Finite Group Databasebeta

← C11×#60046 #14637239

Subgroups — C11×#60046 #14637239

Order 2816.

1898 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#2805C212yesmaximal, complemented
2C11×#2724C211yesmaximal, characteristic, complemented
3C11×#2683C211yesmaximal, characteristic, complemented
4C11×#2599C212yesmaximal, complemented
5C11×#2586C212yesmaximal, complemented
6C11×#2573C214yesmaximal, complemented
7C11×#2477C214yesmaximal, complemented
8C11×#2470C214yesmaximal, complemented
9C11×#2406C212yesmaximal
10C11×#2374C212yesmaximal, complemented
11C11×#2360C214yesmaximal, complemented
12C11×#2297C211yesmaximal, characteristic
13C11×#2296C212yesmaximal, complemented
14C22×C11×#41C2211yescharacteristic
15C2×C11×#123C2212yes—
16C2×C11×#123C2212yes—
17C2×C11×C22⋊Q8C2214yes—
18C2×C4×Q8×C11C2212yes—
19C2×C11×#117C2212yes—
20C2×C11×#117C2212yes—
21C2×C11×#117C2211yescharacteristic
22C22×C11×C4⋊C4C2212yes—
23C22×C42×C11C2211yescharacteristic
24C11×#400C2214yes—
25C11×#400C2214yes—
26C11×#398C2212yes—
27C11×#397C2214yes—
28C11×#397C2212yes—
29C11×#396C2214yes—
30C11×#395C2214yes—
31C11×#395C2212yes—
32C11×#394C2214yes—
33C11×#393C2212yes—
34C11×#391C2214yes—
35C11×#391C2211yescharacteristic
36C11×#391C2211yescharacteristic
37C11×#390C2211yescharacteristic
38C11×#390C2211yescharacteristic
39C11×#389C2212yes—
40C11×#389C2212yes—
41C11×#389C2214yes—
42C11×#389C2214yes—
43C11×#389C2212yes—
44C11×#389C2212yes—
45C11×#388C2214yes—
46C11×#388C2214yes—
47C11×#388C2214yes—
48C11×#387C2214yes—
49C11×#387C2214yes—
50C11×#387C2214yes—
51C11×#387C2214yes—
52C11×#387C2214yes—
53C11×#386C2212yes—
54C11×#386C2212yes—
55C11×#386C2214yes—
56C11×#385C2214yes—
57C11×#385C2214yes—
58C11×#385C2214yes—
59C11×#385C2214yes—
60C11×#383C2212yes—
61C11×#381C2212yes—
62C4×C11×C4⋊C4C2214yes—
63C4×C11×C4⋊C4C2214yes—
64C4×C11×C22⋊C4C2214yes—
65C4×C11×C22⋊C4C2214yes—
66C4×C11×C22⋊C4C2214yes—
67C2×C11×#41—24no—
68C2×C11×#41—42no—
69C2×C11×#41—42no—
70C22×Q8×C11C2312yes—
71C22×Q8×C11C2311yescharacteristic
72C22×D4×C11C2312yes—
73C22×D4×C11C2311yescharacteristic
74C23×C4×C11C2312yes—
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2312yes—
77C23×C4×C11C2312yes—
78C23×C4×C11C2312yes—
79C11×#123—28no—
80C11×#123—44no—
81C11×C22⋊Q8—216no—
82C4×Q8×C11—44no—
83C11×#117—28no—
84C11×#117—42no—
85C11×#117—44no—
86C2×C11×C4⋊C4—44no—
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⋊C4C2312yes—
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2312yes—
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2312yes—
99C2×C11×C4⋊C4C2314yes—
