Finite Group Databasebeta

← #14916496

Subgroups — #14916496

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#13071756C212yesmaximal, complemented
3#13071754C211yesmaximal, characteristic, complemented
4#13071753C211yesmaximal, characteristic, complemented
5#13071600C211yesmaximal, characteristic, complemented
6#13071595C212yesmaximal, complemented
7#13071463C212yesmaximal, complemented
8#13071459C212yesmaximal, complemented
9#13071434C212yesmaximal, complemented
10D4×(C2×D11)⋊C4C212yesmaximal, complemented
11#13071279C212yesmaximal, complemented
12#13071276C212yesmaximal, complemented
13#13071273C212yesmaximal, complemented
14#13071270C212yesmaximal, complemented
15#13071210C212yesmaximal, complemented
16#13071195C211yesmaximal, characteristic, complemented
17#13071190C211yesmaximal, characteristic, complemented
18C2×#10622568C212yesmaximal, complemented
19C11×#2358C211yesmaximal, characteristic, complemented
20C25×D11C2211yescharacteristic
21C22×D4×D11C2212yes—
22C22×D4×D11C2211yescharacteristic
23C2×C11×#120C2211yescharacteristic
24C2×C4×D4×C11C2212yescomplemented
25C22×C11×C22⋊C4C2212yescomplemented
26C2×#67006C2211yescharacteristic
27C22×C22⋊Dic11C2212yescomplemented
28C2×#66990C2211yescharacteristic
29C2×#66990C2212yes—
30C2×D4×Dic11C2212yescomplemented
31C2×C4×C22⋊D11C2212yescomplemented
32C22×(C2×D11)⋊C4C2212yes—
33C22×(C2×D11)⋊C4C2212yes—
34C22×(C2×D11)⋊C4C2212yescomplemented
35C22×(C2×D11)⋊C4C2212yescomplemented
36C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
37D11×#120C4116yescomplemented
38C2×#66945C2211yescharacteristic, complemented
39C2×#66935C2211yescharacteristic
40C2×#66935C2212yes—
41C2×(C22⋊D11)⋊C4C2212yescomplemented
42C2×C22⋊C4×D11C2212yes—
43C2×C22⋊C4×D11C2211yescharacteristic
44C2×C22⋊C4×D11C2211yescharacteristic, complemented
45C2×#66925C2211yescharacteristic, complemented
46C11×#390C2211yescharacteristic, complemented
47C11×#388C2212yescomplemented
48C11×#386C2211yescharacteristic, complemented
49C11×#386C2212yescomplemented
50C11×#385C2212yescomplemented
51C4×C11×C22⋊C4C2212yescomplemented
52#10622834C2211yescharacteristic, complemented
53#10622833C2211yescharacteristic, complemented
54#10622833C2212yescomplemented
55#10622826C2212yescomplemented
56#10622826C2211yescharacteristic, complemented
57#10622826C2212yescomplemented
58#10622823C2212yescomplemented
59C4×C22⋊Dic11C2212yescomplemented
60#10622603C2212yescomplemented
61#10622603C2212yescomplemented
62#10622603C2212yescomplemented
63#10622601C2212yescomplemented
64#10622601C2211yescharacteristic, complemented
65#10622600C2212yescomplemented
66#10622571C2212yescomplemented
67#10622571C2211yescharacteristic, complemented
68#10622571C2212yescomplemented
69#10622570C2212yescomplemented
70#10622570C2212yescomplemented
71#10622570C2212yescomplemented
72#10622570C2212yescomplemented
73#10622569C2212yescomplemented
74#10622568C2212yes—
75#10622568C2212yes—
76#10622568C2212yes—
77#10622568C2212yes—
78#10622568C2212yescomplemented
79#10622568C2212yescomplemented
