Finite Group Databasebeta

← #15638466

Subgroups — #15638466

Order 2816.

2574 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082412C211yesmaximal, characteristic, complemented
2C2×#10623140C211yesmaximal, characteristic
3#13080438C214yesmaximal, complemented
4#13080435C214yesmaximal, complemented
5#13080309C214yesmaximal, complemented
6#13080305C214yesmaximal, complemented
7#13079555C212yesmaximal, complemented
8#13079373C211yesmaximal, characteristic, complemented
9#13079372C212yesmaximal, complemented
10#13078621C212yesmaximal, complemented
11C2×#10622344C211yesmaximal, characteristic, complemented
12C2×#10622659C211yesmaximal, characteristic, complemented
13D11×#450C212yesmaximal, complemented
14#13077638C211yesmaximal, characteristic, complemented
15C11×#3187C211yesmaximal, characteristic, complemented
16C22×D4×D11—21no—
17C22×D4×D11C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic, complemented
20C2×C11×#121C2211yescharacteristic
21Q8×C22⋊D11C2212yescomplemented
22C22×#4325C2212yescomplemented
23C2×#66993C2211yescharacteristic
24C2×#66990—21no—
25C2×C4×C22⋊D11C2211yescharacteristic
26C2×#66977C2211yescharacteristic, complemented
27C2×SD16×D11C2214yescomplemented
28C22×#4314C2212yescomplemented
29#10623167—22no—
30#10623166C2212yescomplemented
31#10623165—21no—
32#10623163C2212yescomplemented
33D11×C22⋊Q8C2212yescomplemented
34#10623154—21no—
35#10623153C2212yescomplemented
36#10623140—22no—
37#10623140—22no—
38#10623140C2214yes—
39#10623140C2214yes—
40#10623042—22no—
41#10623042C2212yescomplemented
42C2×#66948C2211yescharacteristic
43C2×#66946C2211yescharacteristic
44C2×#66937—21no—
45C2×#66935—21no—
46#10623017—21no—
47#10623014—21no—
48C11×#483C2212yescomplemented
49C11×#481C2212yescomplemented
50C11×#465C2214yescomplemented
51C11×#450C2212yescomplemented
52C11×#448C2212yescomplemented
53C2×C11×C22⋊C8C2211yescharacteristic, complemented
54#10622831C2212yescomplemented
55C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
56#10622788C2214yescomplemented
57#10622782C2214yescomplemented
58#10622776C2214yescomplemented
59C2×#66885C2212yescomplemented
60C8×C22⋊D11C2214yescomplemented
61#10622659C2212yes—
62#10622659C2214yescomplemented
63#10622659C2212yescomplemented
64#10622654C2214yescomplemented
65#10622653C2212yescomplemented
66#10622647C2212yescomplemented
67#10622584C2212yescomplemented
68C2×#66873C2212yescomplemented
69#10622483C2214yescomplemented
70#10622477C2214yescomplemented
71#10622476C2214yescomplemented
72#10622465C2214yescomplemented
73#10622431C2214yescomplemented
74#10622420C2214yescomplemented
75#10622419C2214yescomplemented
76#10622401C2214yescomplemented
77#10622389C2214yescomplemented
78D11×#102C2214yescomplemented
79#10622375C2214yescomplemented
80#10622373C2214yescomplemented
81#10622344C2212yes—
82#10622344C2214yescomplemented
83#10622344C2212yescomplemented
84(C22⋊D11)⋊C8C2214yescomplemented
85D11×C22⋊C8C2212yescomplemented
86#10622331C2212yescomplemented
87C24×D11—21no—
