Finite Group Databasebeta

← #15638616

Subgroups — #15638616

Order 2816.

2578 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×D44C211yesmaximal, characteristic, complemented
2#13080751C214yesmaximal, complemented
3#13080631C214yesmaximal, complemented
4#13080112C214yesmaximal, complemented
5#13080097C214yesmaximal, complemented
6#13079631C212yesmaximal, complemented
7#13079426C212yesmaximal, complemented
8#13079369C211yesmaximal, characteristic, complemented
9#13079364C211yesmaximal, characteristic, complemented
10#13078750C212yesmaximal, complemented
11#13077842C212yesmaximal, complemented
12C2×#10622659C211yesmaximal, characteristic, complemented
13C2×#10622649C211yesmaximal, characteristic, complemented
14#13077645C211yesmaximal, characteristic, complemented
15C11×#3505C211yesmaximal, characteristic, complemented
16C22×D4×D11—21no—
17C23×D44C2211yescharacteristic
18C23×D44C2211yescharacteristic, complemented
19C11×#553—22no—
20C11×#553C2212yescomplemented
21C11×#552C2212yescomplemented
22C11×#551—22no—
23C11×#548C2212yescomplemented
24C11×#546C2212yescomplemented
25C11×#539—21no—
26C11×#538—21no—
27C11×#534—21no—
28C11×#529C2212yescomplemented
29C11×#525C2212yescomplemented
30C2×C11×C22⋊Q8C2211yescharacteristic, complemented
31C2×C11×#121C2211yescharacteristic, complemented
32C11×#518—21no—
33C2×C4×D4×C11C2211yescharacteristic
34C2×#67002C2214yescomplemented
35C22×#4325C2212yescomplemented
36C22×#4323C2212yescomplemented
37C2×#66983C2211yescharacteristic
38C2×#66983C2211yescharacteristic, complemented
39D4×D44—22no—
40D4×D44—22no—
41D4×D44C2214yes—
42D4×D44C2214yescomplemented
43C2×#66948—21no—
44C2×#66935—21no—
45C2×#66935—21no—
46C2×#66927C2211yescharacteristic, complemented
47C2×C4×D44C2211yescharacteristic, complemented
48#10622851C2214yescomplemented
49#10622840C2212yescomplemented
50#10622830C2212yescomplemented
51#10622820C2212yescomplemented
52C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
53C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
54#10622680C2214yescomplemented
55#10622679C2214yescomplemented
56#10622671C2214yescomplemented
57#10622670C2214yescomplemented
58#10622662C2214yescomplemented
59#10622661C2214yescomplemented
60#10622659C2212yescomplemented
61#10622659C2214yescomplemented
62#10622659C2214yescomplemented
63#10622659C2212yescomplemented
64#10622659C2212yescomplemented
65#10622656C2212yescomplemented
66#10622652C2214yescomplemented
67#10622651C2214yescomplemented
68#10622649C2212yes—
69#10622649C2214yescomplemented
70#10622649C2214yescomplemented
71#10622649C2212yescomplemented
72#10622649C2212yescomplemented
73#10622646C2212yescomplemented
74#10622640C2214yescomplemented
75#10622639C2214yescomplemented
76#10622628C2214yescomplemented
77#10622627C2214yescomplemented
78#10622624C2214yescomplemented
79#10622624C2214yescomplemented
80#10622616C2214yescomplemented
81#10622614C2214yescomplemented
82#10622581C2212yescomplemented
83#10622580C2212yescomplemented
84C2×#66873C2212yescomplemented
85C2×#66873C2212yescomplemented
86#10622539C2212yescomplemented
87C24×D11—21no—
