Finite Group Databasebeta

← #15638626

Subgroups — #15638626

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
1#13082457C211yesmaximal, characteristic, complemented
2C2×D4×C22⋊D11C211yesmaximal, characteristic, complemented
3#13080753C214yesmaximal, complemented
4#13080641C214yesmaximal, complemented
5#13080111C214yesmaximal, complemented
6#13080100C214yesmaximal, complemented
7#13079637C212yesmaximal, complemented
8#13079433C212yesmaximal, complemented
9#13079369C211yesmaximal, characteristic, complemented
10#13079367C211yesmaximal, characteristic, complemented
11#13078755C212yesmaximal, complemented
12#13077844C212yesmaximal, complemented
13C2×#10622830C211yesmaximal, characteristic, complemented
14#13077642C211yesmaximal, characteristic, complemented
15C2×C11×#450C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C23×C22⋊D11—21no—
18C22×D4×D11C2211yescharacteristic, complemented
19C22×C11×SD16C2212yescomplemented
20C2×C11×C22⋊Q8C2211yescharacteristic, complemented
21C2×#67006—21no—
22#10623348C2212yescomplemented
23C2×#66993C2211yescharacteristic, complemented
24C2×#66992—21no—
25D4×C22⋊D11—22no—
26D4×C22⋊D11—22no—
27D4×C22⋊D11C2214yes—
28D4×C22⋊D11C2214yescomplemented
29C2×#66991C2211yescharacteristic, complemented
30C2×#66990—21no—
31C2×D4×Dic11C2211yescharacteristic, complemented
32C22×#4323C2212yescomplemented
33C2×#66983C2211yescharacteristic
34C2×#66983C2211yescharacteristic, complemented
35C2×C4×C22⋊D11C2211yescharacteristic
36C2×#66967C2214yescomplemented
37#10623176—21no—
38#10623175—21no—
39#10623173C2212yescomplemented
40#10623168—22no—
41#10623161C2212yescomplemented
42#10623158C2212yescomplemented
43#10623155C2212yescomplemented
44#10623045—22no—
45#10623045C2212yescomplemented
46#10623024—21no—
47#10623017—21no—
48C11×#450C2212yescomplemented
49C11×#450C2212yescomplemented
50C11×#450C2214yescomplemented
51C2×C11×#102C2212yescomplemented
52C2×C11×C22⋊C8C2211yescharacteristic, complemented
53#10622840C2212yescomplemented
54#10622830C2212yes—
55#10622830C2212yescomplemented
56#10622830C2214yescomplemented
57C2×#66896C2212yescomplemented
58C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
59#10622789C2214yescomplemented
60#10622787C2214yescomplemented
61#10622785C2214yescomplemented
62#10622782C2214yescomplemented
63#10622778C2214yescomplemented
64#10622777C2214yescomplemented
65#10622776C2214yescomplemented
66#10622728C2214yescomplemented
67#10622724C2214yescomplemented
68#10622661C2214yescomplemented
69#10622659C2212yescomplemented
70#10622656C2212yescomplemented
71#10622581C2212yescomplemented
72#10622399C2214yescomplemented
73#10622398C2214yescomplemented
74#10622397C2214yescomplemented
75#10622395C2214yescomplemented
76#10622386C2214yescomplemented
77#10622383C2214yescomplemented
78#10622379C2214yescomplemented
79#10622377C2214yescomplemented
80#10622349C2212yescomplemented
81#10622349C2212yescomplemented
82#10622345C2212yescomplemented
83#10622345C2212yescomplemented
