Finite Group Databasebeta

← #15639558

Subgroups — #15639558

Order 2816.

2224 conjugacy classes of subgroups.

The subgroup lattice has 1256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082277C211yesmaximal, characteristic, complemented
2#13080811C212yesmaximal, complemented
3#13080751C212yesmaximal, complemented
4#13080616C212yesmaximal, complemented
5#13080512C212yesmaximal, complemented
6D4×#4323C212yesmaximal, complemented
7#13080232C212yesmaximal, complemented
8#13080107C212yesmaximal, complemented
9#13080092C212yesmaximal, complemented
10#13079660C212yesmaximal, complemented
11#13079468C212yesmaximal, complemented
12#13079413C211yesmaximal, characteristic, complemented
13#13079364C211yesmaximal, characteristic, complemented
14#13078809C212yesmaximal, complemented
15#13077882C212yesmaximal, complemented
16#13077866C211yesmaximal, characteristic, complemented
17C2×#10622650C211yesmaximal, characteristic, complemented
18#13077664C211yesmaximal, characteristic, complemented
19C11×#3537C211yesmaximal, characteristic, complemented
20C2×#67042C2211yescharacteristic, complemented
21C22×#4339C2211yescharacteristic, complemented
22C11×#560—22no—
23C11×#553C2212yescomplemented
24C11×#553C2212yescomplemented
25D42×C11—22no—
26D42×C11C2212yescomplemented
27D42×C11C2212yescomplemented
28C11×#540C2212yescomplemented
29C11×#538—21no—
30C11×#538—21no—
31C11×#535C2212yescomplemented
32C11×#534—21no—
33C11×#534—21no—
34C11×#525C2211yescharacteristic
35C2×C11×#121C2211yescharacteristic, complemented
36C2×C11×#121C2211yescharacteristic, complemented
37#10623364C2211yescharacteristic, complemented
38C22×#4324C2211yescharacteristic, complemented
39C2×#66985C2211yescharacteristic, complemented
40C2×#66985C2212yescomplemented
41C2×#66985C2211yescharacteristic, complemented
42C22×#4323C2212yescomplemented
43C22×#4323C2211yescharacteristic, complemented
44C2×#66983C2211yescharacteristic, complemented
45#10623185—22no—
46#10623160—21no—
47#10623158—21no—
48#10623138—21no—
49D11×#121—21no—
50#10623121—22no—
51#10623084C2212yescomplemented
52#10623083C2212yescomplemented
53#10623081C2212yescomplemented
54D4×D44C2212yescomplemented
55#10623056C2211yescharacteristic, complemented
56#10623054C2211yescharacteristic, complemented
57#10622847C2212yescomplemented
58#10622831C2212yescomplemented
59#10622830C2212yescomplemented
60#10622830C2212yescomplemented
61#10622830C2212yescomplemented
62#10622820C2211yescharacteristic, complemented
63C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
64#10622688C2212yescomplemented
65#10622687C2212yescomplemented
66#10622686C2212yescomplemented
67#10622685C2212yescomplemented
68#10622681C2212yescomplemented
69#10622680C2212yescomplemented
70#10622679C2212yescomplemented
71#10622676C2212yescomplemented
72#10622655C2212yescomplemented
73#10622654C2212yescomplemented
74#10622653C2212yescomplemented
75#10622652C2212yescomplemented
76#10622652C2212yescomplemented
77#10622652C2212yescomplemented
78#10622651C2212yescomplemented
79#10622651C2212yescomplemented
80#10622651C2212yescomplemented
81#10622650C2212yescomplemented
82#10622650C2212yescomplemented
83#10622650C2212yescomplemented
84#10622650C2212yescomplemented
85#10622650C2212yescomplemented
86#10622650C2212yescomplemented
87#10622650C2212yescomplemented
88#10622650C2212yescomplemented
89#10622649C2212yescomplemented
90#10622649C2212yescomplemented
91#10622649C2212yescomplemented
92#10622649C2212yescomplemented
93#10622649C2212yescomplemented
94#10622647C2212yescomplemented
95#10622646C2212yescomplemented
96#10622631C2212yescomplemented
97C4×#4324C2212yescomplemented
98#10622629C2212yescomplemented
