Finite Group Databasebeta

← #14916500

Subgroups — #14916500

Order 2816.

4134 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#120C211yesmaximal, characteristic
2#13071757C211yesmaximal, characteristic, complemented
3#13071755C212yesmaximal, complemented
4#13071599C211yesmaximal, characteristic, complemented
5#13071597C211yesmaximal, characteristic, complemented
6#13071594C212yesmaximal, complemented
7#13071464C212yesmaximal, complemented
8#13071460C212yesmaximal, complemented
9#13071437C212yesmaximal, complemented
10#13071434C212yesmaximal, complemented
11#13071278C212yesmaximal, complemented
12#13071275C212yesmaximal, complemented
13#13071272C212yesmaximal, complemented
14#13071269C212yesmaximal, complemented
15#13071210C212yesmaximal, complemented
16#13071195C211yesmaximal, characteristic, complemented
17#13071190C211yesmaximal, characteristic, complemented
18D11×#379C212yesmaximal, complemented
19C11×#2375C211yesmaximal, characteristic, complemented
20C25×D11C2211yescharacteristic
21C22×D4×D11C2212yes—
22C22×D4×D11C2211yescharacteristic
23C2×C11×#120C2211yescharacteristic
24C2×#67006C2211yescharacteristic
25C2×#66990C2212yes—
26C2×#66990C2211yescharacteristic
27C2×C4×C22⋊D11C2212yescomplemented
28C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
29D11×#120C4116yescomplemented
30C2×#66946C2212yescomplemented
31C2×#66945C2211yescharacteristic, complemented
32C2×#66935C2212yes—
33C2×#66935C2211yescharacteristic
34C2×(C22⋊D11)⋊C4C2212yescomplemented
35C2×C22⋊C4×D11C2212yes—
36C2×C22⋊C4×D11C2212yes—
37C2×C22⋊C4×D11C2212yes—
38C2×C22⋊C4×D11C2211yescharacteristic
39C2×C22⋊C4×D11C2212yescomplemented
40C2×C22⋊C4×D11C2212yescomplemented
41C2×C22⋊C4×D11C2212yescomplemented
42C2×C22⋊C4×D11C2212yescomplemented
43C2×C22⋊C4×D11C2211yescharacteristic, complemented
44C2×C4×D44C2212yescomplemented
45C2×#66925C2211yescharacteristic, complemented
46C11×#390C2212yescomplemented
47C11×#390C2211yescharacteristic, complemented
48C11×#388C2212yescomplemented
49C11×#388C2212yescomplemented
50C11×#388C2212yescomplemented
51C11×#386C2212yescomplemented
52C11×#386C2211yescharacteristic, complemented
53C11×#379C2212yescomplemented
54#10622860C2212yescomplemented
55#10622834C2212yescomplemented
56#10622834C2211yescharacteristic, complemented
57#10622833C2212yescomplemented
58#10622833C2211yescharacteristic, complemented
59#10622826C2211yescharacteristic, complemented
60#10622603C2212yescomplemented
61#10622602C2212yescomplemented
62#10622602C2212yescomplemented
63#10622601C2211yescharacteristic, complemented
64#10622600C2212yescomplemented
65#10622571C2211yescharacteristic, complemented
66#10622570C2212yescomplemented
67#10622570C2212yescomplemented
68#10622570C2212yescomplemented
69#10622570C2212yescomplemented
70#10622569C2212yescomplemented
71#10622569C2212yescomplemented
72#10622569C2212yescomplemented
73#10622569C2212yescomplemented
74#10622569C2212yescomplemented
75#10622568C2212yes—
76#10622568C2212yes—
77#10622568C2212yes—
78#10622568C2212yes—
79#10622568C2212yescomplemented
80#10622568C2212yescomplemented
81#10622568C2212yescomplemented
82#10622564C2212yescomplemented
83#10622564C2212yescomplemented
84#10622564C2212yescomplemented
85#10622558C2212yescomplemented
86#10622558C2212yescomplemented
87#10622558C2212yescomplemented
88#10622557C2212yescomplemented
89#10622557C2212yescomplemented
90#10622557C2212yescomplemented
91#10622553C2212yescomplemented
92#10622552C2211yescharacteristic, complemented
93C4×(C2×D11)⋊C4C2212yescomplemented
94C4×(C2×D11)⋊C4C2212yescomplemented
95C4×(C2×D11)⋊C4C2212yescomplemented
96#10622283C2212yescomplemented
97#10622282C2212yescomplemented
98#10622281C2212yescomplemented
99#10622281C2212yescomplemented
