Finite Group Databasebeta

← #14960874

Subgroups — #14960874

Order 2816.

3282 conjugacy classes of subgroups.

The subgroup lattice has 1092 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076892C212yesmaximal, complemented
2#13075660C211yesmaximal, characteristic, complemented
3#13075657C211yesmaximal, characteristic, complemented
4#13075655C212yesmaximal, complemented
5#13075177C212yesmaximal, complemented
6#13075006C212yesmaximal, complemented
7#13075002C212yesmaximal, complemented
8#13074992C212yesmaximal, complemented
9#13074943C212yesmaximal, complemented
10#13074818C211yesmaximal, characteristic, complemented
11#13074420C211yesmaximal, characteristic, complemented
12#13074349C211yesmaximal, characteristic, complemented
13#13072868C212yesmaximal, complemented
14#13072738C212yesmaximal, complemented
15#13072155C212yesmaximal, complemented
16#13072071C212yesmaximal, complemented
17#13071275C212yesmaximal, complemented
18D11×#379C211yesmaximal, characteristic, complemented
19C11×#2670C211yesmaximal, characteristic, complemented
20C25×D11C2211yescharacteristic
21C2×C11×#124C2212yescomplemented
22C2×C11×#120C2212yes—
23C2×#66999C2211yescharacteristic, complemented
24C2×#66992C2212yescomplemented
25C2×#66991C2211yescharacteristic, complemented
26C2×#66990C2212yes—
27C2×#66990C2212yes—
28C2×#66990C2212yes—
29C2×#66990C2212yes—
30C2×#66990C2212yes—
31C2×#66990C2212yes—
32C2×#66988C2212yescomplemented
33C2×#66951C2212yescomplemented
34C2×(C22⋊D11)⋊C4C2212yescomplemented
35C2×C22⋊C4×D11C2212yes—
36C2×C22⋊C4×D11C2212yes—
37C2×C22⋊C4×D11C2211yescharacteristic
38C2×C22⋊C4×D11C2211yescharacteristic
39C11×#394C2212yescomplemented
40C11×#393C2211yescharacteristic, complemented
41C11×#392C2212yescomplemented
42C11×#392C2211yescharacteristic, complemented
43C11×#390C2212yescomplemented
44C11×#388C2212yescomplemented
45C11×#379C2211yescharacteristic
46#10622860C2211yescharacteristic
47#10622860C2212yes—
48#10622844C2211yescharacteristic, complemented
49#10622844C2212yescomplemented
50#10622836C2211yescharacteristic, complemented
51#10622835C2212yescomplemented
52#10622835C2212yescomplemented
53#10622834C2212yescomplemented
54#10622833C2212yescomplemented
55#10622833C2212yescomplemented
56#10622605C2212yescomplemented
57#10622603C2212yescomplemented
58#10622602C2212yescomplemented
59#10622574C2212yescomplemented
60#10622574C2212yescomplemented
61#10622572C2212yescomplemented
62#10622572C2212yescomplemented
63#10622572C2212yescomplemented
64#10622571C2212yescomplemented
65#10622571C2212yescomplemented
66#10622570C2212yescomplemented
67#10622570C2212yescomplemented
68#10622569C2212yescomplemented
69#10622569C2212yescomplemented
70#10622568C2212yes—
71#10622568C2212yes—
72#10622568C2211yescharacteristic
73#10622568C2212yes—
74#10622568C2212yes—
75#10622568C2212yes—
76#10622568C2211yescharacteristic
77#10622568C2212yes—
78#10622568C2212yes—
79#10622568C2212yes—
80#10622566C2211yescharacteristic, complemented
81#10622565C2212yescomplemented
82#10622565C2212yescomplemented
83#10622565C2212yescomplemented
84#10622564C2212yescomplemented
85#10622562C2211yescharacteristic, complemented
86#10622561C2212yescomplemented
87#10622561C2212yescomplemented
88#10622561C2212yescomplemented
89#10622558C2212yescomplemented
