Finite Group Databasebeta

← C11×#34629 #14611822

Subgroups — C11×#34629 #14611822

Order 2816.

1558 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2655C214yesmaximal, complemented
2C11×#2652C214yesmaximal
3C11×#2647C211yesmaximal, characteristic, complemented
4C11×#2645C212yesmaximal, complemented
5C11×#2642C211yesmaximal, characteristic, complemented
6C11×#2629C211yesmaximal, characteristic
7C11×#2625C212yesmaximal
8C11×#2621C211yesmaximal, characteristic
9C11×#2402C214yesmaximal, complemented
10C11×#2401C214yesmaximal
11C4×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
12C4×C11×#125C211yesmaximal, characteristic, complemented
13C4×C11×C22⋊Q8C212yesmaximal
14C11×#2295C212yesmaximal, complemented
15C4×C11×#117C211yesmaximal, characteristic
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#125C2211yescharacteristic
18C2×C11×C22⋊Q8C2212yes—
19C2×C4×Q8×C11C2212yes—
20C2×C11×#117C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C22×C42×C11C2211yescharacteristic
23C11×#401C2214yes—
24C11×#400C2214yes—
25C11×#400C2214yes—
26C11×#400C2214yes—
27C11×#400C2214yes—
28C11×#400C2214yes—
29C11×#400C2214yes—
30C11×#400C2214yes—
31C11×#398C2214yes—
32C11×#398C2214yes—
33C11×#398C2214yes—
34C11×#398C2214yes—
35C11×#397C2214yes—
36C11×#397C2214yes—
37C11×#397C2214yes—
38C11×#396C2214yes—
39C11×#391C2212yes—
40C11×#391C2212yes—
41C11×#391C2212yes—
42C11×#391C2212yes—
43C11×#389C2212yes—
44C11×#389C2212yes—
45C11×#389C2212yes—
46C11×#389C2212yes—
47C11×#389C2214yes—
48C11×#387C2214yes—
49C11×#387C2214yes—
50C11×#387C2214yes—
51C11×#387C2214yes—
52C11×#385C2214yes—
53C11×#384C2211yescharacteristic
54C11×#382C2211yescharacteristic
55C11×#380C2212yes—
56C4×C11×C4⋊C4C2212yes—
57C4×C11×C4⋊C4C2214yes—
58C4×C11×C4⋊C4C2214yes—
59C4×C11×C4⋊C4C2214yes—
60C4×C11×C4⋊C4C2212yes—
61C4×C11×C4⋊C4C2214yes—
62C4×C11×C4⋊C4C2212yes—
63C4×C11×C22⋊C4C2212yes—
64C4×C11×C22⋊C4C2212yes—
65C4×C11×C22⋊C4C2214yes—
66C11×#376C2211yescharacteristic
67C11×#376C2211yescharacteristic
68C11×#376C2214yes—
69C43×C11C2211yescharacteristic
70C43×C11C2211yescharacteristic
71C22×Q8×C11C2312yes—
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C11×C4⋊Q8—24no—
76C11×#125—24no—
77C11×C22⋊Q8—28no—
78C4×Q8×C11—28no—
79C11×#117—24no—
80C11×#117—24no—
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C4⋊C4C2314yes—
86C2×C11×C4⋊C4C2314yes—
87C2×C11×C4⋊C4C2314yes—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C4⋊C4C2314yes—
90C2×C11×C4⋊C4C2314yes—
91C2×C11×C4⋊C4C2314yes—
92C2×C11×C4⋊C4C2314yes—
93C2×C11×C4⋊C4C2314yes—
94C2×C11×C4⋊C4C2314yes—
95C2×C11×C22⋊C4C2312yes—
96C2×C11×C22⋊C4C2312yes—
97C2×C11×C22⋊C4C2314yes—
98C2×C11×C22⋊C4C2314yes—
99C2×C42×C11—24no—
100C2×C42×C11C2311yescharacteristic
101C2×C42×C11C2311yescharacteristic
102C2×C42×C11C2311yescharacteristic
103C2×C42×C11C2311yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C2×C42×C11C2311yescharacteristic
106C2×C42×C11C2312yes—
107C2×C42×C11C2312yes—
108C2×C42×C11C2314yes—
109C2×C42×C11C2314yes—
110C2×C42×C11C2312yes—
111C2×C42×C11C2312yes—
112C2×C42×C11C2311yescharacteristic
