Finite Group Databasebeta

← #14926960

Subgroups — #14926960

Order 2816.

2042 conjugacy classes of subgroups.

The subgroup lattice has 1054 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076927C211yesmaximal, characteristic, complemented
2#13076925C211yesmaximal, characteristic, complemented
3#13076925C211yesmaximal, characteristic, complemented
4#13076921C211yesmaximal, characteristic, complemented
5#13074587C212yesmaximal, complemented
6#13074585C212yesmaximal, complemented
7#13073842C212yesmaximal, complemented
8#13073837C212yesmaximal, complemented
9#13073836C212yesmaximal, complemented
10#13073834C212yesmaximal, complemented
11#13072343C211yesmaximal, characteristic, complemented
12#13072342C211yesmaximal, characteristic, complemented
13#13072341C211yesmaximal, characteristic, complemented
14#13072340C211yesmaximal, characteristic, complemented
15#13072338C211yesmaximal, characteristic, complemented
16#13072336C211yesmaximal, characteristic, complemented
17#13072334C211yesmaximal, characteristic, complemented
18#13071229C212yesmaximal
19#13071227C212yesmaximal
20C2×#10622600C211yesmaximal, characteristic
21D11×#380C211yesmaximal, characteristic
22C4×C22⋊C4×D11C211yesmaximal, characteristic
23C11×#2442C211yesmaximal, characteristic, complemented
24C23×C4×D11C2211yescharacteristic
25C2×C11×#125C2211yescharacteristic, complemented
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2212yes—
28C22×C4⋊Dic11C2211yescharacteristic
29C2×C4⋊C4×D11C2211yescharacteristic
30C2×C4⋊C4×D11C2211yescharacteristic
31C2×#66943C2211yescharacteristic, complemented
32C2×#66943C2211yescharacteristic, complemented
33C2×C22⋊C4×D11C2211yescharacteristic
34C2×C22⋊C4×D11C2211yescharacteristic
35C2×C22⋊C4×D11C2212yes—
36C2×C42×D11C2211yescharacteristic
37C2×C42×D11C2211yescharacteristic
38C2×#66923C2211yescharacteristic, complemented
39C11×#400C2212yescomplemented
40C11×#398C2212yescomplemented
41C11×#389C2211yescharacteristic, complemented
42C11×#389C2211yescharacteristic, complemented
43C11×#385C2212yes—
44C11×#382C2211yescharacteristic, complemented
45C11×#380C2212yes—
46C11×#380C2211yescharacteristic
47C4×C11×C22⋊C4C2211yescharacteristic
48#10622825C2212yes—
49#10622825C2211yescharacteristic
50#10622823C2212yes—
51C4×C22⋊Dic11C2211yescharacteristic
52C2×C11⋊#95C2212yes—
53#10622602C2212yes—
54#10622602C2212yes—
55#10622602C2212yes—
56#10622602C2212yes—
57#10622602C2212yes—
58#10622602C2212yes—
59#10622600C2212yes—
60#10622600C2212yes—
61#10622600C2211yescharacteristic
62#10622600C2211yescharacteristic
63#10622600C2212yes—
64#10622600C2212yes—
65#10622600C2211yescharacteristic
66#10622600C2211yescharacteristic
67#10622600C2211yescharacteristic
68#10622600C2211yescharacteristic
69#10622599C2212yescomplemented
70#10622598C2211yescharacteristic, complemented
71#10622598C2211yescharacteristic, complemented
72#10622597C2212yescomplemented
73#10622597C2212yescomplemented
74#10622596C2212yescomplemented
75#10622595C2212yescomplemented
76#10622594C2212yescomplemented
77#10622594C2212yescomplemented
78#10622593C2212yescomplemented
79#10622591C2212yescomplemented
80#10622591C2212yescomplemented
