Finite Group Databasebeta

← #14917155

Subgroups — #14917155

Order 2816.

2890 conjugacy classes of subgroups.

The subgroup lattice has 1062 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623120C211yesmaximal, characteristic
2#13071768C212yesmaximal, complemented
3#13071759C211yesmaximal, characteristic, complemented
4#13071751C211yesmaximal, characteristic, complemented
5#13071659C212yesmaximal, complemented
6#13071607C212yesmaximal, complemented
7#13071605C212yesmaximal, complemented
8#13071600C211yesmaximal, characteristic, complemented
9#13071464C212yesmaximal, complemented
10#13071432C212yesmaximal, complemented
11#13071411C212yesmaximal, complemented
12#13071379C212yesmaximal, complemented
13#13071304C212yesmaximal, complemented
14#13071275C212yesmaximal, complemented
15#13071271C212yesmaximal, complemented
16#13071195C211yesmaximal, characteristic, complemented
17#13071121C212yesmaximal, complemented
18D11×#386C211yesmaximal, characteristic, complemented
19C11×#2375C211yesmaximal, characteristic, complemented
20C23×C22⋊D11C2211yescharacteristic
21C22×D4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic, complemented
23C2×C11×#120C2211yescharacteristic
24C2×#67006C2211yescharacteristic
25C22×C22⋊Dic11C2212yescomplemented
26C2×#66991C2212yes—
27C2×#66990C2212yes—
28C2×#66988C2211yescharacteristic
29C2×D4×Dic11C2212yescomplemented
30#10623120C4116yescomplemented
31C2×#66945C2212yescomplemented
32C2×#66945C2211yescharacteristic, complemented
33C2×#66939C2211yescharacteristic
34C2×#66937C2212yes—
35C2×#66936C2212yes—
36C2×(C22⋊D11)⋊C4C2212yes—
37C2×(C22⋊D11)⋊C4C2212yes—
38C2×(C22⋊D11)⋊C4C2212yescomplemented
39C2×C22⋊C4×D11C2212yes—
40C2×C22⋊C4×D11C2211yescharacteristic
41C2×C22⋊C4×D11C2211yescharacteristic, complemented
42C2×#66925C2211yescharacteristic, complemented
43C11×#390C2211yescharacteristic
44C11×#390C2212yescomplemented
45C11×#388C2212yescomplemented
46C11×#388C2212yescomplemented
47C11×#388C2212yescomplemented
48C11×#386C2211yescharacteristic
49C11×#386C2212yescomplemented
50C11×#379C2212yescomplemented
51#10622834C2211yescharacteristic
52#10622833C2211yescharacteristic
53#10622833C2212yescomplemented
54#10622826C2211yescharacteristic, complemented
55#10622823C2212yescomplemented
56#10622603C2212yescomplemented
57#10622602C2212yescomplemented
58#10622601C2211yescharacteristic, complemented
59#10622591C2212yescomplemented
60#10622586C2212yescomplemented
61#10622571C2212yescomplemented
62#10622571C2212yescomplemented
63#10622571C2211yescharacteristic, complemented
64#10622571C2212yescomplemented
65#10622570C2212yes—
66#10622570C2212yescomplemented
67#10622570C2212yescomplemented
68#10622570C2212yescomplemented
69#10622570C2212yescomplemented
70#10622569C2212yes—
71#10622569C2212yes—
72#10622569C2212yes—
73#10622569C2212yescomplemented
74#10622568C2212yes—
75#10622568C2212yescomplemented
76#10622564C2212yescomplemented
77#10622563C2212yescomplemented
78#10622559C2212yescomplemented
79#10622558C2212yescomplemented
80#10622558C2212yescomplemented
81#10622558C2212yescomplemented
82#10622558C2212yescomplemented
83#10622557C2212yescomplemented
84#10622557C2212yescomplemented
85#10622555C2212yescomplemented
86C22⋊C4×Dic11C2212yescomplemented
