Finite Group Databasebeta

← #14917151

Subgroups — #14917151

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×#10623184C211yesmaximal, characteristic
2#13071769C212yesmaximal, complemented
3#13071764C211yesmaximal, characteristic, complemented
4#13071753C211yesmaximal, characteristic, complemented
5#13071655C212yesmaximal, complemented
6#13071615C212yesmaximal, complemented
7#13071613C212yesmaximal, complemented
8#13071599C211yesmaximal, characteristic, complemented
9#13071460C212yesmaximal, complemented
10C22⋊C4×D44C212yesmaximal, complemented
11#13071406C212yesmaximal, complemented
12#13071380C212yesmaximal, complemented
13#13071310C212yesmaximal, complemented
14#13071278C212yesmaximal, complemented
15#13071278C212yesmaximal, complemented
16#13071195C211yesmaximal, characteristic, complemented
17C4×#66935C212yesmaximal, complemented
18D11×#386C211yesmaximal, characteristic, complemented
19C11×#2374C211yesmaximal, characteristic, complemented
20C22×D4×D11C2211yescharacteristic
21C23×D44C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic, complemented
23C2×C11×#123C2211yescharacteristic
24C2×#66990C2211yescharacteristic
25C2×#66982C2211yescharacteristic
26C2×C4×C22⋊D11C2212yescomplemented
27#10623184C4116yescomplemented
28C2×#66948C2212yes—
29C2×#66947C2212yes—
30C2×#66945C2211yescharacteristic, complemented
31C2×#66937C2212yes—
32C2×#66935C2212yes—
33C2×#66935C2211yescharacteristic
34C2×C22⋊C4×D11C2212yes—
35C2×C22⋊C4×D11C2211yescharacteristic
36C2×C22⋊C4×D11C2212yescomplemented
37C2×C22⋊C4×D11C2211yescharacteristic, complemented
38C2×C4×D44C2212yes—
39C2×C4×D44C2212yes—
40C2×C4×D44C2212yescomplemented
41C2×#66925C2212yescomplemented
42C2×#66925C2211yescharacteristic, complemented
43C11×#390C2211yescharacteristic
44C11×#388C2212yescomplemented
45C11×#388C2212yescomplemented
46C11×#387C2212yescomplemented
47C11×#386C2211yescharacteristic
48C4×C11×C4⋊C4C2212yescomplemented
49C4×C11×C22⋊C4C2212yescomplemented
50C4×C11×C22⋊C4C2212yescomplemented
51#10622834C2211yescharacteristic
52#10622833C2211yescharacteristic
53#10622826C2211yescharacteristic, complemented
54#10622825C2212yescomplemented
55#10622603C2212yescomplemented
56#10622602C2212yescomplemented
57#10622602C2212yescomplemented
58#10622601C2211yescharacteristic, complemented
59#10622601C2212yescomplemented
60#10622600C2212yescomplemented
61#10622598C2212yescomplemented
62#10622594C2212yescomplemented
63#10622571C2212yescomplemented
64#10622571C2211yescharacteristic, complemented
65#10622570C2212yes—
66#10622570C2212yescomplemented
67#10622570C2212yescomplemented
68#10622569C2212yes—
69#10622569C2212yescomplemented
70#10622568C2212yes—
71#10622568C2212yescomplemented
72#10622568C2212yescomplemented
73#10622564C2212yescomplemented
74#10622564C2212yescomplemented
75#10622563C2212yescomplemented
76#10622558C2212yescomplemented
77#10622557C2212yescomplemented
78#10622553C2212yescomplemented
79#10622553C2212yescomplemented
