Finite Group Databasebeta

← #25967386

Subgroups — #25967386

Order 11008.

2322 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#19147928C211yesmaximal, characteristic, complemented
2C2×#14583465C211yesmaximal, characteristic, complemented
3#19145469C214yesmaximal, complemented
4#19145459C214yesmaximal, complemented
5#19145454C214yesmaximal, complemented
6#19145452C214yesmaximal, complemented
7#19144535C211yesmaximal, characteristic, complemented
8#19144529C212yesmaximal, complemented
9#19144215C212yesmaximal, complemented
10#19144212C212yesmaximal, complemented
11#19143849C211yesmaximal, characteristic, complemented
12#19143845C211yesmaximal, characteristic, complemented
13#19143824C212yesmaximal, complemented
14#19143038C211yesmaximal, characteristic, complemented
15C43×#3094C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621898C2211yescharacteristic, complemented
18C22×D4×D43C2211yescharacteristic, complemented
19C2×#13063353C2212yes—
20C2×#13063351C2212yes—
21C2×M16×D43C2212yescomplemented
22#14583480C2212yescomplemented
23#14583480C2212yescomplemented
24#14583475—21no—
25#14583475C2212yescomplemented
26#14583468—21no—
27#14583468C2212yescomplemented
28#14583465—22no—
29#14583465—22no—
30#14583465C2214yes—
31#14583465C2214yescomplemented
32#14583461—21no—
33#14583461—21no—
34#14583449—22no—
35C2×#13063321—21no—
36C2×#13063311—21no—
37#14583411—22no—
38#14583411C2212yes—
39#14583411C2212yescomplemented
40C2×#13063300C2211yescharacteristic, complemented
41C2×#13063299C2211yescharacteristic
42C2×#13063296C2211yescharacteristic, complemented
43C2×#13063295—21no—
44C2×#13063293—21no—
45C2×#13063283C2211yescharacteristic, complemented
46#14583243C2214yescomplemented
47#14583242C2214yescomplemented
48#14583226C2214yescomplemented
49#14583225C2214yescomplemented
50#14583223C2214yescomplemented
51#14583217C2212yescomplemented
52#14583212C2212yescomplemented
53#14583153C2214yescomplemented
54#14583151C2214yescomplemented
55#14583146C2214yescomplemented
56#14583144C2214yescomplemented
57#14583136C2214yescomplemented
58#14583134C2214yescomplemented
59#14583129C2214yescomplemented
60#14583127C2214yescomplemented
61#14583051C2214yescomplemented
62#14583051C2214yescomplemented
63#14583046C2214yescomplemented
64#14583042C2214yescomplemented
65#14583040C2212yescomplemented
66#14583037C2212yescomplemented
67#14583035C2212yescomplemented
68#14583034C2214yescomplemented
69#14583034C2214yescomplemented
70#14583032C2212yescomplemented
71#14582942C2212yescomplemented
72#14582903C2212yescomplemented
73#14582901C2212yescomplemented
74#14582898C2212yescomplemented
75#14582864C2214yescomplemented
76#14582864C2214yescomplemented
77#14582863C2211yescharacteristic, complemented
78#14582862C2212yescomplemented
79C2×#121×C43C2211yescharacteristic
80C2×#117×C43C2211yescharacteristic, complemented
81C43×#482C2214yescomplemented
82C43×#481C2212yescomplemented
83C43×#480C2212yescomplemented
84C43×#428C2212yescomplemented
