Finite Group Databasebeta

← #14660446

Subgroups — #14660446

Order 2816.

1430 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623364C211yesmaximal, characteristic
2C22×#66869C211yesmaximal, characteristic, complemented
3C2×#10622746C211yesmaximal, characteristic, complemented
4C2×#10622845C211yesmaximal, characteristic, complemented
5C2×#10622192C211yesmaximal, characteristic, complemented
6#13066846C211yesmaximal, characteristic, complemented
7C22×C11×#104C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C22×#4339C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C42×C11C2211yescharacteristic
12#10623364—22no—
13#10623364—22no—
14#10623364—22no—
15#10623364C414yescomplemented
16C2×#66999—21no—
17C2×#66992—22no—
18C2×#66991—21no—
19C2×#66983—21no—
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C2×#66977—21no—
23C22×#4318C2211yescharacteristic
24C2×C11×#104—22no—
25C2×C11×#104—22no—
26C2×C11×#104—22no—
27#10622845—22no—
28#10622845—22no—
29C2×#66899—21no—
30C2×#66896—21no—
31C2×C11⋊#95—22no—
32#10622746—22no—
33#10622746—22no—
34C2×#66885—21no—
35C2×#66880—21no—
36C2×#66869—22no—
37C2×#66869—22no—
38C2×#66869—22no—
39#10622192—22no—
40C2×C11×#41—21no—
41C2×C11×#41—21no—
42C2×C11×#41—21no—
43C2×C11×#41—21no—
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×#41C2×C412yes—
51C2×C11×#41D412yes—
52C22×Q8×C11D411yescharacteristic
53C22×D4×C11—21no—
54C22×D4×C11D411yescharacteristic
55C23×C4×C11—21no—
56C23×C4×C11—21no—
57C23×C4×C11C2311yescharacteristic
58C22×C22⋊D11—21no—
59C22×C22⋊D11—22no—
60C23×Dic11—21no—
61C23×Dic11D412yes—
62C2×#4339—21no—
63C2×#4339—21no—
64C2×#4339—21no—
65C2×#4339—21no—
66C2×#4339—21no—
67C2×#4339—21no—
68C2×#4339—21no—
69C2×#4339—21no—
70C2×#4339—21no—
71C2×#4339—21no—
72C2×#4339C2×C412yes—
73C2×#4339D412yes—
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×M16D412yescomplemented
83C22×C8×C11—21no—
84C2×C42×C11—21no—
85C2×C42×C11—21no—
86C2×C42×C11—21no—
87C2×C42×C11—21no—
88C2×C42×C11—21no—
89C2×C42×C11D412yescomplemented
90C2×C22⋊Dic11—22no—
91#66999—24no—
92#66999—24no—
93#66992—28no—
94#66992—28no—
95#66991—24no—
96#66991—24no—
97#66983—24no—
98#66983—24no—
99C2×(C2×D11)⋊C4—22no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11—21no—
103C2×C4⋊Dic11—21no—
104C2×C4⋊Dic11—21no—
105C2×C4⋊Dic11—21no—
106C2×C4⋊Dic11—21no—
107C2×C4⋊Dic11—21no—
108C2×C4⋊Dic11—21no—
109C2×C4⋊Dic11C2×C412yes—
110C2×C4⋊Dic11D412yes—
111C2×C4⋊Dic11D412yescomplemented
112#66977—24no—
113#66977—24no—
114C2×Dic11⋊C4—22no—
115C2×#4318—21no—
116C2×#4318—21no—
117C2×#4318—21no—
118C2×#4318—21no—
119C2×#4318—21no—
120C2×#4318D412yescomplemented
121C22×C11⋊C8—21no—
122C11×#104—28no—
123#66899—24no—
124#66896—24no—
125C11⋊#95—44no—
126#66885—24no—
127#66880—24no—
128#66869—28no—
129#11002—111nomaximal, Sylow
130C24×C11—21no—
131C24×C11C2×D411yescharacteristic
132C23×D11—21no—
133C11×#41—22no—
134C11×#41—22no—
135C11×#41—22no—
136C11×#41—22no—
137C11×#41—22no—
138C11×#41—22no—
139C11×#41—22no—
140C11×#41—22no—
141C11×#41—41no—
142C11×#41—41no—
143C11×#41—41no—
144C11×#41—41no—
145C11×#41—41no—
