Finite Group Databasebeta

← C11×#24191 #14601384

Subgroups — C11×#24191 #14601384

Order 2816.

1050 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#557C211yesmaximal, characteristic
2C2×C11×#462C211yesmaximal, characteristic
3C2×C4×C11×Q16C211yesmaximal, characteristic
4C11×#2582C211yesmaximal, characteristic
5C11×#2043C212yesmaximal
6C11×#2016C212yesmaximal
7C11×#1984C211yesmaximal, characteristic
8C11×#1956C211yesmaximal, characteristic
9C11×#1878C212yesmaximal
10C11×#1863C212yesmaximal
11C11×#1803C211yesmaximal, characteristic
12C22×C11×Q16C2211yescharacteristic
13C22×C11×Q16C2212yes—
14C11×#557—24no—
15C11×#557—24no—
16C2×C11×C4⋊Q8C2212yes—
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×#125—21no—
19C2×C11×#125—22no—
20C2×C4×Q8×C11—21no—
21C2×C4×Q8×C11C2212yes—
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×Q8×C11C2211yescharacteristic
24C2×C4×Q8×C11C2211yescharacteristic
25C11×#462—24no—
26C4×C11×Q16—24no—
27C2×C11×#107C2211yescharacteristic
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2212yes—
32C2×C11×#103C2212yes—
33C2×C11×#103C2212yes—
34C2×C11×#103C2212yes—
35C2×C4×C8×C11C2211yescharacteristic
36C11×#398—22no—
37C11×#391—21no—
38C11×#391C2212yes—
39C11×#389—21no—
40C11×#389C2212yes—
41C11×#384C2211yescharacteristic
42C11×#340C2212yes—
43C11×#336C2212yes—
44C11×#336C2212yes—
45C22×Q8×C11D411yescharacteristic
46C22×Q8×C11C2312yes—
47C22×Q8×C11C2311yescharacteristic
48C22×Q8×C11C2311yescharacteristic
49C2×C11×Q16—22no—
50C2×C11×Q16—22no—
51C2×C11×Q16—24no—
52C2×C11×Q16—24no—
53C2×C11×Q16—22no—
54C2×C11×Q16—42no—
55C22×C8×C11C2312yes—
56C22×C8×C11C2311yescharacteristic
57C22×C8×C11C2311yescharacteristic
58C11×C4⋊Q8—24no—
59C11×C4⋊Q8—24no—
60C11×C4⋊Q8—22no—
61C11×C4⋊Q8D414yes—
62C11×#125—216no—
63C11×#125—28no—
64C4×Q8×C11—28no—
65C4×Q8×C11—24no—
66C4×Q8×C11—24no—
67C4×Q8×C11—22no—
68C4×Q8×C11—22no—
69C4×Q8×C11—22no—
70C4×Q8×C11—22no—
71C4×Q8×C11—22no—
72C4×Q8×C11D414yes—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4D411yescharacteristic
84C2×C11×C4⋊C4D412yes—
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C42×C11—22no—
89C2×C42×C11—21no—
90C2×C42×C11—21no—
91C2×C42×C11C2312yes—
92C2×C42×C11C2311yescharacteristic
93C11×#107—22no—
94C11×C4⋊C8—22no—
95C11×#103—22no—
96C11×#103—24no—
97C11×#103—24no—
98C11×#103—22no—
99C11×#103—42no—
100C11×#103—42no—
101C4×C8×C11—22no—
102C11×#95—22no—
103C11×#95—22no—
104C11×#95—22no—
105#24191C1111yesmaximal, characteristic, direct product factor, Sylow
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—21no—
113C2×Q8×C11—22no—
114C2×Q8×C11—21no—
115C2×Q8×C11—22no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×Q8×C11—22no—
120C2×Q8×C11—21no—
121C2×Q8×C11—21no—
122C2×Q8×C11—22no—
123C2×Q8×C11Q1614yescomplemented
124C2×Q8×C11C2×D414yes—
125C2×Q8×C11C2×D412yes—
126C2×Q8×C11#4112yes—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—22no—
130C22×C4×C11—21no—
131C22×C4×C11—22no—
132C22×C4×C11—21no—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2411yescharacteristic
138C11×Q16—28no—
139C11×Q16—48no—
140C2×C8×C11—21no—
141C2×C8×C11—21no—
142C2×C8×C11—22no—
143C2×C8×C11—21no—
144C2×C8×C11—22no—
145C2×C8×C11—21no—
146C2×C8×C11—22no—
147C2×C8×C11—21no—
148C2×C8×C11#4112yes—
149C11×C4⋊C4—28no—
150C11×C4⋊C4—28no—
151C11×C4⋊C4—28no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—42no—
163C11×C4⋊C4—42no—
164C11×C4⋊C4—81no—
165C11×C4⋊C4—82no—
166C11×C4⋊C4C2×D412yes—
167C42×C11—28no—