90#10622558C2212yescomplemented
91#10622558C2212yescomplemented
92#10622557C2212yescomplemented
93#10622553C2212yescomplemented
94#10622553C2212yescomplemented
95#10622553C2212yescomplemented
96C4×(C2×D11)⋊C4C2212yescomplemented
97#10622290C2211yescharacteristic, complemented
98#10622289C2212yescomplemented
99#10622288C2212yescomplemented
100#10622288C2212yescomplemented
101#10622287C2211yescharacteristic, complemented
102#10622283C2212yescomplemented
103#10622282C2212yescomplemented
104#10622281C2212yescomplemented
105#10622280C2211yescharacteristic, complemented
106#10622280C2211yescharacteristic, complemented
107C25×C11C2311yescharacteristic
108C24×D11—24no—
109C24×D11—44no—
110C24×D11—42no—
111C24×D11—42no—
112C24×D11—44no—
113C24×D11C2312yes—
114C24×D11C2311yescharacteristic
115C24×D11C2312yes—
116C24×D11C2311yescharacteristic
117C22×Q8×C11C2311yescharacteristic, complemented
118C22×D4×C11C2312yes—
119C22×D4×C11C2312yes—
120C22×D4×C11C2312yes—
121C22×D4×C11C2311yescharacteristic, complemented
122C22×C22⋊D11C2312yes—
123C22×C22⋊D11C2312yes—
124C22×C22⋊D11C2312yes—
125C22×C22⋊D11C2312yes—
126C23×Dic11C2312yescomplemented
127C22×C4×D11C2312yes—
128C22×C4×D11C2311yescharacteristic
129C22×C4×D11C2311yescharacteristic
130C11×#124—44no—
131C11×#120—44no—
132C2×C11×C4⋊C4C2312yescomplemented
133C2×C11×C22⋊C4C2312yes—
134C2×C11×C22⋊C4C2312yes—
135C2×C11×C22⋊C4C2312yes—
136C2×C11×C22⋊C4C2311yescharacteristic
137C2×C11×C22⋊C4C2311yescharacteristic
138C2×C11×C22⋊C4C2312yes—
139C2×C11×C22⋊C4C2312yes—
140C2×C11×C22⋊C4C2312yescomplemented
141C2×C11×C22⋊C4C2312yescomplemented
142C2×C11×C22⋊C4C2312yescomplemented
143C2×C42×C11C2312yescomplemented
144C2×C22⋊Dic11C2312yes—
145C2×C22⋊Dic11C2312yes—
146C2×C22⋊Dic11C2312yes—
147C2×C22⋊Dic11C2311yescharacteristic
148C2×C22⋊Dic11C2311yescharacteristic
149C2×C22⋊Dic11C2312yes—
150C2×C22⋊Dic11C2312yes—
151C2×C22⋊Dic11C2312yes—
152C2×C22⋊Dic11C2312yes—
153C2×C22⋊Dic11C2312yes—
154C2×C22⋊Dic11C2312yescomplemented
155C2×C22⋊Dic11C2312yescomplemented
156C2×C22⋊Dic11C2312yescomplemented
157#66999—42no—
158#66992—44no—
159#66991—42no—
160#66990—28no—
161#66990—44no—
162#66990—44no—
163#66990—44no—
164#66990—44no—
165#66990—44no—
166#66988—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)⋊C4C2311yescharacteristic
177C2×(C2×D11)⋊C4C2311yescharacteristic
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×C4⋊Dic11C2312yescomplemented
187C2×C4⋊Dic11C2311yescharacteristic, complemented
188C2×C4⋊Dic11C2311yescharacteristic, complemented
189C2×Dic11⋊C4C2312yescomplemented
190C2×Dic11⋊C4C2312yescomplemented
191C2×Dic11⋊C4C2312yescomplemented
192C2×Dic11⋊C4C2312yescomplemented
193C2×Dic11⋊C4C2312yescomplemented
194C2×Dic11⋊C4C2312yescomplemented
195C2×C4×Dic11C2312yescomplemented
196C2×C4×Dic11C2312yescomplemented
197#66951—44no—
198(C22⋊D11)⋊C4—44no—
199C22⋊C4×D11—44no—
200C22⋊C4×D11—44no—
201C22⋊C4×D11—42no—
202C22⋊C4×D11—42no—
203C11×#95C2311yescharacteristic, complemented
204C11×#95C2311yescharacteristic, complemented
205C11×#95C2312yescomplemented
206C11⋊#95C2311yescharacteristic, complemented
207C11⋊#95C2311yescharacteristic, complemented
208C11⋊#95C2312yescomplemented
209C11⋊#95C2312yescomplemented
210C11⋊#95C2312yescomplemented
211C11⋊#95C2312yescomplemented
