Finite Group Databasebeta

← #15622700

Subgroups — #15622700

Order 2816.

2134 conjugacy classes of subgroups.

The subgroup lattice has 1244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082348C211yesmaximal, characteristic, complemented
2D11×#520C211yesmaximal, characteristic, complemented
3#13078892C212yesmaximal, complemented
4#13078890C212yesmaximal, complemented
5#13078814C212yesmaximal, complemented
6#13078812C212yesmaximal, complemented
7#13078786C212yesmaximal, complemented
8#13078706C212yesmaximal, complemented
9#13078662C212yesmaximal, complemented
10#13078646C212yesmaximal, complemented
11#13078537C211yesmaximal, characteristic, complemented
12C2×#10622390C211yesmaximal, characteristic, complemented
13#13078480C211yesmaximal, characteristic, complemented
14#13078478C211yesmaximal, characteristic, complemented
15#13078151C211yesmaximal, characteristic, complemented
16#13077864C211yesmaximal, characteristic, complemented
17#13077830C211yesmaximal, characteristic, complemented
18#13077500C211yesmaximal, characteristic, complemented
19#13077495C211yesmaximal, characteristic, complemented
20#13077449C211yesmaximal, characteristic, complemented
21#13077442C211yesmaximal, characteristic, complemented
22#13077273C211yesmaximal, characteristic, complemented
23C11×#3045C211yesmaximal, characteristic, complemented
24C2×#41×D11C2211yescharacteristic
25C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
26C2×C11×#135C2211yescharacteristic
27C11×#535C2211yescharacteristic, complemented
28C11×#520C2211yescharacteristic
29#10623359C2211yescharacteristic
30#10623358C2211yescharacteristic
31#10623358C2211yescharacteristic, complemented
32C2×#67003C2211yescharacteristic
33C2×#66991C2211yescharacteristic
34#10623329C2211yescharacteristic, complemented
35C2×#66985C2211yescharacteristic
36#10623250C2212yescomplemented
37#10623247C2212yes—
38#10623213C2212yescomplemented
39#10623211C2212yes—
40#10623149—21no—
41#10623147—21no—
42#10623145—21no—
43#10623142—21no—
44#10623122—22no—
45#10623118—22no—
46#10623105C2212yescomplemented
47C4×Q8×D11C2212yescomplemented
48#10623077—22no—
49#10623077C2212yescomplemented
50C4×D4×D11—22no—
51C4×D4×D11C2212yescomplemented
52#10623054—21no—
53#10623054C2211yescharacteristic
54D11×#117—21no—
55D11×#117C2211yescharacteristic
56#10623050C2211yescharacteristic, complemented
57#10623035—21no—
58#10623035C2211yescharacteristic
59C2×C4⋊C4×D11—21no—
60C2×C4⋊C4×D11C2211yescharacteristic
61C11×#464C2212yescomplemented
62C11×#463C2212yescomplemented
63C11×#460C2212yescomplemented
64C11×#459C2212yescomplemented
65C11×#424C2211yescharacteristic, complemented
66C11×#417C2211yescharacteristic, complemented
67C2×C11×#102C2211yescharacteristic, complemented
68#10622846C2211yescharacteristic
69#10622845C2211yescharacteristic
70#10622845C2211yescharacteristic, complemented
71C2×#66896C2211yescharacteristic, complemented
72#10622800C2211yescharacteristic, complemented
73#10622799C2211yescharacteristic, complemented
74#10622797C2212yescomplemented
75#10622786C2211yescharacteristic, complemented
76#10622785C2212yes—
77#10622785C2211yescharacteristic, complemented
78#10622783C2212yes—
79#10622783C2211yescharacteristic, complemented
80#10622782C2211yescharacteristic, complemented
81#10622777C2212yescomplemented
82SD16×Dic11C2212yescomplemented
83SD16×Dic11C2212yescomplemented
84SD16×Dic11C2212yescomplemented
85#10622771C2212yes—
86#10622771C2211yescharacteristic, complemented
87#10622769C2212yes—
88#10622769C2211yescharacteristic, complemented
89#10622765C2212yescomplemented
90#10622765C2212yescomplemented
91D8×Dic11C2212yescomplemented
92#10622746C2211yescharacteristic
93#10622739C2211yescharacteristic
94#10622735C2211yescharacteristic, complemented
