Finite Group Databasebeta

← C11×#23992 #14601185

Subgroups — C11×#23992 #14601185

Order 2816.

1128 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3509C211yesmaximal, characteristic, complemented
2C11×#3028C211yesmaximal, characteristic
3C11×#3022C211yesmaximal, characteristic
4C11×#2901C211yesmaximal, characteristic
5C11×#2031C212yesmaximal, complemented
6C11×#2005C212yesmaximal, complemented
7C11×#1915C211yesmaximal, characteristic, complemented
8C11×#1912C212yesmaximal, complemented
9C11×#1909C211yesmaximal, characteristic, complemented
10C11×#1905C212yesmaximal, complemented
11C11×#1827C211yesmaximal, characteristic, complemented
12C11×#585C2211yescharacteristic
13C2×C11×#137C2212yes—
14C11×#568C2211yescharacteristic
15C11×#557—22no—
16C11×#556—22no—
17C11×#552—24no—
18C11×#541—22no—
19C11×#536C2211yescharacteristic
20C11×#536C2211yescharacteristic
21C11×#536C2212yes—
22C11×#533—22no—
23C11×#533C2211yescharacteristic, complemented
24C2×C11×C4⋊Q8C2211yescharacteristic, complemented
25C11×#519C2211yescharacteristic, complemented
26C11×#519C2211yescharacteristic, complemented
27C4×C11×#41C2211yescharacteristic
28C11×#458—24no—
29C11×#456—22no—
30C11×#455—22no—
31C11×#421—22no—
32C11×#421C2212yes—
33C11×#421C2212yes—
34C2×C11×#104—22no—
35C2×C11×#104C2212yes—
36C11×#419C2212yescomplemented
37C11×#413C2211yescharacteristic
38C2×C11×#101C2212yescomplemented
39C11×#410C2212yes—
40C11×#410C2211yescharacteristic
41C11×#344C2212yescomplemented
42C11×#339C2212yescomplemented
43C11×H(3,ℤ/4)C2212yescomplemented
44C11×H(3,ℤ/4)C2212yescomplemented
45C11×2−1+4—22no—
46C11×2−1+4—21no—
47C11×H(5,𝔽2)—22no—
48C11×H(5,𝔽2)—22no—
49C11×H(5,𝔽2)—21no—
50C2×C11×#41—22no—
51C2×C11×#41—42no—
52C2×C11×#41C2312yes—
53C2×C11×#41C2311yescharacteristic
54C22×Q8×C11C2311yescharacteristic
55C22×Q8×C11C2311yescharacteristic
56C11×#137—24no—
57C11×#137—42no—
58C2×C11×Q16—22no—
59C2×C11×SD16—22no—
60C11×#131—42no—
61C2×C11×M16—22no—
62C2×C11×M16C2312yes—
63C2×C11×M16C2312yes—
64C11×C4⋊Q8—22no—
65C11×C4⋊Q8—21no—
66C11×C4⋊Q8—22no—
67C11×C4⋊Q8—21no—
68C11×C4⋊Q8—21no—
69C11×C4⋊Q8—21no—
70C11×C4⋊Q8D412yes—
71C11×#126—24no—
72C11×#126—24no—
73C11×#125—24no—
74C11×#125—24no—
75C11×#125—24no—
76C11×#125—21no—
77C11×#124—21no—
78C11×#124—22no—
79C11×#124D412yes—
80C11×#123—22no—
81C11×#123—24no—
82C11×#123D414yes—
83C11×C22⋊Q8—24no—
84C11×C22⋊Q8—22no—
85C11×C22⋊Q8—22no—
86C11×C22⋊Q8—22no—
87C11×C22⋊Q8—42no—
88C4×Q8×C11—24no—
89C4×Q8×C11—21no—
90C4×Q8×C11—22no—
91C4×Q8×C11—22no—
92C4×Q8×C11—22no—
93C4×Q8×C11—22no—
94C4×Q8×C11—22no—
95C4×D4×C11—22no—
96C4×D4×C11—21no—
97C11×#117—24no—
98C11×#117—22no—
99C11×#117—22no—
100C11×#117D412yes—
101C11×#117C2312yes—
102C11×#117C2311yescharacteristic
103C11×#117C2311yescharacteristic
104C11×#117C2311yescharacteristic
105C2×C11×C4⋊C4—22no—
106C2×C42×C11D412yes—
107C2×C42×C11C2311yescharacteristic
108C11×#104—22no—
109C11×#104—24no—
110C11×#104—22no—
111C11×#104—24no—
112C11×#103—42no—
113C11×#101—21no—
114C11×#101—42no—
115C11×#100—21no—
116C11×#99—22no—
117C11×#99—24no—
118#23992C1111yesmaximal, characteristic, direct product factor, Sylow
