Finite Group Databasebeta

← #14926733

Subgroups — #14926733

Order 2816.

2756 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623144C212yesmaximal, complemented
2#13076980C211yesmaximal, characteristic, complemented
3#13076970C211yesmaximal, characteristic, complemented
4#13076947C211yesmaximal, characteristic, complemented
5#13074757C212yesmaximal, complemented
6#13074745C212yesmaximal, complemented
7#13073689C212yesmaximal, complemented
8#13073681C212yesmaximal, complemented
9#13073198C211yesmaximal, characteristic, complemented
10#13072981C211yesmaximal, characteristic, complemented
11#13072748C212yesmaximal, complemented
12#13072377C211yesmaximal, characteristic, complemented
13#13072321C211yesmaximal, characteristic, complemented
14#13072250C211yesmaximal, characteristic, complemented
15#13072206C211yesmaximal, characteristic, complemented
16#13072149C212yesmaximal, complemented
17#13072052C211yesmaximal, characteristic, complemented
18#13071968C211yesmaximal, characteristic, complemented
19#13071275C212yesmaximal, complemented
20#13071132C211yesmaximal, characteristic, complemented
21D11×#390C211yesmaximal, characteristic, complemented
22C42×C22⋊D11C211yesmaximal, characteristic, complemented
23C11×#2856C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C2×C11×#127C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C2×C11×#121C2212yescomplemented
28C2×C11×#121C2212yescomplemented
29C2×C11×#121C2211yescharacteristic, complemented
30C22×C42×C11C2211yescharacteristic, complemented
31C2×#66993C2211yescharacteristic
32C2×#66992C2212yescomplemented
33C2×#66991C2212yes—
34C2×#66991C2211yescharacteristic
35C2×#66990C2212yes—
36C2×#66990C2212yes—
37C2×#66990C2212yes—
38C2×#66989C2212yescomplemented
39C2×#66988C2212yescomplemented
40C2×D4×Dic11C2211yescharacteristic, complemented
41C2×#66983C2211yescharacteristic
42C2×#66982C2212yescomplemented
43C2×C4×C22⋊D11C2211yescharacteristic
44C2×C4×C22⋊D11C2211yescharacteristic
45C2×C4×C22⋊D11C2211yescharacteristic
46#10623144—216no—
47C2×#66951C2212yescomplemented
48C2×#66949C2212yes—
49C2×C4⋊C4×D11C2211yescharacteristic
50C2×#66941C2211yescharacteristic, complemented
51C2×#66938C2212yescomplemented
52C2×#66938C2212yescomplemented
53C2×(C22⋊D11)⋊C4C2212yes—
54C2×C22⋊C4×D11C2212yes—
55C2×C22⋊C4×D11C2212yes—
56C2×#66932C2212yescomplemented
57C2×C42×D11C2211yescharacteristic
58C11×#390C2211yescharacteristic
59C11×#390C2212yescomplemented
60C11×#390C2211yescharacteristic, complemented
61C11×#390C2212yescomplemented
62C11×#384C2211yescharacteristic, complemented
63#10622836C2212yes—
64#10622836C2212yes—
65#10622836C2212yes—
66#10622836C2212yescomplemented
67#10622835C2212yescomplemented
68#10622835C2212yescomplemented
69#10622835C2212yescomplemented
70#10622835C2212yescomplemented
71#10622834C2211yescharacteristic
72#10622834C2211yescharacteristic
73#10622834C2211yescharacteristic
74#10622834C2211yescharacteristic, complemented
75#10622833C2212yescomplemented
76#10622826C2212yescomplemented
77#10622825C2211yescharacteristic, complemented
78C4×C22⋊Dic11C2211yescharacteristic, complemented
79C4×C22⋊Dic11C2211yescharacteristic, complemented
80C4×C22⋊Dic11C2211yescharacteristic, complemented
81#10622607C2212yescomplemented
82#10622606C2212yescomplemented
83#10622603C2212yescomplemented
84#10622602C2212yes—
85#10622601C2211yescharacteristic
86#10622601C2211yescharacteristic
87#10622600C2211yescharacteristic
88#10622598C2211yescharacteristic, complemented
89#10622593C2212yescomplemented
90#10622592C2212yescomplemented
91C4⋊C4×Dic11C2211yescharacteristic, complemented
92#10622586C2211yescharacteristic, complemented