84#10622343C2214yescomplemented
85#10622339C2212yescomplemented
86#10622332C2212yescomplemented
87C25×C11—21no—
88C24×D11—21no—
89C22×Q8×C11C2311yescharacteristic, complemented
90C22×D4×C11—21no—
91C22×D4×C11—21no—
92C22×D4×C11—21no—
93C22×D4×C11—44no—
94C22×D4×C11C2311yescharacteristic
95C22×D4×C11C2312yes—
96C22×D4×C11C2312yes—
97C22×D4×C11C2311yescharacteristic
98C23×C4×C11C2311yescharacteristic
99C22×C22⋊D11—21no—
100C22×C22⋊D11—21no—
101C22×C22⋊D11—21no—
102C22×C22⋊D11—24no—
103C22×C22⋊D11—24no—
104C22×C22⋊D11—21no—
105C22×C22⋊D11—21no—
106C22×C22⋊D11—21no—
107C22×C22⋊D11—48no—
108C22×C22⋊D11D411yescharacteristic
109C23×Dic11—21no—
110C2×#4343C2312yescomplemented
111C2×D4×D11—22no—
112C2×D4×D11—44no—
113C2×D4×D11C2314yes—
114C22×D44C2311yescharacteristic
115C22×D44C2311yescharacteristic, complemented
116C22×C4×D11C2311yescharacteristic
117C2×C11×SD16—44no—
118C2×C11×SD16C2314yes—
119C2×C11×SD16C2314yescomplemented
120C22×C8×C11C2312yescomplemented
121C11×C22⋊Q8—21no—
122C11×C22⋊Q8—21no—
123C11×C22⋊Q8C2312yes—
124C11×C22⋊Q8C2312yescomplemented
125C2×C11×C4⋊C4—21no—
126C2×C11×C4⋊C4C2311yescharacteristic, complemented
127C2×C11×C22⋊C4—21no—
128#67006—24no—
129#67006—24no—
130C2×C22⋊Dic11—21no—
131C2×C22⋊Dic11—21no—
132C2×C22⋊Dic11D411yescharacteristic
133#67000—22no—
134#67000C2312yescomplemented
135#66999—22no—
136#66999C2312yescomplemented
137Q8×Dic11C2312yescomplemented
138C2×#4325C2314yescomplemented
139#66993—22no—
140#66993C2314yes—
141#66992—24no—
142#66992—24no—
143#66991—22no—
144#66991C2314yes—
145#66990—24no—
146#66990—24no—
147D4×Dic11—22no—
148D4×Dic11C2314yes—
149C2×#4323—44no—
150C2×#4323C2314yes—
151C2×#4323C2314yescomplemented
152#66983—21no—
153#66983—21no—
154#66983—21no—
155#66983—21no—
156#66983—22no—
157#66983—22no—
158#66983C2312yes—
159#66983C2312yes—
160#66983C2312yes—
161#66983C2312yescomplemented
162C4×C22⋊D11—22no—
163C4×C22⋊D11—22no—
164C4×C22⋊D11D412yes—
165C4×C22⋊D11D412yes—
166C4×C22⋊D11C2312yes—
167C4×C22⋊D11C2312yes—
168C2×(C2×D11)⋊C4—21no—
169C2×(C2×D11)⋊C4—21no—
170C2×(C2×D11)⋊C4D411yescharacteristic
171C2×C4⋊Dic11C2311yescharacteristic
172C2×C4⋊Dic11C2311yescharacteristic, complemented
173C2×Dic11⋊C4D411yescharacteristic
174C2×C4×Dic11C2311yescharacteristic
175C22×C11⋊C8C2312yescomplemented
176#66967—48no—
177C2×D88C2314yescomplemented
178C2×#4313C2314yescomplemented
179#66951—22no—
180#66951—22no—
181#66951—22no—
182#66948—22no—
183#66948C2312yescomplemented
184#66947—22no—
185#66947—22no—
186#66947—22no—
187#66946—22no—
188#66946C2312yescomplemented
189#66945—22no—
190#66945C2312yescomplemented
191#66943—22no—
192#66943C2312yescomplemented
193#66939—22no—
194#66939—22no—
195#66935—22no—
196#66935—22no—
197(C22⋊D11)⋊C4—22no—
198(C22⋊D11)⋊C4—22no—
199C22⋊C4×D11—22no—
200#66930—22no—
201C11×#102C2314yes—
202C11×#102C2314yescomplemented
203C11×C22⋊C8C2312yes—
204C11×C22⋊C8C2312yescomplemented
205#66899C2314yescomplemented
206#66896C2314yes—