88C24×D11—21no—
89C22×Q8×C11C2311yescharacteristic, complemented
90C22×D4×C11—21no—
91C22×D4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C22×C22⋊D11—21no—
94C22×C22⋊D11—21no—
95C22×C22⋊D11—21no—
96C22×C22⋊D11D411yescharacteristic
97C2×Q8×D11C2312yescomplemented
98C2×D4×D11—24no—
99C2×D4×D11—24no—
100C2×D4×D11—22no—
101C2×D4×D11—44no—
102C2×D4×D11—48no—
103C2×D4×D11C2314yes—
104C22×D44—21no—
105C22×D44—21no—
106C22×D44—21no—
107C22×D44—21no—
108C22×D44—44no—
109C22×D44C2311yescharacteristic
110C22×D44C2312yes—
111C22×D44C2312yes—
112C22×D44C2311yescharacteristic
113C22×C4×D11—21no—
114C22×C4×D11C2311yescharacteristic
115C22×Dic22C2311yescharacteristic, complemented
116C2×C11×SD16C2314yescomplemented
117C22×C8×C11C2312yescomplemented
118C11×C22⋊Q8—21no—
119C11×C22⋊Q8—21no—
120C11×C22⋊Q8C2312yes—
121C11×C22⋊Q8C2312yescomplemented
122C11×#121—21no—
123C11×#121—21no—
124C11×#121C2312yes—
125C11×#121C2312yes—
126C2×C11×C4⋊C4—21no—
127C2×C11×C4⋊C4C2311yescharacteristic
128C2×C11×C4⋊C4C2311yescharacteristic, complemented
129C2×C11×C22⋊C4—21no—
130C2×C11×C22⋊C4—21no—
131C2×C22⋊Dic11—21no—
132C2×C22⋊Dic11D411yescharacteristic
133#66999—22no—
134#66999C2312yescomplemented
135Q8×Dic11C2312yescomplemented
136#66997—22no—
137#66997C2312yescomplemented
138C2×#4325—44no—
139C2×#4325C2314yes—
140C2×#4325C2314yescomplemented
141#66993—22no—
142#66993C2314yes—
143#66990—24no—
144#66990—24no—
145C2×#4324C2314yescomplemented
146C4×C22⋊D11—22no—
147C4×C22⋊D11—22no—
148C4×C22⋊D11D412yes—
149C4×C22⋊D11D412yes—
150C4×C22⋊D11C2312yes—
151C4×C22⋊D11C2312yes—
152C2×(C2×D11)⋊C4—21no—
153C2×(C2×D11)⋊C4—21no—
154C2×(C2×D11)⋊C4D411yescharacteristic
155C2×C4⋊Dic11C2311yescharacteristic, complemented
156#66977—21no—
157#66977—21no—
158#66977—22no—
159#66977—22no—
160#66977C2312yes—
161#66977C2312yescomplemented
162C2×Dic11⋊C4—21no—
163C2×Dic11⋊C4D411yescharacteristic
164C2×C4×Dic11C2311yescharacteristic
165C22×C11⋊C8C2312yescomplemented
166SD16×D11—48no—
167C2×#4314—44no—
168C2×#4314C2314yes—
169C2×#4314C2314yescomplemented
170C2×C8×D11C2314yescomplemented
171#66950—22no—
172#66950C2312yescomplemented
173#66949—22no—
174#66949—22no—
175#66949—22no—
176#66948—22no—
177#66948C2314yes—
178#66946—22no—
179#66946C2314yes—
180C4⋊C4×D11—22no—
181C4⋊C4×D11C2312yescomplemented
182#66942—22no—
183#66942—22no—
184#66942—22no—
185#66941—22no—
186#66941C2312yescomplemented
187#66940—22no—
188#66940C2312yescomplemented
189#66937—24no—
190#66937—24no—
191#66935—24no—
192#66935—24no—
193(C22⋊D11)⋊C4—22no—
194(C22⋊D11)⋊C4—22no—
195C22⋊C4×D11—22no—
196#66931—22no—
197#66931—22no—
198#66931—22no—
199#66931—22no—
200#66930—22no—
201C11×#106C2314yescomplemented
202C11×#103C2314yescomplemented
203C11×#102C2314yescomplemented
204C11×C22⋊C8C2312yes—
205C11×C22⋊C8C2312yescomplemented
206#66896C2314yescomplemented
207C22⋊(C11⋊C8)C2312yes—
208C22⋊(C11⋊C8)C2312yescomplemented
209#66885C2314yes—
210#66885C2314yescomplemented
211(C2×D11)⋊C8C2314yescomplemented