113C2×C42×C11C2311yescharacteristic
114C11×#95C2312yes—
115C11×#95C2312yes—
116C11×#95C2312yes—
117C11×#95C2312yes—
118C11×#95C2314yes—
119C11×#95C2314yes—
120C11×#95C2314yes—
121C11×#95C2314yes—
122C11×#95C2314yes—
123C11×#95C2314yes—
124C11×#95C2314yes—
125C11×#95C2314yes—
126C11×#95C2314yes—
127C11×#95C2314yes—
128C11×#95C2314yes—
129C11×#95C2314yes—
130C11×#95C2314yes—
131C11×#95C2314yes—
132C11×#95C2314yes—
133#34629C1111yesmaximal, characteristic, direct product factor, Sylow
134C24×C11C2411yescharacteristic
135C2×Q8×C11—24no—
136C2×Q8×C11—24no—
137C2×Q8×C11—24no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—24no—
143C22×C4×C11—42no—
144C22×C4×C11#4114yes—
145C22×C4×C11C2411yescharacteristic
146C22×C4×C11C2412yes—
147C22×C4×C11C2412yes—
148C22×C4×C11C2412yes—
149C22×C4×C11C2411yescharacteristic
150C22×C4×C11C2414yes—
151C22×C4×C11C2414yes—
152C22×C4×C11C2414yes—
153C22×C4×C11C2414yes—
154C22×C4×C11C2411yescharacteristic
155C22×C4×C11C2412yes—
156C22×C4×C11C2411yescharacteristic
157C22×C4×C11C2411yescharacteristic
158C22×C4×C11C2411yescharacteristic
159C11×C4⋊C4—24no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—28no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—28no—
165C11×C4⋊C4—28no—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—28no—
168C11×C4⋊C4—44no—
169C11×C4⋊C4—44no—
170C11×C4⋊C4—44no—
171C11×C4⋊C4—44no—
172C11×C4⋊C4—44no—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—28no—
175C11×C22⋊C4—24no—
176C11×C22⋊C4—44no—
177C42×C11—22no—
178C42×C11—22no—
179C42×C11—22no—
180C42×C11—22no—
181C42×C11—22no—
182C42×C11—22no—
183C42×C11—28no—
184C42×C11—24no—
185C42×C11—24no—
186C42×C11—28no—
187C42×C11—42no—
188C42×C11—42no—
189C42×C11#4114yes—
190C42×C11#4114yes—
191#2655C2×C1114yescomplemented
192#2652C2×C1114yes—
193#2647C2×C1111yescharacteristic, complemented
194#2645C2×C1112yescomplemented
195#2642C2×C1111yescharacteristic, complemented
196#2629C2×C1111yescharacteristic
197#2625C2×C1112yes—
198#2621C2×C1111yescharacteristic
199#2402C2×C1114yescomplemented
200#2401C2×C1114yes—
201C4×C4⋊Q8C2×C1111yescharacteristic, complemented
202C4×#125C2×C1111yescharacteristic, complemented
203C4×C22⋊Q8C2×C1112yes—
204#2295C2×C1112yescomplemented
205C4×#117C2×C1111yescharacteristic
206C23×C11—21no—
207C23×C11—21no—
208C23×C11—22no—
209C23×C11—22no—
210C23×C11C2×#4112yes—
211C23×C11C2511yescharacteristic
212Q8×C11—48no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—28no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—22no—
244C2×C4×C11—44no—
245C2×C4×C11—44no—
246C2×C4×C11C2×#4112yes—
247C2×C4×C11C2×#4114yes—
248C2×C4×C11C2×#4112yes—
249C2×C4×C11C2×#4112yes—
250C2×C4×C11C2×#4112yes—
251C2×C4×C11C2×#4112yes—
252C2×C4×C11C2×#4112yes—
253C2×C4×C112−1+414yes—
254C2×C4⋊Q8C22×C1111yescharacteristic
255C2×#125C22×C1111yescharacteristic
256C2×C22⋊Q8C22×C1112yes—
257C2×C4×Q8C22×C1112yes—
258C2×#117C22×C1111yescharacteristic
259C2×#117C22×C1111yescharacteristic
260C22×C42C22×C1111yescharacteristic
261#401C22×C1114yes—
262#400C22×C1114yes—
263#400C22×C1114yes—
264#400C22×C1114yes—
265#400C22×C1114yes—