81#10622590C2211yescharacteristic, complemented
82#10622590C2211yescharacteristic, complemented
83#10622586C2211yescharacteristic, complemented
84#10622586C2211yescharacteristic, complemented
85#10622563C2212yes—
86#10622559C2212yes—
87#10622555C2212yes—
88#10622555C2212yes—
89#10622555C2212yes—
90C22⋊C4×Dic11C2211yescharacteristic
91C22⋊C4×Dic11C2211yescharacteristic
92C4×(C2×D11)⋊C4C2211yescharacteristic
93C4×(C2×D11)⋊C4C2211yescharacteristic
94#10622549C2211yescharacteristic, complemented
95#10622541C2211yescharacteristic, complemented
96#10622541C2211yescharacteristic, complemented
97#10622281C2212yes—
98#10622281C2212yes—
99#10622281C2212yes—
100#10622281C2212yes—
101#10622281C2212yes—
102#10622281C2212yes—
103#10622280C2212yes—
104#10622280C2212yes—
105#10622280C2212yes—
106#10622279C2211yescharacteristic
107#10622279C2211yescharacteristic
108D11×#95C2211yescharacteristic
109D11×#95C2211yescharacteristic
110D11×#95C2212yes—
111#10622274C2212yescomplemented
112#10622273C2212yescomplemented
113#10622273C2212yescomplemented
114#10622272C2212yescomplemented
115#10622271C2212yescomplemented
116#10622271C2212yescomplemented
117#10622270C2212yescomplemented
118#10622270C2212yescomplemented
119#10622266C2212yescomplemented
120#10622266C2212yescomplemented
121#10622265C2212yescomplemented
122#10622265C2212yescomplemented
123C24×D11C2311yescharacteristic
124C23×C4×C11C2311yescharacteristic
125C23×C4×C11C2312yes—
126C23×Dic11C2312yes—
127C23×Dic11C2311yescharacteristic
128C22×C4×D11—42no—
129C22×C4×D11—42no—
130C22×C4×D11Q818yes—
131C22×C4×D11C2311yescharacteristic
132C22×C4×D11C2311yescharacteristic
133C22×C4×D11C2311yescharacteristic
134C22×C4×D11C2311yescharacteristic
135C22×C4×D11C2311yescharacteristic
136C22×C4×D11C2311yescharacteristic
137C22×C4×D11C2312yes—
138C22×C4×D11C2312yes—
139C22×C4×D11C2311yescharacteristic
140C22×C4×D11C2311yescharacteristic
141C11×#125—42no—
142C2×C11×C4⋊C4—42no—
143C2×C11×C4⋊C4C2311yescharacteristic
144C2×C11×C4⋊C4C2311yescharacteristic
145C2×C11×C4⋊C4C2311yescharacteristic
146C2×C11×C4⋊C4C2311yescharacteristic
147C2×C11×C4⋊C4C2312yes—
148C2×C11×C4⋊C4C2312yes—
149C2×C11×C4⋊C4C2312yes—
150C2×C11×C4⋊C4C2312yes—
151C2×C11×C4⋊C4C2312yes—
152C2×C11×C22⋊C4C2311yescharacteristic
153C2×C11×C22⋊C4C2311yescharacteristic
154C2×C11×C22⋊C4C2312yes—
155C2×C42×C11C2311yescharacteristic
156C2×C42×C11C2311yescharacteristic
157C2×C22⋊Dic11C2311yescharacteristic
158C2×C22⋊Dic11C2311yescharacteristic
159C2×C22⋊Dic11C2312yes—
160C2×(C2×D11)⋊C4—28no—
161C2×(C2×D11)⋊C4C2311yescharacteristic
162C2×(C2×D11)⋊C4C2311yescharacteristic
163C2×(C2×D11)⋊C4C2311yescharacteristic
164C2×(C2×D11)⋊C4C2311yescharacteristic
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×C4⋊Dic11—42no—
172C2×C4⋊Dic11C2311yescharacteristic
173C2×C4⋊Dic11C2311yescharacteristic
174C2×C4⋊Dic11C2311yescharacteristic
175C2×C4⋊Dic11C2311yescharacteristic
176C2×C4⋊Dic11C2312yes—
177C2×C4⋊Dic11C2312yes—
178C2×C4⋊Dic11C2312yes—
179C2×C4⋊Dic11C2312yes—
180C2×C4⋊Dic11C2312yes—
181C2×Dic11⋊C4C2312yes—
182C2×Dic11⋊C4C2312yes—
183C2×Dic11⋊C4C2312yes—
184C2×Dic11⋊C4C2312yes—
185C2×Dic11⋊C4C2312yes—