100C2×C11×C4⋊C4C2312yes—
101C2×C11×C22⋊C4C2314yes—
102C2×C11×C22⋊C4C2314yes—
103C2×C11×C22⋊C4C2314yes—
104C2×C11×C22⋊C4C2314yes—
105C2×C11×C22⋊C4C2314yes—
106C2×C11×C22⋊C4C2314yes—
107C2×C11×C22⋊C4C2312yes—
108C2×C11×C22⋊C4C2312yes—
109C2×C11×C22⋊C4C2312yes—
110C2×C42×C11—42no—
111C2×C42×C11C2312yes—
112C2×C42×C11C2314yes—
113C2×C42×C11C2312yes—
114C2×C42×C11C2311yescharacteristic
115C2×C42×C11C2311yescharacteristic
116C2×C42×C11C2314yes—
117C2×C42×C11C2314yes—
118C11×#95C2314yes—
119C11×#95C2314yes—
120C11×#95C2314yes—
121C11×#95C2314yes—
122C11×#95C2314yes—
123C11×#95C2314yes—
124C11×#95C2314yes—
125C11×#95C2314yes—
126C11×#95C2314yes—
127C11×#95C2312yes—
128C11×#95C2312yes—
129C11×#95C2314yes—
130C11×#95C2314yes—
131C11×#95C2314yes—
132#60046C1111yesmaximal, characteristic, direct product factor, Sylow
133C24×C11C2412yes—
134C24×C11C2411yescharacteristic
135C11×#41—416no—
136C2×Q8×C11—28no—
137C2×Q8×C11—22no—
138C2×Q8×C11—42no—
139C2×Q8×C11—41no—
140C2×Q8×C11—41no—
141C2×D4×C11—24no—
142C2×D4×C11—24no—
143C2×D4×C11—41no—
144C2×D4×C11—41no—
145C2×D4×C11—42no—
146C2×D4×C11#4114yes—
147C22×C4×C11—24no—
148C22×C4×C11—22no—
149C22×C4×C11—24no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—24no—
153C22×C4×C11—24no—
154C22×C4×C11—24no—
155C22×C4×C11—28no—
156C22×C4×C11—24no—
157C22×C4×C11—42no—
158C22×C4×C11—42no—
159C22×C4×C11—42no—
160C22×C4×C11—42no—
161C22×C4×C11C2412yes—
162C22×C4×C11C2414yes—
163C22×C4×C11C2412yes—
164C22×C4×C11C2414yes—
165C22×C4×C11C2412yes—
166C22×C4×C11C2414yes—
167C22×C4×C11C2412yes—
168C22×C4×C11C2414yes—
169C22×C4×C11C2411yescharacteristic
170C22×C4×C11C2411yescharacteristic
171C22×C4×C11C2412yes—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—28no—
174C11×C4⋊C4—28no—
175C11×C4⋊C4—28no—
176C11×C4⋊C4—28no—
177C11×C4⋊C4—28no—
178C11×C4⋊C4—44no—
179C11×C4⋊C4—42no—
180C11×C4⋊C4—42no—
181C11×C4⋊C4—41no—
182C11×C4⋊C4—41no—
183C11×C4⋊C4—42no—
184C11×C4⋊C4—44no—
185C11×C4⋊C4#4118yescomplemented
186C11×C22⋊C4—24no—
187C11×C22⋊C4—28no—
188C11×C22⋊C4—28no—
189C11×C22⋊C4—28no—
190C11×C22⋊C4—28no—
191C11×C22⋊C4—28no—
192C11×C22⋊C4—28no—
193C11×C22⋊C4—42no—
194C11×C22⋊C4—42no—
195C42×C11—28no—
196C42×C11—24no—
197C42×C11—41no—
198C42×C11—42no—
199C42×C11—41no—
200C42×C11—44no—
201C42×C11—44no—
202#2805C2×C1112yescomplemented
203#2724C2×C1111yescharacteristic, complemented
204#2683C2×C1111yescharacteristic, complemented
205#2599C2×C1112yescomplemented
206#2586C2×C1112yescomplemented
207#2573C2×C1114yescomplemented
208#2477C2×C1114yescomplemented
209#2470C2×C1114yescomplemented
210#2406C2×C1112yes—