212Dic11⋊C8C2314yescomplemented
213C8×Dic11C2314yescomplemented
214#66874C2314yescomplemented
215#66873C2314yes—
216#66873C2314yescomplemented
217#66872C2314yescomplemented
218#61560—111nomaximal, Sylow
219C24×C11—21no—
220C24×C11C2×D411yescharacteristic
221C23×D11—21no—
222C23×D11—21no—
223C23×D11—22no—
224C23×D11—22no—
225C23×D11—24no—
226C23×D11—44no—
227C23×D11—44no—
228C23×D11—44no—
229C23×D11—44no—
230C23×D11—82no—
231C23×D11—82no—
232C23×D11C2×D411yescharacteristic
233C2×Q8×C11—21no—
234C2×Q8×C11—42no—
235C2×Q8×C11C2412yes—
236C2×D4×C11—22no—
237C2×D4×C11—22no—
238C2×D4×C11—21no—
239C2×D4×C11—42no—
240C2×D4×C11—44no—
241C2×D4×C11C2412yes—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11—42no—
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2411yescharacteristic
250C22×C4×C11C2411yescharacteristic
251C22×C4×C11C2411yescharacteristic
252C2×C22⋊D11—24no—
253C2×C22⋊D11—24no—
254C2×C22⋊D11—24no—
255C2×C22⋊D11—44no—
256C2×C22⋊D11—44no—
257C2×C22⋊D11—82no—
258C2×C22⋊D11SD1618yescomplemented
259C2×C22⋊D11C2×D412yes—
260C2×C22⋊D11C2×D412yes—
261C22×Dic11—21no—
262C22×Dic11—21no—
263C22×Dic11C2×D411yescharacteristic
264C22×Dic11C2×D411yescharacteristic
265C22×Dic11C2×D411yescharacteristic
266Q8×D11—44no—
267D4×D11—28no—
268D4×D11—44no—
269D4×D11—48no—
270D4×D11—416no—
271D4×D11—416no—
272C2×D44—24no—
273C2×D44—24no—
274C2×D44—24no—
275C2×D44—24no—
276C2×D44—21no—
277C2×D44—22no—
278C2×D44—22no—
279C2×D44—21no—
280C2×D44—42no—
281C2×D44—42no—
282C2×D44—42no—
283C2×D44—44no—
284C2×D44—44no—
285C2×D44—44no—
286C2×D44—44no—
287C2×D44C2412yes—
288C2×D44C2412yes—
289C2×C4×D11—24no—
290C2×C4×D11—22no—
291C2×C4×D11—22no—
292C2×C4×D11—42no—
293C2×C4×D11—44no—
294C2×C4×D11C2×D412yes—
295C2×C4×D11C2412yes—
296C2×Dic22—22no—
297C2×Dic22—22no—
298C2×Dic22—21no—
299C2×Dic22—42no—
300C2×Dic22C2412yes—
301C11×SD16—44no—
302C2×C8×C11—42no—
303C2×C8×C11C2414yes—
304C11×C4⋊C4—22no—
305C11×C4⋊C4—22no—
306C11×C4⋊C4—21no—
307C11×C4⋊C4—21no—
308C11×C4⋊C4C2412yes—
309C11×C4⋊C4C2412yes—
310C11×C22⋊C4—22no—
311C11×C22⋊C4—22no—
312C11×C22⋊C4—22no—
313C11×C22⋊C4—22no—
314C22⋊Dic11—22no—
315C22⋊Dic11—22no—
316C22⋊Dic11C2×D412yes—
317C22⋊Dic11C2×D412yes—
318#4325—28no—
319#4325—44no—
320#4324—44no—
321(C2×D11)⋊C4—24no—
322(C2×D11)⋊C4—24no—
323(C2×D11)⋊C4—22no—
324(C2×D11)⋊C4—22no—
325(C2×D11)⋊C4C2×D412yes—
326(C2×D11)⋊C4C2×D412yes—
327C4⋊Dic11—22no—
328C4⋊Dic11—22no—
329C4⋊Dic11—21no—
330C4⋊Dic11C2412yes—
331Dic11⋊C4—22no—
332Dic11⋊C4—22no—
333Dic11⋊C4—22no—
334Dic11⋊C4—22no—
335Dic11⋊C4—22no—
336Dic11⋊C4—22no—
337Dic11⋊C4—22no—
338Dic11⋊C4—22no—
339Dic11⋊C4C2×D412yes—
340Dic11⋊C4C2×D412yes—
341C4×Dic11—22no—
342C4×Dic11—22no—
343C4×Dic11C2×D412yes—
344C4×Dic11C2412yes—
345C2×C11⋊C8—42no—
346C2×C11⋊C8C2414yes—
347#4314—28no—
348#4314—44no—
349C8×D11—44no—
350#3501—111no—
351C2×D42—111no—
352#3295—114no—
353#3295—114no—
354D4×SD16—114no—
355D4×SD16—114no—
356#3208—112no—
357#3187—112no—
358#3187—111no—
359#3187D1111yescharacteristic, complemented
