Finite Group Databasebeta

← #14755258

Subgroups — #14755258

Order 2816.

1668 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623353C211yesmaximal, characteristic
2C2×#10623276C211yesmaximal, characteristic, complemented
3C2×#10622849C211yesmaximal, characteristic, complemented
4#13077136C211yesmaximal, characteristic, complemented
5#13068981C218yesmaximal, complemented
6C2×#10622194C211yesmaximal, characteristic, complemented
7#13068343C211yesmaximal, characteristic, complemented
8C11×#2879C211yesmaximal, characteristic, complemented
9C22×C11×#41C2211yescharacteristic
10C22×#4339C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C2×#67004—21no—
14#10623353—22no—
15#10623353—22no—
16#10623353C414yescomplemented
17#10623353C2214yes—
18C2×#67003—22no—
19C2×#67002—21no—
20C2×#66995C412yescomplemented
21C2×#66985C412yescomplemented
22C2×#66979C2211yescharacteristic
23C22×#4318C2211yescharacteristic
24C22×#4318C2211yescharacteristic
25#10623276—22no—
26#10623276—22no—
27#10623276—22no—
28#10623276C2214yescomplemented
29C2×#66960—22no—
30C2×M16×D11—22no—
31C2×#66954—22no—
32C11×#408—22no—
33C11×#408C2214yescomplemented
34C11×#407—22no—
35#10622849—22no—
36#10622849C2214yescomplemented
37C2×#66901—22no—
38#10622746—22no—
39#10622744—21no—
40#10622733—21no—
41#10622726C2214yescomplemented
42#10622194C2214yescomplemented
43#10622190C2214yescomplemented
44C2×C11×#41—21no—
45C2×C11×#41—21no—
46C2×C11×#41—21no—
47C2×C11×#41—21no—
48C2×C11×#41—21no—
49C2×C11×#41—21no—
50C2×C11×#41—21no—
51C2×C11×#41—21no—
52C2×C11×#41—21no—
53C2×C11×#41—21no—
54C2×C11×#41C2×C412yes—
55C2×C11×#41C2312yes—
56C22×Q8×C11C2×C411yescharacteristic
57C22×D4×C11—21no—
58C22×D4×C11C2×C411yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11C2311yescharacteristic
61C22×C22⋊D11—21no—
62C2×#4339—21no—
63C2×#4339—21no—
64C2×#4339—21no—
65C2×#4339—21no—
66C2×#4339—21no—
67C2×#4339—21no—
68C2×#4339C2×C412yes—
69C2×#4339C2×C412yes—
70C2×#4339D412yes—
71C2×#4339D412yes—
72C2×#4339D412yes—
73C2×#4339C2312yes—
74C22×D44D411yescharacteristic
75C22×C4×D11—21no—
76C22×Dic22D411yescharacteristic
77C2×C11×M16—21no—
78C2×C11×M16—21no—
79C2×C11×M16—21no—
80C2×C11×M16—21no—
81C2×C11×M16—21no—
82C2×C11×M16—21no—
83C2×C11×M16—21no—
84C2×C11×M16—21no—
85C2×C11×M16—21no—
86C2×C11×M16—21no—
87C2×C11×M16D412yes—
88C2×C11×M16C2312yes—
89C22×C8×C11D412yes—
90C22×C8×C11C2312yes—
91C2×C22⋊Dic11—21no—
92#67004—24no—
93#67004—24no—
94#67003—28no—
95#67003—28no—
96#67002—24no—
97#67002—24no—
98C2×#4326—22no—
99#66995—24no—
100#66995C2×C418yescomplemented
101C2×#4325—22no—
102C2×#4324—22no—
103#66985—24no—
104#66985C2×C418yescomplemented
105C2×#4323—22no—
106#66979—21no—
107#66979—21no—
108#66979—21no—
109#66979C2312yes—
110C2×C4⋊Dic11—21no—
111C2×C4×Dic11—21no—
112C2×#4318—21no—
113C2×#4318—21no—
114C2×#4318—21no—
115C2×#4318—21no—
116C2×#4318—21no—
117C2×#4318—21no—
118C2×#4318C2×C412yes—
119C2×#4318C2×C412yes—
120C2×#4318D412yes—
121C2×#4318D412yes—
