Finite Group Databasebeta

← #15638698

Subgroups — #15638698

Order 2816.

2178 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623084C211yesmaximal, characteristic, complemented
2#13080736C214yesmaximal, complemented
3#13080616C214yesmaximal, complemented
4#13080202C214yesmaximal, complemented
5#13080152C214yesmaximal, complemented
6#13079631C212yesmaximal, complemented
7#13079418C211yesmaximal, characteristic, complemented
8#13079413C211yesmaximal, characteristic, complemented
9#13079377C212yesmaximal, complemented
10#13078783C212yesmaximal, complemented
11#13077874C211yesmaximal, characteristic, complemented
12#13077866C211yesmaximal, characteristic, complemented
13#13077832C212yesmaximal, complemented
14#13077645C211yesmaximal, characteristic, complemented
15C11×#3505C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C22×#4339C2211yescharacteristic, complemented
18C11×#553—22no—
19C11×#553C2212yescomplemented
20C11×#552C2212yescomplemented
21C11×#551—22no—
22C11×#548C2212yescomplemented
23C11×#546C2212yescomplemented
24C11×#539—21no—
25C11×#538—21no—
26C11×#534—21no—
27C11×#529C2212yes—
28C11×#525C2212yes—
29C2×C11×C22⋊Q8C2211yescharacteristic
30C2×C11×#121C2211yescharacteristic
31C11×#518—21no—
32C2×C4×D4×C11C2211yescharacteristic
33C2×#67003C2214yescomplemented
34C2×#66995C2212yescomplemented
35C2×#66993—21no—
36C2×#66985C2212yescomplemented
37C2×#66983C2211yescharacteristic
38C2×#66983C2211yescharacteristic, complemented
39#10623084—22no—
40#10623084—22no—
41#10623084C2214yes—
42#10623084C2214yescomplemented
43C2×#66946—21no—
44C2×#66937—21no—
45C2×#66937—21no—
46C2×#66927C2211yescharacteristic, complemented
47C2×C4×Dic22C2211yescharacteristic, complemented
48#10622851C2214yescomplemented
49#10622840C2212yescomplemented
50#10622830C2212yescomplemented
51#10622820C2211yescharacteristic
52#10622820C2211yescharacteristic
53C2×C22⋊(C11⋊C8)C2212yescomplemented
54#10622680C2214yescomplemented
55#10622676C2214yescomplemented
56#10622671C2214yescomplemented
57#10622667C2214yescomplemented
58#10622663C2212yescomplemented
59#10622662C2214yescomplemented
60#10622661C2214yescomplemented
61#10622660C2214yescomplemented
62#10622660C2214yescomplemented
63#10622659C2212yescomplemented
64#10622659C2212yescomplemented
65#10622657C2212yescomplemented
66#10622653C2212yes—
67#10622652C2214yescomplemented
68#10622651C2214yescomplemented
69#10622650C2214yescomplemented
70#10622650C2214yescomplemented
71#10622649C2212yes—
72#10622649C2212yes—
73#10622647C2212yes—
74#10622643C2214yescomplemented
75#10622640C2214yescomplemented
76#10622631C2214yescomplemented
77#10622628C2214yescomplemented