211#2374C2×C1112yescomplemented
212#2360C2×C1114yescomplemented
213#2297C2×C1111yescharacteristic
214#2296C2×C1112yescomplemented
215C23×C11—24no—
216C23×C11—22no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—24no—
222C23×C11—22no—
223C23×C11C2×#4114yes—
224C23×C11H(5,𝔽2)12yes—
225C23×C11C2511yescharacteristic
226Q8×C11—48no—
227Q8×C11—44no—
228D4×C11—44no—
229D4×C11—48no—
230C2×C4×C11—216no—
231C2×C4×C11—28no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—21no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—24no—
240C2×C4×C11—21no—
241C2×C4×C11—22no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—24no—
256C2×C4×C11—24no—
257C2×C4×C11—24no—
258C2×C4×C11—48no—
259C2×C4×C11—48no—
260C2×C4×C11—84no—
261C2×C4×C11C2×#4118yes—
262C2×C4×C11C2×#4114yes—
263C2×C4×C11C2×#4112yes—
264C2×C4×C11H(5,𝔽2)12yes—
265C2×C4×C112−1+414yes—
266C22×#41C22×C1111yescharacteristic
267C2×#123C22×C1112yes—
268C2×#123C22×C1112yes—
269C2×C22⋊Q8C22×C1114yes—
270C2×C4×Q8C22×C1112yes—
271C2×#117C22×C1112yes—
272C2×#117C22×C1111yescharacteristic
273C2×#117C22×C1112yes—
274C22×C4⋊C4C22×C1112yes—
275C22×C42C22×C1111yescharacteristic
276#400C22×C1114yes—
277#400C22×C1114yes—
278#398C22×C1112yes—
279#397C22×C1114yes—
280#397C22×C1112yes—
281#396C22×C1114yes—
282#395C22×C1112yes—
283#395C22×C1114yes—
284#394C22×C1114yes—
285#393C22×C1112yes—
286#391C22×C1111yescharacteristic
287#391C22×C1114yes—
288#391C22×C1111yescharacteristic
289#390C22×C1111yescharacteristic
290#390C22×C1111yescharacteristic
291#389C22×C1112yes—
292#389C22×C1114yes—
293#389C22×C1112yes—
294#389C22×C1114yes—
295#389C22×C1112yes—
296#389C22×C1112yes—
297#388C22×C1114yes—
298#388C22×C1114yes—
299#388C22×C1114yes—
300#387C22×C1114yes—
301#387C22×C1114yes—
302#387C22×C1114yes—
303#387C22×C1114yes—
304#387C22×C1114yes—
305#386C22×C1112yes—
306#386C22×C1112yes—
307#386C22×C1114yes—
308#385C22×C1114yes—
309#385C22×C1114yes—
310#385C22×C1114yes—
311#385C22×C1114yes—
312#383C22×C1112yes—
313#381C22×C1112yes—
314C4×C4⋊C4C22×C1114yes—
315C4×C4⋊C4C22×C1114yes—
316C4×C22⋊C4C22×C1114yes—
317C4×C22⋊C4C22×C1114yes—
318C4×C22⋊C4C22×C1114yes—
319C22×C11—28no—
320C22×C11—22no—
321C22×C11—24no—
322C22×C11—24no—
323C22×C11—42no—
324C22×C11—41no—
325C22×C11—42no—
326C22×C11—44no—
327C22×C11—41no—
328C22×C11—42no—
329C22×C11C22×#4112yes—
330C22×C11C22×#4111yescharacteristic
331C22×C11C2×H(5,𝔽2)11yescharacteristic
332C22×C11C2×H(5,𝔽2)11yescharacteristic
333C22×C11C2×2−1+412yes—
334C4×C11—28no—
335C4×C11—22no—
336C4×C11—22no—
337C4×C11—24no—
338C4×C11—24no—
339C4×C11—42no—