99#10622629C2212yescomplemented
100#10622628C2212yescomplemented
101#10622628C2212yescomplemented
102#10622627C2212yescomplemented
103C4×#4323C2212yescomplemented
104#10622625C2212yescomplemented
105#10622624C2212yescomplemented
106#10622624C2212yescomplemented
107D4×C11⋊C8C2212yescomplemented
108#10622616C2212yescomplemented
109#10622615C2212yescomplemented
110#10622614C2212yescomplemented
111#10622613C2212yescomplemented
112#10622609C2212yescomplemented
113C2×#66874C2211yescharacteristic, complemented
114#10622581C2212yescomplemented
115#10622580C2212yescomplemented
116#10622579C2211yescharacteristic, complemented
117#10622579C2211yescharacteristic, complemented
118C2×#66873C2211yescharacteristic, complemented
119C2×C11×#41C2311yescharacteristic
120C22×D4×C11—21no—
121C22×D4×C11—21no—
122C22×D4×C11—22no—
123C22×D4×C11—22no—
124C22×D4×C11C2312yes—
125C22×D4×C11C2311yescharacteristic
126C22×D4×C11C2311yescharacteristic
127C23×C4×C11C2311yescharacteristic
128C22×C22⋊D11—21no—
129C22×C22⋊D11—21no—
130#67042—42no—
131#67042—42no—
132C2×#4343—21no—
133C2×D4×D11—22no—
134C2×D4×D11—21no—
135C2×D4×D11—22no—
136C2×#4339—21no—
137C2×#4339—21no—
138C2×#4339—42no—
139C2×#4339—42no—
140C2×#4339C2311yescharacteristic
141C2×#4339C2311yescharacteristic
142C2×#4339C2312yes—
143C2×#4339C2311yescharacteristic
144C2×#4339C2311yescharacteristic
145C22×D44C2311yescharacteristic
146C22×D44C2312yes—
147C22×D44C2311yescharacteristic
148C22×C4×D11—21no—
149C22×Dic22C2311yescharacteristic
150C11×#127—22no—
151C11×#127C2312yes—
152C11×#126—22no—
153C11×#126—22no—
154C11×#125C2312yes—
155C11×#124—22no—
156C11×#123—22no—
157C11×#123—22no—
158C11×#123—22no—
159C11×#123—22no—
160C11×#123D412yes—
161C11×C22⋊Q8D411yescharacteristic
162C11×C22⋊Q8D411yescharacteristic
163C11×#121—22no—
164C11×#121—22no—
165C11×#121—21no—
166C11×#121—21no—
167C11×#121—21no—
168C11×#121—21no—
169C11×#121—22no—
170C11×#121—22no—
171C11×#121—22no—
172C11×#121—22no—
173C11×#121D411yescharacteristic
174C11×#121D411yescharacteristic
175C11×#121C2312yes—
176C11×#121C2312yes—
177C11×#121C2312yes—
178C11×#121C2312yes—
179C11×#121C2312yes—
180C11×#121C2312yes—
181C11×#120—22no—
182C11×#120—22no—
183C11×#120—22no—
184C11×#120—22no—
185C11×#120—22no—
186C11×#120—22no—
187C11×#120D412yes—
188C4×D4×C11—22no—
189C4×D4×C11—22no—
190C4×D4×C11C2312yes—
191C4×D4×C11C2312yes—
192C4×D4×C11C2312yes—
193C4×D4×C11C2312yes—
194C11×#117C2312yes—
195C11×#117C2311yescharacteristic
196C2×C11×C4⋊C4C2311yescharacteristic
197C2×C11×C4⋊C4C2311yescharacteristic
198C2×C11×C22⋊C4—21no—
199C2×C11×C22⋊C4—21no—
200#66999—21no—
201#66993—22no—
202#66992—22no—
203#66992—22no—
204#66991—21no—
205#66990—22no—
206C2×#4324—42no—
207C2×#4324C2312yes—
208C2×#4324C2312yes—
209C2×#4324C2312yes—
210C2×#4324C2312yes—
211#66985—42no—
212#66985—42no—
213#66985—44no—
214C2×#4323—42no—
215C2×#4323—44no—
216C2×#4323C2312yes—
217C2×#4323C2312yes—
218C2×#4323C2312yes—
219C2×#4323C2312yes—
220C2×#4323C2312yes—
221C2×#4323C2312yes—
222C2×#4323C2312yes—
223C2×#4323C2312yes—
224#66983—21no—
225#66983—21no—
226#66983C2312yes—
227#66983C2312yes—
228#66983C2312yes—
229C2×(C2×D11)⋊C4—21no—
230C2×C4⋊Dic11C2311yescharacteristic
231#66977C2312yes—
232C2×#4318C2311yescharacteristic
233C2×#4318C2311yescharacteristic
234C2×#4318C2312yes—
235C22×C11⋊C8C2311yescharacteristic
236C22×C11⋊C8C2312yes—
237C22×C11⋊C8C2311yescharacteristic
238#66949—22no—
239#66948—21no—
240#66948—21no—
241#66948—22no—
242#66947—22no—
243#66946—22no—
244#66945—21no—
245C4⋊C4×D11—21no—
246#66938—22no—
247#66937—22no—
248#66937—22no—
249#66937—22no—
250#66935—22no—
251#66935—22no—
252#66935—22no—
253(C22⋊D11)⋊C4—22no—