360#3101—112no—
361C2×#450—112no—
362C2×#450—111no—
363C2×#450—111no—
364#2972—111no—
365C23×C11—22no—
366C23×C11—41no—
367C23×C11—41no—
368C23×C11—42no—
369C23×C11—42no—
370C23×C11—42no—
371C23×C11C2×SD1614yescomplemented
372C23×C11C22×D411yescharacteristic
373C23×C11C22×D411yescharacteristic
374C23×C11C22×D411yescharacteristic
375C22×D11—24no—
376C22×D11—22no—
377C22×D11—22no—
378C22×D11—41no—
379C22×D11—41no—
380C22×D11—48no—
381C22×D11—44no—
382C22×D11—44no—
383C22×D11—42no—
384C22×D11—42no—
385C22×D11—42no—
386C22×D11—42no—
387C22×D11—42no—
388C22×D11—44no—
389C22×D11—44no—
390C22×D11—48no—
391C22×D11—84no—
392C22×D11—82no—
393C22×D11—82no—
394C22×D11—816no—
395C22×D11—816no—
396C22×D11C2×SD1614yescomplemented
397C22×D11C22×D412yes—
398Q8×C11—24no—
399Q8×C11—81no—
400D4×C11—24no—
401D4×C11—42no—
402D4×C11—44no—
403D4×C11—44no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—41no—
411C2×C4×C11—41no—
412C2×C4×C11—41no—
413C2×C4×C11—42no—
414C2×C4×C11—81no—
415C2×C4×C11—81no—
416C2×C4×C11C22×D411yescharacteristic
417C2×C4×C11C22×D411yescharacteristic
418C2×C4×C11C22×D411yescharacteristic
419C2×C4×C11C2511yescharacteristic
420C22⋊D11—48no—
421C22⋊D11—48no—
422C22⋊D11—84no—
423C22⋊D11C2×SD1618yescomplemented
424C22⋊D11C2×SD1618yescomplemented
425C2×Dic11—22no—
426C2×Dic11—22no—
427C2×Dic11—41no—
428C2×Dic11—41no—
429C2×Dic11—81no—
430C2×Dic11—81no—
431C2×Dic11C2×SD1614yescomplemented
432C2×Dic11C22×D412yes—
433C2×Dic11C22×D412yes—
434C2×Dic11C22×D412yes—
435D44—24no—
436D44—22no—
437D44—22no—
438D44—22no—
439D44—44no—
440D44—44no—
441D44—42no—
442D44—48no—
443D44H(5,𝔽2)14yes—
444C4×D11—24no—
445C4×D11—42no—
446C4×D11—48no—
447C4×D11—82no—
448C4×D11—82no—
449Dic22—24no—
450Dic22—82no—
451Dic22—82no—
452Dic22—81no—
453C8×C11—24no—
454C11⋊C8—24no—
455C23×D4—111no—
456C23×D4—111no—
457C23×D4—221no—
458C22×SD16—112no—
459C22×SD16—114no—
460C22×SD16—112no—
461#554—112no—
462#554—112no—
463#554—222no—
464#554—222no—
465D4×Q8—112no—
466D4×Q8—112no—
467D42—114no—
468D42—114no—
469D42—222no—
470D42—222no—
471#544—221no—
472#543—221no—
473#543—221no—
474#533—112no—
475C2×#127—111no—
476C2×C22⋊Q8—111no—
477C2×C22⋊Q8—112no—
478C2×C22⋊Q8C2×D1111yescharacteristic, complemented
479C2×#121—111no—
480C2×#121—221no—
481C2×#121C2×D1111yescharacteristic
482C2×#120—221no—
483C2×#120—221no—
484#518—221no—
485C2×C4×D4—111no—
486C2×C4×D4—111no—
487#492—114no—
488#486—114no—
489#483—112no—
490#483C2×D1112yescomplemented
491#481—112no—
492#481—114no—
493#481C2×D1112yescomplemented
494#476—114no—
495#465—114no—
496#465—114no—
497#465—114no—
498#465C2×D1114yescomplemented
499#461—114no—
500#460—114no—
501#460—114no—
502#450—112no—
503#450—114no—
504#450—112no—
505#450—112no—
506#450—114no—
507#450—114no—
508#450—112no—
509#450—112no—
510#450—114no—
511#450C2×D1112yescomplemented
512#448—112no—
513#448—114no—
514#448C2×D1112yescomplemented
515C4×SD16—114no—
516C4×SD16—114no—
517C8×D4—114no—
518C8×D4—114no—
519#431—112no—
520C2×#102—112no—
