Finite Group Databasebeta

← #15639864

Subgroups — #15639864

Order 2816.

2222 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082859C211yesmaximal, characteristic, complemented
2#13082247C211yesmaximal, characteristic
3#13080638C212yesmaximal, complemented
4#13080630C212yesmaximal, complemented
5#13080452C212yesmaximal, complemented
6#13080444C212yesmaximal, complemented
7#13080310C212yesmaximal, complemented
8SD16×C22⋊D11C212yesmaximal, complemented
9#13080124C212yesmaximal, complemented
10#13080120C212yesmaximal, complemented
11#13079686C212yesmaximal, complemented
12#13079489C211yesmaximal, characteristic, complemented
13#13079483C211yesmaximal, characteristic, complemented
14#13079395C212yesmaximal, complemented
15#13078862C212yesmaximal, complemented
16#13077893C211yesmaximal, characteristic, complemented
17D11×#450C212yesmaximal, complemented
18#13077668C211yesmaximal, characteristic, complemented
19C11×#3009C211yesmaximal, characteristic, complemented
20C2×C11×H(5,𝔽2)C2211yescharacteristic
21C22×D4×D11C2211yescharacteristic
22C2×C11×#137C2211yescharacteristic, complemented
23C22×C11×SD16C2211yescharacteristic, complemented
24C11×#536C2211yescharacteristic, complemented
25#10623361C2211yescharacteristic
26#10623361C2211yescharacteristic
27#10623360—22no—
28#10623360C2212yes—
29#10623360C2212yes—
30#10623359C2211yescharacteristic
31#10623359C2211yescharacteristic
32#10623356C2211yescharacteristic, complemented
33C2×#67004C2211yescharacteristic, complemented
34Q8×C22⋊D11C2212yescomplemented
35#10623335—21no—
36#10623335—21no—
37D4×C22⋊D11—22no—
38D4×C22⋊D11C2212yes—
39D4×C22⋊D11C2212yes—
40C2×#66990—21no—
41C2×#66990—21no—
42#10623329C2211yescharacteristic
43C22×#4324C2211yescharacteristic, complemented
44C2×SD16×D11C2212yescomplemented
45C2×SD16×D11C2212yescomplemented
46#10623260—22no—
47#10623210—21no—
48#10623203—21no—
49#10623191—22no—
50#10623190—21no—
51#10623182—21no—
52#10623170C2212yescomplemented
53#10623163C2212yescomplemented
54D11×C22⋊Q8C2212yescomplemented
55#10623156C2212yescomplemented
56#10623060C2212yescomplemented
57C11×#452C2212yescomplemented
58C11×#452C2212yescomplemented
59C11×#450C2212yes—
60C11×#450C2212yescomplemented
61C11×#418C2211yescharacteristic, complemented
62C11×#416C2211yescharacteristic, complemented
63C11×#408C2211yescharacteristic, complemented
64#10622852C2212yescomplemented
65#10622852C2212yescomplemented
66#10622847C2211yescharacteristic, complemented
67#10622846C2211yescharacteristic, complemented
68#10622840C2212yescomplemented
69#10622831C2212yes—
70#10622831C2212yescomplemented
71#10622828C2211yescharacteristic, complemented
72#10622803C2212yescomplemented
73#10622801C2212yescomplemented
74#10622799C2212yescomplemented
75#10622798C2212yescomplemented
76#10622788C2212yescomplemented
77#10622784C2212yescomplemented
78#10622783C2212yescomplemented
79#10622782C2212yescomplemented
80#10622782C2212yescomplemented
81#10622777C2212yescomplemented
82#10622776C2212yescomplemented
83#10622775C2212yescomplemented
84#10622775C2212yescomplemented
85SD16×Dic11C2212yescomplemented
86#10622747C2212yescomplemented
87#10622740C2212yescomplemented
88#10622727C2212yescomplemented
89C8×C22⋊D11C2212yescomplemented
90#10622662C2212yescomplemented
91#10622661C2212yescomplemented
92#10622659C2212yescomplemented
93#10622658C2212yescomplemented
94#10622616C2212yescomplemented
95#10622426C2212yescomplemented
96#10622418C2212yescomplemented
97#10622413C2212yescomplemented
98#10622411C2212yescomplemented
99#10622391C2212yescomplemented
100#10622389C2212yescomplemented
101#10622389C2212yescomplemented
102#10622387C2212yescomplemented
103D11×#102C2212yescomplemented