85C43×#418C2212yescomplemented
86C43×#407C2211yescharacteristic, complemented
87C24×D43—21no—
88C2×#10621898—21no—
89C2×#10621898—21no—
90C2×#10621898—44no—
91C2×#10621898—44no—
92C2×#10621898D412yes—
93C2×#10621898D412yes—
94C2×#10621898C2312yes—
95C2×#10621898C2312yes—
96C2×#10621898C2312yes—
97C2×#10621898C2312yescomplemented
98C22×Dic86D411yescharacteristic
99C22×Dic86C2311yescharacteristic, complemented
100C22×D172—21no—
101C22×D172D411yescharacteristic
102C22×D172C2311yescharacteristic
103C22×D172C2311yescharacteristic, complemented
104C22×C22⋊D43—21no—
105C22×C22⋊D43—21no—
106C22×C22⋊D43—21no—
107C22×C22⋊D43—21no—
108C22×C22⋊D43D411yescharacteristic
109C22×C22⋊D43D411yescharacteristic
110C2×D4×D43—22no—
111C2×D4×D43—44no—
112C2×D4×D43C2314yes—
113C22×C4×D43—21no—
114C22×C4×D43C2311yescharacteristic
115C22×C4×D43C2311yescharacteristic
116#13063353—44no—
117#13063351—44no—
118C2×#10621873C2314yes—
119C2×#10621883C2314yes—
120C2×D344C2314yes—
121C2×#10621882C2314yes—
122C2×#10621877C2312yes—
123C2×#10621872C2314yescomplemented
124M16×D43—44no—
125C2×C8×D43C2314yescomplemented
126#13063325—22no—
127#13063322—22no—
128#13063321—24no—
129#13063321—24no—
130#13063313—22no—
131#13063313—22no—
132#13063311—24no—
133#13063311—24no—
134#13063309—22no—
135#13063309—22no—
136#13063309—22no—
137#13063309—22no—
138#13063305—22no—
139#13063305—22no—
140#13063305C2312yes—
141#13063305C2312yes—
142#13063305C2312yescomplemented
143#13063305C2312yescomplemented
144#13063300—22no—
145#13063300—22no—
146#13063300—22no—
147#13063300C2314yes—
148#13063300C2312yes—
149#13063300C2312yes—
150#13063300C2312yescomplemented
151#13063300C2312yescomplemented
152#13063299—21no—
153#13063299—21no—
154#13063299—22no—
155#13063299—22no—
156#13063299—22no—
157#13063299—22no—
158#13063299C2312yes—
159#13063299C2312yes—
160#13063296—22no—
161#13063296C2314yes—
162#13063295—22no—
163#13063295—22no—
164#13063295—22no—
165#13063295—22no—
166#13063295—24no—
167#13063295—24no—
168#13063293—24no—
169#13063293—24no—
170C4×D172—22no—
171C4×D172—22no—
172C4×D172—22no—
173C4×D172—22no—
174#13063283—22no—
175#13063283C2314yes—
176C2×C4⋊Dic43C2311yescharacteristic
177C2×C22⋊Dic43—21no—
178C2×(C2×D43)⋊C4—21no—
179C2×(C2×D43)⋊C4—21no—
180C2×(C2×D43)⋊C4—21no—
181C2×C4×Dic43—21no—
182#13063258C2314yescomplemented
183#13063256C2314yescomplemented
184#13063250C2314yescomplemented
185#13063248C2314yescomplemented
186#13063247C2314yescomplemented
187#13063245C2314yes—
188#13063245C2314yes—
189#13063245C2314yescomplemented
190C22⋊(C43⋊C8)C2312yescomplemented
191C22⋊(C43⋊C8)C2312yescomplemented
192(C2×D43)⋊C8C2314yes—
193(C2×D43)⋊C8C2314yes—
194C22×D4×C43—21no—
195C22×D4×C43C2311yescharacteristic
196C23×C4×C43C2311yescharacteristic
197C2×M16×C43C2312yes—
198#121×C43—21no—
199#121×C43—21no—
200#121×C43C2312yes—
201#121×C43C2312yes—
202#117×C43—21no—
203#117×C43—21no—
204#117×C43C2312yes—
205#117×C43C2312yescomplemented
206C2×C4⋊C4×C43C2311yescharacteristic
