Finite Group Databasebeta

← #14759632

Subgroups — #14759632

Order 2816.

1320 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623281C211yesmaximal, characteristic, complemented
2#13077830C211yesmaximal, characteristic
3C2×#10622757C211yesmaximal, characteristic, complemented
4#13077317C211yesmaximal, characteristic, complemented
5#13068945C211yesmaximal, characteristic, complemented
6#13068940C211yesmaximal, characteristic, complemented
7#13068915C211yesmaximal, characteristic, complemented
8#13068889C211yesmaximal, characteristic, complemented
9#13068888C211yesmaximal, characteristic, complemented
10#13068819C211yesmaximal, characteristic, complemented
11#13068558C211yesmaximal, characteristic, complemented
12#13068460C211yesmaximal, characteristic, complemented
13#13068451C211yesmaximal, characteristic, complemented
14#13068401C211yesmaximal, characteristic, complemented
15C2×C11×#444C211yesmaximal, characteristic, complemented
16C2×#41×D11C2211yescharacteristic
17C2×C11×#135C2211yescharacteristic
18C2×C11×#131C2211yescharacteristic
19C2×C11×#131C2211yescharacteristic, complemented
20#10623359C2211yescharacteristic
21C2×#67003C2211yescharacteristic
22C2×#67001C2211yescharacteristic
23#10623281—24no—
24#10623281—24no—
25C2×#66960—21no—
26C2×#66960C2211yescharacteristic
27C2×M16×D11—21no—
28C2×M16×D11C2211yescharacteristic
29C2×#66954—21no—
30C2×#66954C2211yescharacteristic
31C22×#4313—21no—
32C22×#4313C2211yescharacteristic
33C11×#444—24no—
34C2×C11×#108C2211yescharacteristic, complemented
35C2×C11×#104C2211yescharacteristic
36C2×C11×#104C2211yescharacteristic, complemented
37C2×C11×#97C2211yescharacteristic, complemented
38C2×#66901C2211yescharacteristic
39C2×#66901C2211yescharacteristic, complemented
40#10622847C2211yescharacteristic, complemented
41#10622846C2211yescharacteristic
42#10622800C411yescharacteristic, complemented
43#10622799C411yescharacteristic, complemented
44#10622786C411yescharacteristic, complemented
45#10622785C411yescharacteristic, complemented
46#10622783C411yescharacteristic, complemented
47#10622782C411yescharacteristic, complemented
48#10622771C411yescharacteristic, complemented
49#10622769C411yescharacteristic, complemented
50#10622757—24no—
51C2×#66889C2211yescharacteristic
52#10622741—21no—
53#10622741—21no—
54#10622739C2211yescharacteristic
55C2×#66886C2211yescharacteristic, complemented
56#10622732C2211yescharacteristic, complemented
57#10622726C2211yescharacteristic
58#10622724—21no—
59#10622724—21no—
60C2×(C2×D11)⋊C8C2211yescharacteristic
61#10622714C2211yescharacteristic, complemented
62C2×C8×Dic11C2211yescharacteristic, complemented
63C4×(C2×D11)⋊C4C2211yescharacteristic
64C2×#66869C2211yescharacteristic
65#10622196C2211yescharacteristic, complemented
66#10622193C2211yescharacteristic, complemented
67#10622190C2211yescharacteristic, complemented
68#10622188C2211yescharacteristic, complemented
69#10622162C2211yescharacteristic, complemented
70#10622161C2211yescharacteristic, complemented