212C11⋊#95C2312yescomplemented
213C11⋊#95C2312yescomplemented
214C11⋊#95C2312yescomplemented
215C11⋊#95C2312yescomplemented
216C11⋊#95C2312yescomplemented
217#36725—111nomaximal, Sylow
218C24×C11—22no—
219C24×C11—24no—
220C24×C11—41no—
221C24×C11—42no—
222C24×C11—41no—
223C24×C11C2412yes—
224C24×C11C2411yescharacteristic
225C24×C11C2412yes—
226C23×D11—24no—
227C23×D11—24no—
228C23×D11—24no—
229C23×D11—22no—
230C23×D11—22no—
231C23×D11—22no—
232C23×D11—24no—
233C23×D11—24no—
234C23×D11—24no—
235C23×D11—24no—
236C23×D11—24no—
237C23×D11—24no—
238C23×D11—42no—
239C23×D11—42no—
240C23×D11—42no—
241C23×D11—42no—
242C23×D11—42no—
243C23×D11—42no—
244C23×D11—42no—
245C23×D11—42no—
246C23×D11—41no—
247C23×D11—42no—
248C23×D11—41no—
249C23×D11—432no—
250C23×D11—416no—
251C23×D11—416no—
252C23×D11—432no—
253C23×D11—416no—
254C23×D11#4114yes—
255C23×D11C2411yescharacteristic
256C23×D11C2412yes—
257C23×D11C2411yescharacteristic
258C2×Q8×C11—41no—
259C2×Q8×C11—42no—
260C2×D4×C11—24no—
261C2×D4×C11—24no—
262C2×D4×C11—24no—
263C2×D4×C11—42no—
264C2×D4×C11—42no—
265C2×D4×C11—42no—
266C2×D4×C11—42no—
267C2×D4×C11—41no—
268C2×D4×C11—42no—
269C2×D4×C11—42no—
270C2×D4×C11—42no—
271C22×C4×C11C2412yes—
272C22×C4×C11C2412yes—
273C22×C4×C11C2411yescharacteristic
274C22×C4×C11C2412yes—
275C22×C4×C11C2411yescharacteristic
276C22×C4×C11C2412yes—
277C2×C22⋊D11—24no—
278C2×C22⋊D11—24no—
279C2×C22⋊D11—24no—
280C2×C22⋊D11—24no—
281C2×C22⋊D11—24no—
282C2×C22⋊D11—24no—
283C2×C22⋊D11—42no—
284C2×C22⋊D11—42no—
285C2×C22⋊D11—42no—
286C2×C22⋊D11—42no—
287C2×C22⋊D11—42no—
288C2×C22⋊D11—42no—
289C22×Dic11—42no—
290C22×Dic11—42no—
291C22×Dic11—42no—
292C22×Dic11C2412yes—
293C22×Dic11C2412yes—
294C22×Dic11C2412yes—
295C22×Dic11C2412yes—
296C22×Dic11C2412yes—
297C22×Dic11C2411yescharacteristic
298C22×Dic11C2411yescharacteristic
299C2×C4×D11—24no—
300C2×C4×D11—22no—
301C2×C4×D11—22no—
302C2×C4×D11—42no—
303C2×C4×D11—42no—
304C2×C4×D11—42no—
305C2×C4×D11—42no—
306C11×C4⋊C4—42no—
307C11×C22⋊C4—24no—
308C11×C22⋊C4—24no—
309C11×C22⋊C4—42no—
310C11×C22⋊C4—41no—
311C11×C22⋊C4—41no—
312C11×C22⋊C4—42no—
313C11×C22⋊C4—42no—
314C11×C22⋊C4—42no—
315C11×C22⋊C4—42no—
316C11×C22⋊C4—42no—
317C42×C11—42no—
318C22⋊Dic11—24no—
319C22⋊Dic11—24no—
320C22⋊Dic11—24no—
321C22⋊Dic11—41no—
322C22⋊Dic11—41no—
323C22⋊Dic11—42no—
324C22⋊Dic11—42no—
325C22⋊Dic11—42no—
326C22⋊Dic11—42no—
327C22⋊Dic11—42no—
328C22⋊Dic11—42no—
329C22⋊Dic11—42no—
330C22⋊Dic11—42no—
331(C2×D11)⋊C4—24no—
332(C2×D11)⋊C4—24no—
333(C2×D11)⋊C4—24no—
334(C2×D11)⋊C4—24no—
335(C2×D11)⋊C4—24no—
336(C2×D11)⋊C4—24no—
337(C2×D11)⋊C4—24no—
338(C2×D11)⋊C4—24no—
339(C2×D11)⋊C4—42no—
340(C2×D11)⋊C4—41no—
341(C2×D11)⋊C4—41no—
342(C2×D11)⋊C4—42no—
343(C2×D11)⋊C4—42no—
344(C2×D11)⋊C4—42no—
345(C2×D11)⋊C4—42no—
346(C2×D11)⋊C4—42no—
347(C2×D11)⋊C4—42no—
348(C2×D11)⋊C4—42no—
349(C2×D11)⋊C4—42no—
350C4⋊Dic11—42no—
351C4⋊Dic11—41no—
352C4⋊Dic11—41no—
353Dic11⋊C4—42no—
354Dic11⋊C4—42no—
355Dic11⋊C4—42no—
356Dic11⋊C4—42no—
357Dic11⋊C4—42no—
358Dic11⋊C4—42no—
359C4×Dic11—42no—
360C4×Dic11—42no—
361#2846—112no—
362#2736—111no—
363#2735—112no—
364#2735—111no—
365#2697—112no—
366#2685—112no—
367#2685—112no—
368#2684—112no—
369#2678—112no—
370#2670D1111yescharacteristic, complemented
371#2668—111no—
372#2626—111no—