95#10622734C2211yescharacteristic, complemented
96#10622726C2211yescharacteristic
97C2×(C2×D11)⋊C8C2211yescharacteristic
98C2×#66881C2211yescharacteristic, complemented
99#10622714C2211yescharacteristic, complemented
100#10622688C2212yescomplemented
101#10622685C2212yescomplemented
102#10622670C2212yescomplemented
103#10622667C2212yescomplemented
104#10622635C2212yescomplemented
105#10622633C2212yescomplemented
106#10622622C2212yescomplemented
107#10622621C2212yescomplemented
108#10622612C2211yescharacteristic, complemented
109#10622577C2211yescharacteristic, complemented
110C2×#66872C2211yescharacteristic, complemented
111#10622464C2212yescomplemented
112#10622460C2212yescomplemented
113#10622455C2212yescomplemented
114#10622453C2212yescomplemented
115#10622453C2212yescomplemented
116#10622448C2212yescomplemented
117#10622446C2212yescomplemented
118#10622442C2212yescomplemented
119#10622422C2212yescomplemented
120#10622418C2212yescomplemented
121#10622402C2212yescomplemented
122#10622401C2212yescomplemented
123#10622398C2212yescomplemented
124#10622398C2212yescomplemented
125#10622390C2212yes—
126#10622390C2212yes—
127#10622390C2212yescomplemented
128#10622390C2212yescomplemented
129#10622390C2212yescomplemented
130#10622387C2212yescomplemented
131#10622371C2212yescomplemented
132#10622371C2212yescomplemented
133#10622370C2212yescomplemented
134#10622369C2212yescomplemented
135C2×C11×#41C2311yescharacteristic
136C2×C11×#41C2311yescharacteristic
137C22×D4×C11C2311yescharacteristic
138C22×C22⋊D11—21no—
139#41×D11—24no—
140#41×D11—24no—
141C2×#4343C2311yescharacteristic
142C2×Q8×D11C2311yescharacteristic
143C2×#4341—21no—
144C2×#4341—22no—
145C2×#4341C2311yescharacteristic
146C2×D4×D11—21no—
147C2×D4×D11C2311yescharacteristic
148C2×#4339—21no—
149C2×#4339C2311yescharacteristic
150C22×C4×D11—21no—
151C22×C4×D11—21no—
152C22×C4×D11—22no—
153C22×C4×D11C2311yescharacteristic
154C11×AGL(1,ℤ/8)—24no—
155C11×#135—24no—
156C2×C11×Q16C2311yescharacteristic
157C2×C11×SD16C2311yescharacteristic
158C2×C11×SD16C2311yescharacteristic
159C2×C11×SD16C2312yes—
160C2×C11×D8C2312yes—
161C2×C11×D8C2311yescharacteristic
162C2×C11×M16C2311yescharacteristic
163C22×C8×C11C2311yescharacteristic
164C11×#127C2312yes—
165C11×#124C2312yes—
166C11×#121—21no—
167C11×#121—21no—
168C11×#120—22no—
169C4×Q8×C11C2312yes—
170C4×D4×C11—22no—
171C4×D4×C11C2312yes—
172C11×#117—21no—
173C11×#117C2311yescharacteristic
174C2×C11×C4⋊C4—21no—
175C2×C11×C4⋊C4C2311yescharacteristic
176C2×C22⋊Dic11—21no—
177C2×C22⋊Dic11—22no—
178#67003—24no—
179#66999C2311yescharacteristic
180#66999C2311yescharacteristic
181Q8×Dic11C2312yes—
182Q8×Dic11C2312yes—
183C2×#4326C2311yescharacteristic
184C2×#4325C2311yescharacteristic
185#66992—22no—
186#66992—22no—
187#66991—22no—
188#66991—21no—
189#66991—21no—
190#66991C2311yescharacteristic
191#66991C2312yes—
192#66991C2311yescharacteristic
193#66991C2312yes—
194#66990—21no—
195#66989—22no—
196#66988—21no—
197#66988—22no—
198#66988—22no—
199D4×Dic11—22no—
200D4×Dic11—22no—
201D4×Dic11—21no—
202D4×Dic11—21no—
203D4×Dic11—22no—
204D4×Dic11C2312yes—
205D4×Dic11C2312yes—
206D4×Dic11C2312yes—
207D4×Dic11C2312yes—
208C2×#4324C2312yes—
209C2×#4324C2311yescharacteristic
210#66985—24no—
211C2×#4323C2312yes—
212C2×#4323C2311yescharacteristic
213C4×C22⋊D11—21no—
214C4×C22⋊D11—21no—
215C4×C22⋊D11—22no—
216C4×C22⋊D11—22no—
217C4×C22⋊D11—22no—
218#66979—21no—
219#66979—21no—
220#66979C2311yescharacteristic
221#66979C2311yescharacteristic
222C2×C4⋊Dic11—21no—
223C2×C4⋊Dic11—21no—
224C2×C4⋊Dic11C2311yescharacteristic
225C2×C4⋊Dic11C2311yescharacteristic
226C2×Dic11⋊C4—21no—
227C2×Dic11⋊C4—22no—
228C2×#4318C2311yescharacteristic
229C22×C11⋊C8C2311yescharacteristic
230#66946—22no—
231#66946C2312yes—
