Finite Group Databasebeta

← C11×#22535 #14599728

Subgroups — C11×#22535 #14599728

Order 2816.

1172 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#553C211yesmaximal, characteristic
2C11×#2345C212yesmaximal, complemented
3C11×#1964C212yesmaximal, complemented
4C11×#1964C214yesmaximal, complemented
5C11×#1799C212yesmaximal, complemented
6C11×#1799C211yesmaximal, characteristic, complemented
7C4×C11×#99C211yesmaximal, characteristic, complemented
8C4×C11×#99C212yesmaximal, complemented
9C11×#553—22no—
10C11×#553—24no—
11C11×#553—22no—
12C2×C11×#126C412yescomplemented
13C2×C11×#125C411yescharacteristic, complemented
14C2×C11×#123C412yescomplemented
15C2×C11×#121C411yescharacteristic, complemented
16C2×C11×#121C2212yes—
17C2×C11×#121C2211yescharacteristic
18C2×C4×D4×C11C411yescharacteristic, complemented
19C2×C4×D4×C11C2212yes—
20C2×C4×D4×C11C2211yescharacteristic
21C2×C11×#117C411yescharacteristic, complemented
22C22×C11×C4⋊C4C2211yescharacteristic
23C2×C11×#99C2212yes—
24C2×C11×#99C2214yes—
25C2×C11×#99C2214yes—
26C2×C11×#99C2212yes—
27C11×#389—22no—
28C11×#387—24no—
29C11×#380C2214yes—
30C11×#380C2212yes—
31C4×C11×C4⋊C4—22no—
32C4×C11×C22⋊C4C2212yes—
33C4×C11×C22⋊C4C2214yes—
34C11×#342C2211yescharacteristic
35C11×#342C2211yescharacteristic
36C11×#342C2212yes—
37C22×D4×C11C2×C411yescharacteristic
38C22×D4×C11C2×C412yes—
39C22×D4×C11C2312yes—
40C22×D4×C11C2311yescharacteristic
41C23×C4×C11C2×C411yescharacteristic
42C23×C4×C11C2×C412yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2312yes—
45C11×#126—24no—
46C11×#126—24no—
47C11×#125—22no—
48C11×#125—22no—
49C11×#123—24no—
50C11×#123—24no—
51C11×#121—24no—
52C11×#121—24no—
53C11×#121—22no—
54C11×#121—22no—
55C11×#121—22no—
56C11×#121—22no—
57C4×D4×C11—24no—
58C4×D4×C11—24no—
59C4×D4×C11—22no—
60C4×D4×C11—22no—
61C4×D4×C11—22no—
62C4×D4×C11—21no—
63C4×D4×C11—21no—
64C11×#117—22no—
65C11×#117—21no—
66C11×#117—21no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—24no—
69C2×C11×C4⋊C4C2×C411yescharacteristic
70C2×C11×C4⋊C4C2×C412yes—
71C2×C11×C4⋊C4C2×C411yescharacteristic
72C2×C11×C4⋊C4C2×C412yes—
73C2×C11×C4⋊C4C2×C411yescharacteristic
74C2×C11×C4⋊C4C2×C411yescharacteristic
75C2×C11×C4⋊C4C2×C412yes—
76C2×C11×C4⋊C4D412yes—
77C2×C11×C4⋊C4D414yes—
78C2×C11×C4⋊C4D412yes—
79C2×C11×C22⋊C4C2×C412yes—
80C2×C11×C22⋊C4C2×C412yes—
81C2×C11×C22⋊C4C2×C412yes—
82C2×C11×C22⋊C4C2×C411yescharacteristic
83C2×C11×C22⋊C4C2×C412yes—
84C2×C11×C22⋊C4C2312yes—
85C2×C11×C22⋊C4C2314yes—
86C2×C11×C22⋊C4C2311yescharacteristic
87C2×C11×C22⋊C4C2312yes—
88C2×C42×C11—22no—
89C2×C42×C11—24no—
90C2×C42×C11C2×C412yes—
91C2×C42×C11C2×C411yescharacteristic
92C11×#99—24no—
93C11×#99—28no—
94C11×#99—44no—
95C11×#99—42no—
96C11×#95—22no—
97C11×#95—24no—
98C11×#95—24no—
99C11×#95—22no—
100#22535C1111yesmaximal, characteristic, direct product factor, Sylow
101C24×C11C22×C411yescharacteristic
102C24×C11C22×C412yes—
103C24×C11C2411yescharacteristic
104C2×D4×C11—24no—
105C2×D4×C11—22no—
106C2×D4×C11—24no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—21no—
110C2×D4×C11—22no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—24no—
115C2×D4×C11—42no—
116C2×D4×C11—82no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—24no—
124C22×C4×C11—42no—
125C22×C4×C11—42no—