80#10622553C2212yescomplemented
81#10622552C2212yescomplemented
82#10622552C2212yescomplemented
83#10622552C2211yescharacteristic, complemented
84C4×(C2×D11)⋊C4C2212yescomplemented
85C4×(C2×D11)⋊C4C2212yescomplemented
86#10622546C2212yescomplemented
87C4×Dic11⋊C4C2212yescomplemented
88#10622283C2212yescomplemented
89#10622283C2212yescomplemented
90#10622281C2212yescomplemented
91#10622281C2212yescomplemented
92#10622281C2212yescomplemented
93#10622279C2212yescomplemented
94#10622279C2212yescomplemented
95#10622279C2212yescomplemented
96#10622279C2212yescomplemented
97#10622278C2212yes—
98#10622278C2212yes—
99#10622278C2212yescomplemented
100#10622278C2212yescomplemented
101#10622278C2212yescomplemented
102#10622278C2212yescomplemented
103#10622278C2212yescomplemented
104#10622277C2212yescomplemented
105D11×#95C2212yescomplemented
106#10622268C2212yescomplemented
107#10622260C2212yescomplemented
108C24×D11C2311yescharacteristic
109C24×D11C2311yescharacteristic
110C24×D11C2311yescharacteristic
111C22×D4×C11C2311yescharacteristic
112C23×C4×C11C2311yescharacteristic
113C23×C4×C11C2311yescharacteristic
114C22×C22⋊D11C2312yes—
115C22×C22⋊D11C2311yescharacteristic
116C22×C22⋊D11C2311yescharacteristic
117C23×Dic11C2311yescharacteristic
118C2×D4×D11—42no—
119C2×D4×D11—42no—
120C2×D4×D11C2×C418yescomplemented
121C22×D44—42no—
122C22×D44—42no—
123C22×D44C2×C418yescomplemented
124C22×D44C2312yes—
125C22×D44C2312yes—
126C22×D44C2311yescharacteristic
127C22×D44C2312yes—
128C22×C4×D11—44no—
129C22×C4×D11—42no—
130C22×C4×D11C2312yes—
131C22×C4×D11C2311yescharacteristic
132C22×C4×D11C2312yes—
133C22×C4×D11C2312yes—
134C22×C4×D11C2312yes—
135C22×C4×D11C2312yes—
136C22×C4×D11C2312yes—
137C11×#123C2×C418yescomplemented
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C4⋊C4C2312yes—
140C2×C11×C4⋊C4C2312yes—
141C2×C11×C22⋊C4C2312yes—
142C2×C11×C22⋊C4C2311yescharacteristic
143C2×C11×C22⋊C4C2312yes—
144C2×C11×C22⋊C4C2312yes—
145C2×C11×C22⋊C4C2312yes—
146C2×C11×C22⋊C4C2311yescharacteristic
147C2×C42×C11C2312yes—
148C2×C42×C11C2311yescharacteristic
149C2×C42×C11C2312yes—
150C2×C42×C11C2312yes—
151C2×C22⋊Dic11C2312yes—
152C2×C22⋊Dic11C2312yes—
153C2×C22⋊Dic11C2311yescharacteristic
154C2×C22⋊Dic11C2312yes—
155C2×C22⋊Dic11C2311yescharacteristic
156#66990C2×C418yescomplemented
157#66982C2×C418yescomplemented
158C4×C22⋊D11—44no—
159C2×(C2×D11)⋊C4C2312yes—
160C2×(C2×D11)⋊C4C2312yes—
161C2×(C2×D11)⋊C4C2312yes—
162C2×(C2×D11)⋊C4C2312yes—
163C2×(C2×D11)⋊C4C2312yes—
164C2×(C2×D11)⋊C4C2312yes—
165C2×(C2×D11)⋊C4C2312yes—
166C2×(C2×D11)⋊C4C2312yes—
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⋊Dic11C2312yes—
180C2×C4⋊Dic11C2312yes—
181C2×C4⋊Dic11C2311yescharacteristic
182C2×Dic11⋊C4C2312yes—
183C2×Dic11⋊C4C2312yes—
184C2×Dic11⋊C4C2312yes—
185C2×Dic11⋊C4C2312yes—
186C2×C4×Dic11C2312yes—
187C2×C4×Dic11C2311yescharacteristic
188C2×C4×Dic11C2312yes—
189C2×C4×Dic11C2312yes—
190C2×C4×Dic11C2312yes—
191#66948C2×C4116yescomplemented