80#10622568C2212yescomplemented
81#10622568C2212yescomplemented
82#10622568C2212yescomplemented
83#10622564C2212yescomplemented
84#10622563C2212yescomplemented
85#10622559C2212yescomplemented
86#10622558C2212yescomplemented
87#10622557C2212yescomplemented
88C22⋊C4×Dic11C2212yescomplemented
89C22⋊C4×Dic11C2212yescomplemented
90#10622553C2212yescomplemented
91#10622553C2212yescomplemented
92#10622553C2212yescomplemented
93#10622552C2212yescomplemented
94#10622552C2211yescharacteristic, complemented
95C4×(C2×D11)⋊C4C2212yescomplemented
96#10622283C2212yescomplemented
97#10622283C2212yescomplemented
98#10622283C2212yescomplemented
99#10622282C2212yescomplemented
100#10622282C2212yescomplemented
101#10622282C2212yescomplemented
102#10622280C2212yescomplemented
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×C11C2312yes—
122C23×C4×C11C2312yes—
123C23×C4×C11C2311yescharacteristic, complemented
124C22×C22⋊D11C2312yes—
125C22×C22⋊D11C2311yescharacteristic
126C22×C22⋊D11C2312yes—
127C22×C22⋊D11C2311yescharacteristic
128C23×Dic11C2312yes—
129C23×Dic11C2312yes—
130C23×Dic11C2311yescharacteristic, complemented
131C2×D4×D11—42no—
132C2×D4×D11—42no—
133C2×D4×D11—44no—
134C2×D4×D11—44no—
135C2×D4×D11C2×C418yescomplemented
136C2×D4×D11C2×C4116yescomplemented
137C22×D44C2312yes—
138C22×D44C2311yescharacteristic
139C22×C4×D11C2311yescharacteristic
140C22×C4×D11C2312yes—
141C22×C4×D11C2312yescomplemented
142C11×#120C2×C418yescomplemented
143C4×D4×C11—44no—
144C2×C11×C4⋊C4C2311yescharacteristic, complemented
145C2×C11×C4⋊C4C2312yescomplemented
146C2×C11×C22⋊C4—44no—
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⋊Dic11—44no—
159C2×C22⋊Dic11C2312yes—
160C2×C22⋊Dic11C2312yes—
161C2×C22⋊Dic11C2312yes—
162C2×C22⋊Dic11C2312yes—
163C2×C22⋊Dic11C2312yes—
164C2×C22⋊Dic11C2311yescharacteristic
165C2×C22⋊Dic11C2311yescharacteristic, complemented
166C2×C22⋊Dic11C2312yescomplemented
167#66990C2×C4116yescomplemented
168#66990C2×C418yescomplemented
169D4×Dic11—44no—
170C4×C22⋊D11—44no—
171C2×(C2×D11)⋊C4—44no—
172C2×(C2×D11)⋊C4—44no—
173C2×(C2×D11)⋊C4—42no—
174C2×(C2×D11)⋊C4—44no—
175C2×(C2×D11)⋊C4—44no—
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)⋊C4C2312yes—
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2312yes—
195C2×(C2×D11)⋊C4C2312yescomplemented
196C2×(C2×D11)⋊C4C2312yescomplemented
197C2×(C2×D11)⋊C4C2312yescomplemented
198C2×C4⋊Dic11C2311yescharacteristic, complemented
199C2×C4⋊Dic11C2312yescomplemented
200C2×Dic11⋊C4C2312yescomplemented
201C2×Dic11⋊C4C2312yescomplemented
202C2×Dic11⋊C4C2312yescomplemented
203C2×C4×Dic11C2311yescharacteristic, complemented
204C2×C4×Dic11C2312yescomplemented
205C2×C4×Dic11C2312yescomplemented
206C2×C4×Dic11C2312yescomplemented
207C2×C4×Dic11C2312yescomplemented
208#66945—42no—
209#66935C2×C4116yescomplemented
210#66935C2×C418yescomplemented
211(C22⋊D11)⋊C4—44no—
212C22⋊C4×D11—42no—
213C22⋊C4×D11C2×C4116yescomplemented
214C22⋊C4×D11C2×C418yescomplemented
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—24no—