93#10622572C2212yes—
94#10622572C2212yescomplemented
95#10622571C2212yescomplemented
96#10622570C2212yes—
97#10622570C2212yes—
98#10622570C2212yescomplemented
99#10622570C2212yescomplemented
100#10622569C2212yes—
101#10622569C2212yes—
102#10622568C2212yes—
103#10622564C2212yescomplemented
104#10622561C2212yescomplemented
105#10622560C2212yescomplemented
106#10622558C2212yescomplemented
107#10622558C2212yescomplemented
108#10622558C2212yescomplemented
109#10622557C2212yescomplemented
110C22⋊C4×Dic11C2212yescomplemented
111#10622553C2212yescomplemented
112#10622553C2212yescomplemented
113#10622552C2211yescharacteristic
114#10622552C2211yescharacteristic
115C4×(C2×D11)⋊C4C2211yescharacteristic
116C4×(C2×D11)⋊C4C2211yescharacteristic
117C4×(C2×D11)⋊C4C2211yescharacteristic
118C4×Dic11⋊C4C2211yescharacteristic, complemented
119C4×Dic11⋊C4C2211yescharacteristic, complemented
120C4×Dic11⋊C4C2211yescharacteristic, complemented
121C42×Dic11C2211yescharacteristic, complemented
122#10622541C2211yescharacteristic, complemented
123#10622541C2211yescharacteristic, complemented
124C24×D11C2312yes—
125C22×D4×C11C2311yescharacteristic
126C22×D4×C11C2311yescharacteristic
127C22×D4×C11C2312yes—
128C22×D4×C11C2312yes—
129C22×D4×C11C2312yes—
130C22×D4×C11C2312yes—
131C23×C4×C11C2311yescharacteristic
132C23×C4×C11C2311yescharacteristic
133C23×C4×C11C2311yescharacteristic
134C22×C22⋊D11C2312yes—
135C22×C22⋊D11C2311yescharacteristic
136C22×C22⋊D11C2312yes—
137C22×C22⋊D11C2312yes—
138C22×C22⋊D11C2312yes—
139C22×C22⋊D11C2312yes—
140C23×Dic11C2312yes—
141C2×D4×D11—24no—
142C2×D4×D11—42no—
143C2×D4×D11—42no—
144C22×D44C2311yescharacteristic
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2312yes—
148C22×C4×D11C2311yescharacteristic
149C22×Dic22C2312yes—
150C11×#127—42no—
151C11×#121—28no—
152C11×#121—44no—
153C11×#121—42no—
154C11×#121—42no—
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C4⋊C4C2312yes—
158C2×C11×C4⋊C4C2312yes—
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2312yes—
165C2×C42×C11—42no—
166C2×C42×C11C2311yescharacteristic
167C2×C42×C11C2311yescharacteristic
168C2×C42×C11C2311yescharacteristic
169C2×C42×C11C2311yescharacteristic
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2311yescharacteristic
175C2×C22⋊Dic11C2311yescharacteristic
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2312yes—
179C2×C22⋊Dic11C2312yes—
180C2×C22⋊Dic11C2312yes—
181C2×C22⋊Dic11C2312yes—
182C2×C22⋊Dic11C2312yes—
183C2×C22⋊Dic11C2311yescharacteristic
184#66993—42no—
185#66992—28no—
186#66991—28no—
187#66991—24no—
188#66990—28no—
189#66990—28no—
190#66990—28no—
191#66989—28no—
192#66988—28no—
193D4×Dic11—42no—
194#66983—42no—
195#66982—28no—
196C4×C22⋊D11—24no—
197C4×C22⋊D11—24no—
198C4×C22⋊D11D418yescomplemented
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2312yes—
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2312yes—
205C2×(C2×D11)⋊C4C2311yescharacteristic
206C2×(C2×D11)⋊C4C2312yes—
207C2×(C2×D11)⋊C4C2312yes—
208C2×(C2×D11)⋊C4C2312yes—
209C2×(C2×D11)⋊C4C2312yes—
210C2×(C2×D11)⋊C4C2311yescharacteristic
211C2×(C2×D11)⋊C4C2311yescharacteristic
212C2×C4⋊Dic11C2312yes—
213C2×C4⋊Dic11C2311yescharacteristic
214C2×C4⋊Dic11C2311yescharacteristic
215C2×C4⋊Dic11C2311yescharacteristic
216C2×Dic11⋊C4C2312yes—
217C2×Dic11⋊C4C2312yes—
218C2×Dic11⋊C4C2312yes—
219C2×Dic11⋊C4C2311yescharacteristic
220C2×Dic11⋊C4C2311yescharacteristic
221C2×Dic11⋊C4C2312yes—
222C2×Dic11⋊C4C2312yes—
223C2×Dic11⋊C4C2311yescharacteristic
224C2×C4×Dic11C2311yescharacteristic
225C2×C4×Dic11C2312yes—
226C2×C4×Dic11C2311yescharacteristic
227C2×C4×Dic11C2311yescharacteristic