373#2617—111no—
374#2480—112no—
375#2472—112no—
376#2424—112no—
377#2418—112no—
378#2321—112no—
379C2×#379—111no—
380C23×C11—22no—
381C23×C11—21no—
382C23×C11—21no—
383C23×C11—22no—
384C23×C11—22no—
385C23×C11—22no—
386C23×C11—22no—
387C23×C11—22no—
388C23×C11—22no—
389C23×C11—22no—
390C23×C11—22no—
391C23×C11—22no—
392C23×C11—22no—
393C23×C11—22no—
394C23×C11—22no—
395C23×C11—22no—
396C23×C11—22no—
397C23×C11—48no—
398C23×C11—44no—
399C23×C11—44no—
400C23×C11—48no—
401C23×C11—44no—
402C23×C11C2×#4112yes—
403C23×C11H(5,𝔽2)14yes—
404C23×C11C2511yescharacteristic
405C22×D11—22no—
406C22×D11—22no—
407C22×D11—216no—
408C22×D11—22no—
409C22×D11—22no—
410C22×D11—21no—
411C22×D11—21no—
412C22×D11—22no—
413C22×D11—22no—
414C22×D11—22no—
415C22×D11—22no—
416C22×D11—22no—
417C22×D11—22no—
418C22×D11—28no—
419C22×D11—48no—
420C22×D11—48no—
421C22×D11—48no—
422C22×D11—48no—
423C22×D11—44no—
424C22×D11—48no—
425C22×D11—48no—
426C22×D11—48no—
427C22×D11—48no—
428C22×D11—48no—
429C22×D11—48no—
430C22×D11—44no—
431C22×D11—48no—
432C22×D11—44no—
433C22×D11—48no—
434C22×D11—48no—
435C22×D11—48no—
436C22×D11—44no—
437C22×D11—48no—
438C22×D11—4128no—
439C22×D11—44no—
440C22×D11—48no—
441C22×D11—48no—
442C22×D11C2×#4112yes—
443C22×D11C2×#4112yes—
444C22×D11H(5,𝔽2)14yes—
445C22×D11H(5,𝔽2)12yes—
446C22×D11H(5,𝔽2)12yes—
447Q8×C11—82no—
448D4×C11—84no—
449D4×C11—84no—
450D4×C11—84no—
451D4×C11—82no—
452C2×C4×C11—22no—
453C2×C4×C11—22no—
454C2×C4×C11—22no—
455C2×C4×C11—22no—
456C2×C4×C11—22no—
457C2×C4×C11—22no—
458C2×C4×C11—22no—
459C2×C4×C11—22no—
460C2×C4×C11—22no—
461C2×C4×C11—21no—
462C2×C4×C11—21no—
463C2×C4×C11—22no—
464C2×C4×C11—22no—
465C2×C4×C11—22no—
466C2×C4×C11—22no—
467C2×C4×C11—22no—
468C22⋊D11—48no—
469C22⋊D11—84no—
470C22⋊D11—84no—
471C22⋊D11—84no—
472C2×Dic11—22no—
473C2×Dic11—22no—
474C2×Dic11—22no—
475C2×Dic11—22no—
476C2×Dic11—22no—
477C2×Dic11—22no—
478C2×Dic11—21no—
479C2×Dic11—22no—
480C2×Dic11—22no—
481C2×Dic11—22no—
482C2×Dic11—22no—
483C2×Dic11—22no—
484C2×Dic11—22no—
485C2×Dic11—22no—
486C2×Dic11—22no—
487C2×Dic11—22no—
488C2×Dic11—22no—
489C2×Dic11—22no—
490C2×Dic11—21no—
491C2×Dic11—84no—
492C4×D11—82no—
493C4×D11—82no—
494C4×D11—84no—
495C26—111no—
496C2×#126—112no—
497C2×#124C2×D1112yescomplemented
498C2×#123—112no—
499C2×C22⋊Q8—111no—
500C2×#121—111no—
501C2×#121—112no—
502C2×#120—112no—
503C2×#120—112no—
504C2×#120—112no—
505C2×#120—112no—
506C2×#120—112no—
507C2×#120—112no—
508C2×#120C2×D1112yes—
509C2×C4×D4—112no—
510C22×C22⋊C4—111no—
511C22×C22⋊C4—111no—
512C22×C22⋊C4—112no—
513C22×C22⋊C4—112no—
514#399—112no—
515#399—111no—
516#399—111no—
517#397—111no—
518#397—112no—
519#397—112no—
520#397—112no—
521#397—111no—
522#397—112no—
523#397—112no—
524#396—112no—
525#396—112no—
526#396—112no—
527#396—112no—
528#394—112no—
529#394—112no—
530#394—112no—
531#394—112no—
532#394—112no—
533#394—112no—
534#394—112no—
535#394C2×D1112yescomplemented
536#393—111no—
537#393—112no—
538#393C2×D1111yescharacteristic, complemented
539#392—111no—
540#392C2×D1111yescharacteristic, complemented
541#392C2×D1112yescomplemented
542#390—112no—
543#390—112no—
544#390—112no—
545#390C2×D1112yescomplemented
546#388—112no—
547#388—112no—
548#388—112no—
549#388—112no—
550#388—112no—
551#388—112no—
552#388—112no—
553#388—112no—