230C24×C11—24no—
231C24×C11—41no—
232C24×C11—41no—
233C24×C11C22×C414yes—
234C24×C11C2411yescharacteristic
235C24×C11C2411yescharacteristic
236C24×C11C2412yes—
237C23×D11—24no—
238C23×D11—24no—
239C23×D11—24no—
240C23×D11—24no—
241C23×D11—24no—
242C23×D11—24no—
243C23×D11—22no—
244C23×D11—22no—
245C23×D11—22no—
246C23×D11—22no—
247C23×D11—416no—
248C23×D11—432no—
249C23×D11—42no—
250C23×D11—42no—
251C23×D11—42no—
252C23×D11—42no—
253C23×D11—41no—
254C23×D11—41no—
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—416no—
264C23×D11—432no—
265C23×D11—416no—
266C23×D11C22×C418yes—
267C23×D11C22×C414yes—
268C23×D11C22×C418yes—
269C23×D11C22×C414yes—
270C23×D11C22×C414yes—
271C23×D11C2412yes—
272C23×D11C2411yescharacteristic
273C23×D11C2411yescharacteristic
274C23×D11C2411yescharacteristic
275C2×D4×C11—24no—
276C2×D4×C11—24no—
277C2×D4×C11—41no—
278C2×D4×C11—41no—
279C2×D4×C11C22×C418yes—
280C2×D4×C11C22×C414yes—
281C22×C4×C11—24no—
282C22×C4×C11—24no—
283C22×C4×C11—42no—
284C22×C4×C11—42no—
285C22×C4×C11—41no—
286C22×C4×C11—42no—
287C22×C4×C11—42no—
288C22×C4×C11—42no—
289C22×C4×C11C2412yes—
290C22×C4×C11C2412yes—
291C22×C4×C11C2412yes—
292C22×C4×C11C2412yes—
293C22×C4×C11C2412yes—
294C22×C4×C11C2411yescharacteristic
295C2×C22⋊D11—24no—
296C2×C22⋊D11—24no—
297C2×C22⋊D11—41no—
298C2×C22⋊D11—41no—
299C2×C22⋊D11—41no—
300C2×C22⋊D11—42no—
301C2×C22⋊D11—42no—
302C2×C22⋊D11—41no—
303C2×C22⋊D11C22×C418yes—
304C2×C22⋊D11C22×C414yes—
305C2×C22⋊D11C22×C418yes—
306C2×C22⋊D11C22×C414yes—
307C22×Dic11—24no—
308C22×Dic11—24no—
309C22×Dic11—42no—
310C22×Dic11—42no—
311C22×Dic11—41no—
312C22×Dic11—42no—
313C22×Dic11—42no—
314C22×Dic11—42no—
315C22×Dic11C2412yes—
316C22×Dic11C2412yes—
317C22×Dic11C2412yes—
318C22×Dic11C2412yes—
319C22×Dic11C2411yescharacteristic
320C22×Dic11C2412yes—
321D4×D11—432no—
322D4×D11—416no—
323C2×D44—42no—
324C2×D44—41no—
325C2×D44—41no—
326C2×D44—42no—
327C2×D44C22×C418yes—
328C2×D44C22×C414yes—
329C2×C4×D11—22no—
330C2×C4×D11—22no—
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—24no—
341C11×C22⋊C4—24no—
342C11×C22⋊C4—41no—
343C11×C22⋊C4—42no—
344C11×C22⋊C4—42no—
345C11×C22⋊C4—42no—
346C11×C22⋊C4C22×C414yes—
347C11×C22⋊C4C22×C418yes—
348C42×C11—41no—
349C42×C11—42no—
350C22⋊Dic11—24no—
351C22⋊Dic11—24no—
352C22⋊Dic11—41no—
353C22⋊Dic11—42no—
354C22⋊Dic11—42no—
355C22⋊Dic11—42no—
356C22⋊Dic11C22×C414yes—
357C22⋊Dic11C22×C418yes—
358(C2×D11)⋊C4—24no—
359(C2×D11)⋊C4—24no—
360(C2×D11)⋊C4—24no—
361(C2×D11)⋊C4—24no—
362(C2×D11)⋊C4—42no—
363(C2×D11)⋊C4—42no—
364(C2×D11)⋊C4—42no—
365(C2×D11)⋊C4—42no—
366(C2×D11)⋊C4—42no—
367(C2×D11)⋊C4—42no—
368(C2×D11)⋊C4—42no—
369(C2×D11)⋊C4—42no—
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—41no—
381C4⋊Dic11—42no—
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—111no—
392#2375—112no—
393#2375—111no—
394#2358—111no—
395#2358—112no—
396#2358D1111yescharacteristic, complemented
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—22no—
410C23×C11—22no—
411C23×C11—22no—
412C23×C11—22no—
