Finite Group Databasebeta

← #25981501

Subgroups — #25981501

Order 11008.

2126 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148434C211yesmaximal, characteristic, complemented
2C2×#14583554C211yesmaximal, characteristic, complemented
3#19146693C214yesmaximal, complemented
4#19146573C214yesmaximal, complemented
5#19146155C214yesmaximal, complemented
6#19146125C214yesmaximal, complemented
7#19145624C212yesmaximal, complemented
8#19145419C211yesmaximal, characteristic, complemented
9#19145402C211yesmaximal, characteristic, complemented
10#19145378C212yesmaximal, complemented
11#19144735C212yesmaximal, complemented
12#19143857C211yesmaximal, characteristic, complemented
13#19143849C211yesmaximal, characteristic, complemented
14#19143817C212yesmaximal, complemented
15C43×#2973C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621898C2211yescharacteristic, complemented
18C2×#13063358C2212yescomplemented
19C2×#13063353C2212yescomplemented
20C2×#13063347C2214yescomplemented
21#14583598—22no—
22#14583595C2212yescomplemented
23#14583589C2212yescomplemented
24#14583578—22no—
25#14583558C2212yescomplemented
26#14583554—22no—
27#14583554—22no—
28#14583554C2214yes—
29#14583554C2214yescomplemented
30#14583545C2212yescomplemented
31#14583496—21no—
32#14583487—21no—
33#14583458—21no—
34C2×#13063325C2211yescharacteristic, complemented
35#14583433C2212yes—
36#14583410C2212yes—
37C2×#13063307—21no—
38C2×#13063307—21no—
39C2×#13063304C2211yescharacteristic
40C2×#13063304C2211yescharacteristic
41C2×#13063304C2211yescharacteristic, complemented
42C2×#13063299C2211yescharacteristic
43C2×#13063296—21no—
44#14583372—21no—
45C2×C4×D172C2211yescharacteristic, complemented
46C2×C4⋊C4×D43—21no—
47#14583293C2214yescomplemented
48#14583268C2214yescomplemented
49#14583241C2214yescomplemented
50#14583235C2212yescomplemented
51#14583230C2212yescomplemented
52#14583230C2212yescomplemented
53#14583213C2212yes—
54#14583200C2214yescomplemented
55#14583157C2214yescomplemented
56#14583145C2214yescomplemented
57#14583140C2214yescomplemented
58#14583128C2214yescomplemented
59#14583115C2214yescomplemented
60#14583110C2214yescomplemented
61#14583105C2214yescomplemented
62#14583063C2214yescomplemented
63#14583063C2214yescomplemented
64#14583063C2214yescomplemented
65#14583057C2212yescomplemented
66#14583057C2212yescomplemented
67#14583057C2212yescomplemented
68#14583052C2212yescomplemented
69#14583052C2212yescomplemented
70#14583046C2214yescomplemented
71#14583046C2214yescomplemented
72#14583040C2212yes—
73#14583040C2212yes—
74#14583035C2212yes—
75#14583012C2214yescomplemented
76#14583001C2214yescomplemented
77#14582901C2212yescomplemented