254(C22⋊D11)⋊C4—22no—
255C22⋊C4×D11—22no—
256#66928C2312yes—
257#66927C2312yes—
258C4×D44C2312yes—
259C4×Dic22C2312yes—
260#66896C2312yes—
261#66896C2312yes—
262#66896C2312yes—
263#66896C2312yes—
264C22⋊(C11⋊C8)C2312yes—
265C22⋊(C11⋊C8)C2312yes—
266C22⋊(C11⋊C8)C2312yes—
267C22⋊(C11⋊C8)C2312yes—
268C22⋊(C11⋊C8)C2312yes—
269C22⋊(C11⋊C8)C2312yes—
270#66874C2312yes—
271#66874C2312yes—
272#66874C2312yes—
273#66874C2312yes—
274#66873C2312yes—
275#66873C2312yes—
276#66873C2312yes—
277#66873C2312yes—
278#66873C2312yes—
279#66873C2312yes—
280#66873C2312yes—
281#66873C2312yes—
282#66872C2312yes—
283#66872C2312yes—
284#66871C2312yes—
285#66871C2312yes—
286C4⋊(C11⋊C8)C2312yes—
287C4⋊(C11⋊C8)C2312yes—
288#66867C2312yes—
289C4×C11⋊C8C2312yes—
290#61617—111nomaximal, Sylow
291C24×C11—21no—
292C24×C11—21no—
293C24×C11—22no—
294C24×C11C2×D411yescharacteristic
295C23×D11—21no—
296C23×D11—22no—
297C23×D11—21no—
298C11×#41—41no—
299C11×#41—41no—
300C2×Q8×C11C2×D411yescharacteristic
301C2×D4×C11—22no—
302C2×D4×C11—22no—
303C2×D4×C11—22no—
304C2×D4×C11—22no—
305C2×D4×C11—22no—
306C2×D4×C11—22no—
307C2×D4×C11—21no—
308C2×D4×C11—21no—
309C2×D4×C11—22no—
310C2×D4×C11—22no—
311C2×D4×C11—22no—
312C2×D4×C11—41no—
313C2×D4×C11—42no—
314C2×D4×C11—42no—
315C2×D4×C11—41no—
316C2×D4×C11—41no—
317C2×D4×C11—41no—
318C2×D4×C11—84no—
319C2×D4×C11—82no—
320C2×D4×C11—84no—
321C2×D4×C11—82no—
322C2×D4×C11C2×D412yes—
323C2×D4×C11C2×D412yes—
324C2×D4×C11C2×D411yescharacteristic
325C2×D4×C11C2×D412yes—
326C2×D4×C11C2412yes—
327C2×D4×C11C2412yes—
328C22×C4×C11—21no—
329C22×C4×C11—21no—
330C22×C4×C11—22no—
331C22×C4×C11—22no—
332C22×C4×C11—41no—
333C22×C4×C11—41no—
334C22×C4×C11C2×D411yescharacteristic
335C22×C4×C11C2×D411yescharacteristic
336C22×C4×C11C2×D411yescharacteristic
337C22×C4×C11C2411yescharacteristic
338C22×C4×C11C2411yescharacteristic
339C22×C4×C11C2412yes—
340C22×C4×C11C2411yescharacteristic
341C2×C22⋊D11—21no—
342C2×C22⋊D11—22no—
343C2×C22⋊D11—21no—
344C2×C22⋊D11—21no—
345C2×C22⋊D11—21no—
346C2×C22⋊D11—22no—
347C2×C22⋊D11—22no—
348C2×C22⋊D11—22no—
349C2×C22⋊D11—44no—
350C2×C22⋊D11—82no—
351C22×Dic11—21no—
352C22×Dic11—21no—
353#4343—44no—
354D4×D11—44no—
355D4×D11—48no—
356D4×D11—84no—
357#4339—22no—
358#4339—22no—
359#4339—22no—
360#4339—22no—
361#4339—24no—
362#4339—41no—
363#4339—41no—
364#4339—41no—
365#4339—41no—
366#4339—42no—
367#4339—44no—
368#4339—44no—
369C2×D44—22no—
370C2×D44—24no—
371C2×D44—21no—
372C2×D44—22no—
373C2×D44—21no—
374C2×D44—22no—
375C2×D44—22no—
376C2×D44—41no—
377C2×D44—42no—
378C2×D44—41no—
379C2×D44—41no—
380C2×D44C2411yescharacteristic
381C2×D44C2412yes—
382C2×D44C2411yescharacteristic
383C2×C4×D11—21no—
384C2×C4×D11—21no—
385C2×C4×D11—22no—
386C2×C4×D11—21no—
387C2×C4×D11—21no—
388C2×C4×D11—22no—
389C2×C4×D11—44no—
390C2×Dic22—22no—
391C2×Dic22—21no—
392C2×Dic22—41no—
393C2×Dic22C2411yescharacteristic
394C2×Dic22C2411yescharacteristic
395C11×C4⋊C4—21no—
396C11×C4⋊C4—21no—
397C11×C4⋊C4—22no—
398C11×C4⋊C4—22no—
399C11×C4⋊C4C2×D411yescharacteristic
400C11×C4⋊C4C2×D411yescharacteristic
401C11×C4⋊C4C2×D412yes—
402C11×C4⋊C4C2×D412yes—
403C11×C4⋊C4C2412yes—
404C11×C4⋊C4C2412yes—
405C11×C22⋊C4—22no—
406C11×C22⋊C4—22no—
407C11×C22⋊C4—22no—
408C11×C22⋊C4—22no—
409C11×C22⋊C4—22no—
410C11×C22⋊C4—22no—
411C11×C22⋊C4—22no—
412C11×C22⋊C4—22no—
413C11×C22⋊C4—22no—
414C11×C22⋊C4C2×D412yes—
415C11×C22⋊C4C2×D412yes—
416C11×C22⋊C4C2×D412yes—
417C11×C22⋊C4C2×D412yes—
418C11×C22⋊C4C2×D412yes—
419C42×C11—22no—
420C42×C11C2412yes—
421C22⋊Dic11—22no—
422#4324—24no—
423#4324—24no—
424#4324—42no—
425#4324—42no—
426#4323—24no—
427#4323—24no—
428#4323—42no—
429#4323—42no—
430#4323—42no—