232#66945—21no—
233#66945—21no—
234#66945D411yescharacteristic
235#66945D411yescharacteristic
236C4⋊C4×D11—21no—
237C4⋊C4×D11—22no—
238C4⋊C4×D11—21no—
239C4⋊C4×D11—21no—
240C4⋊C4×D11—21no—
241C4⋊C4×D11—22no—
242C4⋊C4×D11D411yescharacteristic
243C4⋊C4×D11D411yescharacteristic
244C4⋊C4×D11C2312yes—
245C4⋊C4×D11C2312yes—
246#66943—21no—
247#66941—21no—
248#66940—22no—
249#66940C2312yes—
250#66939—22no—
251#66938—22no—
252#66936—22no—
253(C22⋊D11)⋊C4—22no—
254(C22⋊D11)⋊C4—22no—
255(C22⋊D11)⋊C4—22no—
256(C22⋊D11)⋊C4—22no—
257C22⋊C4×D11—22no—
258C22⋊C4×D11D412yes—
259#66932—22no—
260#66932—22no—
261#66931—22no—
262#66931—22no—
263#66930—22no—
264#66930—22no—
265#66930D412yes—
266C4×D44—22no—
267C4×D44C2312yes—
268#66925—22no—
269#66925C2312yes—
270C42×D11—22no—
271C42×D11C2312yes—
272#66923C2312yes—
273#66922C2312yes—
274C4×Dic22—22no—
275C4×Dic22C2312yes—
276C11×C4⋊C8C2312yes—
277C11×C4⋊C8C2312yes—
278C11×#103C2312yes—
279C11×#102C2312yes—
280C11×#102C2312yes—
281C11×#102C2312yes—
282#66899C2311yescharacteristic
283#66899C2312yes—
284#66899C2312yes—
285#66899C2311yescharacteristic
286#66896C2311yescharacteristic
287#66896C2312yes—
288#66896C2311yescharacteristic
289#66896C2312yes—
290#66896C2312yes—
291#66896C2312yes—
292#66885C2311yescharacteristic
293#66885C2311yescharacteristic
294#66885C2312yes—
295(C2×D11)⋊C8C2311yescharacteristic
296(C2×D11)⋊C8C2311yescharacteristic
297(C2×D11)⋊C8C2311yescharacteristic
298(C2×D11)⋊C8C2311yescharacteristic
299(C2×D11)⋊C8C2312yes—
300(C2×D11)⋊C8C2312yes—
301#66882C2312yes—
302#66881C2312yes—
303#66881C2312yes—
304#66881C2312yes—
305#66880C2311yescharacteristic
306#66880C2312yes—
307#66880C2311yescharacteristic
308#66879C2312yes—
309#66879C2312yes—
310C8×Dic11C2312yes—
311C8×Dic11C2312yes—
312#66872C2312yes—
313#66872C2312yes—
314#66872C2312yes—
315#66871C2312yes—
316C4⋊(C11⋊C8)C2312yes—
317C4⋊(C11⋊C8)C2312yes—
318#60588—111nomaximal, Sylow
319C24×C11—21no—
320C23×D11—21no—
321C23×D11C2×D411yescharacteristic
322C11×#41—22no—
323C11×#41—22no—
324C11×#41—22no—
325C11×#41#4114yescomplemented
326C2×Q8×C11C2411yescharacteristic
327C2×Q8×C11C2411yescharacteristic
328C2×D4×C11—21no—
329C2×D4×C11—21no—
330C2×D4×C11—21no—
331C2×D4×C11—22no—
332C2×D4×C11—22no—
333C2×D4×C11—22no—
334C2×D4×C11—22no—
335C2×D4×C11C2412yes—
336C2×D4×C11C2411yescharacteristic
337C2×D4×C11C2411yescharacteristic
338C22×C4×C11—21no—
339C22×C4×C11—21no—
340C22×C4×C11—21no—
341C22×C4×C11—22no—
342C22×C4×C11C2411yescharacteristic
343C2×C22⋊D11—21no—
344C2×C22⋊D11—21no—
345C2×C22⋊D11—21no—
346C2×C22⋊D11—22no—
347C2×C22⋊D11—21no—
348C2×C22⋊D11—22no—
349C2×C22⋊D11—21no—
350C2×C22⋊D11—82no—
351C22×Dic11—21no—
352C22×Dic11—22no—
353C22×Dic11—22no—
354C22×Dic11—22no—
355C22×Dic11—22no—
356C22×Dic11—21no—
357C22×Dic11—21no—
358C22×Dic11C2×D411yescharacteristic
359#4343—22no—
360#4343—22no—
361Q8×D11—22no—
362Q8×D11—22no—
363#4341—28no—
364#4341—22no—
365#4341—22no—
366#4341—84no—
367D4×D11—28no—
368D4×D11—22no—
369D4×D11—22no—
370#4339—28no—
371#4339—22no—
372#4339#4114yescomplemented
373C2×D44—21no—
374C2×D44C2411yescharacteristic
375C2×C4×D11—28no—
376C2×C4×D11—21no—
377C2×C4×D11—22no—
378C2×C4×D11—21no—
379C2×C4×D11—22no—
380C2×C4×D11—22no—
381C2×C4×D11—21no—
382C2×C4×D11—22no—
383C2×C4×D11—22no—
384C2×C4×D11—22no—
385C2×C4×D11—84no—
386C2×C4×D11—82no—
387C2×C4×D11C2×D412yes—
388C2×C4×D11C2×D411yescharacteristic
389C2×C4×D11C2×D411yescharacteristic
390C2×C4×D11C2×D412yes—
391C2×C4×D11C2411yescharacteristic
392C2×C4×D11C2411yescharacteristic
393C2×Dic22—21no—
394C2×Dic22—22no—
395C2×Dic22C2411yescharacteristic
396C11×Q16—22no—
397C11×SD16—22no—
398C11×SD16—24no—
399C11×SD16—22no—
400C11×D8—22no—
401C11×D8—24no—
402C11×M16—22no—
403C2×C8×C11—22no—
404C2×C8×C11C2411yescharacteristic