146C11×#41—41no—
147C11×#41—41no—
148C11×#41—41no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11C22⋊C412yes—
155C2×D4×C11—22no—
156C2×D4×C11—22no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—41no—
163C2×D4×C11—41no—
164C2×D4×C11—41no—
165C2×D4×C11—41no—
166C2×D4×C11C22⋊C412yes—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—21no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—41no—
174C22×C4×C11—41no—
175C22×C4×C11—41no—
176C22×C4×C11—41no—
177C22×C4×C11—41no—
178C22×C4×C11—41no—
179C22×C4×C11—41no—
180C22×C4×C11—41no—
181C22×C4×C11C22×C411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
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×C11#4111yescharacteristic
192C22×C4×C11#4111yescharacteristic
193C22×C4×C11#4111yescharacteristic
194C22×C4×C11#4111yescharacteristic
195C2×C22⋊D11—28no—
196C2×C22⋊D11—22no—
197C2×C22⋊D11—22no—
198C2×C22⋊D11—41no—
199C2×C22⋊D11—41no—
200C2×C22⋊D11—41no—
201C2×C22⋊D11—41no—
202C2×C22⋊D11—82no—
203C2×C22⋊D11—82no—
204C22×Dic11—21no—
205C22×Dic11—22no—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—42no—
209C22×Dic11—42no—
210C22×Dic11—42no—
211C22×Dic11—42no—
212C22×Dic11—41no—
213C22×Dic11—41no—
214C22×Dic11C22⋊C414yes—
215#4339—22no—
216#4339—22no—
217#4339—22no—
218#4339—22no—
219#4339—22no—
220#4339—22no—
221#4339—22no—
222#4339—22no—
223#4339—41no—
224#4339—41no—
225#4339—41no—
226#4339—41no—
227#4339—41no—
228#4339—41no—
229#4339—41no—
230#4339—41no—
231C2×D44—21no—
232C2×D44—21no—
233C2×D44—21no—
234C2×D44—21no—
235C2×D44—21no—
236C2×D44C22⋊C412yes—
237C2×C4×D11—22no—
238C2×C4×D11—22no—
239C2×C4×D11—41no—
240C2×C4×D11—41no—
241C2×C4×D11—41no—
242C2×C4×D11—41no—
243C2×Dic22—21no—
244C2×Dic22—21no—
245C2×Dic22—21no—
246C2×Dic22—21no—
247C2×Dic22—21no—
248C2×Dic22C22⋊C412yes—
249C11×M16—22no—
250C11×M16—22no—
251C11×M16—41no—
252C11×M16—41no—
253C2×C8×C11—22no—
254C2×C8×C11—41no—
255C2×C8×C11—41no—
256C42×C11—22no—
257C42×C11—22no—
258C42×C11—41no—
259C42×C11—41no—
260C22⋊Dic11—28no—
261(C2×D11)⋊C4—28no—
262C4⋊Dic11—22no—
263C4⋊Dic11—22no—
264C4⋊Dic11—22no—
265C4⋊Dic11—22no—
266C4⋊Dic11—22no—
267C4⋊Dic11—22no—
268C4⋊Dic11—41no—
269C4⋊Dic11—41no—
270Dic11⋊C4—28no—
271#4318—22no—
272#4318—22no—
273#4318—41no—
274#4318—41no—
275C2×C11⋊C8—22no—
276C2×C11⋊C8—41no—
277C2×C11⋊C8—41no—
278C2×#537—111no—
279C22×#104—111no—
280C22×#104D1111yescharacteristic, complemented
281C2×#417—111no—
282C2×#417—111no—
283C2×#343—111no—
284C4⋊#95—111no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—21no—
288C23×C11—21no—
289C23×C11—22no—
290C23×C11—41no—
291C23×C11—41no—
292C23×C11—41no—
293C23×C11—41no—
294C23×C11—41no—
295C23×C11—41no—
296C23×C11C2×C22⋊C411yescharacteristic
297C23×C11#12011yescharacteristic
298C23×C11#12011yescharacteristic
299C23×C11#12111yescharacteristic
300C23×C11#12111yescharacteristic
301C23×C11#12411yescharacteristic
302C23×C11#12711yescharacteristic
303C22×D11—22no—
304C22×D11—41no—
305C22×D11—41no—
306C22×D11—41no—
307C22×D11—41no—
308C22×D11—41no—
309C22×D11—41no—
310Q8×C11—22no—
311Q8×C11—22no—
312Q8×C11—41no—
313Q8×C11—41no—