78#10622624C2214yescomplemented
79#10622624C2214yescomplemented
80#10622616C2214yescomplemented
81#10622615C2214yescomplemented
82#10622581C2212yescomplemented
83#10622580C2212yescomplemented
84#10622579C2212yescomplemented
85#10622579C2212yescomplemented
86#10622539C2212yescomplemented
87C2×C11×#41C2312yes—
88C22×Q8×C11C2311yescharacteristic
89C22×D4×C11—21no—
90C22×D4×C11D411yescharacteristic
91C22×D4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C22×C22⋊D11—21no—
95C22×C22⋊D11—21no—
96C22×C22⋊D11—21no—
97C22×C22⋊D11—21no—
98C2×#4339—21no—
99C2×#4339—21no—
100C2×#4339—22no—
101C2×#4339—44no—
102C2×#4339—44no—
103C2×#4339C2312yes—
104C2×#4339C2312yes—
105C2×#4339C2314yes—
106C22×D44—21no—
107C22×D44—21no—
108C22×D44C2311yescharacteristic
109C22×D44C2311yescharacteristic
110C22×C4×D11—21no—
111C22×C4×D11—21no—
112C22×Dic22C2311yescharacteristic
113C11×#126—22no—
114C11×#126—22no—
115C11×#126—22no—
116C11×#125—22no—
117C11×#125C2312yes—
118C11×#124—22no—
119C11×#124C2312yes—
120C11×#123—22no—
121C11×#123—22no—
122C11×#123—22no—
123C11×#123—22no—
124C11×#123—22no—
125C11×C22⋊Q8—21no—
126C11×C22⋊Q8—21no—
127C11×C22⋊Q8—22no—
128C11×C22⋊Q8C2312yes—
129C11×C22⋊Q8C2312yes—
130C11×C22⋊Q8C2312yes—
131C11×#121—22no—
132C11×#121—22no—
133C11×#121—21no—
134C11×#121—21no—
135C11×#121—22no—
136C11×#121C2312yes—
137C11×#121C2312yes—
138C11×#121C2312yes—
139C11×#120—22no—
140C11×#120—22no—
141C4×Q8×C11C2312yes—
142C4×D4×C11—22no—
143C4×D4×C11—22no—
144C4×D4×C11—22no—
145C4×D4×C11—22no—
146C4×D4×C11—22no—
147C4×D4×C11D412yes—
148C4×D4×C11D412yes—
149C4×D4×C11C2312yes—
150C4×D4×C11C2312yes—
151C4×D4×C11C2312yes—
152C11×#117—22no—
153C11×#117—22no—
154C11×#117C2312yes—
155C2×C11×C4⋊C4—21no—
156C2×C11×C4⋊C4D411yescharacteristic
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C22⋊C4—21no—
160C2×C11×C22⋊C4—21no—
161C2×C11×C22⋊C4—22no—
162C2×C11×C22⋊C4D411yescharacteristic
163C2×C11×C22⋊C4D411yescharacteristic
164C2×C42×C11C2311yescharacteristic
165#67003—48no—
166C2×#4326C2314yes—
167#66995—44no—
168C2×#4325C2314yes—
169C2×#4325C2314yes—
170#66993—24no—
171#66993—24no—
172C2×#4324C2314yes—
173#66985—44no—
174C2×#4323C2314yes—
175C2×#4323C2314yes—
176#66983—21no—
177#66983—21no—
178#66983—22no—
179#66983C2312yes—
180#66983C2312yes—
181#66983C2314yes—
182C2×(C2×D11)⋊C4—21no—
183C2×(C2×D11)⋊C4—21no—
184C2×C4⋊Dic11C2311yescharacteristic
185C2×Dic11⋊C4—21no—
186C2×C4×Dic11—21no—
187C2×#4318C2312yes—
188C2×#4318C2312yes—
189C22×C11⋊C8C2314yes—
190#66946—24no—
191#66946—24no—
192#66937—24no—
193#66937—24no—
194#66937—24no—
195#66937—24no—
196#66927—22no—
197#66927C2314yes—
198C4×Dic22—22no—