207#66896C2314yescomplemented
208C22⋊(C11⋊C8)C2312yes—
209C22⋊(C11⋊C8)C2312yescomplemented
210#66885C2314yescomplemented
211#66885C2314yescomplemented
212(C2×D11)⋊C8C2314yescomplemented
213#66882C2314yescomplemented
214#66879C2314yescomplemented
215Dic11⋊C8C2314yescomplemented
216#66873C2314yescomplemented
217#66872C2314yescomplemented
218#61571—111nomaximal, Sylow
219C24×C11—21no—
220C24×C11—21no—
221C24×C11—22no—
222C24×C11—22no—
223C24×C11—44no—
224C24×C11—44no—
225C24×C11—82no—
226C24×C11C2×D411yescharacteristic
227C23×D11—21no—
228C23×D11—21no—
229C23×D11—24no—
230C23×D11—44no—
231C23×D11—44no—
232C23×D11—82no—
233C23×D11C2×D411yescharacteristic
234C2×Q8×C11—21no—
235C2×Q8×C11—42no—
236C2×Q8×C11C2412yes—
237C2×D4×C11—24no—
238C2×D4×C11—24no—
239C2×D4×C11—24no—
240C2×D4×C11—21no—
241C2×D4×C11—22no—
242C2×D4×C11—22no—
243C2×D4×C11—21no—
244C2×D4×C11—42no—
245C2×D4×C11—42no—
246C2×D4×C11—42no—
247C2×D4×C11—44no—
248C2×D4×C11—44no—
249C2×D4×C11—44no—
250C2×D4×C11C2412yes—
251C2×D4×C11C2412yes—
252C22×C4×C11—21no—
253C22×C4×C11—21no—
254C22×C4×C11—42no—
255C22×C4×C11C2×D411yescharacteristic
256C22×C4×C11C2×D411yescharacteristic
257C22×C4×C11C2×D411yescharacteristic
258C22×C4×C11C2411yescharacteristic
259C22×C4×C11C2411yescharacteristic
260C22×C4×C11C2411yescharacteristic
261C2×C22⋊D11—24no—
262C2×C22⋊D11—24no—
263C2×C22⋊D11—24no—
264C2×C22⋊D11—24no—
265C2×C22⋊D11—22no—
266C2×C22⋊D11—22no—
267C2×C22⋊D11—22no—
268C2×C22⋊D11—22no—
269C2×C22⋊D11—24no—
270C2×C22⋊D11—44no—
271C2×C22⋊D11—44no—
272C2×C22⋊D11—44no—
273C2×C22⋊D11—416no—
274C2×C22⋊D11—416no—
275C2×C22⋊D11—44no—
276C2×C22⋊D11—44no—
277C2×C22⋊D11—82no—
278C2×C22⋊D11C2×D412yes—
279C2×C22⋊D11C2×D412yes—
280C22×Dic11—24no—
281C22×Dic11—21no—
282C22×Dic11—21no—
283C22×Dic11—44no—
284C22×Dic11C2×D411yescharacteristic
285C22×Dic11C2×D411yescharacteristic
286C22×Dic11C2×D411yescharacteristic
287#4343—44no—
288D4×D11—28no—
289D4×D11—44no—
290D4×D11—48no—
291C2×D44—22no—
292C2×D44—22no—
293C2×D44—21no—
294C2×D44—21no—
295C2×D44—42no—
296C2×D44—42no—
297C2×D44C2412yes—
298C2×D44C2412yes—
299C2×C4×D11—22no—
300C2×C4×D11—22no—
301C2×C4×D11—42no—
302C2×C4×D11C2×D412yes—
303C2×C4×D11C2412yes—
304C11×SD16—28no—
305C11×SD16—44no—
306C2×C8×C11—42no—
307C2×C8×C11C2414yes—
308C11×C4⋊C4—22no—
309C11×C4⋊C4—22no—
310C11×C4⋊C4—21no—
311C11×C4⋊C4C2412yes—
312C11×C22⋊C4—22no—
313C11×C22⋊C4—22no—
314C22⋊Dic11—24no—
315C22⋊Dic11—24no—
316C22⋊Dic11C2×D412yes—
317C22⋊Dic11C2×D412yes—
318#4325—44no—
319#4323—28no—
320#4323—44no—
321(C2×D11)⋊C4—22no—
322(C2×D11)⋊C4—22no—
323(C2×D11)⋊C4—22no—
324(C2×D11)⋊C4—22no—
325(C2×D11)⋊C4—22no—
326(C2×D11)⋊C4—22no—
327(C2×D11)⋊C4—22no—
328(C2×D11)⋊C4—22no—
329(C2×D11)⋊C4—22no—
330(C2×D11)⋊C4—22no—
331(C2×D11)⋊C4C2×D412yes—
332(C2×D11)⋊C4C2×D412yes—
333C4⋊Dic11—22no—
334C4⋊Dic11—22no—
335C4⋊Dic11—21no—
336C4⋊Dic11—21no—
337C4⋊Dic11C2412yes—
338C4⋊Dic11C2412yes—
339Dic11⋊C4—22no—
340Dic11⋊C4—22no—
341Dic11⋊C4C2×D412yes—
342Dic11⋊C4C2×D412yes—