413C23×C11—216no—
414C23×C11—22no—
415C23×C11—21no—
416C23×C11—22no—
417C23×C11—22no—
418C23×C11—22no—
419C23×C11—21no—
420C23×C11—21no—
421C23×C11—21no—
422C23×C11—44no—
423C23×C11—44no—
424C23×C11—48no—
425C23×C11—44no—
426C23×C11C23×C412yes—
427C23×C11C23×C412yes—
428C23×C11C23×C414yes—
429C23×C11H(5,𝔽2)14yes—
430C23×C11H(5,𝔽2)14yes—
431C23×C11C2511yescharacteristic
432C22×D11—22no—
433C22×D11—22no—
434C22×D11—216no—
435C22×D11—216no—
436C22×D11—21no—
437C22×D11—22no—
438C22×D11—22no—
439C22×D11—22no—
440C22×D11—22no—
441C22×D11—22no—
442C22×D11—22no—
443C22×D11—22no—
444C22×D11—22no—
445C22×D11—21no—
446C22×D11—22no—
447C22×D11—22no—
448C22×D11—21no—
449C22×D11—21no—
450C22×D11—28no—
451C22×D11—216no—
452C22×D11—28no—
453C22×D11—48no—
454C22×D11—48no—
455C22×D11—44no—
456C22×D11—48no—
457C22×D11—48no—
458C22×D11—48no—
459C22×D11—48no—
460C22×D11—48no—
461C22×D11—48no—
462C22×D11—48no—
463C22×D11—48no—
464C22×D11—48no—
465C22×D11—44no—
466C22×D11—44no—
467C22×D11—48no—
468C22×D11—48no—
469C22×D11—48no—
470C22×D11—48no—
471C22×D11—4128no—
472C22×D11—48no—
473C22×D11—44no—
474C22×D11—44no—
475C22×D11—82no—
476C22×D11—82no—
477C22×D11—84no—
478C22×D11C23×C414yes—
479C22×D11C23×C412yes—
480C22×D11C23×C412yes—
481C22×D11C23×C412yes—
482C22×D11H(5,𝔽2)12yes—
483C22×D11H(5,𝔽2)12yes—
484D4×C11—216no—
485D4×C11—44no—
486C2×C4×C11—22no—
487C2×C4×C11—21no—
488C2×C4×C11—21no—
489C2×C4×C11—22no—
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—84no—
503C2×C4×C11—84no—
504C2×C4×C11—82no—
505C2×C4×C11C23×C414yes—
506C2×C4×C11C23×C412yes—
507C22⋊D11—216no—
508C22⋊D11—44no—
509C22⋊D11—44no—
510C22⋊D11—48no—
511C2×Dic11—21no—
512C2×Dic11—22no—
513C2×Dic11—22no—
514C2×Dic11—21no—
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—22no—
526C2×Dic11—22no—
527C2×Dic11—84no—
528C2×Dic11—84no—
529C2×Dic11—82no—
530C2×Dic11C23×C412yes—
531C2×Dic11C23×C414yes—
532D44—48no—
533D44—44no—
534C4×D11—28no—
535C4×D11—48no—
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×D4C2×D1112yescomplemented
551C2×#117—111no—
552C2×#117—111no—
553C22×C22⋊C4—111no—
554C22×C22⋊C4—112no—
555C22×C22⋊C4—112no—
556C22×C22⋊C4—112no—
557C22×C22⋊C4—112no—
558C22×C22⋊C4—112no—
559C22×C22⋊C4—112no—
560C22×C22⋊C4—111no—
561C22×C22⋊C4—111no—
562C22×C22⋊C4C2×D1112yescomplemented
563#390—111no—
564#390—111no—
565#390—112no—
566#390—112no—
567#390—112no—
568#390—112no—
569#390—112no—
570#390—111no—
571#390—112no—
572#390C2×D1111yescharacteristic, complemented
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#388—112no—
587#388—112no—
588#388C2×D1112yescomplemented
589#386—111no—
590#386—112no—
591#386—112no—
592#386—111no—
593#386—112no—
594#386—112no—
595#386—112no—
596#386—111no—
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#385C2×D1112yescomplemented
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#379—112no—
619C4×C22⋊C4—112no—
620C4×C22⋊C4—112no—
621C4×C22⋊C4—112no—
622C4×C22⋊C4—112no—
623C4×C22⋊C4—112no—
624C4×C22⋊C4C2×D1112yescomplemented
625C22×C11—24no—
