Finite Group Databasebeta

← #15639562

Subgroups — #15639562

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#13082851C211yesmaximal, characteristic, complemented
2#13082285C211yesmaximal, characteristic, complemented
3#13080810C212yesmaximal, complemented
4#13080753C212yesmaximal, complemented
5#13080615C212yesmaximal, complemented
6#13080514C212yesmaximal, complemented
7D8×C22⋊D11C212yesmaximal, complemented
8#13080229C212yesmaximal, complemented
9#13080111C212yesmaximal, complemented
10#13080099C212yesmaximal, complemented
11#13079664C212yesmaximal, complemented
12#13079465C212yesmaximal, complemented
13#13079413C211yesmaximal, characteristic, complemented
14#13079367C211yesmaximal, characteristic, complemented
15#13078808C212yesmaximal, complemented
16#13077881C212yesmaximal, complemented
17#13077868C211yesmaximal, characteristic, complemented
18#13077661C211yesmaximal, characteristic, complemented
19C2×C11×#449C211yesmaximal, characteristic, complemented
20C22×C11×#41C2211yescharacteristic, complemented
21C2×#67042C2211yescharacteristic, complemented
22C22×C11×SD16C2211yescharacteristic, complemented
23C22×C11×D8C2211yescharacteristic, complemented
24C2×C11×#121C2211yescharacteristic, complemented
25#10623365C2212yescomplemented
26#10623364—21no—
27#10623364C2211yescharacteristic, complemented
28#10623361—21no—
29#10623361C2211yescharacteristic, complemented
30#10623360—22no—
31#10623360C2212yescomplemented
32#10623358C2211yescharacteristic, complemented
33C2×#67002C2211yescharacteristic, complemented
34C2×#67002C2211yescharacteristic, complemented
35#10623348C2212yescomplemented
36D4×C22⋊D11—22no—
37D4×C22⋊D11—22no—
38D4×C22⋊D11C2212yescomplemented
39D4×C22⋊D11C2212yescomplemented
40#10623322—21no—
41#10623322C2211yescharacteristic
42C2×#66983—21no—
43C2×#66983C2211yescharacteristic, complemented
44C2×#66983C2211yescharacteristic, complemented
45C2×#66967C2212yescomplemented
46C2×D8×D11C2212yescomplemented
47#10623151—22no—
48#10623150C2212yescomplemented
49#10623149C2212yescomplemented
50#10623148—21no—
51#10623140C2212yescomplemented
52#10623138C2212yescomplemented
53#10623136—21no—
54#10623045C2212yescomplemented
55#10623025—21no—
56#10623024—21no—
57C11×#449C2212yescomplemented
58C11×#449C2212yescomplemented
59C11×#449C2212yescomplemented
60C11×#449C2212yescomplemented
61C2×C11×#103C2211yescharacteristic, complemented
62C2×C11×#102C2211yescharacteristic, complemented
63C2×C11×C22⋊C8C2211yescharacteristic, complemented
64#10622851C2212yescomplemented
65#10622851C2212yescomplemented
66#10622845C2211yescharacteristic, complemented
67#10622845C2211yescharacteristic, complemented
68#10622840C2212yescomplemented
69#10622830C2212yescomplemented
70#10622830C2212yescomplemented
71#10622820C2211yescharacteristic, complemented
72#10622789C2212yescomplemented
73#10622787C2212yescomplemented
74#10622785C2212yescomplemented
75#10622782C2212yescomplemented
76#10622778C2212yescomplemented
77#10622777C2212yescomplemented
78#10622776C2212yescomplemented
79#10622770C2212yescomplemented
80#10622769C2212yescomplemented
81#10622769C2212yescomplemented
82#10622764C2212yescomplemented
83#10622763C2212yescomplemented
84#10622763C2212yescomplemented
85D8×Dic11C2212yescomplemented
86#10622728C2212yescomplemented
87#10622728C2212yescomplemented
88#10622724C2212yescomplemented
89C8×C22⋊D11C2212yescomplemented
90#10622652C2212yescomplemented
91#10622652C2212yescomplemented
92#10622649C2212yescomplemented