88C24×D11—21no—
89C2×C11×#41C2312yescomplemented
90C22×Q8×C11C2311yescharacteristic, complemented
91C22×D4×C11—21no—
92C22×D4×C11D411yescharacteristic
93C22×D4×C11C2311yescharacteristic, complemented
94C23×C4×C11C2311yescharacteristic
95C23×C4×C11C2311yescharacteristic
96C22×C22⋊D11—21no—
97C22×C22⋊D11—21no—
98C2×D4×D11—24no—
99C2×D4×D11—24no—
100C2×D4×D11—48no—
101C22×D44—21no—
102C22×D44—21no—
103C22×D44—21no—
104C22×D44—21no—
105C22×D44—21no—
106C22×D44—22no—
107C22×D44—21no—
108C22×D44—44no—
109C22×D44—44no—
110C22×D44C2311yescharacteristic
111C22×D44C2312yes—
112C22×D44C2314yes—
113C22×D44C2312yes—
114C22×D44C2311yescharacteristic
115C22×D44C2311yescharacteristic
116C22×C4×D11—21no—
117C11×#126—22no—
118C11×#126—22no—
119C11×#126—22no—
120C11×#125—22no—
121C11×#125C2312yescomplemented
122C11×#124—22no—
123C11×#124C2312yescomplemented
124C11×#123—22no—
125C11×#123—22no—
126C11×#123—22no—
127C11×#123—22no—
128C11×#123—22no—
129C11×C22⋊Q8—21no—
130C11×C22⋊Q8—21no—
131C11×C22⋊Q8—22no—
132C11×C22⋊Q8C2312yes—
133C11×C22⋊Q8C2312yescomplemented
134C11×C22⋊Q8C2312yescomplemented
135C11×#121—22no—
136C11×#121—22no—
137C11×#121—21no—
138C11×#121—21no—
139C11×#121—22no—
140C11×#121C2312yes—
141C11×#121C2312yescomplemented
142C11×#121C2312yescomplemented
143C11×#120—22no—
144C11×#120—22no—
145C4×Q8×C11C2312yescomplemented
146C4×D4×C11—22no—
147C4×D4×C11—22no—
148C4×D4×C11—22no—
149C4×D4×C11—22no—
150C4×D4×C11—22no—
151C4×D4×C11D412yes—
152C4×D4×C11D412yes—
153C4×D4×C11C2312yes—
154C4×D4×C11C2312yes—
155C4×D4×C11C2312yescomplemented
156C11×#117—22no—
157C11×#117—22no—
158C11×#117C2312yescomplemented
159C2×C11×C4⋊C4—21no—
160C2×C11×C4⋊C4D411yescharacteristic
161C2×C11×C4⋊C4C2311yescharacteristic, complemented
162C2×C11×C4⋊C4C2311yescharacteristic, complemented
163C2×C11×C22⋊C4—21no—
164C2×C11×C22⋊C4—21no—
165C2×C11×C22⋊C4—22no—
166C2×C11×C22⋊C4D411yescharacteristic
167C2×C11×C22⋊C4D411yescharacteristic
168C2×C42×C11C2311yescharacteristic
169#67002—48no—
170C2×#4325—44no—
171C2×#4325C2314yes—
172C2×#4325C2314yescomplemented
173C2×#4325C2314yescomplemented
174C2×#4323—44no—
175C2×#4323C2314yes—
176C2×#4323C2314yescomplemented
177C2×#4323C2314yescomplemented
178#66983—21no—
179#66983—21no—
180#66983—22no—
181#66983C2312yes—
182#66983C2312yes—
183#66983C2314yes—
184C2×(C2×D11)⋊C4—21no—
185C2×(C2×D11)⋊C4—21no—
186C2×(C2×D11)⋊C4—21no—
187C2×C4⋊Dic11C2311yescharacteristic
188C2×#4318C2314yescomplemented
189C22×C11⋊C8C2312yescomplemented
190C22×C11⋊C8C2312yescomplemented
191#66948—24no—
192#66948—24no—
193#66935—24no—
194#66935—24no—
195#66935—24no—
196#66935—24no—
197#66927—22no—
198#66927C2314yes—
199C4×D44—22no—
200C4×D44C2314yes—
201#66899C2314yescomplemented
202#66896C2314yescomplemented
203C22⋊(C11⋊C8)C2312yes—
204C22⋊(C11⋊C8)C2312yes—
205C22⋊(C11⋊C8)C2312yescomplemented
206C22⋊(C11⋊C8)C2312yescomplemented
207C22⋊(C11⋊C8)C2314yescomplemented
208#66873C2314yes—
209#66873C2314yes—
210#66873C2314yescomplemented
211#66873C2314yescomplemented
212#66873C2314yescomplemented
213#66873C2314yescomplemented
214#66872C2314yescomplemented