186C2×Dic11⋊C4C2312yes—
187C2×Dic11⋊C4C2312yes—
188C2×Dic11⋊C4C2312yes—
189C2×Dic11⋊C4C2312yes—
190C2×Dic11⋊C4C2312yes—
191C2×C4×Dic11C2311yescharacteristic
192C2×C4×Dic11C2311yescharacteristic
193C2×C4×Dic11C2311yescharacteristic
194C2×C4×Dic11C2311yescharacteristic
195C2×C4×Dic11C2311yescharacteristic
196C2×C4×Dic11C2311yescharacteristic
197C4⋊C4×D11—42no—
198C4⋊C4×D11—42no—
199#66943—42no—
200#66943—42no—
201C22⋊C4×D11—24no—
202C22⋊C4×D11—24no—
203C22⋊C4×D11—28no—
204C42×D11—42no—
205C42×D11—42no—
206#66923—42no—
207C11×#95C2312yes—
208C11×#95C2312yes—
209C11×#95C2312yes—
210C11×#95C2312yes—
211C11×#95C2311yescharacteristic
212C11×#95C2311yescharacteristic
213C11×#95C2312yes—
214C11⋊#95C2312yes—
215C11⋊#95C2312yes—
216C11⋊#95C2312yes—
217C11⋊#95C2312yes—
218C11⋊#95C2312yes—
219C11⋊#95C2312yes—
220C11⋊#95C2312yes—
221C11⋊#95C2312yes—
222C11⋊#95C2311yescharacteristic
223C11⋊#95C2312yes—
224C11⋊#95C2312yes—
225C11⋊#95C2312yes—
226C11⋊#95C2311yescharacteristic
227C11⋊#95C2312yes—
228C11⋊#95C2312yes—
229C11⋊#95C2312yes—
230C11⋊#95C2312yes—
231C11⋊#95C2312yes—
232C11⋊#95C2311yescharacteristic
233C11⋊#95C2311yescharacteristic
234C11⋊#95C2312yes—
235C11⋊#95C2312yes—
236C11⋊#95C2311yescharacteristic
237C11⋊#95C2311yescharacteristic
238C11⋊#95C2312yes—
239#35020—111nomaximal, Sylow
240C24×C11C2411yescharacteristic
241C23×D11—41no—
242C23×D11—41no—
243C23×D11—41no—
244C23×D11—41no—
245C23×D11C2×Q814yes—
246C23×D11#4114yes—
247C23×D11#4114yes—
248C23×D11C2411yescharacteristic
249C23×D11C2411yescharacteristic
250C22×C4×C11—22no—
251C22×C4×C11—22no—
252C22×C4×C11—24no—
253C22×C4×C11—42no—
254C22×C4×C11—42no—
255C22×C4×C11C2×Q814yes—
256C22×C4×C11C2411yescharacteristic
257C22×C4×C11C2412yes—
258C22×C4×C11C2411yescharacteristic
259C22×C4×C11C2411yescharacteristic
260C22×C4×C11C2412yes—
261C22×C4×C11C2412yes—
262C22×C4×C11C2412yes—
263C22×C4×C11C2411yescharacteristic
264C22×C4×C11C2411yescharacteristic
265C22×C4×C11C2411yescharacteristic
266C22×Dic11—24no—
267C22×Dic11—41no—
268C22×Dic11—41no—
269C22×Dic11—42no—
270C22×Dic11—42no—
271C22×Dic11C2×Q814yes—
272C22×Dic11C2411yescharacteristic
273C22×Dic11C2411yescharacteristic
274C22×Dic11C2411yescharacteristic
275C22×Dic11C2411yescharacteristic
276C22×Dic11C2412yes—
277C22×Dic11C2412yes—
278C22×Dic11C2412yes—
279C22×Dic11C2412yes—
280C22×Dic11C2411yescharacteristic
281C22×Dic11C2411yescharacteristic
282C2×C4×D11—22no—
283C2×C4×D11—22no—
284C2×C4×D11—22no—
285C2×C4×D11—22no—
286C2×C4×D11—24no—
287C2×C4×D11—24no—
288C2×C4×D11—22no—
289C2×C4×D11—22no—
290C2×C4×D11—22no—
291C2×C4×D11—22no—
292C2×C4×D11—41no—
293C2×C4×D11—41no—
294C2×C4×D11—41no—
295C2×C4×D11—41no—
296C2×C4×D11—41no—
297C2×C4×D11—41no—
298C2×C4×D11—41no—
299C2×C4×D11—41no—
300C2×C4×D11—41no—
301C2×C4×D11—41no—
302C2×C4×D11—41no—
303C2×C4×D11—41no—
304C2×C4×D11—42no—
305C2×C4×D11—42no—
306C2×C4×D11—42no—
307C2×C4×D11—42no—
308C2×C4×D11—416no—
309C2×C4×D11C2×Q814yes—
310C2×C4×D11C2×Q814yes—
311C2×C4×D11C2×Q814yes—
312C2×C4×D11C2×Q814yes—
313C11×C4⋊C4—22no—
314C11×C4⋊C4—22no—
315C11×C4⋊C4—22no—
316C11×C4⋊C4—22no—
317C11×C4⋊C4—42no—
318C11×C4⋊C4—42no—
319C11×C4⋊C4—42no—
320C11×C4⋊C4—42no—