100#10622280C2212yescomplemented
101#10622279C2212yescomplemented
102#10622279C2212yescomplemented
103#10622279C2212yescomplemented
104#10622278C2212yescomplemented
105#10622278C2212yescomplemented
106#10622278C2212yescomplemented
107#10622277C2212yescomplemented
108C25×C11C2311yescharacteristic
109C24×D11—42no—
110C24×D11—42no—
111C24×D11—44no—
112C24×D11—44no—
113C24×D11C2×C418yescomplemented
114C24×D11C2312yes—
115C24×D11C2311yescharacteristic
116C24×D11C2311yescharacteristic
117C24×D11C2312yes—
118C24×D11C2311yescharacteristic
119C22×D4×C11C2312yes—
120C22×D4×C11C2311yescharacteristic
121C23×C4×C11C2311yescharacteristic, complemented
122C22×C22⋊D11C2312yes—
123C22×C22⋊D11C2312yes—
124C22×C22⋊D11C2311yescharacteristic
125C22×C22⋊D11C2311yescharacteristic
126C23×Dic11C2311yescharacteristic, complemented
127C2×D4×D11—42no—
128C2×D4×D11—42no—
129C2×D4×D11—44no—
130C2×D4×D11—44no—
131C2×D4×D11C2×C418yescomplemented
132C2×D4×D11C2×C4116yescomplemented
133C22×D44C2312yes—
134C22×D44C2311yescharacteristic
135C22×C4×D11C2311yescharacteristic
136C22×C4×D11C2312yes—
137C22×C4×D11C2312yes—
138C22×C4×D11C2312yes—
139C22×C4×D11C2312yes—
140C22×C4×D11C2312yes—
141C22×C4×D11C2312yescomplemented
142C11×#120C2×C418yescomplemented
143C2×C11×C4⋊C4C2311yescharacteristic, complemented
144C2×C11×C4⋊C4C2312yescomplemented
145C2×C11×C22⋊C4C2312yes—
146C2×C11×C22⋊C4C2312yes—
147C2×C11×C22⋊C4C2312yes—
148C2×C11×C22⋊C4C2312yes—
149C2×C11×C22⋊C4C2312yes—
150C2×C11×C22⋊C4C2312yes—
151C2×C11×C22⋊C4C2312yes—
152C2×C11×C22⋊C4C2311yescharacteristic
153C2×C11×C22⋊C4C2311yescharacteristic, complemented
154C2×C11×C22⋊C4C2312yescomplemented
155C2×C42×C11C2311yescharacteristic, complemented
156C2×C42×C11C2312yescomplemented
157#67006C2×C418yescomplemented
158C2×C22⋊Dic11C2312yes—
159C2×C22⋊Dic11C2312yes—
160C2×C22⋊Dic11C2312yes—
161C2×C22⋊Dic11C2312yes—
162C2×C22⋊Dic11C2312yes—
163C2×C22⋊Dic11C2312yes—
164C2×C22⋊Dic11C2312yes—
165C2×C22⋊Dic11C2311yescharacteristic
166C2×C22⋊Dic11C2311yescharacteristic, complemented
167C2×C22⋊Dic11C2312yescomplemented
168#66990C2×C418yescomplemented
169#66990C2×C4116yescomplemented
170C4×C22⋊D11—44no—
171C2×(C2×D11)⋊C4—42no—
172C2×(C2×D11)⋊C4C2312yes—
173C2×(C2×D11)⋊C4C2312yes—
174C2×(C2×D11)⋊C4C2312yes—
175C2×(C2×D11)⋊C4C2312yes—
176C2×(C2×D11)⋊C4C2312yes—
177C2×(C2×D11)⋊C4C2312yes—
178C2×(C2×D11)⋊C4C2312yes—
179C2×(C2×D11)⋊C4C2312yes—
180C2×(C2×D11)⋊C4C2312yes—
181C2×(C2×D11)⋊C4C2312yes—
182C2×(C2×D11)⋊C4C2312yes—
183C2×(C2×D11)⋊C4C2312yes—
184C2×(C2×D11)⋊C4C2312yes—
185C2×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2312yescomplemented
188C2×(C2×D11)⋊C4C2312yescomplemented
189C2×(C2×D11)⋊C4C2312yescomplemented
190C2×C4⋊Dic11C2312yescomplemented
191C2×C4⋊Dic11C2311yescharacteristic, complemented
192C2×Dic11⋊C4C2312yescomplemented
193C2×Dic11⋊C4C2312yescomplemented
194C2×Dic11⋊C4C2312yescomplemented
195C2×C4×Dic11C2311yescharacteristic, complemented
196C2×C4×Dic11C2312yescomplemented
197C2×C4×Dic11C2312yescomplemented
198C2×C4×Dic11C2312yescomplemented
199C2×C4×Dic11C2312yescomplemented
200#66946—44no—
201#66945—42no—
202#66935C2×C418yescomplemented
203#66935C2×C4116yescomplemented
204(C22⋊D11)⋊C4—44no—
205C22⋊C4×D11—44no—
206C22⋊C4×D11—44no—
207C22⋊C4×D11—44no—
208C22⋊C4×D11—42no—
209C22⋊C4×D11—44no—
210C22⋊C4×D11—44no—
211C22⋊C4×D11—44no—
212C22⋊C4×D11C2×C4116yescomplemented
213C22⋊C4×D11C2×C418yescomplemented
214C4×D44—44no—
215#66925—42no—
216C11×#95C2312yescomplemented
217C11×#95C2312yescomplemented
218C11×#95C2312yescomplemented
219C11⋊#95C2312yescomplemented
220C11⋊#95C2312yescomplemented
221C11⋊#95C2312yescomplemented
222C11⋊#95C2312yescomplemented
223C11⋊#95C2312yescomplemented
224C11⋊#95C2312yescomplemented