431#4323—42no—
432#4323—42no—
433#4323—42no—
434(C2×D11)⋊C4—22no—
435(C2×D11)⋊C4—22no—
436(C2×D11)⋊C4—22no—
437(C2×D11)⋊C4—22no—
438(C2×D11)⋊C4—22no—
439(C2×D11)⋊C4—22no—
440C4⋊Dic11—21no—
441C4⋊Dic11C2412yes—
442Dic11⋊C4—22no—
443Dic11⋊C4—22no—
444C4×Dic11—22no—
445#4318—42no—
446#4318—41no—
447#4318—41no—
448C2×C11⋊C8—41no—
449C2×C11⋊C8—42no—
450C2×C11⋊C8—41no—
451C2×C11⋊C8C2412yes—
452C2×C11⋊C8C2412yes—
453C2×C11⋊C8C2412yes—
454C2×C11⋊C8C2412yes—
455#3537D1111yescharacteristic, complemented
456#3488—111no—
457#3322—112no—
458#3318—112no—
459#3309—112no—
460#3301—112no—
461D4×D8—112no—
462#3274—112no—
463#3265—112no—
464#3264—112no—
465#3220—112no—
466#3198—112no—
467#3192—111no—
468#3186—111no—
469#3119—112no—
470#3008—112no—
471#3006—111no—
472C2×#449—111no—
473#2976—111no—
474C23×C11—22no—
475C23×C11—22no—
476C23×C11—22no—
477C23×C11—41no—
478C23×C11—41no—
479C23×C11—42no—
480C23×C11—42no—
481C23×C11—81no—
482C23×C11—81no—
483C23×C11—82no—
484C23×C11—81no—
485C23×C11—82no—
486C23×C11—81no—
487C23×C11—82no—
488C23×C11C22×D412yes—
489C23×C11C22×D411yescharacteristic
490C23×C11C22×D411yescharacteristic
491C23×C11C22×D411yescharacteristic
492C22×D11—21no—
493C22×D11—22no—
494C22×D11—21no—
495C22×D11—42no—
496C22×D11—44no—
497C22×D11—42no—
498C22×D11—42no—
499C22×D11—81no—
500C22×D11—82no—
501C22×D11—81no—
502C22×D11—82no—
503C22×D11—81no—
504Q8×C11—41no—
505D4×C11—24no—
506D4×C11—22no—
507D4×C11—22no—
508D4×C11—22no—
509D4×C11—22no—
510D4×C11—41no—
511D4×C11—42no—
512D4×C11—42no—
513D4×C11—44no—
514D4×C11—44no—
515D4×C11—81no—
516D4×C11—81no—
517D4×C11—82no—
518D4×C11—82no—
519D4×C11—82no—
520D4×C11—82no—
521D4×C11—82no—
522D4×C11—82no—
523D4×C11—82no—
524C2×C4×C11—21no—
525C2×C4×C11—21no—
526C2×C4×C11—22no—
527C2×C4×C11—22no—
528C2×C4×C11—21no—
529C2×C4×C11—21no—
530C2×C4×C11—21no—
531C2×C4×C11—21no—
532C2×C4×C11—22no—
533C2×C4×C11—22no—
534C2×C4×C11—41no—
535C2×C4×C11—41no—
536C2×C4×C11—41no—
537C2×C4×C11—82no—
538C2×C4×C11—82no—
539C2×C4×C11—81no—
540C2×C4×C11—81no—
541C2×C4×C11C22×D412yes—
542C2×C4×C11C22×D412yes—
543C2×C4×C11C22×D412yes—
544C2×C4×C11C22×D411yescharacteristic
545C2×C4×C11C22×D411yescharacteristic
546C2×C4×C11C22×D411yescharacteristic
547C2×C4×C11C2511yescharacteristic
548C22⋊D11—24no—
549C22⋊D11—42no—
550C22⋊D11—44no—
551C22⋊D11—42no—
552C22⋊D11—42no—
553C22⋊D11—44no—
554C22⋊D11—82no—
555C22⋊D11—82no—
556C2×Dic11—21no—
557C2×Dic11—22no—
558C2×Dic11—21no—
559C2×Dic11—42no—
560C2×Dic11—81no—
561D44—21no—
562D44—22no—
563D44—21no—
564D44—22no—
565D44—21no—
566D44—42no—
567D44—44no—
568D44—42no—
569D44—82no—
570D44—82no—
571D44H(5,𝔽2)12yes—
572C4×D11—24no—
573C4×D11—42no—
574C4×D11—44no—
575C4×D11—42no—
576C4×D11—42no—
577C4×D11—82no—
578Dic22—21no—
579Dic22—21no—
580Dic22—21no—
581Dic22—42no—
582Dic22H(5,𝔽2)12yes—
583C11⋊C8—22no—
584C11⋊C8—22no—
585C11⋊C8—22no—
586C11⋊C8—22no—
587C2×H(5,𝔽2)—111no—
588C22×#41—111no—
589C2×AGL(1,ℤ/8)—111no—
590C2×AGL(1,ℤ/8)—111no—
591C2×AGL(1,ℤ/8)—112no—
592C22×SD16—111no—
593C22×D8—111no—
594C22×D8—112no—
595#560—22no—
596#553C2×D1112yescomplemented
597#553C2×D1112yescomplemented
598#550—112no—
599#548—112no—
600#546—112no—
601#546—222no—
602D42—22no—
603D42—112no—
604D42—222no—
605D42C2×D1112yescomplemented
606D42C2×D1112yescomplemented
607#540C2×D1112yescomplemented
608#538—21no—
609#538—21no—
610#537—111no—
611#537—221no—
612#535—111no—
613#535—221no—
614#535C2×D1112yescomplemented
615#534—21no—
616#534—21no—
617#525—221no—
618#525C2×D1111yescharacteristic
619C2×#121—111no—
620C2×#121—221no—
621C2×#121C2×D1111yescharacteristic, complemented
622C2×#121C2×D1111yescharacteristic, complemented
623#520—111no—