93#10622647C2212yescomplemented
94#10622581C2212yescomplemented
95#10622432C2212yescomplemented
96#10622427C2212yescomplemented
97#10622424C2212yescomplemented
98#10622420C2212yescomplemented
99#10622417C2212yescomplemented
100#10622413C2212yescomplemented
101#10622409C2212yescomplemented
102#10622401C2212yescomplemented
103#10622399C2212yescomplemented
104#10622398C2212yescomplemented
105#10622397C2212yescomplemented
106#10622395C2212yescomplemented
107#10622386C2212yescomplemented
108#10622383C2212yescomplemented
109#10622379C2212yescomplemented
110#10622377C2212yescomplemented
111#10622349C2212yescomplemented
112#10622349C2212yescomplemented
113#10622345C2212yescomplemented
114#10622345C2212yescomplemented
115#10622342C2212yescomplemented
116#10622341C2212yescomplemented
117#10622340C2212yescomplemented
118#10622333C2212yescomplemented
119C2×C11×#41—21no—
120C2×C11×#41—21no—
121C2×C11×#41—42no—
122C2×C11×#41—42no—
123C2×C11×#41C2311yescharacteristic
124C2×C11×#41C2311yescharacteristic
125C2×C11×#41C2311yescharacteristic
126C2×C11×#41C2311yescharacteristic
127C22×Q8×C11C2311yescharacteristic
128C22×D4×C11—21no—
129C22×D4×C11—21no—
130C22×D4×C11C2311yescharacteristic
131C22×D4×C11C2311yescharacteristic
132C23×C4×C11—21no—
133C23×C4×C11C2311yescharacteristic
134C22×C22⋊D11—21no—
135C22×C22⋊D11—21no—
136C22×C22⋊D11—22no—
137C22×C22⋊D11—22no—
138#67042—42no—
139#67042—42no—
140C2×#4343C2312yes—
141C2×D4×D11—22no—
142C2×D4×D11—22no—
143C2×D4×D11C2312yes—
144C2×D4×D11C2312yes—
145C2×#4339—21no—
146C2×#4339C2311yescharacteristic
147C22×D44—21no—
148C22×D44C2311yescharacteristic
149C22×D44C2311yescharacteristic
150C2×C11×SD16—42no—
151C2×C11×SD16C2312yes—
152C2×C11×SD16C2312yes—
153C2×C11×D8—42no—
154C2×C11×D8C2312yes—
155C2×C11×D8C2312yes—
156C22×C8×C11C2311yescharacteristic
157C22×C8×C11C2311yescharacteristic
158C11×#121—21no—
159C11×#121—21no—
160C11×#121C2312yes—
161C11×#121C2312yes—
162C2×C11×C4⋊C4C2311yescharacteristic
163C2×C11×C22⋊C4—21no—
164#67006—22no—
165#67006—22no—
166#67006D412yes—
167#67002—42no—
168#67002—42no—
169#67000—22no—
170#67000C2312yes—
171#66999—22no—
172#66999C2312yes—
173Q8×Dic11C2312yes—
174C2×#4325C2312yes—
175C2×#4325C2312yes—
176#66993—22no—
177#66993—22no—
178#66993C2312yes—
179#66993C2312yes—
180#66992—22no—
181#66992—22no—
182#66992—22no—
183#66992—22no—
184#66992—22no—
185#66992—22no—
186#66991—22no—
187#66991—22no—
188#66991C2312yes—
189#66991C2312yes—
190#66990—22no—
191#66990—22no—
192#66990—22no—
193#66990—22no—
194#66990—22no—
195#66990—22no—
196D4×Dic11—22no—
197D4×Dic11—22no—
198D4×Dic11C2312yes—
199D4×Dic11C2312yes—
200C2×#4323C2312yes—
201C2×#4323C2312yes—
202C2×#4323C2312yes—
203C2×#4323C2312yes—
204#66983—21no—
205#66983—21no—
206#66983—21no—
207#66983—21no—
208#66983—22no—
209#66983—22no—
210#66983—21no—
211#66983—22no—
212#66983—21no—
213#66983—21no—
214#66983D411yescharacteristic
215#66983D411yescharacteristic
216#66983C2312yes—
217#66983C2312yes—
218#66983C2312yes—
219#66983C2312yes—
220#66982—22no—
221#66982D412yes—
222C4×C22⋊D11—22no—
223C4×C22⋊D11—22no—
224C4×C22⋊D11—22no—
225C4×C22⋊D11C2312yes—
226C4×C22⋊D11C2312yes—
227C2×(C2×D11)⋊C4—21no—
228C2×(C2×D11)⋊C4—21no—
229C2×(C2×D11)⋊C4—22no—
230#66979—21no—
231#66979C2311yescharacteristic
232C2×C4⋊Dic11—21no—
233C2×C4⋊Dic11C2311yescharacteristic
234C2×C4⋊Dic11C2311yescharacteristic
235#66977—21no—
236#66977D411yescharacteristic
237#66977D411yescharacteristic
238C2×#4318C2311yescharacteristic
239C2×#4318C2311yescharacteristic