87C22⋊C4×Dic11C2212yescomplemented
88C22⋊C4×Dic11C2212yescomplemented
89C22⋊C4×Dic11C2212yescomplemented
90#10622553C2212yescomplemented
91#10622552C2211yescharacteristic, complemented
92C4×(C2×D11)⋊C4C2212yescomplemented
93C4×(C2×D11)⋊C4C2212yescomplemented
94C4×C4⋊Dic11C2212yescomplemented
95C4×Dic11⋊C4C2212yescomplemented
96#10622281C2212yescomplemented
97#10622281C2212yescomplemented
98#10622280C2212yescomplemented
99#10622279C2212yescomplemented
100#10622279C2212yescomplemented
101#10622278C2212yescomplemented
102#10622277C2212yescomplemented
103D11×#95C2212yescomplemented
104#10622267C2212yescomplemented
105#10622266C2212yescomplemented
106#10622265C2212yescomplemented
107#10622260C2212yescomplemented
108C25×C11C2311yescharacteristic
109C24×D11C2311yescharacteristic
110C24×D11C2311yescharacteristic
111C22×D4×C11C2312yes—
112C22×D4×C11C2311yescharacteristic
113C23×C4×C11C2311yescharacteristic
114C22×C22⋊D11—42no—
115C22×C22⋊D11—42no—
116C22×C22⋊D11C2×C418yescomplemented
117C22×C22⋊D11C2312yes—
118C22×C22⋊D11C2312yes—
119C22×C22⋊D11C2311yescharacteristic
120C22×C22⋊D11C2311yescharacteristic
121C22×C22⋊D11C2312yes—
122C23×Dic11C2311yescharacteristic
123C23×Dic11C2312yes—
124C23×Dic11C2312yes—
125C23×Dic11C2311yescharacteristic
126C2×D4×D11—42no—
127C2×D4×D11—42no—
128C2×D4×D11C2×C418yescomplemented
129C22×D44C2311yescharacteristic
130C22×C4×D11—44no—
131C22×C4×D11—42no—
132C22×C4×D11C2312yes—
133C22×C4×D11C2311yescharacteristic
134C22×C4×D11C2312yes—
135C22×C4×D11C2312yes—
136C22×C4×D11C2312yes—
137C11×#120C2×C418yescomplemented
138C2×C11×C4⋊C4C2312yes—
139C2×C11×C4⋊C4C2311yescharacteristic
140C2×C11×C22⋊C4C2312yes—
141C2×C11×C22⋊C4C2311yescharacteristic
142C2×C11×C22⋊C4C2312yes—
143C2×C11×C22⋊C4C2312yes—
144C2×C11×C22⋊C4C2312yes—
145C2×C11×C22⋊C4C2312yes—
146C2×C11×C22⋊C4C2312yes—
147C2×C11×C22⋊C4C2312yes—
148C2×C11×C22⋊C4C2311yescharacteristic
149C2×C11×C22⋊C4C2312yes—
150C2×C42×C11C2311yescharacteristic
151C2×C42×C11C2312yes—
152#67006C2×C418yescomplemented
153C2×C22⋊Dic11—44no—
154C2×C22⋊Dic11C2312yes—
155C2×C22⋊Dic11C2312yes—
156C2×C22⋊Dic11C2311yescharacteristic
157C2×C22⋊Dic11C2312yes—
158C2×C22⋊Dic11C2312yes—
159C2×C22⋊Dic11C2312yes—
160C2×C22⋊Dic11C2312yes—
161C2×C22⋊Dic11C2311yescharacteristic
162C2×C22⋊Dic11C2312yes—
163#66991C2×C4116yescomplemented
164#66990C2×C4116yescomplemented
165#66988C2×C418yescomplemented
166D4×Dic11—44no—
167C2×(C2×D11)⋊C4C2312yes—
168C2×(C2×D11)⋊C4C2312yes—
169C2×(C2×D11)⋊C4C2312yes—
170C2×(C2×D11)⋊C4C2312yes—
171C2×(C2×D11)⋊C4C2312yes—
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×C4⋊Dic11C2312yes—
179C2×C4⋊Dic11C2311yescharacteristic
180C2×C4⋊Dic11C2312yes—
181C2×Dic11⋊C4C2312yes—
182C2×Dic11⋊C4C2312yes—
183C2×Dic11⋊C4C2312yes—
184C2×Dic11⋊C4C2312yes—
185C2×Dic11⋊C4C2312yes—
186C2×Dic11⋊C4C2312yes—
187C2×C4×Dic11C2312yes—
188C2×C4×Dic11C2311yescharacteristic
189C2×C4×Dic11C2312yes—
190C2×C4×Dic11C2312yes—
191C2×C4×Dic11C2312yes—
192C2×C4×Dic11C2312yes—
193C2×C4×Dic11C2312yes—
194#66945—44no—
195#66945—42no—
196#66939C2×C418yescomplemented
197#66937C2×C4116yescomplemented
198#66936C2×C4116yescomplemented
199(C22⋊D11)⋊C4—44no—
200(C22⋊D11)⋊C4—44no—
201(C22⋊D11)⋊C4—44no—
202C22⋊C4×D11—44no—
203C22⋊C4×D11—42no—
204C22⋊C4×D11C2×C418yescomplemented