215#66871C2314yescomplemented
216C4⋊(C11⋊C8)C2314yescomplemented
217#66867C2314yescomplemented
218#61571—111nomaximal, Sylow
219C24×C11—21no—
220C24×C11C2×D411yescharacteristic
221C24×C11C2×D411yescharacteristic
222C23×D11—21no—
223C23×D11—21no—
224C23×D11—21no—
225C23×D11—24no—
226C23×D11—22no—
227C23×D11—22no—
228C23×D11—44no—
229C23×D11—44no—
230C23×D11—44no—
231C23×D11—44no—
232C23×D11—82no—
233C23×D11—82no—
234C11×#41—44no—
235C2×Q8×C11—21no—
236C2×Q8×C11—42no—
237C2×Q8×C11C2412yes—
238C2×D4×C11—24no—
239C2×D4×C11—22no—
240C2×D4×C11—22no—
241C2×D4×C11—22no—
242C2×D4×C11—22no—
243C2×D4×C11—21no—
244C2×D4×C11—42no—
245C2×D4×C11—44no—
246C2×D4×C11C2×D412yes—
247C2×D4×C11C2×D412yes—
248C2×D4×C11C2412yes—
249C22×C4×C11—21no—
250C22×C4×C11—21no—
251C22×C4×C11—21no—
252C22×C4×C11—22no—
253C22×C4×C11—22no—
254C22×C4×C11—42no—
255C22×C4×C11—42no—
256C22×C4×C11C2×D411yescharacteristic
257C22×C4×C11C2×D411yescharacteristic
258C22×C4×C11C2×D411yescharacteristic
259C22×C4×C11C2×D411yescharacteristic
260C22×C4×C11C2×D411yescharacteristic
261C22×C4×C11C2×D411yescharacteristic
262C22×C4×C11C2×D412yes—
263C22×C4×C11C2411yescharacteristic
264C22×C4×C11C2411yescharacteristic
265C22×C4×C11C2411yescharacteristic
266C22×C4×C11C2412yes—
267C2×C22⋊D11—24no—
268C2×C22⋊D11—22no—
269C2×C22⋊D11—22no—
270C2×C22⋊D11—44no—
271C2×C22⋊D11—44no—
272C22×Dic11—21no—
273D4×D11—416no—
274D4×D11—416no—
275C2×D44—24no—
276C2×D44—24no—
277C2×D44—24no—
278C2×D44—28no—
279C2×D44—21no—
280C2×D44—21no—
281C2×D44—21no—
282C2×D44—24no—
283C2×D44—24no—
284C2×D44—22no—
285C2×D44—22no—
286C2×D44—24no—
287C2×D44—42no—
288C2×D44—42no—
289C2×D44—44no—
290C2×D44—42no—
291C2×D44—42no—
292C2×D44—44no—
293C2×D44—44no—
294C2×D44—44no—
295C2×D44—44no—
296C2×D44—44no—
297C2×D44—48no—
298C2×D44—82no—
299C2×D44C2412yes—
300C2×D44C2412yes—
301C2×D44C2412yes—
302C2×C4×D11—24no—
303C2×C4×D11—44no—
304C11×C4⋊C4—22no—
305C11×C4⋊C4—22no—
306C11×C4⋊C4—21no—
307C11×C4⋊C4—21no—
308C11×C4⋊C4—22no—
309C11×C4⋊C4—22no—
310C11×C4⋊C4—22no—
311C11×C4⋊C4—22no—
312C11×C4⋊C4C2×D412yes—
313C11×C4⋊C4C2×D412yes—
314C11×C4⋊C4C2412yes—
315C11×C4⋊C4C2412yes—
316C11×C22⋊C4—22no—
317C11×C22⋊C4—22no—
318C11×C22⋊C4—22no—
319C11×C22⋊C4—22no—
320C11×C22⋊C4—22no—
321C11×C22⋊C4—22no—
322C11×C22⋊C4—22no—
323C11×C22⋊C4—22no—
324C11×C22⋊C4—22no—
325C11×C22⋊C4—22no—
326C11×C22⋊C4C2×D412yes—
327C11×C22⋊C4C2×D412yes—
328C11×C22⋊C4C2×D412yes—
329C11×C22⋊C4C2×D412yes—
330C42×C11—22no—
331C42×C11—22no—
332C42×C11C2×D412yes—
333C42×C11C2412yes—
334#4325—28no—
335#4325—44no—
336#4325—44no—
337#4323—28no—
338#4323—44no—
339#4323—44no—
340(C2×D11)⋊C4—24no—
341(C2×D11)⋊C4—24no—
342(C2×D11)⋊C4—22no—
343(C2×D11)⋊C4—22no—
344C4⋊Dic11—21no—
345C4⋊Dic11C2412yes—
346#4318—44no—
347C2×C11⋊C8—42no—
348C2×C11⋊C8—42no—
349C2×C11⋊C8C2414yes—
350C2×C11⋊C8C2414yes—
351#3505D1111yescharacteristic, complemented
352C2×D42—111no—
353#3318—114no—
354#3310—114no—
355#3265—114no—
356#3264—114no—
357#3217—112no—
358#3194—112no—
359#3187—111no—
360#3186—111no—
361#3114—112no—
362#3003—112no—
363C2×#450—111no—
364C2×#447—111no—