122C2×#4318C2312yes—
123C2×#4318C2312yes—
124C22×C11⋊C8—21no—
125C22×C11⋊C8—21no—
126#66960—28no—
127#66960—28no—
128M16×D11—28no—
129M16×D11—28no—
130#66954—28no—
131#66954—28no—
132C2×#4313—24no—
133C2×C8×D11—24no—
134C11×C22⋊C8—28no—
135#66901—28no—
136#66885—24no—
137#66880—24no—
138#20939—111nomaximal, Sylow
139C24×C11—21no—
140C24×C11#4111yescharacteristic
141C23×D11—21no—
142C11×#41—22no—
143C11×#41—22no—
144C11×#41—22no—
145C11×#41—22no—
146C11×#41—22no—
147C11×#41—22no—
148C11×#41—22no—
149C11×#41—22no—
150C11×#41—41no—
151C11×#41—41no—
152C11×#41—41no—
153C11×#41—41no—
154C11×#41—41no—
155C11×#41—41no—
156C11×#41—41no—
157C11×#41—41no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11—21no—
161C2×Q8×C11—21no—
162C2×Q8×C11—21no—
163C2×Q8×C11C22×C412yes—
164C2×D4×C11—22no—
165C2×D4×C11—22no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—21no—
171C2×D4×C11—41no—
172C2×D4×C11—41no—
173C2×D4×C11—41no—
174C2×D4×C11—41no—
175C2×D4×C11C22×C412yes—
176C22×C4×C11—21no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—41no—
180C22×C4×C11—41no—
181C22×C4×C11—41no—
182C22×C4×C11—41no—
183C22×C4×C11C22×C411yescharacteristic
184C22×C4×C11C22×C411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11#4111yescharacteristic
194C22×C4×C11#4111yescharacteristic
195C22×C4×C11#4111yescharacteristic
196C22×C4×C11C2411yescharacteristic
197C2×C22⋊D11—22no—
198C2×C22⋊D11—22no—
199C2×C22⋊D11—22no—
200C2×C22⋊D11—22no—
201C2×C22⋊D11—22no—
202C2×C22⋊D11—22no—
203C22×Dic11—21no—
204C22×Dic11—41no—
205#4339—22no—
206#4339—22no—
207#4339—22no—
208#4339—22no—
209#4339—22no—
210#4339—22no—
211#4339—22no—
212#4339—22no—
213#4339—22no—
214#4339—22no—
215#4339—22no—
216#4339—22no—
217#4339C22⋊C414yes—
218#4339C22⋊C414yes—
219#4339C22×C414yes—
220#4339C2×D414yes—
221C2×D44—21no—
222C2×D44—21no—
223C2×D44—21no—
224C2×D44C22⋊C412yes—
225C2×D44C22⋊C412yes—
226C2×D44C2×D412yes—
227C2×C4×D11—22no—
228C2×C4×D11—22no—
229C2×C4×D11—22no—
230C2×C4×D11—22no—
231C2×C4×D11—22no—
232C2×C4×D11—22no—
233C2×Dic22—21no—
234C2×Dic22—21no—
235C2×Dic22—21no—
236C2×Dic22C22⋊C412yes—
237C2×Dic22C22⋊C412yes—
238C2×Dic22C2×D412yes—
239C11×M16—22no—
240C11×M16—22no—
241C11×M16—22no—
242C11×M16—22no—
243C11×M16—41no—
244C11×M16—41no—
245C11×M16—41no—
246C11×M16—41no—
247C2×C8×C11—22no—
248C2×C8×C11—22no—
249C2×C8×C11—22no—
250C2×C8×C11—22no—
251C2×C8×C11—22no—
252C2×C8×C11C2×D414yes—
253C22⋊Dic11—22no—
254C22⋊Dic11—41no—
255#4326—28no—
256#4325—28no—
257#4324—28no—
258#4323—28no—
259C4⋊Dic11—22no—
260C4⋊Dic11—41no—
261C4×Dic11—22no—
262C4×Dic11—41no—
263#4318—22no—
264#4318—22no—
265#4318—22no—
266#4318—22no—
267#4318—22no—
268#4318—22no—
269#4318C22×C414yes—
270#4318C2×D414yes—
271C2×C11⋊C8—22no—
272C2×C11⋊C8—22no—
273C2×C11⋊C8—22no—
274C2×C11⋊C8—22no—
275C2×C11⋊C8—22no—
276C2×C11⋊C8—22no—
277#4313—216no—
278C8×D11—216no—
279C2×#575—111no—
280C2×#568—111no—
281C2×#421—111no—
282#2896—111no—
283#2879D1111yescharacteristic, complemented