314D4×C11—22no—
315D4×C11—22no—
316D4×C11—42no—
317D4×C11—42no—
318D4×C11—42no—
319D4×C11—42no—
320D4×C11—41no—
321D4×C11—41no—
322C2×C4×C11—24no—
323C2×C4×C11—22no—
324C2×C4×C11—42no—
325C2×C4×C11—42no—
326C2×C4×C11—42no—
327C2×C4×C11—42no—
328C2×C4×C11—42no—
329C2×C4×C11—42no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—42no—
333C2×C4×C11—42no—
334C2×C4×C11—42no—
335C2×C4×C11—42no—
336C2×C4×C11C2×C22⋊C411yescharacteristic
337C2×C4×C11C2×C22⋊C411yescharacteristic
338C2×C4×C11C4×D411yescharacteristic
339C2×C4×C11C4×D411yescharacteristic
340C2×C4×C11C4×D411yescharacteristic
341C2×C4×C11C4×D411yescharacteristic
342C2×C4×C11#12011yescharacteristic
343C2×C4×C11#12011yescharacteristic
344C2×C4×C11#12011yescharacteristic
345C2×C4×C11#12011yescharacteristic
346C2×C4×C11#12011yescharacteristic
347C2×C4×C11#12011yescharacteristic
348C2×C4×C11#12111yescharacteristic
349C2×C4×C11#12111yescharacteristic
350C2×C4×C11#12111yescharacteristic
351C2×C4×C11#12111yescharacteristic
352C2×C4×C11#12111yescharacteristic
353C2×C4×C11#12111yescharacteristic
354C2×C4×C11#12111yescharacteristic
355C2×C4×C11#12111yescharacteristic
356C2×C4×C11#12111yescharacteristic
357C2×C4×C11#12111yescharacteristic
358C2×C4×C11#12311yescharacteristic
359C2×C4×C11#12311yescharacteristic
360C2×C4×C11#12311yescharacteristic
361C2×C4×C11#12311yescharacteristic
362C2×C4×C11#12411yescharacteristic
363C2×C4×C11#12711yescharacteristic
364C22⋊D11—42no—
365C22⋊D11—42no—
366C22⋊D11—42no—
367C22⋊D11—42no—
368C22⋊D11—88no—
369C2×Dic11—22no—
370C2×Dic11—24no—
371C2×Dic11—41no—
372C2×Dic11—41no—
373C2×Dic11—42no—
374C2×Dic11—42no—
375C2×Dic11—44no—
376C2×Dic11—44no—
377C2×Dic11—42no—
378C2×Dic11—82no—
379C2×Dic11—82no—
380C2×Dic11—81no—
381C2×Dic11—81no—
382D44—22no—
383D44—22no—
384D44—41no—
385D44—41no—
386C4×D11—42no—
387C4×D11—42no—
388C4×D11—42no—
389C4×D11—42no—
390Dic22—22no—
391Dic22—22no—
392Dic22—41no—
393Dic22—41no—
394C8×C11—42no—
395C11⋊C8—42no—
396C22×#41—111no—
397C22×#41C2×D1111yescharacteristic
398C22×M16—111no—
399C22×M16C2×D1111yescharacteristic
400#537—114no—
401#537—222no—
402#537—222no—
403#537—222no—
404C2×C22⋊Q8—221no—
405C2×C22⋊Q8—221no—
406C2×#121—221no—
407C2×#121—222no—
408C2×#121—221no—
409C22×C4⋊C4—111no—
410C22×C4⋊C4—111no—
411C22×C42C2×D1111yescharacteristic
412C2×#104—22no—
413C2×#104—22no—
414C2×#104—22no—
415C2×#104—222no—
416C2×#104—222no—
417C2×#104—222no—
418#417—222no—
419#417—222no—
420#417—222no—
421#417—222no—
422C2×#103—221no—
423C2×#103—221no—
424C2×#102—221no—
425C2×#102—221no—
426C2×#95—222no—
427#343—222no—
428C22×C11—21no—
429C22×C11—21no—
430C22×C11—21no—
431C22×C11—21no—
432C22×C11—21no—
433C22×C11—21no—
434C22×C11—21no—
435C22×C11—21no—
436C22×C11—21no—
437C22×C11—21no—
438C22×C11—21no—
439C22×C11—21no—
440C22×C11—42no—
441C22×C11—42no—
442C22×C11—42no—
443C22×C11—81no—
444C22×C11—81no—
445C22×C11—81no—
446C22×C11—81no—
447C22×C11#37911yescharacteristic
448C22×C11#39011yescharacteristic
449C22×C11#39011yescharacteristic
450C22×C11#39211yescharacteristic
451C22×C11#39211yescharacteristic
