Finite Group Databasebeta

← C11×#24202 #14601395

Subgroups — C11×#24202 #14601395

Order 2816.

1132 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#559C211yesmaximal, characteristic
2C2×C11×#460C211yesmaximal, characteristic
3C2×C11×#441C211yesmaximal, characteristic, complemented
4C11×#2581C211yesmaximal, characteristic, complemented
5C11×#2042C212yesmaximal, complemented
6C11×#2015C212yesmaximal, complemented
7C11×#1985C211yesmaximal, characteristic, complemented
8C11×#1961C211yesmaximal, characteristic
9C11×#1877C212yesmaximal, complemented
10C11×#1864C212yesmaximal, complemented
11C11×#1805C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13C22×C11×SD16C2212yes—
14C11×#559—24no—
15C11×#559—24no—
16C2×C11×#127C2211yescharacteristic
17C2×C11×#124—21no—
18C2×C11×#124C2212yes—
19C2×C11×#123—22no—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11—21no—
24C2×C4×D4×C11C2212yes—
25C11×#460—24no—
26C11×#441—24no—
27C2×C11×#106C2211yescharacteristic
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×#103C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2212yes—
32C2×C11×#102C2212yes—
33C2×C11×#102C2212yes—
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×C11C2311yescharacteristic
47C22×Q8×C11C2311yescharacteristic
48C22×D4×C11—21no—
49C22×D4×C11—21no—
50C22×D4×C11C2312yes—
51C23×C4×C11—22no—
52C2×C11×Q16—22no—
53C2×C11×Q16—22no—
54C2×C11×Q16—22no—
55C2×C11×SD16—24no—
56C2×C11×SD16—24no—
57C2×C11×SD16—42no—
58C22×C8×C11C2312yes—
59C22×C8×C11C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C11×#127—22no—
62C11×#127D414yes—
63C11×#124—28no—
64C11×#124—24no—
65C11×#124—24no—
66C11×#123—216no—
67C4×Q8×C11—22no—
68C4×Q8×C11—22no—
69C4×Q8×C11—22no—
70C4×Q8×C11—22no—
71C4×Q8×C11—22no—
72C4×Q8×C11D414yes—
73C4×D4×C11—28no—
74C4×D4×C11—24no—
75C4×D4×C11—24no—
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—22no—
86C2×C11×C22⋊C4—22no—
87C2×C42×C11—21no—
88C2×C42×C11—21no—
89C2×C42×C11C2312yes—
90C2×C42×C11C2311yescharacteristic
91C11×#106—22no—
92C11×C4⋊C8—22no—
93C11×#103—22no—
94C11×#103—22no—
95C11×#103—42no—
96C11×#102—24no—
97C11×#102—24no—
98C11×#102—42no—
99C11×#97—22no—
100C11×#95—21no—
101C11×#95—21no—
102C11×#95—22no—
103C11×#95—22no—
104C11×#95—22no—
105#24202C1111yesmaximal, characteristic, direct product factor, Sylow
106C24×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11—42no—
119C2×Q8×C11C2×D412yes—
120C2×Q8×C11#4112yes—
121C2×D4×C11—24no—
122C2×D4×C11—24no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—44no—
129C2×D4×C11—82no—
130C2×D4×C11C2×D414yes—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—28no—
135C22×C4×C11—22no—
136C22×C4×C11—21no—
137C22×C4×C11—84no—
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2411yescharacteristic
143C11×Q16—28no—
144C11×SD16—48no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—22no—
148C2×C8×C11—21no—
149C2×C8×C11—22no—
150C2×C8×C11—21no—
151C2×C8×C11—22no—
152C2×C8×C11—21no—
153C2×C8×C11#4112yes—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—44no—
163C11×C4⋊C4—42no—
164C11×C4⋊C4C2×D412yes—
165C11×C22⋊C4—28no—
166C11×C22⋊C4—28no—
167C11×C22⋊C4—28no—
168C42×C11—24no—
169C42×C11—22no—
170C42×C11—22no—
171C42×C11—42no—
172C42×C11C2×D412yes—
173C42×C11C2×D412yes—
174C2×#559C2×C1111yescharacteristic
175C2×#460C2×C1111yescharacteristic
176C2×#441C2×C1111yescharacteristic, complemented
177#2581C2×C1111yescharacteristic, complemented