78#14582901C2212yescomplemented
79#14582896C2214yescomplemented
80C2×C4×D4×C43C2211yescharacteristic
81C43×#435C2214yescomplemented
82C43×#435C2214yescomplemented
83C43×#432C2212yescomplemented
84C43×#407C2211yescharacteristic
85C43×#407C2211yescharacteristic
86C2×C22⋊C8×C43C2212yescomplemented
87C2×#10621898—21no—
88C2×#10621898—21no—
89C2×#10621898—22no—
90C2×#10621898—44no—
91C2×#10621898—44no—
92C2×#10621898C2312yes—
93C2×#10621898C2314yes—
94C2×#10621898C2312yes—
95C2×#10621898C2312yes—
96C22×Dic86C2311yescharacteristic
97C22×Dic86C2311yescharacteristic
98C22×Dic86C2311yescharacteristic
99C22×D172C2311yescharacteristic
100C22×D172C2311yescharacteristic
101C22×C22⋊D43—21no—
102C22×C22⋊D43—21no—
103C22×C22⋊D43—21no—
104C22×C4×D43—21no—
105C22×C4×D43—21no—
106C22×C4×D43—21no—
107#13063358—44no—
108#13063353—44no—
109#13063347—48no—
110C2×Dic172C2314yes—
111C2×Dic172C2314yes—
112C2×#10621873C2314yes—
113C2×#10621873C2314yes—
114C2×#10621873C2314yes—
115C2×D344C2314yes—
116#13063325—22no—
117#13063325C2314yes—
118#13063320—22no—
119#13063319—22no—
120#13063318—22no—
121#13063317C2312yes—
122#13063315—22no—
123#13063313C2312yes—
124#13063311—22no—
125#13063310—22no—
126#13063308—22no—
127#13063308—22no—
128#13063307—24no—
129#13063307—24no—
130#13063307—24no—
131#13063307—24no—
132#13063307—22no—
133#13063306—22no—
134#13063304—21no—
135#13063304—21no—
136#13063304—22no—
137#13063304—21no—
138#13063304—21no—
139#13063304C2312yes—
140#13063304C2314yes—
141#13063304C2312yes—
142#13063304C2312yes—
143#13063304C2312yes—
144#13063304C2312yes—
145#13063303—22no—
146#13063299—21no—
147#13063299—21no—
148#13063299C2312yes—
149#13063299C2312yes—
150#13063299C2312yes—
151#13063298—22no—
152#13063297—22no—
153#13063297—22no—
154#13063296—24no—
155#13063296—24no—
156#13063294—22no—
157#13063293—22no—
158C4×Dic86C2312yes—
159C4×D172—22no—
160C4×D172C2314yes—
161C4×D172C2312yes—
162C4×C22⋊D43—22no—
163C4×C22⋊D43—22no—
164C4×C22⋊D43—22no—
165(C22⋊D43)⋊C4—22no—
166(C22⋊D43)⋊C4—22no—
167#13063284C2312yes—
168#13063282—22no—
169#13063281—22no—
170C2×C4⋊Dic43—21no—
171C2×C4⋊Dic43—21no—
172C2×C4⋊Dic43C2311yescharacteristic
173C2×C4⋊Dic43C2311yescharacteristic
174C2×C4⋊Dic43C2311yescharacteristic
175C2×Dic43⋊C4—21no—
176C2×Dic43⋊C4—21no—
177C2×Dic43⋊C4—21no—
178C4⋊C4×D43—24no—
179C4⋊C4×D43—24no—
180C2×C22⋊Dic43—21no—
181C2×C22⋊Dic43—21no—
182C2×C22⋊Dic43—21no—
183C2×(C2×D43)⋊C4—21no—
184C2×(C2×D43)⋊C4—21no—
185C22⋊C4×D43—22no—
186#13063259C2314yes—
187#13063257C2314yes—
188#13063250C2314yes—
189#13063250C2314yes—
190#13063250C2314yes—
191#13063250C2314yes—
192#13063250C2314yes—
193#13063247C2314yes—
194#13063247C2314yes—