365#2973—111no—
366C23×C11—22no—
367C23×C11—22no—
368C23×C11—41no—
369C23×C11—41no—
370C23×C11—41no—
371C23×C11—41no—
372C23×C11—42no—
373C23×C11—81no—
374C23×C11—81no—
375C23×C11AGL(1,ℤ/8)14yescomplemented
376C23×C11C22×D412yes—
377C23×C11C22×D411yescharacteristic
378C23×C11C22×D411yescharacteristic
379C23×C11C22×D411yescharacteristic
380C22×D11—24no—
381C22×D11—22no—
382C22×D11—22no—
383C22×D11—22no—
384C22×D11—44no—
385C22×D11—44no—
386C22×D11—48no—
387C22×D11—42no—
388C22×D11—42no—
389C22×D11—42no—
390C22×D11—42no—
391C22×D11—42no—
392C22×D11—42no—
393C22×D11—48no—
394C22×D11—42no—
395C22×D11—42no—
396C22×D11—44no—
397C22×D11—44no—
398C22×D11—82no—
399C22×D11—82no—
400C22×D11—84no—
401C22×D11—816no—
402C22×D11—816no—
403Q8×C11—24no—
404Q8×C11—81no—
405D4×C11—24no—
406D4×C11—24no—
407D4×C11—24no—
408D4×C11—44no—
409D4×C11—44no—
410D4×C11—81no—
411D4×C11—82no—
412D4×C11—82no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—24no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—42no—
422C2×C4×C11—41no—
423C2×C4×C11—41no—
424C2×C4×C11—41no—
425C2×C4×C11—41no—
426C2×C4×C11—41no—
427C2×C4×C11—42no—
428C2×C4×C11—82no—
429C2×C4×C11—82no—
430C2×C4×C11—81no—
431C2×C4×C11—81no—
432C2×C4×C11C22×D411yescharacteristic
433C2×C4×C11C22×D412yes—
434C2×C4×C11C22×D412yes—
435C2×C4×C11C22×D411yescharacteristic
436C2×C4×C11C22×D411yescharacteristic
437C2×C4×C11C22×D412yes—
438C2×C4×C11C2511yescharacteristic
439C22⋊D11—48no—
440C22⋊D11—44no—
441C22⋊D11—44no—
442C2×Dic11—22no—
443C2×Dic11—42no—
444D44—24no—
445D44—22no—
446D44—22no—
447D44—24no—
448D44—22no—
449D44—48no—
450D44—44no—
451D44—44no—
452D44—42no—
453D44—42no—
454D44—48no—
455D44—84no—
456D44H(5,𝔽2)14yes—
457C4×D11—48no—
458C11⋊C8—24no—
459C11⋊C8—24no—
460C23×D4—111no—
461C23×D4—111no—
462C23×D4—221no—
463C2×AGL(1,ℤ/8)—114no—
464C22×SD16—112no—
465C22×D8—112no—
466#553—22no—
467#553C2×D1112yescomplemented
468#552C2×D1112yescomplemented
469#551—22no—
470#548C2×D1112yescomplemented
471#546C2×D1112yescomplemented
472D42—114no—
473D42—114no—
474D42—222no—
475D42—222no—
476#539—21no—
477#538—21no—
478#534—21no—
479C2×#127—111no—
480#529C2×D1112yescomplemented
481#525C2×D1112yescomplemented
482C2×C22⋊Q8C2×D1111yescharacteristic, complemented
483C2×#121—111no—
484C2×#121—111no—
485C2×#121—221no—
486C2×#121C2×D1111yescharacteristic, complemented
487C2×#120—221no—
488C2×#120—221no—
489#518—21no—
490C2×C4×D4—111no—
491C2×C4×D4C2×D1111yescharacteristic
492#496—114no—
493#490—114no—
494#483—112no—
495#482—114no—
496#481—112no—
497#480—112no—
498#480—112no—
499#478—114no—
500#469—114no—
501#468—114no—
502#466—114no—
503#465—114no—
504#463—114no—
505#460—114no—
506#459—114no—
507#450—112no—
508#450—112no—
509#450—112no—
510#450—114no—
511#450—114no—
512#449—114no—
513#448—112no—
514#447—112no—
515#447—112no—
516#447—112no—
517#447—112no—
518#447—114no—
519#447—114no—
520#442—114no—
521#440—114no—
522#435—114no—
523#435—114no—
524#432—112no—
525#418—114no—
526C2×#102—112no—
527C2×#102—112no—
528#407—112no—
529C2×C22⋊C8—111no—
530C2×C22⋊C8—111no—
531C22×C11—21no—
532C22×C11—21no—