626C22×C11—24no—
627C22×C11—24no—
628C22×C11—24no—
629C22×C11—24no—
630C22×C11—24no—
631C22×C11—24no—
632C22×C11—22no—
633C22×C11—22no—
634C22×C11—24no—
635C22×C11—416no—
636C22×C11—41no—
637C22×C11—42no—
638C22×C11—41no—
639C22×C11—41no—
640C22×C11—42no—
641C22×C11—41no—
642C22×C11#51818yes—
643C22×C11C24×C411yescharacteristic
644C22×C11C2×H(5,𝔽2)12yes—
645C22×C11C2×H(5,𝔽2)12yes—
646C22×C11C2×H(5,𝔽2)11yescharacteristic
647C22×C11C2×H(5,𝔽2)11yescharacteristic
648C2×D11—24no—
649C2×D11—24no—
650C2×D11—22no—
651C2×D11—22no—
652C2×D11—24no—
653C2×D11—24no—
654C2×D11—24no—
655C2×D11—22no—
656C2×D11—24no—
657C2×D11—22no—
658C2×D11—24no—
659C2×D11—432no—
660C2×D11—416no—
661C2×D11—432no—
662C2×D11—416no—
663C2×D11—42no—
664C2×D11—42no—
665C2×D11—42no—
666C2×D11—42no—
667C2×D11—41no—
668C2×D11—42no—
669C2×D11—41no—
670C2×D11—41no—
671C2×D11—41no—
672C2×D11—42no—
673C2×D11—88no—
674C2×D11#51814yes—
675C4×C11—24no—
676C4×C11—22no—
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—112no—
688C25—112no—
689C25—111no—
690C25—111no—
691C25—118no—
692C25—111no—
693C25—444no—
694C25—444no—
695C25—442no—
696C25—442no—
697C25C22×D1111yescharacteristic
698C22×D4—112no—
699C22×D4—111no—
700C22×D4—112no—
701C22×D4—111no—
702C22×D4—118no—
703C22×D4—1116no—
704C22×D4—111no—
705C22×D4—112no—
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—112no—
715C23×C4—112no—
716C23×C4—111no—
717C23×C4—112no—
718C23×C4C22×D1112yes—
719C23×C4C22×D1112yes—
720C23×C4C22×D1111yescharacteristic, complemented
721#120—118no—
722#120—1116no—
723#120—118no—
724#120—1116no—
725#120—118no—
726#120C4×D1118yescomplemented
727C4×D4—44no—
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—44no—
741C2×C22⋊C4—112no—
742C2×C22⋊C4—111no—
743C2×C22⋊C4—112no—
744C2×C22⋊C4—112no—
745C2×C22⋊C4—112no—
746C2×C22⋊C4—1116no—
747C2×C22⋊C4—118no—
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—111no—
757C2×C22⋊C4—112no—
758C2×C22⋊C4—112no—
759C2×C22⋊C4—112no—
760C2×C22⋊C4—112no—
761C2×C22⋊C4—112no—
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—112no—
771C2×C22⋊C4—112no—
772C2×C22⋊C4—112no—
773C2×C22⋊C4—442no—
774C2×C22⋊C4—442no—
775C2×C22⋊C4—444no—
776C2×C22⋊C4—444no—
777C2×C22⋊C4—444no—
778C2×C22⋊C4—444no—
779C2×C22⋊C4—444no—
780C2×C22⋊C4C22×D1112yes—
781C2×C22⋊C4C22×D1112yes—
782C2×C22⋊C4C22×D1112yes—
783C2×C22⋊C4C22×D1112yes—
784C2×C22⋊C4C22×D1112yes—
785C2×C22⋊C4C22×D1111yescharacteristic
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—28no—
808C2×C11—42no—
809C2×C11—42no—
810C2×C11C2×#51811yescharacteristic
811C2×C11C2×#51812yes—
812C2×C11#353212yes—
813C2×C11#353211yescharacteristic
814C2×C11#353211yescharacteristic
815D11—24no—
816D11—44no—
817D11—42no—
818D11—42no—
819C24—24no—
820C24—24no—
821C24—41no—
822C24—41no—
823C24—111no—
824C24—111no—
825C24—112no—
826C24—111no—
827C24—118no—
828C24—114no—
829C24—118no—
830C24—114no—
831C24—114no—
832C24—224no—
833C24—224no—
834C24—222no—
835C24—222no—
836C24—222no—
837C24—222no—
838C24—224no—
839C24—224no—
840C24—224no—
841C24—224no—