405C2×C8×C11C2412yes—
406C2×C8×C11C2411yescharacteristic
407C11×C4⋊C4—22no—
408C11×C4⋊C4—21no—
409C11×C4⋊C4C2×D411yescharacteristic
410C11×C4⋊C4C2×D411yescharacteristic
411C11×C4⋊C4C2412yes—
412C11×C22⋊C4—22no—
413C11×C22⋊C4—22no—
414C11×C22⋊C4—22no—
415C11×C22⋊C4C2×D412yes—
416C42×C11—22no—
417C42×C11C2412yes—
418C22⋊Dic11—22no—
419C22⋊Dic11—22no—
420C22⋊Dic11—22no—
421C22⋊Dic11—22no—
422C22⋊Dic11—22no—
423C22⋊Dic11—22no—
424C22⋊Dic11—21no—
425C22⋊Dic11—21no—
426C22⋊Dic11—21no—
427C22⋊Dic11C2×D412yes—
428#4326—22no—
429#4325—22no—
430#4324—24no—
431#4324—22no—
432#4323—24no—
433#4323—22no—
434(C2×D11)⋊C4—22no—
435(C2×D11)⋊C4—21no—
436(C2×D11)⋊C4—21no—
437(C2×D11)⋊C4—22no—
438(C2×D11)⋊C4C2×D412yes—
439(C2×D11)⋊C4C2×D412yes—
440C4⋊Dic11—22no—
441C4⋊Dic11—22no—
442C4⋊Dic11—22no—
443C4⋊Dic11—21no—
444C4⋊Dic11—21no—
445C4⋊Dic11C2×D411yescharacteristic
446C4⋊Dic11C2×D411yescharacteristic
447C4⋊Dic11C2411yescharacteristic
448C4⋊Dic11C2411yescharacteristic
449C4⋊Dic11C2412yes—
450C4⋊Dic11C2412yes—
451Dic11⋊C4—22no—
452Dic11⋊C4—22no—
453Dic11⋊C4—22no—
454Dic11⋊C4—21no—
455Dic11⋊C4—21no—
456Dic11⋊C4—22no—
457Dic11⋊C4—22no—
458Dic11⋊C4—22no—
459Dic11⋊C4C2×D412yes—
460Dic11⋊C4C2×D412yes—
461C4×Dic11—22no—
462C4×Dic11—22no—
463C4×Dic11—22no—
464C4×Dic11—22no—
465C4×Dic11—21no—
466C4×Dic11C2×D412yes—
467C4×Dic11C2×D412yes—
468C4×Dic11C2412yes—
469#4318—22no—
470C2×C11⋊C8—22no—
471C2×C11⋊C8C2412yes—
472C2×C11⋊C8C2411yescharacteristic
473C2×C11⋊C8C2411yescharacteristic
474#3494—111no—
475C2×#520—111no—
476#3125—112no—
477#3125—112no—
478#3119—112no—
479#3119—112no—
480#3117—112no—
481#3109—112no—
482#3105—112no—
483#3103—112no—
484#3092—111no—
485C2×#481—111no—
486#3084—111no—
487#3084—111no—
488#3045—111no—
489#3045D1111yescharacteristic, complemented
490#3006—111no—
491#3002—111no—
492#2952—111no—
493#2952—111no—
494#2946—111no—
495#2946—111no—
496#2924—111no—
497C23×C11—21no—
498C23×C11—22no—
499C23×C11—21no—
500C23×C11—42no—
501C23×C11—81no—
502C23×C11—81no—
503C23×C11C22×D411yescharacteristic
504C22×D11—24no—
505C22×D11—22no—
506C22×D11—21no—
507C22×D11—22no—
508C22×D11—41no—
509C22×D11—42no—
510C22×D11—42no—
511C22×D11C22×D411yescharacteristic
512C22×D11C22×D411yescharacteristic
513Q8×C11—21no—
514Q8×C11—21no—
515Q8×C11—21no—
516Q8×C11C2×#4112yes—
517D4×C11—24no—
518D4×C11—21no—
519D4×C11—22no—
520D4×C11—21no—
521D4×C11—22no—
522D4×C11—21no—
523D4×C11—42no—
524D4×C11—42no—
525D4×C11—82no—
526D4×C11—82no—
527D4×C11C2×#4112yes—
528C2×C4×C11—21no—
529C2×C4×C11—24no—
530C2×C4×C11—21no—
531C2×C4×C11—22no—
532C2×C4×C11—42no—
533C2×C4×C11—82no—
534C2×C4×C11—81no—
535C2×C4×C11C22×D412yes—
536C2×C4×C11C22×D412yes—
537C2×C4×C11C22×D411yescharacteristic
538C2×C4×C11C2×#4112yes—
539C2×C4×C11C2×#4112yes—
540C2×C4×C11C2511yescharacteristic
541C22⋊D11—24no—
542C22⋊D11—24no—
543C22⋊D11—24no—
544C22⋊D11—42no—
545C22⋊D11—44no—
546C22⋊D11—81no—
547C22⋊D11—82no—
548C2×Dic11—24no—
549C2×Dic11—22no—
550C2×Dic11—21no—
551C2×Dic11—22no—
552C2×Dic11—21no—
553C2×Dic11—22no—
554C2×Dic11—21no—
555C2×Dic11—82no—
556C2×Dic11—82no—
557C2×Dic11—82no—
558C2×Dic11—82no—
559C2×Dic11—81no—
560C2×Dic11—81no—
561C2×Dic11C22×D412yes—
562C2×Dic11C22×D412yes—
563C2×Dic11C22×D411yescharacteristic
564C2×Dic11C22×D411yescharacteristic
565D44—24no—
566D44—21no—
567D44C2×#4112yes—
568C4×D11—24no—
569C4×D11—24no—
570C4×D11—24no—
571C4×D11—22no—
572C4×D11—24no—
573C4×D11—22no—
574C4×D11—21no—
575C4×D11—21no—
576C4×D11—21no—
577C4×D11—21no—
578C4×D11—42no—
579C4×D11—44no—
580C4×D11—82no—
581C4×D11—82no—
582C4×D11—82no—
583Dic22—24no—
584Dic22—21no—
585Dic22—82no—
586Dic22C2×#4112yes—
587C8×C11—21no—
588C8×C11—21no—
589C8×C11—22no—
590C11⋊C8—21no—
591C11⋊C8—21no—
592C11⋊C8—22no—
593C22×#41—111no—