624#496—112no—
625#493—112no—
626#490—112no—
627#488—112no—
628#485—112no—
629#482—112no—
630#481—112no—
631#481—112no—
632#480—112no—
633#480—112no—
634#479—112no—
635#478—112no—
636#469—112no—
637#469—112no—
638#469—112no—
639#468—112no—
640#466—112no—
641#466—112no—
642#466—112no—
643#465—112no—
644#463—112no—
645#463—112no—
646#460—112no—
647#459—112no—
648#459—112no—
649#459—112no—
650#450—112no—
651#449—112no—
652#449—112no—
653#449—112no—
654#449—112no—
655#449—112no—
656#449—112no—
657#449—112no—
658#449—112no—
659#448—112no—
660#447—112no—
661#447—112no—
662#447—112no—
663#447—112no—
664#447—112no—
665#447—112no—
666#447—112no—
667#447—112no—
668#442—112no—
669#440—112no—
670C4×SD16—112no—
671C4×D8—112no—
672#436—112no—
673#435—112no—
674#435—112no—
675C8×D4—112no—
676#433—112no—
677#418—112no—
678#417—111no—
679#417—111no—
680#416—112no—
681C2×#103—111no—
682C2×#102—111no—
683#408—112no—
684#407—111no—
685C2×C22⋊C8—111no—
686C22×C11—21no—
687C22×C11—21no—
688C22×C11—21no—
689C22×C11—22no—
690C22×C11—21no—
691C22×C11—21no—
692C22×C11—21no—
693C22×C11—22no—
694C22×C11—21no—
695C22×C11—22no—
696C22×C11—21no—
697C22×C11—42no—
698C22×C11—42no—
699C22×C11—42no—
700C22×C11—42no—
701C22×C11—42no—
702C22×C11—42no—
703C22×C11—82no—
704C22×C11—162no—
705C22×C11—162no—
706C22×C11—164no—
707C22×C11#57612yes—
708C22×C11C23×D411yescharacteristic
709C2×D11—22no—
710C2×D11—41no—
711C2×D11—41no—
712C2×D11—42no—
713C2×D11—41no—
714C2×D11—42no—
715C2×D11—41no—
716C2×D11—41no—
717C2×D11—42no—
718C2×D11—84no—
719C2×D11—164no—
720C2×D11—162no—
721C4×C11—22no—
722C4×C11—21no—
723C4×C11—21no—
724C4×C11—21no—
725C4×C11—22no—
726C4×C11—22no—
727C4×C11—42no—
728C4×C11—42no—
729C4×C11C2×H(5,𝔽2)11yescharacteristic
730C4×C11C2×H(5,𝔽2)11yescharacteristic
731Dic11—22no—
732Dic11—41no—
733Dic11—42no—
734H(5,𝔽2)—442no—
735H(5,𝔽2)—442no—
736C2×#41—111no—
737C2×#41—111no—
738C2×#41—112no—
739C2×#41—111no—
740C2×#41—111no—
741C2×#41—221no—
742C2×#41—221no—
743C2×#41—221no—
744C2×#41—442no—
745C2×#41—442no—
746C2×#41C22×D1111yescharacteristic
747C22×Q8—111no—
748C22×D4—21no—
749C22×D4—21no—
750C22×D4—22no—
751C22×D4—22no—
752C22×D4—111no—
753C22×D4—112no—
754C22×D4—111no—
755C22×D4—221no—
756C22×D4—221no—
757C22×D4—221no—
758C22×D4—222no—
759C22×D4—222no—
760C22×D4C22×D1111yescharacteristic
761C22×D4C22×D1111yescharacteristic
762C22×D4C22×D1112yes—
763C23×C4—221no—
764C23×C4C22×D1111yescharacteristic
765AGL(1,ℤ/8)—442no—
766AGL(1,ℤ/8)—444no—
767AGL(1,ℤ/8)—442no—
768C2×SD16—112no—
769C2×SD16—112no—
770C2×SD16—112no—
771C2×SD16—112no—
772C2×SD16—442no—
773C2×D8—112no—
774C2×D8—112no—
775C2×D8—112no—
776C2×D8—112no—
777C2×D8—112no—
778C2×D8—112no—
779C2×D8—112no—
780C2×D8—112no—
781C2×D8—442no—
782C2×D8—444no—
783C2×M16—111no—
784C2×M16—111no—
785C2×M16—112no—
786C22×C8—111no—
787C22×C8—112no—
788C22×C8—111no—
789#127—22no—
790#127—112no—
791#127—222no—
792#127C22×D1112yes—
793#126—22no—
794#126—22no—
795#125C22×D1112yes—
796#124—22no—
797#124—112no—
798#124—222no—
799#123—22no—
800#123—22no—
801#123—22no—
802#123—22no—
803#123—222no—
804#123C22⋊D1112yes—
805C22⋊Q8—112no—
806C22⋊Q8—221no—
807C22⋊Q8—222no—
808C22⋊Q8C22⋊D1111yescharacteristic
809C22⋊Q8C22⋊D1111yescharacteristic
810#121—22no—
811#121—22no—
812#121—21no—
813#121—21no—
814#121—21no—
815#121—21no—
816#121—22no—
817#121—22no—
818#121—22no—
819#121—22no—
820#121—112no—
821#121—112no—
822#121—112no—
823#121—221no—
824#121—222no—
825#121—222no—
826#121—221no—
827#121—221no—
828#121—221no—
829#121—221no—
830#121—222no—
831#121—222no—
832#121—222no—
833#121—222no—
834#121C22⋊D1111yescharacteristic
835#121C22⋊D1111yescharacteristic
836#121C22×D1112yes—
