22no—
317#103—24no—
318#103—22no—
319#103—24no—
320#97—22no—
321#95—21no—
322#95—21no—
323#95—22no—
324#95—22no—
325#95—22no—
326C2×C11#240911yescharacteristic
327C2×C11#300511yescharacteristic
328C2×C11#301111yescharacteristic
329C2×C11#337712yes—
330C2×C11#339012yes—
331C2×Q8—22no—
332C2×Q8—24no—
333C2×Q8—21no—
334C2×Q8—21no—
335C2×Q8—21no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—42no—
342C2×Q8—44no—
343C2×Q8C2×D4×C1112yes—
344C2×Q8C2×Q8×C1112yes—
345C2×Q8C2×Q8×C1112yes—
346C2×Q8C11×#4112yes—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—21no—
353C22×C4C2×D4×C1112yes—
354C22×C4C2×D4×C1112yes—
355C22×C4C2×D4×C1111yescharacteristic
356C22×C4C2×D4×C1111yescharacteristic
357C22×C4C24×C1111yescharacteristic
358Q16—28no—
359C2×C8—21no—
360C2×C8—21no—
361C2×C8—21no—
362C2×C8—22no—
363C2×C8—22no—
364C2×C8—21no—
365C2×C8—21no—
366C2×C8—22no—
367C2×C8C2×Q8×C1112yes—
368C4⋊C4—28no—
369C4⋊C4—28no—
370C4⋊C4—28no—
371C4⋊C4—24no—
372C4⋊C4—24no—
373C4⋊C4—22no—
374C4⋊C4—24no—
375C4⋊C4—21no—
376C4⋊C4—22no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—44no—
382C4⋊C4—42no—
383C4⋊C4C2×D4×C1112yes—
384C4⋊C4C2×D4×C1114yes—
385C42—28no—
386C42—24no—
387C42—22no—
388C42—22no—
389C42—42no—
390C42C2×D4×C1112yes—
391C42C2×D4×C1112yes—
392C11#2434411yescharacteristic, direct product factor, Sylow
393C23C22×D4×C1111yescharacteristic
394Q8—22no—
395Q8—22no—
396Q8—22no—
397Q8—22no—
398Q8—22no—
399Q8—44no—
400Q8—48no—
401Q8—41no—
402Q8—41no—
403Q8C11×C22⋊Q814yes—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—24no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—24no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—44no—
420C2×C4—42no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4C11×#12012yes—
427C2×C4C11×#12012yes—
428C2×C4C22×D4×C1111yescharacteristic
429C2×C4C22×D4×C1111yescharacteristic
430C2×C4C22×Q8×C1111yescharacteristic
431C2×C4C2×C11×#4111yescharacteristic
432C2×C4C11×2−1+411yescharacteristic
433C2×C4C11×2−1+411yescharacteristic
434C8—22no—
435C8—41no—
436C8—42no—
437C22C2×C11×#12011yescharacteristic
438C22C11×#54811yescharacteristic
439C22D4×Q8×C1111yescharacteristic
440C22C11×#57512yes—
441C22C11×#57812yes—
442C4—24no—
443C4—22no—
444C4—22no—
445C4—42no—
446C4—42no—
447C4—44no—
448C4—42no—
449C4—42no—
450C4—81no—
451C4—82no—
452C4C2×C11×C22⋊Q811yescharacteristic
453C4C11×#53611yescharacteristic
454C4C11×#54811yescharacteristic
455C4D4×Q8×C1111yescharacteristic
456C2C11×#240911yescharacteristic
457C2C11×#300511yescharacteristic
458C2C11×#301111yescharacteristic
459C2C11×#337712yes—
460C2C11×#339012yes—
subgroupG/H
center, socle, prime radicalC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×Q8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
51. C2×C11×Q16Q8semidirect
101. #24344C11direct (N × H)
276. C2×Q16Q8×C11semidirect
392. C11#24344direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5572
C2×C11×#4772
C2×C11×#4412
C11×#25812
C11×#20592
C11×#20262
C11×#19932
C11×#19852
C11×#18782
C11×#18632
C11×#18052
#2434411