228C2×C4×Dic11C2311yescharacteristic
229C2×C4×Dic11C2311yescharacteristic
230C2×C4×Dic11C2311yescharacteristic
231C2×C4×Dic11C2311yescharacteristic
232C2×C4×Dic11C2311yescharacteristic
233C2×C4×Dic11C2311yescharacteristic
234#66951—28no—
235#66949—28no—
236C4⋊C4×D11—42no—
237#66941—42no—
238#66938—28no—
239#66938—44no—
240(C22⋊D11)⋊C4—28no—
241C22⋊C4×D11—28no—
242C22⋊C4×D11—44no—
243#66932—28no—
244C42×D11—42no—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2311yescharacteristic
248C11⋊#95C2311yescharacteristic
249C11⋊#95C2311yescharacteristic
250C11⋊#95C2311yescharacteristic
251C11⋊#95C2311yescharacteristic
252C11⋊#95C2311yescharacteristic
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258#35007—111nomaximal, Sylow
259C24×C11C2412yes—
260C24×C11C2412yes—
261C24×C11C2411yescharacteristic
262C23×D11—24no—
263C23×D11—24no—
264C23×D11—24no—
265C23×D11—42no—
266C23×D11—42no—
267C23×D11—42no—
268C23×D11—42no—
269C23×D11C2412yes—
270C23×D11C2411yescharacteristic
271C2×D4×C11—24no—
272C2×D4×C11—24no—
273C2×D4×C11—24no—
274C2×D4×C11—22no—
275C2×D4×C11—22no—
276C2×D4×C11—24no—
277C2×D4×C11—22no—
278C2×D4×C11—22no—
279C2×D4×C11—22no—
280C2×D4×C11—22no—
281C2×D4×C11—42no—
282C2×D4×C11—42no—
283C2×D4×C11—42no—
284C2×D4×C11—42no—
285C2×D4×C11—42no—
286C2×D4×C11—42no—
287C2×D4×C11—42no—
288C2×D4×C11—42no—
289C22×C4×C11—22no—
290C22×C4×C11—22no—
291C22×C4×C11—22no—
292C22×C4×C11—22no—
293C22×C4×C11—22no—
294C22×C4×C11—41no—
295C22×C4×C11—41no—
296C22×C4×C11—41no—
297C22×C4×C11C2×D414yescomplemented
298C22×C4×C11C2411yescharacteristic
299C22×C4×C11C2412yes—
300C22×C4×C11C2412yes—
301C22×C4×C11C2411yescharacteristic
302C22×C4×C11C2411yescharacteristic
303C22×C4×C11C2411yescharacteristic
304C22×C4×C11C2411yescharacteristic
305C22×C4×C11C2411yescharacteristic
306C2×C22⋊D11—24no—
307C2×C22⋊D11—24no—
308C2×C22⋊D11—24no—
309C2×C22⋊D11—24no—
310C2×C22⋊D11—24no—
311C2×C22⋊D11—22no—
312C2×C22⋊D11—22no—
313C2×C22⋊D11—24no—
314C2×C22⋊D11—24no—
315C2×C22⋊D11—42no—
316C2×C22⋊D11—42no—
317C2×C22⋊D11—42no—
318C2×C22⋊D11—42no—
319C2×C22⋊D11—42no—
320C2×C22⋊D11—42no—
321C2×C22⋊D11—42no—
322C2×C22⋊D11—42no—
323C2×C22⋊D11C2×D414yes—
324C22×Dic11—24no—
325C22×Dic11—42no—
326C22×Dic11—42no—
327C22×Dic11C2411yescharacteristic
328C22×Dic11C2411yescharacteristic
329C22×Dic11C2412yes—
330C22×Dic11C2412yes—
331C22×Dic11C2412yes—
332C22×Dic11C2411yescharacteristic
333C22×Dic11C2411yescharacteristic
334C22×Dic11C2411yescharacteristic
335C22×Dic11C2411yescharacteristic
336C22×Dic11C2411yescharacteristic
337D4×D11—416no—
338C2×D44—22no—
339C2×D44—22no—
340C2×D44—22no—
341C2×C4×D11—24no—
342C2×C4×D11—22no—
343C2×C4×D11—22no—
344C2×C4×D11—22no—
345C2×C4×D11—22no—
346C2×C4×D11—41no—
347C2×C4×D11—41no—
348C2×C4×D11—41no—
349C2×C4×D11—42no—
350C2×C4×D11—42no—
351C2×C4×D11C2×D414yes—
352C2×C4×D11#4114yes—
353C2×Dic22—24no—
354C2×Dic22—42no—
355C2×Dic22—42no—
356C11×C4⋊C4—24no—
357C11×C4⋊C4—22no—
358C11×C4⋊C4—22no—
359C11×C4⋊C4—42no—
360C11×C22⋊C4—24no—
361C11×C22⋊C4—24no—
362C11×C22⋊C4—24no—
363C11×C22⋊C4—24no—
364C11×C22⋊C4—42no—
365C11×C22⋊C4—42no—
366C42×C11—22no—
367C42×C11—22no—
368C42×C11—41no—
369C42×C11—41no—
370C22⋊Dic11—24no—
371C22⋊Dic11—24no—
372C22⋊Dic11—24no—
373C22⋊Dic11—24no—
374C22⋊Dic11—22no—
375C22⋊Dic11—22no—
376C22⋊Dic11—24no—
377C22⋊Dic11—24no—
378C22⋊Dic11—24no—
379C22⋊Dic11—42no—
380C22⋊Dic11—42no—
381C22⋊Dic11—42no—
382C22⋊Dic11—42no—
383C22⋊Dic11C2×D414yescomplemented
384(C2×D11)⋊C4—24no—
385(C2×D11)⋊C4—24no—
386(C2×D11)⋊C4—24no—
387(C2×D11)⋊C4—22no—
388(C2×D11)⋊C4—24no—
389(C2×D11)⋊C4—24no—
390(C2×D11)⋊C4—24no—
391(C2×D11)⋊C4—24no—
392(C2×D11)⋊C4—42no—
393(C2×D11)⋊C4—42no—