195#13063247C2314yes—
196C22×D4×C43D411yescharacteristic
197C23×C4×C43C2311yescharacteristic
198C23×C4×C43C2311yescharacteristic
199C2×M16×C43C2312yes—
200C2×M16×C43C2312yes—
201C22×C8×C43C2314yes—
202C4×D4×C43D412yes—
203C4×D4×C43D412yes—
204C4×D4×C43C2312yes—
205C4×D4×C43C2312yes—
206C2×C4⋊C4×C43D411yescharacteristic
207C2×C22⋊C4×C43D411yescharacteristic
208C2×C22⋊C4×C43D411yescharacteristic
209C2×C42×C43C2311yescharacteristic
210C4⋊C8×C43C2314yes—
211C22⋊C8×C43C2312yes—
212C22⋊C8×C43C2312yes—
213C22⋊C8×C43C2312yes—
214C22⋊C8×C43C2314yes—
215C22⋊C8×C43C2312yes—
216#97×C43C2314yes—
217C24×C43C2×D411yescharacteristic
218C24×C43C2×D411yescharacteristic
219C23×D43—21no—
220C23×D43—21no—
221C2×D4×C43—42no—
222C2×D4×C43C2×D412yes—
223C2×D4×C43C2×D412yes—
224C22×C4×C43—42no—
225C22×C4×C43—42no—
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2×D411yescharacteristic
229C22×C4×C43C2×D411yescharacteristic
230C22×C4×C43C2×D411yescharacteristic
231C22×C4×C43C2×D411yescharacteristic
232C22×C4×C43C2×D412yes—
233C22×C4×C43C2411yescharacteristic
234C22×C4×C43C2412yes—
235C22×C4×C43C2411yescharacteristic
236C22×C4×C43C2411yescharacteristic
237C2×C22⋊D43—22no—
238C2×C22⋊D43—22no—
239C2×C22⋊D43—22no—
240C2×C22⋊D43—24no—
241C2×C22⋊D43—22no—
242C2×C22⋊D43—22no—
243C2×C22⋊D43—22no—
244C2×C22⋊D43—44no—
245C2×C22⋊D43—44no—
246C2×C22⋊D43—44no—
247C22×Dic43—21no—
248C22×Dic43—21no—
249C22×Dic43—21no—
250C22×Dic43—21no—
251C22×Dic43—21no—
252C22×Dic43—21no—
253#10621898—28no—
254#10621898—24no—
255#10621898—24no—
256#10621898—42no—
257#10621898—44no—
258#10621898—42no—
259#10621898—44no—
260#10621898—44no—
261#10621898—44no—
262#10621898—48no—
263C2×D172—21no—
264C2×D172—24no—
265C2×D172—21no—
266C2×D172—42no—
267C2×D172C2412yes—
268C2×D172C2412yes—
269C2×C4×D43—24no—
270C2×C4×D43—24no—
271C2×C4×D43—22no—
272C2×C4×D43—22no—
273C2×C4×D43—22no—
274C2×C4×D43—22no—
275C2×C4×D43—44no—
276C2×C4×D43—44no—
277C2×C4×D43—44no—
278C2×Dic86—21no—
279C2×Dic86—21no—
280C2×Dic86—21no—
281C2×Dic86—42no—
282C2×Dic86—42no—
283C2×Dic86—42no—
284C2×Dic86C2412yes—
285C2×Dic86C2412yes—
286C2×Dic86C2412yes—
287M16×C43—42no—
288M16×C43—42no—
289C2×C8×C43—44no—
290C2×C8×C43C2414yes—
291C2×C8×C43C2414yes—
292C4⋊C4×C43C2×D412yes—
293C4⋊C4×C43C2×D412yes—
294C22⋊C4×C43C2×D412yes—
295C22⋊C4×C43C2×D412yes—
296C22⋊C4×C43C2×D412yes—
297C22⋊C4×C43C2×D412yes—
298C42×C43C2×D412yes—
299C42×C43C2412yes—
300C22⋊Dic43—22no—
301C22⋊Dic43—22no—
302C22⋊Dic43—22no—
303C22⋊Dic43—24no—
304C22⋊Dic43—22no—
305C22⋊Dic43—22no—
306C22⋊Dic43—22no—
307(C2×D43)⋊C4—22no—
308(C2×D43)⋊C4—22no—
309(C2×D43)⋊C4—22no—
310(C2×D43)⋊C4—24no—
311(C2×D43)⋊C4—22no—
312(C2×D43)⋊C4—22no—
313(C2×D43)⋊C4—22no—