192#66947C2×C4116yescomplemented
193#66945—42no—
194#66937C2×C4116yescomplemented
195#66935C2×C4116yescomplemented
196#66935C2×C418yescomplemented
197C22⋊C4×D11—44no—
198C22⋊C4×D11—44no—
199C22⋊C4×D11—42no—
200C22⋊C4×D11C2×C418yescomplemented
201C4×D44—44no—
202C4×D44—44no—
203C4×D44—44no—
204#66925—44no—
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×C11C2411yescharacteristic
224C24×C11C2411yescharacteristic
225C23×D11—22no—
226C23×D11—22no—
227C23×D11—22no—
228C23×D11—22no—
229C23×D11—42no—
230C23×D11—42no—
231C23×D11—42no—
232C23×D11—42no—
233C23×D11—41no—
234C23×D11—41no—
235C23×D11—42no—
236C23×D11—42no—
237C23×D11C22×C414yes—
238C23×D11C22×C414yes—
239C23×D11C22×C414yescomplemented
240C23×D11C2411yescharacteristic
241C23×D11C2412yes—
242C23×D11C2411yescharacteristic
243C23×D11C2411yescharacteristic
244C2×D4×C11—41no—
245C2×D4×C11—41no—
246C2×D4×C11C22×C414yes—
247C22×C4×C11—24no—
248C22×C4×C11—41no—
249C22×C4×C11—41no—
250C22×C4×C11—41no—
251C22×C4×C11C22×C414yescomplemented
252C22×C4×C11C2412yes—
253C22×C4×C11C2412yes—
254C22×C4×C11C2412yes—
255C22×C4×C11C2412yes—
256C22×C4×C11C2411yescharacteristic
257C22×C4×C11C2412yes—
258C22×C4×C11C2412yes—
259C2×C22⋊D11—42no—
260C2×C22⋊D11—41no—
261C2×C22⋊D11—41no—
262C2×C22⋊D11—41no—
263C2×C22⋊D11—41no—
264C2×C22⋊D11—42no—
265C2×C22⋊D11C22×C418yes—
266C2×C22⋊D11C22×C414yes—
267C2×C22⋊D11C22×C414yes—
268C22×Dic11—42no—
269C22×Dic11—41no—
270C22×Dic11C2412yes—
271C22×Dic11C2412yes—
272C22×Dic11C2412yes—
273C22×Dic11C2412yes—
274C22×Dic11C2411yescharacteristic
275C22×Dic11C2412yes—
276D4×D11—416no—
277C2×D44—24no—
278C2×D44—24no—
279C2×D44—42no—
280C2×D44—42no—
281C2×D44—42no—
282C2×D44—42no—
283C2×D44—41no—
284C2×D44—41no—
285C2×D44—416no—
286C2×D44C22×C418yes—
287C2×D44C22×C418yes—
288C2×D44C22×C414yes—
289C2×D44C22×C418yescomplemented
290C2×C4×D11—22no—
291C2×C4×D11—22no—
292C2×C4×D11—24no—
293C2×C4×D11—24no—
294C2×C4×D11—24no—
295C2×C4×D11—24no—
296C2×C4×D11—24no—
297C2×C4×D11—42no—
298C2×C4×D11—42no—
299C2×C4×D11—42no—
300C2×C4×D11—42no—
301C2×C4×D11—42no—
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—41no—
313C11×C4⋊C4—42no—
314C11×C4⋊C4C22×C418yescomplemented
315C11×C22⋊C4—24no—
316C11×C22⋊C4—41no—
317C11×C22⋊C4—42no—
318C11×C22⋊C4—42no—
319C11×C22⋊C4C22×C418yes—
320C11×C22⋊C4C22×C414yescomplemented
321C42×C11—24no—
322C42×C11—41no—
323C42×C11—42no—
324C42×C11—42no—
325C22⋊Dic11—42no—
326C22⋊Dic11—42no—
327C22⋊Dic11—41no—
328C22⋊Dic11—42no—
329C22⋊Dic11C22×C414yescomplemented
330(C2×D11)⋊C4—24no—
331(C2×D11)⋊C4—24no—
332(C2×D11)⋊C4—24no—
333(C2×D11)⋊C4—24no—
334(C2×D11)⋊C4—42no—
335(C2×D11)⋊C4—42no—
336(C2×D11)⋊C4—42no—
337(C2×D11)⋊C4—42no—
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)⋊C4—42no—
345(C2×D11)⋊C4C22×C418yes—
346(C2×D11)⋊C4C22×C418yes—
347(C2×D11)⋊C4C22×C418yescomplemented
348(C2×D11)⋊C4C22×C418yescomplemented
349C4⋊Dic11—42no—
350C4⋊Dic11—42no—
351C4⋊Dic11—42no—
352C4⋊Dic11—41no—
353Dic11⋊C4—24no—
354Dic11⋊C4—42no—