284#1881—118no—
285C2×#344—111no—
286#1738—111no—
287C23×C11—22no—
288C23×C11—41no—
289C23×C11—41no—
290C23×C11—81no—
291C23×C11—82no—
292C23×C11C4×D411yescharacteristic
293C23×C11C4×D411yescharacteristic
294C23×C11#12111yescharacteristic
295C23×C11#12111yescharacteristic
296C23×C11#12311yescharacteristic
297C23×C11#12311yescharacteristic
298C23×C11C2×#4111yescharacteristic
299C22×D11—22no—
300C22×D11—22no—
301C22×D11—22no—
302C22×D11—82no—
303Q8×C11—22no—
304Q8×C11—22no—
305Q8×C11—41no—
306Q8×C11—41no—
307D4×C11—22no—
308D4×C11—22no—
309D4×C11—42no—
310D4×C11—42no—
311D4×C11—42no—
312D4×C11—42no—
313D4×C11—41no—
314D4×C11—41no—
315C2×C4×C11—22no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—42no—
319C2×C4×C11—42no—
320C2×C4×C11—42no—
321C2×C4×C11—42no—
322C2×C4×C11C2×C22⋊C411yescharacteristic
323C2×C4×C11C2×C22⋊C411yescharacteristic
324C2×C4×C11C2×C22⋊C411yescharacteristic
325C2×C4×C11C2×C22⋊C411yescharacteristic
326C2×C4×C11C4×D411yescharacteristic
327C2×C4×C11C4×D411yescharacteristic
328C2×C4×C11C4×D411yescharacteristic
329C2×C4×C11C4×D411yescharacteristic
330C2×C4×C11C4×D411yescharacteristic
331C2×C4×C11C4×D411yescharacteristic
332C2×C4×C11#12011yescharacteristic
333C2×C4×C11#12011yescharacteristic
334C2×C4×C11#12011yescharacteristic
335C2×C4×C11#12011yescharacteristic
336C2×C4×C11#12111yescharacteristic
337C2×C4×C11#12111yescharacteristic
338C2×C4×C11#12111yescharacteristic
339C2×C4×C11#12111yescharacteristic
340C2×C4×C11#12111yescharacteristic
341C2×C4×C11#12111yescharacteristic
342C2×C4×C11#12311yescharacteristic
343C2×C4×C11#12311yescharacteristic
344C2×C4×C11C23×C411yescharacteristic
345C2×C4×C11C22×D411yescharacteristic
346C2×C4×C11C22×D411yescharacteristic
347C2×C4×C11C22×D411yescharacteristic
348C2×C4×C11C22×D411yescharacteristic
349C2×C4×C11C2×#4111yescharacteristic
350C22⋊D11—24no—
351C22⋊D11—24no—
352C22⋊D11—24no—
353C22⋊D11—24no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—42no—
358C2×Dic11—82no—
359D44—22no—
360D44—22no—
361D44—22no—
362D44C2×C22⋊C414yes—
363C4×D11—24no—
364C4×D11—24no—
365C4×D11—24no—
366C4×D11—24no—
367Dic22—22no—
368Dic22—22no—
369Dic22—22no—
370Dic22C2×C22⋊C414yes—
371C8×C11—24no—
372C8×C11—42no—
373C11⋊C8—24no—
374C11⋊C8—24no—
375C22×#41—111no—
376C22×#41C2×D1111yescharacteristic
377#575—114no—
378#575—114no—
379#575—222no—
380#575—222no—
381C2×#137—112no—
382C2×#137—221no—
383C2×AGL(1,ℤ/8)—112no—
384C2×AGL(1,ℤ/8)—221no—
385C2×#135—222no—
386#568—114no—
387#568—222no—
388#568—222no—
389#568—222no—
390C2×#131—222no—
391C2×#131—222no—
392C22×M16—111no—
393C22×M16—111no—
394C22×M16—222no—
395C22×M16C2×D1111yescharacteristic
396C22×M16C2×D1111yescharacteristic
397C2×#117—111no—
398#421—114no—
399#421—222no—
400C2×#104—222no—
401#419—221no—
402#418—221no—
403#417—222no—
404#416—114no—
405#408—22no—
406#408C2×D1114yescomplemented
407#407—22no—
408#344—114no—
409#341—114no—
410C22×C11—41no—
411C22×C11—41no—
412C22×C11—41no—