207C2×C4⋊C4×C43C2311yescharacteristic, complemented
208C2×C4⋊C4×C43C2311yescharacteristic, complemented
209C2×C22⋊C4×C43—21no—
210C2×C22⋊C4×C43—21no—
211C2×C42×C43—21no—
212#107×C43C2314yescomplemented
213#106×C43C2314yescomplemented
214#102×C43C2314yes—
215#102×C43C2314yes—
216C22⋊C8×C43C2312yescomplemented
217C22⋊C8×C43C2312yescomplemented
218C24×C43—21no—
219C24×C43C2×D411yescharacteristic
220C23×D43—21no—
221C23×D43—21no—
222C23×D43—24no—
223C23×D43—44no—
224C23×D43—82no—
225C23×D43—82no—
226C23×D43C2×D411yescharacteristic
227C23×D43C2×D411yescharacteristic
228C2×D4×C43—21no—
229C2×D4×C43—22no—
230C2×D4×C43—22no—
231C2×D4×C43—24no—
232C2×D4×C43—82no—
233C2×D4×C43C2412yes—
234C22×C4×C43—24no—
235C22×C4×C43—21no—
236C22×C4×C43—21no—
237C22×C4×C43—21no—
238C22×C4×C43C2×D411yescharacteristic
239C22×C4×C43C2×D411yescharacteristic
240C22×C4×C43C2×D411yescharacteristic
241C22×C4×C43C2411yescharacteristic
242C22×C4×C43C2411yescharacteristic
243C22×C4×C43C2411yescharacteristic
244C2×C22⋊D43—24no—
245C2×C22⋊D43—22no—
246C2×C22⋊D43—22no—
247C2×C22⋊D43—22no—
248C2×C22⋊D43—22no—
249C2×C22⋊D43—24no—
250C2×C22⋊D43—42no—
251C2×C22⋊D43—42no—
252C2×C22⋊D43—44no—
253C2×C22⋊D43—44no—
254C2×C22⋊D43—82no—
255C2×C22⋊D43—82no—
256C2×C22⋊D43C2×D412yes—
257C2×C22⋊D43C2×D412yes—
258C2×C22⋊D43C2×D412yes—
259C2×C22⋊D43C2×D412yes—
260C22×Dic43—21no—
261C22×Dic43—21no—
262C22×Dic43C2×D411yescharacteristic
263C22×Dic43C2×D411yescharacteristic
264D4×D43—44no—
265D4×D43—44no—
266D4×D43—48no—
267#10621898—24no—
268#10621898—24no—
269#10621898—42no—
270#10621898—42no—
271#10621898—44no—
272#10621898—44no—
273#10621898—42no—
274#10621898—42no—
275#10621898—42no—
276#10621898—42no—
277#10621898—44no—
278#10621898—44no—
279C2×D172—21no—
280C2×D172—21no—
281C2×D172—22no—
282C2×D172—22no—
283C2×D172—22no—
284C2×D172—22no—
285C2×D172—24no—
286C2×D172—24no—
287C2×D172—42no—
288C2×D172—42no—
289C2×D172—82no—
290C2×D172C2×D412yes—
291C2×D172C2×D412yes—
292C2×D172C2412yes—
293C2×D172C2412yes—
294C2×C4×D43—24no—
295C2×C4×D43—24no—
296C2×C4×D43—22no—
297C2×C4×D43—22no—
298C2×C4×D43—44no—
299C2×C4×D43C2×D412yes—
300C2×C4×D43C2×D412yes—
301C2×C4×D43C2412yes—
302C2×C4×D43C2412yes—
303C2×Dic86—21no—
304C2×Dic86—42no—
305C2×Dic86—42no—
306C2×Dic86C2×D412yes—
307C2×Dic86C2×D412yes—
308C2×Dic86C2412yes—
309M16×C43—24no—
310C2×C8×C43C2414yes—
311C4⋊C4×C43—21no—
312C4⋊C4×C43—21no—
313C4⋊C4×C43—21no—
314C4⋊C4×C43C2412yes—
315C4⋊C4×C43C2412yes—
316C4⋊C4×C43C2412yes—
317C22⋊C4×C43—22no—
318C22⋊C4×C43—22no—
319C22⋊C4×C43—22no—
320C22⋊C4×C43—22no—
321C42×C43—22no—
322C42×C43—22no—
323C22⋊Dic43—24no—
324#10621883—44no—
325#10621882—44no—
326(C2×D43)⋊C4—22no—
327(C2×D43)⋊C4—22no—
328(C2×D43)⋊C4—24no—
329(C2×D43)⋊C4—22no—
330(C2×D43)⋊C4—22no—
331(C2×D43)⋊C4—22no—
332(C2×D43)⋊C4—22no—
333(C2×D43)⋊C4—24no—
334(C2×D43)⋊C4—22no—
335(C2×D43)⋊C4—22no—
336(C2×D43)⋊C4—22no—
337(C2×D43)⋊C4—22no—
338C4⋊Dic43—21no—
339C4⋊Dic43—22no—
340C4⋊Dic43—22no—
341C4⋊Dic43—22no—
342C4⋊Dic43—22no—