594C2×AGL(1,ℤ/8)—111no—
595C2×AGL(1,ℤ/8)C2×D1111yescharacteristic
596C2×#135—111no—
597C2×#135C2×D1111yescharacteristic
598#555—221no—
599#553—221no—
600#553—221no—
601#551—222no—
602#547—221no—
603#546—222no—
604#544—111no—
605#542—112no—
606#540—112no—
607#535C2×D1111yescharacteristic, complemented
608#532—112no—
609#529—112no—
610#525—111no—
611C2×#121—111no—
612#520—111no—
613#520—111no—
614#520—112no—
615#520—112no—
616#520—111no—
617#520—111no—
618#520—221no—
619#520—221no—
620#520—222no—
621#520C2×D1111yescharacteristic
622#518—111no—
623C2×C4×Q8—112no—
624C2×C4×D4—112no—
625C2×C4×D4—222no—
626C2×#117—111no—
627C2×#117—221no—
628C22×C4⋊C4—111no—
629C22×C4⋊C4—221no—
630#484—112no—
631#483—112no—
632#481—112no—
633#481—112no—
634#481—112no—
635#481—112no—
636#481—112no—
637#480—112no—
638#479—112no—
639#479—112no—
640#478—112no—
641#478—112no—
642#476—112no—
643#476—112no—
644#475—112no—
645#475—112no—
646#464—112no—
647#464C2×D1112yescomplemented
648#463—112no—
649#463C2×D1112yescomplemented
650#460—112no—
651#460C2×D1112yescomplemented
652#459—112no—
653#459C2×D1112yescomplemented
654#452—111no—
655#452—111no—
656#451—111no—
657#450—111no—
658#449—111no—
659#449—112no—
660#449—111no—
661#449—112no—
662#448—111no—
663#448—112no—
664#447—112no—
665#447—111no—
666#442—112no—
667#442—112no—
668#442—112no—
669#442—112no—
670#441—112no—
671#441—112no—
672#440—112no—
673#440—112no—
674C4×SD16—112no—
675C4×SD16—112no—
676C4×SD16—112no—
677C4×SD16—112no—
678C4×SD16—112no—
679C4×SD16—112no—
680C4×D8—112no—
681C4×D8—112no—
682#433—112no—
683#433—112no—
684#432—112no—
685#431—112no—
686#428—111no—
687#428—111no—
688C2×#106—111no—
689C2×#106—111no—
690#424—111no—
691#424C2×D1111yescharacteristic, complemented
692#417—111no—
693#417—111no—
694#417—111no—
695#417C2×D1111yescharacteristic, complemented
696#416—111no—
697#416—111no—
698C2×#102—111no—
699C2×#102C2×D1111yescharacteristic, complemented
700#407—111no—
701C2×C22⋊C8—111no—
702#405—111no—
703#405—111no—
704C22×C11—21no—
705C22×C11—21no—
706C22×C11—22no—
707C22×C11—41no—
708C22×C11—41no—
709C22×C11—41no—
710C22×C11—42no—
711C22×C11—41no—
712C22×C11—42no—
713C22×C11—41no—
714C22×C11—42no—
715C22×C11—162no—
716C22×C11#52512yes—
717C22×C11C23×D411yescharacteristic
718C2×D11—21no—
719C2×D11—21no—
720C2×D11—21no—
721C2×D11—22no—
722C2×D11—21no—
723C2×D11—21no—
724C2×D11—44no—
725C2×D11—48no—
726C2×D11—41no—
727C2×D11—41no—
728C2×D11#57712yes—
729C4×C11—22no—
730C4×C11—22no—
731C4×C11—22no—
732C4×C11—42no—
733C4×C11—41no—
734C4×C11#52512yes—
735C4×C11C22×#4111yescharacteristic
736C4×C11C22×#4111yescharacteristic
737Dic11—22no—
738Dic11—21no—
739Dic11—22no—
740Dic11—21no—
741Dic11—22no—
742Dic11—42no—
743Dic11—41no—
744Dic11—41no—
745Dic11—42no—
746C2×#41—111no—
747C2×#41—111no—
748C2×#41—111no—
749C2×#41—221no—
750C2×#41—221no—
751C2×#41—222no—
752C2×#41—224no—
753C2×#41—224no—
754C2×#41C22×D1111yescharacteristic
755C2×#41C22×D1111yescharacteristic
756C22×Q8—111no—
757C22×D4—111no—
758C22×D4—221no—
759C22×D4—221no—
760C22×D4C22×D1111yescharacteristic
761C23×C4—111no—
762C23×C4—221no—
763C23×C4—222no—
764C23×C4—221no—
765AGL(1,ℤ/8)—24no—
766AGL(1,ℤ/8)—224no—
767#135—24no—
768#135—224no—
769C2×Q16—111no—
770C2×Q16C22×D1111yescharacteristic
771C2×SD16—111no—
772C2×SD16—111no—
773C2×SD16—112no—
774C2×SD16C22×D1111yescharacteristic
775C2×SD16C22×D1111yescharacteristic
776C2×SD16C22×D1112yes—
777C2×D8—111no—
778C2×D8—112no—
779C2×D8C22×D1111yescharacteristic
780C2×D8C22×D1112yes—
781C2×M16—111no—
782C2×M16C22×D1111yescharacteristic
783C22×C8—111no—
784C22×C8C22×D1111yescharacteristic
785C4⋊Q8—112no—
786C4⋊Q8—221no—
787#127C22×D1112yes—
788#126—222no—
789#126—222no—
790#125—112no—
791#125—221no—
792#124—222no—
793#124—222no—