321C11×C4⋊C4—42no—
322C11×C22⋊C4—22no—
323C11×C22⋊C4—24no—
324C11×C22⋊C4—22no—
325C42×C11—22no—
326C42×C11—22no—
327C22⋊Dic11—22no—
328C22⋊Dic11—24no—
329C22⋊Dic11—22no—
330(C2×D11)⋊C4—22no—
331(C2×D11)⋊C4—22no—
332(C2×D11)⋊C4—24no—
333(C2×D11)⋊C4—24no—
334(C2×D11)⋊C4—22no—
335(C2×D11)⋊C4—22no—
336(C2×D11)⋊C4—24no—
337(C2×D11)⋊C4—24no—
338(C2×D11)⋊C4—24no—
339(C2×D11)⋊C4—24no—
340C4⋊Dic11—22no—
341C4⋊Dic11—22no—
342C4⋊Dic11—22no—
343C4⋊Dic11—22no—
344C4⋊Dic11—42no—
345C4⋊Dic11—42no—
346C4⋊Dic11—42no—
347C4⋊Dic11—42no—
348C4⋊Dic11—42no—
349Dic11⋊C4—42no—
350Dic11⋊C4—42no—
351Dic11⋊C4—42no—
352Dic11⋊C4—42no—
353Dic11⋊C4—42no—
354Dic11⋊C4—42no—
355Dic11⋊C4—42no—
356Dic11⋊C4—42no—
357Dic11⋊C4—42no—
358Dic11⋊C4—42no—
359C4×Dic11—22no—
360C4×Dic11—22no—
361C4×Dic11—41no—
362C4×Dic11—41no—
363C4×Dic11—41no—
364C4×Dic11—41no—
365#2851—111no—
366#2851—111no—
367#2851—111no—
368#2851—111no—
369#2646—112no—
370#2646—112no—
371#2569—112no—
372#2569—112no—
373#2569—112no—
374#2569—112no—
375#2442—111no—
376#2442—111no—
377#2442—111no—
378#2442—111no—
379#2442—111no—
380#2442—111no—
381#2442—111no—
382#2442D1111yescharacteristic, complemented
383#2315—112no—
384#2315—112no—
385C2×#380—111no—
386C2×#380—111no—
387C2×C4×C22⋊C4—111no—
388C23×C11—21no—
389C23×C11—21no—
390C23×C11—21no—
391C23×C11—21no—
392C23×C11C22×Q812yes—
393C23×C11C2×#4112yes—
394C23×C11C2×#4112yes—
395C23×C11C2511yescharacteristic
396C22×D11—21no—
397C22×D11—21no—
398C22×D11—21no—
399C22×D11—21no—
400C22×D11—21no—
401C22×D11—21no—
402C22×D11—21no—
403C22×D11—21no—
404C22×D11—44no—
405C22×D11—44no—
406C22×D11—44no—
407C22×D11—44no—
408C22×D11—44no—
409C22×D11—44no—
410C22×D11#125116yescomplemented
411C22×D11C22×Q812yes—
412C22×D11C22×Q812yes—
413C22×D11C2×#4112yes—
414C22×D11C2×#4112yes—
415C22×D11C2×#4112yes—
416C22×D11C2×#4112yes—
417C2×C4×C11—21no—
418C2×C4×C11—21no—
419C2×C4×C11—28no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—21no—
423C2×C4×C11—21no—
424C2×C4×C11—21no—
425C2×C4×C11—21no—
426C2×C4×C11—22no—
427C2×C4×C11—22no—
428C2×C4×C11—21no—
429C2×C4×C11—21no—
430C2×C4×C11—21no—
431C2×C4×C11—21no—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—21no—
437C2×C4×C11—21no—
438C2×C4×C11—22no—
439C2×C4×C11—22no—
440C2×C4×C11—22no—
441C2×C4×C11—21no—
442C2×C4×C11—21no—
443C2×C4×C11—22no—
444C2×C4×C11—84no—
445C2×C4×C11C22×Q812yes—
446C2×C4×C11C22×Q812yes—
447C2×C4×C11H(5,𝔽2)12yes—
448C2×C4×C11H(5,𝔽2)12yes—
449C2×Dic11—21no—
450C2×Dic11—21no—
451C2×Dic11—21no—
452C2×Dic11—21no—
453C2×Dic11—22no—
454C2×Dic11—22no—
455C2×Dic11—21no—
456C2×Dic11—21no—
457C2×Dic11—21no—
458C2×Dic11—21no—
459C2×Dic11—22no—
460C2×Dic11—22no—
461C2×Dic11—21no—
462C2×Dic11—21no—
463C2×Dic11—21no—
464C2×Dic11—21no—
465C2×Dic11—22no—
466C2×Dic11—22no—
467C2×Dic11—22no—
468C2×Dic11—22no—
469C2×Dic11—21no—
470C2×Dic11—21no—
471C2×Dic11—22no—
472C2×Dic11—22no—
473C2×Dic11—22no—
474C2×Dic11—22no—
475C2×Dic11—21no—
476C2×Dic11—21no—
477C2×Dic11—44no—
478C2×Dic11—84no—
479C2×Dic11C22×Q812yes—
480C2×Dic11C22×Q812yes—
481C4×D11—28no—
482C4×D11—28no—
483C4×D11—44no—
484C4×D11—44no—
485C4×D11—44no—
486C4×D11—44no—
487C4×D11—44no—
488C4×D11—44no—
