Finite Group Databasebeta

← C11×#24703 #14601896

Subgroups — C11×#24703 #14601896

Order 2816.

848 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#475C211yesmaximal, characteristic, complemented
2C2×C11×#431C211yesmaximal, characteristic
3C11×#2857C211yesmaximal, characteristic
4C4×C11×C22⋊Q8C211yesmaximal, characteristic
5C11×#2077C212yesmaximal
6C11×#2035C212yesmaximal
7C11×#1988C211yesmaximal, characteristic, complemented
8C11×#1948C211yesmaximal, characteristic, complemented
9C11×#1941C212yesmaximal, complemented
10C11×#1933C212yesmaximal, complemented
11C11×#1803C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×C22⋊Q8—21no—
14C2×C11×C22⋊Q8C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C11×#475—24no—
18C11×#431—24no—
19C2×C11×#106C2212yes—
20C2×C11×#106C2212yes—
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×#103C2212yes—
24C2×C11×#103C2212yes—
25C2×C11×C22⋊C8C2212yes—
26C2×C4×C8×C11C2212yes—
27C11×#391—21no—
28C11×#391C2211yescharacteristic
29C11×#389—21no—
30C11×#389C2212yes—
31C11×#389C2211yescharacteristic
32C11×#387—21no—
33C11×#385—21no—
34C11×#384C2211yescharacteristic
35C11×#380—21no—
36C11×#380C2212yes—
37C11×#380C2211yescharacteristic
38C4×C11×C4⋊C4—21no—
39C4×C11×C4⋊C4C2211yescharacteristic
40C4×C11×C22⋊C4—21no—
41C11×#340C2212yes—
42C11×#340C2212yes—
43C11×#340C2212yes—
44C11×#340C2212yes—
45C22×Q8×C11—21no—
46C22×Q8×C11C2311yescharacteristic
47C23×C4×C11D411yescharacteristic
48C23×C4×C11D411yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C22×C8×C11C2312yes—
51C22×C8×C11C2312yes—
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8—22no—
54C11×C22⋊Q8—22no—
55C11×C22⋊Q8—22no—
56C11×C22⋊Q8—44no—
57C4×Q8×C11—22no—
58C4×Q8×C11—22no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—22no—
74C2×C42×C11—22no—
75C2×C42×C11—22no—
76C2×C42×C11—21no—
77C2×C42×C11—21no—
78C2×C42×C11D411yescharacteristic
79C2×C42×C11D411yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C11×#106—24no—
83C11×#106—24no—
84C11×C4⋊C8—22no—
85C11×C4⋊C8D414yes—
86C11×#103—24no—
87C11×#103—24no—
88C11×C22⋊C8—24no—
89C4×C8×C11—24no—
90C11×#95—21no—
91C11×#95—21no—
92C11×#95—21no—
93C11×#95—21no—
94C11×#95—21no—
95C11×#95—22no—
96C11×#95—22no—
97#24703C1111yesmaximal, characteristic, direct product factor, Sylow
98C24×C11C2×D411yescharacteristic
99C2×Q8×C11—21no—
100C2×Q8×C11—21no—
101C2×Q8×C11—21no—
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11—42no—
105C2×Q8×C11—42no—
106C2×Q8×C11—42no—
107C2×Q8×C11#4112yes—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—41no—
125C22×C4×C11SD1614yes—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2411yescharacteristic
132C2×C8×C11—22no—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C2×C8×C11C2×D414yes—
138C11×C4⋊C4—24no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—42no—
149C11×C4⋊C4—42no—
150C11×C4⋊C4—42no—
151C11×C4⋊C4—42no—
152C11×C4⋊C4—44no—
153C11×C4⋊C4—42no—
154C11×C4⋊C4#4112yes—
155C11×C22⋊C4—24no—
156C11×C22⋊C4—42no—
157C11×C22⋊C4—44no—
158C42×C11—22no—
159C42×C11—22no—
160C42×C11—21no—
161C42×C11—21no—
162C42×C11—42no—
163C42×C11—42no—
164C42×C11C2×D412yes—
165C42×C11#4112yes—
166C2×#475C2×C1111yescharacteristic, complemented
167C2×#431C2×C1111yescharacteristic
168#2857C2×C1111yescharacteristic
169C4×C22⋊Q8C2×C1111yescharacteristic
170#2077C2×C1112yes—
171#2035C2×C1112yes—
172#1988C2×C1111yescharacteristic, complemented
173#1948C2×C1111yescharacteristic, complemented
174#1941C2×C1112yescomplemented
175#1933C2×C1112yescomplemented
176#1803C2×C1111yescharacteristic, complemented