355Dic11⋊C4—42no—
356Dic11⋊C4C22×C418yescomplemented
357C4×Dic11—42no—
358C4×Dic11—41no—
359C4×Dic11—42no—
360C4×Dic11—42no—
361C4×Dic11—42no—
362C2×#534—111no—
363#2377—112no—
364#2376—111no—
365#2375—111no—
366#2374D1111yescharacteristic, complemented
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—21no—
383C23×C11—22no—
384C23×C11—21no—
385C23×C11—21no—
386C23×C11—21no—
387C23×C11—22no—
388C23×C11—22no—
389C23×C11C23×C412yes—
390C23×C11C23×C412yes—
391C23×C11C2511yescharacteristic
392C22×D11—22no—
393C22×D11—22no—
394C22×D11—22no—
395C22×D11—22no—
396C22×D11—21no—
397C22×D11—22no—
398C22×D11—22no—
399C22×D11—22no—
400C22×D11—22no—
401C22×D11—21no—
402C22×D11—21no—
403C22×D11—21no—
404C22×D11—22no—
405C22×D11—22no—
406C22×D11—22no—
407C22×D11—22no—
408C22×D11—28no—
409C22×D11—28no—
410C22×D11—48no—
411C22×D11—44no—
412C22×D11—48no—
413C22×D11—48no—
414C22×D11—44no—
415C22×D11—44no—
416C22×D11—48no—
417C22×D11—82no—
418C22×D11—82no—
419C22×D11—84no—
420C22×D11—82no—
421C22×D11—82no—
422C22×D11—84no—
423C22×D11C23×C412yes—
424C22×D11C23×C414yes—
425C22×D11C23×C412yes—
426C22×D11C23×C412yes—
427C22×D11H(5,𝔽2)12yes—
428C22×D11H(5,𝔽2)12yes—
429D4×C11—44no—
430C2×C4×C11—22no—
431C2×C4×C11—21no—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—21no—
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×C11—44no—
449C2×C4×C11C23×C414yes—
450C2×C4×C11C23×C414yes—
451C2×C4×C11C23×C412yes—
452C2×C4×C11H(5,𝔽2)14yes—
453C22⋊D11—44no—
454C22⋊D11—44no—
455C22⋊D11—48no—
456C2×Dic11—21no—
457C2×Dic11—22no—
458C2×Dic11—21no—
459C2×Dic11—22no—
460C2×Dic11—22no—
461C2×Dic11—22no—
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×Dic11C23×C412yes—
474C2×Dic11C23×C414yes—
475D44—216no—
476D44—48no—
477D44—48no—
478D44—44no—
479C4×D11—28no—
480C4×D11—48no—
481C4×D11—48no—
482C4×D11—48no—
483C4×D11—84no—
484C4×D11—84no—
485C4×D11—84no—
486C23×D4—111no—
487C23×D4—111no—
488C24×C4—111no—
489#534—1116no—
490C2×#123—111no—
491C2×#123—112no—
492C2×#123C2×D1111yescharacteristic
493C2×#121—112no—
494C2×#121—112no—
495C2×#120—111no—
496C2×#120—111no—
497C2×#120—112no—
498C2×C4×D4—112no—
499C2×C4×D4—112no—
500C2×C4×D4—112no—
501C2×C4×D4—112no—
502C2×#117—111no—
503C2×#117—111no—
504C2×#117—112no—
505C22×C22⋊C4—111no—
506C22×C22⋊C4—111no—
507C22×C22⋊C4—112no—
508C22×C22⋊C4—112no—
509#390—111no—
510#390—111no—
511#390—112no—
512#390—112no—
513#390—112no—
514#390—112no—
515#390—111no—
516#390—112no—
517#390—112no—
518#390C2×D1111yescharacteristic
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#388—112no—
531#388C2×D1112yescomplemented
532#388C2×D1112yescomplemented
533#387—112no—
534#387—112no—
535#387—112no—
536#387C2×D1112yescomplemented
537#386—111no—
538#386—111no—
539#386—112no—
540#386—112no—
541#386—112no—
542#386—111no—
543#386—112no—
544#386—112no—
545#386—112no—
546#386—112no—
547#386—112no—
548#386—112no—
549#386—112no—
550#386C2×D1111yescharacteristic
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#379—112no—