452C22×C11#39411yescharacteristic
453C22×C11#39411yescharacteristic
454C22×C11#45311yescharacteristic
455C22×C11#45411yescharacteristic
456C22×C11#45511yescharacteristic
457C22×C11#45611yescharacteristic
458C2×D11—42no—
459C2×D11—42no—
460C2×D11—42no—
461C2×D11—81no—
462C2×D11—81no—
463C2×D11—81no—
464C2×D11—81no—
465C4×C11—44no—
466C4×C11—42no—
467C4×C11#38611yescharacteristic
468C4×C11#38611yescharacteristic
469C4×C11#38611yescharacteristic
470C4×C11#38611yescharacteristic
471C4×C11#39211yescharacteristic
472C4×C11#39211yescharacteristic
473C4×C11#39411yescharacteristic
474C4×C11#39411yescharacteristic
475Dic11—44no—
476Dic11—42no—
477Dic11—82no—
478C2×#41—21no—
479C2×#41—21no—
480C2×#41—21no—
481C2×#41—21no—
482C2×#41—21no—
483C2×#41—21no—
484C2×#41—21no—
485C2×#41—21no—
486C2×#41—21no—
487C2×#41—21no—
488C2×#41—112no—
489C2×#41—112no—
490C2×#41—221no—
491C2×#41—221no—
492C2×#41—221no—
493C2×#41—221no—
494C2×#41—221no—
495C2×#41—221no—
496C2×#41—221no—
497C2×#41—221no—
498C2×#41—221no—
499C2×#41—221no—
500C2×#41C4×D1112yes—
501C2×#41C22⋊D1112yes—
502C22×Q8—111no—
503C22×Q8D4411yescharacteristic
504C22×D4—21no—
505C22×D4—111no—
506C22×D4—221no—
507C22×D4—222no—
508C22×D4D4411yescharacteristic
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—112no—
512C23×C4—221no—
513C23×C4—221no—
514C23×C4C22×D1111yescharacteristic
515C2×M16—21no—
516C2×M16—21no—
517C2×M16—21no—
518C2×M16—21no—
519C2×M16—21no—
520C2×M16—112no—
521C2×M16—221no—
522C2×M16—221no—
523C2×M16—221no—
524C2×M16—221no—
525C2×M16—221no—
526C2×M16C22⋊D1112yescomplemented
527C22×C8—21no—
528C22×C8—221no—
529C22⋊Q8—224no—
530C22⋊Q8—224no—
531C22⋊Q8—224no—
532C22⋊Q8—224no—
533#121—224no—
534#121—224no—
535#121—228no—
536#121—224no—
537#121—228no—
538#121—224no—
539C2×C4⋊C4—112no—
540C2×C4⋊C4—112no—
541C2×C4⋊C4—112no—
542C2×C4⋊C4—222no—
543C2×C4⋊C4—221no—
544C2×C4⋊C4—221no—
545C2×C4⋊C4—221no—
546C2×C4⋊C4—221no—
547C2×C4⋊C4—221no—
548C2×C4⋊C4—221no—
549C2×C4⋊C4—221no—
550C2×C4⋊C4—221no—
551C2×C4⋊C4—221no—
552C2×C22⋊C4—222no—
553C2×C22⋊C4—222no—
554C2×C42—21no—
555C2×C42—21no—
556C2×C42—21no—
557C2×C42—21no—
558C2×C42—21no—
559C2×C42C22⋊D1112yescomplemented
560#104—28no—
561#104—228no—
562#103—224no—
563#103—224no—
564#102—224no—
565#102—224no—
566#95—444no—
567C2×C11—21no—
568C2×C11—21no—
569C2×C11—21no—
570C2×C11—21no—
571C2×C11—82no—
572C2×C11#143811yescharacteristic
573C2×C11#179211yescharacteristic
574C2×C11#179311yescharacteristic
575C2×C11#200611yescharacteristic
576C2×C11#200711yescharacteristic
577C2×C11#203911yescharacteristic
578C2×C11#204011yescharacteristic
579D11—82no—
580C24—21no—
581C24—221no—
582C24D4×D1111yescharacteristic
583#41—22no—
584#41—22no—
585#41—22no—
586#41—22no—
587#41—22no—
588#41—22no—
589#41—22no—
590#41—22no—
591#41—41no—
592#41—41no—
593#41—41no—
594#41—41no—
595#41—41no—
596#41—41no—
597#41—41no—
598#41—41no—
599#41—222no—
600#41—222no—
601#41—222no—
602#41—222no—
603#41—222no—
604#41—222no—
605#41—222no—
606#41—222no—
607#41—441no—
608#41—441no—
609#41—441no—
610#41—441no—
611#41—441no—
612#41—441no—
613#41—441no—