199C4×Dic22C2314yes—
200#66899C2314yes—
201#66896C2314yes—
202C22⋊(C11⋊C8)C2312yes—
203C22⋊(C11⋊C8)C2312yes—
204C22⋊(C11⋊C8)C2314yes—
205C22⋊(C11⋊C8)C2312yes—
206C22⋊(C11⋊C8)C2312yes—
207#66874C2314yes—
208#66874C2314yes—
209#66873C2314yes—
210#66873C2314yes—
211#66873C2314yes—
212#66873C2314yes—
213#66872C2314yes—
214#66871C2314yes—
215C4⋊(C11⋊C8)C2314yes—
216#66867C2314yes—
217#61577—111nomaximal, Sylow
218C24×C11—21no—
219C24×C11C2×D411yescharacteristic
220C24×C11C2×D411yescharacteristic
221C23×D11—21no—
222C23×D11—21no—
223C11×#41—44no—
224C2×Q8×C11—21no—
225C2×Q8×C11—42no—
226C2×Q8×C11C2412yes—
227C2×D4×C11—22no—
228C2×D4×C11—22no—
229C2×D4×C11—22no—
230C2×D4×C11—22no—
231C2×D4×C11—21no—
232C2×D4×C11—42no—
233C2×D4×C11—42no—
234C2×D4×C11—44no—
235C2×D4×C11C2×D412yes—
236C2×D4×C11C2×D412yes—
237C2×D4×C11C2412yes—
238C22×C4×C11—21no—
239C22×C4×C11—21no—
240C22×C4×C11—21no—
241C22×C4×C11—22no—
242C22×C4×C11—22no—
243C22×C4×C11—42no—
244C22×C4×C11—42no—
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2×D411yescharacteristic
251C22×C4×C11C2×D412yes—
252C22×C4×C11C2411yescharacteristic
253C22×C4×C11C2412yes—
254C22×C4×C11C2411yescharacteristic
255C22×C4×C11C2411yescharacteristic
256C2×C22⋊D11—22no—
257C2×C22⋊D11—24no—
258C2×C22⋊D11—22no—
259C2×C22⋊D11—22no—
260C2×C22⋊D11—24no—
261C2×C22⋊D11—22no—
262C2×C22⋊D11—44no—
263C2×C22⋊D11—44no—
264C2×C22⋊D11—82no—
265C2×C22⋊D11—82no—
266C22×Dic11—21no—
267C22×Dic11—21no—
268#4339—24no—
269#4339—24no—
270#4339—28no—
271#4339—44no—
272#4339—42no—
273#4339—42no—
274#4339—44no—
275#4339—44no—
276#4339—48no—
277C2×D44—21no—
278C2×D44—21no—
279C2×D44—24no—
280C2×D44—24no—
281C2×D44—42no—
282C2×D44—42no—
283C2×D44—44no—
284C2×D44—82no—
285C2×D44C2412yes—
286C2×D44C2412yes—
287C2×C4×D11—24no—
288C2×C4×D11—22no—
289C2×C4×D11—22no—
290C2×C4×D11—44no—
291C2×C4×D11—44no—
292C2×Dic22—24no—
293C2×Dic22—21no—
294C2×Dic22C2412yes—
295C11×C4⋊C4—22no—
296C11×C4⋊C4—22no—
297C11×C4⋊C4—21no—
298C11×C4⋊C4—21no—
299C11×C4⋊C4—22no—
300C11×C4⋊C4—22no—
301C11×C4⋊C4—22no—
302C11×C4⋊C4—22no—
303C11×C4⋊C4C2×D412yes—
304C11×C4⋊C4C2×D412yes—
305C11×C4⋊C4C2412yes—
306C11×C4⋊C4C2412yes—
307C11×C22⋊C4—22no—
308C11×C22⋊C4—22no—
309C11×C22⋊C4—22no—
310C11×C22⋊C4—22no—
311C11×C22⋊C4—22no—
312C11×C22⋊C4—22no—
313C11×C22⋊C4—22no—
314C11×C22⋊C4—22no—
315C11×C22⋊C4—22no—
316C11×C22⋊C4—22no—
317C11×C22⋊C4C2×D412yes—
318C11×C22⋊C4C2×D412yes—
319C11×C22⋊C4C2×D412yes—
320C11×C22⋊C4C2×D412yes—
321C42×C11—22no—
322C42×C11—22no—
323C42×C11C2×D412yes—
324C42×C11C2412yes—
325#4326—28no—
326#4325—44no—
327#4325—44no—
328#4324—28no—
329#4323—44no—
330#4323—44no—
331(C2×D11)⋊C4—24no—
332(C2×D11)⋊C4—22no—