521C2×#102—112no—
522C2×#102—114no—
523C2×C22⋊C8—111no—
524C2×C22⋊C8—112no—
525C2×C22⋊C8C2×D1111yescharacteristic, complemented
526C22×C11—21no—
527C22×C11—21no—
528C22×C11—21no—
529C22×C11—21no—
530C22×C11—21no—
531C22×C11—21no—
532C22×C11—44no—
533C22×C11—42no—
534C22×C11—42no—
535C22×C11—42no—
536C22×C11—84no—
537C22×C11C22×SD1612yes—
538C22×C11C22×SD1612yes—
539C22×C11C22×SD1612yes—
540C22×C11C23×D411yescharacteristic
541C2×D11—22no—
542C2×D11—22no—
543C2×D11—24no—
544C2×D11—44no—
545C2×D11—48no—
546C2×D11—42no—
547C2×D11—42no—
548C2×D11—42no—
549C2×D11—42no—
550C2×D11—42no—
551C2×D11—816no—
552C2×D11—88no—
553C2×D11—88no—
554C2×D11—84no—
555C2×D11C22×SD1614yes—
556C4×C11—21no—
557C4×C11—21no—
558C4×C11—21no—
559C4×C11—42no—
560C4×C11—42no—
561C4×C11—42no—
562C4×C11C2×H(5,𝔽2)12yes—
563Dic11—22no—
564Dic11—22no—
565Dic11—42no—
566Dic11—42no—
567Dic11C22×SD1614yes—
568C25—221no—
569C25—221no—
570C22×Q8—112no—
571C22×Q8—111no—
572C22×Q8C22×D1111yescharacteristic, complemented
573C22×D4—21no—
574C22×D4—111no—
575C22×D4—114no—
576C22×D4—111no—
577C22×D4—112no—
578C22×D4—112no—
579C22×D4—111no—
580C22×D4—221no—
581C22×D4—222no—
582C22×D4—221no—
583C22×D4—221no—
584C22×D4—221no—
585C22×D4—224no—
586C22×D4—224no—
587C22×D4—221no—
588C22×D4—221no—
589C22×D4—221no—
590C22×D4—444no—
591C22×D4—448no—
592C22×D4—444no—
593C22×D4C22×D1111yescharacteristic
594C23×C4—111no—
595C23×C4—221no—
596C23×C4C22×D1111yescharacteristic
597C2×SD16—114no—
598C2×SD16—114no—
599C2×SD16—114no—
600C2×SD16—114no—
601C2×SD16—114no—
602C2×SD16—444no—
603C2×SD16—448no—
604C2×SD16—444no—
605C2×SD16C22×D1114yescomplemented
606C22×C8—112no—
607C22×C8—114no—
608C22×C8C22×D1112yescomplemented
609C4⋊Q8—112no—
610C4⋊Q8—112no—
611C4⋊Q8—222no—
612C4⋊Q8—222no—
613#127—114no—
614#127—222no—
615#125—222no—
616#125—222no—
617#125—222no—
618C22⋊Q8—21no—
619C22⋊Q8—21no—
620C22⋊Q8—112no—
621C22⋊Q8—112no—
622C22⋊Q8—112no—
623C22⋊Q8—112no—
624C22⋊Q8—222no—
625C22⋊Q8—222no—
626C22⋊Q8—222no—
627C22⋊Q8—222no—
628C22⋊Q8—222no—
629C22⋊Q8—222no—
630C22⋊Q8—222no—
631C22⋊Q8—222no—
632C22⋊Q8—222no—
633C22⋊Q8—222no—
634C22⋊Q8—222no—
635C22⋊Q8—221no—
636C22⋊Q8—221no—
637C22⋊Q8C22×D1112yes—
638C22⋊Q8C22×D1112yescomplemented
639#121—21no—
640#121—21no—
641#121—114no—
642#121—224no—
643#121—224no—
644#121—222no—
645#121C22×D1112yes—
646#121C22×D1112yes—
647#120—224no—
648#120—224no—
649#120—224no—
650#120—224no—
651C4×Q8—112no—
652C4×Q8—112no—
653C4×Q8—222no—
654C4×D4—112no—
655C4×D4—112no—
656C4×D4—112no—
657C4×D4—112no—
658C4×D4—114no—
659C4×D4—222no—
660C4×D4—222no—
661C4×D4—222no—
662C4×D4—222no—
663C4×D4—222no—
664#117—222no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—111no—
667C2×C4⋊C4—111no—
668C2×C4⋊C4—112no—
669C2×C4⋊C4—222no—
670C2×C4⋊C4—221no—
671C2×C4⋊C4C22×D1111yescharacteristic
672C2×C4⋊C4C22×D1111yescharacteristic, complemented
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—111no—
676C2×C22⋊C4—111no—
677C2×C22⋊C4—222no—
678C2×C22⋊C4—221no—