104D11×#102C2212yescomplemented
105#10622379C2212yescomplemented
106#10622377C2212yescomplemented
107#10622376C2212yescomplemented
108#10622375C2212yescomplemented
109#10622371C2212yescomplemented
110#10622370C2212yescomplemented
111#10622351C2212yescomplemented
112#10622350C2212yescomplemented
113#10622344C2212yescomplemented
114#10622341C2212yescomplemented
115(C22⋊D11)⋊C8C2212yescomplemented
116D11×C22⋊C8C2212yescomplemented
117#10622336C2212yescomplemented
118#10622333C2212yescomplemented
119C24×D11—21no—
120C11×H(5,𝔽2)—42no—
121C11×H(5,𝔽2)—42no—
122C2×C11×#41—21no—
123C2×C11×#41C2311yescharacteristic
124C2×C11×#41C2311yescharacteristic
125C2×C11×#41C2311yescharacteristic
126C2×C11×#41C2311yescharacteristic
127C22×Q8×C11C2311yescharacteristic, complemented
128C22×D4×C11—21no—
129C22×D4×C11—21no—
130C22×D4×C11—21no—
131C22×D4×C11C2311yescharacteristic
132C22×D4×C11C2311yescharacteristic
133C22×D4×C11C2311yescharacteristic
134C22×C22⋊D11—22no—
135C22×C22⋊D11—22no—
136C22×C22⋊D11—21no—
137C2×Q8×D11C2312yes—
138C2×D4×D11—22no—
139C2×D4×D11—42no—
140C2×D4×D11—42no—
141C2×D4×D11C2312yes—
142C2×D4×D11C2312yes—
143C22×D44C2311yescharacteristic
144C22×C4×D11C2311yescharacteristic
145C22×Dic22C2311yescharacteristic, complemented
146C11×#137—42no—
147C2×C11×Q16C2312yescomplemented
148C2×C11×SD16—42no—
149C2×C11×SD16C2312yes—
150C2×C11×SD16C2312yes—
151C2×C11×SD16C2312yescomplemented
152C2×C11×M16C2311yescharacteristic, complemented
153C22×C8×C11C2311yescharacteristic, complemented
154C11×C4⋊Q8—21no—
155C11×#124—21no—
156C11×#123—21no—
157C11×#123—21no—
158C11×C22⋊Q8C2312yes—
159C11×C22⋊Q8C2312yescomplemented
160C11×#117C2311yescharacteristic, complemented
161#67006—22no—
162#67006—22no—
163C2×C22⋊Dic11—21no—
164C2×C22⋊Dic11—21no—
165#67004—42no—
166#67000—21no—
167#67000C2312yes—
168#66999—22no—
169#66999D412yes—
170#66999C2312yes—
171#66999C2312yes—
172Q8×Dic11C2312yescomplemented
173#66997—21no—
174#66997—22no—
175#66997C2312yescomplemented
176C2×#4326C2312yescomplemented
177C2×#4325C2312yes—
178C2×#4325C2312yes—
179#66993—21no—
180#66993C2312yes—
181#66992—22no—
182#66992—22no—
183#66992—22no—
184#66992—22no—
185#66991D412yes—
186#66991C2312yes—
187#66990—21no—
188#66990—21no—
189#66990—21no—
190#66990—22no—
191#66990—22no—
192#66990—21no—
193#66990—21no—
194#66990—22no—
195#66990—22no—
196#66990D411yescharacteristic
197#66990D411yescharacteristic
198#66989—21no—
199#66988—21no—
200#66988—21no—
201#66988—21no—
202#66988D411yescharacteristic
203#66988D411yescharacteristic
204D4×Dic11—22no—
205D4×Dic11C2312yes—
206D4×Dic11C2312yes—
207C2×#4324—42no—
208C2×#4324C2312yes—
209C2×#4324C2312yes—
210C2×#4324C2312yescomplemented
211#66983—22no—
212#66983C2312yes—
213#66983C2312yes—
214#66982—22no—
215#66982—22no—
216C4×C22⋊D11—22no—
217C4×C22⋊D11—22no—
218C4×C22⋊D11C2312yes—
219C4×C22⋊D11C2312yes—
220C2×(C2×D11)⋊C4—22no—
221C2×(C2×D11)⋊C4—22no—
222#66979C2311yescharacteristic
223#66979C2311yescharacteristic
224#66979C2311yescharacteristic, complemented
225#66977—22no—
226#66977C2312yes—
227#66977C2312yescomplemented
228C2×#4318C2311yescharacteristic, complemented
229C22×C11⋊C8C2311yescharacteristic, complemented
230SD16×D11—44no—
231SD16×D11—44no—
232C2×#4314C2312yes—
233C2×#4314C2312yes—
234C2×C8×D11C2312yes—
235C2×C8×D11C2312yes—
236#66950C2312yes—
237#66949—22no—
238#66949—22no—
239#66945—22no—
240C4⋊C4×D11—22no—
241C4⋊C4×D11C2312yes—
242#66943—22no—
243#66943C2312yescomplemented
244#66942—22no—
245#66942—22no—
246#66941—22no—
247#66940C2312yescomplemented
248#66936—22no—
249#66936—22no—
250(C22⋊D11)⋊C4—22no—
251C22⋊C4×D11—22no—
252#66932—22no—
253#66932—22no—
254#66932—22no—
255#66932—22no—
256#66931—22no—