240#66967—44no—
241D8×D11—44no—
242C2×D88C2312yes—
243C2×D88C2312yes—
244C2×#4313C2312yes—
245C2×C8×D11C2312yes—
246#66951—22no—
247#66948C2312yes—
248#66947—22no—
249#66946C2312yes—
250#66945C2312yes—
251#66943C2312yes—
252#66939—22no—
253#66939—22no—
254#66938—22no—
255#66937—22no—
256#66936—22no—
257#66935—22no—
258#66935—22no—
259#66932—22no—
260C11×#103C2312yes—
261C11×#103C2312yes—
262C11×#102C2312yes—
263C11×#102C2312yes—
264C11×C22⋊C8C2312yes—
265C11×C22⋊C8C2312yes—
266#66899C2312yes—
267#66899C2312yes—
268#66896C2312yes—
269#66896C2312yes—
270#66896C2312yes—
271#66896C2312yes—
272C22⋊(C11⋊C8)C2312yes—
273C22⋊(C11⋊C8)C2312yes—
274#66885C2312yes—
275#66885C2312yes—
276#66885C2312yes—
277#66885C2312yes—
278(C2×D11)⋊C8C2312yes—
279(C2×D11)⋊C8C2312yes—
280#66882C2312yes—
281#66882C2312yes—
282#66879C2312yes—
283Dic11⋊C8C2312yes—
284Dic11⋊C8C2312yes—
285C8×Dic11C2312yes—
286#66873C2312yes—
287#66873C2312yes—
288#66872C2312yes—
289#66872C2312yes—
290#61617—111nomaximal, Sylow
291C24×C11—21no—
292C24×C11—21no—
293C24×C11C2×D411yescharacteristic
294C23×D11—21no—
295C23×D11—21no—
296C23×D11—22no—
297C23×D11—22no—
298C11×#41—22no—
299C11×#41—22no—
300C11×#41—22no—
301C11×#41—22no—
302C11×#41—41no—
303C11×#41—41no—
304C11×#41—41no—
305C11×#41—41no—
306C11×#41—44no—
307C11×#41—44no—
308C2×Q8×C11—21no—
309C2×Q8×C11—22no—
310C2×Q8×C11—41no—
311C2×Q8×C11C2411yescharacteristic
312C2×Q8×C11C2411yescharacteristic
313C2×D4×C11—21no—
314C2×D4×C11—22no—
315C2×D4×C11—22no—
316C2×D4×C11—21no—
317C2×D4×C11—21no—
318C2×D4×C11—21no—
319C2×D4×C11—22no—
320C2×D4×C11—21no—
321C2×D4×C11—21no—
322C2×D4×C11—41no—
323C2×D4×C11—41no—
324C2×D4×C11—41no—
325C2×D4×C11—44no—
326C2×D4×C11—82no—
327C2×D4×C11C2411yescharacteristic
328C2×D4×C11C2412yes—
329C2×D4×C11C2411yescharacteristic
330C22×C4×C11—21no—
331C22×C4×C11—21no—
332C22×C4×C11—21no—
333C22×C4×C11—21no—
334C22×C4×C11—21no—
335C22×C4×C11—21no—
336C22×C4×C11—41no—
337C22×C4×C11—41no—
338C22×C4×C11—44no—
339C22×C4×C11C2×D411yescharacteristic
340C22×C4×C11C2×D411yescharacteristic
341C22×C4×C11C2×D411yescharacteristic
342C22×C4×C11C2411yescharacteristic
343C22×C4×C11C2411yescharacteristic
344C22×C4×C11C2411yescharacteristic
345C2×C22⋊D11—22no—
346C2×C22⋊D11—22no—
347C2×C22⋊D11—22no—
348C2×C22⋊D11—22no—
349C2×C22⋊D11—22no—
350C2×C22⋊D11—22no—
351C2×C22⋊D11—22no—
352C2×C22⋊D11—22no—
353C2×C22⋊D11—22no—
354C2×C22⋊D11—22no—
355C2×C22⋊D11—22no—
356C2×C22⋊D11—22no—
357C2×C22⋊D11—82no—
358C2×C22⋊D11—82no—
359C2×C22⋊D11—84no—
360C2×C22⋊D11—84no—
361C2×C22⋊D11C2×D412yes—
362C2×C22⋊D11C2×D412yes—
363C2×C22⋊D11C2×D412yes—
364C22×Dic11—22no—
365C22×Dic11—22no—
366C22×Dic11—21no—
367C22×Dic11—21no—
368#4343—24no—
369#4343—42no—
370D4×D11—24no—
371D4×D11—42no—
372D4×D11—48no—
373D4×D11—42no—
374D4×D11—42no—
375D4×D11—84no—
376#4339—41no—
377#4339—41no—
378#4339—44no—
379C2×D44—22no—
380C2×D44—22no—
381C2×D44—21no—
382C2×D44—21no—
383C2×D44—41no—
384C2×D44—41no—
385C2×D44—44no—
386C2×D44—41no—
387C2×D44—41no—
388C2×D44C2×D411yescharacteristic
389C2×D44C2412yes—
390C2×D44C2412yes—
391C2×C4×D11—22no—
392C2×C4×D11—22no—
393C2×C4×D11C2412yes—
394C2×Dic22C2×D411yescharacteristic
395C11×SD16—24no—
396C11×SD16—42no—
397C11×D8—24no—
398C11×D8—42no—
399C2×C8×C11—41no—
400C2×C8×C11—41no—
401C2×C8×C11C2412yes—
402C2×C8×C11C2412yes—
403C11×C4⋊C4—21no—
404C11×C4⋊C4C2412yes—
405C11×C22⋊C4—22no—
406C11×C22⋊C4—22no—
407C22⋊Dic11—22no—
408C22⋊Dic11—22no—
409C22⋊Dic11—22no—
410C22⋊Dic11—22no—
411C22⋊Dic11C2×D412yes—