679C2×C22⋊C4—221no—
680C2×C22⋊C4—221no—
681C2×C42—111no—
682#106—114no—
683#106C22×D1114yescomplemented
684C4⋊C8—114no—
685#103—114no—
686#103C22×D1114yescomplemented
687#102—114no—
688#102—114no—
689#102—114no—
690#102—114no—
691#102—114no—
692#102C22×D1114yescomplemented
693C22⋊C8—112no—
694C22⋊C8—112no—
695C22⋊C8—114no—
696C22⋊C8C22×D1112yes—
697C22⋊C8C22×D1112yescomplemented
698C4×C8—114no—
699C2×C11—22no—
700C2×C11—22no—
701C2×C11—22no—
702C2×C11—82no—
703C2×C11#348411yescharacteristic
704C2×C11C23×SD1611yescharacteristic
705C2×C11#358511yescharacteristic
706D11—24no—
707D11—44no—
708D11—82no—
709C24—21no—
710C24—111no—
711C24—224no—
712C24—221no—
713C24—221no—
714C24—222no—
715C24—222no—
716C24—444no—
717C24—444no—
718C24—444no—
719C24—444no—
720C24—882no—
721C24—882no—
722C24D4×D1111yescharacteristic
723C2×Q8—21no—
724C2×Q8—42no—
725C2×Q8—112no—
726C2×Q8—222no—
727C2×Q8—222no—
728C2×Q8—221no—
729C2×Q8—442no—
730C2×Q8—444no—
731C2×Q8C23×D1112yes—
732C2×D4—22no—
733C2×D4—22no—
734C2×D4—21no—
735C2×D4—42no—
736C2×D4—44no—
737C2×D4—118no—
738C2×D4—112no—
739C2×D4—112no—
740C2×D4—112no—
741C2×D4—112no—
742C2×D4—224no—
743C2×D4—224no—
744C2×D4—224no—
745C2×D4—224no—
746C2×D4—224no—
747C2×D4—224no—
748C2×D4—224no—
749C2×D4—228no—
750C2×D4—221no—
751C2×D4—222no—
752C2×D4—222no—
753C2×D4—221no—
754C2×D4—442no—
755C2×D4—442no—
756C2×D4—442no—
757C2×D4—444no—
758C2×D4—444no—
759C2×D4—444no—
760C2×D4—444no—
761C2×D4—444no—
762C2×D4—444no—
763C2×D4—4416no—
764C2×D4—4416no—
765C2×D4—448no—
766C2×D4—444no—
767C2×D4—882no—
768C2×D4C23×D1112yes—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—42no—
773C22×C4—111no—
774C22×C4—111no—
775C22×C4—111no—
776C22×C4—112no—
777C22×C4—112no—
778C22×C4—224no—
779C22×C4—222no—
780C22×C4—222no—
781C22×C4—221no—
782C22×C4—221no—
783C22×C4—442no—
784C22×C4—444no—
785C22×C4D4×D1111yescharacteristic
786C22×C4D4×D1111yescharacteristic
787C22×C4D4×D1111yescharacteristic
788C22×C4C23×D1111yescharacteristic
789C22×C4C23×D1111yescharacteristic
790C22×C4C23×D1111yescharacteristic
791SD16—44no—
792SD16—228no—
793SD16—228no—
794SD16—444no—
795SD16—444no—
796SD16—444no—
797C2×C8—42no—
798C2×C8—114no—
799C2×C8—444no—
800C2×C8—442no—
801C2×C8C23×D1114yes—
802C4⋊C4—22no—
803C4⋊C4—22no—
804C4⋊C4—21no—
805C4⋊C4—21no—
806C4⋊C4—112no—
807C4⋊C4—112no—
808C4⋊C4—112no—
809C4⋊C4—222no—
810C4⋊C4—222no—
811C4⋊C4—222no—
812C4⋊C4—222no—
813C4⋊C4—222no—
814C4⋊C4—222no—
815C4⋊C4—222no—
816C4⋊C4—222no—
817C4⋊C4—221no—
818C4⋊C4—222no—
819C4⋊C4—222no—
820C4⋊C4C23×D1112yes—
821C4⋊C4C23×D1112yes—
822C22⋊C4—22no—
823C22⋊C4—22no—
824C22⋊C4—22no—
825C22⋊C4—22no—
826C22⋊C4—112no—
827C22⋊C4—112no—
828C22⋊C4—112no—
829C22⋊C4—112no—
830C22⋊C4—224no—
831C22⋊C4—224no—
832C22⋊C4—222no—
833C22⋊C4—222no—
834C22⋊C4—222no—
835C22⋊C4—222no—
836C42—112no—
837C42—112no—
838C42—222no—
839C42—222no—
840C11#6156011yescharacteristic, complemented, Sylow
841C23—22no—
842C23—41no—
843C23—41no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—112no—