343C4⋊Dic43C2412yes—
344C4×Dic43—24no—
345#10621877—24no—
346C2×C43⋊C8C2414yes—
347D344—44no—
348#10621873—44no—
349#10621872—44no—
350C8×D43—44no—
351C23×C43—22no—
352C23×C43—22no—
353C23×C43—41no—
354C23×C43—41no—
355C23×C43—42no—
356C23×C43—42no—
357C23×C43—42no—
358C23×C43C22×D411yescharacteristic
359C23×C43C22×D411yescharacteristic
360C23×C43C22×D411yescharacteristic
361C22×D43—22no—
362C22×D43—22no—
363C22×D43—22no—
364C22×D43—22no—
365C22×D43—41no—
366C22×D43—41no—
367C22×D43—41no—
368C22×D43—41no—
369C22×D43—48no—
370C22×D43—42no—
371C22×D43—42no—
372C22×D43—42no—
373C22×D43—42no—
374C22×D43—84no—
375C22×D43—84no—
376C22×D43—81no—
377C22×D43—81no—
378C22×D43—816no—
379C22×D43C22×D412yes—
380C22×D43C22×D412yes—
381D4×C43—24no—
382D4×C43—42no—
383D4×C43—82no—
384D4×C43—82no—
385C2×C4×C43—22no—
386C2×C4×C43—22no—
387C2×C4×C43—22no—
388C2×C4×C43—22no—
389C2×C4×C43—22no—
390C2×C4×C43—22no—
391C2×C4×C43—22no—
392C2×C4×C43—22no—
393C2×C4×C43—42no—
394C2×C4×C43—81no—
395C2×C4×C43—81no—
396C2×C4×C43C22×D411yescharacteristic
397C2×C4×C43C22×D411yescharacteristic
398C2×C4×C43C22×D411yescharacteristic
399C2×C4×C43H(5,𝔽2)14yes—
400C2×C4×C43C2511yescharacteristic
401C22⋊D43—42no—
402C22⋊D43—42no—
403C22⋊D43—42no—
404C22⋊D43—42no—
405C22⋊D43—48no—
406C22⋊D43—44no—
407C22⋊D43—44no—
408C22⋊D43—84no—
409C22⋊D43—82no—
410C22⋊D43—82no—
411C2×Dic43—22no—
412C2×Dic43—22no—
413C2×Dic43—22no—
414C2×Dic43—22no—
415C2×Dic43—42no—
416C2×Dic43—42no—
417C2×Dic43C22×D412yes—
418C2×Dic43C22×D412yes—
419D172—24no—
420D172—22no—
421D172—22no—
422D172—42no—
423D172—42no—
424D172—42no—
425D172—42no—
426D172—82no—
427D172—82no—
428D172—82no—
429D172—82no—
430D172—84no—
431C4×D43—24no—
432C4×D43—24no—
433C4×D43—22no—
434C4×D43—22no—
435C4×D43—22no—
436C4×D43—22no—
437C4×D43—44no—
438C4×D43—44no—
439Dic86—22no—
440Dic86—22no—
441Dic86—42no—
442Dic86—42no—
443Dic86—42no—
444C8×C43—24no—
445C43⋊C8—24no—
446#60753—431nomaximal, Sylow
447C22×C43—21no—
448C22×C43—21no—
449C22×C43—21no—
450C22×C43—21no—
451C22×C43—21no—
452C22×C43—21no—
453C22×C43—21no—
454C22×C43—21no—
455C22×C43—42no—
456C22×C43—42no—
457C22×C43—42no—
458C22×C43—82no—
459C22×C43—84no—
460C22×C43#53412yes—
461C22×C43C23×D411yescharacteristic
462C2×D43—22no—
463C2×D43—22no—
464C2×D43—22no—
465C2×D43—22no—
466C2×D43—22no—
467C2×D43—22no—
468C2×D43—44no—
469C2×D43—42no—
470C2×D43—42no—
471C2×D43—42no—
472C2×D43—42no—
473C2×D43—42no—
474C2×D43—42no—
475C2×D43—82no—
476C2×D43—816no—
477C2×D43—84no—
478C2×D43—84no—
479C4×C43—21no—
480C4×C43—21no—
481C4×C43—42no—
482C4×C43—42no—
483C4×C43—42no—
484C4×C43#53412yes—
485C4×C43C2×H(5,𝔽2)12yes—
486Dic43—22no—
487Dic43—22no—
488Dic43—42no—
489Dic43—42no—
490#3449—431no—
491C2×#535—431no—
492#3200—434no—
493#3199—434no—
494#3198—434no—
495#3198—434no—
496#3094—431no—
497#3094D4311yescharacteristic, complemented
498#3093—432no—
499#3055—432no—
500#3055—432no—
501#3006—431no—
502#3006—431no—
503#3003—432no—
504#2879—431no—
505C2×C43—22no—