266#400C22×C1114yes—
267#400C22×C1114yes—
268#400C22×C1114yes—
269#398C22×C1114yes—
270#398C22×C1114yes—
271#398C22×C1114yes—
272#398C22×C1114yes—
273#397C22×C1114yes—
274#397C22×C1114yes—
275#397C22×C1114yes—
276#396C22×C1114yes—
277#391C22×C1112yes—
278#391C22×C1112yes—
279#391C22×C1112yes—
280#391C22×C1112yes—
281#389C22×C1112yes—
282#389C22×C1114yes—
283#389C22×C1112yes—
284#389C22×C1112yes—
285#389C22×C1112yes—
286#387C22×C1114yes—
287#387C22×C1114yes—
288#387C22×C1114yes—
289#387C22×C1114yes—
290#385C22×C1114yes—
291#384C22×C1111yescharacteristic
292#382C22×C1111yescharacteristic
293#380C22×C1112yes—
294C4×C4⋊C4C22×C1114yes—
295C4×C4⋊C4C22×C1112yes—
296C4×C4⋊C4C22×C1114yes—
297C4×C4⋊C4C22×C1112yes—
298C4×C4⋊C4C22×C1114yes—
299C4×C4⋊C4C22×C1112yes—
300C4×C4⋊C4C22×C1114yes—
301C4×C22⋊C4C22×C1112yes—
302C4×C22⋊C4C22×C1112yes—
303C4×C22⋊C4C22×C1114yes—
304#376C22×C1111yescharacteristic
305#376C22×C1111yescharacteristic
306#376C22×C1114yes—
307C43C22×C1111yescharacteristic
308C43C22×C1111yescharacteristic
309C22×C11—22no—
310C22×C11—24no—
311C22×C11—41no—
312C22×C11—41no—
313C22×C11—42no—
314C22×C11C22×#4111yescharacteristic
315C22×C11C22×#4111yescharacteristic
316C22×C11C22×#4111yescharacteristic
317C22×C11C2×2−1+412yes—
318C22×C11#58512yes—
319C4×C11—22no—
320C4×C11—22no—
321C4×C11—24no—
322C4×C11—44no—
323C4×C11—41no—
324C4×C11—44no—
325C4×C11—41no—
326C4×C11—42no—
327C4×C11—44no—
328C4×C11—42no—
329C4×C11—42no—
330C4×C11—44no—
331C4×C11#52914yes—
332C4×C11#54114yes—
333C22×Q8C23×C1112yes—
334C23×C4C23×C1111yescharacteristic
335C23×C4C23×C1111yescharacteristic
336C23×C4C23×C1111yescharacteristic
337C4⋊Q8—24no—
338#125—24no—
339C22⋊Q8—28no—
340C4×Q8—28no—
341#117—24no—
342#117—24no—
343C2×C4⋊C4C23×C1112yes—
344C2×C4⋊C4C23×C1112yes—
345C2×C4⋊C4C23×C1112yes—
346C2×C4⋊C4C23×C1114yes—
347C2×C4⋊C4C23×C1112yes—
348C2×C4⋊C4C23×C1114yes—
349C2×C4⋊C4C23×C1112yes—
350C2×C4⋊C4C23×C1114yes—
351C2×C4⋊C4C23×C1114yes—
352C2×C4⋊C4C23×C1114yes—
353C2×C4⋊C4C23×C1114yes—
354C2×C4⋊C4C23×C1114yes—
355C2×C4⋊C4C23×C1114yes—
356C2×C4⋊C4C23×C1114yes—
357C2×C22⋊C4C23×C1112yes—
358C2×C22⋊C4C23×C1112yes—
359C2×C22⋊C4C23×C1114yes—
360C2×C22⋊C4C23×C1114yes—
361C2×C42—24no—
362C2×C42C23×C1111yescharacteristic
363C2×C42C23×C1111yescharacteristic
364C2×C42C23×C1111yescharacteristic
365C2×C42C23×C1114yes—
366C2×C42C23×C1112yes—
367C2×C42C23×C1112yes—
368C2×C42C23×C1111yescharacteristic
369C2×C42C23×C1114yes—
370C2×C42C23×C1111yescharacteristic
371C2×C42C23×C1111yescharacteristic
372C2×C42C23×C1112yes—
373C2×C42C23×C1112yes—
374C2×C42C23×C1111yescharacteristic
375C2×C42C23×C1111yescharacteristic
376#95C23×C1112yes—
377#95C23×C1112yes—
378#95C23×C1112yes—
379#95C23×C1112yes—
380#95C23×C1114yes—
381#95C23×C1114yes—
382#95C23×C1114yes—
383#95C23×C1114yes—
384#95C23×C1114yes—
385#95C23×C1114yes—
386#95C23×C1114yes—
387#95C23×C1114yes—
388#95C23×C1114yes—
389#95C23×C1114yes—
390#95C23×C1114yes—
391#95C23×C1114yes—
392#95C23×C1114yes—
393#95C23×C1114yes—
394#95C23×C1114yes—
395C2×C11—42no—
396C2×C11C2×#52911yescharacteristic
397C2×C11C2×#54111yescharacteristic