333(C2×D11)⋊C4—22no—
334C4⋊Dic11—21no—
335C4⋊Dic11C2412yes—
336Dic11⋊C4—24no—
337C4×Dic11—24no—
338#4318—42no—
339#4318—42no—
340C2×C11⋊C8—44no—
341C2×C11⋊C8C2414yes—
342C2×C11⋊C8C2414yes—
343#3505D1111yescharacteristic, complemented
344C2×#550—111no—
345#3317—114no—
346#3309—114no—
347#3271—114no—
348#3268—114no—
349#3217—112no—
350#3193—111no—
351#3192—111no—
352#3188—112no—
353#3117—112no—
354#3007—111no—
355#3006—111no—
356#3002—112no—
357#2973—111no—
358C23×C11—22no—
359C23×C11—22no—
360C23×C11—22no—
361C23×C11—41no—
362C23×C11—41no—
363C23×C11—41no—
364C23×C11—41no—
365C23×C11—42no—
366C23×C11—81no—
367C23×C11—81no—
368C23×C11C22×D411yescharacteristic
369C23×C11C22×D412yes—
370C23×C11C22×D411yescharacteristic
371C23×C11C22×D411yescharacteristic
372C22×D11—22no—
373C22×D11—22no—
374C22×D11—42no—
375C22×D11—42no—
376C22×D11—42no—
377C22×D11—42no—
378C22×D11—42no—
379C22×D11—42no—
380Q8×C11—24no—
381Q8×C11—81no—
382D4×C11—24no—
383D4×C11—42no—
384D4×C11—42no—
385D4×C11—44no—
386D4×C11—44no—
387D4×C11—81no—
388D4×C11—82no—
389D4×C11—82no—
390C2×C4×C11—22no—
391C2×C4×C11—24no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11—41no—
401C2×C4×C11—42no—
402C2×C4×C11—41no—
403C2×C4×C11—41no—
404C2×C4×C11—42no—
405C2×C4×C11—82no—
406C2×C4×C11—82no—
407C2×C4×C11—81no—
408C2×C4×C11—81no—
409C2×C4×C11C22×D412yes—
410C2×C4×C11C22×D412yes—
411C2×C4×C11C22×D411yescharacteristic
412C2×C4×C11C22×D412yes—
413C2×C4×C11C22×D411yescharacteristic
414C2×C4×C11C22×D411yescharacteristic
415C2×C4×C11C2511yescharacteristic
416C22⋊D11—44no—
417C22⋊D11—48no—
418C22⋊D11—44no—
419C22⋊D11—82no—
420C22⋊D11—84no—
421C22⋊D11—82no—
422C2×Dic11—24no—
423C2×Dic11—22no—
424C2×Dic11—22no—
425C2×Dic11—42no—
426D44—22no—
427D44—24no—
428D44—22no—
429D44—48no—
430D44—42no—
431D44—42no—
432D44—84no—
433C4×D11—48no—
434C4×D11—44no—
435C4×D11—44no—
436Dic22—24no—
437Dic22—22no—
438Dic22H(5,𝔽2)14yes—
439C11⋊C8—24no—
440C11⋊C8—24no—
441C22×#41—111no—
442C22×#41—111no—
443C2×#137—112no—
444C2×AGL(1,ℤ/8)—112no—
445C2×#135—114no—
446#553—22no—
447#553C2×D1112yescomplemented
448#552C2×D1112yescomplemented
449#551—22no—
450#550—114no—
451#550—114no—
452#550—222no—
453#550—222no—
454#548C2×D1112yescomplemented
455#546C2×D1112yescomplemented
456#539—21no—
457#538—21no—
458#534—21no—
459C2×#127—111no—
460C2×#127—221no—
461#529C2×D1112yes—
462#525C2×D1112yes—
463C2×C22⋊Q8C2×D1111yescharacteristic
464C2×#121—111no—
465C2×#121—111no—
466C2×#121—221no—
467C2×#121—221no—
468C2×#121C2×D1111yescharacteristic
469#518—21no—
470C2×C4×Q8—111no—
471C2×C4×D4—221no—
472C2×C4×D4C2×D1111yescharacteristic
473#496—114no—
474#490—114no—