533C22×C11—21no—
534C22×C11—21no—
535C22×C11—21no—
536C22×C11—21no—
537C22×C11—22no—
538C22×C11—22no—
539C22×C11—22no—
540C22×C11—44no—
541C22×C11—44no—
542C22×C11—42no—
543C22×C11—42no—
544C22×C11—42no—
545C22×C11—162no—
546C22×C11C2×AGL(1,ℤ/8)12yes—
547C22×C11C2×AGL(1,ℤ/8)12yes—
548C22×C11C2×AGL(1,ℤ/8)12yes—
549C22×C11C23×D411yescharacteristic
550C2×D11—24no—
551C2×D11—48no—
552C2×D11—42no—
553C2×D11—42no—
554C2×D11—42no—
555C2×D11—42no—
556C2×D11—42no—
557C2×D11—42no—
558C2×D11—42no—
559C2×D11—42no—
560C2×D11—88no—
561C2×D11—88no—
562C2×D11—816no—
563C2×D11—84no—
564C2×D11—84no—
565C4×C11—22no—
566C4×C11—21no—
567C4×C11—22no—
568C4×C11—21no—
569C4×C11—21no—
570C4×C11—22no—
571C4×C11—42no—
572C4×C11—42no—
573C4×C11—42no—
574C4×C11C2×H(5,𝔽2)12yes—
575Dic11—42no—
576C25—221no—
577C25—221no—
578C2×#41C22×D1112yescomplemented
579C22×Q8C22×D1111yescharacteristic, complemented
580C22×D4—21no—
581C22×D4—111no—
582C22×D4—112no—
583C22×D4—112no—
584C22×D4—114no—
585C22×D4—111no—
586C22×D4—111no—
587C22×D4—221no—
588C22×D4—221no—
589C22×D4—224no—
590C22×D4—224no—
591C22×D4—221no—
592C22×D4—221no—
593C22×D4—221no—
594C22×D4—221no—
595C22×D4—221no—
596C22×D4—222no—
597C22×D4—221no—
598C22×D4—444no—
599C22×D4—444no—
600C22×D4—448no—
601C22×D4C22⋊D1111yescharacteristic
602C22×D4C22×D1111yescharacteristic, complemented
603C23×C4—221no—
604C23×C4C22×D1111yescharacteristic
605C23×C4C22×D1111yescharacteristic
606AGL(1,ℤ/8)—448no—
607C2×SD16—114no—
608C2×SD16—114no—
609C2×SD16—114no—
610C2×SD16—444no—
611C2×D8—114no—
612C2×D8—114no—
613C2×D8—114no—
614C2×D8—444no—
615C2×M16—114no—
616C22×C8—112no—
617C22×C8—112no—
618#127—114no—
619#127—222no—
620#126—22no—
621#126—22no—
622#126—22no—
623#125—22no—
624#125C22×D1112yescomplemented
625#124—22no—
626#124C22×D1112yescomplemented
627#123—22no—
628#123—22no—
629#123—22no—
630#123—22no—
631#123—22no—
632C22⋊Q8—21no—
633C22⋊Q8—21no—
634C22⋊Q8—22no—
635C22⋊Q8C22×D1112yes—
636C22⋊Q8C22×D1112yescomplemented
637C22⋊Q8C22×D1112yescomplemented
638#121—22no—
639#121—22no—
640#121—21no—
641#121—21no—
642#121—22no—
643#121—112no—
644#121—112no—
645#121—114no—
646#121—221no—
647#121—221no—
648#121—222no—
649#121—224no—
650#121—224no—
651#121C22×D1112yes—
652#121C22×D1112yescomplemented
653#121C22×D1112yescomplemented
654#120—22no—
655#120—22no—
656#120—224no—
657#120—224no—
658#120—224no—
659#120—224no—
660C4×Q8C22×D1112yescomplemented
661C4×D4—22no—
662C4×D4—22no—
663C4×D4—22no—
664C4×D4—22no—
665C4×D4—22no—
666C4×D4—114no—
667C4×D4—222no—
668C4×D4C22⋊D1112yes—
669C4×D4C22⋊D1112yes—
670C4×D4C22×D1112yes—
671C4×D4C22×D1112yes—
672C4×D4C22×D1112yescomplemented
673#117—22no—
674#117—22no—
675#117C22×D1112yescomplemented
676C2×C4⋊C4—21no—
677C2×C4⋊C4—111no—
678C2×C4⋊C4C22⋊D1111yescharacteristic
679C2×C4⋊C4C22×D1111yescharacteristic, complemented
680C2×C4⋊C4C22×D1111yescharacteristic, complemented
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—221no—
685C2×C22⋊C4—221no—
686C2×C22⋊C4—221no—
687C2×C22⋊C4C22⋊D1111yescharacteristic
688C2×C22⋊C4C22⋊D1111yescharacteristic
689C2×C42C22×D1111yescharacteristic