794#124C22×D1112yes—
795#123—222no—
796#123—222no—
797#123—222no—
798#123—222no—
799#123—221no—
800C22⋊Q8—111no—
801C22⋊Q8—111no—
802C22⋊Q8—222no—
803C22⋊Q8—222no—
804#121—21no—
805#121—21no—
806#121—112no—
807#121—112no—
808#121—111no—
809#121—111no—
810#121—222no—
811#121—222no—
812#121—221no—
813#121—221no—
814#121—222no—
815#120—22no—
816#120—221no—
817C4×Q8—112no—
818C4×Q8—112no—
819C4×Q8—112no—
820C4×Q8—112no—
821C4×Q8—222no—
822C4×Q8—222no—
823C4×Q8C22×D1112yes—
824C4×D4—22no—
825C4×D4—112no—
826C4×D4—112no—
827C4×D4—112no—
828C4×D4—112no—
829C4×D4—112no—
830C4×D4—112no—
831C4×D4—222no—
832C4×D4—222no—
833C4×D4—222no—
834C4×D4—222no—
835C4×D4—222no—
836C4×D4—222no—
837C4×D4—222no—
838C4×D4—222no—
839C4×D4—222no—
840C4×D4—222no—
841C4×D4—222no—
842C4×D4—221no—
843C4×D4—221no—
844C4×D4—221no—
845C4×D4—221no—
846C4×D4—222no—
847C4×D4C22×D1112yes—
848#117—21no—
849#117—111no—
850#117—111no—
851#117—111no—
852#117—112no—
853#117—112no—
854#117—111no—
855#117—222no—
856#117—222no—
857#117—222no—
858#117—221no—
859#117—221no—
860#117—221no—
861#117—221no—
862#117C22×D1111yescharacteristic
863C2×C4⋊C4—21no—
864C2×C4⋊C4—111no—
865C2×C4⋊C4—111no—
866C2×C4⋊C4—111no—
867C2×C4⋊C4—111no—
868C2×C4⋊C4—112no—
869C2×C4⋊C4—112no—
870C2×C4⋊C4—221no—
871C2×C4⋊C4—222no—
872C2×C4⋊C4—221no—
873C2×C4⋊C4—221no—
874C2×C4⋊C4—222no—
875C2×C4⋊C4—222no—
876C2×C4⋊C4—221no—
877C2×C4⋊C4—221no—
878C2×C4⋊C4—221no—
879C2×C4⋊C4—221no—
880C2×C4⋊C4C22×D1111yescharacteristic
881C2×C22⋊C4—112no—
882C2×C22⋊C4—222no—
883C2×C22⋊C4—222no—
884C2×C22⋊C4—221no—
885C2×C42—112no—
886C2×C42—222no—
887#107—112no—
888#107—112no—
889#106—112no—
890#106—112no—
891#106—112no—
892#106—112no—
893#106—112no—
894#106—112no—
895C4⋊C8—112no—
896C4⋊C8—112no—
897C4⋊C8C22×D1112yes—
898C4⋊C8C22×D1112yes—
899#103—111no—
900#103—111no—
901#103—112no—
902#103—112no—
903#103—111no—
904#103—111no—
905#103—112no—
906#103C22×D1112yes—
907#102—112no—
908#102—112no—
909#102—111no—
910#102—111no—
911#102—112no—
912#102—112no—
913#102—111no—
914#102—111no—
915#102—112no—
916#102C22×D1112yes—
917#102C22×D1112yes—
918#102C22×D1112yes—
919C22⋊C8—111no—
920C22⋊C8—111no—
921C22⋊C8—111no—
922C22⋊C8—111no—
923C22⋊C8—112no—
924C22⋊C8—112no—
925#97—112no—
926#97—112no—
927C4×C8—112no—
928C4×C8—112no—
929C2×C11—22no—
930C2×C11—42no—
931C2×C11—81no—
932C2×C11—82no—
933C2×C11C2×#52511yescharacteristic
934C2×C11C2×#57711yescharacteristic
935C2×C11#358511yescharacteristic
936D11—22no—
937D11—41no—
938D11—42no—
939C24—21no—
940C24—111no—
941C24—221no—
942#41—22no—
943#41—22no—
944#41—22no—
945#41—114no—
946#41—228no—
947#41—222no—
948#41—228no—
949#41—222no—
950#41—222no—
951#41—222no—
952#41—222no—
953#41—884no—
954#41#434114yescomplemented
955C2×Q8—111no—
956C2×Q8—221no—
957C2×Q8—222no—
958C2×Q8—222no—
959C2×Q8—222no—
960C2×Q8C23×D1111yescharacteristic
961C2×Q8C23×D1111yescharacteristic
962C2×D4—21no—
963C2×D4—21no—
964C2×D4—21no—
965C2×D4—22no—
966C2×D4—22no—
967C2×D4—22no—
968C2×D4—22no—
969C2×D4—111no—
970C2×D4—221no—
971C2×D4—221no—
972C2×D4—222no—
973C2×D4—228no—
974C2×D4—221no—
975C2×D4—221no—
976C2×D4—222no—
977C2×D4—221no—
978C2×D4—222no—
979C2×D4—221no—
980C2×D4—222no—
981C2×D4—882no—
982C2×D4C23×D1112yes—
983C2×D4C23×D1111yescharacteristic
984C2×D4C23×D1111yescharacteristic
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—22no—
989C22×C4—111no—
990C22×C4—112no—
991C22×C4—111no—
992C22×C4—111no—
993C22×C4—111no—
994C22×C4—111no—
995C22×C4—112no—
996C22×C4—221no—
997C22×C4—222no—
998C22×C4—221no—
999C22×C4—228no—
1000C22×C4—222no—
1001C22×C4—222no—
1002C22×C4—221no—
1003C22×C4—222no—
1004C22×C4—222no—
1005C22×C4—222no—
1006C22×C4—222no—
1007C22×C4—221no—
1008C22×C4—222no—
1009C22×C4—222no—
1010C22×C4—221no—
1011C22×C4—221no—
1012C22×C4—222no—