119C11×#41—22no—
120C11×#41—22no—
121C11×#41—24no—
122C11×#41—22no—
123C11×#41—22no—
124C11×#41—22no—
125C11×#41—22no—
126C11×#41—44no—
127C11×#41—42no—
128C11×#41—42no—
129C11×#41—42no—
130C11×#41—42no—
131C2×Q8×C11—22no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—22no—
136C2×Q8×C11—22no—
137C2×Q8×C11—22no—
138C2×Q8×C11—22no—
139C2×Q8×C11—22no—
140C2×Q8×C11—42no—
141C2×Q8×C11C2×D412yes—
142C2×Q8×C11C2×D411yescharacteristic
143C2×Q8×C11#4112yes—
144C2×D4×C11—22no—
145C2×D4×C11—22no—
146C2×D4×C11—42no—
147C2×D4×C11—44no—
148C2×D4×C11—42no—
149C2×D4×C11C2×D412yes—
150C2×D4×C11C2×D411yescharacteristic
151C2×D4×C11#4112yes—
152C22×C4×C11—22no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—22no—
156C22×C4×C11—42no—
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2411yescharacteristic
160C11×Q16—44no—
161C11×SD16—44no—
162C11×M16—22no—
163C11×M16—22no—
164C11×M16—22no—
165C11×M16—22no—
166C11×M16—42no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—42no—
170C11×C4⋊C4—24no—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—24no—
179C11×C4⋊C4—24no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—44no—
185C11×C22⋊C4—24no—
186C11×C22⋊C4—24no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—21no—
189C11×C22⋊C4—21no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—44no—
192C11×C22⋊C4C2×D412yes—
193C42×C11—24no—
194C42×C11—24no—
195C42×C11—22no—
196C42×C11—21no—
197C42×C11—21no—
198C42×C11—22no—
199C42×C11C2×D411yescharacteristic
200C42×C11C2×D412yes—
201C42×C11C2×D411yescharacteristic
202C42×C11C2×D412yes—
203#3509C2×C1111yescharacteristic, complemented
204#3028C2×C1111yescharacteristic
205#3022C2×C1111yescharacteristic
206#2901C2×C1111yescharacteristic
207#2031C2×C1112yescomplemented
208#2005C2×C1112yescomplemented
209#1915C2×C1111yescharacteristic, complemented
210#1912C2×C1112yescomplemented
211#1909C2×C1111yescharacteristic, complemented
212#1905C2×C1112yescomplemented
213#1827C2×C1111yescharacteristic, complemented
214C23×C11—22no—
215C23×C11—42no—
216C23×C11#12012yes—
217C23×C11C22×D411yescharacteristic
218Q8×C11—22no—
219Q8×C11—22no—
220Q8×C11—24no—
221Q8×C11—22no—
222Q8×C11—44no—
223Q8×C11—42no—
224Q8×C11—41no—
225Q8×C11—41no—
226Q8×C11—41no—
227Q8×C11—41no—
228Q8×C11—42no—
229D4×C11—24no—
230D4×C11—22no—
231D4×C11—22no—
232D4×C11—22no—
233D4×C11—42no—
234D4×C11—44no—
235D4×C11—42no—
236D4×C11—42no—
237C2×C4×C11—21no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—21no—
246C2×C4×C11—24no—
247C2×C4×C11—22no—
248C2×C4×C11—42no—
249C2×C4×C11—44no—
250C2×C4×C11—44no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11#12012yes—
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C2×#4112yes—
260C2×C4×C11H(5,𝔽2)12yes—
261C8×C11—42no—
262C8×C11—42no—
263#585C22×C1111yescharacteristic
264C2×#137C22×C1112yes—
265#568C22×C1111yescharacteristic
266#557—22no—
267#556—22no—
268#552—24no—
269#541—22no—
270#536C22×C1111yescharacteristic
271#536C22×C1111yescharacteristic
272#536C22×C1112yes—
273#533—22no—
274#533C22×C1111yescharacteristic, complemented
275C2×C4⋊Q8C22×C1111yescharacteristic, complemented