475#484—112no—
476#482—114no—
477#481—112no—
478#481—112no—
479#480—112no—
480#479—114no—
481#469—114no—
482#468—114no—
483#466—114no—
484#465—114no—
485#464—114no—
486#460—114no—
487#459—114no—
488#452—114no—
489#452—114no—
490#451—112no—
491#450—112no—
492#450—112no—
493#449—114no—
494#449—114no—
495#449—114no—
496#448—112no—
497#448—112no—
498#447—112no—
499#447—112no—
500#447—112no—
501#441—114no—
502#440—114no—
503#435—114no—
504#435—114no—
505#432—112no—
506#417—112no—
507#417—112no—
508#416—114no—
509#407—111no—
510#407—111no—
511C2×C22⋊C8—112no—
512C22×C11—21no—
513C22×C11—21no—
514C22×C11—21no—
515C22×C11—22no—
516C22×C11—21no—
517C22×C11—21no—
518C22×C11—22no—
519C22×C11—21no—
520C22×C11—21no—
521C22×C11—21no—
522C22×C11—22no—
523C22×C11—42no—
524C22×C11—42no—
525C22×C11—42no—
526C22×C11—82no—
527C22×C11—82no—
528C22×C11—162no—
529C22×C11#57512yes—
530C22×C11C23×D411yescharacteristic
531C2×D11—42no—
532C2×D11—42no—
533C2×D11—42no—
534C2×D11—42no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—84no—
538C2×D11—84no—
539C4×C11—22no—
540C4×C11—21no—
541C4×C11—22no—
542C4×C11—21no—
543C4×C11—21no—
544C4×C11—22no—
545C4×C11—42no—
546C4×C11—42no—
547C4×C11—42no—
548C4×C11C2×H(5,𝔽2)12yes—
549Dic11—24no—
550Dic11—42no—
551C2×#41—114no—
552C2×#41—112no—
553C2×#41—112no—
554C2×#41—221no—
555C2×#41—221no—
556C2×#41—222no—
557C2×#41—444no—
558C2×#41—444no—
559C2×#41C22×D1112yes—
560C22×Q8—111no—
561C22×Q8C22×D1111yescharacteristic
562C22×D4—21no—
563C22×D4—111no—
564C22×D4—111no—
565C22×D4—221no—
566C22×D4—221no—
567C22×D4—221no—
568C22×D4—221no—
569C22×D4—221no—
570C22×D4—221no—
571C22×D4C22⋊D1111yescharacteristic
572C22×D4C22×D1111yescharacteristic
573C23×C4—221no—
574C23×C4—221no—
575C23×C4C22×D1111yescharacteristic
576C23×C4C22×D1111yescharacteristic
577#137—444no—
578AGL(1,ℤ/8)—444no—
579#135—448no—
580C2×Q16—114no—
581C2×SD16—114no—
582C2×SD16—114no—
583C2×SD16—114no—
584C2×D8—114no—
585C2×D8—114no—
586C2×M16—112no—
587C2×M16—112no—
588C22×C8—114no—
589#127—114no—
590#127—224no—
591#127—224no—
592#127—222no—
593#126—22no—
594#126—22no—
595#126—22no—
596#125—22no—
597#125C22×D1112yes—
598#124—22no—
599#124C22×D1112yes—
600#123—22no—
601#123—22no—
602#123—22no—
603#123—22no—
604#123—22no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—22no—
608C22⋊Q8C22×D1112yes—
609C22⋊Q8C22×D1112yes—
610C22⋊Q8C22×D1112yes—
611#121—22no—
612#121—22no—
613#121—21no—
614#121—21no—
615#121—22no—
616#121—112no—
617#121—112no—
618#121—114no—
619#121—221no—
620#121—221no—
621#121—222no—
622#121—224no—
623#121—224no—
624#121—224no—
625#121—224no—
626#121C22×D1112yes—
627#121C22×D1112yes—