837#121C22×D1112yes—
838#121C22×D1112yes—
839#121C22×D1112yes—
840#121C22×D1112yes—
841#121C22×D1112yes—
842#120—22no—
843#120—22no—
844#120—22no—
845#120—22no—
846#120—22no—
847#120—22no—
848#120—222no—
849#120—222no—
850#120—222no—
851#120—222no—
852#120C22⋊D1112yes—
853C4×Q8—112no—
854C4×D4—22no—
855C4×D4—22no—
856C4×D4—112no—
857C4×D4—222no—
858C4×D4—222no—
859C4×D4—222no—
860C4×D4C22×D1112yes—
861C4×D4C22×D1112yes—
862C4×D4C22×D1112yes—
863C4×D4C22×D1112yes—
864#117—221no—
865#117C22×D1112yes—
866#117C22×D1111yescharacteristic
867C2×C4⋊C4—111no—
868C2×C4⋊C4—221no—
869C2×C4⋊C4C22×D1111yescharacteristic
870C2×C4⋊C4C22×D1111yescharacteristic
871C2×C22⋊C4—21no—
872C2×C22⋊C4—21no—
873C2×C22⋊C4—221no—
874C2×C22⋊C4—222no—
875#107—112no—
876#107—112no—
877#106—112no—
878#106—112no—
879C4⋊C8—112no—
880C4⋊C8—112no—
881#103—112no—
882#103—112no—
883#103—112no—
884#103—112no—
885#102—112no—
886#102—112no—
887#102—112no—
888#102—112no—
889#102—112no—
890#102—112no—
891#102—112no—
892#102—112no—
893#102—112no—
894#102—112no—
895#102—112no—
896#102—112no—
897C22⋊C8—112no—
898C22⋊C8—112no—
899C22⋊C8—112no—
900C22⋊C8—112no—
901C22⋊C8—112no—
902C22⋊C8—112no—
903#97—112no—
904C4×C8—112no—
905C2×C11—22no—
906C2×C11—41no—
907C2×C11—42no—
908C2×C11—41no—
909C2×C11—82no—
910C2×C11—82no—
911C2×C11#348411yescharacteristic
912C2×C11C2×#57611yescharacteristic
913C2×C11#358511yescharacteristic
914D11—42no—
915D11—81no—
916D11—82no—
917C24—21no—
918C24—21no—
919C24—22no—
920C24—221no—
921C24—222no—
922C24—221no—
923C24C2×C22⋊D1111yescharacteristic
924#41—41no—
925#41—41no—
926#41—222no—
927#41—222no—
928#41—222no—
929#41—222no—
930#41—224no—
931#41—441no—
932#41—441no—
933#41—441no—
934#41—441no—
935#41—442no—
936#41—444no—
937#41—444no—
938#41—444no—
939C2×Q8—111no—
940C2×Q8—111no—
941C2×Q8—222no—
942C2×Q8—221no—
943C2×Q8—441no—
944C2×Q8C2×C22⋊D1111yescharacteristic
945C2×D4—22no—
946C2×D4—22no—
947C2×D4—22no—
948C2×D4—22no—
949C2×D4—22no—
950C2×D4—22no—
951C2×D4—21no—
952C2×D4—21no—
953C2×D4—22no—
954C2×D4—22no—
955C2×D4—22no—
956C2×D4—41no—
957C2×D4—42no—
958C2×D4—41no—
959C2×D4—41no—
960C2×D4—41no—
961C2×D4—42no—
962C2×D4—84no—
963C2×D4—82no—
964C2×D4—84no—
965C2×D4—82no—
966C2×D4—111no—
967C2×D4—112no—
968C2×D4—111no—
969C2×D4—222no—
970C2×D4—224no—
971C2×D4—221no—
972C2×D4—222no—
973C2×D4—221no—
974C2×D4—221no—
975C2×D4—222no—
976C2×D4—221no—
977C2×D4—222no—
978C2×D4—222no—
979C2×D4—221no—
980C2×D4—222no—
981C2×D4—221no—
982C2×D4—222no—
983C2×D4—222no—
984C2×D4—441no—
985C2×D4—442no—
986C2×D4—441no—
987C2×D4—441no—
988C2×D4—444no—
989C2×D4—448no—
990C2×D4—444no—
991C2×D4—884no—
992C2×D4—882no—
993C2×D4C2×C22⋊D1112yes—
994C2×D4C2×C22⋊D1112yes—
995C2×D4C2×C22⋊D1111yescharacteristic
996C2×D4C2×C22⋊D1112yes—
997C2×D4C23×D1112yes—
998C2×D4C23×D1112yes—
999C22×C4—21no—
1000C22×C4—21no—
1001C22×C4—22no—
1002C22×C4—22no—
1003C22×C4—41no—
1004C22×C4—41no—
1005C22×C4—221no—
1006C22×C4—221no—
1007C22×C4—221no—
1008C22×C4—221no—
1009C22×C4—221no—
1010C22×C4—222no—
1011C22×C4—221no—
1012C22×C4—222no—
1013C22×C4—444no—
1014C22×C4C2×C22⋊D1111yescharacteristic
1015C22×C4C2×C22⋊D1111yescharacteristic
1016C22×C4C2×C22⋊D1111yescharacteristic
1017C22×C4C23×D1111yescharacteristic
1018C22×C4C23×D1111yescharacteristic
1019C22×C4C23×D1111yescharacteristic
1020C22×C4C23×D1112yes—
1021SD16—224no—
1022SD16—224no—
1023SD16—442no—
1024SD16—442no—
1025D8—224no—
1026D8—224no—
1027D8—442no—
1028D8—442no—
1029D8—442no—
1030D8—442no—
1031D8—442no—
1032D8—442no—
1033M16—441no—
1034M16—442no—
1035M16—441no—
1036C2×C8—112no—
1037C2×C8—112no—
1038C2×C8—112no—
1039C2×C8—112no—
1040C2×C8—441no—
1041C2×C8—442no—