842C24—442no—
843C24—442no—
844C24—442no—
845C24—442no—
846C24—442no—
847C24—442no—
848C24—4432no—
849C24—442no—
850C24—442no—
851C24—442no—
852C24—442no—
853C24—441no—
854C24—441no—
855C24—442no—
856C24—442no—
857C24—4416no—
858C24—4432no—
859C24—4416no—
860C24—4416no—
861C24C2×C4×D1114yes—
862C24C23×D1111yescharacteristic
863C24C23×D1111yescharacteristic
864C24C23×D1112yes—
865C2×D4—24no—
866C2×D4—24no—
867C2×D4—41no—
868C2×D4—41no—
869C2×D4—118no—
870C2×D4—114no—
871C2×D4—118no—
872C2×D4—114no—
873C2×D4—114no—
874C2×D4—118no—
875C2×D4—224no—
876C2×D4—224no—
877C2×D4—442no—
878C2×D4—442no—
879C2×D4—441no—
880C2×D4—441no—
881C2×D4—4416no—
882C2×D4—442no—
883C2×D4—442no—
884C2×D4—441no—
885C2×D4—441no—
886C2×D4—441no—
887C2×D4—441no—
888C2×D4—4432no—
889C2×D4C2×C4×D1118yes—
890C2×D4C2×C4×D1114yes—
891C22×C4—24no—
892C22×C4—24no—
893C22×C4—42no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—41no—
898C22×C4—42no—
899C22×C4—112no—
900C22×C4—111no—
901C22×C4—114no—
902C22×C4—118no—
903C22×C4—112no—
904C22×C4—112no—
905C22×C4—112no—
906C22×C4—112no—
907C22×C4—222no—
908C22×C4—222no—
909C22×C4—224no—
910C22×C4—224no—
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×D1112yes—
927C22×C4C23×D1111yescharacteristic
928C4⋊C4—41no—
929C4⋊C4—42no—
930C4⋊C4—442no—
931C4⋊C4—441no—
932C4⋊C4—442no—
933C4⋊C4—442no—
934C4⋊C4—442no—
935C22⋊C4—24no—
936C22⋊C4—24no—
937C22⋊C4—42no—
938C22⋊C4—42no—
939C22⋊C4—41no—
940C22⋊C4—42no—
941C22⋊C4—114no—
942C22⋊C4—118no—
943C22⋊C4—118no—
944C22⋊C4—118no—
945C22⋊C4—118no—
946C22⋊C4—224no—
947C22⋊C4—224no—
948C22⋊C4—224no—
949C22⋊C4—224no—
950C22⋊C4—224no—
951C22⋊C4—224no—
952C22⋊C4—442no—
953C22⋊C4—442no—
954C22⋊C4—442no—
955C22⋊C4—442no—
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—442no—
969C22⋊C4—441no—
970C22⋊C4—442no—
971C22⋊C4C2×C4×D1114yes—
972C22⋊C4C2×C4×D1118yes—
973C42—41no—
974C42—42no—
975C42—441no—
976C42—442no—
977C42—442no—
978C42—442no—
979C42—442no—
980C11#3435611yescharacteristic, complemented, Sylow
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—216no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—21no—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—44no—
995C23—48no—
996C23—44no—
997C23—44no—
998C23—112no—
999C23—112no—
1000C23—112no—
1001C23—112no—
1002C23—114no—
1003C23—112no—
1004C23—228no—
1005C23—2216no—
1006C23—228no—
1007C23—222no—
1008C23—222no—
1009C23—2216no—
1010C23—2216no—
1011C23—222no—
1012C23—222no—
1013C23—222no—
1014C23—222no—
1015C23—222no—
1016C23—222no—
1017C23—222no—
1018C23—222no—
1019C23—221no—
1020C23—222no—
1021C23—222no—
1022C23—221no—
1023C23—221no—
1024C23—221no—
1025C23—448no—
1026C23—448no—
1027C23—448no—
1028C23—444no—
1029C23—448no—
1030C23—448no—
1031C23—448no—
1032C23—448no—
1033C23—448no—
1034C23—448no—
1035C23—448no—
1036C23—448no—
1037C23—448no—
1038C23—448no—
1039C23—448no—
1040C23—448no—
1041C23—444no—
1042C23—444no—
1043C23—44128no—
1044C23—448no—
1045C23—444no—
1046C23—444no—
1047C23—884no—
1048C23—882no—
1049C23—882no—