413C22×C11—41no—
414C22×C11—41no—
415C22×C11—41no—
416C22×C11—41no—
417C22×C11—44no—
418C22×C11—42no—
419C22×C11—82no—
420C22×C11—82no—
421C22×C11#38611yescharacteristic
422C22×C11#38611yescharacteristic
423C22×C11#38611yescharacteristic
424C22×C11#38611yescharacteristic
425C22×C11C2×C4×D411yescharacteristic
426C22×C11C2×#12111yescharacteristic
427C22×C11C2×#12311yescharacteristic
428C2×D11—24no—
429C2×D11—44no—
430C2×D11—82no—
431C2×D11—82no—
432C4×C11—42no—
433C4×C11#38611yescharacteristic
434C4×C11#38611yescharacteristic
435C4×C11#38611yescharacteristic
436C4×C11#38611yescharacteristic
437C4×C11C22×C22⋊C411yescharacteristic
438C4×C11C2×C4×D411yescharacteristic
439C4×C11C2×#12011yescharacteristic
440C4×C11C2×#12111yescharacteristic
441Dic11—24no—
442Dic11—82no—
443C2×#41—21no—
444C2×#41—21no—
445C2×#41—21no—
446C2×#41—21no—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—112no—
454C2×#41—112no—
455C2×#41—112no—
456C2×#41—112no—
457C2×#41—112no—
458C2×#41—112no—
459C2×#41—221no—
460C2×#41—221no—
461C2×#41—221no—
462C2×#41—221no—
463C2×#41—221no—
464C2×#41—221no—
465C2×#41C4×D1112yes—
466C2×#41C22×D1112yes—
467C22×Q8—111no—
468C22×Q8C4×D1111yescharacteristic
469C22×D4—21no—
470C22×D4—111no—
471C22×D4—221no—
472C22×D4C4×D1111yescharacteristic
473C23×C4—21no—
474C23×C4—221no—
475C23×C4C22×D1111yescharacteristic
476#137—118no—
477#137—224no—
478#137—224no—
479#137—224no—
480AGL(1,ℤ/8)—118no—
481AGL(1,ℤ/8)—224no—
482AGL(1,ℤ/8)—224no—
483AGL(1,ℤ/8)—224no—
484#135—228no—
485#135—228no—
486C2×Q16—222no—
487C2×SD16—222no—
488C2×SD16—222no—
489C2×D8—222no—
490#131—228no—
491#131—228no—
492#131—228no—
493#131—228no—
494C2×M16—21no—
495C2×M16—21no—
496C2×M16—21no—
497C2×M16—21no—
498C2×M16—21no—
499C2×M16—21no—
500C2×M16—21no—
501C2×M16—21no—
502C2×M16—21no—
503C2×M16—21no—
504C2×M16—112no—
505C2×M16—112no—
506C2×M16—112no—
507C2×M16—112no—
508C2×M16—112no—
509C2×M16—112no—
510C2×M16—224no—
511C2×M16—228no—
512C2×M16—228no—
513C2×M16—221no—
514C2×M16—221no—
515C2×M16—221no—
516C2×M16—221no—
517C2×M16—221no—
518C2×M16—221no—
519C2×M16C22⋊D1112yes—
520C2×M16C22×D1112yes—
521C22×C8—224no—
522C22×C8—221no—
523C22×C8—221no—
524C22×C8C22⋊D1112yes—
525C22×C8C22×D1112yes—
526#117—112no—
527#117—221no—
528#117—221no—
529#117—221no—
530C2×C4⋊C4—221no—
531C2×C22⋊C4—221no—
532C2×C42—221no—
533#104—228no—
534#103—224no—
535#102—224no—
536C22⋊C8—28no—
537C2×C11—21no—
538C2×C11—21no—
539C2×C11—21no—
540C2×C11—21no—
541C2×C11—21no—
542C2×C11—21no—
543C2×C11—21no—
544C2×C11—82no—
545C2×C11C2×#38611yescharacteristic
546D11—44no—
547C24—21no—
548C24—221no—
549C24#433911yescharacteristic
550#41—22no—
551#41—22no—
552#41—22no—
553#41—22no—
554#41—22no—
555#41—22no—
556#41—22no—
557#41—22no—
558#41—41no—
559#41—41no—
560#41—41no—
561#41—41no—
562#41—41no—
563#41—41no—
564#41—41no—
565#41—41no—
566#41—114no—
567#41—114no—
568#41—114no—
569#41—114no—
570#41—222no—
571#41—222no—
572#41—222no—
573#41—222no—
574#41—222no—