554#388—112no—
555#388—112no—
556#388—112no—
557#388C2×D1112yescomplemented
558#386—112no—
559#386—112no—
560#386—112no—
561#386—112no—
562#386—112no—
563#386—112no—
564#385—112no—
565#385—112no—
566#380—111no—
567#380—111no—
568#379—112no—
569#379—111no—
570#379—112no—
571#379—112no—
572#379—112no—
573#379—112no—
574#379—112no—
575#379—112no—
576#379—111no—
577#379—112no—
578#379—112no—
579#379—111no—
580#379C2×D1111yescharacteristic
581C4×C22⋊C4—112no—
582C22×C11—22no—
583C22×C11—24no—
584C22×C11—24no—
585C22×C11—24no—
586C22×C11—24no—
587C22×C11—416no—
588C22×C11—42no—
589C22×C11—42no—
590C22×C11—41no—
591C22×C11—42no—
592C22×C11—42no—
593C22×C11—41no—
594C22×C11—42no—
595C22×C11—42no—
596C22×C11—42no—
597C22×C11—42no—
598C22×C11—42no—
599C22×C11—42no—
600C22×C11—42no—
601C22×C11—42no—
602C22×C11C22×#4111yescharacteristic
603C22×C11C2×H(5,𝔽2)12yes—
604C22×C11C2×H(5,𝔽2)11yescharacteristic
605C22×C11C2×H(5,𝔽2)11yescharacteristic
606C22×C11C2×H(5,𝔽2)12yes—
607C2×D11—24no—
608C2×D11—22no—
609C2×D11—24no—
610C2×D11—22no—
611C2×D11—22no—
612C2×D11—24no—
613C2×D11—24no—
614C2×D11—24no—
615C2×D11—24no—
616C2×D11—432no—
617C2×D11—416no—
618C2×D11—432no—
619C2×D11—416no—
620C2×D11—42no—
621C2×D11—42no—
622C2×D11—42no—
623C2×D11—41no—
624C2×D11—42no—
625C2×D11—42no—
626C2×D11—41no—
627C2×D11#53814yes—
628C4×C11—42no—
629C4×C11—42no—
630C4×C11—42no—
631C4×C11—41no—
632C4×C11—41no—
633C4×C11—42no—
634Dic11—42no—
635Dic11—42no—
636Dic11—41no—
637Dic11—41no—
638Dic11—42no—
639Dic11—42no—
640Dic11—42no—
641C25—111no—
642C25—112no—
643C25—111no—
644C25—112no—
645C25—224no—
646C25—444no—
647C25—442no—
648C25—444no—
649C25—442no—
650C25C22×D1111yescharacteristic
651C22×Q8C22×D1111yescharacteristic, complemented
652C22×D4—112no—
653C22×D4—112no—
654C22×D4—112no—
655C22×D4—112no—
656C22×D4C22×D1112yes—
657C22×D4C22×D1112yes—
658C22×D4C22×D1112yes—
659C22×D4C22×D1111yescharacteristic, complemented
660C23×C4—112no—
661C23×C4—112no—
662C23×C4—111no—
663C23×C4—111no—
664#126—444no—
665#124—44no—
666#123—444no—
667C22⋊Q8—442no—
668#121—444no—
669#121—442no—
670#120—44no—
671#120—228no—
672#120—444no—
673#120—444no—
674#120—444no—
675#120—444no—
676#120—444no—
677C4×D4—444no—
678C2×C4⋊C4—112no—
679C2×C4⋊C4—112no—
680C2×C4⋊C4—111no—
681C2×C4⋊C4—111no—
682C2×C4⋊C4—112no—
683C2×C4⋊C4—112no—
684C2×C4⋊C4—112no—
685C2×C4⋊C4—112no—
686C2×C4⋊C4—112no—
687C2×C4⋊C4C22×D1112yescomplemented
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—112no—
696C2×C22⋊C4—112no—
697C2×C22⋊C4—112no—
698C2×C22⋊C4—112no—
699C2×C22⋊C4—111no—
700C2×C22⋊C4—112no—
701C2×C22⋊C4—111no—
702C2×C22⋊C4—112no—
703C2×C22⋊C4—112no—
704C2×C22⋊C4—112no—
705C2×C22⋊C4—112no—
706C2×C22⋊C4—112no—
707C2×C22⋊C4—112no—
708C2×C22⋊C4—112no—
709C2×C22⋊C4—112no—
710C2×C22⋊C4—112no—
711C2×C22⋊C4—112no—
712C2×C22⋊C4—111no—
713C2×C22⋊C4—111no—
714C2×C22⋊C4—112no—
715C2×C22⋊C4—112no—
716C2×C22⋊C4—112no—
717C2×C22⋊C4—112no—
718C2×C22⋊C4—112no—
719C2×C22⋊C4—112no—
720C2×C22⋊C4—444no—
721C2×C22⋊C4—444no—
722C2×C22⋊C4—442no—
723C2×C22⋊C4—442no—
724C2×C22⋊C4C22×D1112yes—
725C2×C22⋊C4C22×D1112yes—
726C2×C22⋊C4C22×D1111yescharacteristic
727C2×C22⋊C4C22×D1112yes—
728C2×C22⋊C4C22×D1111yescharacteristic
729C2×C22⋊C4C22×D1112yes—
730C2×C22⋊C4C22×D1112yes—
731C2×C22⋊C4C22×D1112yescomplemented