340C4×C11—44no—
341C4×C11—42no—
342C4×C11—44no—
343C4×C11—44no—
344C4×C11—42no—
345C2×#41—24no—
346C2×#41—42no—
347C2×#41—42no—
348C22×Q8C23×C1112yes—
349C22×Q8C23×C1111yescharacteristic
350C22×D4C23×C1112yes—
351C22×D4C23×C1111yescharacteristic
352C23×C4C23×C1112yes—
353C23×C4C23×C1111yescharacteristic
354C23×C4C23×C1112yes—
355C23×C4C23×C1112yes—
356C23×C4C23×C1112yes—
357#123—28no—
358#123—44no—
359C22⋊Q8—216no—
360C4×Q8—44no—
361#117—28no—
362#117—42no—
363#117—44no—
364C2×C4⋊C4—44no—
365C2×C4⋊C4C23×C1114yes—
366C2×C4⋊C4C23×C1112yes—
367C2×C4⋊C4C23×C1114yes—
368C2×C4⋊C4C23×C1114yes—
369C2×C4⋊C4C23×C1114yes—
370C2×C4⋊C4C23×C1114yes—
371C2×C4⋊C4C23×C1114yes—
372C2×C4⋊C4C23×C1112yes—
373C2×C4⋊C4C23×C1111yescharacteristic
374C2×C4⋊C4C23×C1112yes—
375C2×C4⋊C4C23×C1111yescharacteristic
376C2×C4⋊C4C23×C1112yes—
377C2×C4⋊C4C23×C1114yes—
378C2×C4⋊C4C23×C1112yes—
379C2×C22⋊C4C23×C1114yes—
380C2×C22⋊C4C23×C1114yes—
381C2×C22⋊C4C23×C1114yes—
382C2×C22⋊C4C23×C1114yes—
383C2×C22⋊C4C23×C1114yes—
384C2×C22⋊C4C23×C1112yes—
385C2×C22⋊C4C23×C1114yes—
386C2×C22⋊C4C23×C1112yes—
387C2×C22⋊C4C23×C1112yes—
388C2×C42—42no—
389C2×C42C23×C1112yes—
390C2×C42C23×C1114yes—
391C2×C42C23×C1114yes—
392C2×C42C23×C1114yes—
393C2×C42C23×C1112yes—
394C2×C42C23×C1111yescharacteristic
395C2×C42C23×C1111yescharacteristic
396#95C23×C1114yes—
397#95C23×C1114yes—
398#95C23×C1114yes—
399#95C23×C1114yes—
400#95C23×C1114yes—
401#95C23×C1114yes—
402#95C23×C1114yes—
403#95C23×C1114yes—
404#95C23×C1114yes—
405#95C23×C1112yes—
406#95C23×C1112yes—
407#95C23×C1114yes—
408#95C23×C1114yes—
409#95C23×C1114yes—
410C2×C11—44no—
411C2×C11—42no—
412C2×C11#348111yescharacteristic
413C2×C11#348212yes—
414C2×C11#349011yescharacteristic
415C2×C11#349212yes—
416C2×C11#355011yescharacteristic
417C24C24×C1112yes—
418C24C24×C1111yescharacteristic
419#41—416no—
420C2×Q8—28no—
421C2×Q8—22no—
422C2×Q8—42no—
423C2×Q8—41no—
424C2×Q8—41no—
425C2×D4—24no—
426C2×D4—24no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—42no—
430C2×D4C11×#4114yes—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—28no—
440C22×C4—24no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4C24×C1112yes—
446C22×C4C24×C1114yes—
447C22×C4C24×C1112yes—
448C22×C4C24×C1114yes—
449C22×C4C24×C1112yes—
450C22×C4C24×C1114yes—
451C22×C4C24×C1112yes—
452C22×C4C24×C1114yes—
453C22×C4C24×C1111yescharacteristic
454C22×C4C24×C1111yescharacteristic
455C22×C4C24×C1112yes—
456C4⋊C4—24no—
457C4⋊C4—28no—
458C4⋊C4—28no—
459C4⋊C4—28no—
460C4⋊C4—28no—
461C4⋊C4—28no—
462C4⋊C4—44no—
463C4⋊C4—42no—
