Finite Group Databasebeta

← C11×#21814 #14599007

Subgroups — C11×#21814 #14599007

Order 2816.

1250 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#536C211yesmaximal, characteristic
2C2×C11×#433C211yesmaximal, characteristic, complemented
3C11×#2314C211yesmaximal, characteristic, complemented
4C11×#1983C212yesmaximal, complemented
5C11×#1981C212yesmaximal, complemented
6C11×#1960C211yesmaximal, characteristic, complemented
7C11×#1959C211yesmaximal, characteristic, complemented
8C11×#1958C211yesmaximal, characteristic, complemented
9C11×#1956C211yesmaximal, characteristic, complemented
10C11×#1788C212yesmaximal
11C11×#1787C212yesmaximal, complemented
12C22×C11×#41C2211yescharacteristic
13C23×Q8×C11C2211yescharacteristic
14C11×#536—24no—
15C11×#536C418yescomplemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×#124C2211yescharacteristic
19C2×C11×#124C2211yescharacteristic
20C2×C11×#123—22no—
21C2×C11×C22⋊Q8—22no—
22C2×C11×#117C2211yescharacteristic
23C11×#433—24no—
24C2×C11×C4⋊C8C2212yes—
25C2×C11×#103C2212yes—
26C2×C11×#103C2212yes—
27C2×C11×#103C2212yes—
28C2×C11×#103C2212yes—
29C2×C11×#103C2212yes—
30C2×C11×#103C2212yes—
31C2×C11×#102C2212yes—
32C2×C11×#102C2212yes—
33C2×C11×C22⋊C8C2212yes—
34C2×C11×#97C2211yescharacteristic
35C2×C4×C8×C11C2211yescharacteristic
36C11×#388—22no—
37C11×#387—22no—
38C11×#384C2211yescharacteristic
39C11×#382C2211yescharacteristic
40C11×#380C2212yes—
41C4×C11×C4⋊C4C2212yes—
42C2×C11×#41—22no—
43C2×C11×#41—42no—
44C2×C11×#41—42no—
45C2×C11×#41C2×C414yes—
46C22×Q8×C11—21no—
47C22×Q8×C11—22no—
48C22×Q8×C11—42no—
49C22×Q8×C11—42no—
50C22×Q8×C11C2×C414yes—
51C22×Q8×C11C2311yescharacteristic
52C22×Q8×C11C2311yescharacteristic
53C22×Q8×C11C2311yescharacteristic
54C22×D4×C11—21no—
55C22×D4×C11C2311yescharacteristic
56C23×C4×C11—21no—
57C23×C4×C11—21no—
58C23×C4×C11C2311yescharacteristic
59C22×C8×C11C2312yes—
60C22×C8×C11C2312yes—
61C11×C4⋊Q8—22no—
62C11×C4⋊Q8—22no—
63C11×C4⋊Q8C2×C414yes—
64C11×C4⋊Q8C2×C414yes—
65C11×#124—22no—
66C11×#124—22no—
67C11×#124C2×C414yes—
68C11×#124C2×C414yes—
69C11×#123—216no—
70C11×C22⋊Q8—216no—
71C11×#117C2×C414yes—
72C11×#117D414yes—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4D412yes—
77C2×C11×C4⋊C4C2312yes—
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4D412yes—
83C2×C42×C11—22no—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C11×C4⋊C8—24no—
87C11×#103—42no—
88C11×#103—42no—
89C11×#103—42no—
90C11×#103—42no—
91C11×#103—42no—
92C11×#103—42no—
93C11×#102—42no—
94C11×#102—42no—
95C11×C22⋊C8—24no—
96C11×#97—22no—
97C4×C8×C11—22no—
98C11×#95—22no—
99C11×#95—22no—
100C11×#95—22no—
101#21814C1111yesmaximal, characteristic, direct product factor, Sylow
102C24×C11—21no—
103C24×C11C2×D411yescharacteristic
104C11×#41—48no—
105C11×#41—48no—
106C2×Q8×C11—24no—
107C2×Q8×C11—21no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11—48no—
117C2×Q8×C11—42no—
118C2×Q8×C11—42no—
119C2×Q8×C11—48no—
120C2×Q8×C11C22×C412yes—
121C2×Q8×C11C22×C412yes—
122C2×Q8×C11C22×C412yes—
123C2×D4×C11—24no—
124C2×D4×C11—21no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—42no—
128C2×D4×C11—42no—
129C2×D4×C11C22×C412yes—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—24no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—24no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11—42no—
142C22×C4×C11—42no—
143C22×C4×C11C22×C412yes—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2411yescharacteristic
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C11×C4⋊C4—28no—
156C11×C4⋊C4—28no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—82no—
162C11×C4⋊C4C22⋊C418yes—
163C11×C22⋊C4—28no—
164C11×C22⋊C4—28no—
165C11×C22⋊C4—82no—