394(C2×D11)⋊C4—42no—
395(C2×D11)⋊C4C2×D414yes—
396(C2×D11)⋊C4#4114yes—
397C4⋊Dic11—24no—
398C4⋊Dic11—22no—
399C4⋊Dic11—22no—
400C4⋊Dic11—22no—
401Dic11⋊C4—24no—
402Dic11⋊C4—22no—
403Dic11⋊C4—24no—
404Dic11⋊C4—24no—
405Dic11⋊C4—22no—
406Dic11⋊C4—42no—
407Dic11⋊C4—42no—
408Dic11⋊C4C2×D414yescomplemented
409C4×Dic11—24no—
410C4×Dic11—22no—
411C4×Dic11—22no—
412C4×Dic11—22no—
413C4×Dic11—22no—
414C4×Dic11—22no—
415C4×Dic11—41no—
416C4×Dic11—41no—
417C4×Dic11—41no—
418C4×Dic11C2×D414yescomplemented
419C2×#538—112no—
420#2860—111no—
421#2858—111no—
422#2856D1111yescharacteristic, complemented
423#2854—111no—
424#2662—112no—
425#2661—112no—
426#2555—112no—
427#2554—112no—
428#2512—111no—
429#2491—111no—
430#2472—112no—
431#2445—111no—
432#2440—111no—
433#2433—111no—
434#2428—111no—
435#2424—112no—
436#2416—111no—
437#2408—111no—
438#2321—112no—
439C4×#121—111no—
440C2×#390—111no—
441C42×D4—111no—
442C23×C11—21no—
443C23×C11—21no—
444C23×C11—21no—
445C23×C11—21no—
446C23×C11—21no—
447C23×C11—21no—
448C23×C11—22no—
449C23×C11—22no—
450C23×C11—22no—
451C23×C11—22no—
452C23×C11—22no—
453C23×C11—22no—
454C23×C11—22no—
455C23×C11—22no—
456C23×C11—22no—
457C23×C11—22no—
458C23×C11—22no—
459C23×C11—22no—
460C23×C11—22no—
461C23×C11—22no—
462C23×C11C22×D412yes—
463C23×C11C2511yescharacteristic
464C22×D11—21no—
465C22×D11—21no—
466C22×D11—21no—
467C22×D11—21no—
468C22×D11—22no—
469C22×D11—22no—
470C22×D11—22no—
471C22×D11—22no—
472C22×D11—22no—
473C22×D11—22no—
474C22×D11—22no—
475C22×D11—48no—
476C22×D11—48no—
477C22×D11—48no—
478C22×D11—84no—
479C22×D11—84no—
480C22×D11—84no—
481C22×D11—84no—
482C22×D11C22×D412yes—
483C22×D11C2×#4112yes—
484C22×D11C2×#4112yes—
485D4×C11—44no—
486D4×C11—44no—
487D4×C11—84no—
488D4×C11—84no—
489D4×C11—84no—
490D4×C11—84no—
491C2×C4×C11—21no—
492C2×C4×C11—21no—
493C2×C4×C11—21no—
494C2×C4×C11—21no—
495C2×C4×C11—21no—
496C2×C4×C11—21no—
497C2×C4×C11—21no—
498C2×C4×C11—21no—
499C2×C4×C11—22no—
500C2×C4×C11—22no—
501C2×C4×C11—21no—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—21no—
505C2×C4×C11—22no—
506C2×C4×C11—22no—
507C2×C4×C11—21no—
508C2×C4×C11—44no—
509C2×C4×C11—44no—
510C2×C4×C11—44no—
511C2×C4×C11C22×D412yes—
512C2×C4×C11C22×D412yes—
513C2×C4×C11C2×#4112yes—
514C2×C4×C11C2×#4112yes—
515C2×C4×C11H(5,𝔽2)12yes—
516C2×C4×C11H(5,𝔽2)12yes—
517C2×C4×C11H(5,𝔽2)12yes—
518C22⋊D11—28no—
519C22⋊D11—48no—
520C22⋊D11—48no—
521C22⋊D11—84no—
522C22⋊D11—84no—
523C22⋊D11—84no—
524C2×Dic11—21no—
525C2×Dic11—21no—
526C2×Dic11—21no—
527C2×Dic11—21no—
528C2×Dic11—21no—
529C2×Dic11—21no—
530C2×Dic11—21no—
531C2×Dic11—21no—
532C2×Dic11—21no—
533C2×Dic11—21no—
534C2×Dic11—22no—
535C2×Dic11—22no—
536C2×Dic11—22no—
537C2×Dic11—21no—
538C2×Dic11—21no—
539C2×Dic11—22no—
540C2×Dic11—22no—
541C2×Dic11—21no—
542C2×Dic11—21no—
543C2×Dic11—22no—
544C2×Dic11—22no—
545C2×Dic11—22no—
546C2×Dic11—21no—
547C2×Dic11—21no—
548C2×Dic11—22no—
549C2×Dic11—84no—
550C2×Dic11C22×D412yes—
551C2×Dic11C22×D412yes—
552C2×Dic11C22×D412yes—
553C2×Dic11C2×#4112yes—
554C2×Dic11C2×#4112yes—
555D44—44no—
556C4×D11—28no—
557C4×D11—44no—
558C4×D11—44no—
559C4×D11—84no—
560Dic22—84no—
561C23×D4—111no—
562#538—2216no—
563C2×C4⋊Q8—111no—
564C2×#127—111no—
565C2×#127C2×D1111yescharacteristic
566C2×#126—112no—
567C2×#126—112no—
568C2×#124—112no—
569C2×#124—112no—
570C2×#124—112no—
571C2×#123—112no—
572C2×#123—112no—
573C2×C22⋊Q8—112no—
574C2×#121—112no—
575C2×#121—111no—
576C2×#121—112no—
577C2×#121—111no—
578C2×#121C2×D1111yescharacteristic
579C2×#121C2×D1112yescomplemented
580C2×#121C2×D1111yescharacteristic, complemented
581C2×#121C2×D1112yescomplemented
582C2×#120—112no—
583C2×#120—112no—