506C2×C43—41no—
507C2×C43—41no—
508C2×C43—82no—
509C2×C43C2×#53411yescharacteristic
510C2×C43#358511yescharacteristic
511C2×C43#358511yescharacteristic
512D43—42no—
513D43—42no—
514D43—82no—
515D43—82no—
516C22×#41—431no—
517C22×#41—431no—
518C23×D4—431no—
519C2×AGL(1,ℤ/8)—432no—
520C2×AGL(1,ℤ/8)—432no—
521C22×M16—432no—
522#537—432no—
523#537—432no—
524#536—432no—
525#536—861no—
526#535—434no—
527#535—434no—
528#535—432no—
529#535—861no—
530#535—862no—
531#535—862no—
532#534—861no—
533#534—861no—
534#532—862no—
535C2×#127—861no—
536C2×#124—861no—
537#525—432no—
538#525—432no—
539#525—862no—
540C2×#121—431no—
541C2×#121—431no—
542C2×#121—431no—
543C2×#121C2×D4311yescharacteristic
544C2×#120—861no—
545C2×#120—861no—
546C2×#117—431no—
547C2×#117C2×D4311yescharacteristic, complemented
548#485—434no—
549#485—434no—
550#482—434no—
551#482—434no—
552#482—434no—
553#482C2×D4314yescomplemented
554#481—432no—
555#481C2×D4312yescomplemented
556#480—432no—
557#480C2×D4312yescomplemented
558#469—434no—
559#469—434no—
560#468—434no—
561#468—434no—
562#466—434no—
563#466—434no—
564#465—434no—
565#465—434no—
566#450—434no—
567#450—434no—
568#449—434no—
569#449—434no—
570#448—432no—
571#448—432no—
572#447—432no—
573#447—434no—
574#447—434no—
575#447—432no—
576#428—432no—
577#428C2×D4312yescomplemented
578#418—432no—
579#418C2×D4312yescomplemented
580#417—432no—
581#417—432no—
582#408—434no—
583#408—434no—
584#407—431no—
585#407—432no—
586#407C2×D4311yescharacteristic, complemented
587C43#6075311yescharacteristic, complemented, Sylow
588C25—861no—
589C2×#41—432no—
590C2×#41—432no—
591C2×#41—432no—
592C2×#41—432no—
593C2×#41—432no—
594C2×#41—432no—
595C2×#41—861no—
596C2×#41—861no—
597C2×#41—1724no—
598C2×#41—1724no—
599C22×Q8—431no—
600C22×Q8—431no—
601C22×D4—21no—
602C22×D4—431no—
603C22×D4—431no—
604C22×D4—434no—
605C22×D4—431no—
606C22×D4—431no—
607C22×D4—431no—
608C22×D4—861no—
609C22×D4—862no—
610C22×D4—861no—
611C22×D4—861no—
612C22×D4—861no—
613C22×D4—861no—
614C22×D4—1724no—
615C22×D4C22×D4311yescharacteristic
616C23×C4—431no—
617C23×C4—431no—
618C23×C4—861no—
619C23×C4C22×D4311yescharacteristic
620AGL(1,ℤ/8)—1724no—
621AGL(1,ℤ/8)—1724no—
622C2×SD16—434no—
623C2×SD16—434no—
624C2×D8—434no—
625C2×D8—434no—
626C2×M16—432no—
627C2×M16—434no—
628C2×M16—1724no—
629C2×M16C22×D4312yes—
630C22×C8—434no—
631C4⋊Q8—862no—
632#127—862no—
633#127—864no—
634#127—864no—
635#124—862no—
636#124—862no—
637#124—864no—
638#124—864no—
639#123—862no—
640#123—862no—
641#123—862no—
642#123—862no—
643C22⋊Q8—432no—
644C22⋊Q8—432no—
645C22⋊Q8—432no—
646C22⋊Q8—432no—
647C22⋊Q8—862no—
648C22⋊Q8—862no—
649#121—21no—
650#121—21no—
651#121—434no—
652#121—432no—
653#121—432no—
654#121—434no—
655#121—432no—
656#121—432no—
657#121—432no—
658#121—432no—
659#121—862no—
660#121—862no—
661#121—862no—
662#121—862no—
663#121—862no—
664#121—862no—
665#121—862no—
666#121—862no—
667#121—861no—
668#121—861no—
669#121C22×D4312yes—
670#121C22×D4312yes—
671#120—864no—