563C4×C4⋊C4—112no—
564C4×C4⋊C4C2×D1112yescomplemented
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⋊C4C2×D1112yescomplemented
572C4×C22⋊C4C2×D1112yescomplemented
573C2×#95—112no—
574C22×C11—22no—
575C22×C11—22no—
576C22×C11—24no—
577C22×C11—24no—
578C22×C11—41no—
579C22×C11—41no—
580C22×C11—41no—
581C22×C11—41no—
582C22×C11—42no—
583C22×C11—42no—
584C22×C11C24×C411yescharacteristic
585C22×C11C2×H(5,𝔽2)12yes—
586C22×C11C2×H(5,𝔽2)11yescharacteristic
587C22×C11C2×H(5,𝔽2)11yescharacteristic
588C22×C11#58512yes—
589C2×D11—24no—
590C2×D11—22no—
591C2×D11—22no—
592C2×D11—24no—
593C2×D11—22no—
594C2×D11—22no—
595C2×D11—24no—
596C2×D11—24no—
597C2×D11—24no—
598C2×D11—24no—
599C2×D11—24no—
600C2×D11—416no—
601C2×D11—41no—
602C2×D11—41no—
603C2×D11—42no—
604C2×D11—41no—
605C2×D11—42no—
606C2×D11—41no—
607C2×D11—42no—
608C2×D11—42no—
609C2×D11—42no—
610C2×D11—42no—
611C2×D11—88no—
612C2×D11—88no—
613C2×D11#51814yes—
614C4×C11—24no—
615C4×C11—22no—
616C4×C11—24no—
617C4×C11—24no—
618C4×C11—42no—
619C4×C11—42no—
620C4×C11—42no—
621Dic11—22no—
622Dic11—24no—
623Dic11—42no—
624Dic11—42no—
625Dic11—42no—
626Dic11—42no—
627C25—111no—
628C25—111no—
629C25—111no—
630C22×D4—112no—
631C22×D4—111no—
632C22×D4—111no—
633C22×D4—118no—
634C22×D4—118no—
635C22×D4—112no—
636C22×D4—112no—
637C22×D4—111no—
638C22×D4—112no—
639C22×D4—442no—
640C22×D4—442no—
641C22×D4—442no—
642C22×D4—442no—
643C22×D4C22×D1111yescharacteristic
644C23×C4—111no—
645C23×C4—112no—
646C23×C4—111no—
647C23×C4—112no—
648C23×C4—112no—
649C23×C4—112no—
650C23×C4—112no—
651C23×C4—112no—
652C23×C4—444no—
653C23×C4—442no—
654C23×C4C22×D1111yescharacteristic
655C23×C4C22×D1111yescharacteristic
656#123—118no—
657#123—1116no—
658#123C4×D1118yescomplemented
659#121—1116no—
660#121—1116no—
661#120—118no—
662#120—1116no—
663#120—118no—
664C4×D4—444no—
665C4×D4—444no—
666C4×D4—444no—
667C4×D4—444no—
668#117—444no—
669#117—442no—
670#117—442no—
671C2×C4⋊C4—112no—
672C2×C4⋊C4—112no—
673C2×C4⋊C4—111no—
674C2×C4⋊C4—112no—
675C2×C4⋊C4—112no—
676C2×C4⋊C4—112no—
677C2×C4⋊C4—112no—
678C2×C4⋊C4—112no—
679C2×C4⋊C4C22×D1111yescharacteristic
680C2×C4⋊C4C22×D1112yes—
681C2×C4⋊C4C22×D1112yes—
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—111no—
695C2×C22⋊C4—112no—
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—112no—
704C2×C22⋊C4—112no—
705C2×C22⋊C4—112no—
706C2×C22⋊C4—112no—
707C2×C22⋊C4—444no—
708C2×C22⋊C4—444no—
709C2×C22⋊C4—442no—
710C2×C22⋊C4C22×D1112yes—
711C2×C22⋊C4C22×D1111yescharacteristic
712C2×C22⋊C4C22×D1112yes—
713C2×C22⋊C4C22×D1112yes—
714C2×C22⋊C4C22×D1112yes—
715C2×C22⋊C4C22×D1111yescharacteristic
716C2×C42—111no—
717C2×C42—112no—
718C2×C42—112no—
719C2×C42—112no—
720C2×C42—112no—
721C2×C42C22×D1112yes—
722C2×C42C22×D1111yescharacteristic
723C2×C42C22×D1112yes—
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#95C22×D1112yes—
737#95C22×D1112yes—
738#95C22×D1112yes—
739#95C22×D1112yes—
740#95C22×D1112yes—
741C2×C11—42no—