225C11⋊#95C2312yescomplemented
226C11⋊#95C2312yescomplemented
227C11⋊#95C2312yescomplemented
228#34356—111nomaximal, Sylow
229C24×C11—41no—
230C24×C11—42no—
231C24×C11—42no—
232C24×C11—41no—
233C24×C11C22×C414yes—
234C24×C11C2412yes—
235C24×C11C2411yescharacteristic
236C24×C11C2411yescharacteristic
237C23×D11—24no—
238C23×D11—24no—
239C23×D11—24no—
240C23×D11—24no—
241C23×D11—24no—
242C23×D11—24no—
243C23×D11—24no—
244C23×D11—24no—
245C23×D11—22no—
246C23×D11—22no—
247C23×D11—22no—
248C23×D11—22no—
249C23×D11—432no—
250C23×D11—416no—
251C23×D11—41no—
252C23×D11—41no—
253C23×D11—42no—
254C23×D11—42no—
255C23×D11—42no—
256C23×D11—42no—
257C23×D11—42no—
258C23×D11—42no—
259C23×D11—42no—
260C23×D11—42no—
261C23×D11—42no—
262C23×D11—42no—
263C23×D11—432no—
264C23×D11—416no—
265C23×D11—416no—
266C23×D11C22×C418yes—
267C23×D11C22×C414yes—
268C23×D11C22×C414yes—
269C23×D11C22×C418yes—
270C23×D11C22×C414yes—
271C23×D11C2411yescharacteristic
272C23×D11C2411yescharacteristic
273C23×D11C2411yescharacteristic
274C23×D11C2412yes—
275C2×D4×C11—41no—
276C2×D4×C11—42no—
277C2×D4×C11—42no—
278C2×D4×C11—41no—
279C2×D4×C11C22×C414yes—
280C2×D4×C11C22×C418yes—
281C22×C4×C11—41no—
282C22×C4×C11—42no—
283C22×C4×C11C2412yes—
284C22×C4×C11C2412yes—
285C22×C4×C11C2412yes—
286C22×C4×C11C2412yes—
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2412yes—
289C2×C22⋊D11—24no—
290C2×C22⋊D11—24no—
291C2×C22⋊D11—41no—
292C2×C22⋊D11—42no—
293C2×C22⋊D11—42no—
294C2×C22⋊D11—41no—
295C2×C22⋊D11—41no—
296C2×C22⋊D11—41no—
297C2×C22⋊D11C22×C418yes—
298C2×C22⋊D11C22×C418yes—
299C2×C22⋊D11C22×C414yes—
300C2×C22⋊D11C22×C414yes—
301C22×Dic11—42no—
302C22×Dic11—41no—
303C22×Dic11C2412yes—
304C22×Dic11C2412yes—
305C22×Dic11C2412yes—
306C22×Dic11C2412yes—
307C22×Dic11C2411yescharacteristic
308C22×Dic11C2412yes—
309D4×D11—416no—
310D4×D11—432no—
311C2×D44—24no—
312C2×D44—24no—
313C2×D44—41no—
314C2×D44—41no—
315C2×D44C22×C418yes—
316C2×D44C22×C414yes—
317C2×C4×D11—22no—
318C2×C4×D11—22no—
319C2×C4×D11—24no—
320C2×C4×D11—24no—
321C2×C4×D11—24no—
322C2×C4×D11—24no—
323C2×C4×D11—42no—
324C2×C4×D11—42no—
325C2×C4×D11—42no—
326C2×C4×D11—42no—
327C2×C4×D11—42no—
328C2×C4×D11—42no—
329C2×C4×D11—42no—
330C2×C4×D11—42no—
331C2×C4×D11—42no—
332C2×C4×D11—42no—
333C2×C4×D11—42no—
334C2×C4×D11—42no—
335C2×C4×D11—42no—
336C2×C4×D11C22×C414yes—
337C2×C4×D11C22×C418yes—
338C11×C4⋊C4—41no—
339C11×C4⋊C4—42no—
340C11×C22⋊C4—42no—
341C11×C22⋊C4—42no—
342C11×C22⋊C4—42no—
343C11×C22⋊C4—42no—
344C11×C22⋊C4—42no—
345C11×C22⋊C4—42no—
346C11×C22⋊C4—41no—
347C11×C22⋊C4—42no—
348C11×C22⋊C4C22×C418yes—
349C11×C22⋊C4C22×C414yes—
350C42×C11—41no—
351C42×C11—42no—
352C22⋊Dic11—42no—
353C22⋊Dic11—42no—
354C22⋊Dic11—42no—
355C22⋊Dic11—42no—
356C22⋊Dic11—42no—
357C22⋊Dic11—42no—
358C22⋊Dic11—41no—
359C22⋊Dic11—42no—
360C22⋊Dic11C22×C418yes—
361C22⋊Dic11C22×C414yes—
362(C2×D11)⋊C4—24no—
363(C2×D11)⋊C4—24no—
364(C2×D11)⋊C4—24no—
365(C2×D11)⋊C4—24no—
366(C2×D11)⋊C4—24no—
367(C2×D11)⋊C4—24no—
368(C2×D11)⋊C4—24no—
369(C2×D11)⋊C4—24no—
370(C2×D11)⋊C4—42no—
371(C2×D11)⋊C4—42no—
372(C2×D11)⋊C4—42no—
373(C2×D11)⋊C4—42no—
374(C2×D11)⋊C4—42no—
375(C2×D11)⋊C4—42no—
376(C2×D11)⋊C4—42no—
377(C2×D11)⋊C4C22×C418yes—
378(C2×D11)⋊C4C22×C418yes—
379(C2×D11)⋊C4C22×C418yes—
380C4⋊Dic11—42no—
381C4⋊Dic11—41no—
382Dic11⋊C4—42no—
383Dic11⋊C4—42no—
384Dic11⋊C4—42no—
385C4×Dic11—41no—
386C4×Dic11—42no—
387C4×Dic11—42no—
388C4×Dic11—42no—
389C4×Dic11—42no—
390C22×#120—111no—
391#2375—112no—
392#2375—111no—
393#2375D1111yescharacteristic, complemented
394#2358—111no—
395#2358—112no—
396#2358—111no—
397#2342—112no—
398#2342—112no—
399D4×C22⋊C4—112no—
400D4×C22⋊C4—112no—
401#2321—112no—
402#2321—112no—
403#2321—112no—
404#2321—112no—