168C42×C11—24no—
169C42×C11—22no—
170C42×C11—22no—
171C42×C11—42no—
172C42×C11C2×D412yes—
173C42×C11C2×D412yes—
174C2×#557C2×C1111yescharacteristic
175C2×#462C2×C1111yescharacteristic
176C2×C4×Q16C2×C1111yescharacteristic
177#2582C2×C1111yescharacteristic
178#2043C2×C1112yes—
179#2016C2×C1112yes—
180#1984C2×C1111yescharacteristic
181#1956C2×C1111yescharacteristic
182#1878C2×C1112yes—
183#1863C2×C1112yes—
184#1803C2×C1111yescharacteristic
185C23×C11C22×D411yescharacteristic
186Q8×C11—28no—
187Q8×C11—22no—
188Q8×C11—22no—
189Q8×C11—22no—
190Q8×C11—22no—
191Q8×C11—24no—
192Q8×C11—24no—
193Q8×C11—42no—
194Q8×C11—42no—
195Q8×C11—41no—
196Q8×C11—41no—
197Q8×C11—41no—
198Q8×C11—41no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—24no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—42no—
213C2×C4×C11—41no—
214C2×C4×C11—42no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11#12012yes—
225C2×C4×C11#12012yes—
226C2×C4×C11C2×Q1614yes—
227C2×C4×C11C2×Q1612yes—
228C2×C4×C11#13712yes—
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C2×C4×C11H(5,𝔽2)11yescharacteristic
234C2×C4×C112−1+411yescharacteristic
235C8×C11—22no—
236C8×C11—41no—
237C8×C11—42no—
238C22×Q16C22×C1111yescharacteristic
239C22×Q16C22×C1112yes—
240#557—24no—
241#557—24no—
242C2×C4⋊Q8C22×C1112yes—
243C2×C4⋊Q8C22×C1111yescharacteristic
244C2×#125—21no—
245C2×#125—22no—
246C2×C4×Q8—21no—
247C2×C4×Q8C22×C1111yescharacteristic
248C2×C4×Q8C22×C1112yes—
249C2×C4×Q8C22×C1111yescharacteristic
250C2×C4×Q8C22×C1111yescharacteristic
251#462—24no—
252C4×Q16—24no—
253C2×#107C22×C1111yescharacteristic
254C2×C4⋊C8C22×C1111yescharacteristic
255C2×#103C22×C1112yes—
256C2×#103C22×C1112yes—
257C2×#103C22×C1111yescharacteristic
258C2×#103C22×C1111yescharacteristic
259C2×#103C22×C1112yes—
260C2×#103C22×C1112yes—
261C2×C4×C8C22×C1111yescharacteristic
262#398—22no—
263#391—21no—
264#391C22×C1112yes—
265#389—21no—
266#389C22×C1112yes—
267#384C22×C1111yescharacteristic
268#340C22×C1112yes—
269#336C22×C1112yes—
270#336C22×C1112yes—
271C22×C11C2×#12011yescharacteristic
272C22×C11#54811yescharacteristic
273C22×C11#55011yescharacteristic
274C22×C11C22×Q1611yescharacteristic
275C22×C11C2×#13711yescharacteristic
276C22×C11#57711yescharacteristic
277C22×C11#57811yescharacteristic
278C4×C11—24no—
279C4×C11—22no—
280C4×C11—42no—
281C4×C11—44no—
282C4×C11—42no—
283C4×C11—42no—
284C4×C11—42no—
285C4×C11—82no—
286C4×C11—81no—
287C4×C11#45114yes—
288C4×C11#52511yescharacteristic
289C4×C11#53711yescharacteristic
290C4×C11#54611yescharacteristic
291C4×C11#54711yescharacteristic
292C22×Q8D4×C1111yescharacteristic
293C22×Q8C23×C1112yes—
294C22×Q8C23×C1111yescharacteristic
295C22×Q8C23×C1111yescharacteristic
296C2×Q16—22no—
297C2×Q16—22no—
298C2×Q16—24no—
299C2×Q16—24no—
300C2×Q16—22no—
301C2×Q16—42no—
302C22×C8C23×C1112yes—
303C22×C8C23×C1111yescharacteristic
304C22×C8C23×C1111yescharacteristic
305C4⋊Q8—24no—
306C4⋊Q8—24no—
307C4⋊Q8—22no—
308C4⋊Q8D4×C1114yes—
309#125—216no—
310#125—28no—
311C4×Q8—28no—
312C4×Q8—24no—
313C4×Q8—24no—
314C4×Q8—22no—
315C4×Q8—22no—
316C4×Q8—22no—
317C4×Q8—22no—
318C4×Q8—22no—
319C4×Q8D4×C1114yes—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4D4×C1111yescharacteristic
331C2×C4⋊C4D4×C1112yes—
332C2×C4⋊C4C23×C1111yescharacteristic
333C2×C4⋊C4C23×C1112yes—
334C2×C4⋊C4C23×C1111yescharacteristic
335C2×C42—22no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42C23×C1112yes—
339C2×C42C23×C1111yescharacteristic