742C2×C11—42no—
743C2×C11C2×#51811yescharacteristic
744C2×C11C4×H(5,𝔽2)12yes—
745C2×C11#353211yescharacteristic
746C2×C11#353311yescharacteristic
747C2×C11#354212yes—
748D11—24no—
749D11—42no—
750D11—42no—
751D11—44no—
752C24—111no—
753C24—112no—
754C24—111no—
755C24—111no—
756C24—114no—
757C24—114no—
758C24—114no—
759C24—222no—
760C24—222no—
761C24—222no—
762C24—222no—
763C24—442no—
764C24—442no—
765C24—442no—
766C24—442no—
767C24—441no—
768C24—441no—
769C24—442no—
770C24—442no—
771C24C23×D1111yescharacteristic
772C24C23×D1111yescharacteristic
773C2×D4—41no—
774C2×D4—41no—
775C2×D4—118no—
776C2×D4—114no—
777C2×D4—114no—
778C2×D4—118no—
779C2×D4—118no—
780C2×D4—114no—
781C2×D4—118no—
782C2×D4—224no—
783C2×D4—224no—
784C2×D4—442no—
785C2×D4—441no—
786C2×D4—442no—
787C2×D4—442no—
788C2×D4—441no—
789C2×D4—442no—
790C2×D4—4416no—
791C2×D4—4416no—
792C2×D4—442no—
793C2×D4—441no—
794C2×D4—441no—
795C2×D4—441no—
796C2×D4—441no—
797C2×D4—442no—
798C2×D4C2×C4×D1114yes—
799C22×C4—24no—
800C22×C4—41no—
801C22×C4—41no—
802C22×C4—41no—
803C22×C4—112no—
804C22×C4—111no—
805C22×C4—114no—
806C22×C4—118no—
807C22×C4—112no—
808C22×C4—112no—
809C22×C4—112no—
810C22×C4—112no—
811C22×C4—222no—
812C22×C4—222no—
813C22×C4—224no—
814C22×C4—224no—
815C22×C4—224no—
816C22×C4—224no—
817C22×C4—224no—
818C22×C4—442no—
819C22×C4—442no—
820C22×C4—442no—
821C22×C4—442no—
822C22×C4—442no—
823C22×C4—442no—
824C22×C4—442no—
825C22×C4—442no—
826C22×C4—442no—
827C22×C4—442no—
828C22×C4—442no—
829C22×C4—442no—
830C22×C4—4416no—
831C22×C4—442no—
832C22×C4—441no—
833C22×C4C2×C4×D1114yescomplemented
834C22×C4C23×D1112yes—
835C22×C4C23×D1112yes—
836C22×C4C23×D1112yes—
837C22×C4C23×D1112yes—
838C22×C4C23×D1111yescharacteristic
839C22×C4C23×D1112yes—
840C22×C4C23×D1112yes—
841C4⋊C4—41no—
842C4⋊C4—42no—
843C4⋊C4—118no—
844C4⋊C4—224no—
845C4⋊C4—442no—
846C4⋊C4—442no—
847C4⋊C4—441no—
848C4⋊C4—442no—
849C4⋊C4—442no—
850C4⋊C4—442no—
851C4⋊C4C2×C4×D1118yescomplemented
852C22⋊C4—24no—
853C22⋊C4—41no—
854C22⋊C4—42no—
855C22⋊C4—42no—
856C22⋊C4—114no—
857C22⋊C4—118no—
858C22⋊C4—118no—
859C22⋊C4—118no—
860C22⋊C4—118no—
861C22⋊C4—224no—
862C22⋊C4—224no—
863C22⋊C4—224no—
864C22⋊C4—224no—
865C22⋊C4—442no—
866C22⋊C4—442no—
867C22⋊C4—442no—
868C22⋊C4—442no—
869C22⋊C4—442no—
870C22⋊C4—442no—
871C22⋊C4—442no—
872C22⋊C4—442no—
873C22⋊C4—442no—
874C22⋊C4—442no—
875C22⋊C4—442no—
876C22⋊C4—442no—
877C22⋊C4—442no—
878C22⋊C4—441no—
879C22⋊C4—442no—
880C22⋊C4C2×C4×D1118yes—
881C22⋊C4C2×C4×D1114yescomplemented
882C42—24no—
883C42—41no—
884C42—42no—
885C42—42no—
886C42—442no—
887C42—441no—
888C42—442no—
889C42—442no—
890C42—442no—
891C11#3440711yescharacteristic, complemented, Sylow
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—21no—
897C23—21no—
898C23—21no—
899C23—21no—
900C23—112no—
901C23—112no—
902C23—112no—
903C23—114no—
904C23—112no—
905C23—112no—
906C23—228no—
907C23—228no—
908C23—222no—
909C23—222no—
910C23—222no—
911C23—222no—
912C23—222no—