1042C2×C8—441no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—22no—
1046C4⋊C4—22no—
1047C4⋊C4—112no—
1048C4⋊C4—221no—
1049C4⋊C4—222no—
1050C4⋊C4—222no—
1051C4⋊C4C2×C22⋊D1111yescharacteristic
1052C4⋊C4C2×C22⋊D1111yescharacteristic
1053C4⋊C4C2×C22⋊D1112yes—
1054C4⋊C4C2×C22⋊D1112yes—
1055C4⋊C4C23×D1112yes—
1056C4⋊C4C23×D1112yes—
1057C22⋊C4—22no—
1058C22⋊C4—22no—
1059C22⋊C4—22no—
1060C22⋊C4—22no—
1061C22⋊C4—22no—
1062C22⋊C4—22no—
1063C22⋊C4—22no—
1064C22⋊C4—22no—
1065C22⋊C4—22no—
1066C22⋊C4—222no—
1067C22⋊C4—222no—
1068C22⋊C4—222no—
1069C22⋊C4—222no—
1070C22⋊C4—222no—
1071C22⋊C4—222no—
1072C22⋊C4—222no—
1073C22⋊C4C2×C22⋊D1112yes—
1074C22⋊C4C2×C22⋊D1112yes—
1075C22⋊C4C2×C22⋊D1112yes—
1076C22⋊C4C2×C22⋊D1112yes—
1077C22⋊C4C2×C22⋊D1112yes—
1078C42—22no—
1079C42—222no—
1080C42C23×D1112yes—
1081C11#6161711yescharacteristic, complemented, Sylow
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—41no—
1086C23—41no—
1087C23—42no—
1088C23—42no—
1089C23—81no—
1090C23—81no—
1091C23—82no—
1092C23—81no—
1093C23—82no—
1094C23—81no—
1095C23—82no—
1096C23—221no—
1097C23—222no—
1098C23—221no—
1099C23—442no—
1100C23—444no—
1101C23—442no—
1102C23—442no—
1103C23—881no—
1104C23—881no—
1105C23—882no—
1106C23—882no—
1107C23—881no—
1108C23C22×C22⋊D1112yes—
1109C23C22×C22⋊D1111yescharacteristic
1110C23C22×C22⋊D1111yescharacteristic
1111C23C22×C22⋊D1111yescharacteristic
1112Q8—41no—
1113Q8—112no—
1114Q8—221no—
1115Q8—221no—
1116Q8—221no—
1117Q8—442no—
1118D4—24no—
1119D4—22no—
1120D4—22no—
1121D4—22no—
1122D4—22no—
1123D4—42no—
1124D4—41no—
1125D4—42no—
1126D4—44no—
1127D4—44no—
1128D4—81no—
1129D4—81no—
1130D4—82no—
1131D4—82no—
1132D4—82no—
1133D4—82no—
1134D4—82no—
1135D4—82no—
1136D4—82no—
1137D4—112no—
1138D4—224no—
1139D4—221no—
1140D4—222no—
1141D4—221no—
1142D4—222no—
1143D4—221no—
1144D4—444no—
1145D4—442no—
1146D4—442no—
1147D4—444no—
1148D4—442no—
1149D4—442no—
1150D4—442no—
1151D4—444no—
1152D4—882no—
1153D4—882no—
1154D4—882no—
1155D4—882no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—22no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—22no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—82no—
1170C2×C4—82no—
1171C2×C4—81no—
1172C2×C4—81no—
1173C2×C4—224no—
1174C2×C4—221no—
1175C2×C4—222no—
1176C2×C4—221no—
1177C2×C4—442no—
1178C2×C4—444no—
1179C2×C4—442no—
1180C2×C4—442no—
1181C2×C4—442no—
1182C2×C4—882no—
1183C2×C4—881no—
1184C2×C4C22×C22⋊D1112yes—
1185C2×C4C22×C22⋊D1112yes—
1186C2×C4C22×C22⋊D1112yes—
1187C2×C4C22×C22⋊D1111yescharacteristic
1188C2×C4C22×C22⋊D1111yescharacteristic
1189C2×C4C22×C22⋊D1111yescharacteristic
1190C2×C4C24×D1111yescharacteristic
1191C8—222no—
1192C8—222no—
1193C8—222no—
1194C8—222no—
1195C22—21no—
1196C22—21no—
1197C22—21no—
1198C22—22no—
1199C22—21no—
1200C22—21no—
1201C22—21no—
1202C22—22no—
1203C22—21no—
1204C22—21no—
1205C22—22no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—82no—
1213C22—162no—
1214C22—162no—
1215C22—164no—
1216C22—222no—
1217C22—441no—
1218C22—441no—
1219C22—441no—
1220C22—442no—
1221C22—441no—
1222C22—442no—
1223C22—442no—
1224C22—441no—
1225C22—884no—
1226C22—1764no—
1227C22—1762no—
1228C22#1062336612yes—
1229C22C23×C22⋊D1111yescharacteristic
1230C4—22no—
1231C4—21no—
1232C4—21no—
1233C4—21no—
1234C4—22no—
1235C4—22no—
1236C4—42no—
1237C4—42no—
1238C4—222no—
1239C4—441no—
1240C4—442no—
1241C4D11×H(5,𝔽2)11yescharacteristic
1242C4D11×H(5,𝔽2)11yescharacteristic
1243C2—22no—
1244C2—41no—
1245C2—41no—
1246C2—42no—
1247C2—82no—
1248C2—82no—
1249C2—442no—
1250C2—881no—
1251C2—882no—
1252C2#1308224711yescharacteristic
1253C2C2×#1062336611yescharacteristic
1254C2#1308339611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3537C2