848C23—114no—
849C23—224no—
850C23—222no—
851C23—222no—
852C23—441no—
853C23—441no—
854C23—444no—
855C23—444no—
856C23—442no—
857C23—442no—
858C23—442no—
859C23—448no—
860C23—448no—
861C23—442no—
862C23—444no—
863C23—444no—
864C23—442no—
865C23—882no—
866C23—882no—
867C23—884no—
868C23—8816no—
869C23—8816no—
870C23SD16×D1114yescomplemented
871C23C2×D4×D1111yescharacteristic
872C23C2×D4×D1111yescharacteristic
873C23C2×D4×D1111yescharacteristic
874Q8—24no—
875Q8—81no—
876Q8—224no—
877Q8—881no—
878Q8—882no—
879Q8—882no—
880D4—24no—
881D4—42no—
882D4—44no—
883D4—44no—
884D4—118no—
885D4—118no—
886D4—114no—
887D4—224no—
888D4—222no—
889D4—222no—
890D4—222no—
891D4—444no—
892D4—444no—
893D4—442no—
894D4—448no—
895D4—448no—
896D4—448no—
897D4—884no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—42no—
908C2×C4—81no—
909C2×C4—81no—
910C2×C4—114no—
911C2×C4—112no—
912C2×C4—112no—
913C2×C4—112no—
914C2×C4—224no—
915C2×C4—222no—
916C2×C4—222no—
917C2×C4—442no—
918C2×C4—448no—
919C2×C4—441no—
920C2×C4—441no—
921C2×C4—882no—
922C2×C4—882no—
923C2×C4—881no—
924C2×C4—881no—
925C2×C4C2×D4×D1111yescharacteristic
926C2×C4C2×D4×D1111yescharacteristic
927C2×C4C2×D4×D1111yescharacteristic
928C2×C4C24×D1111yescharacteristic
929C8—24no—
930C8—224no—
931C22—21no—
932C22—21no—
933C22—21no—
934C22—21no—
935C22—21no—
936C22—21no—
937C22—44no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—84no—
942C22—114no—
943C22—222no—
944C22—222no—
945C22—224no—
946C22—444no—
947C22—448no—
948C22—442no—
949C22—442no—
950C22—442no—
951C22—442no—
952C22—442no—
953C22—888no—
954C22—888no—
955C22—884no—
956C22—8816no—
957C22C2×SD16×D1112yes—
958C22C2×SD16×D1112yes—
959C22C2×SD16×D1112yes—
960C22C22×D4×D1111yescharacteristic
961C4—21no—
962C4—21no—
963C4—21no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—114no—
968C4—222no—
969C4—222no—
970C4—442no—
971C4—442no—
972C4D11×H(5,𝔽2)12yes—
973C2—22no—
974C2—22no—
975C2—22no—
976C2—82no—
977C2—224no—
978C2—444no—
979C2—882no—
980C2#1308224811yescharacteristic
981C2C22×SD16×D1111yescharacteristic
982C2#1308339311yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3187C2
socleC22×C11C23×D4
prime radicalC2×#10623140C2
hypercenter#3187D11
hypocenterC11#61560
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3187

Complements

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

NH ≅ G/Ntype
1. #13082412C2semidirect
3. #13080438C2semidirect
4. #13080435C2semidirect
5. #13080309C2semidirect
6. #13080305C2semidirect
7. #13079555C2semidirect
8. #13079373C2semidirect
9. #13079372C2semidirect
10. #13078621C2semidirect
11. C2×#10622344C2semidirect
12. C2×#10622659C2semidirect
13. D11×#450C2semidirect
14. #13077638C2semidirect
15. C11×#3187C2semidirect
19. C2×C11×C22⋊Q8C22semidirect
21. Q8×C22⋊D11C22semidirect
22. C22×#4325C22semidirect
26. C2×#66977C22semidirect
27. C2×SD16×D11C22semidirect
28. C22×#4314C22semidirect
30. #10623166C22semidirect
32. #10623163C22semidirect
33. D11×C22⋊Q8C22semidirect