489C4×D11—84no—
490C4×D11—84no—
491C24×C4—111no—
492C2×#125—111no—
493C2×#125—111no—
494C2×#125—111no—
495C2×#125C2×D1111yescharacteristic, complemented
496C22×C4⋊C4—111no—
497C22×C4⋊C4—111no—
498C22×C4⋊C4—111no—
499C22×C4⋊C4C2×D1111yescharacteristic
500C22×C22⋊C4—112no—
501C22×C22⋊C4—111no—
502C22×C22⋊C4—111no—
503C22×C22⋊C4—112no—
504C22×C42—111no—
505C22×C42—111no—
506#400—112no—
507#400—112no—
508#400—112no—
509#400—112no—
510#400—112no—
511#400—112no—
512#400—112no—
513#400C2×D1112yescomplemented
514#398—112no—
515#398—112no—
516#398—112no—
517#398—112no—
518#398—112no—
519#398—112no—
520#398—112no—
521#398C2×D1112yescomplemented
522#389—111no—
523#389—111no—
524#389—111no—
525#389—111no—
526#389—111no—
527#389—111no—
528#389C2×D1111yescharacteristic, complemented
529#389C2×D1111yescharacteristic, complemented
530#387—112no—
531#387—112no—
532#387—112no—
533#387—112no—
534#387—112no—
535#387—112no—
536#387—112no—
537#387—112no—
538#385—112no—
539#385—112no—
540#385—112no—
541#385—112no—
542#385—112no—
543#385—112no—
544#385—112no—
545#385—112no—
546#385—112no—
547#385—112no—
548#385—112no—
549#385—112no—
550#385—112no—
551#385—112no—
552#385—112no—
553#385C2×D1112yes—
554#382—111no—
555#382—111no—
556#382—111no—
557#382C2×D1111yescharacteristic, complemented
558#380—112no—
559#380—111no—
560#380—112no—
561#380—112no—
562#380—112no—
563#380—111no—
564#380—111no—
565#380—111no—
566#380—111no—
567#380—112no—
568#380—111no—
569#380—111no—
570#380—112no—
571#380—112no—
572#380—112no—
573#380—112no—
574#380—112no—
575#380—112no—
576#380C2×D1112yes—
577#380C2×D1111yescharacteristic
578C4×C22⋊C4—111no—
579C4×C22⋊C4—111no—
580C4×C22⋊C4—111no—
581C4×C22⋊C4—111no—
582C4×C22⋊C4—111no—
583C4×C22⋊C4—111no—
584C4×C22⋊C4—111no—
585C4×C22⋊C4C2×D1111yescharacteristic
586C2×#95—112no—
587C2×#95—112no—
588C2×#95—111no—
589C2×#95—111no—
590C22×C11—22no—
591C22×C11—22no—
592C22×C11—22no—
593C22×C11—22no—
594C22×C11—22no—
595C22×C11—22no—
596C22×C11C2×#12514yes—
597C22×C11C23×Q811yescharacteristic
598C22×C11C22×#4111yescharacteristic
599C22×C11C22×#4111yescharacteristic
600C22×C11C2×H(5,𝔽2)11yescharacteristic
601C22×C11C2×H(5,𝔽2)11yescharacteristic
602C22×C11#58511yescharacteristic
603C22×C11#58511yescharacteristic
604C2×D11—22no—
605C2×D11—22no—
606C2×D11—22no—
607C2×D11—22no—
608C2×D11—22no—
609C2×D11—22no—
610C2×D11—22no—
611C2×D11—22no—
612C2×D11—22no—
613C2×D11—22no—
614C2×D11—22no—
615C2×D11—22no—
616C2×D11—416no—
617C2×D11C2×#12514yes—
618C2×D11C2×#12514yes—
619C4×C11—22no—
620C4×C11—42no—
621C4×C11—42no—
622C4×C11—41no—
623C4×C11—41no—
624C4×C11—41no—
625C4×C11—41no—
626C4×C11—42no—
627C4×C11—42no—
628C4×C11#54314yes—
629Dic11—22no—
630Dic11—22no—
631Dic11—41no—
632Dic11—41no—
633Dic11—41no—
634Dic11—41no—
635Dic11—42no—
636Dic11—42no—
637Dic11—42no—
638Dic11—42no—
639C25—111no—
640C23×C4—111no—
641C23×C4—111no—
642C23×C4—111no—
643C23×C4—118no—
644C23×C4—111no—
645C23×C4—111no—
646C23×C4—112no—
647C23×C4—112no—
648C23×C4—112no—
649C23×C4—111no—
650C23×C4—111no—
651C23×C4—111no—
652C23×C4—111no—
653C23×C4—442no—
654C23×C4—442no—
655C23×C4C22×D1111yescharacteristic
656C23×C4C22×D1112yes—