1013C22×C4—884no—
1014C22×C4—882no—
1015C22×C4C23×D1111yescharacteristic
1016Q16—22no—
1017Q16—222no—
1018SD16—22no—
1019SD16—24no—
1020SD16—22no—
1021SD16—222no—
1022SD16—224no—
1023SD16—222no—
1024D8—22no—
1025D8—24no—
1026D8—222no—
1027D8—224no—
1028M16—22no—
1029M16—222no—
1030C2×C8—22no—
1031C2×C8—111no—
1032C2×C8—112no—
1033C2×C8—111no—
1034C2×C8—222no—
1035C2×C8C23×D1111yescharacteristic
1036C2×C8C23×D1112yes—
1037C2×C8C23×D1111yescharacteristic
1038C4⋊C4—21no—
1039C4⋊C4—22no—
1040C4⋊C4—111no—
1041C4⋊C4—112no—
1042C4⋊C4—111no—
1043C4⋊C4—112no—
1044C4⋊C4—112no—
1045C4⋊C4—112no—
1046C4⋊C4—111no—
1047C4⋊C4—111no—
1048C4⋊C4—222no—
1049C4⋊C4—222no—
1050C4⋊C4—222no—
1051C4⋊C4—222no—
1052C4⋊C4—222no—
1053C4⋊C4—221no—
1054C4⋊C4—221no—
1055C4⋊C4—221no—
1056C4⋊C4—221no—
1057C4⋊C4—222no—
1058C4⋊C4—222no—
1059C4⋊C4—222no—
1060C4⋊C4—222no—
1061C4⋊C4D4×D1111yescharacteristic
1062C4⋊C4D4×D1111yescharacteristic
1063C4⋊C4C23×D1112yes—
1064C22⋊C4—22no—
1065C22⋊C4—22no—
1066C22⋊C4—22no—
1067C22⋊C4—112no—
1068C22⋊C4—112no—
1069C22⋊C4—112no—
1070C22⋊C4—222no—
1071C22⋊C4—221no—
1072C22⋊C4—221no—
1073C22⋊C4—222no—
1074C22⋊C4—222no—
1075C22⋊C4—222no—
1076C22⋊C4—222no—
1077C22⋊C4—222no—
1078C22⋊C4—222no—
1079C22⋊C4—221no—
1080C22⋊C4—221no—
1081C22⋊C4—221no—
1082C22⋊C4—222no—
1083C22⋊C4D4×D1112yes—
1084C42—22no—
1085C42—112no—
1086C42—112no—
1087C42—112no—
1088C42—222no—
1089C42—222no—
1090C42—222no—
1091C42—222no—
1092C42—221no—
1093C42C23×D1112yes—
1094C11#6058811yescharacteristic, complemented, Sylow
1095C23—21no—
1096C23—22no—
1097C23—21no—
1098C23—42no—
1099C23—81no—
1100C23—81no—
1101C23—111no—
1102C23—111no—
1103C23—222no—
1104C23—224no—
1105C23—222no—
1106C23—221no—
1107C23—441no—
1108C23—442no—
1109C23—442no—
1110C23C2×D4×D1111yescharacteristic
1111Q8—21no—
1112Q8—21no—
1113Q8—21no—
1114Q8—112no—
1115Q8—224no—
1116Q8—221no—
1117Q8—882no—
1118Q8C2×#434112yes—
1119D4—24no—
1120D4—22no—
1121D4—21no—
1122D4—21no—
1123D4—22no—
1124D4—21no—
1125D4—42no—
1126D4—42no—
1127D4—82no—
1128D4—82no—
1129D4—112no—
1130D4—224no—
1131D4—224no—
1132D4—224no—
1133D4—224no—
1134D4—221no—
1135D4—444no—
1136D4—442no—
1137D4—882no—
1138D4—881no—
1139D4C2×#434112yes—
1140C2×C4—21no—
1141C2×C4—24no—
1142C2×C4—22no—
1143C2×C4—21no—
1144C2×C4—42no—
1145C2×C4—82no—
1146C2×C4—81no—
1147C2×C4—111no—
1148C2×C4—112no—
1149C2×C4—112no—
1150C2×C4—111no—
1151C2×C4—224no—
1152C2×C4—224no—
1153C2×C4—224no—
1154C2×C4—224no—
1155C2×C4—222no—
1156C2×C4—221no—
1157C2×C4—222no—
1158C2×C4—222no—
1159C2×C4—224no—
1160C2×C4—221no—
1161C2×C4—221no—
1162C2×C4—221no—
1163C2×C4—221no—
1164C2×C4—222no—
1165C2×C4—221no—
1166C2×C4—221no—
1167C2×C4—222no—
1168C2×C4—442no—
1169C2×C4—444no—
1170C2×C4—882no—
1171C2×C4—882no—
1172C2×C4—882no—
1173C2×C4—882no—
1174C2×C4—882no—
1175C2×C4—882no—
1176C2×C4—882no—
1177C2×C4—881no—
1178C2×C4—881no—
1179C2×C4C2×D4×D1112yes—
1180C2×C4C2×D4×D1112yes—
1181C2×C4C2×D4×D1111yescharacteristic
1182C2×C4C2×#434112yes—
1183C2×C4#41×D1112yes—
1184C2×C4C24×D1111yescharacteristic
1185C8—21no—
1186C8—21no—
1187C8—22no—
1188C8—221no—
1189C8—221no—
1190C8—222no—
1191C22—21no—
1192C22—21no—
1193C22—22no—
1194C22—41no—
1195C22—41no—
1196C22—41no—
1197C22—42no—
1198C22—41no—
1199C22—42no—
1200C22—42no—
1201C22—41no—
1202C22—112no—
1203C22—162no—
1204C22—221no—
1205C22—221no—
1206C22—222no—
1207C22—221no—
1208C22—221no—
1209C22—221no—
1210C22—444no—
1211C22—448no—
1212C22—441no—
1213C22—441no—
1214C22#1062313712yes—
1215C22C22×D4×D1111yescharacteristic
1216C4—22no—
1217C4—22no—
1218C4—22no—
1219C4—41no—
1220C4—42no—
1221C4—221no—
1222C4—221no—
1223C4—222no—
1224C4—222no—
1225C4—222no—
1226C4—442no—
1227C4—441no—
1228C4—442no—
1229C4—441no—
1230C4#1062313712yes—
1231C4C22×#434111yescharacteristic
