Finite Group Databasebeta

← C11×#24270 #14601463

Subgroups — C11×#24270 #14601463

Order 2816.

1452 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×#135C211yesmaximal, characteristic, complemented
2C2×C11×#468C212yesmaximal, complemented
3C2×C11×#435C211yesmaximal, characteristic, complemented
4C11×#2407C212yesmaximal, complemented
5C11×#2056C211yesmaximal, characteristic, complemented
6C11×#2054C211yesmaximal, characteristic, complemented
7C11×#2001C211yesmaximal, characteristic, complemented
8C11×#1999C211yesmaximal, characteristic, complemented
9C11×#1973C212yesmaximal, complemented
10C11×#1808C211yesmaximal, characteristic, complemented
11C11×#1788C212yesmaximal, complemented
12C22×C11×#41C2212yes—
13C2×C11×#135—28no—
14C2×C11×#135—24no—
15C22×C11×Q16C2211yescharacteristic
16C22×C11×SD16C2212yes—
17C22×C11×D8C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C2×C11×C22⋊Q8C2212yes—
21C2×C11×#121C2212yes—
22C2×C4×D4×C11C2211yescharacteristic
23C11×#468—28no—
24C11×#435—24no—
25C2×C11×#107C2212yes—
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×#103C2212yes—
28C2×C11×#103C2212yes—
29C2×C11×#102C2212yes—
30C2×C11×#102C2212yes—
31C2×C11×C22⋊C8C2211yescharacteristic
32C2×C11×C22⋊C8C2211yescharacteristic
33C2×C11×#97C2211yescharacteristic
34C11×#394—22no—
35C11×#392—22no—
36C11×#391C2212yes—
37C11×#390C2212yes—
38C11×#386—22no—
39C11×#385—22no—
40C11×#380C2212yes—
41C11×#340C2211yescharacteristic
42C11×#340C2211yescharacteristic
43C2×C11×#41—24no—
44C2×C11×#41—24no—
45C2×C11×#41—24no—
46C2×C11×#41—24no—
47C2×C11×#41—42no—
48C2×C11×#41—42no—
49C22×Q8×C11C2312yes—
50C22×D4×C11—22no—
51C22×D4×C11—22no—
52C22×D4×C11D411yescharacteristic
53C22×D4×C11C2312yes—
54C23×C4×C11—22no—
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C11×#135—232no—
58C2×C11×Q16—24no—
59C2×C11×Q16—22no—
60C2×C11×SD16—24no—
61C2×C11×SD16—24no—
62C2×C11×SD16D418yescomplemented
63C2×C11×D8—24no—
64C2×C11×D8—22no—
65C2×C11×M16—22no—
66C2×C11×M16—24no—
67C22×C8×C11—24no—
68C22×C8×C11D414yescomplemented
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C11×C22⋊Q8—24no—
74C11×C22⋊Q8—42no—
75C11×#121—24no—
76C11×#121—42no—
77C4×D4×C11—22no—
78C4×D4×C11—22no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4D411yescharacteristic
89C2×C11×C22⋊C4D411yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C11×#107—24no—
92C11×C4⋊C8—22no—
93C11×#103—24no—
94C11×#103—42no—
95C11×#102—24no—
96C11×#102—42no—
97C11×C22⋊C8—22no—
98C11×C22⋊C8—22no—
99C11×#97—22no—
100C11×#95—22no—
101C11×#95—22no—
102C11×#95—22no—
103#24270C1111yesmaximal, characteristic, direct product factor, Sylow
104C24×C11—22no—
105C24×C11C2×D411yescharacteristic
106C24×C11C2×D411yescharacteristic
107C11×#41—216no—
108C11×#41—48no—
109C11×#41—48no—
110C11×#41—48no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11C2×D414yes—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—42no—
124C2×D4×C11—44no—
125C2×D4×C11—44no—
126C2×D4×C11—44no—
127C2×D4×C11—44no—
128C2×D4×C11—44no—
129C2×D4×C11—82no—
130C2×D4×C11C2×D414yes—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
136C22×C4×C11—21no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—44no—
141C22×C4×C11—44no—
142C22×C4×C11—44no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D412yes—
148C22×C4×C11#4112yes—
149C22×C4×C11C2411yescharacteristic
150C11×Q16—28no—
151C11×SD16—216no—
152C11×D8—28no—
153C11×M16—44no—
154C2×C8×C11—28no—
155C2×C8×C11—22no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—22no—
159C2×C8×C11—22no—
160C2×C8×C11C2×D412yes—
161C2×C8×C11C2×D412yes—
162C2×C8×C11C2×D414yes—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—44no—
169C11×C22⋊C4—22no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—44no—
172C11×C22⋊C4—44no—
173C11×C22⋊C4—44no—
174C11×C22⋊C4—82no—
175C11×C22⋊C4—82no—
176C42×C11—21no—
177C42×C11—21no—
178C22×#135C2×C1111yescharacteristic, complemented
179C2×#468C2×C1112yescomplemented