657#125—42no—
658#125—442no—
659#125—442no—
660#125—442no—
661C2×C4⋊C4—42no—
662C2×C4⋊C4—111no—
663C2×C4⋊C4—111no—
664C2×C4⋊C4—111no—
665C2×C4⋊C4—111no—
666C2×C4⋊C4—112no—
667C2×C4⋊C4—112no—
668C2×C4⋊C4—112no—
669C2×C4⋊C4—112no—
670C2×C4⋊C4—112no—
671C2×C4⋊C4—112no—
672C2×C4⋊C4—112no—
673C2×C4⋊C4—112no—
674C2×C4⋊C4—112no—
675C2×C4⋊C4—112no—
676C2×C4⋊C4—112no—
677C2×C4⋊C4—112no—
678C2×C4⋊C4—112no—
679C2×C4⋊C4—112no—
680C2×C4⋊C4—112no—
681C2×C4⋊C4—442no—
682C2×C4⋊C4—442no—
683C2×C4⋊C4—442no—
684C2×C4⋊C4C22×D1111yescharacteristic
685C2×C4⋊C4C22×D1111yescharacteristic
686C2×C4⋊C4C22×D1111yescharacteristic
687C2×C4⋊C4C22×D1111yescharacteristic
688C2×C4⋊C4C22×D1112yes—
689C2×C4⋊C4C22×D1112yes—
690C2×C4⋊C4C22×D1112yes—
691C2×C4⋊C4C22×D1112yes—
692C2×C4⋊C4C22×D1112yes—
693C2×C22⋊C4—111no—
694C2×C22⋊C4—111no—
695C2×C22⋊C4—112no—
696C2×C22⋊C4—111no—
697C2×C22⋊C4—111no—
698C2×C22⋊C4—111no—
699C2×C22⋊C4—111no—
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—224no—
707C2×C22⋊C4—224no—
708C2×C22⋊C4—228no—
709C2×C22⋊C4—228no—
710C2×C22⋊C4C22×D1111yescharacteristic
711C2×C22⋊C4C22×D1111yescharacteristic
712C2×C22⋊C4C22×D1112yes—
713C2×C42—111no—
714C2×C42—111no—
715C2×C42—111no—
716C2×C42—111no—
717C2×C42—111no—
718C2×C42—111no—
719C2×C42—442no—
720C2×C42—442no—
721C2×C42C22×D1111yescharacteristic
722C2×C42C22×D1111yescharacteristic
723#95—111no—
724#95—111no—
725#95—111no—
726#95—111no—
727#95—111no—
728#95—111no—
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#95—112no—
739#95—112no—
740#95—112no—
741#95—112no—
742#95—112no—
743#95—112no—
744#95—112no—
745#95—112no—
746#95—112no—
747#95—112no—
748#95C22×D1111yescharacteristic
749#95C22×D1111yescharacteristic
750#95C22×D1112yes—
751#95C22×D1112yes—
752#95C22×D1112yes—
753#95C22×D1112yes—
754#95C22×D1112yes—
755C2×C11—24no—
756C2×C11C22×#12511yescharacteristic
757C2×C11C2×#54311yescharacteristic
758C2×C11#345811yescharacteristic
759C2×C11#350511yescharacteristic
760C2×C11#350511yescharacteristic
761C2×C11#350511yescharacteristic
762C2×C11#350511yescharacteristic
763D11—24no—
764D11—24no—
765C24—111no—
766C24—111no—
767C24—114no—
768C24—114no—
769C24—114no—
770C24—441no—
771C24—441no—
772C24—441no—
773C24—441no—
774C24C23×D1111yescharacteristic
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—24no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—111no—
781C22×C4—111no—
782C22×C4—114no—
783C22×C4—114no—
784C22×C4—114no—
785C22×C4—114no—
786C22×C4—114no—
787C22×C4—111no—
788C22×C4—111no—
789C22×C4—111no—
790C22×C4—111no—
791C22×C4—112no—
792C22×C4—112no—
793C22×C4—112no—
794C22×C4—112no—
795C22×C4—222no—
796C22×C4—222no—
797C22×C4—222no—
798C22×C4—222no—
799C22×C4—224no—
800C22×C4—224no—
801C22×C4—222no—
802C22×C4—222no—
803C22×C4—222no—
804C22×C4—222no—
805C22×C4—224no—
806C22×C4—4416no—
807C22×C4—441no—
808C22×C4—441no—
809C22×C4—441no—
810C22×C4—441no—
811C22×C4—441no—
812C22×C4—441no—
813C22×C4—441no—
814C22×C4—441no—
815C22×C4—441no—
816C22×C4—441no—
817C22×C4—441no—
818C22×C4—441no—
819C22×C4—442no—
820C22×C4—442no—
821C22×C4—442no—
822C22×C4—442no—
823C22×C4—441no—
824C22×C4—441no—
825C22×C4—442no—
826C22×C4—442no—