314C4⋊Dic43—24no—
315C4⋊Dic43—24no—
316C4⋊Dic43—21no—
317C4⋊Dic43—21no—
318C4⋊Dic43—21no—
319C4⋊Dic43C2412yes—
320C4⋊Dic43C2412yes—
321C4⋊Dic43C2412yes—
322Dic43⋊C4—24no—
323Dic43⋊C4—22no—
324Dic43⋊C4—22no—
325Dic43⋊C4—22no—
326Dic43⋊C4—22no—
327Dic43⋊C4—22no—
328Dic43⋊C4—22no—
329Dic43⋊C4—22no—
330Dic43⋊C4—22no—
331C4×Dic43—22no—
332C4×Dic43—22no—
333Dic172—44no—
334Dic172—44no—
335D344—28no—
336#10621873—28no—
337#10621873—44no—
338#10621873—44no—
339C23×C43—22no—
340C23×C43—22no—
341C23×C43—41no—
342C23×C43—41no—
343C23×C43—41no—
344C23×C43—41no—
345C23×C43C22×D411yescharacteristic
346C23×C43C22×D412yes—
347C23×C43C22×D411yescharacteristic
348C23×C43C22×D411yescharacteristic
349C22×D43—24no—
350C22×D43—22no—
351C22×D43—22no—
352C22×D43—42no—
353C22×D43—42no—
354C22×D43—42no—
355C22×D43—81no—
356C22×D43—81no—
357D4×C43—42no—
358D4×C43—42no—
359C2×C4×C43—22no—
360C2×C4×C43—24no—
361C2×C4×C43—22no—
362C2×C4×C43—22no—
363C2×C4×C43—22no—
364C2×C4×C43—41no—
365C2×C4×C43—41no—
366C2×C4×C43—41no—
367C2×C4×C43—42no—
368C2×C4×C43—41no—
369C2×C4×C43—41no—
370C2×C4×C43C22×D412yes—
371C2×C4×C43C22×D412yes—
372C2×C4×C43C22×D411yescharacteristic
373C2×C4×C43C22×D412yes—
374C2×C4×C43C22×D411yescharacteristic
375C2×C4×C43C22×D411yescharacteristic
376C2×C4×C43C2511yescharacteristic
377C22⋊D43—44no—
378C22⋊D43—44no—
379C22⋊D43—48no—
380C22⋊D43—44no—
381C22⋊D43—44no—
382C22⋊D43—82no—
383C22⋊D43—82no—
384C2×Dic43—22no—
385C2×Dic43—22no—
386C2×Dic43—22no—
387C2×Dic43—22no—
388C2×Dic43—22no—
389C2×Dic43—22no—
390C2×Dic43—42no—
391C2×Dic43—42no—
392C2×Dic43—42no—
393C2×Dic43—42no—
394C2×Dic43—81no—
395C2×Dic43—81no—
396D172—24no—
397D172—22no—
398D172—24no—
399D172—81no—
400D172H(5,𝔽2)14yes—
401C4×D43—44no—
402C4×D43—48no—
403C4×D43—44no—
404C4×D43—48no—
405C4×D43—82no—
406C4×D43—82no—
407Dic86—24no—
408Dic86—22no—
409Dic86—24no—
410Dic86—22no—
411Dic86—42no—
412Dic86—42no—
413Dic86—81no—
414C8×C43—24no—
415C8×C43—24no—
416#61575—431nomaximal, Sylow
417C22×C43—21no—
418C22×C43—21no—
419C22×C43—21no—
420C22×C43—21no—
421C22×C43—22no—
422C22×C43—21no—
423C22×C43—21no—
424C22×C43—22no—
425C22×C43—21no—
426C22×C43—21no—
427C22×C43—22no—
428C22×C43—82no—
429C22×C43—82no—
430C22×C43#57512yes—
431C22×C43C23×D411yescharacteristic
432C2×D43—24no—
433C2×D43—48no—
434C2×D43—42no—
435C2×D43—42no—
436C2×D43—42no—
437C2×D43—42no—
438C2×D43—42no—
439C2×D43—162no—
440C4×C43—22no—
441C4×C43—21no—
442C4×C43—21no—
443C4×C43—22no—
444C4×C43—21no—
445C4×C43—22no—
446C4×C43C2×H(5,𝔽2)12yes—
447Dic43—42no—
448Dic43—42no—
449Dic43—42no—
450Dic43—42no—
451Dic43—42no—
452Dic43—42no—
453#3505—431no—
454C2×#547—431no—
455#3315—434no—
456#3307—434no—