166C11×C22⋊C4C22⋊C418yes—
167C42×C11—82no—
168C42×C11C22×C412yes—
169C42×C11C22×C412yes—
170C42×C11C2×D412yes—
171C42×C11C2×D412yes—
172C2×#536C2×C1111yescharacteristic
173C2×#433C2×C1111yescharacteristic, complemented
174#2314C2×C1111yescharacteristic, complemented
175#1983C2×C1112yescomplemented
176#1981C2×C1112yescomplemented
177#1960C2×C1111yescharacteristic, complemented
178#1959C2×C1111yescharacteristic, complemented
179#1958C2×C1111yescharacteristic, complemented
180#1956C2×C1111yescharacteristic, complemented
181#1788C2×C1112yes—
182#1787C2×C1112yescomplemented
183C23×C11—21no—
184C23×C11—21no—
185C23×C11—22no—
186C23×C11—22no—
187C23×C11—22no—
188C23×C11—41no—
189C23×C11—41no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11C2×C22⋊C412yes—
193C23×C11C22×D411yescharacteristic
194Q8×C11—24no—
195Q8×C11—24no—
196Q8×C11—24no—
197Q8×C11—48no—
198Q8×C11—42no—
199Q8×C11—42no—
200Q8×C11—42no—
201D4×C11—24no—
202D4×C11—48no—
203D4×C11—42no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—48no—
216C2×C4×C11—48no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11C2×C22⋊C414yes—
230C2×C4×C11C2×C22⋊C414yes—
231C2×C4×C11C2×C22⋊C412yes—
232C2×C4×C11C23×C411yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11H(5,𝔽2)12yes—
235C2×C4×C11H(5,𝔽2)12yes—
236C8×C11—42no—
237C8×C11—42no—
238C22×#41C22×C1111yescharacteristic
239C23×Q8C22×C1111yescharacteristic
240#536—24no—
241#536C4×C1118yescomplemented
242C2×C4⋊Q8C22×C1111yescharacteristic
243C2×C4⋊Q8C22×C1111yescharacteristic
244C2×#124C22×C1111yescharacteristic
245C2×#124C22×C1111yescharacteristic
246C2×#123—22no—
247C2×C22⋊Q8—22no—
248C2×#117C22×C1111yescharacteristic
249#433—24no—
250C2×C4⋊C8C22×C1112yes—
251C2×#103C22×C1112yes—
252C2×#103C22×C1112yes—
253C2×#103C22×C1112yes—
254C2×#103C22×C1112yes—
255C2×#103C22×C1112yes—
256C2×#103C22×C1112yes—
257C2×#102C22×C1112yes—
258C2×#102C22×C1112yes—
259C2×C22⋊C8C22×C1112yes—
260C2×#97C22×C1111yescharacteristic
261C2×C4×C8C22×C1111yescharacteristic
262#388—22no—
263#387—22no—
264#384C22×C1111yescharacteristic
265#382C22×C1111yescharacteristic
266#380C22×C1112yes—
267C4×C4⋊C4C22×C1112yes—
268C22×C11—22no—
269C22×C11—24no—
270C22×C11—41no—
271C22×C11—41no—
272C22×C11—42no—
273C22×C11—42no—
274C22×C11—44no—
275C22×C11—81no—
276C22×C11—81no—
277C22×C11—82no—
278C22×C11C22×C22⋊C411yescharacteristic
279C22×C11#53511yescharacteristic
280C22×C11#53511yescharacteristic
281C22×C11#57712yes—
282C22×C11#57812yes—
283C4×C11—22no—
284C4×C11—24no—
285C4×C11—24no—
286C4×C11—42no—
287C4×C11—42no—
288C4×C11—42no—
289C4×C11—82no—
290C4×C11—82no—
291C4×C11#51812yes—
292C4×C11#53512yes—
293C2×#41—22no—
294C2×#41—42no—
295C2×#41—42no—
296C2×#41C2×C4×C1114yes—
297C22×Q8—21no—
298C22×Q8—22no—
299C22×Q8—42no—
300C22×Q8—42no—
301C22×Q8C2×C4×C1114yes—
302C22×Q8C23×C1111yescharacteristic
303C22×Q8C23×C1111yescharacteristic
304C22×Q8C23×C1111yescharacteristic
305C22×D4—21no—
306C22×D4C23×C1111yescharacteristic
307C23×C4—21no—
308C23×C4—21no—
309C23×C4C23×C1111yescharacteristic
310C22×C8C23×C1112yes—
311C22×C8C23×C1112yes—
312C4⋊Q8—22no—
313C4⋊Q8—22no—
314C4⋊Q8C2×C4×C1114yes—
315C4⋊Q8C2×C4×C1114yes—
316#124—22no—
317#124—22no—
318#124C2×C4×C1114yes—
319#124C2×C4×C1114yes—
320#123—216no—
321C22⋊Q8—216no—
322#117C2×C4×C1114yes—
323#117D4×C1114yes—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4D4×C1112yes—
328C2×C4⋊C4C23×C1112yes—
329C2×C4⋊C4C23×C1112yes—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4D4×C1112yes—
334C2×C42—22no—
335C2×C42C23×C1111yescharacteristic
336C2×C42C23×C1111yescharacteristic
337C4⋊C8—24no—
338#103—42no—
339#103—42no—
340#103—42no—
341#103—42no—
342#103—42no—
343#103—42no—
344#102—42no—
345#102—42no—