205#66925—42no—
206C11×#95C2312yes—
207C11×#95C2312yes—
208C11×#95C2312yes—
209C11⋊#95C2312yes—
210C11⋊#95C2312yes—
211C11⋊#95C2312yes—
212C11⋊#95C2312yes—
213C11⋊#95C2312yes—
214C11⋊#95C2312yes—
215C11⋊#95C2312yes—
216C11⋊#95C2312yes—
217C11⋊#95C2312yes—
218C11⋊#95C2312yes—
219C11⋊#95C2312yes—
220C11⋊#95C2312yes—
221C11⋊#95C2312yes—
222#34407—111nomaximal, Sylow
223C24×C11—42no—
224C24×C11—41no—
225C24×C11—41no—
226C24×C11—42no—
227C24×C11C22×C414yescomplemented
228C24×C11C2411yescharacteristic
229C24×C11C2411yescharacteristic
230C24×C11C2412yes—
231C23×D11—22no—
232C23×D11—22no—
233C23×D11—22no—
234C23×D11—22no—
235C23×D11—42no—
236C23×D11—42no—
237C23×D11—42no—
238C23×D11—42no—
239C23×D11C22×C414yes—
240C23×D11C22×C414yes—
241C23×D11C2411yescharacteristic
242C23×D11C2411yescharacteristic
243C23×D11C2411yescharacteristic
244C2×D4×C11—42no—
245C2×D4×C11—41no—
246C2×D4×C11—41no—
247C2×D4×C11—42no—
248C2×D4×C11C22×C414yes—
249C2×D4×C11C22×C418yes—
250C22×C4×C11—41no—
251C22×C4×C11—42no—
252C22×C4×C11C2412yes—
253C22×C4×C11C2412yes—
254C22×C4×C11C2412yes—
255C22×C4×C11C2412yes—
256C22×C4×C11C2411yescharacteristic
257C22×C4×C11C2412yes—
258C2×C22⋊D11—24no—
259C2×C22⋊D11—24no—
260C2×C22⋊D11—42no—
261C2×C22⋊D11—41no—
262C2×C22⋊D11—41no—
263C2×C22⋊D11—41no—
264C2×C22⋊D11—41no—
265C2×C22⋊D11—42no—
266C2×C22⋊D11—42no—
267C2×C22⋊D11—42no—
268C2×C22⋊D11—416no—
269C2×C22⋊D11C22×C418yes—
270C2×C22⋊D11C22×C418yes—
271C2×C22⋊D11C22×C414yes—
272C2×C22⋊D11C22×C414yes—
273C2×C22⋊D11C22×C418yescomplemented
274C22×Dic11—24no—
275C22×Dic11—24no—
276C22×Dic11—41no—
277C22×Dic11—41no—
278C22×Dic11—41no—
279C22×Dic11—42no—
280C22×Dic11—42no—
281C22×Dic11—42no—
282C22×Dic11—42no—
283C22×Dic11—42no—
284C22×Dic11C22×C414yescomplemented
285C22×Dic11C2412yes—
286C22×Dic11C2412yes—
287C22×Dic11C2412yes—
288C22×Dic11C2412yes—
289C22×Dic11C2412yes—
290C22×Dic11C2411yescharacteristic
291C22×Dic11C2412yes—
292D4×D11—416no—
293C2×D44—41no—
294C2×D44—41no—
295C2×D44C22×C414yes—
296C2×C4×D11—24no—
297C2×C4×D11—24no—
298C2×C4×D11—22no—
299C2×C4×D11—22no—
300C2×C4×D11—24no—
301C2×C4×D11—24no—
302C2×C4×D11—42no—
303C2×C4×D11—42no—
304C2×C4×D11—42no—
305C2×C4×D11—42no—
306C2×C4×D11—42no—
307C2×C4×D11—42no—
308C2×C4×D11—42no—
309C2×C4×D11—416no—
310C2×C4×D11C22×C414yes—
311C2×C4×D11C22×C418yescomplemented
312C11×C4⋊C4—42no—
313C11×C4⋊C4—41no—
314C11×C22⋊C4—42no—
315C11×C22⋊C4—41no—
316C11×C22⋊C4—42no—
317C11×C22⋊C4—42no—
318C11×C22⋊C4—42no—
319C11×C22⋊C4—42no—
320C11×C22⋊C4—42no—
321C11×C22⋊C4—42no—
322C11×C22⋊C4C22×C414yescomplemented
323C11×C22⋊C4C22×C418yescomplemented
324C42×C11—41no—
325C42×C11—42no—
326C22⋊Dic11—24no—
327C22⋊Dic11—24no—
328C22⋊Dic11—41no—
329C22⋊Dic11—42no—
330C22⋊Dic11—42no—
331C22⋊Dic11—42no—
332C22⋊Dic11C22×C418yes—
333C22⋊Dic11C22×C414yescomplemented
334C22⋊Dic11C22×C418yescomplemented
335(C2×D11)⋊C4—24no—
336(C2×D11)⋊C4—24no—
337(C2×D11)⋊C4—24no—
338(C2×D11)⋊C4—42no—
339(C2×D11)⋊C4—42no—
340(C2×D11)⋊C4—42no—
341(C2×D11)⋊C4—42no—
342(C2×D11)⋊C4—42no—
343(C2×D11)⋊C4—42no—
344(C2×D11)⋊C4C22×C418yes—
345(C2×D11)⋊C4C22×C418yes—
346C4⋊Dic11—24no—
347C4⋊Dic11—41no—
348C4⋊Dic11C22×C418yescomplemented
349Dic11⋊C4—42no—
350Dic11⋊C4—42no—
351Dic11⋊C4—42no—
352Dic11⋊C4—42no—
353Dic11⋊C4—42no—