126C22×C4×C11—82no—
127C22×C4×C11—82no—
128C22×C4×C11C22×C412yes—
129C22×C4×C11C22×C411yescharacteristic
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C22×C411yescharacteristic
133C22×C4×C11C22×C412yes—
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C22×C412yes—
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D414yes—
139C22×C4×C11C2×D414yes—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—44no—
146C11×C4⋊C4—84no—
147C11×C4⋊C4C22⋊C412yes—
148C11×C4⋊C4C22⋊C411yescharacteristic
149C11×C4⋊C4C22⋊C411yescharacteristic
150C11×C4⋊C4C22⋊C412yes—
151C11×C4⋊C4C22⋊C412yes—
152C11×C4⋊C4C22⋊C414yes—
153C11×C4⋊C4C22⋊C414yes—
154C11×C22⋊C4—22no—
155C11×C22⋊C4—22no—
156C11×C22⋊C4—22no—
157C11×C22⋊C4—22no—
158C11×C22⋊C4—24no—
159C11×C22⋊C4—22no—
160C11×C22⋊C4—22no—
161C11×C22⋊C4—22no—
162C11×C22⋊C4—24no—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—24no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—24no—
167C11×C22⋊C4#4114yes—
168C42×C11—22no—
169C42×C11—22no—
170C42×C11—21no—
171C42×C11—21no—
172C42×C11—44no—
173C42×C11—84no—
174C2×#553C2×C1111yescharacteristic
175#2345C2×C1112yescomplemented
176#1964C2×C1114yescomplemented
177#1964C2×C1112yescomplemented
178#1799C2×C1112yescomplemented
179#1799C2×C1111yescharacteristic, complemented
180C4×#99C2×C1112yescomplemented
181C4×#99C2×C1111yescharacteristic, complemented
182C23×C11—21no—
183C23×C11—22no—
184C23×C11—21no—
185C23×C11—22no—
186C23×C11—21no—
187C23×C11—22no—
188C23×C11—41no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—41no—
194C23×C11C23×C411yescharacteristic
195C23×C11C22×D412yes—
196C23×C11C2×#4112yes—
197C23×C11H(5,𝔽2)11yescharacteristic
198C23×C112−1+411yescharacteristic
199D4×C11—42no—
200D4×C11—44no—
201D4×C11—42no—
202D4×C11—44no—
203D4×C11—42no—
204D4×C11—42no—
205D4×C11—84no—
206C2×C4×C11—24no—
207C2×C4×C11—22no—
208C2×C4×C11—21no—
209C2×C4×C11—22no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—22no—
213C2×C4×C11—21no—
214C2×C4×C11—22no—
215C2×C4×C11—21no—
216C2×C4×C11—24no—
217C2×C4×C11—44no—
218C2×C4×C11—44no—
219C2×C4×C11—41no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—42no—
230C2×C4×C11—44no—
231C2×C4×C11—44no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—44no—
235C2×C4×C11—82no—
236C2×C4×C11—82no—
237C2×C4×C11C2×C22⋊C412yes—
238C2×C4×C11C2×C22⋊C412yes—
239C2×C4×C11C2×C22⋊C411yescharacteristic
240C2×C4×C11C2×C22⋊C412yes—
241C2×C4×C11C2×C22⋊C414yes—
242C2×C4×C11C2×C22⋊C411yescharacteristic
243#553—22no—
244#553—24no—
245#553—22no—
246C2×#126C4×C1112yescomplemented
247C2×#125C4×C1111yescharacteristic, complemented
248C2×#123C4×C1112yescomplemented
249C2×#121C4×C1111yescharacteristic, complemented
250C2×#121C22×C1112yes—
251C2×#121C22×C1111yescharacteristic
252C2×C4×D4C4×C1111yescharacteristic, complemented
253C2×C4×D4C22×C1112yes—
254C2×C4×D4C22×C1111yescharacteristic
255C2×#117C4×C1111yescharacteristic, complemented
256C22×C4⋊C4C22×C1111yescharacteristic
257C2×#99C22×C1112yes—
258C2×#99C22×C1114yes—
259C2×#99C22×C1114yes—
260C2×#99C22×C1112yes—
261#389—22no—
262#387—24no—
263#380C22×C1114yes—
264#380C22×C1112yes—
265C4×C4⋊C4—22no—
266C4×C22⋊C4C22×C1112yes—
267C4×C22⋊C4C22×C1114yes—
268#342C22×C1111yescharacteristic
269#342C22×C1112yes—
270#342C22×C1111yescharacteristic