346C22⋊C8—24no—
347#97—22no—
348C4×C8—22no—
349#95—22no—
350#95—22no—
351#95—22no—
352C2×C11—42no—
353C2×C11—82no—
354C2×C11#230911yescharacteristic
355C2×C11#289812yes—
356C2×C11#322111yescharacteristic
357C2×C11#322311yescharacteristic
358C2×C11#322512yes—
359C24—21no—
360C24C2×D4×C1111yescharacteristic
361#41—48no—
362#41—48no—
363C2×Q8—24no—
364C2×Q8—21no—
365C2×Q8—21no—
366C2×Q8—21no—
367C2×Q8—22no—
368C2×Q8—22no—
369C2×Q8—22no—
370C2×Q8—22no—
371C2×Q8—22no—
372C2×Q8—22no—
373C2×Q8—48no—
374C2×Q8—42no—
375C2×Q8—42no—
376C2×Q8—48no—
377C2×Q8C22×C4×C1112yes—
378C2×Q8C22×C4×C1112yes—
379C2×Q8C22×C4×C1112yes—
380C2×D4—24no—
381C2×D4—21no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4C22×C4×C1112yes—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—24no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—24no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—42no—
397C22×C4—42no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4C22×C4×C1112yes—
401C22×C4C2×D4×C1111yescharacteristic
402C22×C4C2×D4×C1112yes—
403C22×C4C2×D4×C1112yes—
404C22×C4C2×D4×C1112yes—
405C22×C4C24×C1111yescharacteristic
406C2×C8—22no—
407C2×C8—22no—
408C2×C8—22no—
409C2×C8—22no—
410C2×C8—22no—
411C2×C8—22no—
412C4⋊C4—28no—
413C4⋊C4—28no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—82no—
419C4⋊C4C11×C22⋊C418yes—
420C22⋊C4—28no—
421C22⋊C4—28no—
422C22⋊C4—82no—
423C22⋊C4C11×C22⋊C418yes—
424C42—82no—
425C42C22×C4×C1112yes—
426C42C22×C4×C1112yes—
427C42C2×D4×C1112yes—
428C42C2×D4×C1112yes—
429C11#2181411yescharacteristic, direct product factor, Sylow
430C23—21no—
431C23—21no—
432C23—22no—
433C23—22no—
434C23—22no—
435C23—41no—
436C23—41no—
437C23—42no—
438C23—42no—
439C23C2×C11×C22⋊C412yes—
440C23C22×D4×C1111yescharacteristic
441Q8—24no—
442Q8—24no—
443Q8—24no—
444Q8—48no—
445Q8—42no—
446Q8—42no—
447Q8—42no—
448D4—24no—
449D4—48no—
450D4—42no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—48no—
463C2×C4—48no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4C2×C11×C22⋊C414yes—
477C2×C4C2×C11×C22⋊C414yes—
478C2×C4C2×C11×C22⋊C412yes—
479C2×C4C23×C4×C1111yescharacteristic
480C2×C4C22×D4×C1111yescharacteristic
481C2×C4C11×H(5,𝔽2)12yes—
482C2×C4C11×H(5,𝔽2)12yes—
483C8—42no—
484C8—42no—
485C22—24no—
486C22—22no—
487C22—41no—
488C22—41no—
489C22—42no—
490C22—44no—
491C22—42no—
492C22—81no—
493C22—81no—
494C22—82no—
495C22C22×C11×C22⋊C411yescharacteristic
496C22C11×#53511yescharacteristic
497C22C11×#53511yescharacteristic
498C22C11×#57712yes—
499C22C11×#57812yes—
500C4—24no—
501C4—24no—
502C4—22no—
503C4—42no—
504C4—42no—
505C4—42no—
506C4—82no—
507C4—82no—
508C4C11×#51812yes—
509C4C11×#53512yes—
510C2—42no—
511C2—82no—
512C2C11×#230911yescharacteristic
513C2C11×#289812yes—
514C2C11×#322111yescharacteristic
515C2C11×#322311yescharacteristic
516C2C11×#322512yes—
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC22×C11×#41C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#433C2semidirect
3. C11×#2314C2semidirect
4. C11×#1983C2semidirect
5. C11×#1981C2semidirect
6. C11×#1960C2semidirect
7. C11×#1959C2semidirect
8. C11×#1958C2semidirect
9. C11×#1956C2semidirect
11. C11×#1787C2semidirect
15. C11×#536C4semidirect
101. #21814C11direct (N × H)
173. C2×#433C2×C11semidirect
174. #2314C2×C11semidirect
175. #1983C2×C11semidirect
176. #1981C2×C11semidirect
177. #1960C2×C11semidirect
178. #1959C2×C11semidirect
179. #1958C2×C11semidirect
180. #1956C2×C11semidirect
182. #1787C2×C11semidirect
241. #536C4×C11semidirect
429. C11#21814direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5362
C2×C11×#4332
C11×#23142
C11×#19832
C11×#19812
C11×#19602
C11×#19592
C11×#19582
C11×#19562
C11×#17882
C11×#17872
#2181411