354Dic11⋊C4C22×C418yescomplemented
355C4×Dic11—24no—
356C4×Dic11—41no—
357C4×Dic11—42no—
358C4×Dic11—42no—
359C4×Dic11—42no—
360C4×Dic11—42no—
361C4×Dic11—42no—
362C2×#534—111no—
363#2377—112no—
364#2376—111no—
365#2375D1111yescharacteristic, complemented
366#2374—111no—
367#2363—112no—
368#2359—112no—
369#2359—112no—
370#2358—111no—
371#2342—112no—
372D4×C22⋊C4—112no—
373#2335—112no—
374#2333—112no—
375#2324—112no—
376#2321—112no—
377#2321—112no—
378#2309—111no—
379C4×#120—112no—
380C2×#386—111no—
381C23×C11—22no—
382C23×C11—22no—
383C23×C11—21no—
384C23×C11—22no—
385C23×C11—22no—
386C23×C11—22no—
387C23×C11—22no—
388C23×C11—21no—
389C23×C11—21no—
390C23×C11—21no—
391C23×C11—22no—
392C23×C11—22no—
393C23×C11—22no—
394C23×C11—22no—
395C23×C11—44no—
396C23×C11—48no—
397C23×C11—82no—
398C23×C11—82no—
399C23×C11—84no—
400C23×C11C23×C412yes—
401C23×C11C23×C412yes—
402C23×C11C23×C414yes—
403C23×C11C2511yescharacteristic
404C22×D11—22no—
405C22×D11—22no—
406C22×D11—22no—
407C22×D11—21no—
408C22×D11—22no—
409C22×D11—21no—
410C22×D11—21no—
411C22×D11—21no—
412C22×D11—22no—
413C22×D11—22no—
414C22×D11—28no—
415C22×D11—28no—
416C22×D11—48no—
417C22×D11—48no—
418C22×D11—44no—
419C22×D11—44no—
420C22×D11—48no—
421C22×D11—82no—
422C22×D11—82no—
423C22×D11—84no—
424C22×D11C23×C412yes—
425C22×D11C23×C412yes—
426C22×D11C23×C412yes—
427C22×D11H(5,𝔽2)12yes—
428C22×D11H(5,𝔽2)12yes—
429D4×C11—44no—
430D4×C11—48no—
431C2×C4×C11—22no—
432C2×C4×C11—21no—
433C2×C4×C11—21no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—22no—
437C2×C4×C11—22no—
438C2×C4×C11—22no—
439C2×C4×C11—22no—
440C2×C4×C11—22no—
441C2×C4×C11—22no—
442C2×C4×C11—22no—
443C2×C4×C11—22no—
444C2×C4×C11—22no—
445C2×C4×C11—22no—
446C2×C4×C11—22no—
447C2×C4×C11—44no—
448C2×C4×C11C23×C412yes—
449C2×C4×C11C23×C414yes—
450C22⋊D11—216no—
451C22⋊D11—44no—
452C22⋊D11—44no—
453C22⋊D11—48no—
454C22⋊D11—48no—
455C2×Dic11—22no—
456C2×Dic11—21no—
457C2×Dic11—22no—
458C2×Dic11—22no—
459C2×Dic11—22no—
460C2×Dic11—22no—
461C2×Dic11—21no—
462C2×Dic11—22no—
463C2×Dic11—22no—
464C2×Dic11—22no—
465C2×Dic11—22no—
466C2×Dic11—22no—
467C2×Dic11—22no—
468C2×Dic11—22no—
469C2×Dic11—22no—
470C2×Dic11—22no—
471C2×Dic11—22no—
472C2×Dic11—44no—
473C2×Dic11—44no—
474C2×Dic11—84no—
475C2×Dic11—84no—
476C2×Dic11C23×C414yes—
477C2×Dic11C23×C414yes—
478C2×Dic11C23×C412yes—
479C2×Dic11H(5,𝔽2)14yes—
480D44—44no—
481C4×D11—28no—
482C4×D11—48no—
483C4×D11—48no—
484C4×D11—48no—
485C4×D11—84no—
486C23×D4—111no—
487C23×D4—111no—
488C24×C4—111no—
489#534—1116no—
490C2×#123—111no—
491C2×#123—111no—
492C2×#123—112no—
493C2×#121—112no—
494C2×#121—112no—
495C2×#120—111no—
496C2×#120—112no—
497C2×#120C2×D1111yescharacteristic
498C2×C4×D4—112no—
499C2×C4×D4—112no—
500C2×C4×D4—112no—
501C2×C4×D4—112no—
502C2×#117—111no—
503C2×#117—112no—
504C2×#117—111no—
505C22×C22⋊C4—111no—
506C22×C22⋊C4—112no—
507C22×C22⋊C4—111no—
508C22×C22⋊C4—112no—
509#390—111no—
510#390—111no—
511#390—112no—
512#390—112no—
513#390—112no—
514#390—112no—
515#390—112no—
516#390—111no—
517#390C2×D1111yescharacteristic
518#390C2×D1112yescomplemented
519#389—112no—
520#389—112no—
521#388—112no—
522#388—112no—
523#388—112no—
524#388—112no—
525#388—112no—
526#388—112no—
527#388—112no—
528#388—112no—