672#120—864no—
673#120—862no—
674#120—862no—
675#120—862no—
676#120—862no—
677#120—864no—
678#120—864no—
679C4×D4—862no—
680C4×D4—862no—
681C4×D4—862no—
682C4×D4—862no—
683#117—21no—
684#117—21no—
685#117—434no—
686#117—862no—
687#117C22×D4312yes—
688#117C22×D4312yescomplemented
689C2×C4⋊C4—431no—
690C2×C4⋊C4C22×D4311yescharacteristic
691C2×C4⋊C4C22×D4311yescharacteristic, complemented
692C2×C4⋊C4C22×D4311yescharacteristic, complemented
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—861no—
696C2×C22⋊C4—861no—
697C2×C22⋊C4—861no—
698C2×C22⋊C4—861no—
699C2×C42—21no—
700C2×C42—861no—
701#107—434no—
702#107C22×D4314yescomplemented
703#106—434no—
704#106C22×D4314yescomplemented
705#103—434no—
706#103—434no—
707#102—434no—
708#102—434no—
709#102—434no—
710#102—434no—
711#102C22×D4314yes—
712#102C22×D4314yes—
713C22⋊C8—432no—
714C22⋊C8—432no—
715C22⋊C8—434no—
716C22⋊C8—434no—
717C22⋊C8C22×D4312yescomplemented
718C22⋊C8C22×D4312yescomplemented
719C24—21no—
720C24—431no—
721C24—431no—
722C24—864no—
723C24—861no—
724C24—861no—
725C24—3442no—
726C24—3442no—
727C24—1724no—
728C24D4×D4311yescharacteristic
729#41—864no—
730#41—864no—
731#41—1724no—
732#41—1724no—
733#41—1722no—
734#41—1722no—
735#41—1722no—
736#41—1722no—
737#41—1722no—
738#41—1722no—
739#41—1724no—
740#41—1724no—
741C2×Q8—432no—
742C2×Q8—432no—
743C2×Q8—432no—
744C2×Q8—861no—
745C2×Q8—1722no—
746C2×Q8—1722no—
747C2×D4—22no—
748C2×D4—22no—
749C2×D4—21no—
750C2×D4—24no—
751C2×D4—82no—
752C2×D4—432no—
753C2×D4—432no—
754C2×D4—432no—
755C2×D4—432no—
756C2×D4—432no—
757C2×D4—432no—
758C2×D4—432no—
759C2×D4—432no—
760C2×D4—862no—
761C2×D4—862no—
762C2×D4—862no—
763C2×D4—862no—
764C2×D4—864no—
765C2×D4—864no—
766C2×D4—864no—
767C2×D4—862no—
768C2×D4—862no—
769C2×D4—862no—
770C2×D4—862no—
771C2×D4—861no—
772C2×D4—861no—
773C2×D4—864no—
774C2×D4—3442no—
775C2×D4—3442no—
776C2×D4—3442no—
777C2×D4—1722no—
778C2×D4—1722no—
779C2×D4—1724no—
780C2×D4—1724no—
781C2×D4—1728no—
782C2×D4—1722no—
783C2×D4—1722no—
784C2×D4—1724no—
785C2×D4—1724no—
786C2×D4C23×D4312yes—
787C22×C4—24no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—431no—
792C22×C4—431no—
793C22×C4—432no—
794C22×C4—432no—
795C22×C4—432no—
796C22×C4—432no—
797C22×C4—864no—
798C22×C4—864no—
799C22×C4—861no—
800C22×C4—861no—
801C22×C4—862no—
802C22×C4—862no—
803C22×C4—1724no—
804C22×C4D4×D4311yescharacteristic
805C22×C4D4×D4311yescharacteristic
806C22×C4D4×D4311yescharacteristic
807C22×C4C23×D4311yescharacteristic
808C22×C4C23×D4311yescharacteristic
809C22×C4C23×D4311yescharacteristic
810SD16—1724no—
811SD16—1724no—
812D8—1724no—
813D8—1724no—
814M16—24no—
815M16—864no—
816M16—1724no—
817C2×C8—434no—
818C2×C8—1724no—
819C2×C8C23×D4314yes—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—432no—
824C4⋊C4—862no—
825C4⋊C4—862no—
826C4⋊C4—862no—
827C4⋊C4—862no—
828C4⋊C4—861no—
829C4⋊C4C23×D4312yes—
830C4⋊C4C23×D4312yes—
831C4⋊C4C23×D4312yes—
832C22⋊C4—22no—
833C22⋊C4—22no—
834C22⋊C4—22no—