405#2312—112no—
406#2309—111no—
407#2308—111no—
408C2×#379—112no—
409C23×C11—21no—
410C23×C11—22no—
411C23×C11—22no—
412C23×C11—22no—
413C23×C11—22no—
414C23×C11—22no—
415C23×C11—22no—
416C23×C11—22no—
417C23×C11—22no—
418C23×C11—21no—
419C23×C11—21no—
420C23×C11—22no—
421C23×C11—22no—
422C23×C11—21no—
423C23×C11—44no—
424C23×C11—48no—
425C23×C11—48no—
426C23×C11—44no—
427C23×C11—44no—
428C23×C11C23×C414yes—
429C23×C11C23×C412yes—
430C23×C11C23×C412yes—
431C23×C11C2511yescharacteristic
432C22×D11—22no—
433C22×D11—22no—
434C22×D11—22no—
435C22×D11—22no—
436C22×D11—22no—
437C22×D11—22no—
438C22×D11—21no—
439C22×D11—22no—
440C22×D11—22no—
441C22×D11—22no—
442C22×D11—22no—
443C22×D11—21no—
444C22×D11—21no—
445C22×D11—21no—
446C22×D11—216no—
447C22×D11—28no—
448C22×D11—216no—
449C22×D11—216no—
450C22×D11—216no—
451C22×D11—28no—
452C22×D11—48no—
453C22×D11—48no—
454C22×D11—44no—
455C22×D11—48no—
456C22×D11—48no—
457C22×D11—48no—
458C22×D11—48no—
459C22×D11—48no—
460C22×D11—48no—
461C22×D11—48no—
462C22×D11—44no—
463C22×D11—44no—
464C22×D11—48no—
465C22×D11—48no—
466C22×D11—44no—
467C22×D11—44no—
468C22×D11—48no—
469C22×D11—48no—
470C22×D11—48no—
471C22×D11—48no—
472C22×D11—4128no—
473C22×D11—82no—
474C22×D11—82no—
475C22×D11—84no—
476C22×D11C23×C412yes—
477C22×D11C23×C412yes—
478C22×D11C23×C414yes—
479C22×D11C23×C412yes—
480C22×D11H(5,𝔽2)12yes—
481C22×D11H(5,𝔽2)12yes—
482C22×D11H(5,𝔽2)14yes—
483C22×D11H(5,𝔽2)14yes—
484D4×C11—44no—
485D4×C11—48no—
486C2×C4×C11—21no—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
489C2×C4×C11—21no—
490C2×C4×C11—22no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11—22no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—22no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11—82no—
503C2×C4×C11C23×C412yes—
504C2×C4×C11C23×C414yes—
505C22⋊D11—216no—
506C22⋊D11—44no—
507C22⋊D11—44no—
508C22⋊D11—48no—
509C2×Dic11—21no—
510C2×Dic11—22no—
511C2×Dic11—22no—
512C2×Dic11—21no—
513C2×Dic11—22no—
514C2×Dic11—22no—
515C2×Dic11—22no—
516C2×Dic11—22no—
517C2×Dic11—22no—
518C2×Dic11—22no—
519C2×Dic11—22no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—22no—
525C2×Dic11—82no—
526C2×Dic11C23×C412yes—
527C2×Dic11C23×C414yes—
528D44—216no—
529D44—44no—
530C4×D11—28no—
531C4×D11—48no—
532C4×D11—84no—
533C4×D11—84no—
534C4×D11—84no—
535C4×D11—84no—
536C4×D11—84no—
537C26—111no—
538C23×D4—111no—
539C23×D4—112no—
540C2×#120—111no—
541C2×#120—112no—
542C2×#120—111no—
543C2×#120—1116no—
544C2×#120—112no—
545C2×#120—111no—
546C2×#120C2×D1111yescharacteristic
547C2×C4×D4—112no—
548C2×C4×D4—112no—
549C2×C4×D4—112no—
550C2×C4×D4—112no—
551C2×#117—111no—
552C2×#117—111no—
553C22×C22⋊C4—111no—
554C22×C22⋊C4—112no—
555C22×C22⋊C4—111no—
556C22×C22⋊C4—112no—
557C22×C22⋊C4—112no—
558C22×C22⋊C4—112no—
559C22×C22⋊C4—112no—
560C22×C22⋊C4—112no—
561C22×C22⋊C4—112no—
562C22×C22⋊C4—111no—
563#390—111no—
564#390—112no—
565#390—111no—
566#390—112no—
567#390—112no—
568#390—112no—
569#390—112no—
570#390—111no—
571#390C2×D1111yescharacteristic, complemented
572#390C2×D1112yescomplemented
573#388—112no—
574#388—112no—
575#388—112no—
576#388—112no—
577#388—112no—
578#388—112no—
579#388—112no—
580#388—112no—
581#388—112no—
582#388—112no—
583#388—112no—
584#388—112no—
585#388—112no—
586#388C2×D1112yescomplemented
587#388C2×D1112yescomplemented
588#388C2×D1112yescomplemented
589#386—111no—
590#386—112no—
591#386—111no—
592#386—112no—
593#386—112no—
594#386—112no—
595#386—111no—
596#386—112no—
597#386—112no—
598#386—112no—
599#386—112no—
600#386—112no—
601#386C2×D1111yescharacteristic, complemented
602#386C2×D1112yescomplemented
603#385—112no—
604#385—112no—
605#385—112no—
606#385—112no—
607#381—112no—
608#380—112no—