412C22⋊Dic11C2×D412yes—
413C22⋊Dic11C2×D412yes—
414#4325—24no—
415#4325—42no—
416#4323—24no—
417#4323—42no—
418#4323—42no—
419#4323—42no—
420(C2×D11)⋊C4—22no—
421(C2×D11)⋊C4—22no—
422(C2×D11)⋊C4—22no—
423(C2×D11)⋊C4—22no—
424(C2×D11)⋊C4—22no—
425(C2×D11)⋊C4—22no—
426(C2×D11)⋊C4—22no—
427(C2×D11)⋊C4—22no—
428(C2×D11)⋊C4—22no—
429(C2×D11)⋊C4—22no—
430(C2×D11)⋊C4C2×D412yes—
431(C2×D11)⋊C4C2×D412yes—
432C4⋊Dic11—22no—
433C4⋊Dic11—22no—
434C4⋊Dic11—21no—
435C4⋊Dic11—21no—
436C4⋊Dic11C2×D411yescharacteristic
437C4⋊Dic11C2×D411yescharacteristic
438C4⋊Dic11C2412yes—
439C4⋊Dic11C2412yes—
440Dic11⋊C4—22no—
441Dic11⋊C4—22no—
442Dic11⋊C4C2×D412yes—
443Dic11⋊C4C2×D412yes—
444C4×Dic11—22no—
445C4×Dic11—22no—
446C4×Dic11C2412yes—
447#4318—41no—
448#4318—41no—
449C2×C11⋊C8C2412yes—
450C2×C11⋊C8C2412yes—
451D88—42no—
452D88—42no—
453#4313—42no—
454C8×D11—42no—
455#3537—111no—
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×#449D1111yescharacteristic, complemented
473#2976—111no—
474C23×C11—21no—
475C23×C11—22no—
476C23×C11—22no—
477C23×C11—21no—
478C23×C11—41no—
479C23×C11—41no—
480C23×C11—42no—
481C23×C11—42no—
482C23×C11—42no—
483C23×C11—81no—
484C23×C11—81no—
485C23×C11—81no—
486C23×C11C22×D411yescharacteristic
487C23×C11C22×D411yescharacteristic
488C23×C11C22×D411yescharacteristic
489C22×D11—22no—
490C22×D11—22no—
491C22×D11—44no—
492C22×D11—42no—
493C22×D11—42no—
494C22×D11—82no—
495C22×D11—82no—
496C22×D11—82no—
497C22×D11—82no—
498C22×D11—82no—
499C22×D11—81no—
500C22×D11—81no—
501C22×D11—81no—
502C22×D11—81no—
503C22×D11C22×D412yes—
504Q8×C11—21no—
505Q8×C11—21no—
506Q8×C11—21no—
507Q8×C11—42no—
508Q8×C11H(5,𝔽2)12yes—
509D4×C11—24no—
510D4×C11—21no—
511D4×C11—21no—
512D4×C11—22no—
513D4×C11—22no—
514D4×C11—21no—
515D4×C11—42no—
516D4×C11—42no—
517D4×C11—42no—
518D4×C11—44no—
519D4×C11—42no—
520D4×C11—81no—
521D4×C11—82no—
522D4×C11H(5,𝔽2)12yes—
523C2×C4×C11—24no—
524C2×C4×C11—21no—
525C2×C4×C11—21no—
526C2×C4×C11—21no—
527C2×C4×C11—21no—
528C2×C4×C11—21no—
529C2×C4×C11—21no—
530C2×C4×C11—21no—
531C2×C4×C11—22no—
532C2×C4×C11—21no—
533C2×C4×C11—41no—
534C2×C4×C11—41no—
535C2×C4×C11—41no—
536C2×C4×C11—42no—
537C2×C4×C11—42no—
538C2×C4×C11—42no—
539C2×C4×C11—42no—
540C2×C4×C11—81no—
541C2×C4×C11C22×D411yescharacteristic
542C2×C4×C11C22×D411yescharacteristic
543C2×C4×C11C22×D411yescharacteristic
544C2×C4×C11C2511yescharacteristic
545C22⋊D11—24no—
546C22⋊D11—42no—
547C22⋊D11—42no—
548C22⋊D11—44no—
549C22⋊D11—44no—
550C22⋊D11—44no—
551C22⋊D11—82no—
552C22⋊D11—82no—
553C22⋊D11—82no—
554C22⋊D11—82no—
555C22⋊D11—82no—
556C22⋊D11—82no—
557C22⋊D11—82no—
558C22⋊D11—82no—
559C22⋊D11—82no—
560C2×Dic11—22no—
561C2×Dic11—22no—
562C2×Dic11—82no—
563C2×Dic11—82no—
564C2×Dic11—81no—
565C2×Dic11—81no—
566C2×Dic11C22×D412yes—
567C2×Dic11C22×D412yes—
568C2×Dic11C22×D412yes—
569D44—22no—
570D44—22no—
571D44—22no—
572D44—22no—
573D44—41no—
574D44—44no—
575D44—42no—
576D44—81no—
577D44—82no—
578C4×D11—22no—
579C4×D11—22no—
580C4×D11—44no—
581C4×D11—82no—
582Dic22—41no—
583C8×C11—22no—
584C8×C11—22no—
585C11⋊C8—22no—
586C11⋊C8—22no—
587C2×H(5,𝔽2)—111no—
588C22×#41C2×D1111yescharacteristic, complemented
589C2×AGL(1,ℤ/8)—111no—
590C2×AGL(1,ℤ/8)—111no—
591C2×AGL(1,ℤ/8)—112no—
592C22×SD16C2×D1111yescharacteristic, complemented
593C22×D8—112no—
594C22×D8C2×D1111yescharacteristic, complemented
595#560—222no—
596#553—112no—
597#553—112no—
598#550—112no—
599#548—112no—
600#546—112no—
601#546—222no—
602D42—112no—
603D42—112no—