343C4×Dic11—22no—
344C4×Dic11—22no—
345C4×Dic11C2×D412yes—
346C4×Dic11C2412yes—
347C2×C11⋊C8—42no—
348C2×C11⋊C8C2414yes—
349D88—44no—
350#4313—44no—
351#3505—111no—
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×#450D1111yescharacteristic, complemented
364C2×#447—111no—
365#2973—111no—
366C23×C11—24no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—41no—
370C23×C11—41no—
371C23×C11—44no—
372C23×C11—44no—
373C23×C11—42no—
374C23×C11—42no—
375C23×C11—42no—
376C23×C11—42no—
377C23×C11—44no—
378C23×C11—44no—
379C23×C11—42no—
380C23×C11—82no—
381C23×C11—82no—
382C23×C11—816no—
383C23×C11AGL(1,ℤ/8)14yescomplemented
384C23×C11C22×D411yescharacteristic
385C23×C11C22×D411yescharacteristic
386C23×C11C22×D411yescharacteristic
387C22×D11—22no—
388C22×D11—22no—
389C22×D11—22no—
390C22×D11—41no—
391C22×D11—41no—
392C22×D11—48no—
393C22×D11—48no—
394C22×D11—42no—
395C22×D11—42no—
396C22×D11—42no—
397C22×D11—42no—
398C22×D11—84no—
399C22×D11—81no—
400C22×D11—81no—
401C22×D11—816no—
402C22×D11C22×D412yes—
403Q8×C11—24no—
404Q8×C11—81no—
405D4×C11—24no—
406D4×C11—22no—
407D4×C11—22no—
408D4×C11—22no—
409D4×C11—44no—
410D4×C11—44no—
411D4×C11—42no—
412D4×C11H(5,𝔽2)14yes—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—41no—
419C2×C4×C11—41no—
420C2×C4×C11—41no—
421C2×C4×C11—81no—
422C2×C4×C11—81no—
423C2×C4×C11C22×D411yescharacteristic
424C2×C4×C11C22×D411yescharacteristic
425C2×C4×C11C22×D411yescharacteristic
426C2×C4×C11C2511yescharacteristic
427C22⋊D11—24no—
428C22⋊D11—24no—
429C22⋊D11—48no—
430C22⋊D11—48no—
431C22⋊D11—48no—
432C22⋊D11—44no—
433C22⋊D11—44no—
434C22⋊D11—44no—
435C22⋊D11—44no—
436C22⋊D11—84no—
437C2×Dic11—22no—
438C2×Dic11—22no—
439C2×Dic11—22no—
440C2×Dic11—41no—
441C2×Dic11—41no—
442C2×Dic11—48no—
443C2×Dic11—42no—
444C2×Dic11—42no—
445C2×Dic11C22×D412yes—
446C2×Dic11C22×D412yes—
447C2×Dic11C22×D412yes—
448D44—24no—
449D44—24no—
450D44—42no—
451D44—81no—
452D44—82no—
453D44—82no—
454C4×D11—24no—
455C4×D11—42no—
456C4×D11—82no—
457C4×D11—82no—
458C8×C11—24no—
459C11⋊C8—24no—
460C23×D4—111no—
461C23×D4—221no—
462C23×D4C2×D1111yescharacteristic
463C2×AGL(1,ℤ/8)—114no—
464C22×SD16C2×D1112yescomplemented
465C22×D8—112no—
466#553—112no—
467#553—222no—
468#552—112no—
469#551—222no—
470#548—112no—
471#546—112no—
472D42—114no—
473D42—114no—
474D42—222no—
475D42—222no—
476#539—221no—
477#538—221no—
478#534—221no—
479C2×#127—111no—
480#529—112no—
481#525—112no—
482C2×C22⋊Q8C2×D1111yescharacteristic, complemented
483C2×#121—111no—
484C2×#121—111no—
485C2×#121—111no—
486C2×#121—221no—
487C2×#120—221no—
488C2×#120—221no—
489#518—221no—
490C2×C4×D4—111no—
491C2×C4×D4—111no—
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—114no—
508#450—112no—
509#450C2×D1112yescomplemented
510#450C2×D1112yescomplemented
511#450C2×D1114yescomplemented
512#449—114no—
513#448—112no—
514#447—112no—
515#447—112no—
516#447—114no—
517#447—114no—
518#447—112no—
519#447—112no—
520#442—114no—
521#440—114no—