71C2×C11×#41C2311yescharacteristic
72C2×C11×#41C2311yescharacteristic
73#41×D11—22no—
74#41×D11—22no—
75#41×D11—22no—
76#41×D11—22no—
77C2×#4343C2×C411yescharacteristic
78C2×Q8×D11C2×C411yescharacteristic
79C2×#4341—21no—
80C2×#4341C2×C411yescharacteristic
81C2×D4×D11—21no—
82C2×D4×D11C2×C411yescharacteristic
83C2×#4339—21no—
84C2×#4339C2311yescharacteristic
85C22×C4×D11—21no—
86C22×C4×D11C2311yescharacteristic
87C11×#135—22no—
88C11×#135—22no—
89C2×C11×Q16C2×C411yescharacteristic
90C2×C11×SD16C2×C411yescharacteristic
91C2×C11×SD16C2×C411yescharacteristic
92C2×C11×D8C2×C411yescharacteristic
93C11×#131—22no—
94C11×#131—22no—
95C11×#131—22no—
96C11×#131D414yescomplemented
97C2×C11×M16—21no—
98C2×C11×M16—21no—
99C2×C11×M16C2311yescharacteristic
100C2×C11×M16C2311yescharacteristic
101C22×C8×C11—21no—
102C22×C8×C11—21no—
103C22×C8×C11C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C2×C42×C11C2311yescharacteristic
106#67003—22no—
107#67003—22no—
108#67001—22no—
109#67001—22no—
110#66999C2×C411yescharacteristic
111#66999C2×C411yescharacteristic
112C2×#4326C2×C411yescharacteristic
113C2×#4325C2×C411yescharacteristic
114#66991C2×C411yescharacteristic
115#66991C2×C411yescharacteristic
116#66990—21no—
117#66988—21no—
118C2×#4324C2×C411yescharacteristic
119C2×#4323C2×C411yescharacteristic
120C4×C22⋊D11—21no—
121C4×C22⋊D11—21no—
122C2×(C2×D11)⋊C4—21no—
123#66979C2311yescharacteristic
124C2×C4×Dic11C2311yescharacteristic
125C2×#4318—21no—
126C2×#4318C2311yescharacteristic
127C2×#4318C2311yescharacteristic
128C22×C11⋊C8—21no—
129C22×C11⋊C8C2311yescharacteristic
130C22×C11⋊C8C2311yescharacteristic
131#66960—28no—
132#66960—22no—
133#66960—22no—
134M16×D11—28no—
135M16×D11—22no—
136M16×D11—22no—
137#66954—28no—
138#66954—22no—
139#66954D414yescomplemented
140C2×#4313—28no—
141C2×#4313—21no—
142C2×#4313—21no—
143C2×#4313—22no—
144C2×#4313—22no—
145C2×#4313—21no—
146C2×#4313D411yescharacteristic
147C2×#4313D411yescharacteristic
148C2×#4313D411yescharacteristic
149C2×#4313D411yescharacteristic
150C2×C8×D11—21no—
151C2×C8×D11—21no—
152C2×C8×D11—21no—
153C11×#108—22no—
154C11×#104—22no—
155C11×#104—22no—
156C11×#97—22no—
157#66901—22no—
158#66901—22no—
159#66899C2×C411yescharacteristic
160#66899C2×C411yescharacteristic
161#66896C2×C411yescharacteristic
162#66896C2×C411yescharacteristic
163C11⋊#95—21no—
164C22⋊(C11⋊C8)—21no—
165C22⋊(C11⋊C8)—21no—
166#66889—22no—
167#66886—22no—
168#66885C2×C411yescharacteristic
169#66885C2×C411yescharacteristic
170(C2×D11)⋊C8—21no—
171(C2×D11)⋊C8—21no—
172(C2×D11)⋊C8C2×C411yescharacteristic
173(C2×D11)⋊C8C2×C411yescharacteristic
174(C2×D11)⋊C8C2×C411yescharacteristic
175(C2×D11)⋊C8C2×C411yescharacteristic
176#66880C2×C411yescharacteristic
177#66880C2×C411yescharacteristic
178#66879—21no—
179Dic11⋊C8—21no—
180Dic11⋊C8—21no—
181C8×Dic11—21no—
182C8×Dic11—22no—
183#66869—22no—
184#21468—111nomaximal, Sylow
185C23×D11—21no—
186C23×D11#4111yescharacteristic
187C11×#41—21no—
188C11×#41—21no—
189C11×#41—21no—