732C2×C22⋊C4C22×D1112yescomplemented
733C2×C22⋊C4C22×D1112yescomplemented
734C2×C42—112no—
735C2×C42—112no—
736C2×C42C22×D1112yescomplemented
737#95—112no—
738#95—112no—
739#95—111no—
740#95—111no—
741#95—112no—
742#95—112no—
743#95—112no—
744#95—112no—
745#95—112no—
746#95—112no—
747#95—112no—
748#95C22×D1111yescharacteristic, complemented
749#95C22×D1111yescharacteristic, complemented
750#95C22×D1112yescomplemented
751C2×C11—42no—
752C2×C11—44no—
753C2×C11—82no—
754C2×C11C2×#53811yescharacteristic
755C2×C11#349012yes—
756C2×C11#353211yescharacteristic
757C2×C11#353212yes—
758C2×C11#353211yescharacteristic
759D11—24no—
760D11—42no—
761D11—44no—
762C24—24no—
763C24—22no—
764C24—41no—
765C24—42no—
766C24—41no—
767C24—111no—
768C24—111no—
769C24—112no—
770C24—114no—
771C24—222no—
772C24—222no—
773C24—224no—
774C24—224no—
775C24—224no—
776C24—224no—
777C24—224no—
778C24—224no—
779C24—224no—
780C24—224no—
781C24—224no—
782C24—222no—
783C24—442no—
784C24—442no—
785C24—442no—
786C24—442no—
787C24—442no—
788C24—441no—
789C24—441no—
790C24—442no—
791C24—442no—
792C24—442no—
793C24—442no—
794C24—4432no—
795C24—4416no—
796C24—4416no—
797C24—4432no—
798C24—4416no—
799C24C23×D1112yes—
800C24C23×D1112yes—
801C24C23×D1111yescharacteristic
802C2×Q8—41no—
803C2×Q8—42no—
804C2×D4—24no—
805C2×D4—24no—
806C2×D4—24no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—42no—
812C2×D4—42no—
813C2×D4—42no—
814C2×D4—41no—
815C2×D4—224no—
816C2×D4—224no—
817C2×D4—224no—
818C2×D4—224no—
819C2×D4—224no—
820C2×D4—224no—
821C2×D4—442no—
822C2×D4—442no—
823C2×D4—442no—
824C2×D4—442no—
825C2×D4—442no—
826C2×D4—442no—
827C22×C4—112no—
828C22×C4—112no—
829C22×C4—112no—
830C22×C4—112no—
831C22×C4—112no—
832C22×C4—111no—
833C22×C4—111no—
834C22×C4—224no—
835C22×C4—222no—
836C22×C4—222no—
837C22×C4—442no—
838C22×C4—442no—
839C22×C4—442no—
840C22×C4—442no—
841C22×C4—442no—
842C22×C4—442no—
843C22×C4—442no—
844C22×C4C23×D1112yes—
845C22×C4C23×D1112yes—
846C22×C4C23×D1111yescharacteristic
847C22×C4C23×D1112yes—
848C22×C4C23×D1111yescharacteristic
849C22×C4C23×D1112yes—
850C4⋊C4—42no—
851C4⋊C4—442no—
852C4⋊C4—442no—
853C4⋊C4—441no—
854C4⋊C4—442no—
855C4⋊C4—441no—
856C4⋊C4—442no—
857C4⋊C4—442no—
858C4⋊C4—442no—
859C4⋊C4—442no—
860C22⋊C4—24no—
861C22⋊C4—24no—
862C22⋊C4—42no—
863C22⋊C4—41no—
864C22⋊C4—41no—
865C22⋊C4—42no—
866C22⋊C4—42no—
867C22⋊C4—42no—
868C22⋊C4—42no—
869C22⋊C4—42no—
870C22⋊C4—224no—
871C22⋊C4—224no—
872C22⋊C4—224no—
873C22⋊C4—224no—
874C22⋊C4—224no—
875C22⋊C4—224no—
876C22⋊C4—224no—
877C22⋊C4—224no—
878C22⋊C4—224no—
879C22⋊C4—224no—
880C22⋊C4—224no—
881C22⋊C4—442no—
882C22⋊C4—442no—
883C22⋊C4—442no—
884C22⋊C4—441no—
885C22⋊C4—441no—
886C22⋊C4—442no—
887C22⋊C4—442no—
888C22⋊C4—442no—
889C22⋊C4—442no—
890C22⋊C4—442no—
891C22⋊C4—442no—
892C22⋊C4—441no—
893C22⋊C4—442no—
894C22⋊C4—441no—
895C22⋊C4—442no—
896C22⋊C4—442no—
897C22⋊C4—442no—
898C22⋊C4—442no—
899C22⋊C4—442no—
900C22⋊C4—442no—
901C22⋊C4—442no—
902C42—42no—
903C42—442no—
904C42—442no—
905C11#3672511yescharacteristic, complemented, Sylow
906C23—22no—
907C23—22no—
908C23—22no—
909C23—21no—
910C23—21no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—44no—
924C23—48no—
925C23—44no—
926C23—48no—
927C23—44no—
928C23—112no—
929C23—112no—
930C23—112no—