827C22×C4Q8×D1114yes—
828C22×C4C23×D1111yescharacteristic
829C22×C4C23×D1112yes—
830C22×C4C23×D1111yescharacteristic
831C22×C4C23×D1111yescharacteristic
832C22×C4C23×D1112yes—
833C22×C4C23×D1112yes—
834C22×C4C23×D1112yes—
835C22×C4C23×D1111yescharacteristic
836C22×C4C23×D1111yescharacteristic
837C22×C4C23×D1111yescharacteristic
838C4⋊C4—22no—
839C4⋊C4—22no—
840C4⋊C4—22no—
841C4⋊C4—22no—
842C4⋊C4—42no—
843C4⋊C4—42no—
844C4⋊C4—42no—
845C4⋊C4—42no—
846C4⋊C4—42no—
847C4⋊C4—222no—
848C4⋊C4—222no—
849C4⋊C4—222no—
850C4⋊C4—222no—
851C4⋊C4—442no—
852C4⋊C4—442no—
853C4⋊C4—442no—
854C4⋊C4—442no—
855C4⋊C4—442no—
856C4⋊C4—442no—
857C4⋊C4—442no—
858C4⋊C4—442no—
859C4⋊C4—442no—
860C4⋊C4—442no—
861C4⋊C4—442no—
862C4⋊C4—442no—
863C4⋊C4—442no—
864C4⋊C4—442no—
865C4⋊C4—442no—
866C22⋊C4—22no—
867C22⋊C4—24no—
868C22⋊C4—22no—
869C22⋊C4—222no—
870C22⋊C4—222no—
871C22⋊C4—224no—
872C22⋊C4—224no—
873C22⋊C4—222no—
874C22⋊C4—222no—
875C22⋊C4—224no—
876C22⋊C4—224no—
877C22⋊C4—224no—
878C22⋊C4—224no—
879C22⋊C4—222no—
880C22⋊C4—224no—
881C22⋊C4—222no—
882C42—22no—
883C42—22no—
884C42—222no—
885C42—222no—
886C42—441no—
887C42—441no—
888C42—441no—
889C42—441no—
890C11#3502011yescharacteristic, complemented, Sylow
891C23—21no—
892C23—21no—
893C23—21no—
894C23—21no—
895C23—112no—
896C23—112no—
897C23—112no—
898C23—112no—
899C23—112no—
900C23—112no—
901C23—1116no—
902C23—221no—
903C23—221no—
904C23—221no—
905C23—221no—
906C23—221no—
907C23—221no—
908C23—221no—
909C23—221no—
910C23—444no—
911C23—444no—
912C23—444no—
913C23—444no—
914C23—444no—
915C23—444no—
916C23C2×Q8×D1112yes—
917C23#41×D1112yes—
918C23#41×D1112yes—
919C23C24×D1111yescharacteristic
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—28no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—22no—
931C2×C4—21no—
932C2×C4—22no—
933C2×C4—21no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—22no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—21no—
945C2×C4—22no—
946C2×C4—21no—
947C2×C4—84no—
948C2×C4—112no—
949C2×C4—112no—
950C2×C4—221no—
951C2×C4—221no—
952C2×C4—221no—
953C2×C4—221no—
954C2×C4—228no—
955C2×C4—228no—
956C2×C4—221no—
957C2×C4—221no—
958C2×C4—222no—
959C2×C4—221no—
960C2×C4—221no—
961C2×C4—222no—
962C2×C4—221no—
963C2×C4—222no—
964C2×C4—221no—
965C2×C4—222no—
966C2×C4—222no—
967C2×C4—221no—
968C2×C4—221no—
969C2×C4—222no—
970C2×C4—222no—
971C2×C4—222no—
972C2×C4—221no—
973C2×C4—221no—
974C2×C4—222no—
975C2×C4—221no—
976C2×C4—222no—
977C2×C4—221no—
978C2×C4—222no—
979C2×C4—222no—
980C2×C4—444no—
981C2×C4—444no—
982C2×C4—444no—
983C2×C4—444no—
984C2×C4—444no—
985C2×C4—444no—
986C2×C4—444no—
987C2×C4—884no—
988C2×C4—884no—
989C2×C4—884no—
990C2×C4#6703712yes—
991C2×C4C2×Q8×D1112yes—
992C2×C4C2×Q8×D1112yes—
993C2×C4#6704212yes—
994C22—22no—
995C22—22no—
996C22—22no—
997C22—22no—
998C22—22no—
999C22—22no—
1000C22—114no—
1001C22—114no—
1002C22—222no—
1003C22—222no—
1004C22—222no—
1005C22—222no—
1006C22—222no—
1007C22—222no—
1008C22—222no—
1009C22—222no—
1010C22—222no—
1011C22—222no—
1012C22—222no—
1013C22—222no—
1014C22—4416no—
1015C22D11×#12514yes—
1016C22C2×#6703711yescharacteristic
1017C22C22×Q8×D1111yescharacteristic