190C11×#41—21no—
191C11×#41—21no—
192C11×#41—21no—
193C11×#41C2×D412yes—
194C11×#41#4112yes—
195C2×Q8×C11C22×C411yescharacteristic
196C2×Q8×C11C22×C411yescharacteristic
197C2×D4×C11—21no—
198C2×D4×C11—21no—
199C2×D4×C11C22×C411yescharacteristic
200C2×D4×C11C22×C411yescharacteristic
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11C2411yescharacteristic
205C2×C22⋊D11—21no—
206C2×C22⋊D11—21no—
207C2×C22⋊D11—21no—
208C2×C22⋊D11—21no—
209C2×C22⋊D11—21no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11#4111yescharacteristic
213#4343—22no—
214#4343—22no—
215Q8×D11—22no—
216Q8×D11—22no—
217#4341—24no—
218#4341—24no—
219#4341—22no—
220#4341—22no—
221D4×D11—24no—
222D4×D11—24no—
223D4×D11—22no—
224D4×D11—22no—
225#4339—24no—
226#4339—24no—
227#4339—21no—
228#4339—21no—
229#4339C2×D412yes—
230#4339#4112yes—
231C2×D44—21no—
232C2×D44C22×C411yescharacteristic
233C2×C4×D11—24no—
234C2×C4×D11—24no—
235C2×C4×D11—21no—
236C2×C4×D11—21no—
237C2×C4×D11—21no—
238C2×C4×D11—21no—
239C2×C4×D11—21no—
240C2×C4×D11—21no—
241C2×C4×D11—21no—
242C2×C4×D11C22×C411yescharacteristic
243C2×C4×D11C22×C411yescharacteristic
244C2×C4×D11C2×D411yescharacteristic
245C2×C4×D11C2×D411yescharacteristic
246C2×Dic22—21no—
247C2×Dic22C22×C411yescharacteristic
248C11×Q16—22no—
249C11×SD16—22no—
250C11×SD16—22no—
251C11×D8—22no—
252C11×M16—24no—
253C11×M16—21no—
254C11×M16—21no—
255C11×M16—21no—
256C11×M16—42no—
257C11×M16C2×D412yes—
258C2×C8×C11—24no—
259C2×C8×C11—21no—
260C2×C8×C11—21no—
261C2×C8×C11—21no—
262C2×C8×C11—21no—
263C2×C8×C11—42no—
264C2×C8×C11C22×C411yescharacteristic
265C2×C8×C11C22×C411yescharacteristic
266C2×C8×C11C2×D411yescharacteristic
267C2×C8×C11C2×D412yes—
268C2×C8×C11C2×D411yescharacteristic
269C2×C8×C11C2×D412yes—
270C42×C11—21no—
271C42×C11—21no—
272C22⋊Dic11—21no—
273C22⋊Dic11—21no—
274C22⋊Dic11—21no—
275#4326—22no—
276#4325—22no—
277#4324—22no—
278#4323—22no—
279(C2×D11)⋊C4—21no—
280(C2×D11)⋊C4—21no—
281(C2×D11)⋊C4—42no—
282C4⋊Dic11C22×C411yescharacteristic
283C4⋊Dic11C22×C411yescharacteristic
284Dic11⋊C4—21no—
285Dic11⋊C4—21no—
286C4×Dic11—21no—
287C4×Dic11—21no—
288C4×Dic11—21no—
289#4318—24no—
290#4318—21no—
291#4318—21no—
292#4318—21no—
293#4318C2×D412yes—
294C2×C11⋊C8—24no—
295C2×C11⋊C8—21no—
296C2×C11⋊C8—21no—
297C2×C11⋊C8—21no—
298C2×C11⋊C8—21no—
299C2×C11⋊C8—21no—
300C2×C11⋊C8—21no—
301C2×C11⋊C8C22×C411yescharacteristic
302C2×C11⋊C8C22×C411yescharacteristic
303C2×C11⋊C8C2×D411yescharacteristic
304C2×C11⋊C8C2×D411yescharacteristic
305#4313—24no—
306#4313—24no—
307#4313—22no—
308#4313—24no—
309#4313—22no—
310#4313—22no—
311#4313—22no—
312C8×D11—24no—
313C8×D11—24no—
314C8×D11—24no—
315C2×#568—111no—
316#3002—111no—
317C2×#444D1111yescharacteristic, complemented
318C2×#443—111no—
319#2930—111no—
320#1876—111no—
321#1876—111no—
322#1871—111no—
323#1866—111no—
324#1866—111no—
325#1855—111no—
326#1789—111no—
327#1765—111no—
328#1764—111no—
329#1753—111no—
330C23×C11—21no—
331C23×C11—21no—
332C23×C11C2×#4111yescharacteristic