584C2×#120—112no—
585C2×C4×D4—111no—
586C2×C4×D4—111no—
587C2×C4×D4—111no—
588C2×C4×D4—111no—
589C2×C4×D4—112no—
590C22×C4⋊C4—111no—
591C22×C22⋊C4—112no—
592C22×C22⋊C4—112no—
593C22×C42—111no—
594C22×C42C2×D1111yescharacteristic, complemented
595#398—112no—
596#397—112no—
597#396—112no—
598#396—112no—
599#395—112no—
600#394—112no—
601#394—112no—
602#394—112no—
603#394—112no—
604#394—112no—
605#394—112no—
606#393—112no—
607#392—112no—
608#392—112no—
609#392—112no—
610#392—112no—
611#390—111no—
612#390—111no—
613#390—111no—
614#390—111no—
615#390—111no—
616#390—111no—
617#390—112no—
618#390—112no—
619#390—112no—
620#390—112no—
621#390—111no—
622#390—111no—
623#390C2×D1111yescharacteristic
624#390C2×D1112yescomplemented
625#390C2×D1111yescharacteristic, complemented
626#390C2×D1112yescomplemented
627#389—111no—
628#389—111no—
629#389—111no—
630#389—111no—
631#388—112no—
632#388—112no—
633#388—112no—
634#388—112no—
635#388—112no—
636#388—112no—
637#388—112no—
638#388—112no—
639#386—112no—
640#386—112no—
641#386—112no—
642#386—112no—
643#386—112no—
644#385—112no—
645#384C2×D1111yescharacteristic, complemented
646#380—111no—
647#380—111no—
648#379—112no—
649C4×C4⋊C4—111no—
650C4×C4⋊C4—111no—
651C4×C4⋊C4—111no—
652C4×C4⋊C4—111no—
653C4×C22⋊C4—111no—
654C4×C22⋊C4—111no—
655C4×C22⋊C4—111no—
656C4×C22⋊C4—112no—
657C4×C22⋊C4—111no—
658C4×C22⋊C4—111no—
659C4×C22⋊C4—111no—
660C43—111no—
661C22×C11—22no—
662C22×C11—22no—
663C22×C11—22no—
664C22×C11—41no—
665C22×C11—41no—
666C22×C11—41no—
667C22×C11—41no—
668C22×C11—42no—
669C22×C11—42no—
670C22×C11—42no—
671C22×C11—42no—
672C22×C11—42no—
673C22×C11—42no—
674C22×C11—42no—
675C22×C11—42no—
676C22×C11—42no—
677C22×C11—42no—
678C22×C11—42no—
679C22×C11—42no—
680C22×C11—42no—
681C22×C11—42no—
682C22×C11C23×D411yescharacteristic
683C22×C11C22×#4111yescharacteristic
684C22×C11C22×#4111yescharacteristic
685C22×C11C2×H(5,𝔽2)11yescharacteristic
686C22×C11C2×H(5,𝔽2)11yescharacteristic
687C22×C11C2×H(5,𝔽2)11yescharacteristic
688C22×C11#58511yescharacteristic
689C2×D11—22no—
690C2×D11—22no—
691C2×D11—22no—
692C2×D11—22no—
693C2×D11—22no—
694C2×D11—22no—
695C2×D11—42no—
696C2×D11—42no—
697C2×D11—42no—
698C2×D11—42no—
699C2×D11—42no—
700C2×D11—42no—
701C2×D11—42no—
702C2×D11—816no—
703C2×D11#53214yes—
704C4×C11—22no—
705C4×C11—22no—
706C4×C11—22no—
707C4×C11—22no—
708C4×C11—41no—
709C4×C11—42no—
710C4×C11—42no—
711C4×C11#53814yescomplemented
712Dic11—22no—
713Dic11—22no—
714Dic11—22no—
715Dic11—22no—
716Dic11—22no—
717Dic11—42no—
718Dic11—41no—
719Dic11—42no—
720Dic11—42no—
721Dic11—41no—
722C25—112no—
723C22×Q8—112no—
724C22×D4—111no—
725C22×D4—112no—
726C22×D4—112no—
727C22×D4—112no—
728C22×D4—112no—
729C22×D4—112no—
730C22×D4—111no—
731C22×D4—224no—
732C22×D4—442no—
733C22×D4—442no—
734C22×D4C22×D1111yescharacteristic
735C22×D4C22×D1111yescharacteristic
736C22×D4C22×D1112yes—
737C22×D4C22×D1112yes—
738C22×D4C22×D1112yes—
739C22×D4C22×D1112yes—
740C23×C4—111no—
741C23×C4—111no—
742C23×C4—112no—
743C23×C4—111no—
744C23×C4—112no—
745C23×C4C22×D1111yescharacteristic
746C23×C4C22×D1111yescharacteristic
747C23×C4C22×D1111yescharacteristic
748C4⋊Q8—442no—
749#127—42no—
750#127—442no—
751#126—228no—
752#126—228no—
753#124—228no—
754#124—228no—
755#124—444no—
756#123—228no—
757#123—228no—
758C22⋊Q8—228no—
759#121—28no—
760#121—44no—
761#121—42no—
762#121—42no—
763#121—228no—
764#121—224no—
765#121—228no—
766#121—442no—
767#120—228no—
768#120—228no—
769#120—228no—
770C4×D4—118no—
771C4×D4—228no—
772C4×D4—224no—
773C4×D4—224no—
774C4×D4—442no—
775C2×C4⋊C4—111no—
776C2×C4⋊C4—111no—
777C2×C4⋊C4—111no—
778C2×C4⋊C4—112no—
779C2×C4⋊C4—111no—