178#2042C2×C1112yescomplemented
179#2015C2×C1112yescomplemented
180#1985C2×C1111yescharacteristic, complemented
181#1961C2×C1111yescharacteristic
182#1877C2×C1112yescomplemented
183#1864C2×C1112yescomplemented
184#1805C2×C1111yescharacteristic, complemented
185C23×C11—24no—
186C23×C11—42no—
187C23×C11—42no—
188C23×C11—44no—
189C23×C11—44no—
190C23×C11C22×D411yescharacteristic
191Q8×C11—22no—
192Q8×C11—22no—
193Q8×C11—22no—
194Q8×C11—22no—
195Q8×C11—44no—
196Q8×C11—41no—
197Q8×C11—41no—
198Q8×C11—41no—
199Q8×C11—41no—
200D4×C11—24no—
201D4×C11—24no—
202D4×C11—48no—
203D4×C11—42no—
204D4×C11—42no—
205D4×C11—84no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—24no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—42no—
221C2×C4×C11—41no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—88no—
227C2×C4×C11#12012yes—
228C2×C4×C11#12012yes—
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×SD16C22×C1112yes—
240#559—24no—
241#559—24no—
242C2×#127C22×C1111yescharacteristic
243C2×#124—21no—
244C2×#124C22×C1112yes—
245C2×#123—22no—
246C2×C4×Q8C22×C1111yescharacteristic
247C2×C4×Q8C22×C1111yescharacteristic
248C2×C4×Q8C22×C1111yescharacteristic
249C2×C4×D4—21no—
250C2×C4×D4C22×C1112yes—
251#460—24no—
252#441—24no—
253C2×#106C22×C1111yescharacteristic
254C2×C4⋊C8C22×C1111yescharacteristic
255C2×#103C22×C1111yescharacteristic
256C2×#103C22×C1111yescharacteristic
257C2×#103C22×C1112yes—
258C2×#102C22×C1112yes—
259C2×#102C22×C1112yes—
260C2×#102C22×C1112yes—
261C2×#97C22×C1111yescharacteristic
262#400—21no—
263#395—21no—
264#391C22×C1112yes—
265#389C22×C1112yes—
266#387—22no—
267#382C22×C1111yescharacteristic
268#340C22×C1112yes—
269#336C22×C1112yes—
270#336C22×C1112yes—
271C22×C11—44no—
272C22×C11—44no—
273C22×C11—44no—
274C22×C11—84no—
275C22×C11—84no—
276C22×C11C2×#12011yescharacteristic
277C22×C11#54811yescharacteristic
278C22×C11#55011yescharacteristic
279C22×C11#57512yes—
280C22×C11#57712yes—
281C4×C11—22no—
282C4×C11—22no—
283C4×C11—42no—
284C4×C11—42no—
285C4×C11—42no—
286C4×C11—42no—
287C4×C11—42no—
288C4×C11—82no—
289C4×C11—81no—
290C4×C11#52511yescharacteristic
291C4×C11#53711yescharacteristic
292C4×C11#54611yescharacteristic
293C4×C11#54711yescharacteristic
294C22×Q8D4×C1111yescharacteristic
295C22×Q8C23×C1111yescharacteristic
296C22×Q8C23×C1111yescharacteristic
297C22×D4—21no—
298C22×D4—21no—
299C22×D4C23×C1112yes—
300C23×C4—22no—
301C2×Q16—22no—
302C2×Q16—22no—
303C2×Q16—22no—
304C2×SD16—24no—
305C2×SD16—24no—
306C2×SD16—42no—
307C22×C8C23×C1112yes—
308C22×C8C23×C1111yescharacteristic
309C22×C8C23×C1111yescharacteristic
310#127—22no—
311#127D4×C1114yes—
312#124—28no—
313#124—24no—
314#124—24no—
315#123—216no—
316C4×Q8—22no—
317C4×Q8—22no—
318C4×Q8—22no—
319C4×Q8—22no—
320C4×Q8—22no—
321C4×Q8D4×C1114yes—
322C4×D4—28no—
323C4×D4—24no—
324C4×D4—24no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4D4×C1111yescharacteristic
329C2×C4⋊C4D4×C1112yes—
330C2×C4⋊C4C23×C1111yescharacteristic
331C2×C4⋊C4C23×C1112yes—
332C2×C4⋊C4C23×C1111yescharacteristic
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42C23×C1112yes—
339C2×C42C23×C1111yescharacteristic
340#106—22no—
341C4⋊C8—22no—
342#103—22no—
343#103—22no—
344#103—42no—
345#102—24no—
346#102—24no—
347#102—42no—
348#97—22no—
349#95—21no—
350#95—21no—
351#95—22no—
352#95—22no—
353#95—22no—
354C2×C11—84no—
355C2×C11#240711yescharacteristic
356C2×C11#300511yescharacteristic
