Finite Group Databasebeta

← C11×#24201 #14601394

Subgroups — C11×#24201 #14601394

Order 2816.

1068 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#556C211yesmaximal, characteristic
2C2×C11×#462C211yesmaximal, characteristic, complemented
3C2×C11×#440C211yesmaximal, characteristic
4C11×#2581C211yesmaximal, characteristic, complemented
5C11×#2042C212yesmaximal
6C11×#2015C212yesmaximal
7C11×#1985C211yesmaximal, characteristic, complemented
8C11×#1960C211yesmaximal, characteristic, complemented
9C11×#1878C212yesmaximal, complemented
10C11×#1863C212yesmaximal, complemented
11C11×#1804C211yesmaximal, characteristic
12C22×C11×Q16C2212yes—
13C22×C11×SD16C2211yescharacteristic
14C11×#556—24no—
15C11×#556—24no—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#126—22no—
18C2×C11×#124C2212yes—
19C2×C11×C22⋊Q8—21no—
20C2×C4×Q8×C11C2212yes—
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C2×C11×#117—21no—
25C11×#462—24no—
26C11×#440—24no—
27C2×C11×#107C2211yescharacteristic
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#103C2212yes—
31C2×C11×#103C2212yes—
32C2×C11×#103C2212yes—
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2212yes—
35C2×C11×#97C2211yescharacteristic
36C11×#400—21no—
37C11×#395—21no—
38C11×#391C2212yes—
39C11×#389C2212yes—
40C11×#387—22no—
41C11×#382C2211yescharacteristic
42C11×#340C2212yes—
43C11×#336C2212yes—
44C11×#336C2212yes—
45C22×Q8×C11D411yescharacteristic
46C22×Q8×C11C2312yes—
47C22×Q8×C11C2311yescharacteristic
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C2×C11×Q16—24no—
51C2×C11×Q16—24no—
52C2×C11×Q16—42no—
53C2×C11×SD16—22no—
54C2×C11×SD16—22no—
55C2×C11×SD16—22no—
56C22×C8×C11C2312yes—
57C22×C8×C11C2311yescharacteristic
58C22×C8×C11C2311yescharacteristic
59C11×C4⋊Q8—22no—
60C11×C4⋊Q8D414yes—
61C11×#126—216no—
62C11×#124—24no—
63C11×#124—24no—
64C11×C22⋊Q8—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×D4×C11—22no—
72C4×D4×C11D414yes—
73C11×#117—28no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4D412yes—
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—22no—
87C2×C42×C11—22no—
88C2×C42×C11—21no—
89C2×C42×C11C2312yes—
90C2×C42×C11C2311yescharacteristic
91C11×#107—22no—
92C11×C4⋊C8—22no—
93C11×#103—24no—
94C11×#103—24no—
95C11×#103—22no—
96C11×#103—42no—
97C11×#102—22no—
98C11×#102—42no—
99C11×#97—22no—
100C11×#95—21no—
101C11×#95—21no—
102C11×#95—22no—
103C11×#95—22no—
104C11×#95—22no—
105#24201C1111yesmaximal, characteristic, direct product factor, Sylow
106C24×C11—21no—
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—21no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11—21no—
117C2×Q8×C11—22no—
118C2×Q8×C11—42no—
119C2×Q8×C11C2×D414yes—
120C2×Q8×C11#4112yes—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11C2×D412yes—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—22no—
130C22×C4×C11—24no—
131C22×C4×C11—22no—
132C22×C4×C11—21no—
133C22×C4×C11—44no—
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C11×Q16—48no—
140C11×SD16—28no—
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11—22no—
144C2×C8×C11—21no—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11#4112yes—
150C11×C4⋊C4—28no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—44no—
161C11×C4⋊C4—42no—
162C11×C4⋊C4C2×D412yes—
163C11×C22⋊C4—28no—
164C11×C22⋊C4—28no—
165C11×C22⋊C4—24no—
166C42×C11—28no—
167C42×C11—22no—
168C42×C11—22no—
169C42×C11—42no—
170C42×C11C2×D412yes—
171C42×C11C2×D412yes—
172C2×#556C2×C1111yescharacteristic
173C2×#462C2×C1111yescharacteristic, complemented
174C2×#440C2×C1111yescharacteristic