604D42—112no—
605D42—222no—
606D42—222no—
607#540—112no—
608#538—221no—
609#538—221no—
610#537—111no—
611#537—221no—
612#535—112no—
613#535—111no—
614#535—221no—
615#534—221no—
616#534—221no—
617#525—111no—
618#525—221no—
619C2×#121—111no—
620C2×#121—111no—
621C2×#121—221no—
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#449C2×D1112yescomplemented
656#449C2×D1112yescomplemented
657#449C2×D1112yescomplemented
658#449C2×D1112yescomplemented
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×#103C2×D1111yescharacteristic, complemented
682C2×#102C2×D1111yescharacteristic, complemented
683#408—112no—
684#407—111no—
685C2×C22⋊C8C2×D1111yescharacteristic, complemented
686C22×C11—21no—
687C22×C11—21no—
688C22×C11—21no—
689C22×C11—21no—
690C22×C11—21no—
691C22×C11—22no—
692C22×C11—21no—
693C22×C11—21no—
694C22×C11—21no—
695C22×C11—41no—
696C22×C11—41no—
697C22×C11—42no—
698C22×C11—41no—
699C22×C11—41no—
700C22×C11—42no—
701C22×C11—42no—
702C22×C11—41no—
703C22×C11—82no—
704C22×C11—84no—
705C22×C11—162no—
706C22×C11#57612yes—
707C22×C11C23×D411yescharacteristic
708C2×D11—22no—
709C2×D11—22no—
710C2×D11—22no—
711C2×D11—42no—
712C2×D11—42no—
713C2×D11—42no—
714C2×D11—42no—
715C2×D11—42no—
716C2×D11—42no—
717C2×D11—164no—
718C2×D11—164no—
719C2×D11—162no—
720C2×D11—162no—
721C4×C11—21no—
722C4×C11—22no—
723C4×C11—21no—
724C4×C11—21no—
725C4×C11—42no—
726C4×C11—41no—
727C4×C11C2×H(5,𝔽2)11yescharacteristic
728C4×C11C2×H(5,𝔽2)11yescharacteristic
729Dic11—22no—
730Dic11—22no—
731Dic11—22no—
732Dic11—42no—
733Dic11—42no—
734H(5,𝔽2)—442no—
735H(5,𝔽2)—442no—
736C2×#41—21no—
737C2×#41—21no—
738C2×#41—42no—
739C2×#41—42no—
740C2×#41—111no—
741C2×#41—112no—
742C2×#41—221no—
743C2×#41C22×D1111yescharacteristic
744C2×#41C22×D1111yescharacteristic
745C2×#41C22×D1111yescharacteristic
746C2×#41C22×D1111yescharacteristic
747C22×Q8C22×D1111yescharacteristic
748C22×D4—21no—
749C22×D4—21no—
750C22×D4—112no—
751C22×D4—112no—
752C22×D4—111no—
753C22×D4—111no—
754C22×D4—221no—
755C22×D4—222no—
756C22×D4—222no—
757C22×D4—222no—
758C22×D4—222no—
759C22×D4—221no—
760C22×D4—221no—
761C22×D4C22×D1111yescharacteristic
762C22×D4C22×D1111yescharacteristic
763C23×C4—21no—
764C23×C4C22×D1111yescharacteristic
765AGL(1,ℤ/8)—442no—
766AGL(1,ℤ/8)—444no—
767AGL(1,ℤ/8)—442no—
768C2×SD16—42no—
769C2×SD16—112no—
770C2×SD16—112no—
771C2×SD16C22×D1112yes—
772C2×SD16C22×D1112yes—
773C2×D8—42no—
774C2×D8—112no—
775C2×D8—112no—
776C2×D8—112no—
777C2×D8—112no—
778C2×D8—112no—
779C2×D8—112no—
780C2×D8—444no—
781C2×D8C22×D1112yes—
782C2×D8C22×D1112yes—
783C2×M16—111no—
784C2×M16—111no—
785C2×M16—112no—
786C22×C8—112no—
787C22×C8C22×D1111yescharacteristic
788C22×C8C22×D1111yescharacteristic
789#127—112no—
790#127—112no—
791#127—222no—
792#127—222no—
793#126—222no—
794#126—222no—
795#125—112no—
796#124—112no—
797#124—222no—
798#124—222no—
799#123—112no—
800#123—222no—
801#123—222no—
802#123—222no—
803#123—222no—
804#123—222no—
805C22⋊Q8—111no—
806C22⋊Q8—111no—
807C22⋊Q8—112no—
808C22⋊Q8—222no—
809C22⋊Q8—221no—
810#121—21no—
811#121—21no—
812#121—111no—
813#121—111no—
814#121—112no—
815#121—112no—
816#121—112no—
817#121—112no—
818#121—112no—
819#121—112no—
820#121—112no—
821#121—222no—
822#121—222no—
823#121—222no—
824#121—222no—
825#121—222no—
826#121—222no—
827#121—221no—
828#121—221no—
829#121—222no—
830#121—222no—
831#121—221no—
832#121—222no—
833#121—222no—
834#121—222no—
835#121—222no—
836#121—221no—
837#121—221no—
838#121—221no—
839#121—221no—