357C2×C11#300911yescharacteristic
358C2×C11#337112yes—
359C2×C11#340112yes—
360C24—22no—
361C2×Q8—22no—
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×Q8—21no—
366C2×Q8—21no—
367C2×Q8—21no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—21no—
371C2×Q8—21no—
372C2×Q8—42no—
373C2×Q8C2×D4×C1112yes—
374C2×Q8C11×#4112yes—
375C2×D4—24no—
376C2×D4—24no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—44no—
383C2×D4—82no—
384C2×D4C2×D4×C1114yes—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—28no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—84no—
392C22×C4C2×D4×C1112yes—
393C22×C4C2×D4×C1112yes—
394C22×C4C2×D4×C1111yescharacteristic
395C22×C4C2×D4×C1111yescharacteristic
396C22×C4C24×C1111yescharacteristic
397Q16—28no—
398SD16—48no—
399C2×C8—21no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—22no—
403C2×C8—22no—
404C2×C8—21no—
405C2×C8—22no—
406C2×C8—21no—
407C2×C8C11×#4112yes—
408C4⋊C4—24no—
409C4⋊C4—22no—
410C4⋊C4—24no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—44no—
417C4⋊C4—42no—
418C4⋊C4C2×D4×C1112yes—
419C22⋊C4—28no—
420C22⋊C4—28no—
421C22⋊C4—28no—
422C42—24no—
423C42—22no—
424C42—22no—
425C42—42no—
426C42C2×D4×C1112yes—
427C42C2×D4×C1112yes—
428C11#2420211yescharacteristic, direct product factor, Sylow
429C23—24no—
430C23—42no—
431C23—42no—
432C23—44no—
433C23—44no—
434C23C22×D4×C1111yescharacteristic
435Q8—22no—
436Q8—22no—
437Q8—22no—
438Q8—22no—
439Q8—44no—
440Q8—41no—
441Q8—41no—
442Q8—41no—
443Q8—41no—
444D4—24no—
445D4—24no—
446D4—48no—
447D4—42no—
448D4—42no—
449D4—84no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—24no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—42no—
465C2×C4—41no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—88no—
471C2×C4C11×#12012yes—
472C2×C4C11×#12012yes—
473C2×C4C22×D4×C1111yescharacteristic
474C2×C4C22×D4×C1111yescharacteristic
475C2×C4C2×C11×#4111yescharacteristic
476C2×C4C2×C11×#4111yescharacteristic
477C2×C4C11×H(5,𝔽2)11yescharacteristic
478C2×C4C11×2−1+411yescharacteristic
479C8—22no—
480C8—41no—
481C8—42no—
482C22—44no—
483C22—44no—
484C22—44no—
485C22—84no—
486C22—84no—
487C22C2×C11×#12011yescharacteristic
488C22C11×#54811yescharacteristic
489C22C11×#55011yescharacteristic
490C22C11×#57512yes—
491C22C11×#57712yes—
492C4—22no—
493C4—22no—
494C4—42no—
495C4—42no—
496C4—42no—
497C4—42no—
498C4—42no—
499C4—81no—
500C4—82no—
501C4C11×#52511yescharacteristic
502C4C11×#53711yescharacteristic
503C4C11×#54611yescharacteristic
504C4C11×#54711yescharacteristic
505C2—84no—
506C2C11×#240711yescharacteristic
507C2C11×#300511yescharacteristic
508C2C11×#300911yescharacteristic
509C2C11×#337112yes—
510C2C11×#340112yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#127C22
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
3. C2×C11×#441C2semidirect
4. C11×#2581C2semidirect
5. C11×#2042C2semidirect
6. C11×#2015C2semidirect
7. C11×#1985C2semidirect
9. C11×#1877C2semidirect
10. C11×#1864C2semidirect
11. C11×#1805C2semidirect
105. #24202C11direct (N × H)
176. C2×#441C2×C11semidirect
177. #2581C2×C11semidirect
178. #2042C2×C11semidirect
179. #2015C2×C11semidirect
180. #1985C2×C11semidirect
182. #1877C2×C11semidirect
183. #1864C2×C11semidirect
184. #1805C2×C11semidirect
428. C11#24202direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5592
C2×C11×#4602
C2×C11×#4412
C11×#25812
C11×#20422
C11×#20152
C11×#19852
C11×#19612
C11×#18772
C11×#18642
C11×#18052
#2420211