257#66931—22no—
258#66925—22no—
259#66923—22no—
260C11×#103C2312yescomplemented
261C11×#102C2312yes—
262C11×#102C2312yes—
263C11×#102C2312yescomplemented
264C11×C22⋊C8C2312yes—
265C11×C22⋊C8C2312yescomplemented
266#66899C2312yescomplemented
267#66899C2312yescomplemented
268#66899C2312yescomplemented
269#66896C2312yes—
270#66896C2312yes—
271#66896C2312yescomplemented
272C22⋊(C11⋊C8)C2312yes—
273C22⋊(C11⋊C8)C2312yescomplemented
274#66885C2312yes—
275#66885C2312yes—
276(C2×D11)⋊C8C2312yes—
277(C2×D11)⋊C8C2312yes—
278#66882C2312yescomplemented
279#66881C2312yescomplemented
280#66880C2312yescomplemented
281#66880C2312yescomplemented
282#66879C2312yescomplemented
283Dic11⋊C8C2312yescomplemented
284Dic11⋊C8C2312yescomplemented
285C8×Dic11C2312yescomplemented
286#66873C2312yes—
287#66873C2312yes—
288#66872C2312yescomplemented
289#66871C2312yescomplemented
290#61631—111nomaximal, Sylow
291C24×C11—21no—
292C24×C11—21no—
293C24×C11—21no—
294C23×D11—21no—
295C23×D11—22no—
296C23×D11—22no—
297C23×D11—44no—
298C23×D11—84no—
299C23×D11C2×D411yescharacteristic
300C11×#41—22no—
301C11×#41—22no—
302C11×#41—41no—
303C11×#41—41no—
304C11×#41—41no—
305C11×#41—41no—
306C11×#41—41no—
307C11×#41—41no—
308C11×#41—44no—
309C2×Q8×C11—21no—
310C2×Q8×C11—41no—
311C2×Q8×C11—41no—
312C2×Q8×C11C2×D411yescharacteristic
313C2×Q8×C11C2411yescharacteristic
314C2×Q8×C11C2412yes—
315C2×D4×C11—22no—
316C2×D4×C11—22no—
317C2×D4×C11—22no—
318C2×D4×C11—22no—
319C2×D4×C11—21no—
320C2×D4×C11—21no—
321C2×D4×C11—21no—
322C2×D4×C11—21no—
323C2×D4×C11—21no—
324C2×D4×C11—21no—
325C2×D4×C11—41no—
326C2×D4×C11—41no—
327C2×D4×C11—44no—
328C2×D4×C11—44no—
329C2×D4×C11—44no—
330C2×D4×C11C2×D411yescharacteristic
331C2×D4×C11C2×D411yescharacteristic
332C2×D4×C11C2×D411yescharacteristic
333C2×D4×C11C2411yescharacteristic
334C2×D4×C11C2411yescharacteristic
335C2×D4×C11C2411yescharacteristic
336C22×C4×C11—21no—
337C22×C4×C11—21no—
338C22×C4×C11—21no—
339C22×C4×C11—21no—
340C22×C4×C11C2411yescharacteristic
341C22×C4×C11C2411yescharacteristic
342C22×C4×C11C2411yescharacteristic
343C2×C22⋊D11—22no—
344C2×C22⋊D11—22no—
345C2×C22⋊D11—22no—
346C2×C22⋊D11—22no—
347C2×C22⋊D11—22no—
348C2×C22⋊D11—22no—
349C2×C22⋊D11—22no—
350C2×C22⋊D11—44no—
351C2×C22⋊D11—84no—
352C2×C22⋊D11—84no—
353C2×C22⋊D11C2×D412yes—
354C2×C22⋊D11C2×D412yes—
355C22×Dic11—22no—
356C22×Dic11—22no—
357C22×Dic11—21no—
358C22×Dic11C2×D411yescharacteristic
359Q8×D11—42no—
360Q8×D11—42no—
361D4×D11—24no—
362D4×D11—24no—
363D4×D11—42no—
364D4×D11—42no—
365D4×D11—48no—
366C2×D44—21no—
367C2×D44—41no—
368C2×D44—41no—
369C2×D44C2412yes—
370C2×C4×D11—22no—
371C2×C4×D11—22no—
372C2×C4×D11—41no—
373C2×C4×D11—41no—
374C2×C4×D11C2×D412yes—
375C2×C4×D11C2412yes—
376C2×Dic22—22no—
377C2×Dic22—21no—
378C2×Dic22—41no—
379C2×Dic22—41no—
380C2×Dic22C2412yes—
381C11×Q16—42no—
382C11×SD16—24no—
383C11×SD16—24no—
384C11×SD16—42no—
385C11×M16—41no—
386C2×C8×C11—41no—
387C2×C8×C11C2412yes—
388C2×C8×C11C2412yes—
389C11×C4⋊C4—22no—
390C11×C4⋊C4—22no—
391C11×C4⋊C4C2412yes—
392C11×C22⋊C4—22no—
393C11×C22⋊C4—22no—
394C11×C22⋊C4—21no—
395C42×C11—21no—
396C22⋊Dic11—22no—
397C22⋊Dic11—22no—
398C22⋊Dic11—22no—
399C22⋊Dic11—22no—
400C22⋊Dic11—21no—
401C22⋊Dic11—22no—
402C22⋊Dic11—21no—
403C22⋊Dic11C2×D412yes—
404C22⋊Dic11C2×D411yescharacteristic
405C22⋊Dic11C2×D411yescharacteristic
406C22⋊Dic11C2×D412yes—
407#4326—42no—
408#4325—42no—
409#4325—42no—
410#4324—24no—
411#4324—24no—
412#4324—42no—
413(C2×D11)⋊C4—22no—
414(C2×D11)⋊C4—22no—
415(C2×D11)⋊C4—22no—
416(C2×D11)⋊C4—22no—
417(C2×D11)⋊C4—22no—
418(C2×D11)⋊C4—22no—
419(C2×D11)⋊C4—22no—
420(C2×D11)⋊C4C2×D412yes—
421(C2×D11)⋊C4C2×D412yes—
422C4⋊Dic11—22no—
423C4⋊Dic11—22no—