840#121C22×D1112yes—
841#121C22×D1112yes—
842#120—112no—
843#120—222no—
844#120—222no—
845#120—222no—
846#120—222no—
847#120—222no—
848#120—222no—
849#120—222no—
850#120—222no—
851#120—222no—
852#120—222no—
853C4×Q8—112no—
854C4×D4—112no—
855C4×D4—112no—
856C4×D4—112no—
857C4×D4—112no—
858C4×D4—112no—
859C4×D4—222no—
860C4×D4—222no—
861C4×D4—222no—
862C4×D4—222no—
863C4×D4—222no—
864#117—111no—
865#117—112no—
866#117—221no—
867C2×C4⋊C4—111no—
868C2×C4⋊C4—111no—
869C2×C4⋊C4—221no—
870C2×C4⋊C4C22×D1111yescharacteristic
871C2×C22⋊C4—21no—
872C2×C22⋊C4—222no—
873C2×C22⋊C4—221no—
874C2×C22⋊C4—221no—
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#103C22×D1112yes—
884#103C22×D1112yes—
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#102C22×D1112yes—
896#102C22×D1112yes—
897C22⋊C8—112no—
898C22⋊C8—112no—
899C22⋊C8—112no—
900C22⋊C8—112no—
901C22⋊C8C22×D1112yes—
902C22⋊C8C22×D1112yes—
903#97—112no—
904C4×C8—112no—
905C2×C11—22no—
906C2×C11—41no—
907C2×C11—41no—
908C2×C11—42no—
909C2×C11—82no—
910C2×C11—81no—
911C2×C11#348411yescharacteristic
912C2×C11C2×#57611yescharacteristic
913C2×C11#358511yescharacteristic
914D11—42no—
915D11—82no—
916D11—82no—
917C24—21no—
918C24—21no—
919C24—222no—
920C24—222no—
921C24—221no—
922C24—221no—
923C24D4×D1111yescharacteristic
924#41—22no—
925#41—22no—
926#41—22no—
927#41—22no—
928#41—41no—
929#41—41no—
930#41—41no—
931#41—41no—
932#41—44no—
933#41—44no—
934#41—224no—
935#41—441no—
936#41—441no—
937#41—444no—
938#41—442no—
939C2×Q8—21no—
940C2×Q8—22no—
941C2×Q8—41no—
942C2×Q8—111no—
943C2×Q8C23×D1111yescharacteristic
944C2×Q8C23×D1111yescharacteristic
945C2×D4—21no—
946C2×D4—22no—
947C2×D4—22no—
948C2×D4—21no—
949C2×D4—21no—
950C2×D4—21no—
951C2×D4—22no—
952C2×D4—21no—
953C2×D4—21no—
954C2×D4—41no—
955C2×D4—41no—
956C2×D4—41no—
957C2×D4—44no—
958C2×D4—82no—
959C2×D4—112no—
960C2×D4—112no—
961C2×D4—112no—
962C2×D4—111no—
963C2×D4—112no—
964C2×D4—112no—
965C2×D4—222no—
966C2×D4—222no—
967C2×D4—222no—
968C2×D4—222no—
969C2×D4—222no—
970C2×D4—222no—
971C2×D4—222no—
972C2×D4—222no—
973C2×D4—224no—
974C2×D4—222no—
975C2×D4—222no—
976C2×D4—222no—
977C2×D4—222no—
978C2×D4—222no—
979C2×D4—222no—
980C2×D4—221no—
981C2×D4—221no—
982C2×D4—441no—
983C2×D4—441no—
984C2×D4—441no—
985C2×D4—441no—
986C2×D4—444no—
987C2×D4—442no—
988C2×D4—442no—
989C2×D4—442no—
990C2×D4—448no—
991C2×D4—884no—
992C2×D4—884no—
993C2×D4—884no—
994C2×D4—882no—
995C2×D4—882no—
996C2×D4C23×D1111yescharacteristic
997C2×D4C23×D1112yes—
998C2×D4C23×D1111yescharacteristic
999C22×C4—21no—
1000C22×C4—21no—
1001C22×C4—21no—
1002C22×C4—21no—
1003C22×C4—21no—
1004C22×C4—21no—
1005C22×C4—41no—
1006C22×C4—41no—
1007C22×C4—44no—
1008C22×C4—112no—
1009C22×C4—222no—
1010C22×C4—222no—
1011C22×C4—222no—
1012C22×C4—222no—
1013C22×C4—221no—
1014C22×C4—221no—
1015C22×C4D4×D1111yescharacteristic
1016C22×C4D4×D1111yescharacteristic
1017C22×C4D4×D1111yescharacteristic
1018C22×C4C23×D1111yescharacteristic
1019C22×C4C23×D1111yescharacteristic
1020C22×C4C23×D1111yescharacteristic
1021SD16—24no—
1022SD16—42no—
1023SD16—224no—
1024SD16—442no—
1025D8—24no—
1026D8—42no—
1027D8—224no—
1028D8—442no—
1029D8—442no—
1030D8—442no—
1031D8—442no—
1032D8—442no—
1033M16—442no—
1034M16—441no—
1035M16—441no—
1036C2×C8—41no—
1037C2×C8—41no—
1038C2×C8—112no—
1039C2×C8—112no—
1040C2×C8—442no—
1041C2×C8C23×D1112yes—
1042C2×C8C23×D1112yes—
1043C4⋊C4—21no—
1044C4⋊C4—111no—
1045C4⋊C4—111no—
1046C4⋊C4—112no—
1047C4⋊C4—112no—
1048C4⋊C4—112no—
1049C4⋊C4—112no—