276#519C22×C1111yescharacteristic, complemented
277#519C22×C1111yescharacteristic, complemented
278C4×#41C22×C1111yescharacteristic
279#458—24no—
280#456—22no—
281#455—22no—
282#421—22no—
283#421C22×C1112yes—
284#421C22×C1112yes—
285C2×#104—22no—
286C2×#104C22×C1112yes—
287#419C22×C1112yescomplemented
288#413C22×C1111yescharacteristic
289C2×#101C22×C1112yescomplemented
290#410C22×C1111yescharacteristic
291#410C22×C1112yes—
292#344C22×C1112yescomplemented
293#339C22×C1112yescomplemented
294H(3,ℤ/4)C22×C1112yescomplemented
295H(3,ℤ/4)C22×C1112yescomplemented
296C22×C11—22no—
297C22×C11—41no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—82no—
301C22×C11—162no—
302C22×C11C2×#12011yescharacteristic
303C22×C11#54612yes—
304C4×C11—22no—
305C4×C11—22no—
306C4×C11—42no—
307C4×C11—41no—
308C4×C11—42no—
309C4×C11—42no—
310C4×C11—42no—
311C4×C11—42no—
312C4×C11—42no—
313C4×C11—82no—
314C4×C11#52511yescharacteristic
315C4×C11#53511yescharacteristic
316C4×C11#54612yes—
3172−1+4—22no—
3182−1+4—21no—
319H(5,𝔽2)—22no—
320H(5,𝔽2)—22no—
321H(5,𝔽2)—21no—
322C2×#41—22no—
323C2×#41—42no—
324C2×#41C23×C1112yes—
325C2×#41C23×C1111yescharacteristic
326C22×Q8C23×C1111yescharacteristic
327C22×Q8C23×C1111yescharacteristic
328#137—24no—
329#137—42no—
330C2×Q16—22no—
331C2×SD16—22no—
332#131—42no—
333C2×M16—22no—
334C2×M16C23×C1112yes—
335C2×M16C23×C1112yes—
336C4⋊Q8—22no—
337C4⋊Q8—21no—
338C4⋊Q8—22no—
339C4⋊Q8—21no—
340C4⋊Q8—21no—
341C4⋊Q8—21no—
342C4⋊Q8D4×C1112yes—
343#126—24no—
344#126—24no—
345#125—24no—
346#125—24no—
347#125—24no—
348#125—21no—
349#124—21no—
350#124—22no—
351#124D4×C1112yes—
352#123—22no—
353#123—24no—
354#123D4×C1114yes—
355C22⋊Q8—24no—
356C22⋊Q8—22no—
357C22⋊Q8—22no—
358C22⋊Q8—22no—
359C22⋊Q8—42no—
360C4×Q8—24no—
361C4×Q8—21no—
362C4×Q8—22no—
363C4×Q8—22no—
364C4×Q8—22no—
365C4×Q8—22no—
366C4×Q8—22no—
367C4×D4—22no—
368C4×D4—21no—
369#117—24no—
370#117—22no—
371#117—22no—
372#117D4×C1112yes—
373#117C23×C1112yes—
374#117C23×C1111yescharacteristic
375#117C23×C1111yescharacteristic
376#117C23×C1111yescharacteristic
377C2×C4⋊C4—22no—
378C2×C42D4×C1112yes—
379C2×C42C23×C1111yescharacteristic
380#104—22no—
381#104—24no—
382#104—22no—
383#104—24no—
384#103—42no—
385#101—21no—
386#101—42no—
387#100—21no—
388#99—22no—
389#99—24no—
390C2×C11—21no—
391C2×C11—22no—
392C2×C11—42no—
393C2×C11—82no—
394C2×C11#240411yescharacteristic
395#41—22no—
396#41—22no—
397#41—24no—
398#41—22no—
399#41—22no—
400#41—22no—
401#41—22no—
402#41—44no—
403#41—42no—
404#41—42no—
405#41—42no—
406#41—42no—
407C2×Q8—22no—
408C2×Q8—21no—
409C2×Q8—21no—
410C2×Q8—21no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—42no—
417C2×Q8C2×D4×C1112yes—
418C2×Q8C2×D4×C1111yescharacteristic
419C2×Q8C11×#4112yes—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—42no—
423C2×D4—44no—
424C2×D4—42no—
425C2×D4C2×D4×C1112yes—
426C2×D4C2×D4×C1111yescharacteristic
427C2×D4C11×#4112yes—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—42no—
433C22×C4C2×D4×C1112yes—
434C22×C4C2×D4×C1112yes—
435C22×C4C24×C1111yescharacteristic
436Q16—44no—
437SD16—44no—
438M16—22no—
439M16—22no—
440M16—22no—
441M16—22no—