457#3269—434no—
458#3267—434no—
459#3218—432no—
460#3195—431no—
461#3193—431no—
462#3190—432no—
463#3114—432no—
464#3007—431no—
465#3006—431no—
466#3002—432no—
467#2973D4311yescharacteristic, complemented
468C2×C43—22no—
469C2×C43—41no—
470C2×C43—41no—
471C2×C43—42no—
472C2×C43#348411yescharacteristic
473C2×C43C2×#57511yescharacteristic
474C2×C43#358611yescharacteristic
475D43—44no—
476D43—82no—
477C22×#41—431no—
478C22×#41—431no—
479C2×#137—432no—
480C2×AGL(1,ℤ/8)—432no—
481C2×#135—434no—
482#553—432no—
483#553—862no—
484#552—432no—
485#551—862no—
486#548—432no—
487#547—434no—
488#547—434no—
489#547—862no—
490#547—862no—
491#546—432no—
492#539—861no—
493#538—861no—
494#534—861no—
495C2×C4⋊Q8—431no—
496#529—432no—
497#525—432no—
498C2×#123—861no—
499C2×#123—861no—
500C2×C22⋊Q8—431no—
501C2×C22⋊Q8—431no—
502C2×C22⋊Q8—431no—
503C2×#121—431no—
504C2×#121—861no—
505#518—861no—
506C2×C4×D4—431no—
507C2×C4×D4C2×D4311yescharacteristic
508C22×C4⋊C4—861no—
509#497—434no—
510#491—434no—
511#485—434no—
512#484—432no—
513#483—432no—
514#483—432no—
515#480—432no—
516#478—434no—
517#470—434no—
518#468—434no—
519#467—434no—
520#465—434no—
521#463—434no—
522#462—434no—
523#461—434no—
524#452—434no—
525#452—434no—
526#452—434no—
527#451—432no—
528#451—432no—
529#451—432no—
530#450—432no—
531#450—432no—
532#449—434no—
533#449—434no—
534#448—432no—
535#448—432no—
536#447—432no—
537#442—434no—
538#440—434no—
539#435C2×D4314yescomplemented
540#435C2×D4314yescomplemented
541#432C2×D4312yescomplemented
542#417—432no—
543#417—432no—
544#416—434no—
545#407C2×D4311yescharacteristic
546#407C2×D4311yescharacteristic
547C2×C22⋊C8C2×D4312yescomplemented
548C43#6157511yescharacteristic, complemented, Sylow
549C2×#41—434no—
550C2×#41—432no—
551C2×#41—432no—
552C2×#41—432no—
553C2×#41—861no—
554C2×#41—861no—
555C2×#41—862no—
556C2×#41—1724no—
557C2×#41—1724no—
558C22×Q8—431no—
559C22×Q8—431no—
560C22×Q8—431no—
561C22×D4—431no—
562C22×D4—431no—
563C22×D4—861no—
564C22×D4—861no—
565C22×D4—861no—
566C22×D4D17211yescharacteristic
567C23×C4—861no—
568C23×C4—861no—
569C23×C4—861no—
570C23×C4C22×D4311yescharacteristic
571C23×C4C22×D4311yescharacteristic
572#137—1724no—
573AGL(1,ℤ/8)—1724no—
574#135—1728no—
575C2×Q16—434no—
576C2×Q16—434no—
577C2×SD16—434no—
578C2×SD16—434no—
579C2×SD16—434no—
580C2×D8—434no—
581C2×M16C22×D4312yes—
582C2×M16C22×D4312yes—
583C22×C8C22×D4314yes—
584C4⋊Q8—434no—
585C4⋊Q8—862no—
586#126—862no—
587#126—862no—
588#126—862no—
589#125—432no—
590#125—862no—
591#124—432no—
592#124—862no—
593#123—862no—
594#123—862no—
595#123—862no—
596#123—862no—
597#123—864no—
598#123—864no—
599#123—864no—
600#123—864no—
601#123—862no—