529#388—112no—
530#388C2×D1112yescomplemented
531#388C2×D1112yescomplemented
532#388C2×D1112yescomplemented
533#387—112no—
534#387—112no—
535#387—112no—
536#387—112no—
537#386—112no—
538#386—111no—
539#386—111no—
540#386—112no—
541#386—112no—
542#386—112no—
543#386—112no—
544#386—112no—
545#386—112no—
546#386—112no—
547#386—111no—
548#386—112no—
549#386C2×D1111yescharacteristic
550#386C2×D1112yescomplemented
551#385—112no—
552#385—112no—
553#385—112no—
554#385—112no—
555#385—112no—
556#385—112no—
557#381—112no—
558#380—112no—
559#380—112no—
560#379—112no—
561#379—112no—
562#379C2×D1112yescomplemented
563C4×C4⋊C4—112no—
564C4×C4⋊C4—112no—
565C4×C22⋊C4—112no—
566C4×C22⋊C4—112no—
567C4×C22⋊C4—112no—
568C4×C22⋊C4—112no—
569C4×C22⋊C4—112no—
570C4×C22⋊C4—112no—
571C4×C22⋊C4—112no—
572C4×C22⋊C4—112no—
573C2×#95—112no—
574C22×C11—22no—
575C22×C11—22no—
576C22×C11—24no—
577C22×C11—24no—
578C22×C11—24no—
579C22×C11—24no—
580C22×C11—24no—
581C22×C11—41no—
582C22×C11—41no—
583C22×C11—42no—
584C22×C11—41no—
585C22×C11—41no—
586C22×C11—42no—
587C22×C11—42no—
588C22×C11—42no—
589C22×C11—42no—
590C22×C11—42no—
591C22×C11—88no—
592C22×C11C24×C411yescharacteristic
593C22×C11C2×H(5,𝔽2)11yescharacteristic
594C22×C11C2×H(5,𝔽2)11yescharacteristic
595C22×C11C2×H(5,𝔽2)12yes—
596C22×C11#58512yes—
597C2×D11—24no—
598C2×D11—22no—
599C2×D11—22no—
600C2×D11—24no—
601C2×D11—22no—
602C2×D11—22no—
603C2×D11—24no—
604C2×D11—24no—
605C2×D11—416no—
606C2×D11—41no—
607C2×D11—41no—
608C2×D11—41no—
609C2×D11—41no—
610C2×D11—42no—
611C2×D11—42no—
612C2×D11—88no—
613C2×D11#51814yes—
614C4×C11—22no—
615C4×C11—24no—
616C4×C11—42no—
617C4×C11—42no—
618C4×C11—42no—
619C4×C11—42no—
620Dic11—22no—
621Dic11—24no—
622Dic11—24no—
623Dic11—24no—
624Dic11—42no—
625Dic11—42no—
626Dic11—42no—
627C25—111no—
628C25—111no—
629C25C22×D1111yescharacteristic
630C22×D4—112no—
631C22×D4—118no—
632C22×D4—112no—
633C22×D4—111no—
634C22×D4—111no—
635C22×D4—112no—
636C22×D4—118no—
637C22×D4—111no—
638C22×D4—442no—
639C22×D4—442no—
640C22×D4—442no—
641C22×D4—442no—
642C22×D4C22×D1112yes—
643C22×D4C22×D1111yescharacteristic
644C23×C4—111no—
645C23×C4—111no—
646C23×C4—112no—
647C23×C4—111no—
648C23×C4—112no—
649C23×C4—112no—
650C23×C4—112no—
651C23×C4—112no—
652C23×C4—112no—
653C23×C4—444no—
654C23×C4—442no—
655C23×C4C22×D1111yescharacteristic
656#123—118no—
657#123—1116no—
658#123—118no—
659#121—1116no—
660#121—1116no—
661#120—118no—
662#120—1116no—
663#120C4×D1118yescomplemented
664C4×D4—444no—
665C4×D4—444no—
666C4×D4—444no—
667C4×D4—444no—
668#117—442no—
669#117—444no—
670#117—442no—
671C2×C4⋊C4—112no—
672C2×C4⋊C4—112no—
673C2×C4⋊C4—112no—
674C2×C4⋊C4—111no—
675C2×C4⋊C4—112no—
676C2×C4⋊C4—112no—
677C2×C4⋊C4—112no—
678C2×C4⋊C4—112no—
679C2×C4⋊C4—112no—
680C2×C4⋊C4C22×D1112yes—
681C2×C4⋊C4C22×D1111yescharacteristic
682C2×C22⋊C4—111no—
683C2×C22⋊C4—112no—
684C2×C22⋊C4—112no—
685C2×C22⋊C4—112no—
686C2×C22⋊C4—112no—
687C2×C22⋊C4—118no—
688C2×C22⋊C4—112no—
689C2×C22⋊C4—112no—
690C2×C22⋊C4—112no—
691C2×C22⋊C4—112no—
692C2×C22⋊C4—112no—
693C2×C22⋊C4—112no—
694C2×C22⋊C4—112no—
695C2×C22⋊C4—111no—
696C2×C22⋊C4—112no—
697C2×C22⋊C4—112no—
698C2×C22⋊C4—112no—
699C2×C22⋊C4—112no—
700C2×C22⋊C4—112no—
701C2×C22⋊C4—112no—
702C2×C22⋊C4—112no—
703C2×C22⋊C4—444no—