690#107—114no—
691#106—114no—
692C4⋊C8—114no—
693#103—114no—
694#102—114no—
695#102—114no—
696#102—114no—
697#102—114no—
698#102—114no—
699#102—114no—
700#102—114no—
701C22⋊C8—112no—
702C22⋊C8—112no—
703C22⋊C8—112no—
704C22⋊C8—112no—
705C22⋊C8—114no—
706#97—114no—
707C2×C11—22no—
708C2×C11—22no—
709C2×C11—22no—
710C2×C11—42no—
711C2×C11—82no—
712C2×C11#348411yescharacteristic
713C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
714C2×C11#358511yescharacteristic
715D11—44no—
716D11—82no—
717D11—82no—
718C24—21no—
719C24—221no—
720C24—221no—
721C24—221no—
722C24—224no—
723C24—222no—
724C24—222no—
725C24—444no—
726C24—444no—
727C24—444no—
728C24—444no—
729C24—882no—
730C24—882no—
731C24C2×C22⋊D1111yescharacteristic
732C24C2×C22⋊D1111yescharacteristic
733#41—44no—
734C2×Q8—21no—
735C2×Q8—42no—
736C2×Q8C23×D1112yes—
737C2×D4—24no—
738C2×D4—22no—
739C2×D4—22no—
740C2×D4—22no—
741C2×D4—22no—
742C2×D4—21no—
743C2×D4—42no—
744C2×D4—44no—
745C2×D4—112no—
746C2×D4—112no—
747C2×D4—112no—
748C2×D4—224no—
749C2×D4—224no—
750C2×D4—224no—
751C2×D4—228no—
752C2×D4—224no—
753C2×D4—222no—
754C2×D4—222no—
755C2×D4—221no—
756C2×D4—224no—
757C2×D4—222no—
758C2×D4—222no—
759C2×D4—224no—
760C2×D4—221no—
761C2×D4—221no—
762C2×D4—224no—
763C2×D4—442no—
764C2×D4—442no—
765C2×D4—444no—
766C2×D4—442no—
767C2×D4—442no—
768C2×D4—444no—
769C2×D4—448no—
770C2×D4—444no—
771C2×D4—444no—
772C2×D4—444no—
773C2×D4—444no—
774C2×D4—4416no—
775C2×D4—4416no—
776C2×D4—444no—
777C2×D4—444no—
778C2×D4—882no—
779C2×D4C2×C22⋊D1112yes—
780C2×D4C2×C22⋊D1112yes—
781C2×D4C23×D1112yes—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—42no—
788C22×C4—42no—
789C22×C4—221no—
790C22×C4—224no—
791C22×C4—444no—
792C22×C4C2×C22⋊D1111yescharacteristic
793C22×C4C2×C22⋊D1111yescharacteristic
794C22×C4C2×C22⋊D1111yescharacteristic
795C22×C4C2×C22⋊D1111yescharacteristic
796C22×C4C2×C22⋊D1111yescharacteristic
797C22×C4C2×C22⋊D1111yescharacteristic
798C22×C4C2×C22⋊D1112yes—
799C22×C4C23×D1111yescharacteristic
800C22×C4C23×D1111yescharacteristic
801C22×C4C23×D1111yescharacteristic
802C22×C4C23×D1112yes—
803SD16—228no—
804SD16—444no—
805SD16—444no—
806D8—228no—
807D8—444no—
808D8—444no—
809M16—444no—
810C2×C8—114no—
811C2×C8—114no—
812C2×C8—442no—
813C2×C8—442no—
814C4⋊C4—22no—
815C4⋊C4—22no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—22no—
819C4⋊C4—22no—
820C4⋊C4—22no—
821C4⋊C4—22no—
822C4⋊C4—112no—
823C4⋊C4—221no—
824C4⋊C4C2×C22⋊D1112yes—
825C4⋊C4C2×C22⋊D1112yes—
826C4⋊C4C23×D1112yes—
827C4⋊C4C23×D1112yes—
828C22⋊C4—22no—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—22no—
832C22⋊C4—22no—
833C22⋊C4—22no—
834C22⋊C4—22no—
835C22⋊C4—22no—
836C22⋊C4—22no—
837C22⋊C4—22no—
838C22⋊C4—224no—
839C22⋊C4—224no—
840C22⋊C4—222no—
841C22⋊C4—222no—
842C22⋊C4C2×C22⋊D1112yes—
843C22⋊C4C2×C22⋊D1112yes—
844C22⋊C4C2×C22⋊D1112yes—
845C22⋊C4C2×C22⋊D1112yes—
846C42—22no—
847C42—22no—
848C42C2×C22⋊D1112yes—
849C42C23×D1112yes—
850C11#6157111yescharacteristic, complemented, Sylow
851C23—22no—
852C23—22no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—42no—