522#435—114no—
523#435—114no—
524#432—112no—
525#418—114no—
526C2×#102—112no—
527C2×#102C2×D1112yescomplemented
528#407—112no—
529C2×C22⋊C8—111no—
530C2×C22⋊C8C2×D1111yescharacteristic, complemented
531C22×C11—21no—
532C22×C11—21no—
533C22×C11—21no—
534C22×C11—21no—
535C22×C11—21no—
536C22×C11—21no—
537C22×C11—24no—
538C22×C11—44no—
539C22×C11—48no—
540C22×C11—42no—
541C22×C11—42no—
542C22×C11—42no—
543C22×C11—42no—
544C22×C11—42no—
545C22×C11—88no—
546C22×C11—88no—
547C22×C11—84no—
548C22×C11C2×AGL(1,ℤ/8)12yes—
549C22×C11C2×AGL(1,ℤ/8)12yes—
550C22×C11C2×AGL(1,ℤ/8)12yes—
551C22×C11C23×D411yescharacteristic
552C2×D11—22no—
553C2×D11—22no—
554C2×D11—22no—
555C2×D11—44no—
556C2×D11—42no—
557C2×D11—42no—
558C2×D11—42no—
559C2×D11—42no—
560C2×D11—42no—
561C2×D11—42no—
562C2×D11—816no—
563C2×D11—84no—
564C2×D11—162no—
565C4×C11—21no—
566C4×C11—21no—
567C4×C11—21no—
568C4×C11—42no—
569C4×C11—42no—
570C4×C11C2×H(5,𝔽2)12yes—
571Dic11—22no—
572Dic11—22no—
573Dic11—22no—
574Dic11—42no—
575Dic11—42no—
576C25—21no—
577C25—221no—
578C2×#41—112no—
579C22×Q8C22×D1111yescharacteristic, complemented
580C22×D4—21no—
581C22×D4—21no—
582C22×D4—21no—
583C22×D4—44no—
584C22×D4—111no—
585C22×D4—114no—
586C22×D4—111no—
587C22×D4—111no—
588C22×D4—222no—
589C22×D4—221no—
590C22×D4—221no—
591C22×D4—221no—
592C22×D4—224no—
593C22×D4—224no—
594C22×D4—221no—
595C22×D4—221no—
596C22×D4—221no—
597C22×D4—444no—
598C22×D4—448no—
599C22×D4C22×D1111yescharacteristic
600C22×D4C22×D1112yes—
601C22×D4C22×D1112yes—
602C22×D4C22×D1111yescharacteristic
603C23×C4—111no—
604C23×C4—221no—
605C23×C4C22×D1111yescharacteristic
606AGL(1,ℤ/8)—448no—
607C2×SD16—44no—
608C2×SD16—114no—
609C2×SD16C22×D1114yes—
610C2×SD16C22×D1114yescomplemented
611C2×D8—114no—
612C2×D8—114no—
613C2×D8—114no—
614C2×D8—444no—
615C2×M16—114no—
616C22×C8—112no—
617C22×C8C22×D1112yescomplemented
618#127—114no—
619#127—222no—
620#126—222no—
621#126—222no—
622#126—222no—
623#125—112no—
624#125—222no—
625#124—112no—
626#124—222no—
627#123—222no—
628#123—222no—
629#123—222no—
630#123—222no—
631#123—222no—
632C22⋊Q8—21no—
633C22⋊Q8—21no—
634C22⋊Q8—112no—
635C22⋊Q8—222no—
636C22⋊Q8C22×D1112yes—
637C22⋊Q8C22×D1112yescomplemented
638#121—114no—
639#121—112no—
640#121—112no—
641#121—112no—
642#121—112no—
643#121—112no—
644#121—222no—
645#121—224no—
646#121—224no—
647#121—222no—
648#121—222no—
649#121—222no—
650#121—221no—
651#121—221no—
652#121—221no—
653#121—221no—
654#120—222no—
655#120—222no—
656#120—224no—
657#120—224no—
658#120—224no—
659#120—224no—
660C4×Q8—112no—
661C4×D4—112no—
662C4×D4—112no—
663C4×D4—112no—
664C4×D4—112no—
665C4×D4—114no—
666C4×D4—112no—
667C4×D4—222no—
668C4×D4—222no—
669C4×D4—222no—
670C4×D4—222no—
671C4×D4—222no—
672C4×D4—222no—
673#117—112no—
674#117—222no—
675#117—222no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—111no—
678C2×C4⋊C4—111no—
679C2×C4⋊C4—111no—
680C2×C4⋊C4C22×D1111yescharacteristic, complemented
681C2×C22⋊C4—21no—