609#380—112no—
610#379—112no—
611#379—112no—
612#379—112no—
613#379—112no—
614#379—112no—
615#379—112no—
616#379—112no—
617#379—112no—
618#379C2×D1112yescomplemented
619C4×C22⋊C4—112no—
620C4×C22⋊C4—112no—
621C4×C22⋊C4—112no—
622C4×C22⋊C4—112no—
623C4×C22⋊C4—112no—
624C4×C22⋊C4—112no—
625C22×C11—22no—
626C22×C11—24no—
627C22×C11—22no—
628C22×C11—24no—
629C22×C11—24no—
630C22×C11—24no—
631C22×C11—24no—
632C22×C11—416no—
633C22×C11—41no—
634C22×C11—42no—
635C22×C11—42no—
636C22×C11—42no—
637C22×C11—42no—
638C22×C11—41no—
639C22×C11—42no—
640C22×C11—41no—
641C22×C11—42no—
642C22×C11—41no—
643C22×C11C24×C411yescharacteristic
644C22×C11C2×H(5,𝔽2)11yescharacteristic
645C22×C11C2×H(5,𝔽2)12yes—
646C22×C11C2×H(5,𝔽2)12yes—
647C22×C11C2×H(5,𝔽2)11yescharacteristic
648C2×D11—24no—
649C2×D11—24no—
650C2×D11—24no—
651C2×D11—24no—
652C2×D11—22no—
653C2×D11—22no—
654C2×D11—24no—
655C2×D11—24no—
656C2×D11—24no—
657C2×D11—24no—
658C2×D11—24no—
659C2×D11—22no—
660C2×D11—22no—
661C2×D11—24no—
662C2×D11—432no—
663C2×D11—416no—
664C2×D11—416no—
665C2×D11—432no—
666C2×D11—42no—
667C2×D11—41no—
668C2×D11—41no—
669C2×D11—41no—
670C2×D11—41no—
671C2×D11—42no—
672C2×D11—88no—
673C2×D11#51814yes—
674C2×D11#51818yes—
675C4×C11—22no—
676C4×C11—24no—
677C4×C11—42no—
678C4×C11—42no—
679C4×C11—42no—
680C4×C11—42no—
681Dic11—22no—
682Dic11—24no—
683Dic11—42no—
684Dic11—42no—
685Dic11—42no—
686Dic11—42no—
687C25—111no—
688C25—112no—
689C25—112no—
690C25—111no—
691C25—111no—
692C25—118no—
693C25—442no—
694C25—442no—
695C25—444no—
696C25—444no—
697C25C22×D1111yescharacteristic
698C22×D4—112no—
699C22×D4—111no—
700C22×D4—112no—
701C22×D4—111no—
702C22×D4—118no—
703C22×D4—1116no—
704C22×D4—112no—
705C22×D4—111no—
706C22×D4—442no—
707C22×D4—442no—
708C22×D4—444no—
709C22×D4—444no—
710C22×D4C22×D1112yes—
711C22×D4C22×D1111yescharacteristic
712C23×C4—111no—
713C23×C4—112no—
714C23×C4—111no—
715C23×C4—112no—
716C23×C4—112no—
717C23×C4—112no—
718C23×C4—112no—
719C23×C4—112no—
720C23×C4C22×D1111yescharacteristic, complemented
721#120—118no—
722#120—118no—
723#120—1116no—
724#120—118no—
725#120—1116no—
726#120C4×D1118yescomplemented
727C4×D4—444no—
728C4×D4—444no—
729C4×D4—444no—
730C4×D4—444no—
731#117—442no—
732#117—442no—
733C2×C4⋊C4—112no—
734C2×C4⋊C4—111no—
735C2×C4⋊C4—112no—
736C2×C4⋊C4—112no—
737C2×C4⋊C4—112no—
738C2×C4⋊C4C22×D1111yescharacteristic, complemented
739C2×C4⋊C4C22×D1112yescomplemented
740C2×C22⋊C4—111no—
741C2×C22⋊C4—112no—
742C2×C22⋊C4—112no—
743C2×C22⋊C4—112no—
744C2×C22⋊C4—112no—
745C2×C22⋊C4—1116no—
746C2×C22⋊C4—118no—
747C2×C22⋊C4—112no—
748C2×C22⋊C4—112no—
749C2×C22⋊C4—112no—
750C2×C22⋊C4—112no—
751C2×C22⋊C4—112no—
752C2×C22⋊C4—112no—
753C2×C22⋊C4—112no—
754C2×C22⋊C4—112no—
755C2×C22⋊C4—112no—
756C2×C22⋊C4—112no—
757C2×C22⋊C4—112no—
758C2×C22⋊C4—112no—
759C2×C22⋊C4—112no—
760C2×C22⋊C4—112no—
761C2×C22⋊C4—111no—
762C2×C22⋊C4—112no—
763C2×C22⋊C4—112no—
764C2×C22⋊C4—112no—
765C2×C22⋊C4—112no—
766C2×C22⋊C4—112no—
767C2×C22⋊C4—112no—
768C2×C22⋊C4—112no—
769C2×C22⋊C4—112no—
770C2×C22⋊C4—444no—
771C2×C22⋊C4—444no—
772C2×C22⋊C4—444no—
773C2×C22⋊C4—444no—
774C2×C22⋊C4—442no—
775C2×C22⋊C4—444no—
776C2×C22⋊C4—444no—
777C2×C22⋊C4—442no—
778C2×C22⋊C4C22×D1112yes—
779C2×C22⋊C4C22×D1112yes—
780C2×C22⋊C4C22×D1112yes—
781C2×C22⋊C4C22×D1112yes—
782C2×C22⋊C4C22×D1112yes—
783C2×C22⋊C4C22×D1112yes—
784C2×C22⋊C4C22×D1111yescharacteristic
785C2×C22⋊C4C22×D1112yes—
786C2×C22⋊C4C22×D1111yescharacteristic, complemented
787C2×C22⋊C4C22×D1112yescomplemented
788C2×C42—112no—
789C2×C42—111no—
790C2×C42—112no—
791C2×C42—112no—
792C2×C42—112no—
793C2×C42C22×D1111yescharacteristic, complemented
794C2×C42C22×D1112yescomplemented
795#95—112no—
796#95—112no—
797#95—112no—
798#95—112no—