614#41—441no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—112no—
621C2×Q8—221no—
622C2×Q8—221no—
623C2×Q8—221no—
624C2×Q8—221no—
625C2×Q8—221no—
626C2×Q8(C2×D11)⋊C412yes—
627C2×D4—22no—
628C2×D4—22no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—41no—
635C2×D4—41no—
636C2×D4—41no—
637C2×D4—41no—
638C2×D4—112no—
639C2×D4—222no—
640C2×D4—222no—
641C2×D4—228no—
642C2×D4—221no—
643C2×D4—221no—
644C2×D4—221no—
645C2×D4—221no—
646C2×D4—221no—
647C2×D4—441no—
648C2×D4—441no—
649C2×D4—441no—
650C2×D4—441no—
651C2×D4—882no—
652C2×D4—882no—
653C2×D4(C2×D11)⋊C412yes—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—21no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—41no—
661C22×C4—41no—
662C22×C4—41no—
663C22×C4—41no—
664C22×C4—41no—
665C22×C4—41no—
666C22×C4—41no—
667C22×C4—41no—
668C22×C4—114no—
669C22×C4—222no—
670C22×C4—221no—
671C22×C4—222no—
672C22×C4—222no—
673C22×C4—222no—
674C22×C4—222no—
675C22×C4—441no—
676C22×C4—441no—
677C22×C4—441no—
678C22×C4—441no—
679C22×C4—442no—
680C22×C4—442no—
681C22×C4—442no—
682C22×C4—442no—
683C22×C4—441no—
684C22×C4—441no—
685C22×C4C2×C4×D1111yescharacteristic
686C22×C4C2×D4411yescharacteristic
687C22×C4#433911yescharacteristic
688C22×C4#433911yescharacteristic
689C22×C4D4×D1111yescharacteristic
690C22×C4D4×D1111yescharacteristic
691C22×C4D4×D1111yescharacteristic
692C22×C4D4×D1111yescharacteristic
693C22×C4D4×D1111yescharacteristic
694C22×C4#434111yescharacteristic
695C22×C4#434111yescharacteristic
696C22×C4C2×C22⋊D1111yescharacteristic
697C22×C4C2×C22⋊D1111yescharacteristic
698C22×C4C2×C22⋊D1111yescharacteristic
699M16—22no—
700M16—22no—
701M16—41no—
702M16—41no—
703M16—222no—
704M16—222no—
705M16—441no—
706M16—441no—
707C2×C8—22no—
708C2×C8—41no—
709C2×C8—41no—
710C2×C8—222no—
711C2×C8—441no—
712C2×C8—441no—
713C4⋊C4—228no—
714C4⋊C4—222no—
715C4⋊C4—222no—
716C4⋊C4—222no—
717C4⋊C4—222no—
718C4⋊C4—222no—
719C4⋊C4—222no—
720C4⋊C4—441no—
721C4⋊C4—441no—
722C22⋊C4—228no—
723C22⋊C4—228no—
724C42—22no—
725C42—22no—
726C42—41no—
727C42—41no—
728C11#1100211yescharacteristic, complemented, Sylow
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—222no—
741C23—441no—
742C23—441no—
743C23—441no—
744C23—441no—
745C23—441no—
746C23—441no—
747C23C22⋊C4×D1111yescharacteristic
748C23#6693511yescharacteristic
749C23#6693711yescharacteristic
750C23#6693811yescharacteristic
751C23#6699011yescharacteristic
752C23#6699211yescharacteristic
753C23#6699311yescharacteristic
754Q8—22no—
755Q8—22no—
756Q8—41no—
757Q8—41no—
758Q8—222no—
759Q8—222no—
760Q8—441no—
761Q8—441no—
762D4—22no—
763D4—22no—
764D4—42no—
765D4—42no—
766D4—42no—
767D4—42no—
768D4—41no—
769D4—41no—
770D4—222no—
771D4—222no—
772D4—442no—
773D4—442no—
774D4—442no—
775D4—442no—
776D4—441no—
777D4—441no—
778D4—888no—
779C2×C4—24no—
780C2×C4—22no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—224no—
794C2×C4—222no—
795C2×C4—441no—
796C2×C4—441no—
797C2×C4—442no—
798C2×C4—442no—
799C2×C4—442no—
800C2×C4—442no—
801C2×C4—442no—
802C2×C4—442no—
803C2×C4—444no—
804C2×C4—444no—
805C2×C4—442no—
806C2×C4—882no—
807C2×C4—882no—