1050C23C22×C4×D1112yes—
1051C23C22×C4×D1112yes—
1052C23C22×C4×D1114yes—
1053C23#6703714yes—
1054C23#6704214yes—
1055C23C24×D1111yescharacteristic
1056D4—216no—
1057D4—44no—
1058D4—2216no—
1059D4—444no—
1060D4—448no—
1061D4—444no—
1062D4—444no—
1063D4—448no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—21no—
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—84no—
1081C2×C4—84no—
1082C2×C4—82no—
1083C2×C4—112no—
1084C2×C4—114no—
1085C2×C4—228no—
1086C2×C4—222no—
1087C2×C4—222no—
1088C2×C4—221no—
1089C2×C4—221no—
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—222no—
1101C2×C4—222no—
1102C2×C4—448no—
1103C2×C4—884no—
1104C2×C4—884no—
1105C2×C4—884no—
1106C2×C4—882no—
1107C2×C4C22×C4×D1112yes—
1108C2×C4C22×C4×D1114yes—
1109C22—24no—
1110C22—24no—
1111C22—24no—
1112C22—24no—
1113C22—24no—
1114C22—24no—
1115C22—22no—
1116C22—22no—
1117C22—24no—
1118C22—24no—
1119C22—416no—
1120C22—42no—
1121C22—42no—
1122C22—41no—
1123C22—41no—
1124C22—41no—
1125C22—41no—
1126C22—114no—
1127C22—224no—
1128C22—222no—
1129C22—222no—
1130C22—224no—
1131C22—222no—
1132C22—222no—
1133C22—224no—
1134C22—224no—
1135C22—224no—
1136C22—224no—
1137C22—224no—
1138C22—4432no—
1139C22—4432no—
1140C22—4416no—
1141C22—4416no—
1142C22—442no—
1143C22—442no—
1144C22—442no—
1145C22—442no—
1146C22—441no—
1147C22—442no—
1148C22—441no—
1149C22—441no—
1150C22—442no—
1151C22—441no—
1152C22—888no—
1153C22#1062307618yes—
1154C22C23×C4×D1111yescharacteristic
1155C22C2×#6703712yes—
1156C22C2×#6704212yes—
1157C22D11×H(5,𝔽2)11yescharacteristic
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—28no—
1172C2—42no—
1173C2—42no—
1174C2—224no—
1175C2—442no—
1176C2—444no—
1177C2—442no—
1178C2D11×#51811yescharacteristic
1179C2C2×#1062307612yes—
1180C2#1308276512yes—
1181C2#1308276611yescharacteristic
1182C2#1308277211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2358C2
socle, cosocleC23×C11C25
prime radicalC2×D11×#120C2
hypercenter#2358D11
hypocenterC11#34356
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2358

Complements

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

NH ≅ G/Ntype
2. #13071756C2semidirect
3. #13071754C2semidirect
4. #13071753C2semidirect
5. #13071600C2semidirect
6. #13071595C2semidirect
7. #13071463C2semidirect
8. #13071459C2semidirect
9. #13071434C2semidirect
10. D4×(C2×D11)⋊C4C2semidirect
11. #13071279C2semidirect
12. #13071276C2semidirect
13. #13071273C2semidirect
14. #13071270C2semidirect
15. #13071210C2semidirect
16. #13071195C2semidirect
17. #13071190C2semidirect
18. C2×#10622568C2semidirect
19. C11×#2358C2semidirect
24. C2×C4×D4×C11C22semidirect
25. C22×C11×C22⋊C4C22semidirect
27. C22×C22⋊Dic11C22semidirect
30. C2×D4×Dic11C22semidirect
31. C2×C4×C22⋊D11C22semidirect
34. C22×(C2×D11)⋊C4C22semidirect
35. C22×(C2×D11)⋊C4C22semidirect
36. C22×(C2×D11)⋊C4C22semidirect
37. D11×#120C4semidirect
38. C2×#66945C22semidirect
41. C2×(C22⋊D11)⋊C4C22semidirect
44. C2×C22⋊C4×D11C22semidirect
45. C2×#66925C22semidirect
46. C11×#390C22semidirect
47. C11×#388C22semidirect