858C23—81no—
859C23—81no—
860C23—224no—
861C23—222no—
862C23—222no—
863C23—222no—
864C23—444no—
865C23—444no—
866C23—448no—
867C23—442no—
868C23—442no—
869C23—442no—
870C23—448no—
871C23—442no—
872C23—442no—
873C23—442no—
874C23—444no—
875C23—444no—
876C23—442no—
877C23—442no—
878C23—882no—
879C23—882no—
880C23—884no—
881C23—8816no—
882C23—8816no—
883C23#6700214yescomplemented
884C23C22×C22⋊D1112yes—
885C23C22×C22⋊D1111yescharacteristic
886C23C22×C22⋊D1111yescharacteristic
887C23C22×C22⋊D1111yescharacteristic
888Q8—24no—
889Q8—81no—
890D4—24no—
891D4—24no—
892D4—24no—
893D4—44no—
894D4—44no—
895D4—81no—
896D4—82no—
897D4—82no—
898D4—114no—
899D4—224no—
900D4—222no—
901D4—222no—
902D4—224no—
903D4—222no—
904D4—448no—
905D4—444no—
906D4—444no—
907D4—442no—
908D4—442no—
909D4—448no—
910D4—448no—
911D4—444no—
912D4—444no—
913D4—884no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—24no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—42no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—42no—
929C2×C4—82no—
930C2×C4—82no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—222no—
934C2×C4—448no—
935C2×C4—442no—
936C2×C4C22×C22⋊D1112yes—
937C2×C4C22×C22⋊D1112yes—
938C2×C4C22×C22⋊D1111yescharacteristic
939C2×C4C22×C22⋊D1112yes—
940C2×C4C22×C22⋊D1111yescharacteristic
941C2×C4C22×C22⋊D1111yescharacteristic
942C2×C4C24×D1111yescharacteristic
943C8—224no—
944C8—224no—
945C22—21no—
946C22—21no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—22no—
952C22—22no—
953C22—22no—
954C22—44no—
955C22—44no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—162no—
960C22—224no—
961C22—448no—
962C22—442no—
963C22—442no—
964C22—442no—
965C22—442no—
966C22—442no—
967C22—442no—
968C22—442no—
969C22—442no—
970C22—888no—
971C22—888no—
972C22—884no—
973C22—884no—
974C22—8816no—
975C22C2×#6700212yes—
976C22C2×#6700212yes—
977C22C2×#6700212yes—
978C22C23×C22⋊D1111yescharacteristic
979C4—22no—
980C4—21no—
981C4—22no—
982C4—21no—
983C4—21no—
984C4—22no—
985C4—42no—
986C4—42no—
987C4—42no—
988C4—442no—
989C4D11×H(5,𝔽2)12yes—
990C2—22no—
991C2—22no—
992C2—22no—
993C2—42no—
994C2—82no—
995C2—444no—
996C2—882no—
997C2—882no—
998C2#1308224711yescharacteristic
999C2C22×#6700211yescharacteristic
1000C2#1308339511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3505C2
socleC22×C11C23×D4
hypercenter#3505D11
hypocenterC11#61571
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×D4×D44C2semidirect
2. #13080751C2semidirect
3. #13080631C2semidirect
4. #13080112C2semidirect
5. #13080097C2semidirect
6. #13079631C2semidirect
7. #13079426C2semidirect
8. #13079369C2semidirect
9. #13079364C2semidirect
10. #13078750C2semidirect
11. #13077842C2semidirect
12. C2×#10622659C2semidirect
13. C2×#10622649C2semidirect
14. #13077645C2semidirect
15. C11×#3505C2semidirect
18. C23×D44C22semidirect
20. C11×#553C22semidirect
21. C11×#552C22semidirect
23. C11×#548C22semidirect
24. C11×#546C22semidirect
28. C11×#529C22semidirect
29. C11×#525C22semidirect
30. C2×C11×C22⋊Q8C22semidirect
31. C2×C11×#121C22semidirect
34. C2×#67002C22semidirect