575#41—222no—
576#41—222no—
577#41—222no—
578#41—222no—
579#41—222no—
580#41—222no—
581#41—222no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—112no—
588C2×Q8—112no—
589C2×Q8—112no—
590C2×Q8—221no—
591C2×Q8—221no—
592C2×Q8—221no—
593C2×Q8C2×C4×D1112yes—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—41no—
602C2×D4—41no—
603C2×D4—41no—
604C2×D4—41no—
605C2×D4—112no—
606C2×D4—112no—
607C2×D4—112no—
608C2×D4—222no—
609C2×D4—222no—
610C2×D4—222no—
611C2×D4—222no—
612C2×D4—222no—
613C2×D4—222no—
614C2×D4—221no—
615C2×D4—221no—
616C2×D4—221no—
617C2×D4C2×C4×D1112yes—
618C22×C4—21no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—41no—
622C22×C4—41no—
623C22×C4—41no—
624C22×C4—41no—
625C22×C4—221no—
626C22×C4—222no—
627C22×C4—222no—
628C22×C4—222no—
629C22×C4—222no—
630C22×C4—222no—
631C22×C4—222no—
632C22×C4—441no—
633C22×C4C2×C4×D1111yescharacteristic
634C22×C4C2×C4×D1111yescharacteristic
635C22×C4#433911yescharacteristic
636C22×C4D4×D1111yescharacteristic
637C22×C4D4×D1111yescharacteristic
638C22×C4D4×D1111yescharacteristic
639C22×C4D4×D1111yescharacteristic
640C22×C4D4×D1111yescharacteristic
641C22×C4D4×D1111yescharacteristic
642C22×C4#434111yescharacteristic
643C22×C4#434111yescharacteristic
644C22×C4C2×C22⋊D1111yescharacteristic
645C22×C4C2×C22⋊D1111yescharacteristic
646C22×C4C23×D1111yescharacteristic
647Q16—228no—
648SD16—228no—
649SD16—228no—
650D8—228no—
651M16—22no—
652M16—22no—
653M16—22no—
654M16—22no—
655M16—41no—
656M16—41no—
657M16—41no—
658M16—41no—
659M16—114no—
660M16—114no—
661M16—2216no—
662M16—222no—
663M16—222no—
664M16—222no—
665M16—222no—
666M16—222no—
667M16—222no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—22no—
672C2×C8—22no—
673C2×C8—2216no—
674C2×C8—222no—
675C2×C8—222no—
676C2×C8—222no—
677C2×C8—222no—
678C2×C8—222no—
679C2×C8—222no—
680C2×C8C2×C22⋊D1114yes—
681C4⋊C4—222no—
682C4⋊C4—441no—
683C22⋊C4—222no—
684C22⋊C4—441no—
685C42—222no—
686C42—441no—
687C11#2093911yescharacteristic, complemented, Sylow
688C23—22no—
689C23—41no—
690C23—41no—
691C23—81no—
692C23—82no—
693C23—222no—
694C23—222no—
695C23—222no—
696C23—882no—
697C23#6693611yescharacteristic
698C23#6693611yescharacteristic
699C23#6693711yescharacteristic
700C23#6693711yescharacteristic
701C23C4×C22⋊D1111yescharacteristic
702C23C4×C22⋊D1111yescharacteristic
703C23C2×#433911yescharacteristic
704Q8—22no—
705Q8—22no—
706Q8—41no—
707Q8—41no—
708Q8—114no—
709Q8—222no—
710Q8—222no—
711Q8—222no—
712D4—22no—
713D4—22no—
714D4—42no—
715D4—42no—
716D4—42no—
717D4—42no—
718D4—41no—
719D4—41no—
720D4—114no—
721D4—224no—
722D4—224no—
723D4—224no—
724D4—224no—
725D4—222no—
726D4—222no—
727D4—222no—
728C2×C4—22no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—222no—
736C2×C4—222no—
737C2×C4—222no—
738C2×C4—224no—
739C2×C4—224no—
740C2×C4—224no—
741C2×C4—224no—
742C2×C4—442no—
743C2×C4—882no—
744C2×C4C22⋊C4×D1111yescharacteristic
745C2×C4C22⋊C4×D1111yescharacteristic