704C2×C22⋊C4—442no—
705C2×C22⋊C4—444no—
706C2×C22⋊C4C22×D1112yes—
707C2×C22⋊C4C22×D1111yescharacteristic
708C2×C22⋊C4C22×D1112yes—
709C2×C22⋊C4C22×D1112yes—
710C2×C22⋊C4C22×D1112yes—
711C2×C22⋊C4C22×D1112yes—
712C2×C22⋊C4C22×D1112yes—
713C2×C22⋊C4C22×D1112yes—
714C2×C22⋊C4C22×D1111yescharacteristic
715C2×C22⋊C4C22×D1112yes—
716C2×C42—112no—
717C2×C42—111no—
718C2×C42—112no—
719C2×C42—112no—
720C2×C42—112no—
721C2×C42—112no—
722C2×C42—112no—
723C2×C42C22×D1111yescharacteristic
724C2×C42C22×D1112yes—
725#95—112no—
726#95—112no—
727#95—112no—
728#95—112no—
729#95—112no—
730#95—112no—
731#95—112no—
732#95—112no—
733#95—112no—
734#95—112no—
735#95—112no—
736#95—112no—
737#95—112no—
738#95C22×D1112yes—
739#95C22×D1112yes—
740#95C22×D1112yes—
741C2×C11—42no—
742C2×C11—42no—
743C2×C11—44no—
744C2×C11C2×#51811yescharacteristic
745C2×C11C4×H(5,𝔽2)12yes—
746C2×C11#353211yescharacteristic
747C2×C11#353311yescharacteristic
748C2×C11#354212yes—
749D11—24no—
750D11—42no—
751D11—42no—
752C24—42no—
753C24—41no—
754C24—41no—
755C24—42no—
756C24—111no—
757C24—111no—
758C24—111no—
759C24—114no—
760C24—114no—
761C24—222no—
762C24—222no—
763C24—222no—
764C24—222no—
765C24—442no—
766C24—442no—
767C24—442no—
768C24—442no—
769C24C2×C4×D1114yescomplemented
770C24C23×D1111yescharacteristic
771C24C23×D1111yescharacteristic
772C24C23×D1112yes—
773C2×D4—42no—
774C2×D4—41no—
775C2×D4—41no—
776C2×D4—42no—
777C2×D4—118no—
778C2×D4—118no—
779C2×D4—114no—
780C2×D4—114no—
781C2×D4—118no—
782C2×D4—114no—
783C2×D4—224no—
784C2×D4—224no—
785C2×D4—441no—
786C2×D4—441no—
787C2×D4—4416no—
788C2×D4—442no—
789C2×D4—441no—
790C2×D4—441no—
791C2×D4—442no—
792C2×D4—442no—
793C2×D4—441no—
794C2×D4—441no—
795C2×D4—442no—
796C2×D4—4416no—
797C2×D4C2×C4×D1118yes—
798C2×D4C2×C4×D1114yes—
799C22×C4—42no—
800C22×C4—41no—
801C22×C4—112no—
802C22×C4—112no—
803C22×C4—111no—
804C22×C4—112no—
805C22×C4—114no—
806C22×C4—114no—
807C22×C4—118no—
808C22×C4—112no—
809C22×C4—112no—
810C22×C4—112no—
811C22×C4—224no—
812C22×C4—224no—
813C22×C4—222no—
814C22×C4—222no—
815C22×C4—224no—
816C22×C4—224no—
817C22×C4—224no—
818C22×C4—224no—
819C22×C4—442no—
820C22×C4—442no—
821C22×C4—442no—
822C22×C4—442no—
823C22×C4—442no—
824C22×C4—442no—
825C22×C4—442no—
826C22×C4—4416no—
827C22×C4—441no—
828C22×C4—441no—
829C22×C4—441no—
830C22×C4—442no—
831C22×C4—442no—
832C22×C4—442no—
833C22×C4—442no—
834C22×C4—442no—
835C22×C4C23×D1112yes—
836C22×C4C23×D1112yes—
837C22×C4C23×D1112yes—
838C22×C4C23×D1112yes—
839C22×C4C23×D1112yes—
840C22×C4C23×D1111yescharacteristic
841C4⋊C4—42no—
842C4⋊C4—41no—
843C4⋊C4—118no—
844C4⋊C4—118no—
845C4⋊C4—224no—
846C4⋊C4—442no—
847C4⋊C4—441no—
848C4⋊C4—442no—
849C4⋊C4—442no—
850C4⋊C4—442no—
851C4⋊C4—442no—
852C22⋊C4—42no—
853C22⋊C4—41no—
854C22⋊C4—42no—
855C22⋊C4—42no—
856C22⋊C4—42no—
857C22⋊C4—42no—
858C22⋊C4—42no—
859C22⋊C4—42no—
860C22⋊C4—114no—
861C22⋊C4—118no—
862C22⋊C4—118no—
863C22⋊C4—118no—
864C22⋊C4—118no—
865C22⋊C4—224no—
866C22⋊C4—224no—
867C22⋊C4—224no—
868C22⋊C4—224no—
869C22⋊C4—224no—
870C22⋊C4—442no—
871C22⋊C4—442no—
872C22⋊C4—442no—
873C22⋊C4—442no—
874C22⋊C4—442no—
875C22⋊C4—442no—
876C22⋊C4—442no—
877C22⋊C4—441no—
878C22⋊C4—442no—
879C22⋊C4—442no—
880C22⋊C4C2×C4×D1114yescomplemented
881C22⋊C4C2×C4×D1118yescomplemented