682C2×C22⋊C4—111no—
683C2×C22⋊C4—111no—
684C2×C22⋊C4—222no—
685C2×C22⋊C4—221no—
686C2×C22⋊C4—221no—
687C2×C22⋊C4—221no—
688C2×C22⋊C4—221no—
689C2×C42—111no—
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#102C22×D1114yes—
700#102C22×D1114yescomplemented
701C22⋊C8—112no—
702C22⋊C8—112no—
703C22⋊C8—114no—
704C22⋊C8C22×D1112yes—
705C22⋊C8C22×D1112yescomplemented
706#97—114no—
707C2×C11—22no—
708C2×C11—22no—
709C2×C11—22no—
710C2×C11—44no—
711C2×C11—82no—
712C2×C11#348411yescharacteristic
713C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
714C2×C11#358511yescharacteristic
715D11—42no—
716D11—82no—
717D11—82no—
718C24—21no—
719C24—21no—
720C24—22no—
721C24—22no—
722C24—44no—
723C24—44no—
724C24—82no—
725C24—111no—
726C24—224no—
727C24—221no—
728C24—221no—
729C24—444no—
730C24—444no—
731C24—882no—
732C24D4×D1111yescharacteristic
733#41—444no—
734C2×Q8—21no—
735C2×Q8—42no—
736C2×Q8C23×D1112yes—
737C2×D4—24no—
738C2×D4—24no—
739C2×D4—24no—
740C2×D4—21no—
741C2×D4—22no—
742C2×D4—22no—
743C2×D4—21no—
744C2×D4—42no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—112no—
751C2×D4—112no—
752C2×D4—112no—
753C2×D4—112no—
754C2×D4—222no—
755C2×D4—222no—
756C2×D4—224no—
757C2×D4—224no—
758C2×D4—224no—
759C2×D4—224no—
760C2×D4—228no—
761C2×D4—224no—
762C2×D4—222no—
763C2×D4—222no—
764C2×D4—222no—
765C2×D4—222no—
766C2×D4—221no—
767C2×D4—221no—
768C2×D4—442no—
769C2×D4—442no—
770C2×D4—444no—
771C2×D4—444no—
772C2×D4—448no—
773C2×D4—4416no—
774C2×D4—4416no—
775C2×D4—444no—
776C2×D4—444no—
777C2×D4—444no—
778C2×D4—444no—
779C2×D4—882no—
780C2×D4C23×D1112yes—
781C2×D4C23×D1112yes—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—42no—
785C22×C4—111no—
786C22×C4—111no—
787C22×C4—111no—
788C22×C4—112no—
789C22×C4—112no—
790C22×C4—222no—
791C22×C4—222no—
792C22×C4—224no—
793C22×C4—221no—
794C22×C4—221no—
795C22×C4—442no—
796C22×C4—444no—
797C22×C4D4×D1111yescharacteristic
798C22×C4D4×D1111yescharacteristic
799C22×C4D4×D1111yescharacteristic
800C22×C4C23×D1111yescharacteristic
801C22×C4C23×D1111yescharacteristic
802C22×C4C23×D1111yescharacteristic
803SD16—28no—
804SD16—44no—
805SD16—444no—
806D8—228no—
807D8—444no—
808D8—444no—
809M16—444no—
810C2×C8—42no—
811C2×C8—114no—
812C2×C8—442no—
813C2×C8C23×D1114yes—
814C4⋊C4—22no—
815C4⋊C4—22no—
816C4⋊C4—21no—
817C4⋊C4—112no—
818C4⋊C4—112no—
819C4⋊C4—112no—
820C4⋊C4—112no—
821C4⋊C4—222no—
822C4⋊C4—222no—
823C4⋊C4—222no—
824C4⋊C4—222no—
825C4⋊C4—221no—
826C4⋊C4—221no—
827C4⋊C4C23×D1112yes—
828C22⋊C4—22no—
829C22⋊C4—22no—
830C22⋊C4—112no—
831C22⋊C4—112no—
832C22⋊C4—112no—
833C22⋊C4—112no—
834C22⋊C4—222no—
835C22⋊C4—222no—
836C22⋊C4—222no—
837C22⋊C4—222no—
838C22⋊C4—222no—
839C22⋊C4—222no—
840C22⋊C4—224no—
841C22⋊C4—224no—
842C22⋊C4—222no—
843C22⋊C4—222no—
844C22⋊C4—222no—
845C22⋊C4—222no—
846C42—112no—
847C42—112no—
848C42—222no—
849C42—222no—
850C11#6157111yescharacteristic, complemented, Sylow
851C23—24no—
852C23—22no—
853C23—22no—
854C23—41no—
855C23—41no—