180C2×#435C2×C1111yescharacteristic, complemented
181#2407C2×C1112yescomplemented
182#2056C2×C1111yescharacteristic, complemented
183#2054C2×C1111yescharacteristic, complemented
184#2001C2×C1111yescharacteristic, complemented
185#1999C2×C1111yescharacteristic, complemented
186#1973C2×C1112yescomplemented
187#1808C2×C1111yescharacteristic, complemented
188#1788C2×C1112yescomplemented
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—21no—
192C23×C11—21no—
193C23×C11—21no—
194C23×C11—22no—
195C23×C11—24no—
196C23×C11—22no—
197C23×C11—21no—
198C23×C11—21no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11#12112yes—
206C23×C11C22×D411yescharacteristic
207Q8×C11—24no—
208Q8×C11—24no—
209Q8×C11—42no—
210Q8×C11—42no—
211D4×C11—24no—
212D4×C11—24no—
213D4×C11—44no—
214D4×C11—416no—
215D4×C11—42no—
216D4×C11—42no—
217D4×C11—88no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—24no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—22no—
226C2×C4×C11—24no—
227C2×C4×C11—22no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—416no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11#12112yes—
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D412yes—
245C2×C4×C11C2×#4111yescharacteristic
246C2×C4×C11H(5,𝔽2)12yes—
247C8×C11—22no—
248C8×C11—41no—
249C8×C11—41no—
250C8×C11#12014yes—
251C22×#41C22×C1112yes—
252C2×#135—28no—
253C2×#135—24no—
254C22×Q16C22×C1111yescharacteristic
255C22×SD16C22×C1112yes—
256C22×D8C22×C1111yescharacteristic
257C22×M16C22×C1111yescharacteristic
258C23×C8C22×C1111yescharacteristic
259C2×C22⋊Q8C22×C1112yes—
260C2×#121C22×C1112yes—
261C2×C4×D4C22×C1111yescharacteristic
262#468—28no—
263#435—24no—
264C2×#107C22×C1112yes—
265C2×C4⋊C8C22×C1111yescharacteristic
266C2×#103C22×C1112yes—
267C2×#103C22×C1112yes—
268C2×#102C22×C1112yes—
269C2×#102C22×C1112yes—
270C2×C22⋊C8C22×C1111yescharacteristic
271C2×C22⋊C8C22×C1111yescharacteristic
272C2×#97C22×C1111yescharacteristic
273#394—22no—
274#392—22no—
275#391C22×C1112yes—
276#390C22×C1112yes—
277#386—22no—
278#385—22no—
279#380C22×C1112yes—
280#340C22×C1111yescharacteristic
281#340C22×C1111yescharacteristic
282C22×C11—22no—
283C22×C11—22no—
284C22×C11—22no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—44no—
288C22×C11—41no—
289C22×C11—42no—
290C22×C11—44no—
291C22×C11—42no—
292C22×C11—44no—
293C22×C11—41no—
294C22×C11—41no—
295C22×C11—82no—
296C22×C11—82no—
297C22×C11—82no—
298C22×C11—82no—
299C22×C11C2×#12111yescharacteristic
300C22×C11D4212yes—
301C22×C11#57512yes—
302C22×C11#57611yescharacteristic
303C22×C11#57811yescharacteristic
304C4×C11—22no—
305C4×C11—41no—
306C4×C11—44no—
307C4×C11—41no—
308C4×C11—41no—
309C4×C11—82no—
310C4×C11—82no—
311C4×C11C2×#12011yescharacteristic
312C4×C11#53511yescharacteristic
313C4×C11#54612yes—
314C2×#41—24no—
315C2×#41—24no—
316C2×#41—24no—
317C2×#41—24no—
318C2×#41—42no—
319C2×#41—42no—
320C22×Q8C23×C1112yes—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4D4×C1111yescharacteristic
324C22×D4C23×C1112yes—
325C23×C4—22no—
326C23×C4C23×C1111yescharacteristic
327C23×C4C23×C1111yescharacteristic
328#135—232no—
329C2×Q16—24no—
330C2×Q16—22no—
331C2×SD16—24no—
332C2×SD16—24no—
333C2×SD16D4×C1118yescomplemented
334C2×D8—24no—
335C2×D8—22no—
336C2×M16—22no—
337C2×M16—24no—
338C22×C8—24no—
339C22×C8D4×C1114yescomplemented
340C22×C8C23×C1111yescharacteristic
341C22×C8C23×C1111yescharacteristic
342C22×C8C23×C1111yescharacteristic
343C22×C8C23×C1111yescharacteristic
344C22⋊Q8—24no—
345C22⋊Q8—42no—
346#121—24no—
347#121—42no—
348C4×D4—22no—
349C4×D4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4D4×C1111yescharacteristic
352C2×C4⋊C4C23×C1112yes—
353C2×C4⋊C4C23×C1112yes—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4D4×C1111yescharacteristic
360C2×C22⋊C4D4×C1111yescharacteristic
361C2×C42C23×C1111yescharacteristic
362#107—24no—
363C4⋊C8—22no—
364#103—24no—
365#103—42no—
366#102—24no—
367#102—42no—
368C22⋊C8—22no—