333C22×D11—21no—
334C22×D11—24no—
335C22×D11—21no—
336C22×D11—21no—
337C22×D11—41no—
338C22×D11—41no—
339C22×D11—81no—
340C22×D11—81no—
341C22×D11C4×D411yescharacteristic
342C22×D11C4×D411yescharacteristic
343Q8×C11—21no—
344Q8×C11—21no—
345Q8×C11—21no—
346Q8×C11C4×D412yes—
347D4×C11—22no—
348D4×C11—22no—
349D4×C11—21no—
350D4×C11—21no—
351D4×C11—21no—
352D4×C11—41no—
353D4×C11—41no—
354D4×C11C4×D412yes—
355C2×C4×C11—21no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—21no—
359C2×C4×C11—41no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11C23×C411yescharacteristic
365C2×C4×C11C22×D411yescharacteristic
366C2×C4×C11C22×D411yescharacteristic
367C2×C4×C11C22×D411yescharacteristic
368C2×C4×C11C2×#4111yescharacteristic
369C2×C4×C11C2×#4111yescharacteristic
370C22⋊D11—24no—
371C22⋊D11—24no—
372C22⋊D11—22no—
373C22⋊D11—22no—
374C22⋊D11—81no—
375C22⋊D11—81no—
376C2×Dic11—24no—
377C2×Dic11—21no—
378C2×Dic11—21no—
379C2×Dic11—21no—
380C2×Dic11—22no—
381C2×Dic11—21no—
382C2×Dic11—21no—
383C2×Dic11—41no—
384C2×Dic11—41no—
385C2×Dic11C4×D411yescharacteristic
386C2×Dic11C4×D411yescharacteristic
387D44—24no—
388D44—21no—
389D44C4×D412yes—
390C4×D11—24no—
391C4×D11—24no—
392C4×D11—21no—
393C4×D11—21no—
394C4×D11—21no—
395C4×D11—21no—
396C4×D11—22no—
397C4×D11—21no—
398C4×D11—21no—
399C4×D11—21no—
400C4×D11—22no—
401C4×D11—21no—
402Dic22—24no—
403Dic22—21no—
404Dic22C4×D412yes—
405C8×C11—21no—
406C8×C11—21no—
407C8×C11—22no—
408C8×C11—41no—
409C8×C11#12012yes—
410C8×C11#12012yes—
411C11⋊C8—21no—
412C11⋊C8—21no—
413C11⋊C8—22no—
414C11⋊C8—21no—
415C11⋊C8—21no—
416C11⋊C8—41no—
417C22×#41—111no—
418C2×#135—111no—
419C2×#135C2×D1111yescharacteristic
420#568—224no—
421#568—224no—
422C2×#131—111no—
423C2×#131—111no—
424C2×#131—111no—
425C2×#131—221no—
426C2×#131—221no—
427C2×#131C2×D1111yescharacteristic
428C2×#131C2×D1111yescharacteristic, complemented
429C22×M16—111no—
430C22×M16—111no—
431C22×M16—221no—
432C22×M16—221no—
433#525—111no—
434#452—111no—
435#452—111no—
436#451—111no—
437#450—111no—
438#449—111no—
439#449—111no—
440#448—111no—
441#447—111no—
442#444—24no—
443#443—224no—
444#436—221no—
445#436—221no—
446#435—221no—
447#435—221no—
448C2×#108—111no—
449C2×#108C2×D1111yescharacteristic, complemented
450#424—111no—
451C2×#104—111no—
452C2×#104—111no—
453C2×#104—111no—
454C2×#104—111no—
455C2×#104C2×D1111yescharacteristic
456C2×#104C2×D1111yescharacteristic, complemented
457#416—111no—
458#416—111no—
459#408—111no—
460#407—111no—
461C2×C22⋊C8—111no—
462#405—111no—
463C2×#97C2×D1111yescharacteristic, complemented
464C2×C4×C8—111no—
465C4×C22⋊C4—111no—
466#341—111no—
467#341—111no—
468#339—111no—
469#339—111no—
470#336—111no—
471#336—111no—
472C22×C11—21no—
473C22×C11—21no—
474C22×C11—22no—
475C22×C11—41no—
476C22×C11—41no—
477C22×C11—41no—
478C22×C11—41no—
479C22×C11—41no—
480C22×C11C2×C4×D411yescharacteristic
481C22×C11#52511yescharacteristic
482C22×C11#52511yescharacteristic
483C2×D11—21no—
484C2×D11—21no—
485C2×D11—21no—