799#95—112no—
800#95—112no—
801#95—112no—
802#95—112no—
803#95—112no—
804#95C22×D1112yescomplemented
805#95C22×D1112yescomplemented
806#95C22×D1112yescomplemented
807C2×C11—44no—
808C2×C11—42no—
809C2×C11—42no—
810C2×C11C2×#51811yescharacteristic
811C2×C11C2×#51812yes—
812C2×C11#353212yes—
813C2×C11#353211yescharacteristic
814C2×C11#353211yescharacteristic
815D11—24no—
816D11—28no—
817D11—42no—
818D11—42no—
819C24—41no—
820C24—42no—
821C24—42no—
822C24—41no—
823C24—111no—
824C24—112no—
825C24—111no—
826C24—111no—
827C24—118no—
828C24—114no—
829C24—114no—
830C24—118no—
831C24—114no—
832C24—224no—
833C24—224no—
834C24—224no—
835C24—224no—
836C24—224no—
837C24—224no—
838C24—222no—
839C24—222no—
840C24—224no—
841C24—224no—
842C24—222no—
843C24—222no—
844C24—442no—
845C24—442no—
846C24—442no—
847C24—442no—
848C24—442no—
849C24—442no—
850C24—441no—
851C24—441no—
852C24—442no—
853C24—442no—
854C24—442no—
855C24—442no—
856C24—4416no—
857C24—4432no—
858C24—4432no—
859C24—4416no—
860C24—4416no—
861C24C2×C4×D1114yes—
862C24C23×D1111yescharacteristic
863C24C23×D1112yes—
864C24C23×D1111yescharacteristic
865C2×D4—41no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—41no—
869C2×D4—118no—
870C2×D4—114no—
871C2×D4—114no—
872C2×D4—118no—
873C2×D4—118no—
874C2×D4—114no—
875C2×D4—224no—
876C2×D4—224no—
877C2×D4—224no—
878C2×D4—224no—
879C2×D4—441no—
880C2×D4—441no—
881C2×D4—4416no—
882C2×D4—441no—
883C2×D4—441no—
884C2×D4—442no—
885C2×D4—442no—
886C2×D4—441no—
887C2×D4—441no—
888C2×D4—4432no—
889C2×D4C2×C4×D1114yes—
890C2×D4C2×C4×D1118yes—
891C22×C4—41no—
892C22×C4—42no—
893C22×C4—111no—
894C22×C4—112no—
895C22×C4—114no—
896C22×C4—118no—
897C22×C4—112no—
898C22×C4—112no—
899C22×C4—112no—
900C22×C4—112no—
901C22×C4—222no—
902C22×C4—222no—
903C22×C4—224no—
904C22×C4—224no—
905C22×C4—224no—
906C22×C4—224no—
907C22×C4—442no—
908C22×C4—442no—
909C22×C4—442no—
910C22×C4—442no—
911C22×C4—442no—
912C22×C4—442no—
913C22×C4—442no—
914C22×C4—442no—
915C22×C4—442no—
916C22×C4—442no—
917C22×C4—442no—
918C22×C4—442no—
919C22×C4—442no—
920C22×C4—441no—
921C22×C4—442no—
922C22×C4C23×D1112yes—
923C22×C4C23×D1112yes—
924C22×C4C23×D1112yes—
925C22×C4C23×D1112yes—
926C22×C4C23×D1111yescharacteristic
927C22×C4C23×D1112yes—
928C4⋊C4—41no—
929C4⋊C4—42no—
930C4⋊C4—442no—
931C4⋊C4—441no—
932C4⋊C4—442no—
933C4⋊C4—442no—
934C4⋊C4—442no—
935C22⋊C4—42no—
936C22⋊C4—42no—
937C22⋊C4—42no—
938C22⋊C4—42no—
939C22⋊C4—42no—
940C22⋊C4—42no—
941C22⋊C4—41no—
942C22⋊C4—42no—
943C22⋊C4—118no—
944C22⋊C4—114no—
945C22⋊C4—118no—
946C22⋊C4—118no—
947C22⋊C4—118no—
948C22⋊C4—224no—
949C22⋊C4—224no—
950C22⋊C4—224no—
951C22⋊C4—224no—
952C22⋊C4—224no—
953C22⋊C4—224no—
954C22⋊C4—224no—
955C22⋊C4—224no—
956C22⋊C4—442no—
957C22⋊C4—442no—
958C22⋊C4—442no—
959C22⋊C4—442no—
960C22⋊C4—442no—
961C22⋊C4—442no—
962C22⋊C4—442no—
963C22⋊C4—442no—
964C22⋊C4—442no—
965C22⋊C4—442no—
966C22⋊C4—442no—
967C22⋊C4—442no—
968C22⋊C4—441no—
969C22⋊C4—442no—
970C22⋊C4—442no—
971C22⋊C4C2×C4×D1118yes—
972C22⋊C4C2×C4×D1114yes—
973C42—41no—
974C42—42no—
975C42—441no—
976C42—442no—
977C42—442no—
978C42—442no—
979C42—442no—
980C11#3435611yescharacteristic, complemented, Sylow
981C23—21no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—21no—
991C23—21no—
992C23—22no—
993C23—22no—
994C23—21no—
995C23—44no—
996C23—48no—
997C23—48no—
998C23—44no—
999C23—44no—
1000C23—114no—
1001C23—112no—
1002C23—112no—
1003C23—112no—
1004C23—114no—
1005C23—114no—
1006C23—112no—
1007C23—112no—
1008C23—228no—
1009C23—2216no—
1010C23—2216no—
1011C23—2216no—
1012C23—2216no—
1013C23—228no—
1014C23—222no—
1015C23—222no—
1016C23—222no—
1017C23—222no—
1018C23—222no—
1019C23—222no—
1020C23—221no—
1021C23—222no—
1022C23—222no—
1023C23—222no—