424C4⋊Dic11—22no—
425C4⋊Dic11C2×D412yes—
426C4⋊Dic11C2412yes—
427C4⋊Dic11C2412yes—
428Dic11⋊C4—22no—
429Dic11⋊C4—22no—
430Dic11⋊C4—22no—
431Dic11⋊C4—22no—
432Dic11⋊C4—22no—
433Dic11⋊C4—22no—
434Dic11⋊C4—22no—
435Dic11⋊C4—22no—
436Dic11⋊C4—22no—
437Dic11⋊C4C2×D412yes—
438Dic11⋊C4C2×D412yes—
439C4×Dic11—22no—
440C4×Dic11—22no—
441C4×Dic11—21no—
442C4×Dic11—21no—
443C4×Dic11C2412yes—
444#4318—41no—
445C2×C11⋊C8—41no—
446C2×C11⋊C8C2412yes—
447C2×C11⋊C8C2412yes—
448#4314—42no—
449#4314—42no—
450C8×D11—42no—
451C8×D11—42no—
452#3538—111no—
453#3484—111no—
454#3310—112no—
455#3310—112no—
456#3296—112no—
457#3296—112no—
458D4×SD16—112no—
459D4×SD16—112no—
460#3266—112no—
461#3266—112no—
462#3222—112no—
463#3200—111no—
464#3200—111no—
465#3190—112no—
466#3123—112no—
467#3009—111no—
468#3009D1111yescharacteristic, complemented
469C2×#450—112no—
470#2977—111no—
471C23×C11—24no—
472C23×C11—21no—
473C23×C11—21no—
474C23×C11—21no—
475C23×C11—42no—
476C23×C11—42no—
477C23×C11—82no—
478C23×C11—82no—
479C23×C11—82no—
480C23×C11C22×D411yescharacteristic
481C23×C11C22×D411yescharacteristic
482C23×C11C22×D411yescharacteristic
483C22×D11—24no—
484C22×D11—22no—
485C22×D11—41no—
486C22×D11—44no—
487C22×D11—44no—
488C22×D11—42no—
489C22×D11—44no—
490C22×D11—44no—
491C22×D11—82no—
492C22×D11—82no—
493C22×D11—82no—
494C22×D11—816no—
495C22×D11C22×D412yes—
496Q8×C11—22no—
497Q8×C11—22no—
498Q8×C11—21no—
499Q8×C11—21no—
500Q8×C11—41no—
501Q8×C11—81no—
502D4×C11—24no—
503D4×C11—21no—
504D4×C11—21no—
505D4×C11—21no—
506D4×C11—21no—
507D4×C11—41no—
508D4×C11—41no—
509D4×C11—41no—
510D4×C11—42no—
511D4×C11—42no—
512D4×C11—42no—
513D4×C11—42no—
514D4×C11—42no—
515D4×C11H(5,𝔽2)12yes—
516D4×C11H(5,𝔽2)12yes—
517C2×C4×C11—21no—
518C2×C4×C11—21no—
519C2×C4×C11—21no—
520C2×C4×C11—21no—
521C2×C4×C11—21no—
522C2×C4×C11—21no—
523C2×C4×C11—22no—
524C2×C4×C11—22no—
525C2×C4×C11—21no—
526C2×C4×C11—42no—
527C2×C4×C11—42no—
528C2×C4×C11—42no—
529C2×C4×C11—81no—
530C2×C4×C11C22×D411yescharacteristic
531C2×C4×C11C22×D411yescharacteristic
532C2×C4×C11C22×D411yescharacteristic
533C2×C4×C11C2511yescharacteristic
534C22⋊D11—24no—
535C22⋊D11—24no—
536C22⋊D11—44no—
537C22⋊D11—44no—
538C22⋊D11—44no—
539C22⋊D11—82no—
540C22⋊D11—82no—
541C22⋊D11—82no—
542C22⋊D11—82no—
543C2×Dic11—22no—
544C2×Dic11—22no—
545C2×Dic11—22no—
546C2×Dic11—41no—
547C2×Dic11—82no—
548C2×Dic11—82no—
549C2×Dic11—81no—
550C2×Dic11C22×D412yes—
551C2×Dic11C22×D412yes—
552C2×Dic11C22×D412yes—
553D44—22no—
554D44—22no—
555D44—42no—
556C4×D11—22no—
557C4×D11—22no—
558C4×D11—42no—
559C4×D11—44no—
560C4×D11—82no—
561Dic22—22no—
562Dic22—22no—
563Dic22—82no—
564Dic22—81no—
565C8×C11—22no—
566C8×C11—22no—
567C11⋊C8—22no—
568C11⋊C8—22no—
569C2×H(5,𝔽2)C2×D1111yescharacteristic
570C23×D4—111no—
571C2×#137—111no—
572C2×#137C2×D1111yescharacteristic, complemented
573C22×SD16—111no—
574C22×SD16—112no—
575C22×SD16—112no—
576C22×SD16C2×D1111yescharacteristic, complemented
577#563—221no—
578#563—221no—
579#552—112no—
580#552—112no—
581#551—221no—
582#551—221no—
583D4×Q8—112no—
584D4×Q8—112no—
585#546—112no—
586#546—112no—
587#546—222no—
588D42—112no—
589D42—112no—
590D42—222no—
591#544—222no—
592#541—112no—
593#539—222no—
594#536—111no—
595#536C2×D1111yescharacteristic, complemented
596#535—111no—
597#535—111no—
598#534—221no—
599#534—221no—
600#525—111no—
601#525—111no—
602C2×C22⋊Q8—112no—
603C2×#120—221no—
604C2×#120—221no—
605#518—111no—
606#497—112no—
607#492—112no—
608#490—112no—
609#488—112no—
610#485—112no—
611#485—112no—
612#483—112no—
613#482—112no—
614#482—112no—
615#480—112no—
616#478—112no—
617#478—112no—
618#468—112no—
619#468—112no—
620#467—112no—
621#467—112no—
622#465—112no—
623#465—112no—