486C2×D11—21no—
487C2×D11—21no—
488C2×D11—22no—
489C2×D11—21no—
490C2×D11—41no—
491C2×D11—41no—
492C2×D11—81no—
493C2×D11—81no—
494C2×D11—84no—
495C4×C11—22no—
496C4×C11—41no—
497C4×C11—81no—
498C4×C11C2×C4×D411yescharacteristic
499C4×C11C2×C4×D411yescharacteristic
500C4×C11C2×#12011yescharacteristic
501C4×C11#52511yescharacteristic
502Dic11—21no—
503Dic11—22no—
504Dic11—21no—
505Dic11—42no—
506Dic11—41no—
507Dic11—41no—
508C2×#41—111no—
509C2×#41—111no—
510C2×#41—111no—
511C2×#41—221no—
512C2×#41—221no—
513C2×#41—222no—
514C2×#41—222no—
515C2×#41—222no—
516C2×#41—222no—
517C2×#41C22×D1111yescharacteristic
518C2×#41C22×D1111yescharacteristic
519C22×Q8—111no—
520C22×D4—111no—
521C22×D4—221no—
522C23×C4—111no—
523C23×C4—221no—
524#135—22no—
525#135—22no—
526#135—222no—
527#135—222no—
528C2×Q16—111no—
529C2×Q16C4×D1111yescharacteristic
530C2×SD16—111no—
531C2×SD16—111no—
532C2×SD16C4×D1111yescharacteristic
533C2×SD16C4×D1111yescharacteristic
534C2×D8—111no—
535C2×D8C4×D1111yescharacteristic
536#131—22no—
537#131—22no—
538#131—22no—
539#131—114no—
540#131—228no—
541#131—222no—
542#131—228no—
543#131—222no—
544#131—222no—
545#131—222no—
546#131—222no—
547#131C22⋊D1114yescomplemented
548C2×M16—21no—
549C2×M16—21no—
550C2×M16—111no—
551C2×M16—111no—
552C2×M16—111no—
553C2×M16—111no—
554C2×M16—111no—
555C2×M16—111no—
556C2×M16—221no—
557C2×M16—221no—
558C2×M16—228no—
559C2×M16—221no—
560C2×M16—222no—
561C2×M16—228no—
562C2×M16—222no—
563C2×M16—222no—
564C2×M16—221no—
565C2×M16—222no—
566C2×M16C22×D1111yescharacteristic
567C2×M16C22×D1111yescharacteristic
568C22×C8—21no—
569C22×C8—21no—
570C22×C8—111no—
571C22×C8—111no—
572C22×C8—221no—
573C22×C8—221no—
574C22×C8—221no—
575C22×C8—221no—
576C22×C8C22×D1111yescharacteristic
577C22×C8C22×D1111yescharacteristic
578#123—221no—
579C22⋊Q8—111no—
580C22⋊Q8—111no—
581#121—111no—
582#121—111no—
583#120—221no—
584C4×D4—221no—
585C4×D4—221no—
586#117—111no—
587C2×C22⋊C4—221no—
588C2×C42—111no—
589C2×C42C22×D1111yescharacteristic
590#108—22no—
591#108—222no—
592C4⋊C8—221no—
593C4⋊C8—221no—
594#104—22no—
595#104—22no—
596#104—222no—
597#104—222no—
598#104—222no—
599#104—222no—
600#103—111no—
601#103—111no—
602#103—111no—
603#103—111no—
604#102—111no—
605#102—111no—
606#102—111no—
607#102—111no—
608C22⋊C8—111no—
609C22⋊C8—111no—
610C22⋊C8—111no—
611C22⋊C8—111no—
612C22⋊C8—221no—
613C22⋊C8—221no—
614C22⋊C8—221no—
615C22⋊C8—221no—
616#97—22no—
617#97—221no—
618C4×C8—222no—
619C4×C8—221no—
620#95—221no—
621C2×C11—21no—
622C2×C11—21no—
623C2×C11—42no—
624C2×C11—81no—
625C2×C11C4×#12011yescharacteristic
626C2×C11#295611yescharacteristic
627C2×C11#295711yescharacteristic
628D11—41no—
629D11—41no—
630D11—42no—
631C24—111no—
632C24—221no—
633#41—21no—
634#41—21no—
635#41—21no—
636#41—21no—
637#41—21no—
638#41—21no—
639#41—112no—
640#41—112no—
641#41—224no—
642#41—224no—
643#41—222no—
644#41—224no—
645#41—224no—
646#41—222no—
647#41—222no—
648#41—222no—
649#41—221no—
650#41—221no—
651#41#433912yes—