913C23—222no—
914C23—222no—
915C23—222no—
916C23—222no—
917C23—222no—
918C23—221no—
919C23—222no—
920C23—222no—
921C23—221no—
922C23—221no—
923C23—221no—
924C23—448no—
925C23—444no—
926C23—448no—
927C23—448no—
928C23—444no—
929C23—448no—
930C23—444no—
931C23—884no—
932C23—882no—
933C23—882no—
934C23—884no—
935C23—882no—
936C23—882no—
937C23C22×C4×D1112yes—
938C23C22×C4×D1112yes—
939C23C24×D1111yescharacteristic
940D4—44no—
941D4—2216no—
942D4—448no—
943D4—444no—
944D4—448no—
945D4—444no—
946D4—444no—
947D4—448no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—21no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—21no—
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—22no—
965C2×C4—44no—
966C2×C4—44no—
967C2×C4—114no—
968C2×C4—112no—
969C2×C4—228no—
970C2×C4—222no—
971C2×C4—222no—
972C2×C4—221no—
973C2×C4—221no—
974C2×C4—222no—
975C2×C4—222no—
976C2×C4—222no—
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—448no—
987C2×C4—448no—
988C2×C4—448no—
989C2×C4—444no—
990C2×C4—884no—
991C2×C4—884no—
992C2×C4—884no—
993C2×C4C22×C4×D1114yes—
994C2×C4C22×C4×D1112yes—
995C2×C4C22×C4×D1114yes—
996C2×C4#6704214yes—
997C22—22no—
998C22—22no—
999C22—24no—
1000C22—24no—
1001C22—42no—
1002C22—42no—
1003C22—41no—
1004C22—41no—
1005C22—41no—
1006C22—41no—
1007C22—114no—
1008C22—224no—
1009C22—222no—
1010C22—222no—
1011C22—224no—
1012C22—224no—
1013C22—222no—
1014C22—222no—
1015C22—224no—
1016C22—224no—
1017C22—224no—
1018C22—224no—
1019C22—4416no—
1020C22—442no—
1021C22—442no—
1022C22—442no—
1023C22—442no—
1024C22—441no—
1025C22—442no—
1026C22—441no—
1027C22—441no—
1028C22—441no—
1029C22—442no—
1030C22—888no—
1031C22—888no—
1032C22C23×C4×D1111yescharacteristic
1033C22C2×#6704212yes—
1034C22#1062345312yes—
1035C22D11×H(5,𝔽2)11yescharacteristic
1036C22D11×H(5,𝔽2)11yescharacteristic
1037C4—24no—
1038C4—24no—
1039C4—22no—
1040C4—24no—
1041C4—42no—
1042C4—42no—
1043C4—42no—
1044C4—222no—
1045C4—224no—
1046C4—442no—
1047C4—442no—
1048C4—442no—
1049C4—442no—
1050C2—42no—
1051C2—42no—
1052C2—224no—
1053C2—442no—
1054C2—444no—
1055C2—442no—
1056C2D11×#51811yescharacteristic
1057C2C4×#6704212yes—
1058C2#1308277211yescharacteristic
1059C2#1308279011yescharacteristic
1060C2#1308293512yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2374C2
socle, cosocleC23×C11C25
prime radicalC2×#10623184C2
hypercenter#2374D11
hypocenterC11#34407
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2374

Complements

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

NH ≅ G/Ntype
2. #13071769C2semidirect
3. #13071764C2semidirect
4. #13071753C2semidirect
5. #13071655C2semidirect
6. #13071615C2semidirect
7. #13071613C2semidirect
8. #13071599C2semidirect
9. #13071460C2semidirect
10. C22⋊C4×D44C2semidirect
11. #13071406C2semidirect
12. #13071380C2semidirect
13. #13071310C2semidirect
14. #13071278C2semidirect
15. #13071278C2semidirect
16. #13071195C2semidirect
17. C4×#66935C2semidirect
18. D11×#386C2semidirect