746C2×C4C22⋊C4×D1111yescharacteristic
747C2×C4C22⋊C4×D1111yescharacteristic
748C2×C4(C22⋊D11)⋊C411yescharacteristic
749C2×C4(C22⋊D11)⋊C411yescharacteristic
750C2×C4(C22⋊D11)⋊C411yescharacteristic
751C2×C4(C22⋊D11)⋊C411yescharacteristic
752C2×C4#6693611yescharacteristic
753C2×C4#6693611yescharacteristic
754C2×C4#6693711yescharacteristic
755C2×C4#6693711yescharacteristic
756C2×C4C4×C22⋊D1111yescharacteristic
757C2×C4C4×C22⋊D1111yescharacteristic
758C2×C4#6699011yescharacteristic
759C2×C4#6699011yescharacteristic
760C2×C4#6699011yescharacteristic
761C2×C4#6699011yescharacteristic
762C2×C4#6699111yescharacteristic
763C2×C4#6699111yescharacteristic
764C2×C4#6699111yescharacteristic
765C2×C4#6699111yescharacteristic
766C2×C4C22×C4×D1111yescharacteristic
767C2×C4C2×D4×D1111yescharacteristic
768C2×C4C2×D4×D1111yescharacteristic
769C2×C4C2×D4×D1111yescharacteristic
770C2×C4C2×#434111yescharacteristic
771C2×C4C22×C22⋊D1111yescharacteristic
772C8—24no—
773C8—42no—
774C8—224no—
775C8—224no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—44no—
784C22—42no—
785C22—82no—
786C22—82no—
787C22—224no—
788C22—444no—
789C22—882no—
790C22—882no—
791C22#1062256911yescharacteristic
792C22#1062256911yescharacteristic
793C22#1062256911yescharacteristic
794C22#1062256911yescharacteristic
795C22C2×#6693611yescharacteristic
796C22C2×#6693711yescharacteristic
797C22C2×C4×C22⋊D1111yescharacteristic
798C4—42no—
799C4—224no—
800C4—882no—
801C4#1062256911yescharacteristic
802C4#1062256911yescharacteristic
803C4#1062256911yescharacteristic
804C4#1062256911yescharacteristic
805C4C2×C22⋊C4×D1111yescharacteristic
806C4C2×(C22⋊D11)⋊C411yescharacteristic
807C4C2×#6699011yescharacteristic
808C4C2×#6699111yescharacteristic
809C2—21no—
810C2—21no—
811C2—21no—
812C2—21no—
813C2—21no—
814C2—21no—
815C2—21no—
816C2—82no—
817C2—444no—
818C2C2×#1062256911yescharacteristic
subgroupG/H
centerC4C2×#66990
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2879C2
socleC2×C11C2×#386
prime radicalC2×#10623353C2
cosocleC22×C4×C11C24
hypercenter#2879D11
hypocenterC11#20939
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C23×C4 ◁ #2879

Complements

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

NH ≅ G/Ntype
2. C2×#10623276C2semidirect
3. C2×#10622849C2semidirect
4. #13077136C2semidirect
5. #13068981C2semidirect
6. C2×#10622194C2semidirect
7. #13068343C2semidirect
8. C11×#2879C2semidirect
16. #10623353C4semidirect
20. C2×#66995C4semidirect
21. C2×#66985C4semidirect
28. #10623276C22semidirect
33. C11×#408C22semidirect
36. #10622849C22semidirect
41. #10622726C22semidirect
42. #10622194C22semidirect
43. #10622190C22semidirect
100. #66995C2×C4semidirect
104. #66985C2×C4semidirect
283. #2879D11semidirect
406. #408C2×D11semidirect
687. C11#20939semidirect

Maximal subgroups

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

subgroupindex
C2×#106233532
C2×#106232762
C2×#106228492
#130771362
#130689812
C2×#106221942
#130683432
C11×#28792
#2093911