35. C22×#4325C22semidirect
36. C22×#4323C22semidirect
38. C2×#66983C22semidirect
42. D4×D44C22semidirect
46. C2×#66927C22semidirect
47. C2×C4×D44C22semidirect
48. #10622851C22semidirect
49. #10622840C22semidirect
50. #10622830C22semidirect
51. #10622820C22semidirect
52. C2×C22⋊(C11⋊C8)C22semidirect
53. C2×C22⋊(C11⋊C8)C22semidirect
54. #10622680C22semidirect
55. #10622679C22semidirect
56. #10622671C22semidirect
57. #10622670C22semidirect
58. #10622662C22semidirect
59. #10622661C22semidirect
60. #10622659C22semidirect
61. #10622659C22semidirect
62. #10622659C22semidirect
63. #10622659C22semidirect
64. #10622659C22semidirect
65. #10622656C22semidirect
66. #10622652C22semidirect
67. #10622651C22semidirect
69. #10622649C22semidirect
70. #10622649C22semidirect
71. #10622649C22semidirect
72. #10622649C22semidirect
73. #10622646C22semidirect
74. #10622640C22semidirect
75. #10622639C22semidirect
76. #10622628C22semidirect
77. #10622627C22semidirect
78. #10622624C22semidirect
79. #10622624C22semidirect
80. #10622616C22semidirect
81. #10622614C22semidirect
82. #10622581C22semidirect
83. #10622580C22semidirect
84. C2×#66873C22semidirect
85. C2×#66873C22semidirect
86. #10622539C22semidirect
89. C2×C11×#41C23semidirect
90. C22×Q8×C11C23semidirect
93. C22×D4×C11C23semidirect
121. C11×#125C23semidirect
123. C11×#124C23semidirect
133. C11×C22⋊Q8C23semidirect
134. C11×C22⋊Q8C23semidirect
141. C11×#121C23semidirect
142. C11×#121C23semidirect
145. C4×Q8×C11C23semidirect
155. C4×D4×C11C23semidirect
158. C11×#117C23semidirect
161. C2×C11×C4⋊C4C23semidirect
162. C2×C11×C4⋊C4C23semidirect
172. C2×#4325C23semidirect
173. C2×#4325C23semidirect
176. C2×#4323C23semidirect
177. C2×#4323C23semidirect
188. C2×#4318C23semidirect
189. C22×C11⋊C8C23semidirect
190. C22×C11⋊C8C23semidirect
201. #66899C23semidirect
202. #66896C23semidirect
205. C22⋊(C11⋊C8)C23semidirect
206. C22⋊(C11⋊C8)C23semidirect
207. C22⋊(C11⋊C8)C23semidirect
210. #66873C23semidirect
211. #66873C23semidirect
212. #66873C23semidirect
213. #66873C23semidirect
214. #66872C23semidirect
215. #66871C23semidirect
216. C4⋊(C11⋊C8)C23semidirect
217. #66867C23semidirect
351. #3505D11semidirect
375. C23×C11AGL(1,ℤ/8)semidirect
467. #553C2×D11semidirect
468. #552C2×D11semidirect
470. #548C2×D11semidirect
471. #546C2×D11semidirect
480. #529C2×D11semidirect
481. #525C2×D11semidirect
482. C2×C22⋊Q8C2×D11semidirect
486. C2×#121C2×D11semidirect
578. C2×#41C22×D11semidirect
579. C22×Q8C22×D11semidirect
602. C22×D4C22×D11semidirect
624. #125C22×D11semidirect
626. #124C22×D11semidirect
636. C22⋊Q8C22×D11semidirect
637. C22⋊Q8C22×D11semidirect
652. #121C22×D11semidirect
653. #121C22×D11semidirect
660. C4×Q8C22×D11semidirect
672. C4×D4C22×D11semidirect
675. #117C22×D11semidirect
679. C2×C4⋊C4C22×D11semidirect
680. C2×C4⋊C4C22×D11semidirect
850. C11#61571semidirect
883. C23#67002semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D442
#130807512
#130806312
#130801122
#130800972
#130796312
#130794262
#130793692
#130793642
#130787502
#130778422
C2×#106226592
C2×#106226492
#130776452
C11×#35052
#6157111