socleC22×C11C23×D4
hypercenter#3537D11
hypocenterC11#61617
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #525 ◁ #3537

Complements

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

NH ≅ G/Ntype
1. #13082277C2semidirect
2. #13080811C2semidirect
3. #13080751C2semidirect
4. #13080616C2semidirect
5. #13080512C2semidirect
6. D4×#4323C2semidirect
7. #13080232C2semidirect
8. #13080107C2semidirect
9. #13080092C2semidirect
10. #13079660C2semidirect
11. #13079468C2semidirect
12. #13079413C2semidirect
13. #13079364C2semidirect
14. #13078809C2semidirect
15. #13077882C2semidirect
16. #13077866C2semidirect
17. C2×#10622650C2semidirect
18. #13077664C2semidirect
19. C11×#3537C2semidirect
20. C2×#67042C22semidirect
21. C22×#4339C22semidirect
23. C11×#553C22semidirect
24. C11×#553C22semidirect
26. D42×C11C22semidirect
27. D42×C11C22semidirect
28. C11×#540C22semidirect
31. C11×#535C22semidirect
35. C2×C11×#121C22semidirect
36. C2×C11×#121C22semidirect
37. #10623364C22semidirect
38. C22×#4324C22semidirect
39. C2×#66985C22semidirect
40. C2×#66985C22semidirect
41. C2×#66985C22semidirect
42. C22×#4323C22semidirect
43. C22×#4323C22semidirect
44. C2×#66983C22semidirect
51. #10623084C22semidirect
52. #10623083C22semidirect
53. #10623081C22semidirect
54. D4×D44C22semidirect
55. #10623056C22semidirect
56. #10623054C22semidirect
57. #10622847C22semidirect
58. #10622831C22semidirect
59. #10622830C22semidirect
60. #10622830C22semidirect
61. #10622830C22semidirect
62. #10622820C22semidirect
63. C2×C22⋊(C11⋊C8)C22semidirect
64. #10622688C22semidirect
65. #10622687C22semidirect
66. #10622686C22semidirect
67. #10622685C22semidirect
68. #10622681C22semidirect
69. #10622680C22semidirect
70. #10622679C22semidirect
71. #10622676C22semidirect
72. #10622655C22semidirect
73. #10622654C22semidirect
74. #10622653C22semidirect
75. #10622652C22semidirect
76. #10622652C22semidirect
77. #10622652C22semidirect
78. #10622651C22semidirect
79. #10622651C22semidirect
80. #10622651C22semidirect
81. #10622650C22semidirect
82. #10622650C22semidirect
83. #10622650C22semidirect
84. #10622650C22semidirect
85. #10622650C22semidirect
86. #10622650C22semidirect
87. #10622650C22semidirect
88. #10622650C22semidirect
89. #10622649C22semidirect
90. #10622649C22semidirect
91. #10622649C22semidirect
92. #10622649C22semidirect
93. #10622649C22semidirect
94. #10622647C22semidirect
95. #10622646C22semidirect
96. #10622631C22semidirect
97. C4×#4324C22semidirect
98. #10622629C22semidirect
99. #10622629C22semidirect
100. #10622628C22semidirect
101. #10622628C22semidirect
102. #10622627C22semidirect
103. C4×#4323C22semidirect
104. #10622625C22semidirect
105. #10622624C22semidirect
106. #10622624C22semidirect
107. D4×C11⋊C8C22semidirect
108. #10622616C22semidirect
109. #10622615C22semidirect
110. #10622614C22semidirect
111. #10622613C22semidirect
112. #10622609C22semidirect
113. C2×#66874C22semidirect
114. #10622581C22semidirect
115. #10622580C22semidirect
116. #10622579C22semidirect
117. #10622579C22semidirect
118. C2×#66873C22semidirect
455. #3537D11semidirect
596. #553C2×D11semidirect
597. #553C2×D11semidirect
605. D42C2×D11semidirect
606. D42C2×D11semidirect
607. #540C2×D11semidirect
614. #535C2×D11semidirect
621. C2×#121C2×D11semidirect
622. C2×#121C2×D11semidirect
1081. C11#61617semidirect

Maximal subgroups

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

subgroupindex
#130822772
#130808112
#130807512
#130806162
#130805122
D4×#43232
#130802322
#130801072
#130800922
#130796602
#130794682
#130794132
#130793642
#130788092
#130778822
#130778662
C2×#106226502
#130776642
C11×#35372
#6161711