628#121C22×D1112yes—
629#120—22no—
630#120—22no—
631C4×Q8—114no—
632C4×Q8—222no—
633C4×Q8C22×D1112yes—
634C4×D4—22no—
635C4×D4—22no—
636C4×D4—22no—
637C4×D4—22no—
638C4×D4—22no—
639C4×D4—224no—
640C4×D4—224no—
641C4×D4C22⋊D1112yes—
642C4×D4C22⋊D1112yes—
643C4×D4C22×D1112yes—
644C4×D4C22×D1112yes—
645C4×D4C22×D1112yes—
646#117—22no—
647#117—22no—
648#117C22×D1112yes—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—111no—
651C2×C4⋊C4—221no—
652C2×C4⋊C4C22⋊D1111yescharacteristic
653C2×C4⋊C4C22×D1111yescharacteristic
654C2×C4⋊C4C22×D1111yescharacteristic
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—22no—
658C2×C22⋊C4—221no—
659C2×C22⋊C4—221no—
660C2×C22⋊C4C22⋊D1111yescharacteristic
661C2×C22⋊C4C22⋊D1111yescharacteristic
662C2×C42—221no—
663C2×C42C22×D1111yescharacteristic
664#107—114no—
665#106—114no—
666C4⋊C8—114no—
667#103—114no—
668#103—114no—
669#103—114no—
670#102—114no—
671#102—114no—
672#102—114no—
673#102—114no—
674#102—114no—
675C22⋊C8—112no—
676C22⋊C8—112no—
677C22⋊C8—114no—
678C22⋊C8—112no—
679C22⋊C8—112no—
680#97—114no—
681C2×C11—22no—
682C2×C11—41no—
683C2×C11—42no—
684C2×C11—41no—
685C2×C11—82no—
686C2×C11#348411yescharacteristic
687C2×C11C2×#57511yescharacteristic
688C2×C11#358511yescharacteristic
689D11—82no—
690D11—82no—
691C24—21no—
692C24—221no—
693C24—221no—
694C24C2×C22⋊D1111yescharacteristic
695C24C2×C22⋊D1111yescharacteristic
696#41—44no—
697#41—228no—
698#41—224no—
699#41—224no—
700#41—444no—
701#41—442no—
702#41—442no—
703#41—448no—
704#41—444no—
705#41—444no—
706C2×Q8—21no—
707C2×Q8—42no—
708C2×Q8—112no—
709C2×Q8—224no—
710C2×Q8—221no—
711C2×Q8C23×D1112yes—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—22no—
715C2×D4—22no—
716C2×D4—21no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—44no—
720C2×D4—112no—
721C2×D4—112no—
722C2×D4—222no—
723C2×D4—224no—
724C2×D4—222no—
725C2×D4—222no—
726C2×D4—224no—
727C2×D4—222no—
728C2×D4—224no—
729C2×D4—221no—
730C2×D4—221no—
731C2×D4—224no—
732C2×D4—442no—
733C2×D4—442no—
734C2×D4—444no—
735C2×D4—444no—
736C2×D4—444no—
737C2×D4—882no—
738C2×D4—882no—
739C2×D4—882no—
740C2×D4C2×C22⋊D1112yes—
741C2×D4C2×C22⋊D1112yes—
742C2×D4C23×D1112yes—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4—221no—
751C22×C4—221no—
752C22×C4—224no—
753C22×C4—222no—
754C22×C4—222no—
755C22×C4—444no—
756C22×C4—444no—
757C22×C4C2×C22⋊D1111yescharacteristic
758C22×C4C2×C22⋊D1111yescharacteristic
759C22×C4C2×C22⋊D1111yescharacteristic
760C22×C4C2×C22⋊D1111yescharacteristic
761C22×C4C2×C22⋊D1111yescharacteristic
762C22×C4C2×C22⋊D1111yescharacteristic
763C22×C4C2×C22⋊D1112yes—
764C22×C4C23×D1111yescharacteristic