1018C22C2×#41×D1111yescharacteristic
1019C22C2×#41×D1111yescharacteristic
1020C22C2×#6704211yescharacteristic
1021C22#1062345511yescharacteristic
1022C22#1062345711yescharacteristic
1023C4—22no—
1024C4—42no—
1025C4—42no—
1026C4—41no—
1027C4—41no—
1028C4—42no—
1029C4—41no—
1030C4—42no—
1031C4—41no—
1032C4—222no—
1033C4—222no—
1034C4—441no—
1035C4—441no—
1036C4—442no—
1037C4—441no—
1038C4—442no—
1039C4—441no—
1040C4—442no—
1041C4—442no—
1042C4#1062316514yes—
1043C2—24no—
1044C2—224no—
1045C2—224no—
1046C2C2×D11×#12511yescharacteristic
1047C2C2×#1062316511yescharacteristic
1048C2#1308202011yescharacteristic
1049C2#1308244311yescharacteristic
1050C2#1308244511yescharacteristic
1051C2#1308245211yescharacteristic
1052C2#1308245611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2442C2
prime radicalC24×D11C23
hypercenter#2442D11
hypocenterC11#35020
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2442

Complements

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

NH ≅ G/Ntype
1. #13076927C2semidirect
2. #13076925C2semidirect
3. #13076925C2semidirect
4. #13076921C2semidirect
5. #13074587C2semidirect
6. #13074585C2semidirect
7. #13073842C2semidirect
8. #13073837C2semidirect
9. #13073836C2semidirect
10. #13073834C2semidirect
11. #13072343C2semidirect
12. #13072342C2semidirect
13. #13072341C2semidirect
14. #13072340C2semidirect
15. #13072338C2semidirect
16. #13072336C2semidirect
17. #13072334C2semidirect
23. C11×#2442C2semidirect
25. C2×C11×#125C22semidirect
31. C2×#66943C22semidirect
32. C2×#66943C22semidirect
38. C2×#66923C22semidirect
39. C11×#400C22semidirect
40. C11×#398C22semidirect
41. C11×#389C22semidirect
42. C11×#389C22semidirect
44. C11×#382C22semidirect
69. #10622599C22semidirect
70. #10622598C22semidirect
71. #10622598C22semidirect
72. #10622597C22semidirect
73. #10622597C22semidirect
74. #10622596C22semidirect
75. #10622595C22semidirect
76. #10622594C22semidirect
77. #10622594C22semidirect
78. #10622593C22semidirect
79. #10622591C22semidirect
80. #10622591C22semidirect
81. #10622590C22semidirect
82. #10622590C22semidirect
83. #10622586C22semidirect
84. #10622586C22semidirect
94. #10622549C22semidirect
95. #10622541C22semidirect
96. #10622541C22semidirect
111. #10622274C22semidirect
112. #10622273C22semidirect
113. #10622273C22semidirect
114. #10622272C22semidirect
115. #10622271C22semidirect
116. #10622271C22semidirect
117. #10622270C22semidirect
118. #10622270C22semidirect
119. #10622266C22semidirect
120. #10622266C22semidirect
121. #10622265C22semidirect
122. #10622265C22semidirect
382. #2442D11semidirect
410. C22×D11#125semidirect
495. C2×#125C2×D11semidirect
513. #400C2×D11semidirect
521. #398C2×D11semidirect
528. #389C2×D11semidirect
529. #389C2×D11semidirect
557. #382C2×D11semidirect
890. C11#35020semidirect

Maximal subgroups

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

subgroupindex
#130769272
#130769252
#130769212
#130745872
#130745852
#130738422
#130738372
#130738362
#130738342
#130723432
#130723422
#130723412
#130723402
#130723382
#130723362
#130723342
#130712292
#130712272
C2×#106226002
D11×#3802
C4×C22⋊C4×D112
C11×#24422
#3502011