780C2×C4⋊C4—111no—
781C2×C4⋊C4—112no—
782C2×C4⋊C4—112no—
783C2×C4⋊C4—111no—
784C2×C4⋊C4—112no—
785C2×C4⋊C4—112no—
786C2×C4⋊C4—112no—
787C2×C4⋊C4—442no—
788C2×C4⋊C4C22×D1111yescharacteristic
789C2×C4⋊C4C22×D1111yescharacteristic
790C2×C4⋊C4C22×D1112yes—
791C2×C4⋊C4C22×D1112yes—
792C2×C22⋊C4—111no—
793C2×C22⋊C4—111no—
794C2×C22⋊C4—111no—
795C2×C22⋊C4—112no—
796C2×C22⋊C4—111no—
797C2×C22⋊C4—111no—
798C2×C22⋊C4—112no—
799C2×C22⋊C4—112no—
800C2×C22⋊C4—112no—
801C2×C22⋊C4—112no—
802C2×C22⋊C4—112no—
803C2×C22⋊C4—112no—
804C2×C22⋊C4—112no—
805C2×C22⋊C4—112no—
806C2×C22⋊C4—112no—
807C2×C22⋊C4—112no—
808C2×C22⋊C4—111no—
809C2×C22⋊C4—112no—
810C2×C22⋊C4—112no—
811C2×C22⋊C4—112no—
812C2×C22⋊C4—112no—
813C2×C22⋊C4—112no—
814C2×C22⋊C4—112no—
815C2×C22⋊C4—112no—
816C2×C22⋊C4—112no—
817C2×C22⋊C4—112no—
818C2×C22⋊C4—112no—
819C2×C22⋊C4—228no—
820C2×C22⋊C4—444no—
821C2×C22⋊C4C22×D1112yes—
822C2×C22⋊C4C22×D1112yes—
823C2×C22⋊C4C22×D1112yes—
824C2×C22⋊C4C22×D1112yes—
825C2×C22⋊C4C22×D1112yes—
826C2×C22⋊C4C22×D1112yes—
827C2×C42—42no—
828C2×C42—111no—
829C2×C42—112no—
830C2×C42—111no—
831C2×C42—111no—
832C2×C42—111no—
833C2×C42—111no—
834C2×C42—111no—
835C2×C42—111no—
836C2×C42—111no—
837C2×C42—111no—
838C2×C42—442no—
839C2×C42C22×D1111yescharacteristic
840C2×C42C22×D1111yescharacteristic
841C2×C42C22×D1111yescharacteristic
842C2×C42C22×D1111yescharacteristic
843#95—111no—
844#95—111no—
845#95—111no—
846#95—111no—
847#95—111no—
848#95—111no—
849#95—112no—
850#95—112no—
851#95—112no—
852#95—112no—
853#95—112no—
854#95—112no—
855#95—112no—
856C2×C11—42no—
857C2×C11—82no—
858C2×C11—82no—
859C2×C11C2×#53211yescharacteristic
860C2×C11C2×#53811yescharacteristic
861C2×C11#346011yescharacteristic
862C2×C11#349611yescharacteristic
863C2×C11#349811yescharacteristic
864C2×C11#351411yescharacteristic
865C2×C11#351911yescharacteristic
866D11—24no—
867D11—82no—
868C24—111no—
869C24—112no—
870C24—224no—
871C24—224no—
872C24—224no—
873C24—442no—
874C24—442no—
875C24—442no—
876C24—442no—
877C24C23×D1112yes—
878C24C23×D1112yes—
879C24C23×D1111yescharacteristic
880C2×Q8—224no—
881C2×Q8—442no—
882C2×Q8—442no—
883C2×D4—24no—
884C2×D4—24no—
885C2×D4—24no—
886C2×D4—22no—
887C2×D4—22no—
888C2×D4—22no—
889C2×D4—22no—
890C2×D4—22no—
891C2×D4—22no—
892C2×D4—24no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—114no—
902C2×D4—224no—
903C2×D4—224no—
904C2×D4—224no—
905C2×D4—222no—
906C2×D4—222no—
907C2×D4—224no—
908C2×D4—224no—
909C2×D4—224no—
910C2×D4—224no—
911C2×D4—222no—
912C2×D4—222no—
913C2×D4—222no—
914C2×D4—4416no—
915C2×D4—442no—
916C2×D4—442no—
917C2×D4—442no—
918C2×D4—442no—
919C2×D4—442no—
920C2×D4—442no—
921C2×D4—442no—
922C2×D4—442no—
923C22×C4—22no—
924C22×C4—22no—
925C22×C4—22no—
926C22×C4—22no—
927C22×C4—22no—
928C22×C4—41no—
929C22×C4—41no—
930C22×C4—41no—
931C22×C4—111no—
932C22×C4—111no—
933C22×C4—111no—
934C22×C4—111no—
935C22×C4—111no—
936C22×C4—114no—
937C22×C4—114no—
938C22×C4—111no—
939C22×C4—111no—
940C22×C4—112no—
941C22×C4—112no—
942C22×C4—112no—
943C22×C4—222no—
944C22×C4—224no—
945C22×C4—224no—
946C22×C4—222no—
947C22×C4—222no—
948C22×C4—222no—
949C22×C4—441no—
950C22×C4—441no—
951C22×C4—441no—
952C22×C4—442no—
953C22×C4—442no—
954C22×C4—442no—
955C22×C4—442no—
956C22×C4D4×D1114yescomplemented
957C22×C4C23×D1111yescharacteristic
958C22×C4C23×D1112yes—
959C22×C4C23×D1112yes—
960C22×C4C23×D1111yescharacteristic
961C22×C4C23×D1111yescharacteristic
962C22×C4C23×D1111yescharacteristic
963C22×C4C23×D1111yescharacteristic
964C22×C4C23×D1111yescharacteristic
965C4⋊C4—24no—
966C4⋊C4—22no—
967C4⋊C4—22no—
968C4⋊C4—42no—
969C4⋊C4—114no—
970C4⋊C4—222no—
971C4⋊C4—224no—