835C22⋊C4—22no—
836C22⋊C4—864no—
837C22⋊C4—862no—
838C22⋊C4—862no—
839C22⋊C4—862no—
840C22⋊C4—862no—
841C22⋊C4—864no—
842C22⋊C4—862no—
843C22⋊C4—862no—
844C22⋊C4—862no—
845C22⋊C4—862no—
846C22⋊C4—864no—
847C22⋊C4—862no—
848C22⋊C4—862no—
849C42—22no—
850C42—22no—
851C42—864no—
852C23—22no—
853C23—22no—
854C23—41no—
855C23—41no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—432no—
860C23—432no—
861C23—862no—
862C23—862no—
863C23—862no—
864C23—862no—
865C23—3441no—
866C23—3441no—
867C23—3444no—
868C23—3444no—
869C23—34416no—
870C23—1721no—
871C23—1721no—
872C23—1721no—
873C23—1721no—
874C23—1722no—
875C23—1722no—
876C23—1722no—
877C23—1728no—
878C23—1722no—
879C23C2×D4×D4311yescharacteristic
880C23C2×D4×D4311yescharacteristic
881C23C2×D4×D4311yescharacteristic
882Q8—862no—
883Q8—862no—
884Q8—1722no—
885Q8—1722no—
886Q8—1722no—
887D4—24no—
888D4—42no—
889D4—82no—
890D4—82no—
891D4—862no—
892D4—862no—
893D4—864no—
894D4—3444no—
895D4—3442no—
896D4—3442no—
897D4—3442no—
898D4—3442no—
899D4—3442no—
900D4—3442no—
901D4—3444no—
902D4—1722no—
903D4—1722no—
904D4—1722no—
905D4—1722no—
906D4—1722no—
907D4—1722no—
908D4—1722no—
909D4—1728no—
910D4—1724no—
911D4—1724no—
912D4—1722no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—42no—
922C2×C4—81no—
923C2×C4—81no—
924C2×C4—432no—
925C2×C4—432no—
926C2×C4—862no—
927C2×C4—862no—
928C2×C4—864no—
929C2×C4—864no—
930C2×C4—862no—
931C2×C4—862no—
932C2×C4—862no—
933C2×C4—862no—
934C2×C4—862no—
935C2×C4—862no—
936C2×C4—1724no—
937C2×C4—1722no—
938C2×C4—1722no—
939C2×C4—1724no—
940C2×C4C2×D4×D4311yescharacteristic
941C2×C4C2×D4×D4311yescharacteristic
942C2×C4C2×D4×D4311yescharacteristic
943C2×C4#1306337114yes—
944C2×C4C24×D4311yescharacteristic
945C8—24no—
946C8—864no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—82no—
959C22—84no—
960C22—862no—
961C22—862no—
962C22—862no—
963C22—862no—
964C22—862no—
965C22—862no—
966C22—3444no—
967C22—3442no—
968C22—3444no—
969C22—34416no—
970C22—1724no—
971C22—1722no—
972C22—1722no—
973C22—1722no—
974C22—1722no—
975C22—1722no—
976C22—1722no—
977C22#1458346012yes—
978C22C22×D4×D4311yescharacteristic
979C4—21no—
980C4—21no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—862no—
985C4—862no—
986C4—1722no—
987C4—1722no—
988C4#1458346012yes—
989C4C2×#1306337112yes—
990C2—22no—
991C2—41no—
992C2—41no—
993C2—82no—
994C2—3442no—
995C2—3442no—
996C2—1722no—
997C2—1722no—
998C2C2×#1458346011yescharacteristic
999C2#1914937111yescharacteristic
1000C2#1914937211yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3094C2
socleC22×C43C23×D4
hypercenter#3094D43
hypocenterC43#60753
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3094

Complements

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

NH ≅ G/Ntype
1. #19147928C2semidirect
2. C2×#14583465C2semidirect
3. #19145469C2semidirect
4. #19145459C2semidirect
5. #19145454C2semidirect
6. #19145452C2semidirect
7. #19144535C2semidirect
8. #19144529C2semidirect
9. #19144215C2semidirect