464C4⋊C4—42no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—42no—
468C4⋊C4—44no—
469C4⋊C4C11×#4118yescomplemented
470C22⋊C4—24no—
471C22⋊C4—28no—
472C22⋊C4—28no—
473C22⋊C4—28no—
474C22⋊C4—28no—
475C22⋊C4—28no—
476C22⋊C4—28no—
477C22⋊C4—42no—
478C22⋊C4—42no—
479C42—28no—
480C42—24no—
481C42—41no—
482C42—42no—
483C42—41no—
484C42—44no—
485C42—44no—
486C11#6004611yescharacteristic, direct product factor, Sylow
487C23—24no—
488C23—22no—
489C23—21no—
490C23—21no—
491C23—22no—
492C23—22no—
493C23—24no—
494C23—22no—
495C23C2×C11×#4114yes—
496C23C11×H(5,𝔽2)12yes—
497C23C25×C1111yescharacteristic
498Q8—48no—
499Q8—44no—
500D4—44no—
501D4—48no—
502C2×C4—216no—
503C2×C4—28no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—24no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—48no—
531C2×C4—48no—
532C2×C4—84no—
533C2×C4C2×C11×#4118yes—
534C2×C4C2×C11×#4114yes—
535C2×C4C2×C11×#4112yes—
536C2×C4C11×H(5,𝔽2)12yes—
537C2×C4C11×2−1+414yes—
538C22—28no—
539C22—22no—
540C22—24no—
541C22—24no—
542C22—42no—
543C22—41no—
544C22—42no—
545C22—44no—
546C22—41no—
547C22—42no—
548C22C22×C11×#4112yes—
549C22C22×C11×#4111yescharacteristic
550C22C2×C11×H(5,𝔽2)11yescharacteristic
551C22C2×C11×H(5,𝔽2)11yescharacteristic
552C22C2×C11×2−1+412yes—
553C4—28no—
554C4—22no—
555C4—22no—
556C4—24no—
557C4—24no—
558C4—42no—
559C4—44no—
560C4—42no—
561C4—44no—
562C4—44no—
563C4—42no—
564C2—44no—
565C2—42no—
566C2C11×#348111yescharacteristic
567C2C11×#348212yes—
568C2C11×#349011yescharacteristic
569C2C11×#349212yes—
570C2C11×#355011yescharacteristic
subgroupG/H
center, socleC23×C11C25
commutator, Frattini, cosocleC23C25×C11
prime radicalC22×C11×#41C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#2805C2semidirect
2. C11×#2724C2semidirect
3. C11×#2683C2semidirect
4. C11×#2599C2semidirect
5. C11×#2586C2semidirect
6. C11×#2573C2semidirect
7. C11×#2477C2semidirect
8. C11×#2470C2semidirect
10. C11×#2374C2semidirect
11. C11×#2360C2semidirect
13. C11×#2296C2semidirect
132. #60046C11direct (N × H)
185. C11×C4⋊C4#41semidirect
202. #2805C2×C11semidirect
203. #2724C2×C11semidirect
204. #2683C2×C11semidirect
205. #2599C2×C11semidirect
206. #2586C2×C11semidirect
207. #2573C2×C11semidirect
208. #2477C2×C11semidirect
209. #2470C2×C11semidirect
211. #2374C2×C11semidirect
212. #2360C2×C11semidirect
214. #2296C2×C11semidirect
469. C4⋊C4C11×#41semidirect
486. C11#60046direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28052
C11×#27242
C11×#26832
C11×#25992
C11×#25862
C11×#25732
C11×#24772
C11×#24702
C11×#24062
C11×#23742
C11×#23602
C11×#22972
C11×#22962
#6004611