972C4⋊C4—224no—
973C4⋊C4—224no—
974C4⋊C4—224no—
975C4⋊C4—222no—
976C4⋊C4—222no—
977C4⋊C4—222no—
978C4⋊C4—222no—
979C4⋊C4—442no—
980C4⋊C4—442no—
981C22⋊C4—24no—
982C22⋊C4—24no—
983C22⋊C4—24no—
984C22⋊C4—24no—
985C22⋊C4—42no—
986C22⋊C4—42no—
987C22⋊C4—114no—
988C22⋊C4—114no—
989C22⋊C4—114no—
990C22⋊C4—224no—
991C22⋊C4—224no—
992C22⋊C4—224no—
993C22⋊C4—222no—
994C22⋊C4—224no—
995C22⋊C4—222no—
996C22⋊C4—222no—
997C22⋊C4—224no—
998C22⋊C4—224no—
999C22⋊C4—224no—
1000C22⋊C4—224no—
1001C22⋊C4—224no—
1002C22⋊C4—224no—
1003C22⋊C4—224no—
1004C22⋊C4—224no—
1005C22⋊C4—224no—
1006C22⋊C4—224no—
1007C22⋊C4—442no—
1008C22⋊C4—442no—
1009C22⋊C4—442no—
1010C22⋊C4—442no—
1011C22⋊C4—442no—
1012C22⋊C4—442no—
1013C22⋊C4—442no—
1014C42—22no—
1015C42—22no—
1016C42—41no—
1017C42—41no—
1018C42—114no—
1019C42—224no—
1020C42—222no—
1021C42—222no—
1022C42—222no—
1023C42—222no—
1024C42—222no—
1025C42—441no—
1026C42—441no—
1027C42—441no—
1028C11#3500711yescharacteristic, complemented, Sylow
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23—21no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—112no—
1050C23—112no—
1051C23—112no—
1052C23—221no—
1053C23—221no—
1054C23—221no—
1055C23—221no—
1056C23—222no—
1057C23—222no—
1058C23—222no—
1059C23—222no—
1060C23—222no—
1061C23—222no—
1062C23—222no—
1063C23—448no—
1064C23—448no—
1065C23—448no—
1066C23—884no—
1067C23—884no—
1068C23—884no—
1069C23—884no—
1070C23C2×D4×D1112yes—
1071C23C24×D1111yescharacteristic
1072Q8—884no—
1073D4—44no—
1074D4—44no—
1075D4—84no—
1076D4—84no—
1077D4—84no—
1078D4—84no—
1079D4—228no—
1080D4—448no—
1081D4—448no—
1082D4—444no—
1083D4—884no—
1084D4—884no—
1085D4—884no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—21no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—21no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—21no—
1103C2×C4—44no—
1104C2×C4—44no—
1105C2×C4—44no—
1106C2×C4—112no—
1107C2×C4—112no—
1108C2×C4—112no—
1109C2×C4—112no—
1110C2×C4—112no—
1111C2×C4—221no—
1112C2×C4—221no—
1113C2×C4—221no—
1114C2×C4—221no—
1115C2×C4—221no—
1116C2×C4—221no—
1117C2×C4—221no—
1118C2×C4—221no—
1119C2×C4—221no—
1120C2×C4—221no—
1121C2×C4—228no—
1122C2×C4—222no—
1123C2×C4—222no—
1124C2×C4—222no—
1125C2×C4—221no—
1126C2×C4—221no—
1127C2×C4—222no—
1128C2×C4—221no—
1129C2×C4—222no—
1130C2×C4—222no—
1131C2×C4—221no—
1132C2×C4—222no—
1133C2×C4—221no—
1134C2×C4—222no—
1135C2×C4—221no—
1136C2×C4—222no—
1137C2×C4—444no—
1138C2×C4—444no—
1139C2×C4—884no—
1140C2×C4—884no—
1141C2×C4C2×D4×D1112yes—
1142C2×C4C2×D4×D1112yes—
1143C2×C4#6703712yes—
1144C2×C4#6703712yes—
1145C2×C4#6703712yes—
1146C2×C4#41×D1112yes—
1147C2×C4#41×D1112yes—
1148C22—22no—
1149C22—22no—
1150C22—22no—
1151C22—41no—
1152C22—41no—
1153C22—41no—
1154C22—41no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22—42no—
1160C22—42no—
1161C22—42no—
1162C22—42no—
1163C22—42no—
1164C22—42no—
1165C22—42no—
1166C22—42no—
1167C22—42no—
1168C22—42no—
1169C22—114no—
1170C22—222no—
1171C22—222no—
1172C22—222no—
1173C22—222no—
1174C22—222no—
1175C22—222no—
1176C22—442no—
1177C22—442no—
1178C22—442no—
1179C22—442no—
1180C22—442no—
1181C22—442no—
1182C22—442no—
1183C22—8816no—
1184C22C22×D4×D1111yescharacteristic
1185C22C2×#6703711yescharacteristic
1186C22C2×#6703711yescharacteristic
1187C22C2×#6703711yescharacteristic
1188C22C2×#41×D1111yescharacteristic
1189C22C2×#41×D1111yescharacteristic
1190C22#1062345311yescharacteristic
1191C4—22no—
1192C4—22no—
1193C4—22no—
1194C4—22no—
1195C4—42no—
1196C4—42no—
1197C4—41no—
1198C4—222no—
1199C4—222no—
1200C4—222no—
1201C4—222no—
1202C4—222no—
1203C4—442no—
1204C4—441no—
1205C4—442no—
1206C4—442no—
1207C4—441no—