369C22⋊C8—22no—
370#97—22no—
371#95—22no—
372#95—22no—
373#95—22no—
374C2×C11—42no—
375C2×C11—81no—
376C2×C11—84no—
377C2×C11#240811yescharacteristic
378C2×C11#305411yescharacteristic
379C2×C11#306111yescharacteristic
380C2×C11#326812yes—
381C2×C11#326912yes—
382C24—22no—
383C24C2×D4×C1111yescharacteristic
384C24C2×D4×C1111yescharacteristic
385#41—216no—
386#41—48no—
387#41—48no—
388#41—48no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8C2×D4×C1114yes—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—42no—
402C2×D4—44no—
403C2×D4—44no—
404C2×D4—44no—
405C2×D4—44no—
406C2×D4—44no—
407C2×D4—82no—
408C2×D4C2×D4×C1114yes—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—44no—
419C22×C4—44no—
420C22×C4—44no—
421C22×C4C2×D4×C1111yescharacteristic
422C22×C4C2×D4×C1111yescharacteristic
423C22×C4C2×D4×C1111yescharacteristic
424C22×C4C2×D4×C1111yescharacteristic
425C22×C4C2×D4×C1112yes—
426C22×C4C11×#4112yes—
427C22×C4C24×C1111yescharacteristic
428Q16—28no—
429SD16—216no—
430D8—28no—
431M16—44no—
432C2×C8—22no—
433C2×C8—28no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8C2×D4×C1112yes—
439C2×C8C2×D4×C1112yes—
440C2×C8C2×D4×C1114yes—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—44no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—44no—
450C22⋊C4—44no—
451C22⋊C4—44no—
452C22⋊C4—82no—
453C22⋊C4—82no—
454C42—21no—
455C42—21no—
456C11#2427011yescharacteristic, direct product factor, Sylow
457C23—22no—
458C23—22no—
459C23—21no—
460C23—21no—
461C23—21no—
462C23—22no—
463C23—24no—
464C23—22no—
465C23—21no—
466C23—21no—
467C23—42no—
468C23—42no—
469C23—42no—
470C23—42no—
471C23—42no—
472C23—42no—
473C23C11×#12112yes—
474C23C22×D4×C1111yescharacteristic
475Q8—24no—
476Q8—24no—
477Q8—42no—
478Q8—42no—
479D4—24no—
480D4—24no—
481D4—44no—
482D4—416no—
483D4—42no—
484D4—42no—
485D4—88no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—22no—
494C2×C4—24no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—416no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4C11×#12112yes—
511C2×C4C22×D4×C1111yescharacteristic
512C2×C4C22×D4×C1112yes—
513C2×C4C2×C11×#4111yescharacteristic
514C2×C4C11×H(5,𝔽2)12yes—
515C8—22no—
516C8—41no—
517C8—41no—
518C8C11×#12014yes—
519C22—22no—
520C22—22no—
521C22—22no—
522C22—42no—
523C22—42no—
524C22—44no—
525C22—41no—
526C22—42no—
527C22—44no—
528C22—42no—
529C22—44no—
530C22—41no—
531C22—41no—
532C22—82no—
533C22—82no—
534C22—82no—
535C22—82no—
536C22C2×C11×#12111yescharacteristic
537C22D42×C1112yes—
538C22C11×#57512yes—
539C22C11×#57611yescharacteristic
540C22C11×#57811yescharacteristic
541C4—22no—
542C4—41no—
543C4—44no—
544C4—41no—
545C4—41no—
546C4—82no—
547C4—82no—
548C4C2×C11×#12011yescharacteristic
549C4C11×#53511yescharacteristic
550C4C11×#54612yes—
551C2—42no—
552C2—81no—
553C2—84no—
554C2C11×#240811yescharacteristic
555C2C11×#305411yescharacteristic
556C2C11×#306111yescharacteristic
557C2C11×#326812yes—
558C2C11×#326912yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×#135C2semidirect
2. C2×C11×#468C2semidirect
3. C2×C11×#435C2semidirect
4. C11×#2407C2semidirect
5. C11×#2056C2semidirect
6. C11×#2054C2semidirect
7. C11×#2001C2semidirect
8. C11×#1999C2semidirect
9. C11×#1973C2semidirect
10. C11×#1808C2semidirect
11. C11×#1788C2semidirect
62. C2×C11×SD16D4semidirect
68. C22×C8×C11D4semidirect
103. #24270C11direct (N × H)
178. C22×#135C2×C11semidirect
179. C2×#468C2×C11semidirect
180. C2×#435C2×C11semidirect
181. #2407C2×C11semidirect
182. #2056C2×C11semidirect
183. #2054C2×C11semidirect
184. #2001C2×C11semidirect
185. #1999C2×C11semidirect
186. #1973C2×C11semidirect
187. #1808C2×C11semidirect
188. #1788C2×C11semidirect
333. C2×SD16D4×C11semidirect
339. C22×C8D4×C11semidirect
456. C11#24270direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×#1352
C2×C11×#4682
C2×C11×#4352
C11×#24072
C11×#20562
C11×#20542
C11×#20012
C11×#19992
C11×#19732
C11×#18082
C11×#17882
#2427011