175#2581C2×C1111yescharacteristic, complemented
176#2042C2×C1112yes—
177#2015C2×C1112yes—
178#1985C2×C1111yescharacteristic, complemented
179#1960C2×C1111yescharacteristic, complemented
180#1878C2×C1112yescomplemented
181#1863C2×C1112yescomplemented
182#1804C2×C1111yescharacteristic
183C23×C11—22no—
184C23×C11—41no—
185C23×C11—41no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11C22×D411yescharacteristic
189Q8×C11—22no—
190Q8×C11—22no—
191Q8×C11—24no—
192Q8×C11—24no—
193Q8×C11—44no—
194Q8×C11—42no—
195Q8×C11—42no—
196Q8×C11—41no—
197Q8×C11—41no—
198D4×C11—22no—
199D4×C11—22no—
200D4×C11—41no—
201D4×C11—41no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—24no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—24no—
212C2×C4×C11—48no—
213C2×C4×C11—41no—
214C2×C4×C11—42no—
215C2×C4×C11—41no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—41no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11#12012yes—
224C2×C4×C11#12012yes—
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C2×#4111yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229C2×C4×C11H(5,𝔽2)11yescharacteristic
230C2×C4×C112−1+411yescharacteristic
231C8×C11—22no—
232C8×C11—41no—
233C8×C11—42no—
234C22×Q16C22×C1112yes—
235C22×SD16C22×C1111yescharacteristic
236#556—24no—
237#556—24no—
238C2×C4⋊Q8C22×C1111yescharacteristic
239C2×#126—22no—
240C2×#124C22×C1112yes—
241C2×C22⋊Q8—21no—
242C2×C4×Q8C22×C1111yescharacteristic
243C2×C4×Q8C22×C1112yes—
244C2×C4×Q8C22×C1111yescharacteristic
245C2×C4×D4C22×C1111yescharacteristic
246C2×#117—21no—
247#462—24no—
248#440—24no—
249C2×#107C22×C1111yescharacteristic
250C2×C4⋊C8C22×C1111yescharacteristic
251C2×#103C22×C1112yes—
252C2×#103C22×C1112yes—
253C2×#103C22×C1111yescharacteristic
254C2×#103C22×C1112yes—
255C2×#102C22×C1111yescharacteristic
256C2×#102C22×C1112yes—
257C2×#97C22×C1111yescharacteristic
258#400—21no—
259#395—21no—
260#391C22×C1112yes—
261#389C22×C1112yes—
262#387—22no—
263#382C22×C1111yescharacteristic
264#340C22×C1112yes—
265#336C22×C1112yes—
266#336C22×C1112yes—
267C22×C11—42no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—82no—
271C22×C11—82no—
272C22×C11C2×#12011yescharacteristic
273C22×C11#54811yescharacteristic
274C22×C11#55011yescharacteristic
275C22×C11#57512yes—
276C22×C11#57812yes—
277C4×C11—22no—
278C4×C11—22no—
279C4×C11—44no—
280C4×C11—42no—
281C4×C11—42no—
282C4×C11—42no—
283C4×C11—42no—
284C4×C11—82no—
285C4×C11—81no—
286C4×C11#52511yescharacteristic
287C4×C11#53711yescharacteristic
288C4×C11#54611yescharacteristic
289C4×C11#54711yescharacteristic
290C22×Q8D4×C1111yescharacteristic
291C22×Q8C23×C1112yes—
292C22×Q8C23×C1111yescharacteristic
293C22×D4C23×C1111yescharacteristic
294C23×C4—21no—
295C2×Q16—24no—
296C2×Q16—24no—
297C2×Q16—42no—
298C2×SD16—22no—
299C2×SD16—22no—
300C2×SD16—22no—
301C22×C8C23×C1112yes—
302C22×C8C23×C1111yescharacteristic
303C22×C8C23×C1111yescharacteristic
304C4⋊Q8—22no—
305C4⋊Q8D4×C1114yes—
306#126—216no—
307#124—24no—
308#124—24no—
309C22⋊Q8—28no—
310C4×Q8—24no—
311C4×Q8—24no—
312C4×Q8—22no—
313C4×Q8—22no—
314C4×Q8—22no—
315C4×Q8—22no—
316C4×D4—22no—
317C4×D4D4×C1114yes—
318#117—28no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4D4×C1111yescharacteristic
325C2×C4⋊C4D4×C1112yes—
326C2×C4⋊C4C23×C1111yescharacteristic
327C2×C4⋊C4C23×C1112yes—
328C2×C4⋊C4C23×C1111yescharacteristic
329C2×C22⋊C4—22no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—22no—
332C2×C42—22no—
333C2×C42—21no—
334C2×C42C23×C1112yes—
335C2×C42C23×C1111yescharacteristic
336#107—22no—