177C23×C11—21no—
178C23×C11—21no—
179C23×C11—21no—
180C23×C11—21no—
181C23×C11—21no—
182C23×C11—21no—
183C23×C11C2×SD1612yes—
184C23×C11C22×D411yescharacteristic
185Q8×C11—22no—
186Q8×C11—22no—
187Q8×C11—41no—
188Q8×C11—41no—
189Q8×C11—84no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—28no—
197C2×C4×C11—21no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—44no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—41no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—41no—
218C2×C4×C11—42no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—42no—
223C2×C4×C11#12112yes—
224C2×C4×C11#12112yes—
225C2×C4×C11C2×SD1612yes—
226C2×C4×C11C2×SD1612yes—
227C2×C4×C11#13512yes—
228C2×C4×C11#13712yes—
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C2×C4×C112−1+411yescharacteristic
234C2×C4×C112−1+411yescharacteristic
235C8×C11—24no—
236C8×C11—42no—
237C2×C4⋊Q8C22×C1111yescharacteristic
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8C22×C1111yescharacteristic
240C2×C4×Q8C22×C1111yescharacteristic
241C22×C42C22×C1111yescharacteristic
242#475—24no—
243#431—24no—
244C2×#106C22×C1112yes—
245C2×#106C22×C1112yes—
246C2×C4⋊C8C22×C1111yescharacteristic
247C2×C4⋊C8C22×C1111yescharacteristic
248C2×#103C22×C1112yes—
249C2×#103C22×C1112yes—
250C2×C22⋊C8C22×C1112yes—
251C2×C4×C8C22×C1112yes—
252#391—21no—
253#391C22×C1111yescharacteristic
254#389—21no—
255#389C22×C1112yes—
256#389C22×C1111yescharacteristic
257#387—21no—
258#385—21no—
259#384C22×C1111yescharacteristic
260#380—21no—
261#380C22×C1111yescharacteristic
262#380C22×C1112yes—
263C4×C4⋊C4—21no—
264C4×C4⋊C4C22×C1111yescharacteristic
265C4×C22⋊C4—21no—
266#340C22×C1112yes—
267#340C22×C1112yes—
268#340C22×C1112yes—
269#340C22×C1112yes—
270C22×C11—22no—
271C22×C11—22no—
272C22×C11—22no—
273C22×C11—41no—
274C22×C11—41no—
275C22×C11—41no—
276C22×C11—41no—
277C22×C11C2×#12111yescharacteristic
278C22×C11#52511yescharacteristic
279C22×C11#53611yescharacteristic
280C22×C11C22×SD1611yescharacteristic
281C22×C11C2×#13511yescharacteristic
282C22×C11C2×#13711yescharacteristic
283C22×C11#57511yescharacteristic
284C4×C11—22no—
285C4×C11—22no—
286C4×C11—22no—
287C4×C11—42no—
288C4×C11—41no—
289C4×C11—42no—
290C4×C11—82no—
291C4×C11—81no—
292C4×C11—82no—
293C4×C11—81no—
294C4×C11#46514yes—
295C4×C11#54711yescharacteristic
296C4×C11#54811yescharacteristic
297C4×C11#55211yescharacteristic
298C4×C11#55611yescharacteristic
299C22×Q8—21no—
300C22×Q8C23×C1111yescharacteristic
301C23×C4D4×C1111yescharacteristic
302C23×C4D4×C1111yescharacteristic
303C23×C4C23×C1111yescharacteristic
304C22×C8C23×C1112yes—
305C22×C8C23×C1112yes—
306C4⋊Q8—22no—
307C4⋊Q8—22no—
308C22⋊Q8—22no—
309C22⋊Q8—22no—
310C22⋊Q8—44no—
311C4×Q8—22no—
312C4×Q8—22no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4C23×C1111yescharacteristic
321C2×C4⋊C4C23×C1112yes—
322C2×C4⋊C4C23×C1111yescharacteristic
323C2×C4⋊C4C23×C1112yes—
324C2×C4⋊C4C23×C1111yescharacteristic
325C2×C22⋊C4—21no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—21no—
328C2×C42—22no—
329C2×C42—22no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42D4×C1111yescharacteristic
333C2×C42D4×C1111yescharacteristic
334C2×C42C23×C1111yescharacteristic
335C2×C42C23×C1111yescharacteristic
336#106—24no—
337#106—24no—
338C4⋊C8—22no—
339C4⋊C8D4×C1114yes—
340#103—24no—
341#103—24no—
342C22⋊C8—24no—
343C4×C8—24no—
344#95—21no—
345#95—21no—
346#95—21no—
347#95—21no—
348#95—21no—
349#95—22no—
350#95—22no—
351C2×C11—42no—
352C2×C11#241511yescharacteristic
353C2×C11C2×#46511yescharacteristic