652#41C2×C22⋊D1112yes—
653C2×Q8—111no—
654C2×Q8—221no—
655C2×Q8—222no—
656C2×Q8—222no—
657C2×Q8C2×C4×D1111yescharacteristic
658C2×Q8C2×C4×D1111yescharacteristic
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—111no—
662C2×D4—221no—
663C2×D4—221no—
664C2×D4—222no—
665C2×D4—224no—
666C2×D4—224no—
667C2×D4—221no—
668C2×D4—221no—
669C2×D4—222no—
670C2×D4—221no—
671C2×D4—221no—
672C2×D4C2×C4×D1111yescharacteristic
673C2×D4C2×C4×D1111yescharacteristic
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—111no—
678C22×C4—111no—
679C22×C4—111no—
680C22×C4—111no—
681C22×C4—111no—
682C22×C4—221no—
683C22×C4—221no—
684C22×C4—224no—
685C22×C4—224no—
686C22×C4—221no—
687C22×C4—221no—
688C22×C4—221no—
689C22×C4—221no—
690C22×C4—221no—
691C22×C4—221no—
692C22×C4—221no—
693C22×C4C23×D1111yescharacteristic
694Q16—22no—
695Q16—222no—
696SD16—22no—
697SD16—22no—
698SD16—222no—
699SD16—222no—
700D8—22no—
701D8—222no—
702M16—21no—
703M16—24no—
704M16—21no—
705M16—21no—
706M16—42no—
707M16—112no—
708M16—224no—
709M16—224no—
710M16—224no—
711M16—221no—
712M16—222no—
713M16—222no—
714M16—222no—
715M16—222no—
716M16—224no—
717M16—221no—
718M16—221no—
719M16C2×C22⋊D1112yes—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—24no—
724C2×C8—21no—
725C2×C8—42no—
726C2×C8—111no—
727C2×C8—111no—
728C2×C8—111no—
729C2×C8—111no—
730C2×C8—224no—
731C2×C8—224no—
732C2×C8—224no—
733C2×C8—221no—
734C2×C8—221no—
735C2×C8—221no—
736C2×C8—221no—
737C2×C8—221no—
738C2×C8—224no—
739C2×C8—221no—
740C2×C8C2×C4×D1111yescharacteristic
741C2×C8C2×C4×D1111yescharacteristic
742C2×C8D4×D1112yes—
743C2×C8D4×D1111yescharacteristic
744C2×C8D4×D1111yescharacteristic
745C2×C8C2×C22⋊D1112yes—
746C4⋊C4—111no—
747C4⋊C4—111no—
748C4⋊C4—221no—
749C4⋊C4—221no—
750C22⋊C4—221no—
751C22⋊C4—221no—
752C22⋊C4—221no—
753C22⋊C4—221no—
754C22⋊C4—221no—
755C22⋊C4—442no—
756C42—21no—
757C42—21no—
758C42—221no—
759C42—221no—
760C42—221no—
761C11#2146811yescharacteristic, complemented, Sylow
762C23—21no—
763C23—21no—
764C23—111no—
765C23—111no—
766C23—224no—
767C23—221no—
768C23—221no—
769C23—221no—
770C23—441no—
771C23—441no—
772C23—881no—
773C23—881no—
774C23#41×D1111yescharacteristic
775Q8—21no—
776Q8—21no—
777Q8—21no—
778Q8—112no—
779Q8—224no—
780Q8—221no—
781Q8C4×C22⋊D1112yes—
782D4—22no—
783D4—22no—
784D4—21no—
785D4—21no—
786D4—21no—
787D4—41no—
788D4—41no—
789D4—112no—
790D4—224no—
791D4—224no—
792D4—224no—
793D4—222no—
794D4—222no—
795D4—221no—
796D4—881no—
797D4—881no—
798D4C4×C22⋊D1112yes—
799C2×C4—21no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—21no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—111no—
809C2×C4—111no—
810C2×C4—224no—
811C2×C4—224no—
812C2×C4—224no—
813C2×C4—221no—
814C2×C4—221no—
815C2×C4—221no—
816C2×C4—221no—
817C2×C4—221no—
818C2×C4—221no—
819C2×C4—222no—
820C2×C4—221no—
821C2×C4—221no—
822C2×C4—221no—
823C2×C4—221no—
824C2×C4—221no—
825C2×C4—222no—
826C2×C4—222no—
827C2×C4—221no—
828C2×C4—221no—
829C2×C4—441no—
830C2×C4—441no—
831C2×C4C22×C4×D1111yescharacteristic