624#465—112no—
625#465—112no—
626#464—112no—
627#464—112no—
628#461—112no—
629#461—112no—
630#460—112no—
631#460—112no—
632#452—112no—
633#452—112no—
634#452C2×D1112yescomplemented
635#452C2×D1112yescomplemented
636#451—112no—
637#450—112no—
638#450—112no—
639#450—112no—
640#450—112no—
641#450—112no—
642#450—112no—
643#450—112no—
644#450—112no—
645#450C2×D1112yes—
646#450C2×D1112yescomplemented
647#448—112no—
648#448—112no—
649#448—112no—
650#440—112no—
651#440—112no—
652C4×SD16—112no—
653C4×SD16—112no—
654#435—112no—
655#435—112no—
656C8×D4—112no—
657C8×D4—112no—
658#433—112no—
659#418—111no—
660#418C2×D1111yescharacteristic, complemented
661#416—111no—
662#416C2×D1111yescharacteristic, complemented
663C2×#102—112no—
664C2×#102—112no—
665#408—111no—
666#408C2×D1111yescharacteristic, complemented
667C2×C22⋊C8—112no—
668C22×C11—21no—
669C22×C11—21no—
670C22×C11—21no—
671C22×C11—22no—
672C22×C11—22no—
673C22×C11—22no—
674C22×C11—22no—
675C22×C11—22no—
676C22×C11—42no—
677C22×C11—42no—
678C22×C11—41no—
679C22×C11—42no—
680C22×C11—84no—
681C22×C11—162no—
682C22×C11—162no—
683C22×C11C23×D411yescharacteristic
684C2×D11—22no—
685C2×D11—22no—
686C2×D11—44no—
687C2×D11—42no—
688C2×D11—42no—
689C2×D11—42no—
690C2×D11—88no—
691C2×D11—88no—
692C2×D11—84no—
693C2×D11#57714yes—
694C4×C11—21no—
695C4×C11—21no—
696C4×C11—21no—
697C4×C11—41no—
698C4×C11—42no—
699C4×C11—42no—
700C4×C11C2×H(5,𝔽2)11yescharacteristic
701C4×C11C2×H(5,𝔽2)11yescharacteristic
702Dic11—22no—
703Dic11—22no—
704Dic11—22no—
705Dic11—42no—
706Dic11—42no—
707Dic11—42no—
708C25—221no—
709H(5,𝔽2)—42no—
710H(5,𝔽2)—42no—
711C2×#41—21no—
712C2×#41C22×D1111yescharacteristic
713C2×#41C22×D1111yescharacteristic
714C2×#41C22×D1111yescharacteristic
715C2×#41C22×D1111yescharacteristic
716C22×Q8—112no—
717C22×Q8—111no—
718C22×Q8C22×D1111yescharacteristic, complemented
719C22×D4—21no—
720C22×D4—21no—
721C22×D4—21no—
722C22×D4—112no—
723C22×D4—112no—
724C22×D4—111no—
725C22×D4—222no—
726C22×D4—221no—
727C22×D4—222no—
728C22×D4—222no—
729C22×D4—442no—
730C22×D4—442no—
731C22×D4C22×D1111yescharacteristic
732C22×D4C22×D1111yescharacteristic
733C22×D4C22×D1111yescharacteristic
734C23×C4—111no—
735#137—42no—
736#137—442no—
737C2×Q16—112no—
738C2×Q16C22×D1112yescomplemented
739C2×SD16—42no—
740C2×SD16—112no—
741C2×SD16—112no—
742C2×SD16—112no—
743C2×SD16—112no—
744C2×SD16—112no—
745C2×SD16—112no—
746C2×SD16—112no—
747C2×SD16—444no—
748C2×SD16—444no—
749C2×SD16—442no—
750C2×SD16C22×D1112yes—
751C2×SD16C22×D1112yes—
752C2×SD16C22×D1112yescomplemented
753C2×M16—111no—
754C2×M16C22×D1111yescharacteristic, complemented
755C22×C8—111no—
756C22×C8—112no—
757C22×C8—112no—
758C22×C8C22×D1111yescharacteristic, complemented
759C4⋊Q8—21no—
760C4⋊Q8—112no—
761C4⋊Q8—222no—
762C4⋊Q8—222no—
763C4⋊Q8—221no—
764#127—112no—
765#127—221no—
766#126—222no—
767#126—222no—
768#126—222no—
769#126—222no—
770#125—112no—
771#125—222no—
772#125—222no—
773#125—222no—
774#125—222no—
775#124—21no—
776#124—112no—
777#124—221no—
778#124—221no—
779#123—21no—
780#123—21no—
781#123—111no—
782#123—111no—
783#123—222no—
784#123—222no—
785#123—222no—
786#123—222no—
787#123—221no—
788#123—221no—
789#123—221no—
790C22⋊Q8—112no—
791C22⋊Q8—112no—
792C22⋊Q8—112no—
793C22⋊Q8—112no—
794C22⋊Q8—112no—
795C22⋊Q8—112no—
796C22⋊Q8—222no—
797C22⋊Q8—222no—
798C22⋊Q8—222no—
799C22⋊Q8—222no—
800C22⋊Q8—222no—
801C22⋊Q8—222no—
802C22⋊Q8C22×D1112yes—
803C22⋊Q8C22×D1112yescomplemented
804#121—112no—
805#121—112no—
806#121—112no—
807#121—112no—
808#121—222no—
809#121—222no—
810#121—222no—
811#121—222no—
812#121—222no—
813#120—111no—
814#120—111no—
815#120—221no—
816#120—221no—
817#120—222no—
818#120—222no—
819#120—222no—