271C22×C11—22no—
272C22×C11—21no—
273C22×C11—22no—
274C22×C11—21no—
275C22×C11—42no—
276C22×C11—41no—
277C22×C11—41no—
278C22×C11—41no—
279C22×C11—42no—
280C22×C11—41no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—41no—
284C22×C11—81no—
285C22×C11—82no—
286C22×C11—81no—
287C22×C11—82no—
288C22×C11C22×C22⋊C411yescharacteristic
289C22×C11C4×#4111yescharacteristic
290C22×C11#52011yescharacteristic
291C22×C11#54812yes—
292C22×C11#55012yes—
293C4×C11—21no—
294C4×C11—22no—
295C4×C11—22no—
296C4×C11—22no—
297C4×C11—24no—
298C4×C11—44no—
299C4×C11—42no—
300C4×C11—41no—
301C4×C11—41no—
302C4×C11—41no—
303C4×C11—82no—
304C4×C11—84no—
305C4×C11#41012yes—
306C22×D4C2×C4×C1111yescharacteristic
307C22×D4C2×C4×C1112yes—
308C22×D4C23×C1112yes—
309C22×D4C23×C1111yescharacteristic
310C23×C4C2×C4×C1111yescharacteristic
311C23×C4C2×C4×C1112yes—
312C23×C4C23×C1111yescharacteristic
313C23×C4C23×C1112yes—
314#126—24no—
315#126—24no—
316#125—22no—
317#125—22no—
318#123—24no—
319#123—24no—
320#121—24no—
321#121—24no—
322#121—22no—
323#121—22no—
324#121—22no—
325#121—22no—
326C4×D4—24no—
327C4×D4—24no—
328C4×D4—22no—
329C4×D4—22no—
330C4×D4—22no—
331C4×D4—21no—
332C4×D4—21no—
333#117—22no—
334#117—21no—
335#117—21no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4C2×C4×C1111yescharacteristic
339C2×C4⋊C4C2×C4×C1112yes—
340C2×C4⋊C4C2×C4×C1111yescharacteristic
341C2×C4⋊C4C2×C4×C1112yes—
342C2×C4⋊C4C2×C4×C1111yescharacteristic
343C2×C4⋊C4C2×C4×C1111yescharacteristic
344C2×C4⋊C4C2×C4×C1112yes—
345C2×C4⋊C4D4×C1112yes—
346C2×C4⋊C4D4×C1114yes—
347C2×C4⋊C4D4×C1112yes—
348C2×C22⋊C4C2×C4×C1112yes—
349C2×C22⋊C4C2×C4×C1112yes—
350C2×C22⋊C4C2×C4×C1112yes—
351C2×C22⋊C4C2×C4×C1111yescharacteristic
352C2×C22⋊C4C2×C4×C1112yes—
353C2×C22⋊C4C23×C1112yes—
354C2×C22⋊C4C23×C1114yes—
355C2×C22⋊C4C23×C1111yescharacteristic
356C2×C22⋊C4C23×C1112yes—
357C2×C42—22no—
358C2×C42—24no—
359C2×C42C2×C4×C1112yes—
360C2×C42C2×C4×C1111yescharacteristic
361#99—24no—
362#99—28no—
363#99—44no—
364#99—42no—
365#95—22no—
366#95—24no—
367#95—24no—
368#95—22no—
369C2×C11—22no—
370C2×C11—22no—
371C2×C11—21no—
372C2×C11—21no—
373C2×C11—81no—
374C2×C11—82no—
375C2×C11#234111yescharacteristic
376C2×C11C2×#41011yescharacteristic
377C2×C11#288311yescharacteristic
378C24C22×C4×C1111yescharacteristic
379C24C22×C4×C1112yes—
380C24C24×C1111yescharacteristic
381C2×D4—24no—
382C2×D4—22no—
383C2×D4—24no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—21no—
387C2×D4—22no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—24no—
392C2×D4—42no—
393C2×D4—82no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—24no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—82no—
404C22×C4—82no—
405C22×C4C22×C4×C1112yes—
406C22×C4C22×C4×C1111yescharacteristic
407C22×C4C22×C4×C1111yescharacteristic
408C22×C4C22×C4×C1111yescharacteristic
409C22×C4C22×C4×C1111yescharacteristic
410C22×C4C22×C4×C1112yes—
411C22×C4C22×C4×C1111yescharacteristic
412C22×C4C22×C4×C1112yes—
413C22×C4C2×D4×C1112yes—
414C22×C4C2×D4×C1112yes—
415C22×C4C2×D4×C1114yes—
416C22×C4C2×D4×C1114yes—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—24no—
420C4⋊C4—22no—
421C4⋊C4—24no—
422C4⋊C4—44no—
423C4⋊C4—84no—
424C4⋊C4C11×C22⋊C412yes—
425C4⋊C4C11×C22⋊C411yescharacteristic