48. C11×#386C22semidirect
49. C11×#386C22semidirect
50. C11×#385C22semidirect
51. C4×C11×C22⋊C4C22semidirect
52. #10622834C22semidirect
53. #10622833C22semidirect
54. #10622833C22semidirect
55. #10622826C22semidirect
56. #10622826C22semidirect
57. #10622826C22semidirect
58. #10622823C22semidirect
59. C4×C22⋊Dic11C22semidirect
60. #10622603C22semidirect
61. #10622603C22semidirect
62. #10622603C22semidirect
63. #10622601C22semidirect
64. #10622601C22semidirect
65. #10622600C22semidirect
66. #10622571C22semidirect
67. #10622571C22semidirect
68. #10622571C22semidirect
69. #10622570C22semidirect
70. #10622570C22semidirect
71. #10622570C22semidirect
72. #10622570C22semidirect
73. #10622569C22semidirect
78. #10622568C22semidirect
79. #10622568C22semidirect
80. #10622568C22semidirect
81. #10622568C22semidirect
82. #10622568C22semidirect
83. #10622564C22semidirect
84. #10622563C22semidirect
85. #10622559C22semidirect
86. #10622558C22semidirect
87. #10622557C22semidirect
88. C22⋊C4×Dic11C22semidirect
89. C22⋊C4×Dic11C22semidirect
90. #10622553C22semidirect
91. #10622553C22semidirect
92. #10622553C22semidirect
93. #10622552C22semidirect
94. #10622552C22semidirect
95. C4×(C2×D11)⋊C4C22semidirect
96. #10622283C22semidirect
97. #10622283C22semidirect
98. #10622283C22semidirect
99. #10622282C22semidirect
100. #10622282C22semidirect
101. #10622282C22semidirect
102. #10622280C22semidirect
103. #10622279C22semidirect
104. #10622278C22semidirect
105. #10622278C22semidirect
106. #10622278C22semidirect
107. #10622277C22semidirect
113. C24×D11C2×C4semidirect
123. C23×C4×C11C23semidirect
130. C23×Dic11C23semidirect
135. C2×D4×D11C2×C4semidirect
136. C2×D4×D11C2×C4semidirect
141. C22×C4×D11C23semidirect
142. C11×#120C2×C4semidirect
144. C2×C11×C4⋊C4C23semidirect
145. 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
165. C2×C22⋊Dic11C23semidirect
166. C2×C22⋊Dic11C23semidirect
167. #66990C2×C4semidirect
168. #66990C2×C4semidirect
195. C2×(C2×D11)⋊C4C23semidirect
196. C2×(C2×D11)⋊C4C23semidirect
197. C2×(C2×D11)⋊C4C23semidirect
198. C2×C4⋊Dic11C23semidirect
199. C2×C4⋊Dic11C23semidirect
200. C2×Dic11⋊C4C23semidirect
201. C2×Dic11⋊C4C23semidirect
202. C2×Dic11⋊C4C23semidirect
203. C2×C4×Dic11C23semidirect
204. C2×C4×Dic11C23semidirect
205. C2×C4×Dic11C23semidirect
206. C2×C4×Dic11C23semidirect
207. C2×C4×Dic11C23semidirect
209. #66935C2×C4semidirect
210. #66935C2×C4semidirect
213. C22⋊C4×D11C2×C4semidirect
214. 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
396. #2358D11semidirect
550. C2×C4×D4C2×D11semidirect
562. C22×C22⋊C4C2×D11semidirect
572. #390C2×D11semidirect
588. #388C2×D11semidirect
601. #386C2×D11semidirect
602. #386C2×D11semidirect
606. #385C2×D11semidirect
624. C4×C22⋊C4C2×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
#130717562
#130717542
#130717532
#130716002
#130715952
#130714632
#130714592
#130714342
D4×(C2×D11)⋊C42
#130712792
#130712762
#130712732
#130712702
#130712102
#130711952
#130711902
C2×#106225682
C11×#23582
#3435611