340#107—22no—
341C4⋊C8—22no—
342#103—22no—
343#103—24no—
344#103—24no—
345#103—22no—
346#103—42no—
347#103—42no—
348C4×C8—22no—
349#95—22no—
350#95—22no—
351#95—22no—
352C2×C11#240711yescharacteristic
353C2×C11C2×#45111yescharacteristic
354C2×C11#301311yescharacteristic
355C2×C11#336311yescharacteristic
356C2×C11#337411yescharacteristic
357C2×C11#339511yescharacteristic
358C2×C11#340011yescharacteristic
359C2×Q8—22no—
360C2×Q8—22no—
361C2×Q8—22no—
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×Q8—21no—
366C2×Q8—22no—
367C2×Q8—21no—
368C2×Q8—22no—
369C2×Q8—21no—
370C2×Q8—21no—
371C2×Q8—21no—
372C2×Q8—22no—
373C2×Q8—21no—
374C2×Q8—21no—
375C2×Q8—22no—
376C2×Q8C11×Q1614yescomplemented
377C2×Q8C2×D4×C1114yes—
378C2×Q8C2×D4×C1112yes—
379C2×Q8C11×#4112yes—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—21no—
384C22×C4—22no—
385C22×C4—21no—
386C22×C4C2×D4×C1112yes—
387C22×C4C2×D4×C1111yescharacteristic
388C22×C4C2×D4×C1112yes—
389C22×C4C2×D4×C1111yescharacteristic
390C22×C4C24×C1111yescharacteristic
391Q16—28no—
392Q16—48no—
393C2×C8—21no—
394C2×C8—21no—
395C2×C8—21no—
396C2×C8—22no—
397C2×C8—22no—
398C2×C8—21no—
399C2×C8—22no—
400C2×C8—21no—
401C2×C8C11×#4112yes—
402C4⋊C4—28no—
403C4⋊C4—28no—
404C4⋊C4—28no—
405C4⋊C4—24no—
406C4⋊C4—24no—
407C4⋊C4—24no—
408C4⋊C4—24no—
409C4⋊C4—22no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—42no—
416C4⋊C4—42no—
417C4⋊C4—81no—
418C4⋊C4—82no—
419C4⋊C4C2×D4×C1112yes—
420C42—28no—
421C42—24no—
422C42—22no—
423C42—22no—
424C42—42no—
425C42C2×D4×C1112yes—
426C42C2×D4×C1112yes—
427C11#2419111yescharacteristic, direct product factor, Sylow
428C23C22×D4×C1111yescharacteristic
429Q8—28no—
430Q8—22no—
431Q8—22no—
432Q8—22no—
433Q8—22no—
434Q8—24no—
435Q8—24no—
436Q8—42no—
437Q8—42no—
438Q8—41no—
439Q8—41no—
440Q8—41no—
441Q8—41no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—24no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—41no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4C11×#12012yes—
468C2×C4C11×#12012yes—
469C2×C4C2×C11×Q1614yes—
470C2×C4C2×C11×Q1612yes—
471C2×C4C11×#13712yes—
472C2×C4C22×D4×C1111yescharacteristic
473C2×C4C22×D4×C1111yescharacteristic
474C2×C4C2×C11×#4111yescharacteristic
475C2×C4C2×C11×#4111yescharacteristic
476C2×C4C11×H(5,𝔽2)11yescharacteristic
477C2×C4C11×2−1+411yescharacteristic
478C8—22no—
479C8—41no—
480C8—42no—
481C22C2×C11×#12011yescharacteristic
482C22C11×#54811yescharacteristic
483C22C11×#55011yescharacteristic
484C22C22×C11×Q1611yescharacteristic
485C22C2×C11×#13711yescharacteristic
486C22C11×#57711yescharacteristic
487C22C11×#57811yescharacteristic
488C4—24no—
489C4—22no—
490C4—42no—
491C4—44no—
492C4—42no—
493C4—42no—
494C4—42no—
495C4—81no—
496C4—82no—
497C4C11×#45114yes—
498C4C11×#52511yescharacteristic
499C4C11×#53711yescharacteristic
500C4C11×#54611yescharacteristic
501C4C11×#54711yescharacteristic
502C2C11×#240711yescharacteristic
503C2C2×C11×#45111yescharacteristic
504C2C11×#301311yescharacteristic
505C2C11×#336311yescharacteristic
506C2C11×#337411yescharacteristic
507C2C11×#339511yescharacteristic
508C2C11×#340011yescharacteristic
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
105. #24191C11direct (N × H)
123. C2×Q8×C11Q16semidirect
376. C2×Q8C11×Q16semidirect
427. C11#24191direct (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×#4622
C2×C4×C11×Q162
C11×#25822
C11×#20432
C11×#20162
C11×#19842
C11×#19562
C11×#18782
C11×#18632
C11×#18032
#2419111