426C4⋊C4C11×C22⋊C411yescharacteristic
427C4⋊C4C11×C22⋊C412yes—
428C4⋊C4C11×C22⋊C412yes—
429C4⋊C4C11×C22⋊C414yes—
430C4⋊C4C11×C22⋊C414yes—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—24no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—24no—
440C22⋊C4—22no—
441C22⋊C4—24no—
442C22⋊C4—22no—
443C22⋊C4—24no—
444C22⋊C4C11×#4114yes—
445C42—22no—
446C42—22no—
447C42—21no—
448C42—21no—
449C42—44no—
450C42—84no—
451C11#2253511yescharacteristic, direct product factor, Sylow
452C23—21no—
453C23—22no—
454C23—21no—
455C23—22no—
456C23—21no—
457C23—22no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—42no—
462C23—42no—
463C23—41no—
464C23C23×C4×C1111yescharacteristic
465C23C22×D4×C1112yes—
466C23C2×C11×#4112yes—
467C23C11×H(5,𝔽2)11yescharacteristic
468C23C11×2−1+411yescharacteristic
469D4—42no—
470D4—44no—
471D4—42no—
472D4—44no—
473D4—42no—
474D4—42no—
475D4—84no—
476C2×C4—24no—
477C2×C4—22no—
478C2×C4—21no—
479C2×C4—22no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—22no—
483C2×C4—21no—
484C2×C4—22no—
485C2×C4—21no—
486C2×C4—24no—
487C2×C4—44no—
488C2×C4—44no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—44no—
501C2×C4—44no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—44no—
505C2×C4—82no—
506C2×C4—82no—
507C2×C4C2×C11×C22⋊C412yes—
508C2×C4C2×C11×C22⋊C412yes—
509C2×C4C2×C11×C22⋊C411yescharacteristic
510C2×C4C2×C11×C22⋊C412yes—
511C2×C4C2×C11×C22⋊C414yes—
512C2×C4C2×C11×C22⋊C411yescharacteristic
513C22—22no—
514C22—21no—
515C22—22no—
516C22—21no—
517C22—42no—
518C22—41no—
519C22—41no—
520C22—41no—
521C22—42no—
522C22—41no—
523C22—42no—
524C22—42no—
525C22—41no—
526C22—81no—
527C22—82no—
528C22—81no—
529C22—82no—
530C22C22×C11×C22⋊C411yescharacteristic
531C22C4×C11×#4111yescharacteristic
532C22C11×#52011yescharacteristic
533C22C11×#54812yes—
534C22C11×#55012yes—
535C4—21no—
536C4—22no—
537C4—22no—
538C4—22no—
539C4—24no—
540C4—44no—
541C4—42no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—82no—
546C4—84no—
547C4C11×#41012yes—
548C2—22no—
549C2—22no—
550C2—21no—
551C2—21no—
552C2—81no—
553C2—82no—
554C2C11×#234111yescharacteristic
555C2C2×C11×#41011yescharacteristic
556C2C11×#288311yescharacteristic
subgroupG/H
center, socleC22×C11C22×C22⋊C4
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
prime radicalC2×C11×#553C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C11×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2345C2semidirect
3. C11×#1964C2semidirect
4. C11×#1964C2semidirect
5. C11×#1799C2semidirect
6. C11×#1799C2semidirect
7. C4×C11×#99C2semidirect
8. C4×C11×#99C2semidirect
12. C2×C11×#126C4semidirect
13. C2×C11×#125C4semidirect
14. C2×C11×#123C4semidirect
15. C2×C11×#121C4semidirect
18. C2×C4×D4×C11C4semidirect
21. C2×C11×#117C4semidirect
100. #22535C11direct (N × H)
175. #2345C2×C11semidirect
176. #1964C2×C11semidirect
177. #1964C2×C11semidirect
178. #1799C2×C11semidirect
179. #1799C2×C11semidirect
180. C4×#99C2×C11semidirect
181. C4×#99C2×C11semidirect
246. C2×#126C4×C11semidirect
247. C2×#125C4×C11semidirect
248. C2×#123C4×C11semidirect
249. C2×#121C4×C11semidirect
252. C2×C4×D4C4×C11semidirect
255. C2×#117C4×C11semidirect
451. C11#22535direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5532
C11×#23452
C11×#19642
C11×#17992
C4×C11×#992
#2253511