820#120—222no—
821#120—222no—
822#120—222no—
823#120—221no—
824#120—221no—
825#120—221no—
826C4×Q8—112no—
827C4×Q8—112no—
828C4×D4—112no—
829C4×D4—112no—
830C4×D4—112no—
831C4×D4—112no—
832C4×D4—222no—
833C4×D4—222no—
834C4×D4—222no—
835C4×D4—222no—
836#117—111no—
837#117—111no—
838#117—111no—
839#117—222no—
840#117—222no—
841#117C22×D1111yescharacteristic, complemented
842C2×C4⋊C4—112no—
843C2×C4⋊C4—222no—
844C2×C22⋊C4—222no—
845C2×C22⋊C4—222no—
846C2×C22⋊C4—222no—
847C2×C22⋊C4—221no—
848C2×C22⋊C4—221no—
849#107—112no—
850#107—112no—
851#106—112no—
852#106—112no—
853C4⋊C8—112no—
854C4⋊C8—112no—
855#103—112no—
856#103—112no—
857#103—112no—
858#103—112no—
859#103—112no—
860#103C22×D1112yescomplemented
861#102—112no—
862#102—112no—
863#102—112no—
864#102—112no—
865#102—112no—
866#102—112no—
867#102—112no—
868#102C22×D1112yes—
869#102C22×D1112yes—
870#102C22×D1112yescomplemented
871C22⋊C8—112no—
872C22⋊C8—112no—
873C22⋊C8—112no—
874C22⋊C8—112no—
875C22⋊C8C22×D1112yes—
876C22⋊C8C22×D1112yescomplemented
877#97—112no—
878C4×C8—112no—
879C2×C11—41no—
880C2×C11—42no—
881C2×C11—42no—
882C2×C11—41no—
883C2×C11—41no—
884C2×C11—81no—
885C2×C11#348411yescharacteristic
886C2×C11C2×#57712yes—
887D11—24no—
888D11—82no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—111no—
893C24—222no—
894C24—222no—
895C24—221no—
896C24—444no—
897C24—884no—
898#41—22no—
899#41—22no—
900#41—41no—
901#41—41no—
902#41—41no—
903#41—41no—
904#41—41no—
905#41—41no—
906#41—44no—
907C2×Q8—21no—
908C2×Q8—41no—
909C2×Q8—41no—
910C2×Q8—112no—
911C2×Q8—222no—
912C2×Q8—221no—
913C2×Q8—441no—
914C2×Q8—441no—
915C2×Q8—442no—
916C2×Q8—442no—
917C2×Q8D4×D1111yescharacteristic
918C2×Q8C23×D1111yescharacteristic
919C2×Q8C23×D1112yes—
920C2×D4—22no—
921C2×D4—22no—
922C2×D4—22no—
923C2×D4—22no—
924C2×D4—21no—
925C2×D4—21no—
926C2×D4—21no—
927C2×D4—21no—
928C2×D4—21no—
929C2×D4—21no—
930C2×D4—41no—
931C2×D4—41no—
932C2×D4—44no—
933C2×D4—44no—
934C2×D4—44no—
935C2×D4—112no—
936C2×D4—112no—
937C2×D4—112no—
938C2×D4—222no—
939C2×D4—222no—
940C2×D4—222no—
941C2×D4—222no—
942C2×D4—224no—
943C2×D4—224no—
944C2×D4—222no—
945C2×D4—222no—
946C2×D4—222no—
947C2×D4—221no—
948C2×D4—441no—
949C2×D4—441no—
950C2×D4—442no—
951C2×D4—442no—
952C2×D4—448no—
953C2×D4—444no—
954C2×D4—884no—
955C2×D4—884no—
956C2×D4D4×D1111yescharacteristic
957C2×D4D4×D1111yescharacteristic
958C2×D4D4×D1111yescharacteristic
959C2×D4C23×D1111yescharacteristic
960C2×D4C23×D1111yescharacteristic
961C2×D4C23×D1111yescharacteristic
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—111no—
967C22×C4—112no—
968C22×C4—112no—
969C22×C4—222no—
970C22×C4—222no—
971C22×C4—222no—
972C22×C4—222no—
973C22×C4—221no—
974C22×C4—441no—
975C22×C4—441no—
976C22×C4C23×D1111yescharacteristic
977C22×C4C23×D1111yescharacteristic
978C22×C4C23×D1111yescharacteristic
979Q16—42no—
980Q16—442no—
981SD16—24no—
982SD16—24no—
983SD16—42no—
984SD16—224no—
985SD16—224no—
986SD16—442no—
987SD16—442no—
988SD16—442no—
989SD16—442no—
990SD16—442no—
991M16—41no—
992M16—441no—
993C2×C8—41no—
994C2×C8—112no—
995C2×C8—112no—
996C2×C8—442no—
997C2×C8—442no—
998C2×C8—441no—
999C2×C8C23×D1112yes—
1000C2×C8C23×D1112yes—
1001C4⋊C4—22no—
1002C4⋊C4—22no—
1003C4⋊C4—112no—
1004C4⋊C4—112no—
1005C4⋊C4—112no—
1006C4⋊C4—112no—
1007C4⋊C4—112no—
1008C4⋊C4—222no—
1009C4⋊C4—222no—
1010C4⋊C4—222no—
1011C4⋊C4—222no—
1012C4⋊C4—222no—
1013C4⋊C4—222no—
1014C4⋊C4—222no—
1015C4⋊C4—222no—
1016C4⋊C4—222no—
1017C4⋊C4—222no—
1018C4⋊C4—222no—
1019C4⋊C4—222no—
1020C4⋊C4C23×D1112yes—
1021C22⋊C4—22no—
1022C22⋊C4—21no—
1023C22⋊C4—22no—
1024C22⋊C4—111no—
1025C22⋊C4—111no—
1026C22⋊C4—112no—
1027C22⋊C4—112no—
1028C22⋊C4—112no—
1029C22⋊C4—112no—