19. C11×#2374C2semidirect
22. C23×C4×D11C22semidirect
26. C2×C4×C22⋊D11C22semidirect
27. #10623184C4semidirect
30. C2×#66945C22semidirect
36. C2×C22⋊C4×D11C22semidirect
37. C2×C22⋊C4×D11C22semidirect
40. C2×C4×D44C22semidirect
41. C2×#66925C22semidirect
42. C2×#66925C22semidirect
44. C11×#388C22semidirect
45. C11×#388C22semidirect
46. C11×#387C22semidirect
48. C4×C11×C4⋊C4C22semidirect
49. C4×C11×C22⋊C4C22semidirect
50. C4×C11×C22⋊C4C22semidirect
53. #10622826C22semidirect
54. #10622825C22semidirect
55. #10622603C22semidirect
56. #10622602C22semidirect
57. #10622602C22semidirect
58. #10622601C22semidirect
59. #10622601C22semidirect
60. #10622600C22semidirect
61. #10622598C22semidirect
62. #10622594C22semidirect
63. #10622571C22semidirect
64. #10622571C22semidirect
66. #10622570C22semidirect
67. #10622570C22semidirect
69. #10622569C22semidirect
71. #10622568C22semidirect
72. #10622568C22semidirect
73. #10622564C22semidirect
74. #10622564C22semidirect
75. #10622563C22semidirect
76. #10622558C22semidirect
77. #10622557C22semidirect
78. #10622553C22semidirect
79. #10622553C22semidirect
80. #10622553C22semidirect
81. #10622552C22semidirect
82. #10622552C22semidirect
83. #10622552C22semidirect
84. C4×(C2×D11)⋊C4C22semidirect
85. C4×(C2×D11)⋊C4C22semidirect
86. #10622546C22semidirect
87. C4×Dic11⋊C4C22semidirect
88. #10622283C22semidirect
89. #10622283C22semidirect
90. #10622281C22semidirect
91. #10622281C22semidirect
92. #10622281C22semidirect
93. #10622279C22semidirect
94. #10622279C22semidirect
95. #10622279C22semidirect
96. #10622279C22semidirect
99. #10622278C22semidirect
100. #10622278C22semidirect
101. #10622278C22semidirect
102. #10622278C22semidirect
103. #10622278C22semidirect
104. #10622277C22semidirect
105. D11×#95C22semidirect
106. #10622268C22semidirect
107. #10622260C22semidirect
120. C2×D4×D11C2×C4semidirect
123. C22×D44C2×C4semidirect
137. C11×#123C2×C4semidirect
156. #66990C2×C4semidirect
157. #66982C2×C4semidirect
191. #66948C2×C4semidirect
192. #66947C2×C4semidirect
194. #66937C2×C4semidirect
195. #66935C2×C4semidirect
196. #66935C2×C4semidirect
200. C22⋊C4×D11C2×C4semidirect
239. C23×D11C22×C4semidirect
251. C22×C4×C11C22×C4semidirect
289. C2×D44C22×C4semidirect
311. C2×C4×D11C22×C4semidirect
314. C11×C4⋊C4C22×C4semidirect
320. C11×C22⋊C4C22×C4semidirect
329. C22⋊Dic11C22×C4semidirect
347. (C2×D11)⋊C4C22×C4semidirect
348. (C2×D11)⋊C4C22×C4semidirect
356. Dic11⋊C4C22×C4semidirect
366. #2374D11semidirect
531. #388C2×D11semidirect
532. #388C2×D11semidirect
536. #387C2×D11semidirect
564. C4×C4⋊C4C2×D11semidirect
571. C4×C22⋊C4C2×D11semidirect
572. C4×C22⋊C4C2×D11semidirect
658. #123C4×D11semidirect
833. C22×C4C2×C4×D11semidirect
851. C4⋊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×#106231842
#130717692
#130717642
#130717532
#130716552
#130716152
#130716132
#130715992
#130714602
C22⋊C4×D442
#130714062
#130713802
#130713102
#130712782
#130711952
C4×#669352
D11×#3862
C11×#23742
#3440711