882C42—41no—
883C42—42no—
884C42—224no—
885C42—441no—
886C42—442no—
887C42—442no—
888C42—442no—
889C42—442no—
890C42—442no—
891C11#3440711yescharacteristic, complemented, Sylow
892C23—22no—
893C23—21no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—21no—
900C23—21no—
901C23—21no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—44no—
907C23—48no—
908C23—84no—
909C23—82no—
910C23—82no—
911C23—112no—
912C23—112no—
913C23—112no—
914C23—112no—
915C23—112no—
916C23—228no—
917C23—228no—
918C23—222no—
919C23—222no—
920C23—222no—
921C23—221no—
922C23—222no—
923C23—221no—
924C23—221no—
925C23—221no—
926C23—222no—
927C23—222no—
928C23—448no—
929C23—448no—
930C23—444no—
931C23—448no—
932C23—444no—
933C23—884no—
934C23—882no—
935C23—882no—
936C23C22×C4×D1112yes—
937C23C22×C4×D1112yes—
938C23C22×C4×D1114yes—
939C23C24×D1111yescharacteristic
940D4—44no—
941D4—48no—
942D4—2216no—
943D4—444no—
944D4—444no—
945D4—444no—
946D4—448no—
947D4—448no—
948C2×C4—21no—
949C2×C4—22no—
950C2×C4—21no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—44no—
965C2×C4—114no—
966C2×C4—112no—
967C2×C4—114no—
968C2×C4—114no—
969C2×C4—228no—
970C2×C4—222no—
971C2×C4—221no—
972C2×C4—222no—
973C2×C4—222no—
974C2×C4—222no—
975C2×C4—222no—
976C2×C4—221no—
977C2×C4—222no—
978C2×C4—222no—
979C2×C4—222no—
980C2×C4—222no—
981C2×C4—222no—
982C2×C4—222no—
983C2×C4—222no—
984C2×C4—222no—
985C2×C4—222no—
986C2×C4—222no—
987C2×C4—448no—
988C2×C4—448no—
989C2×C4—448no—
990C2×C4—444no—
991C2×C4—444no—
992C2×C4—884no—
993C2×C4—884no—
994C2×C4—884no—
995C2×C4C22×C4×D1114yes—
996C2×C4C22×C4×D1112yes—
997C22—22no—
998C22—22no—
999C22—24no—
1000C22—24no—
1001C22—24no—
1002C22—24no—
1003C22—24no—
1004C22—42no—
1005C22—42no—
1006C22—42no—
1007C22—42no—
1008C22—41no—
1009C22—42no—
1010C22—41no—
1011C22—41no—
1012C22—42no—
1013C22—41no—
1014C22—88no—
1015C22—114no—
1016C22—224no—
1017C22—222no—
1018C22—222no—
1019C22—224no—
1020C22—222no—
1021C22—222no—
1022C22—224no—
1023C22—224no—
1024C22—4416no—
1025C22—442no—
1026C22—442no—
1027C22—441no—
1028C22—441no—
1029C22—441no—
1030C22—441no—
1031C22—888no—
1032C22C23×C4×D1111yescharacteristic
1033C22D11×H(5,𝔽2)11yescharacteristic
1034C22D11×H(5,𝔽2)12yes—
1035C22D11×H(5,𝔽2)11yescharacteristic
1036C22#1062345512yes—
1037C4—22no—
1038C4—24no—
1039C4—42no—
1040C4—42no—
1041C4—42no—
1042C4—42no—
1043C4—224no—
1044C4—222no—
1045C4—224no—
1046C4—224no—
1047C4—442no—
1048C4—442no—
1049C4—442no—
1050C2—42no—
1051C2—44no—
1052C2—42no—
1053C2—224no—
1054C2—442no—
1055C2—442no—
1056C2D11×#51811yescharacteristic
1057C2#1308182012yes—
1058C2#1308277311yescharacteristic
1059C2#1308278511yescharacteristic
1060C2#1308292112yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2375C2
socle, cosocleC23×C11C25
prime radicalC2×#10623120C2
hypercenter#2375D11
hypocenterC11#34407
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2375

Complements

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

NH ≅ G/Ntype
2. #13071768C2semidirect
3. #13071759C2semidirect
4. #13071751C2semidirect
5. #13071659C2semidirect
6. #13071607C2semidirect
7. #13071605C2semidirect
8. #13071600C2semidirect
9. #13071464C2semidirect
10. #13071432C2semidirect
11. #13071411C2semidirect
12. #13071379C2semidirect