602C22⋊Q8—432no—
603C22⋊Q8—432no—
604C22⋊Q8—432no—
605C22⋊Q8—432no—
606C22⋊Q8—434no—
607C22⋊Q8—432no—
608C22⋊Q8—861no—
609C22⋊Q8—861no—
610C22⋊Q8—861no—
611C22⋊Q8—862no—
612C22⋊Q8—861no—
613C22⋊Q8—862no—
614#121—432no—
615#121—432no—
616#121—432no—
617#121—864no—
618#121—864no—
619#121—862no—
620#121—862no—
621#121—861no—
622#121—861no—
623#121—862no—
624#120—862no—
625#120—862no—
626C4×Q8—432no—
627C4×D4—434no—
628C4×D4—432no—
629C4×D4—862no—
630C4×D4—862no—
631C4×D4—862no—
632C4×D4—862no—
633C4×D4—862no—
634C4×D4—862no—
635C4×D4D17212yes—
636C4×D4D17212yes—
637C4×D4C22×D4312yes—
638C4×D4C22×D4312yes—
639#117—432no—
640#117—862no—
641#117—862no—
642C2×C4⋊C4—431no—
643C2×C4⋊C4—431no—
644C2×C4⋊C4—431no—
645C2×C4⋊C4—861no—
646C2×C4⋊C4—861no—
647C2×C4⋊C4—861no—
648C2×C4⋊C4—861no—
649C2×C4⋊C4—861no—
650C2×C4⋊C4—864no—
651C2×C4⋊C4—864no—
652C2×C4⋊C4D17211yescharacteristic
653C2×C22⋊C4—861no—
654C2×C22⋊C4—861no—
655C2×C22⋊C4—861no—
656C2×C22⋊C4—861no—
657C2×C22⋊C4—861no—
658C2×C22⋊C4—862no—
659C2×C22⋊C4D17211yescharacteristic
660C2×C22⋊C4D17211yescharacteristic
661C2×C42C22×D4311yescharacteristic
662#107—434no—
663#106—434no—
664C4⋊C8C22×D4314yes—
665#103—434no—
666#103—434no—
667#103—434no—
668#103—434no—
669#103—434no—
670#102—434no—
671#102—434no—
672#102—434no—
673C22⋊C8C22×D4312yes—
674C22⋊C8C22×D4312yes—
675C22⋊C8C22×D4314yes—
676C22⋊C8C22×D4312yes—
677C22⋊C8C22×D4312yes—
678#97C22×D4314yes—
679C24—861no—
680C24—861no—
681C24C2×D17211yescharacteristic
682C24C2×D17211yescharacteristic
683#41—868no—
684#41—864no—
685#41—864no—
686#41—1724no—
687#41—1724no—
688#41—1722no—
689#41—1722no—
690#41—1728no—
691#41—1724no—
692#41—1724no—
693C2×Q8—432no—
694C2×Q8—432no—
695C2×Q8—432no—
696C2×Q8—861no—
697C2×Q8—861no—
698C2×Q8—861no—
699C2×Q8—1722no—
700C2×Q8—1722no—
701C2×Q8—1722no—
702C2×D4—42no—
703C2×D4—432no—
704C2×D4—432no—
705C2×D4—864no—
706C2×D4—862no—
707C2×D4—862no—
708C2×D4—862no—
709C2×D4—862no—
710C2×D4—862no—
711C2×D4—864no—
712C2×D4—862no—
713C2×D4—861no—
714C2×D4—861no—
715C2×D4—1722no—
716C2×D4—1724no—
717C2×D4—1724no—
718C2×D4—1724no—
719C2×D4C2×D17212yes—
720C2×D4C2×D17212yes—
721C22×C4—42no—
722C22×C4—42no—
723C22×C4—861no—
724C22×C4—861no—
725C22×C4—861no—
726C22×C4—861no—
727C22×C4—861no—
728C22×C4—861no—
729C22×C4—862no—
730C22×C4—862no—
731C22×C4—864no—
732C22×C4—864no—
733C22×C4—862no—
734C22×C4—862no—
735C22×C4—1724no—
736C22×C4—1724no—
737C22×C4—1724no—
738C22×C4C2×D17211yescharacteristic
739C22×C4C2×D17211yescharacteristic
740C22×C4C2×D17211yescharacteristic
741C22×C4C2×D17211yescharacteristic
742C22×C4C2×D17211yescharacteristic
743C22×C4C2×D17211yescharacteristic
744C22×C4C2×D17212yes—