337C4⋊C8—22no—
338#103—24no—
339#103—24no—
340#103—22no—
341#103—42no—
342#102—22no—
343#102—42no—
344#97—22no—
345#95—21no—
346#95—21no—
347#95—22no—
348#95—22no—
349#95—22no—
350C2×C11—82no—
351C2×C11#240711yescharacteristic
352C2×C11#300511yescharacteristic
353C2×C11#301111yescharacteristic
354C2×C11#337712yes—
355C2×C11#340212yes—
356C24—21no—
357C2×Q8—22no—
358C2×Q8—22no—
359C2×Q8—21no—
360C2×Q8—21no—
361C2×Q8—21no—
362C2×Q8—22no—
363C2×Q8—21no—
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—21no—
367C2×Q8—22no—
368C2×Q8—42no—
369C2×Q8C2×D4×C1114yes—
370C2×Q8C11×#4112yes—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4C2×D4×C1112yes—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—22no—
380C22×C4—24no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—44no—
384C22×C4C2×D4×C1112yes—
385C22×C4C2×D4×C1112yes—
386C22×C4C2×D4×C1111yescharacteristic
387C22×C4C2×D4×C1111yescharacteristic
388C22×C4C24×C1111yescharacteristic
389Q16—48no—
390SD16—28no—
391C2×C8—21no—
392C2×C8—21no—
393C2×C8—21no—
394C2×C8—22no—
395C2×C8—22no—
396C2×C8—22no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8C11×#4112yes—
400C4⋊C4—28no—
401C4⋊C4—24no—
402C4⋊C4—24no—
403C4⋊C4—22no—
404C4⋊C4—24no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—44no—
411C4⋊C4—42no—
412C4⋊C4C2×D4×C1112yes—
413C22⋊C4—28no—
414C22⋊C4—28no—
415C22⋊C4—24no—
416C42—28no—
417C42—22no—
418C42—22no—
419C42—42no—
420C42C2×D4×C1112yes—
421C42C2×D4×C1112yes—
422C11#2420111yescharacteristic, direct product factor, Sylow
423C23—22no—
424C23—41no—
425C23—41no—
426C23—42no—
427C23—42no—
428C23C22×D4×C1111yescharacteristic
429Q8—22no—
430Q8—22no—
431Q8—24no—
432Q8—24no—
433Q8—44no—
434Q8—42no—
435Q8—42no—
436Q8—41no—
437Q8—41no—
438D4—22no—
439D4—22no—
440D4—41no—
441D4—41no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—24no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—24no—
452C2×C4—48no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4C11×#12012yes—
464C2×C4C11×#12012yes—
465C2×C4C22×D4×C1111yescharacteristic
466C2×C4C22×D4×C1111yescharacteristic
467C2×C4C2×C11×#4111yescharacteristic
468C2×C4C2×C11×#4111yescharacteristic
469C2×C4C11×H(5,𝔽2)11yescharacteristic
470C2×C4C11×2−1+411yescharacteristic
471C8—22no—
472C8—41no—
473C8—42no—
474C22—42no—
475C22—42no—
476C22—42no—
477C22—82no—
478C22—82no—
479C22C2×C11×#12011yescharacteristic
480C22C11×#54811yescharacteristic
481C22C11×#55011yescharacteristic
482C22C11×#57512yes—
483C22C11×#57812yes—
484C4—22no—
485C4—22no—
486C4—44no—
487C4—42no—
488C4—42no—
489C4—42no—
490C4—42no—
491C4—82no—
492C4—81no—
493C4C11×#52511yescharacteristic
494C4C11×#53711yescharacteristic
495C4C11×#54611yescharacteristic
496C4C11×#54711yescharacteristic
497C2—82no—
498C2C11×#240711yescharacteristic
499C2C11×#300511yescharacteristic
500C2C11×#301111yescharacteristic
501C2C11×#337712yes—
502C2C11×#340212yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC22×D4×C11C23
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
2. C2×C11×#462C2semidirect
4. C11×#2581C2semidirect
7. C11×#1985C2semidirect
8. C11×#1960C2semidirect
9. C11×#1878C2semidirect
10. C11×#1863C2semidirect
105. #24201C11direct (N × H)
173. C2×#462C2×C11semidirect
175. #2581C2×C11semidirect
178. #1985C2×C11semidirect
179. #1960C2×C11semidirect
180. #1878C2×C11semidirect
181. #1863C2×C11semidirect
422. C11#24201direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5562
C2×C11×#4622
C2×C11×#4402
C11×#25812
C11×#20422
C11×#20152
C11×#19852
C11×#19602
C11×#18782
C11×#18632
C11×#18042
#2420111