1024C23—222no—
1025C23—221no—
1026C23—221no—
1027C23—221no—
1028C23—444no—
1029C23—448no—
1030C23—448no—
1031C23—448no—
1032C23—448no—
1033C23—448no—
1034C23—448no—
1035C23—444no—
1036C23—448no—
1037C23—448no—
1038C23—448no—
1039C23—444no—
1040C23—448no—
1041C23—448no—
1042C23—448no—
1043C23—448no—
1044C23—448no—
1045C23—444no—
1046C23—448no—
1047C23—444no—
1048C23—44128no—
1049C23—882no—
1050C23—884no—
1051C23—882no—
1052C23C22×C4×D1114yes—
1053C23C22×C4×D1112yes—
1054C23C22×C4×D1112yes—
1055C23C24×D1111yescharacteristic
1056D4—44no—
1057D4—48no—
1058D4—2216no—
1059D4—2216no—
1060D4—444no—
1061D4—444no—
1062D4—444no—
1063D4—448no—
1064C2×C4—21no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—21no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—82no—
1081C2×C4—112no—
1082C2×C4—114no—
1083C2×C4—228no—
1084C2×C4—221no—
1085C2×C4—222no—
1086C2×C4—222no—
1087C2×C4—221no—
1088C2×C4—222no—
1089C2×C4—222no—
1090C2×C4—222no—
1091C2×C4—222no—
1092C2×C4—222no—
1093C2×C4—222no—
1094C2×C4—222no—
1095C2×C4—222no—
1096C2×C4—222no—
1097C2×C4—222no—
1098C2×C4—222no—
1099C2×C4—222no—
1100C2×C4—448no—
1101C2×C4—884no—
1102C2×C4—884no—
1103C2×C4—884no—
1104C2×C4—884no—
1105C2×C4—884no—
1106C2×C4—882no—
1107C2×C4C22×C4×D1112yes—
1108C2×C4C22×C4×D1114yes—
1109C22—24no—
1110C22—22no—
1111C22—24no—
1112C22—22no—
1113C22—24no—
1114C22—24no—
1115C22—24no—
1116C22—416no—
1117C22—41no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—41no—
1122C22—42no—
1123C22—42no—
1124C22—41no—
1125C22—41no—
1126C22—42no—
1127C22—114no—
1128C22—118no—
1129C22—224no—
1130C22—224no—
1131C22—224no—
1132C22—224no—
1133C22—222no—
1134C22—224no—
1135C22—222no—
1136C22—224no—
1137C22—224no—
1138C22—224no—
1139C22—224no—
1140C22—222no—
1141C22—222no—
1142C22—224no—
1143C22—4432no—
1144C22—4416no—
1145C22—4416no—
1146C22—4432no—
1147C22—442no—
1148C22—442no—
1149C22—441no—
1150C22—441no—
1151C22—441no—
1152C22—441no—
1153C22—888no—
1154C22C23×C4×D1111yescharacteristic
1155C22D11×H(5,𝔽2)11yescharacteristic
1156C22D11×H(5,𝔽2)12yes—
1157C22D11×H(5,𝔽2)12yes—
1158C22D11×H(5,𝔽2)11yescharacteristic
1159C4—22no—
1160C4—24no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—42no—
1165C4—222no—
1166C4—224no—
1167C4—442no—
1168C4—442no—
1169C4—442no—
1170C4—442no—
1171C2—44no—
1172C2—42no—
1173C2—42no—
1174C2—224no—
1175C2—228no—
1176C2—442no—
1177C2—442no—
1178C2D11×#51811yescharacteristic
1179C2D11×#51812yes—
1180C2#1308276912yes—
1181C2#1308276911yescharacteristic
1182C2#1308277311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2375C2
socle, cosocleC23×C11C25
prime radicalC2×D11×#120C2
hypercenter#2375D11
hypocenterC11#34356
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2375

Complements

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

NH ≅ G/Ntype
2. #13071757C2semidirect
3. #13071755C2semidirect
4. #13071599C2semidirect
5. #13071597C2semidirect
6. #13071594C2semidirect
7. #13071464C2semidirect
8. #13071460C2semidirect
9. #13071437C2semidirect
10. #13071434C2semidirect
11. #13071278C2semidirect
12. #13071275C2semidirect
13. #13071272C2semidirect
14. #13071269C2semidirect
15. #13071210C2semidirect
16. #13071195C2semidirect
17. #13071190C2semidirect
18. D11×#379C2semidirect
19. C11×#2375C2semidirect
27. C2×C4×C22⋊D11C22semidirect
28. C22×(C2×D11)⋊C4C22semidirect
29. D11×#120C4semidirect
30. C2×#66946C22semidirect
31. C2×#66945C22semidirect
34. C2×(C22⋊D11)⋊C4C22semidirect
39. C2×C22⋊C4×D11C22semidirect
40. C2×C22⋊C4×D11C22semidirect
41. C2×C22⋊C4×D11C22semidirect
42. C2×C22⋊C4×D11C22semidirect
43. C2×C22⋊C4×D11C22semidirect
44. C2×C4×D44C22semidirect
45. C2×#66925C22semidirect
46. C11×#390C22semidirect
47. C11×#390C22semidirect
48. C11×#388C22semidirect