1030C22⋊C4—222no—
1031C22⋊C4—222no—
1032C22⋊C4—222no—
1033C22⋊C4—222no—
1034C22⋊C4—222no—
1035C22⋊C4—222no—
1036C22⋊C4—222no—
1037C22⋊C4—222no—
1038C22⋊C4—221no—
1039C22⋊C4—222no—
1040C22⋊C4—221no—
1041C22⋊C4—222no—
1042C22⋊C4—222no—
1043C22⋊C4—222no—
1044C42—21no—
1045C42—112no—
1046C42—222no—
1047C42—222no—
1048C42—221no—
1049C42—221no—
1050C11#6163111yescharacteristic, complemented, Sylow
1051C23—24no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—42no—
1056C23—42no—
1057C23—82no—
1058C23—82no—
1059C23—82no—
1060C23—112no—
1061C23—224no—
1062C23—222no—
1063C23—441no—
1064C23—444no—
1065C23—444no—
1066C23—442no—
1067C23—444no—
1068C23—444no—
1069C23—882no—
1070C23—882no—
1071C23—882no—
1072C23—8816no—
1073C23C2×D4×D1111yescharacteristic
1074C23C2×D4×D1111yescharacteristic
1075C23C2×D4×D1111yescharacteristic
1076Q8—22no—
1077Q8—22no—
1078Q8—21no—
1079Q8—21no—
1080Q8—41no—
1081Q8—81no—
1082Q8—222no—
1083Q8—222no—
1084Q8—881no—
1085Q8—882no—
1086D4—24no—
1087D4—21no—
1088D4—21no—
1089D4—21no—
1090D4—21no—
1091D4—41no—
1092D4—41no—
1093D4—41no—
1094D4—42no—
1095D4—42no—
1096D4—42no—
1097D4—42no—
1098D4—42no—
1099D4—224no—
1100D4—224no—
1101D4—222no—
1102D4—222no—
1103D4—442no—
1104D4—444no—
1105D4—444no—
1106D4—444no—
1107D4—882no—
1108D4—882no—
1109D4—882no—
1110D4—882no—
1111D4#6703712yes—
1112D4#6703712yes—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—21no—
1122C2×C4—42no—
1123C2×C4—42no—
1124C2×C4—42no—
1125C2×C4—81no—
1126C2×C4—112no—
1127C2×C4—112no—
1128C2×C4—112no—
1129C2×C4—222no—
1130C2×C4—222no—
1131C2×C4—222no—
1132C2×C4—222no—
1133C2×C4—222no—
1134C2×C4—442no—
1135C2×C4—444no—
1136C2×C4—441no—
1137C2×C4—882no—
1138C2×C4—882no—
1139C2×C4—882no—
1140C2×C4—881no—
1141C2×C4C2×D4×D1111yescharacteristic
1142C2×C4C2×D4×D1111yescharacteristic
1143C2×C4C2×D4×D1111yescharacteristic
1144C2×C4C24×D1111yescharacteristic
1145C8—22no—
1146C8—22no—
1147C8—222no—
1148C8—222no—
1149C22—21no—
1150C22—21no—
1151C22—21no—
1152C22—22no—
1153C22—22no—
1154C22—22no—
1155C22—22no—
1156C22—22no—
1157C22—42no—
1158C22—42no—
1159C22—41no—
1160C22—42no—
1161C22—84no—
1162C22—114no—
1163C22—162no—
1164C22—162no—
1165C22—222no—
1166C22—222no—
1167C22—444no—
1168C22—442no—
1169C22—442no—
1170C22—442no—
1171C22—888no—
1172C22—888no—
1173C22—884no—
1174C22C22×D4×D1111yescharacteristic
1175C4—21no—
1176C4—21no—
1177C4—21no—
1178C4—41no—
1179C4—42no—
1180C4—42no—
1181C4—222no—
1182C4—222no—
1183C4—222no—
1184C4—442no—
1185C4—442no—
1186C4—442no—
1187C4C2×#6703711yescharacteristic
1188C4C2×#6703711yescharacteristic
1189C2—41no—
1190C2—41no—
1191C2—41no—
1192C2—42no—
1193C2—42no—
1194C2—81no—
1195C2—224no—
1196C2—882no—
1197C2#1308224511yescharacteristic
1198C2D11×#57712yes—
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3009C2
socleC22×C11C23×D4
prime radical#13082247C2
hypercenter#3009D11
hypocenterC11#61631
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3009

Complements

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

NH ≅ G/Ntype
1. #13082859C2semidirect
3. #13080638C2semidirect
4. #13080630C2semidirect
5. #13080452C2semidirect
6. #13080444C2semidirect
7. #13080310C2semidirect
8. SD16×C22⋊D11C2semidirect
9. #13080124C2semidirect
10. #13080120C2semidirect
11. #13079686C2semidirect
12. #13079489C2semidirect
13. #13079483C2semidirect
14. #13079395C2semidirect
15. #13078862C2semidirect
16. #13077893C2semidirect
17. D11×#450C2semidirect
18. #13077668C2semidirect
19. C11×#3009C2semidirect
22. C2×C11×#137C22semidirect
23. C22×C11×SD16C22semidirect
24. C11×#536C22semidirect
32. #10623356C22semidirect
33. C2×#67004C22semidirect
34. Q8×C22⋊D11C22semidirect
43. C22×#4324C22semidirect
44. C2×SD16×D11C22semidirect