1232C4C2×#41×D1111yescharacteristic
1233C2—22no—
1234C2—42no—
1235C2—82no—
1236C2—81no—
1237C2—222no—
1238C2—441no—
1239C2—442no—
1240C2C2×#1062313711yescharacteristic
1241C2D11×#57711yescharacteristic
1242C2#1308339111yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3045C2
socleC22×C11C23×D4
hypercenter#3045D11
hypocenterC11#60588
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #3045

Complements

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

NH ≅ G/Ntype
1. #13082348C2semidirect
2. D11×#520C2semidirect
3. #13078892C2semidirect
4. #13078890C2semidirect
5. #13078814C2semidirect
6. #13078812C2semidirect
7. #13078786C2semidirect
8. #13078706C2semidirect
9. #13078662C2semidirect
10. #13078646C2semidirect
11. #13078537C2semidirect
12. C2×#10622390C2semidirect
13. #13078480C2semidirect
14. #13078478C2semidirect
15. #13078151C2semidirect
16. #13077864C2semidirect
17. #13077830C2semidirect
18. #13077500C2semidirect
19. #13077495C2semidirect
20. #13077449C2semidirect
21. #13077442C2semidirect
22. #13077273C2semidirect
23. C11×#3045C2semidirect
27. C11×#535C22semidirect
31. #10623358C22semidirect
34. #10623329C22semidirect
36. #10623250C22semidirect
38. #10623213C22semidirect
46. #10623105C22semidirect
47. C4×Q8×D11C22semidirect
49. #10623077C22semidirect
51. C4×D4×D11C22semidirect
56. #10623050C22semidirect
61. C11×#464C22semidirect
62. C11×#463C22semidirect
63. C11×#460C22semidirect
64. C11×#459C22semidirect
65. C11×#424C22semidirect
66. C11×#417C22semidirect
67. C2×C11×#102C22semidirect
70. #10622845C22semidirect
71. C2×#66896C22semidirect
72. #10622800C22semidirect
73. #10622799C22semidirect
74. #10622797C22semidirect
75. #10622786C22semidirect
77. #10622785C22semidirect
79. #10622783C22semidirect
80. #10622782C22semidirect
81. #10622777C22semidirect
82. SD16×Dic11C22semidirect
83. SD16×Dic11C22semidirect
84. SD16×Dic11C22semidirect
86. #10622771C22semidirect
88. #10622769C22semidirect
89. #10622765C22semidirect
90. #10622765C22semidirect
91. D8×Dic11C22semidirect
94. #10622735C22semidirect
95. #10622734C22semidirect
98. C2×#66881C22semidirect
99. #10622714C22semidirect
100. #10622688C22semidirect
101. #10622685C22semidirect
102. #10622670C22semidirect
103. #10622667C22semidirect
104. #10622635C22semidirect
105. #10622633C22semidirect
106. #10622622C22semidirect
107. #10622621C22semidirect
108. #10622612C22semidirect
109. #10622577C22semidirect
110. C2×#66872C22semidirect
111. #10622464C22semidirect
112. #10622460C22semidirect
113. #10622455C22semidirect
114. #10622453C22semidirect
115. #10622453C22semidirect
116. #10622448C22semidirect
117. #10622446C22semidirect
118. #10622442C22semidirect
119. #10622422C22semidirect
120. #10622418C22semidirect
121. #10622402C22semidirect
122. #10622401C22semidirect
123. #10622398C22semidirect
124. #10622398C22semidirect
127. #10622390C22semidirect
128. #10622390C22semidirect
129. #10622390C22semidirect
130. #10622387C22semidirect
131. #10622371C22semidirect
132. #10622371C22semidirect
133. #10622370C22semidirect
134. #10622369C22semidirect
325. C11×#41#41semidirect
372. #4339#41semidirect
489. #3045D11semidirect
607. #535C2×D11semidirect
647. #464C2×D11semidirect
649. #463C2×D11semidirect
651. #460C2×D11semidirect
653. #459C2×D11semidirect
691. #424C2×D11semidirect
695. #417C2×D11semidirect
699. C2×#102C2×D11semidirect
954. #41#4341semidirect
1094. C11#60588semidirect

Maximal subgroups

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

subgroupindex
#130823482
D11×#5202
#130788922
#130788902
#130788142
#130788122
#130787862
#130787062
#130786622
#130786462
#130785372
C2×#106223902
#130784802
#130784782
#130781512
#130778642
#130778302
#130775002
#130774952
#130774492
#130774422
#130772732
C11×#30452
#6058811