49. C11×#388C22semidirect
50. C11×#388C22semidirect
51. C11×#386C22semidirect
52. C11×#386C22semidirect
53. C11×#379C22semidirect
54. #10622860C22semidirect
55. #10622834C22semidirect
56. #10622834C22semidirect
57. #10622833C22semidirect
58. #10622833C22semidirect
59. #10622826C22semidirect
60. #10622603C22semidirect
61. #10622602C22semidirect
62. #10622602C22semidirect
63. #10622601C22semidirect
64. #10622600C22semidirect
65. #10622571C22semidirect
66. #10622570C22semidirect
67. #10622570C22semidirect
68. #10622570C22semidirect
69. #10622570C22semidirect
70. #10622569C22semidirect
71. #10622569C22semidirect
72. #10622569C22semidirect
73. #10622569C22semidirect
74. #10622569C22semidirect
79. #10622568C22semidirect
80. #10622568C22semidirect
81. #10622568C22semidirect
82. #10622564C22semidirect
83. #10622564C22semidirect
84. #10622564C22semidirect
85. #10622558C22semidirect
86. #10622558C22semidirect
87. #10622558C22semidirect
88. #10622557C22semidirect
89. #10622557C22semidirect
90. #10622557C22semidirect
91. #10622553C22semidirect
92. #10622552C22semidirect
93. C4×(C2×D11)⋊C4C22semidirect
94. C4×(C2×D11)⋊C4C22semidirect
95. C4×(C2×D11)⋊C4C22semidirect
96. #10622283C22semidirect
97. #10622282C22semidirect
98. #10622281C22semidirect
99. #10622281C22semidirect
100. #10622280C22semidirect
101. #10622279C22semidirect
102. #10622279C22semidirect
103. #10622279C22semidirect
104. #10622278C22semidirect
105. #10622278C22semidirect
106. #10622278C22semidirect
107. #10622277C22semidirect
113. C24×D11C2×C4semidirect
121. C23×C4×C11C23semidirect
126. C23×Dic11C23semidirect
131. C2×D4×D11C2×C4semidirect
132. C2×D4×D11C2×C4semidirect
141. C22×C4×D11C23semidirect
142. C11×#120C2×C4semidirect
143. C2×C11×C4⋊C4C23semidirect
144. C2×C11×C4⋊C4C23semidirect
153. C2×C11×C22⋊C4C23semidirect
154. C2×C11×C22⋊C4C23semidirect
155. C2×C42×C11C23semidirect
156. C2×C42×C11C23semidirect
157. #67006C2×C4semidirect
166. C2×C22⋊Dic11C23semidirect
167. C2×C22⋊Dic11C23semidirect
168. #66990C2×C4semidirect
169. #66990C2×C4semidirect
187. C2×(C2×D11)⋊C4C23semidirect
188. C2×(C2×D11)⋊C4C23semidirect
189. C2×(C2×D11)⋊C4C23semidirect
190. C2×C4⋊Dic11C23semidirect
191. C2×C4⋊Dic11C23semidirect
192. C2×Dic11⋊C4C23semidirect
193. C2×Dic11⋊C4C23semidirect
194. C2×Dic11⋊C4C23semidirect
195. C2×C4×Dic11C23semidirect
196. C2×C4×Dic11C23semidirect
197. C2×C4×Dic11C23semidirect
198. C2×C4×Dic11C23semidirect
199. C2×C4×Dic11C23semidirect
202. #66935C2×C4semidirect
203. #66935C2×C4semidirect
212. C22⋊C4×D11C2×C4semidirect
213. C22⋊C4×D11C2×C4semidirect
216. C11×#95C23semidirect
217. C11×#95C23semidirect
218. C11×#95C23semidirect
219. C11⋊#95C23semidirect
220. C11⋊#95C23semidirect
221. C11⋊#95C23semidirect
222. C11⋊#95C23semidirect
223. C11⋊#95C23semidirect
224. C11⋊#95C23semidirect
225. C11⋊#95C23semidirect
226. C11⋊#95C23semidirect
227. C11⋊#95C23semidirect
393. #2375D11semidirect
571. #390C2×D11semidirect
572. #390C2×D11semidirect
586. #388C2×D11semidirect
587. #388C2×D11semidirect
588. #388C2×D11semidirect
601. #386C2×D11semidirect
602. #386C2×D11semidirect
618. #379C2×D11semidirect
720. C23×C4C22×D11semidirect
726. #120C4×D11semidirect
738. C2×C4⋊C4C22×D11semidirect
739. C2×C4⋊C4C22×D11semidirect
786. C2×C22⋊C4C22×D11semidirect
787. C2×C22⋊C4C22×D11semidirect
793. C2×C42C22×D11semidirect
794. C2×C42C22×D11semidirect
804. #95C22×D11semidirect
805. #95C22×D11semidirect
806. #95C22×D11semidirect
980. C11#34356semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1202
#130717572
#130717552
#130715992
#130715972
#130715942
#130714642
#130714602
#130714372
#130714342
#130712782
#130712752
#130712722
#130712692
#130712102
#130711952
#130711902
D11×#3792
C11×#23752
#3435611