765C22×C4C23×D1111yescharacteristic
766C22×C4C23×D1111yescharacteristic
767C22×C4C23×D1112yes—
768Q16—228no—
769SD16—228no—
770SD16—444no—
771SD16—444no—
772D8—444no—
773D8—444no—
774M16—442no—
775M16—442no—
776C2×C8—114no—
777C2×C8—114no—
778C2×C8—444no—
779C4⋊C4—22no—
780C4⋊C4—22no—
781C4⋊C4—21no—
782C4⋊C4—21no—
783C4⋊C4—22no—
784C4⋊C4—22no—
785C4⋊C4—22no—
786C4⋊C4—22no—
787C4⋊C4—112no—
788C4⋊C4—221no—
789C4⋊C4—224no—
790C4⋊C4C2×C22⋊D1112yes—
791C4⋊C4C2×C22⋊D1112yes—
792C4⋊C4C23×D1112yes—
793C4⋊C4C23×D1112yes—
794C22⋊C4—22no—
795C22⋊C4—22no—
796C22⋊C4—22no—
797C22⋊C4—22no—
798C22⋊C4—22no—
799C22⋊C4—22no—
800C22⋊C4—22no—
801C22⋊C4—22no—
802C22⋊C4—22no—
803C22⋊C4—22no—
804C22⋊C4—224no—
805C22⋊C4—222no—
806C22⋊C4—222no—
807C22⋊C4C2×C22⋊D1112yes—
808C22⋊C4C2×C22⋊D1112yes—
809C22⋊C4C2×C22⋊D1112yes—
810C22⋊C4C2×C22⋊D1112yes—
811C42—22no—
812C42—22no—
813C42—224no—
814C42C2×C22⋊D1112yes—
815C42C23×D1112yes—
816C11#6157711yescharacteristic, complemented, Sylow
817C23—22no—
818C23—22no—
819C23—22no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—42no—
825C23—81no—
826C23—81no—
827C23—222no—
828C23—222no—
829C23—442no—
830C23—442no—
831C23—442no—
832C23—442no—
833C23—442no—
834C23—442no—
835C23C22×C22⋊D1111yescharacteristic
836C23C22×C22⋊D1112yes—
837C23C22×C22⋊D1111yescharacteristic
838C23C22×C22⋊D1111yescharacteristic
839Q8—24no—
840Q8—81no—
841Q8—114no—
842Q8—224no—
843Q8—222no—
844D4—24no—
845D4—42no—
846D4—42no—
847D4—44no—
848D4—44no—
849D4—81no—
850D4—82no—
851D4—82no—
852D4—222no—
853D4—224no—
854D4—222no—
855D4—442no—
856D4—442no—
857D4—448no—
858D4—444no—
859D4—448no—
860D4—444no—
861D4—884no—
862D4—882no—
863D4—884no—
864D4—882no—
865C2×C4—22no—
866C2×C4—24no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—42no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—42no—
880C2×C4—82no—
881C2×C4—82no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—224no—
885C2×C4—222no—
886C2×C4—222no—
887C2×C4—448no—
888C2×C4—444no—
889C2×C4—444no—
890C2×C4—442no—
891C2×C4C22×C22⋊D1112yes—
892C2×C4C22×C22⋊D1112yes—
893C2×C4C22×C22⋊D1112yes—
894C2×C4C22×C22⋊D1111yescharacteristic
895C2×C4C22×C22⋊D1111yescharacteristic
896C2×C4C22×C22⋊D1111yescharacteristic
897C2×C4C24×D1111yescharacteristic
898C8—224no—
899C8—224no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—22no—
904C22—21no—
905C22—21no—
906C22—22no—
907C22—21no—
908C22—21no—
909C22—21no—
910C22—22no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—82no—
915C22—82no—
916C22—162no—
917C22—442no—
918C22—442no—
919C22—442no—
920C22—442no—
921C22—442no—
922C22—442no—
923C22—884no—
924C22—884no—
925C22#1062335312yes—
926C22C23×C22⋊D1111yescharacteristic