35. #10623153C22semidirect
41. #10623042C22semidirect
48. C11×#483C22semidirect
49. C11×#481C22semidirect
50. C11×#465C22semidirect
51. C11×#450C22semidirect
52. C11×#448C22semidirect
53. C2×C11×C22⋊C8C22semidirect
54. #10622831C22semidirect
55. C2×C22⋊(C11⋊C8)C22semidirect
56. #10622788C22semidirect
57. #10622782C22semidirect
58. #10622776C22semidirect
59. C2×#66885C22semidirect
60. C8×C22⋊D11C22semidirect
62. #10622659C22semidirect
63. #10622659C22semidirect
64. #10622654C22semidirect
65. #10622653C22semidirect
66. #10622647C22semidirect
67. #10622584C22semidirect
68. C2×#66873C22semidirect
69. #10622483C22semidirect
70. #10622477C22semidirect
71. #10622476C22semidirect
72. #10622465C22semidirect
73. #10622431C22semidirect
74. #10622420C22semidirect
75. #10622419C22semidirect
76. #10622401C22semidirect
77. #10622389C22semidirect
78. D11×#102C22semidirect
79. #10622375C22semidirect
80. #10622373C22semidirect
82. #10622344C22semidirect
83. #10622344C22semidirect
84. (C22⋊D11)⋊C8C22semidirect
85. D11×C22⋊C8C22semidirect
86. #10622331C22semidirect
89. C22×Q8×C11C23semidirect
97. C2×Q8×D11C23semidirect
115. C22×Dic22C23semidirect
116. C2×C11×SD16C23semidirect
117. C22×C8×C11C23semidirect
121. C11×C22⋊Q8C23semidirect
128. C2×C11×C4⋊C4C23semidirect
134. #66999C23semidirect
135. Q8×Dic11C23semidirect
137. #66997C23semidirect
140. C2×#4325C23semidirect
145. C2×#4324C23semidirect
155. C2×C4⋊Dic11C23semidirect
161. #66977C23semidirect
165. C22×C11⋊C8C23semidirect
169. C2×#4314C23semidirect
170. C2×C8×D11C23semidirect
172. #66950C23semidirect
181. C4⋊C4×D11C23semidirect
186. #66941C23semidirect
188. #66940C23semidirect
201. C11×#106C23semidirect
202. C11×#103C23semidirect
203. C11×#102C23semidirect
205. C11×C22⋊C8C23semidirect
206. #66896C23semidirect
208. C22⋊(C11⋊C8)C23semidirect
210. #66885C23semidirect
211. (C2×D11)⋊C8C23semidirect
212. Dic11⋊C8C23semidirect
213. C8×Dic11C23semidirect
214. #66874C23semidirect
216. #66873C23semidirect
217. #66872C23semidirect
258. C2×C22⋊D11SD16semidirect
359. #3187D11semidirect
371. C23×C11C2×SD16semidirect
396. C22×D11C2×SD16semidirect
423. C22⋊D11C2×SD16semidirect
424. C22⋊D11C2×SD16semidirect
431. C2×Dic11C2×SD16semidirect
478. C2×C22⋊Q8C2×D11semidirect
490. #483C2×D11semidirect
493. #481C2×D11semidirect
498. #465C2×D11semidirect
511. #450C2×D11semidirect
514. #448C2×D11semidirect
525. C2×C22⋊C8C2×D11semidirect
572. C22×Q8C22×D11semidirect
605. C2×SD16C22×D11semidirect
608. C22×C8C22×D11semidirect
638. C22⋊Q8C22×D11semidirect
672. C2×C4⋊C4C22×D11semidirect
683. #106C22×D11semidirect
686. #103C22×D11semidirect
692. #102C22×D11semidirect
697. C22⋊C8C22×D11semidirect
840. C11#61560semidirect
870. C23SD16×D11semidirect

Maximal subgroups

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

subgroupindex
#130824122
C2×#106231402
#130804382
#130804352
#130803092
#130803052
#130795552
#130793732
#130793722
#130786212
C2×#106223442
C2×#106226592
D11×#4502
#130776382
C11×#31872
#6156011