745C22×C4C23×D4311yescharacteristic
746C22×C4C23×D4311yescharacteristic
747C22×C4C23×D4311yescharacteristic
748C22×C4C23×D4312yes—
749Q16—1724no—
750Q16—1724no—
751SD16—868no—
752SD16—1724no—
753SD16—1724no—
754D8—868no—
755M16—42no—
756M16—42no—
757C2×C8—44no—
758C2×C8C23×D4314yes—
759C2×C8C23×D4314yes—
760C4⋊C4—432no—
761C4⋊C4—432no—
762C4⋊C4—432no—
763C4⋊C4—861no—
764C4⋊C4—861no—
765C4⋊C4—861no—
766C4⋊C4—864no—
767C4⋊C4—864no—
768C4⋊C4—862no—
769C4⋊C4—862no—
770C4⋊C4—862no—
771C4⋊C4—862no—
772C4⋊C4—864no—
773C4⋊C4—862no—
774C4⋊C4—862no—
775C4⋊C4—862no—
776C4⋊C4—862no—
777C4⋊C4C2×D17212yes—
778C4⋊C4C2×D17212yes—
779C22⋊C4—862no—
780C22⋊C4—862no—
781C22⋊C4—862no—
782C22⋊C4—864no—
783C22⋊C4—862no—
784C22⋊C4—862no—
785C22⋊C4—862no—
786C22⋊C4—862no—
787C22⋊C4—864no—
788C22⋊C4—862no—
789C22⋊C4—862no—
790C22⋊C4—862no—
791C22⋊C4—862no—
792C22⋊C4—862no—
793C22⋊C4C2×D17212yes—
794C22⋊C4C2×D17212yes—
795C22⋊C4C2×D17212yes—
796C22⋊C4C2×D17212yes—
797C42—862no—
798C42—862no—
799C42C2×D17212yes—
800C42C23×D4312yes—
801C23—22no—
802C23—22no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—864no—
808C23—862no—
809C23—862no—
810C23—3441no—
811C23—3441no—
812C23—1722no—
813C23—1722no—
814C23—1722no—
815C23C22×D17211yescharacteristic
816C23C22×D17212yes—
817C23C22×D17211yescharacteristic
818C23C22×D17211yescharacteristic
819Q8—864no—
820Q8—862no—
821Q8—864no—
822Q8—862no—
823Q8—3441no—
824Q8—1722no—
825Q8—1722no—
826D4—42no—
827D4—42no—
828D4—434no—
829D4—864no—
830D4—862no—
831D4—864no—
832D4—3441no—
833D4—3442no—
834D4—3442no—
835D4—1724no—
836D4—1728no—
837D4—1724no—
838D4—1724no—
839D4—1724no—
840C2×C4—22no—
841C2×C4—24no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—42no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—862no—
852C2×C4—862no—
853C2×C4—862no—
854C2×C4—862no—
855C2×C4—862no—
856C2×C4—862no—
857C2×C4—3442no—
858C2×C4—3442no—
859C2×C4—3441no—
860C2×C4—3441no—
861C2×C4—1728no—
862C2×C4—1724no—
863C2×C4—1724no—
864C2×C4—1728no—
865C2×C4—1722no—
866C2×C4—1722no—
867C2×C4—1722no—
868C2×C4—1722no—
869C2×C4C22×D17212yes—
870C2×C4C22×D17212yes—
871C2×C4C22×D17211yescharacteristic
872C2×C4C22×D17212yes—
873C2×C4C22×D17211yescharacteristic
874C2×C4C22×D17211yescharacteristic
875C2×C4C24×D4311yescharacteristic
876C8—24no—
877C8—24no—
878C22—21no—
879C22—21no—
880C22—21no—
881C22—21no—
882C22—22no—
883C22—21no—
884C22—22no—
885C22—21no—
886C22—21no—
887C22—22no—
888C22—21no—
889C22—82no—
890C22—82no—
891C22—864no—
892C22—1728no—
893C22—1722no—
894C22—1722no—
895C22—1722no—
896C22—1722no—
897C22—1722no—
898C22—6882no—
899C22#1458369912yes—
900C22C23×D17211yescharacteristic
901C4—22no—
902C4—22no—
903C4—21no—