13. #13071304C2semidirect
14. #13071275C2semidirect
15. #13071271C2semidirect
16. #13071195C2semidirect
17. #13071121C2semidirect
18. D11×#386C2semidirect
19. C11×#2375C2semidirect
22. C23×C4×D11C22semidirect
25. C22×C22⋊Dic11C22semidirect
29. C2×D4×Dic11C22semidirect
30. #10623120C4semidirect
31. C2×#66945C22semidirect
32. C2×#66945C22semidirect
38. C2×(C22⋊D11)⋊C4C22semidirect
41. C2×C22⋊C4×D11C22semidirect
42. C2×#66925C22semidirect
44. C11×#390C22semidirect
45. C11×#388C22semidirect
46. C11×#388C22semidirect
47. C11×#388C22semidirect
49. C11×#386C22semidirect
50. C11×#379C22semidirect
53. #10622833C22semidirect
54. #10622826C22semidirect
55. #10622823C22semidirect
56. #10622603C22semidirect
57. #10622602C22semidirect
58. #10622601C22semidirect
59. #10622591C22semidirect
60. #10622586C22semidirect
61. #10622571C22semidirect
62. #10622571C22semidirect
63. #10622571C22semidirect
64. #10622571C22semidirect
66. #10622570C22semidirect
67. #10622570C22semidirect
68. #10622570C22semidirect
69. #10622570C22semidirect
73. #10622569C22semidirect
75. #10622568C22semidirect
76. #10622564C22semidirect
77. #10622563C22semidirect
78. #10622559C22semidirect
79. #10622558C22semidirect
80. #10622558C22semidirect
81. #10622558C22semidirect
82. #10622558C22semidirect
83. #10622557C22semidirect
84. #10622557C22semidirect
85. #10622555C22semidirect
86. C22⋊C4×Dic11C22semidirect
87. C22⋊C4×Dic11C22semidirect
88. C22⋊C4×Dic11C22semidirect
89. C22⋊C4×Dic11C22semidirect
90. #10622553C22semidirect
91. #10622552C22semidirect
92. C4×(C2×D11)⋊C4C22semidirect
93. C4×(C2×D11)⋊C4C22semidirect
94. C4×C4⋊Dic11C22semidirect
95. C4×Dic11⋊C4C22semidirect
96. #10622281C22semidirect
97. #10622281C22semidirect
98. #10622280C22semidirect
99. #10622279C22semidirect
100. #10622279C22semidirect
101. #10622278C22semidirect
102. #10622277C22semidirect
103. D11×#95C22semidirect
104. #10622267C22semidirect
105. #10622266C22semidirect
106. #10622265C22semidirect
107. #10622260C22semidirect
116. C22×C22⋊D11C2×C4semidirect
128. C2×D4×D11C2×C4semidirect
137. C11×#120C2×C4semidirect
152. #67006C2×C4semidirect
163. #66991C2×C4semidirect
164. #66990C2×C4semidirect
165. #66988C2×C4semidirect
196. #66939C2×C4semidirect
197. #66937C2×C4semidirect
198. #66936C2×C4semidirect
204. C22⋊C4×D11C2×C4semidirect
227. C24×C11C22×C4semidirect
273. C2×C22⋊D11C22×C4semidirect
284. C22×Dic11C22×C4semidirect
311. C2×C4×D11C22×C4semidirect
322. C11×C22⋊C4C22×C4semidirect
323. C11×C22⋊C4C22×C4semidirect
333. C22⋊Dic11C22×C4semidirect
334. C22⋊Dic11C22×C4semidirect
348. C4⋊Dic11C22×C4semidirect
354. Dic11⋊C4C22×C4semidirect
365. #2375D11semidirect
518. #390C2×D11semidirect
530. #388C2×D11semidirect
531. #388C2×D11semidirect
532. #388C2×D11semidirect
550. #386C2×D11semidirect
562. #379C2×D11semidirect
663. #120C4×D11semidirect
769. C24C2×C4×D11semidirect
880. C22⋊C4C2×C4×D11semidirect
881. C22⋊C4C2×C4×D11semidirect
891. C11#34407semidirect

Maximal subgroups

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

subgroupindex
C2×#106231202
#130717682
#130717592
#130717512
#130716592
#130716072
#130716052
#130716002
#130714642
#130714322
#130714112
#130713792
#130713042
#130712752
#130712712
#130711952
#130711212
D11×#3862
C11×#23752
#3440711