856C23—44no—
857C23—44no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—42no—
862C23—44no—
863C23—44no—
864C23—42no—
865C23—82no—
866C23—82no—
867C23—816no—
868C23—112no—
869C23—222no—
870C23—222no—
871C23—222no—
872C23—441no—
873C23—441no—
874C23—448no—
875C23—442no—
876C23—442no—
877C23—448no—
878C23—442no—
879C23—442no—
880C23—881no—
881C23—881no—
882C23—884no—
883C23—8816no—
884C23#6696714yescomplemented
885C23C2×D4×D1111yescharacteristic
886C23C2×D4×D1111yescharacteristic
887C23C2×D4×D1111yescharacteristic
888Q8—24no—
889Q8—81no—
890D4—24no—
891D4—22no—
892D4—22no—
893D4—22no—
894D4—44no—
895D4—44no—
896D4—42no—
897D4—224no—
898D4—224no—
899D4—224no—
900D4—224no—
901D4—442no—
902D4—448no—
903D4—448no—
904D4—448no—
905D4—444no—
906D4—444no—
907D4—444no—
908D4—444no—
909D4—881no—
910D4—882no—
911D4—882no—
912D4—884no—
913D4#6703714yes—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—81no—
923C2×C4—81no—
924C2×C4—112no—
925C2×C4—112no—
926C2×C4—112no—
927C2×C4—222no—
928C2×C4—224no—
929C2×C4—222no—
930C2×C4—222no—
931C2×C4—442no—
932C2×C4—441no—
933C2×C4—441no—
934C2×C4—448no—
935C2×C4—442no—
936C2×C4—442no—
937C2×C4—882no—
938C2×C4—882no—
939C2×C4C2×D4×D1111yescharacteristic
940C2×C4C2×D4×D1111yescharacteristic
941C2×C4C2×D4×D1111yescharacteristic
942C2×C4C24×D1111yescharacteristic
943C8—24no—
944C8—224no—
945C22—21no—
946C22—21no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—24no—
952C22—44no—
953C22—48no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—88no—
960C22—88no—
961C22—84no—
962C22—222no—
963C22—222no—
964C22—222no—
965C22—444no—
966C22—442no—
967C22—442no—
968C22—442no—
969C22—442no—
970C22—442no—
971C22—442no—
972C22—884no—
973C22—8816no—
974C22—1762no—
975C22C2×#6696712yes—
976C22C2×#6696712yes—
977C22C2×#6696712yes—
978C22C22×D4×D1111yescharacteristic
979C4—21no—
980C4—21no—
981C4—21no—
982C4—42no—
983C4—42no—
984C4—222no—
985C4—222no—
986C4—222no—
987C4—442no—
988C4—442no—
989C4C2×#6703712yes—
990C2—22no—
991C2—22no—
992C2—22no—
993C2—44no—
994C2—82no—
995C2—442no—
996C2—882no—
997C2—882no—
998C2#1308224511yescharacteristic
999C2C22×#6696711yescharacteristic
1000C2#1308339211yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#450C2
socleC22×C11C23×D4
hypercenterC2×#450D11
hypocenterC11#61571
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
1. #13082457C2semidirect
2. C2×D4×C22⋊D11C2semidirect
3. #13080753C2semidirect
4. #13080641C2semidirect
5. #13080111C2semidirect
6. #13080100C2semidirect
7. #13079637C2semidirect
8. #13079433C2semidirect
9. #13079369C2semidirect
10. #13079367C2semidirect
11. #13078755C2semidirect
12. #13077844C2semidirect
13. C2×#10622830C2semidirect
14. #13077642C2semidirect
15. C2×C11×#450C2semidirect
18. C22×D4×D11C22semidirect
19. C22×C11×SD16C22semidirect
20. C2×C11×C22⋊Q8C22semidirect
22. #10623348C22semidirect
23. C2×#66993C22semidirect
28. D4×C22⋊D11C22semidirect
29. C2×#66991C22semidirect
31. C2×D4×Dic11C22semidirect