904C4—22no—
905C4—21no—
906C4—21no—
907C4—1722no—
908C4—1722no—
909C4—1722no—
910C4—1722no—
911C4—1722no—
912C4—1722no—
913C4H(5,𝔽2)×D4312yes—
914C2—22no—
915C2—41no—
916C2—41no—
917C2—42no—
918C2—3442no—
919C2—1724no—
920C2#1914823111yescharacteristic
921C2C2×#1458369911yescharacteristic
922C2#1914938311yescharacteristic
subgroupG/H
centerC22C23×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#2973C2
socleC22×C43C23×D4
hypercenter#2973D43
hypocenterC43#61575
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2973

Complements

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

NH ≅ G/Ntype
1. #19148434C2semidirect
2. C2×#14583554C2semidirect
3. #19146693C2semidirect
4. #19146573C2semidirect
5. #19146155C2semidirect
6. #19146125C2semidirect
7. #19145624C2semidirect
8. #19145419C2semidirect
9. #19145402C2semidirect
10. #19145378C2semidirect
11. #19144735C2semidirect
12. #19143857C2semidirect
13. #19143849C2semidirect
14. #19143817C2semidirect
15. C43×#2973C2semidirect
17. C22×#10621898C22semidirect
18. C2×#13063358C22semidirect
19. C2×#13063353C22semidirect
20. C2×#13063347C22semidirect
22. #14583595C22semidirect
23. #14583589C22semidirect
25. #14583558C22semidirect
29. #14583554C22semidirect
30. #14583545C22semidirect
34. C2×#13063325C22semidirect
41. C2×#13063304C22semidirect
45. C2×C4×D172C22semidirect
47. #14583293C22semidirect
48. #14583268C22semidirect
49. #14583241C22semidirect
50. #14583235C22semidirect
51. #14583230C22semidirect
52. #14583230C22semidirect
54. #14583200C22semidirect
55. #14583157C22semidirect
56. #14583145C22semidirect
57. #14583140C22semidirect
58. #14583128C22semidirect
59. #14583115C22semidirect
60. #14583110C22semidirect
61. #14583105C22semidirect
62. #14583063C22semidirect
63. #14583063C22semidirect
64. #14583063C22semidirect
65. #14583057C22semidirect
66. #14583057C22semidirect
67. #14583057C22semidirect
68. #14583052C22semidirect
69. #14583052C22semidirect
70. #14583046C22semidirect
71. #14583046C22semidirect
75. #14583012C22semidirect
76. #14583001C22semidirect
77. #14582901C22semidirect
78. #14582901C22semidirect
79. #14582896C22semidirect
81. C43×#435C22semidirect
82. C43×#435C22semidirect
83. C43×#432C22semidirect
86. C2×C22⋊C8×C43C22semidirect
467. #2973D43semidirect
539. #435C2×D43semidirect
540. #435C2×D43semidirect
541. #432C2×D43semidirect
547. C2×C22⋊C8C2×D43semidirect
548. C43#61575semidirect

Maximal subgroups

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

subgroupindex
#191484342
C2×#145835542
#191466932
#191465732
#191461552
#191461252
#191456242
#191454192
#191454022
#191453782
#191447352
#191438572
#191438492
#191438172
C43×#29732
#6157543