927C4—22no—
928C4—21no—
929C4—22no—
930C4—21no—
931C4—21no—
932C4—22no—
933C4—42no—
934C4—42no—
935C4—42no—
936C4—224no—
937C4—442no—
938C4D11×H(5,𝔽2)12yes—
939C2—22no—
940C2—41no—
941C2—41no—
942C2—42no—
943C2—82no—
944C2—882no—
945C2—882no—
946C2#1308224711yescharacteristic
947C2C2×#1062335311yescharacteristic
948C2#1308339511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3505C2
socleC22×C11C23×D4
hypercenter#3505D11
hypocenterC11#61577
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3505

Complements

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

NH ≅ G/Ntype
1. C2×#10623084C2semidirect
2. #13080736C2semidirect
3. #13080616C2semidirect
4. #13080202C2semidirect
5. #13080152C2semidirect
6. #13079631C2semidirect
7. #13079418C2semidirect
8. #13079413C2semidirect
9. #13079377C2semidirect
10. #13078783C2semidirect
11. #13077874C2semidirect
12. #13077866C2semidirect
13. #13077832C2semidirect
14. #13077645C2semidirect
15. C11×#3505C2semidirect
17. C22×#4339C22semidirect
19. C11×#553C22semidirect
20. C11×#552C22semidirect
22. C11×#548C22semidirect
23. C11×#546C22semidirect
33. C2×#67003C22semidirect
34. C2×#66995C22semidirect
36. C2×#66985C22semidirect
38. C2×#66983C22semidirect
42. #10623084C22semidirect
46. C2×#66927C22semidirect
47. C2×C4×Dic22C22semidirect
48. #10622851C22semidirect
49. #10622840C22semidirect
50. #10622830C22semidirect
53. C2×C22⋊(C11⋊C8)C22semidirect
54. #10622680C22semidirect
55. #10622676C22semidirect
56. #10622671C22semidirect
57. #10622667C22semidirect
58. #10622663C22semidirect
59. #10622662C22semidirect
60. #10622661C22semidirect
61. #10622660C22semidirect
62. #10622660C22semidirect
63. #10622659C22semidirect
64. #10622659C22semidirect
65. #10622657C22semidirect
67. #10622652C22semidirect
68. #10622651C22semidirect
69. #10622650C22semidirect
70. #10622650C22semidirect
74. #10622643C22semidirect
75. #10622640C22semidirect
76. #10622631C22semidirect
77. #10622628C22semidirect
78. #10622624C22semidirect
79. #10622624C22semidirect
80. #10622616C22semidirect
81. #10622615C22semidirect
82. #10622581C22semidirect
83. #10622580C22semidirect
84. #10622579C22semidirect
85. #10622579C22semidirect
86. #10622539C22semidirect
343. #3505D11semidirect
447. #553C2×D11semidirect
448. #552C2×D11semidirect
454. #548C2×D11semidirect
455. #546C2×D11semidirect
816. C11#61577semidirect

Maximal subgroups

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

subgroupindex
C2×#106230842
#130807362
#130806162
#130802022
#130801522
#130796312
#130794182
#130794132
#130793772
#130787832
#130778742
#130778662
#130778322
#130776452
C11×#35052
#6157711