931C23—112no—
932C23—114no—
933C23—228no—
934C23—2216no—
935C23—222no—
936C23—222no—
937C23—222no—
938C23—222no—
939C23—222no—
940C23—222no—
941C23—221no—
942C23—221no—
943C23—222no—
944C23—222no—
945C23—222no—
946C23—222no—
947C23—448no—
948C23—448no—
949C23—448no—
950C23—448no—
951C23—448no—
952C23—448no—
953C23—444no—
954C23—448no—
955C23—448no—
956C23—448no—
957C23—448no—
958C23—444no—
959C23—448no—
960C23—448no—
961C23—444no—
962C23—448no—
963C23—448no—
964C23—444no—
965C23—448no—
966C23—448no—
967C23—44128no—
968C23—444no—
969C23—448no—
970C23#6703714yes—
971C23#41×D1112yes—
972C23C24×D1111yescharacteristic
973Q8—82no—
974D4—84no—
975D4—84no—
976D4—84no—
977D4—82no—
978D4—448no—
979D4—884no—
980D4—884no—
981D4—884no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—222no—
999C2×C4—222no—
1000C2×C4—222no—
1001C2×C4—222no—
1002C2×C4—222no—
1003C2×C4—222no—
1004C2×C4—222no—
1005C2×C4—222no—
1006C2×C4—222no—
1007C2×C4—222no—
1008C2×C4—222no—
1009C2×C4—222no—
1010C2×C4—222no—
1011C2×C4—222no—
1012C2×C4—221no—
1013C2×C4—222no—
1014C2×C4—222no—
1015C2×C4—221no—
1016C2×C4—222no—
1017C2×C4—882no—
1018C2×C4—884no—
1019C2×C4—882no—
1020C2×C4—884no—
1021C22—22no—
1022C22—24no—
1023C22—24no—
1024C22—24no—
1025C22—24no—
1026C22—416no—
1027C22—42no—
1028C22—41no—
1029C22—42no—
1030C22—42no—
1031C22—41no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—114no—
1042C22—222no—
1043C22—224no—
1044C22—222no—
1045C22—224no—
1046C22—222no—
1047C22—224no—
1048C22—224no—
1049C22—224no—
1050C22—224no—
1051C22—4416no—
1052C22—4432no—
1053C22—4416no—
1054C22—4432no—
1055C22—442no—
1056C22—442no—
1057C22—441no—
1058C22—442no—
1059C22—442no—
1060C22—441no—
1061C22—442no—
1062C22C2×#6703712yes—
1063C22C2×#41×D1111yescharacteristic
1064C22D11×H(5,𝔽2)11yescharacteristic
1065C22D11×H(5,𝔽2)11yescharacteristic
1066C22D11×H(5,𝔽2)12yes—
1067C4—41no—
1068C4—42no—
1069C4—42no—
1070C4—42no—
1071C4—41no—
1072C4—42no—
1073C4—442no—
1074C4—441no—
1075C4—442no—
1076C4—442no—
1077C4—441no—
1078C4—442no—
1079C4—442no—
1080C2—42no—
1081C2—44no—
1082C2—82no—
1083C2—224no—
1084C2—442no—
1085C2—444no—
1086C2D11×#53811yescharacteristic
1087C2#1308229812yes—
1088C2#1308276611yescharacteristic
1089C2#1308277012yes—
1090C2#1308277311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2670C2
hypercenter#2670D11
hypocenterC11#36725
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2670

Complements

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

NH ≅ G/Ntype
1. #13076892C2semidirect
2. #13075660C2semidirect
3. #13075657C2semidirect
4. #13075655C2semidirect
5. #13075177C2semidirect
6. #13075006C2semidirect
7. #13075002C2semidirect
8. #13074992C2semidirect
9. #13074943C2semidirect
10. #13074818C2semidirect
11. #13074420C2semidirect
12. #13074349C2semidirect
13. #13072868C2semidirect
14. #13072738C2semidirect
15. #13072155C2semidirect
16. #13072071C2semidirect
17. #13071275C2semidirect
18. D11×#379C2semidirect
19. C11×#2670C2semidirect
21. C2×C11×#124C22semidirect
23. C2×#66999C22semidirect
24. C2×#66992C22semidirect
25. C2×#66991C22semidirect
32. C2×#66988C22semidirect
33. C2×#66951C22semidirect
34. C2×(C22⋊D11)⋊C4C22semidirect
39. C11×#394C22semidirect
40. C11×#393C22semidirect
41. C11×#392C22semidirect
42. C11×#392C22semidirect