10. #19144212C2semidirect
11. #19143849C2semidirect
12. #19143845C2semidirect
13. #19143824C2semidirect
14. #19143038C2semidirect
15. C43×#3094C2semidirect
17. C22×#10621898C22semidirect
18. C22×D4×D43C22semidirect
21. C2×M16×D43C22semidirect
22. #14583480C22semidirect
23. #14583480C22semidirect
25. #14583475C22semidirect
27. #14583468C22semidirect
31. #14583465C22semidirect
39. #14583411C22semidirect
40. C2×#13063300C22semidirect
42. C2×#13063296C22semidirect
45. C2×#13063283C22semidirect
46. #14583243C22semidirect
47. #14583242C22semidirect
48. #14583226C22semidirect
49. #14583225C22semidirect
50. #14583223C22semidirect
51. #14583217C22semidirect
52. #14583212C22semidirect
53. #14583153C22semidirect
54. #14583151C22semidirect
55. #14583146C22semidirect
56. #14583144C22semidirect
57. #14583136C22semidirect
58. #14583134C22semidirect
59. #14583129C22semidirect
60. #14583127C22semidirect
61. #14583051C22semidirect
62. #14583051C22semidirect
63. #14583046C22semidirect
64. #14583042C22semidirect
65. #14583040C22semidirect
66. #14583037C22semidirect
67. #14583035C22semidirect
68. #14583034C22semidirect
69. #14583034C22semidirect
70. #14583032C22semidirect
71. #14582942C22semidirect
72. #14582903C22semidirect
73. #14582901C22semidirect
74. #14582898C22semidirect
75. #14582864C22semidirect
76. #14582864C22semidirect
77. #14582863C22semidirect
78. #14582862C22semidirect
80. C2×#117×C43C22semidirect
81. C43×#482C22semidirect
82. C43×#481C22semidirect
83. C43×#480C22semidirect
84. C43×#428C22semidirect
85. C43×#418C22semidirect
86. C43×#407C22semidirect
97. C2×#10621898C23semidirect
99. C22×Dic86C23semidirect
103. C22×D172C23semidirect
123. C2×#10621872C23semidirect
125. C2×C8×D43C23semidirect
142. #13063305C23semidirect
143. #13063305C23semidirect
150. #13063300C23semidirect
151. #13063300C23semidirect
182. #13063258C23semidirect
183. #13063256C23semidirect
184. #13063250C23semidirect
185. #13063248C23semidirect
186. #13063247C23semidirect
189. #13063245C23semidirect
190. C22⋊(C43⋊C8)C23semidirect
191. C22⋊(C43⋊C8)C23semidirect
205. #117×C43C23semidirect
207. C2×C4⋊C4×C43C23semidirect
208. C2×C4⋊C4×C43C23semidirect
212. #107×C43C23semidirect
213. #106×C43C23semidirect
216. C22⋊C8×C43C23semidirect
217. C22⋊C8×C43C23semidirect
497. #3094D43semidirect
547. C2×#117C2×D43semidirect
553. #482C2×D43semidirect
555. #481C2×D43semidirect
557. #480C2×D43semidirect
577. #428C2×D43semidirect
579. #418C2×D43semidirect
586. #407C2×D43semidirect
587. C43#60753semidirect
688. #117C22×D43semidirect
691. C2×C4⋊C4C22×D43semidirect
692. C2×C4⋊C4C22×D43semidirect
702. #107C22×D43semidirect
704. #106C22×D43semidirect
717. C22⋊C8C22×D43semidirect
718. C22⋊C8C22×D43semidirect

Maximal subgroups

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

subgroupindex
#191479282
C2×#145834652
#191454692
#191454592
#191454542
#191454522
#191445352
#191445292
#191442152
#191442122
#191438492
#191438452
#191438242
#191430382
C43×#30942
#6075343