808C2×C4—881no—
809C2×C4—881no—
810C2×C4C22⋊C4×D1111yescharacteristic
811C2×C4(C22⋊D11)⋊C411yescharacteristic
812C2×C4(C22⋊D11)⋊C411yescharacteristic
813C2×C4#6693511yescharacteristic
814C2×C4#6693511yescharacteristic
815C2×C4#6693611yescharacteristic
816C2×C4#6693611yescharacteristic
817C2×C4#6693711yescharacteristic
818C2×C4#6693711yescharacteristic
819C2×C4#6693711yescharacteristic
820C2×C4#6693811yescharacteristic
821C2×C4#6693911yescharacteristic
822C2×C4C2×(C2×D11)⋊C411yescharacteristic
823C2×C4C4×C22⋊D1111yescharacteristic
824C2×C4C4×C22⋊D1111yescharacteristic
825C2×C4#6698211yescharacteristic
826C2×C4#6698311yescharacteristic
827C2×C4#6698311yescharacteristic
828C2×C4#6699011yescharacteristic
829C2×C4#6699011yescharacteristic
830C2×C4#6699011yescharacteristic
831C2×C4#6699111yescharacteristic
832C2×C4#6699111yescharacteristic
833C2×C4#6699211yescharacteristic
834C2×C4#6699211yescharacteristic
835C2×C4#6699211yescharacteristic
836C2×C4#6699311yescharacteristic
837C2×C4#6700611yescharacteristic
838C8—42no—
839C8—442no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—442no—
860C22—442no—
861C22—442no—
862C22—881no—
863C22—881no—
864C22—881no—
865C22—881no—
866C22#1062243511yescharacteristic
867C22#1062243811yescharacteristic
868C22#1062243911yescharacteristic
869C22#1062244011yescharacteristic
870C22#1062256811yescharacteristic
871C22#1062257011yescharacteristic
872C22#1062257011yescharacteristic
873C22#1062257211yescharacteristic
874C22#1062257311yescharacteristic
875C22#1062257411yescharacteristic
876C22#1062283611yescharacteristic
877C4—44no—
878C4—42no—
879C4—444no—
880C4—442no—
881C4—882no—
882C4#1062256911yescharacteristic
883C4#1062256911yescharacteristic
884C4#1062257111yescharacteristic
885C4#1062257211yescharacteristic
886C4#1062257311yescharacteristic
887C4#1062257411yescharacteristic
888C4#1062282611yescharacteristic
889C4#1062283611yescharacteristic
890C2—21no—
891C2—21no—
892C2—21no—
893C2—21no—
894C2—82no—
895C2—882no—
896C2#1306685511yescharacteristic
897C2#1306857111yescharacteristic
898C2#1306857611yescharacteristic
899C2#1306965911yescharacteristic
900C2#1306966411yescharacteristic
901C2#1306983911yescharacteristic
902C2#1306984411yescharacteristic
subgroupG/H
centerC23#66935
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC22×C11×#104C2
socleC23×C11#120
prime radicalC2×#10623364C2
cosocleC23×C4×C11C23
hypercenterC22×#104D11
hypocenterC11#11002
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
2. C22×#66869C2semidirect
3. C2×#10622746C2semidirect
4. C2×#10622845C2semidirect
5. C2×#10622192C2semidirect
6. #13066846C2semidirect
7. C22×C11×#104C2semidirect
15. #10623364C4semidirect
82. C2×C11×M16D4semidirect
89. C2×C42×C11D4semidirect
111. C2×C4⋊Dic11D4semidirect
120. C2×#4318D4semidirect
280. C22×#104D11semidirect
526. C2×M16C22⋊D11semidirect
559. C2×C42C22⋊D11semidirect
728. C11#11002semidirect

Maximal subgroups

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

subgroupindex
C2×#106233642
C22×#668692
C2×#106227462
C2×#106228452
C2×#106221922
#130668462
C22×C11×#1042
#1100211