1050C4⋊C4—222no—
1051C4⋊C4—222no—
1052C4⋊C4—222no—
1053C4⋊C4—222no—
1054C4⋊C4—221no—
1055C4⋊C4—221no—
1056C4⋊C4C23×D1112yes—
1057C22⋊C4—22no—
1058C22⋊C4—22no—
1059C22⋊C4—112no—
1060C22⋊C4—112no—
1061C22⋊C4—112no—
1062C22⋊C4—112no—
1063C22⋊C4—112no—
1064C22⋊C4—222no—
1065C22⋊C4—222no—
1066C22⋊C4—222no—
1067C22⋊C4—222no—
1068C22⋊C4—222no—
1069C22⋊C4—222no—
1070C22⋊C4—222no—
1071C22⋊C4—222no—
1072C22⋊C4—222no—
1073C22⋊C4—222no—
1074C22⋊C4—222no—
1075C22⋊C4—222no—
1076C22⋊C4—222no—
1077C22⋊C4—222no—
1078C42—112no—
1079C42—222no—
1080C42—222no—
1081C11#6161711yescharacteristic, complemented, Sylow
1082C23—21no—
1083C23—22no—
1084C23—22no—
1085C23—21no—
1086C23—41no—
1087C23—41no—
1088C23—42no—
1089C23—42no—
1090C23—42no—
1091C23—81no—
1092C23—81no—
1093C23—81no—
1094C23—112no—
1095C23—222no—
1096C23—222no—
1097C23—444no—
1098C23—442no—
1099C23—442no—
1100C23—881no—
1101C23—881no—
1102C23—881no—
1103C23—881no—
1104C23—882no—
1105C23—882no—
1106C23—882no—
1107C23—882no—
1108C23—882no—
1109C23C2×D4×D1111yescharacteristic
1110C23C2×D4×D1111yescharacteristic
1111C23C2×D4×D1111yescharacteristic
1112Q8—21no—
1113Q8—21no—
1114Q8—21no—
1115Q8—42no—
1116Q8—441no—
1117Q8#6703712yes—
1118D4—24no—
1119D4—21no—
1120D4—22no—
1121D4—21no—
1122D4—21no—
1123D4—22no—
1124D4—42no—
1125D4—42no—
1126D4—42no—
1127D4—42no—
1128D4—44no—
1129D4—81no—
1130D4—82no—
1131D4—224no—
1132D4—222no—
1133D4—222no—
1134D4—222no—
1135D4—222no—
1136D4—441no—
1137D4—444no—
1138D4—442no—
1139D4—442no—
1140D4—442no—
1141D4—444no—
1142D4—444no—
1143D4—444no—
1144D4—881no—
1145D4—882no—
1146D4—882no—
1147D4—882no—
1148D4—882no—
1149D4—882no—
1150D4—882no—
1151D4—882no—
1152D4—882no—
1153D4—882no—
1154D4—882no—
1155D4#6703712yes—
1156C2×C4—24no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—22no—
1165C2×C4—21no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—81no—
1174C2×C4—112no—
1175C2×C4—112no—
1176C2×C4—112no—
1177C2×C4—222no—
1178C2×C4—222no—
1179C2×C4—222no—
1180C2×C4—222no—
1181C2×C4—444no—
1182C2×C4—882no—
1183C2×C4—882no—
1184C2×C4—882no—
1185C2×C4—881no—
1186C2×C4—881no—
1187C2×C4C2×D4×D1111yescharacteristic
1188C2×C4C2×D4×D1111yescharacteristic
1189C2×C4C2×D4×D1111yescharacteristic
1190C2×C4C24×D1111yescharacteristic
1191C8—22no—
1192C8—22no—
1193C8—222no—
1194C8—222no—
1195C22—21no—
1196C22—21no—
1197C22—21no—
1198C22—21no—
1199C22—21no—
1200C22—22no—
1201C22—21no—
1202C22—21no—
1203C22—21no—
1204C22—41no—
1205C22—41no—
1206C22—42no—
1207C22—41no—
1208C22—41no—
1209C22—42no—
1210C22—42no—
1211C22—41no—
1212C22—82no—
1213C22—84no—
1214C22—162no—
1215C22—222no—
1216C22—222no—
1217C22—222no—
1218C22—442no—
1219C22—442no—
1220C22—442no—
1221C22—442no—
1222C22—442no—
1223C22—442no—
1224C22—1764no—
1225C22—1762no—
1226C22—1762no—
1227C22—1764no—
1228C22#1062330012yes—
1229C22C22×D4×D1111yescharacteristic
1230C4—21no—
1231C4—22no—
1232C4—21no—
1233C4—21no—
1234C4—42no—
1235C4—41no—
1236C4—222no—
1237C4—222no—
1238C4—222no—
1239C4—442no—
1240C4—442no—
1241C4C2×#6703711yescharacteristic
1242C4C2×#6703711yescharacteristic
1243C2—22no—
1244C2—41no—
1245C2—41no—
1246C2—42no—
1247C2—81no—
1248C2—82no—
1249C2—442no—
1250C2—882no—
1251C2—882no—
1252C2#1308224511yescharacteristic
1253C2C2×#1062330011yescharacteristic
1254C2#1308339211yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#449C2
socleC22×C11C23×D4
hypercenterC2×#449D11
hypocenterC11#61617
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. #13082851C2semidirect
2. #13082285C2semidirect