32. C22×#4323C22semidirect
34. C2×#66983C22semidirect
36. C2×#66967C22semidirect
39. #10623173C22semidirect
41. #10623161C22semidirect
42. #10623158C22semidirect
43. #10623155C22semidirect
45. #10623045C22semidirect
48. C11×#450C22semidirect
49. C11×#450C22semidirect
50. C11×#450C22semidirect
51. C2×C11×#102C22semidirect
52. C2×C11×C22⋊C8C22semidirect
53. #10622840C22semidirect
55. #10622830C22semidirect
56. #10622830C22semidirect
57. C2×#66896C22semidirect
58. C2×C22⋊(C11⋊C8)C22semidirect
59. #10622789C22semidirect
60. #10622787C22semidirect
61. #10622785C22semidirect
62. #10622782C22semidirect
63. #10622778C22semidirect
64. #10622777C22semidirect
65. #10622776C22semidirect
66. #10622728C22semidirect
67. #10622724C22semidirect
68. #10622661C22semidirect
69. #10622659C22semidirect
70. #10622656C22semidirect
71. #10622581C22semidirect
72. #10622399C22semidirect
73. #10622398C22semidirect
74. #10622397C22semidirect
75. #10622395C22semidirect
76. #10622386C22semidirect
77. #10622383C22semidirect
78. #10622379C22semidirect
79. #10622377C22semidirect
80. #10622349C22semidirect
81. #10622349C22semidirect
82. #10622345C22semidirect
83. #10622345C22semidirect
84. #10622343C22semidirect
85. #10622339C22semidirect
86. #10622332C22semidirect
89. C22×Q8×C11C23semidirect
110. C2×#4343C23semidirect
115. C22×D44C23semidirect
119. C2×C11×SD16C23semidirect
120. C22×C8×C11C23semidirect
124. C11×C22⋊Q8C23semidirect
126. C2×C11×C4⋊C4C23semidirect
134. #67000C23semidirect
136. #66999C23semidirect
137. Q8×Dic11C23semidirect
138. C2×#4325C23semidirect
151. C2×#4323C23semidirect
161. #66983C23semidirect
172. C2×C4⋊Dic11C23semidirect
175. C22×C11⋊C8C23semidirect
177. C2×D88C23semidirect
178. C2×#4313C23semidirect
183. #66948C23semidirect
188. #66946C23semidirect
190. #66945C23semidirect
192. #66943C23semidirect
202. C11×#102C23semidirect
204. C11×C22⋊C8C23semidirect
205. #66899C23semidirect
207. #66896C23semidirect
209. C22⋊(C11⋊C8)C23semidirect
210. #66885C23semidirect
211. #66885C23semidirect
212. (C2×D11)⋊C8C23semidirect
213. #66882C23semidirect
214. #66879C23semidirect
215. Dic11⋊C8C23semidirect
216. #66873C23semidirect
217. #66872C23semidirect
363. C2×#450D11semidirect
383. C23×C11AGL(1,ℤ/8)semidirect
464. C22×SD16C2×D11semidirect
482. C2×C22⋊Q8C2×D11semidirect
509. #450C2×D11semidirect
510. #450C2×D11semidirect
511. #450C2×D11semidirect
527. C2×#102C2×D11semidirect
530. C2×C22⋊C8C2×D11semidirect
579. C22×Q8C22×D11semidirect
610. C2×SD16C22×D11semidirect
617. C22×C8C22×D11semidirect
637. C22⋊Q8C22×D11semidirect
680. C2×C4⋊C4C22×D11semidirect
700. #102C22×D11semidirect
705. C22⋊C8C22×D11semidirect
850. C11#61571semidirect
884. C23#66967semidirect

Maximal subgroups

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

subgroupindex
#130824572
C2×D4×C22⋊D112
#130807532
#130806412
#130801112
#130801002
#130796372
#130794332
#130793692
#130793672
#130787552
#130778442
C2×#106228302
#130776422
C2×C11×#4502
#6157111