832C2×C4C2×#433911yescharacteristic
833C2×C4C2×D4×D1111yescharacteristic
834C2×C4C2×D4×D1111yescharacteristic
835C2×C4#41×D1111yescharacteristic
836C2×C4C22×C22⋊D1111yescharacteristic
837C8—21no—
838C8—21no—
839C8—22no—
840C8—41no—
841C8—221no—
842C8—221no—
843C8—222no—
844C8—221no—
845C8—221no—
846C8—441no—
847C8#6699012yes—
848C8#6699012yes—
849C22—21no—
850C22—21no—
851C22—22no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—221no—
858C22—222no—
859C22—221no—
860C22—221no—
861C22—221no—
862C22—221no—
863C22—221no—
864C22—441no—
865C22—441no—
866C22—881no—
867C22—881no—
868C22—884no—
869C22C4×D4×D1111yescharacteristic
870C22#1062307811yescharacteristic
871C22#1062335911yescharacteristic
872C4—22no—
873C4—41no—
874C4—81no—
875C4—221no—
876C4—221no—
877C4—222no—
878C4—442no—
879C4—441no—
880C4—441no—
881C4C4×D4×D1111yescharacteristic
882C4#1062307811yescharacteristic
883C4C2×C4×C22⋊D1111yescharacteristic
884C4C2×#6699011yescharacteristic
885C2—21no—
886C2—21no—
887C2—42no—
888C2—81no—
889C2—441no—
890C2—441no—
891C2—442no—
892C2C4×#6699011yescharacteristic
893C2#1307752411yescharacteristic
894C2#1307753011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#444C2
socleC22×C11C2×C4×D4
prime radical#13077830C2
cosocleC22×C4×C11C24
hypercenterC2×#444D11
hypocenterC11#21468
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#444

Complements

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

NH ≅ G/Ntype
1. C2×#10623281C2semidirect
3. C2×#10622757C2semidirect
4. #13077317C2semidirect
5. #13068945C2semidirect
6. #13068940C2semidirect
7. #13068915C2semidirect
8. #13068889C2semidirect
9. #13068888C2semidirect
10. #13068819C2semidirect
11. #13068558C2semidirect
12. #13068460C2semidirect
13. #13068451C2semidirect
14. #13068401C2semidirect
15. C2×C11×#444C2semidirect
19. C2×C11×#131C22semidirect
34. C2×C11×#108C22semidirect
36. C2×C11×#104C22semidirect
37. C2×C11×#97C22semidirect
39. C2×#66901C22semidirect
40. #10622847C22semidirect
42. #10622800C4semidirect
43. #10622799C4semidirect
44. #10622786C4semidirect
45. #10622785C4semidirect
46. #10622783C4semidirect
47. #10622782C4semidirect
48. #10622771C4semidirect
49. #10622769C4semidirect
55. C2×#66886C22semidirect
56. #10622732C22semidirect
61. #10622714C22semidirect
62. C2×C8×Dic11C22semidirect
65. #10622196C22semidirect
66. #10622193C22semidirect
67. #10622190C22semidirect
68. #10622188C22semidirect
69. #10622162C22semidirect
70. #10622161C22semidirect
96. C11×#131D4semidirect
139. #66954D4semidirect
317. C2×#444D11semidirect
428. C2×#131C2×D11semidirect
449. C2×#108C2×D11semidirect
456. C2×#104C2×D11semidirect
463. C2×#97C2×D11semidirect
547. #131C22⋊D11semidirect
761. C11#21468semidirect

Maximal subgroups

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

subgroupindex
C2×#106232812
#130778302
C2×#106227572
#130773172
#130689452
#130689402
#130689152
#130688892
#130688882
#130688192
#130685582
#130684602
#130684512
#130684012
C2×C11×#4442
#2146811