3. #13080810C2semidirect
4. #13080753C2semidirect
5. #13080615C2semidirect
6. #13080514C2semidirect
7. D8×C22⋊D11C2semidirect
8. #13080229C2semidirect
9. #13080111C2semidirect
10. #13080099C2semidirect
11. #13079664C2semidirect
12. #13079465C2semidirect
13. #13079413C2semidirect
14. #13079367C2semidirect
15. #13078808C2semidirect
16. #13077881C2semidirect
17. #13077868C2semidirect
18. #13077661C2semidirect
19. C2×C11×#449C2semidirect
20. C22×C11×#41C22semidirect
21. C2×#67042C22semidirect
22. C22×C11×SD16C22semidirect
23. C22×C11×D8C22semidirect
24. C2×C11×#121C22semidirect
25. #10623365C22semidirect
27. #10623364C22semidirect
29. #10623361C22semidirect
31. #10623360C22semidirect
32. #10623358C22semidirect
33. C2×#67002C22semidirect
34. C2×#67002C22semidirect
35. #10623348C22semidirect
38. D4×C22⋊D11C22semidirect
39. D4×C22⋊D11C22semidirect
43. C2×#66983C22semidirect
44. C2×#66983C22semidirect
45. C2×#66967C22semidirect
46. C2×D8×D11C22semidirect
48. #10623150C22semidirect
49. #10623149C22semidirect
51. #10623140C22semidirect
52. #10623138C22semidirect
54. #10623045C22semidirect
57. C11×#449C22semidirect
58. C11×#449C22semidirect
59. C11×#449C22semidirect
60. C11×#449C22semidirect
61. C2×C11×#103C22semidirect
62. C2×C11×#102C22semidirect
63. C2×C11×C22⋊C8C22semidirect
64. #10622851C22semidirect
65. #10622851C22semidirect
66. #10622845C22semidirect
67. #10622845C22semidirect
68. #10622840C22semidirect
69. #10622830C22semidirect
70. #10622830C22semidirect
71. #10622820C22semidirect
72. #10622789C22semidirect
73. #10622787C22semidirect
74. #10622785C22semidirect
75. #10622782C22semidirect
76. #10622778C22semidirect
77. #10622777C22semidirect
78. #10622776C22semidirect
79. #10622770C22semidirect
80. #10622769C22semidirect
81. #10622769C22semidirect
82. #10622764C22semidirect
83. #10622763C22semidirect
84. #10622763C22semidirect
85. D8×Dic11C22semidirect
86. #10622728C22semidirect
87. #10622728C22semidirect
88. #10622724C22semidirect
89. C8×C22⋊D11C22semidirect
90. #10622652C22semidirect
91. #10622652C22semidirect
92. #10622649C22semidirect
93. #10622647C22semidirect
94. #10622581C22semidirect
95. #10622432C22semidirect
96. #10622427C22semidirect
97. #10622424C22semidirect
98. #10622420C22semidirect
99. #10622417C22semidirect
100. #10622413C22semidirect
101. #10622409C22semidirect
102. #10622401C22semidirect
103. #10622399C22semidirect
104. #10622398C22semidirect
105. #10622397C22semidirect
106. #10622395C22semidirect
107. #10622386C22semidirect
108. #10622383C22semidirect
109. #10622379C22semidirect
110. #10622377C22semidirect
111. #10622349C22semidirect
112. #10622349C22semidirect
113. #10622345C22semidirect
114. #10622345C22semidirect
115. #10622342C22semidirect
116. #10622341C22semidirect
117. #10622340C22semidirect
118. #10622333C22semidirect
472. C2×#449D11semidirect
588. C22×#41C2×D11semidirect
592. C22×SD16C2×D11semidirect
594. C22×D8C2×D11semidirect
622. C2×#121C2×D11semidirect
655. #449C2×D11semidirect
656. #449C2×D11semidirect
657. #449C2×D11semidirect
658. #449C2×D11semidirect
681. C2×#103C2×D11semidirect
682. C2×#102C2×D11semidirect
685. C2×C22⋊C8C2×D11semidirect
1081. C11#61617semidirect

Maximal subgroups

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

subgroupindex
#130828512
#130822852
#130808102
#130807532
#130806152
#130805142
D8×C22⋊D112
#130802292
#130801112
#130800992
#130796642
#130794652
#130794132
#130793672
#130788082
#130778812
#130778682
#130776612
C2×C11×#4492
#6161711