354C2×C11#305611yescharacteristic
355C2×C11#310311yescharacteristic
356C2×C11#310711yescharacteristic
357C2×C11#322911yescharacteristic
358C2×C11#323311yescharacteristic
359C24C2×D4×C1111yescharacteristic
360C2×Q8—21no—
361C2×Q8—21no—
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×Q8—42no—
366C2×Q8—42no—
367C2×Q8—42no—
368C2×Q8C11×#4112yes—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—41no—
386C22×C4C11×SD1614yes—
387C22×C4C2×D4×C1111yescharacteristic
388C22×C4C2×D4×C1111yescharacteristic
389C22×C4C2×D4×C1111yescharacteristic
390C22×C4C2×D4×C1111yescharacteristic
391C22×C4C2×D4×C1111yescharacteristic
392C22×C4C24×C1111yescharacteristic
393C2×C8—22no—
394C2×C8—22no—
395C2×C8—22no—
396C2×C8—22no—
397C2×C8—22no—
398C2×C8C2×D4×C1114yes—
399C4⋊C4—24no—
400C4⋊C4—21no—
401C4⋊C4—22no—
402C4⋊C4—21no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—21no—
406C4⋊C4—22no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—42no—
410C4⋊C4—42no—
411C4⋊C4—42no—
412C4⋊C4—42no—
413C4⋊C4—44no—
414C4⋊C4—42no—
415C4⋊C4C11×#4112yes—
416C22⋊C4—24no—
417C22⋊C4—42no—
418C22⋊C4—44no—
419C42—22no—
420C42—22no—
421C42—21no—
422C42—21no—
423C42—42no—
424C42—42no—
425C42C2×D4×C1112yes—
426C42C11×#4112yes—
427C11#2470311yescharacteristic, direct product factor, Sylow
428C23—21no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23C2×C11×SD1612yes—
435C23C22×D4×C1111yescharacteristic
436Q8—22no—
437Q8—22no—
438Q8—41no—
439Q8—41no—
440Q8—84no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—28no—
448C2×C4—21no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—44no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—41no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4C11×#12112yes—
475C2×C4C11×#12112yes—
476C2×C4C2×C11×SD1612yes—
477C2×C4C2×C11×SD1612yes—
478C2×C4C11×#13512yes—
479C2×C4C11×#13712yes—
480C2×C4C22×D4×C1111yescharacteristic
481C2×C4C2×C11×#4111yescharacteristic
482C2×C4C2×C11×#4111yescharacteristic
483C2×C4C2×C11×#4111yescharacteristic
484C2×C4C11×2−1+411yescharacteristic
485C2×C4C11×2−1+411yescharacteristic
486C8—24no—
487C8—42no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22C2×C11×#12111yescharacteristic
496C22C11×#52511yescharacteristic
497C22C11×#53611yescharacteristic
498C22C22×C11×SD1611yescharacteristic
499C22C2×C11×#13511yescharacteristic
500C22C2×C11×#13711yescharacteristic
501C22C11×#57511yescharacteristic
502C4—22no—
503C4—22no—
504C4—22no—
505C4—41no—
506C4—42no—
507C4—42no—
508C4—81no—
509C4—82no—
510C4—81no—
511C4—82no—
512C4C11×#46514yes—
513C4C11×#54711yescharacteristic
514C4C11×#54811yescharacteristic
515C4C11×#55211yescharacteristic
516C4C11×#55611yescharacteristic
517C2—42no—
518C2C11×#241511yescharacteristic
519C2C2×C11×#46511yescharacteristic
520C2C11×#305611yescharacteristic
521C2C11×#310311yescharacteristic
522C2C11×#310711yescharacteristic
523C2C11×#322911yescharacteristic
524C2C11×#323311yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC24×C11C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#475C2semidirect
7. C11×#1988C2semidirect
8. C11×#1948C2semidirect
9. C11×#1941C2semidirect
10. C11×#1933C2semidirect
11. C11×#1803C2semidirect
97. #24703C11direct (N × H)
166. C2×#475C2×C11semidirect
172. #1988C2×C11semidirect
173. #1948C2×C11semidirect
174. #1941C2×C11semidirect
175. #1933C2×C11semidirect
176. #1803C2×C11semidirect
427. C11#24703direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4752
C2×C11×#4312
C11×#28572
C4×C11×C22⋊Q82
C11×#20772
C11×#20352
C11×#19882
C11×#19482
C11×#19412
C11×#19332
C11×#18032
#2470311