43. C11×#390C22semidirect
44. C11×#388C22semidirect
48. #10622844C22semidirect
49. #10622844C22semidirect
50. #10622836C22semidirect
51. #10622835C22semidirect
52. #10622835C22semidirect
53. #10622834C22semidirect
54. #10622833C22semidirect
55. #10622833C22semidirect
56. #10622605C22semidirect
57. #10622603C22semidirect
58. #10622602C22semidirect
59. #10622574C22semidirect
60. #10622574C22semidirect
61. #10622572C22semidirect
62. #10622572C22semidirect
63. #10622572C22semidirect
64. #10622571C22semidirect
65. #10622571C22semidirect
66. #10622570C22semidirect
67. #10622570C22semidirect
68. #10622569C22semidirect
69. #10622569C22semidirect
80. #10622566C22semidirect
81. #10622565C22semidirect
82. #10622565C22semidirect
83. #10622565C22semidirect
84. #10622564C22semidirect
85. #10622562C22semidirect
86. #10622561C22semidirect
87. #10622561C22semidirect
88. #10622561C22semidirect
89. #10622558C22semidirect
90. #10622558C22semidirect
91. #10622558C22semidirect
92. #10622557C22semidirect
93. #10622553C22semidirect
94. #10622553C22semidirect
95. #10622553C22semidirect
96. C4×(C2×D11)⋊C4C22semidirect
97. #10622290C22semidirect
98. #10622289C22semidirect
99. #10622288C22semidirect
100. #10622288C22semidirect
101. #10622287C22semidirect
102. #10622283C22semidirect
103. #10622282C22semidirect
104. #10622281C22semidirect
105. #10622280C22semidirect
106. #10622280C22semidirect
117. C22×Q8×C11C23semidirect
121. C22×D4×C11C23semidirect
126. C23×Dic11C23semidirect
132. C2×C11×C4⋊C4C23semidirect
140. C2×C11×C22⋊C4C23semidirect
141. C2×C11×C22⋊C4C23semidirect
142. C2×C11×C22⋊C4C23semidirect
143. C2×C42×C11C23semidirect
154. C2×C22⋊Dic11C23semidirect
155. C2×C22⋊Dic11C23semidirect
156. C2×C22⋊Dic11C23semidirect
186. C2×C4⋊Dic11C23semidirect
187. C2×C4⋊Dic11C23semidirect
188. C2×C4⋊Dic11C23semidirect
189. C2×Dic11⋊C4C23semidirect
190. C2×Dic11⋊C4C23semidirect
191. C2×Dic11⋊C4C23semidirect
192. C2×Dic11⋊C4C23semidirect
193. C2×Dic11⋊C4C23semidirect
194. C2×Dic11⋊C4C23semidirect
195. C2×C4×Dic11C23semidirect
196. C2×C4×Dic11C23semidirect
203. C11×#95C23semidirect
204. C11×#95C23semidirect
205. C11×#95C23semidirect
206. C11⋊#95C23semidirect
207. C11⋊#95C23semidirect
208. C11⋊#95C23semidirect
209. C11⋊#95C23semidirect
210. C11⋊#95C23semidirect
211. C11⋊#95C23semidirect
212. C11⋊#95C23semidirect
213. C11⋊#95C23semidirect
214. C11⋊#95C23semidirect
215. C11⋊#95C23semidirect
216. C11⋊#95C23semidirect
370. #2670D11semidirect
497. C2×#124C2×D11semidirect
535. #394C2×D11semidirect
538. #393C2×D11semidirect
540. #392C2×D11semidirect
541. #392C2×D11semidirect
545. #390C2×D11semidirect
557. #388C2×D11semidirect
651. C22×Q8C22×D11semidirect
659. C22×D4C22×D11semidirect
687. C2×C4⋊C4C22×D11semidirect
731. C2×C22⋊C4C22×D11semidirect
732. C2×C22⋊C4C22×D11semidirect
733. C2×C22⋊C4C22×D11semidirect
736. C2×C42C22×D11semidirect
748. #95C22×D11semidirect
749. #95C22×D11semidirect
750. #95C22×D11semidirect
905. C11#36725semidirect

Maximal subgroups

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

subgroupindex
#130768922
#130756602
#130756572
#130756552
#130751772
#130750062
#130750022
#130749922
#130749432
#130748182
#130744202
#130743492
#130728682
#130727382
#130721552
#130720712
#130712752
D11×#3792
C11×#26702
#3672511