45. C2×SD16×D11C22semidirect
52. #10623170C22semidirect
53. #10623163C22semidirect
54. D11×C22⋊Q8C22semidirect
55. #10623156C22semidirect
56. #10623060C22semidirect
57. C11×#452C22semidirect
58. C11×#452C22semidirect
60. C11×#450C22semidirect
61. C11×#418C22semidirect
62. C11×#416C22semidirect
63. C11×#408C22semidirect
64. #10622852C22semidirect
65. #10622852C22semidirect
66. #10622847C22semidirect
67. #10622846C22semidirect
68. #10622840C22semidirect
70. #10622831C22semidirect
71. #10622828C22semidirect
72. #10622803C22semidirect
73. #10622801C22semidirect
74. #10622799C22semidirect
75. #10622798C22semidirect
76. #10622788C22semidirect
77. #10622784C22semidirect
78. #10622783C22semidirect
79. #10622782C22semidirect
80. #10622782C22semidirect
81. #10622777C22semidirect
82. #10622776C22semidirect
83. #10622775C22semidirect
84. #10622775C22semidirect
85. SD16×Dic11C22semidirect
86. #10622747C22semidirect
87. #10622740C22semidirect
88. #10622727C22semidirect
89. C8×C22⋊D11C22semidirect
90. #10622662C22semidirect
91. #10622661C22semidirect
92. #10622659C22semidirect
93. #10622658C22semidirect
94. #10622616C22semidirect
95. #10622426C22semidirect
96. #10622418C22semidirect
97. #10622413C22semidirect
98. #10622411C22semidirect
99. #10622391C22semidirect
100. #10622389C22semidirect
101. #10622389C22semidirect
102. #10622387C22semidirect
103. D11×#102C22semidirect
104. D11×#102C22semidirect
105. #10622379C22semidirect
106. #10622377C22semidirect
107. #10622376C22semidirect
108. #10622375C22semidirect
109. #10622371C22semidirect
110. #10622370C22semidirect
111. #10622351C22semidirect
112. #10622350C22semidirect
113. #10622344C22semidirect
114. #10622341C22semidirect
115. (C22⋊D11)⋊C8C22semidirect
116. D11×C22⋊C8C22semidirect
117. #10622336C22semidirect
118. #10622333C22semidirect
127. C22×Q8×C11C23semidirect
145. C22×Dic22C23semidirect
147. C2×C11×Q16C23semidirect
151. C2×C11×SD16C23semidirect
152. C2×C11×M16C23semidirect
153. C22×C8×C11C23semidirect
159. C11×C22⋊Q8C23semidirect
160. C11×#117C23semidirect
172. Q8×Dic11C23semidirect
175. #66997C23semidirect
176. C2×#4326C23semidirect
210. C2×#4324C23semidirect
224. #66979C23semidirect
227. #66977C23semidirect
228. C2×#4318C23semidirect
229. C22×C11⋊C8C23semidirect
243. #66943C23semidirect
247. #66940C23semidirect
260. C11×#103C23semidirect
263. C11×#102C23semidirect
265. C11×C22⋊C8C23semidirect
266. #66899C23semidirect
267. #66899C23semidirect
268. #66899C23semidirect
271. #66896C23semidirect
273. C22⋊(C11⋊C8)C23semidirect
278. #66882C23semidirect
279. #66881C23semidirect
280. #66880C23semidirect
281. #66880C23semidirect
282. #66879C23semidirect
283. Dic11⋊C8C23semidirect
284. Dic11⋊C8C23semidirect
285. C8×Dic11C23semidirect
288. #66872C23semidirect
289. #66871C23semidirect
468. #3009D11semidirect
572. C2×#137C2×D11semidirect
576. C22×SD16C2×D11semidirect
595. #536C2×D11semidirect
634. #452C2×D11semidirect
635. #452C2×D11semidirect
646. #450C2×D11semidirect
660. #418C2×D11semidirect
662. #416C2×D11semidirect
666. #408C2×D11semidirect
718. C22×Q8C22×D11semidirect
738. C2×Q16C22×D11semidirect
752. C2×SD16C22×D11semidirect
754. C2×M16C22×D11semidirect
758. C22×C8C22×D11semidirect
803. C22⋊Q8C22×D11semidirect
841. #117C22×D11semidirect
860. #103C22×D11semidirect
870. #102C22×D11semidirect
876. C22⋊C8C22×D11semidirect
1050. C11#61631semidirect

Maximal subgroups

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

subgroupindex
#130828592
#130822472
#130806382
#130806302
#130804522
#130804442
#130803102
SD16×C22⋊D112
#130801242
#130801202
#130796862
#130794892
#130794832
#130793952
#130788622
#130778932
D11×#4502
#130776682
C11×#30092
#6163111