442M16—42no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—42no—
446C4⋊C4—24no—
447C4⋊C4—24no—
448C4⋊C4—22no—
449C4⋊C4—24no—
450C4⋊C4—24no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—24no—
455C4⋊C4—24no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—22no—
460C4⋊C4—44no—
461C22⋊C4—24no—
462C22⋊C4—24no—
463C22⋊C4—22no—
464C22⋊C4—21no—
465C22⋊C4—21no—
466C22⋊C4—22no—
467C22⋊C4—44no—
468C22⋊C4C2×D4×C1112yes—
469C42—24no—
470C42—24no—
471C42—22no—
472C42—21no—
473C42—21no—
474C42—22no—
475C42C2×D4×C1111yescharacteristic
476C42C2×D4×C1112yes—
477C42C2×D4×C1111yescharacteristic
478C42C2×D4×C1112yes—
479C11#2399211yescharacteristic, direct product factor, Sylow
480C23—22no—
481C23—42no—
482C23C11×#12012yes—
483C23C22×D4×C1111yescharacteristic
484Q8—22no—
485Q8—22no—
486Q8—24no—
487Q8—22no—
488Q8—44no—
489Q8—42no—
490Q8—41no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—42no—
495D4—24no—
496D4—22no—
497D4—22no—
498D4—22no—
499D4—42no—
500D4—44no—
501D4—42no—
502D4—42no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—21no—
512C2×C4—24no—
513C2×C4—22no—
514C2×C4—42no—
515C2×C4—44no—
516C2×C4—44no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4C11×#12012yes—
523C2×C4C22×D4×C1111yescharacteristic
524C2×C4C22×D4×C1111yescharacteristic
525C2×C4C2×C11×#4112yes—
526C2×C4C11×H(5,𝔽2)12yes—
527C8—42no—
528C8—42no—
529C22—22no—
530C22—41no—
531C22—42no—
532C22—42no—
533C22—82no—
534C22—162no—
535C22C2×C11×#12011yescharacteristic
536C22C11×#54612yes—
537C4—22no—
538C4—22no—
539C4—42no—
540C4—41no—
541C4—42no—
542C4—42no—
543C4—42no—
544C4—42no—
545C4—42no—
546C4—82no—
547C4C11×#52511yescharacteristic
548C4C11×#53511yescharacteristic
549C4C11×#54612yes—
550C2—21no—
551C2—22no—
552C2—42no—
553C2—82no—
554C2C11×#240411yescharacteristic
subgroupG/H
center, socleC2×C11#2404
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#585C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3509C2semidirect
5. C11×#2031C2semidirect
6. C11×#2005C2semidirect
7. C11×#1915C2semidirect
8. C11×#1912C2semidirect
9. C11×#1909C2semidirect
10. C11×#1905C2semidirect
11. C11×#1827C2semidirect
23. C11×#533C22semidirect
24. C2×C11×C4⋊Q8C22semidirect
25. C11×#519C22semidirect
26. C11×#519C22semidirect
36. C11×#419C22semidirect
38. C2×C11×#101C22semidirect
41. C11×#344C22semidirect
42. C11×#339C22semidirect
43. C11×H(3,ℤ/4)C22semidirect
44. C11×H(3,ℤ/4)C22semidirect
118. #23992C11direct (N × H)
203. #3509C2×C11semidirect
207. #2031C2×C11semidirect
208. #2005C2×C11semidirect
209. #1915C2×C11semidirect
210. #1912C2×C11semidirect
211. #1909C2×C11semidirect
212. #1905C2×C11semidirect
213. #1827C2×C11semidirect
274. #533C22×C11semidirect
275. C2×C4⋊Q8C22×C11semidirect
276. #519C22×C11semidirect
277. #519C22×C11semidirect
287. #419C22×C11semidirect
289. C2×#101C22×C11semidirect
292. #344C22×C11semidirect
293. #339C22×C11semidirect
294. H(3,ℤ/4)C22×C11semidirect
295. H(3,ℤ/4)C22×C11semidirect
479. C11#23992direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35092
C11×#30282
C11×#30222
C11×#29012
C11×#20312
C11×#20052
C11×#19152
C11×#19122
C11×#19092
C11×#19052
C11×#18272
#2399211