398C2×C11#345511yescharacteristic
399C2×C11#346112yes—
400C2×C11#346112yes—
401C24C24×C1111yescharacteristic
402C2×Q8—24no—
403C2×Q8—24no—
404C2×Q8—24no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—24no—
410C22×C4—42no—
411C22×C4C11×#4114yes—
412C22×C4C24×C1111yescharacteristic
413C22×C4C24×C1112yes—
414C22×C4C24×C1112yes—
415C22×C4C24×C1112yes—
416C22×C4C24×C1111yescharacteristic
417C22×C4C24×C1114yes—
418C22×C4C24×C1114yes—
419C22×C4C24×C1114yes—
420C22×C4C24×C1114yes—
421C22×C4C24×C1111yescharacteristic
422C22×C4C24×C1112yes—
423C22×C4C24×C1111yescharacteristic
424C22×C4C24×C1111yescharacteristic
425C22×C4C24×C1111yescharacteristic
426C4⋊C4—24no—
427C4⋊C4—24no—
428C4⋊C4—24no—
429C4⋊C4—28no—
430C4⋊C4—24no—
431C4⋊C4—28no—
432C4⋊C4—28no—
433C4⋊C4—24no—
434C4⋊C4—28no—
435C4⋊C4—44no—
436C4⋊C4—44no—
437C4⋊C4—44no—
438C4⋊C4—44no—
439C4⋊C4—44no—
440C22⋊C4—24no—
441C22⋊C4—28no—
442C22⋊C4—24no—
443C22⋊C4—44no—
444C42—22no—
445C42—22no—
446C42—22no—
447C42—22no—
448C42—22no—
449C42—22no—
450C42—28no—
451C42—24no—
452C42—24no—
453C42—28no—
454C42—42no—
455C42—42no—
456C42C11×#4114yes—
457C42C11×#4114yes—
458C11#3462911yescharacteristic, direct product factor, Sylow
459C23—21no—
460C23—21no—
461C23—22no—
462C23—22no—
463C23C2×C11×#4112yes—
464C23C25×C1111yescharacteristic
465Q8—48no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—28no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—22no—
497C2×C4—44no—
498C2×C4—44no—
499C2×C4C2×C11×#4112yes—
500C2×C4C2×C11×#4114yes—
501C2×C4C2×C11×#4112yes—
502C2×C4C2×C11×#4112yes—
503C2×C4C2×C11×#4112yes—
504C2×C4C2×C11×#4112yes—
505C2×C4C2×C11×#4112yes—
506C2×C4C11×2−1+414yes—
507C22—22no—
508C22—24no—
509C22—41no—
510C22—41no—
511C22—42no—
512C22C22×C11×#4111yescharacteristic
513C22C22×C11×#4111yescharacteristic
514C22C22×C11×#4111yescharacteristic
515C22C2×C11×2−1+412yes—
516C22C11×#58512yes—
517C4—22no—
518C4—22no—
519C4—24no—
520C4—44no—
521C4—41no—
522C4—41no—
523C4—44no—
524C4—42no—
525C4—44no—
526C4—42no—
527C4—42no—
528C4—44no—
529C4C11×#52914yes—
530C4C11×#54114yes—
531C2—42no—
532C2C2×C11×#52911yescharacteristic
533C2C2×C11×#54111yescharacteristic
534C2C11×#345511yescharacteristic
535C2C11×#346112yes—
536C2C11×#346112yes—
subgroupG/H
centerC22×C4×C11C24
commutator, Frattini, cosocleC23C25×C11
socleC23×C11C25
prime radicalC24×C11C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2655C2semidirect
3. C11×#2647C2semidirect
4. C11×#2645C2semidirect
5. C11×#2642C2semidirect
9. C11×#2402C2semidirect
11. C4×C11×C4⋊Q8C2semidirect
12. C4×C11×#125C2semidirect
14. C11×#2295C2semidirect
133. #34629C11direct (N × H)
191. #2655C2×C11semidirect
193. #2647C2×C11semidirect
194. #2645C2×C11semidirect
195. #2642C2×C11semidirect
199. #2402C2×C11semidirect
201. C4×C4⋊Q8C2×C11semidirect
202. C4×#125C2×C11semidirect
204. #2295C2×C11semidirect
458. C11#34629direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#26552
C11×#26522
C11×#26472
C11×#26452
C11×#26422
C11×#26292
C11×#26252
C11×#26212
C11×#24022
C11×#24012
C4×C11×C4⋊Q82
C4×C11×#1252
C4×C11×C22⋊Q82
C11×#22952
C4×C11×#1172
#3462911