1208C4#1062314414yescomplemented
1209C2—42no—
1210C2—82no—
1211C2—82no—
1212C2—224no—
1213C2—882no—
1214C2D11×#53211yescharacteristic
1215C2C2×#1062314411yescharacteristic
1216C2#1308203011yescharacteristic
1217C2#1308237311yescharacteristic
1218C2#1308239211yescharacteristic
1219C2#1308257211yescharacteristic
1220C2#1308264211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2856C2
hypercenter#2856D11
hypocenterC11#35007
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2856

Complements

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

NH ≅ G/Ntype
1. C2×#10623144C2semidirect
2. #13076980C2semidirect
3. #13076970C2semidirect
4. #13076947C2semidirect
5. #13074757C2semidirect
6. #13074745C2semidirect
7. #13073689C2semidirect
8. #13073681C2semidirect
9. #13073198C2semidirect
10. #13072981C2semidirect
11. #13072748C2semidirect
12. #13072377C2semidirect
13. #13072321C2semidirect
14. #13072250C2semidirect
15. #13072206C2semidirect
16. #13072149C2semidirect
17. #13072052C2semidirect
18. #13071968C2semidirect
19. #13071275C2semidirect
20. #13071132C2semidirect
21. D11×#390C2semidirect
22. C42×C22⋊D11C2semidirect
23. C11×#2856C2semidirect
27. C2×C11×#121C22semidirect
28. C2×C11×#121C22semidirect
29. C2×C11×#121C22semidirect
30. C22×C42×C11C22semidirect
32. C2×#66992C22semidirect
38. C2×#66989C22semidirect
39. C2×#66988C22semidirect
40. C2×D4×Dic11C22semidirect
42. C2×#66982C22semidirect
47. C2×#66951C22semidirect
50. C2×#66941C22semidirect
51. C2×#66938C22semidirect
52. C2×#66938C22semidirect
56. C2×#66932C22semidirect
59. C11×#390C22semidirect
60. C11×#390C22semidirect
61. C11×#390C22semidirect
62. C11×#384C22semidirect
66. #10622836C22semidirect
67. #10622835C22semidirect
68. #10622835C22semidirect
69. #10622835C22semidirect
70. #10622835C22semidirect
74. #10622834C22semidirect
75. #10622833C22semidirect
76. #10622826C22semidirect
77. #10622825C22semidirect
78. C4×C22⋊Dic11C22semidirect
79. C4×C22⋊Dic11C22semidirect
80. C4×C22⋊Dic11C22semidirect
81. #10622607C22semidirect
82. #10622606C22semidirect
83. #10622603C22semidirect
88. #10622598C22semidirect
89. #10622593C22semidirect
90. #10622592C22semidirect
91. C4⋊C4×Dic11C22semidirect
92. #10622586C22semidirect
94. #10622572C22semidirect
95. #10622571C22semidirect
98. #10622570C22semidirect
99. #10622570C22semidirect
103. #10622564C22semidirect
104. #10622561C22semidirect
105. #10622560C22semidirect
106. #10622558C22semidirect
107. #10622558C22semidirect
108. #10622558C22semidirect
109. #10622557C22semidirect
110. C22⋊C4×Dic11C22semidirect
111. #10622553C22semidirect
112. #10622553C22semidirect
118. C4×Dic11⋊C4C22semidirect
119. C4×Dic11⋊C4C22semidirect
120. C4×Dic11⋊C4C22semidirect
121. C42×Dic11C22semidirect
122. #10622541C22semidirect
123. #10622541C22semidirect
198. C4×C22⋊D11D4semidirect
297. C22×C4×C11C2×D4semidirect
383. C22⋊Dic11C2×D4semidirect
408. Dic11⋊C4C2×D4semidirect
418. C4×Dic11C2×D4semidirect
422. #2856D11semidirect
579. C2×#121C2×D11semidirect
580. C2×#121C2×D11semidirect
581. C2×#121C2×D11semidirect
594. C22×C42C2×D11semidirect
624. #390C2×D11semidirect
625. #390C2×D11semidirect
626. #390C2×D11semidirect
645. #384C2×D11semidirect
711. C4×C11#538semidirect
956. C22×C4D4×D11semidirect
1028. C11#35007semidirect
1208. C4#10623144semidirect

Maximal subgroups

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

subgroupindex
C2×#106231442
#130769802
#130769702
#130769472
#130747572
#130747452
#130736892
#130736812
#130731982
#130729812
#130727482
#130723772
#130723212
#130722502
#130722062
#130721492
#130720522
#130719682
#130712752
#130711322
D11×#3902
C42×C22⋊D112
C11×#28562
#3500711