Finite Group Databasebeta

← #25965120

Subgroups — #25965120

Order 11008.

2138 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583502C211yesmaximal, characteristic, complemented
2#19147796C211yesmaximal, characteristic, complemented
3#19144882C214yesmaximal, complemented
4#19144834C214yesmaximal, complemented
5#19144797C214yesmaximal, complemented
6#19144789C214yesmaximal, complemented
7#19144535C211yesmaximal, characteristic, complemented
8#19144416C212yesmaximal, complemented
9#19144074C212yesmaximal, complemented
10#19143849C211yesmaximal, characteristic, complemented
11#19143845C211yesmaximal, characteristic, complemented
12#19143402C212yesmaximal, complemented
13#19143399C212yesmaximal, complemented
14#19143230C211yesmaximal, characteristic, complemented
15C43×#3094C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C2×#13063353C2212yes—
18C2×#13063351C2212yes—
19#14583502—22no—
20#14583502—22no—
21#14583502C2214yes—
22#14583502C2214yescomplemented
23C2×#13063321C2211yescharacteristic, complemented
24C2×#13063316C2211yescharacteristic, complemented
25C2×#13063309—21no—
26C2×#13063307—21no—
27C2×#13063299C2211yescharacteristic
28C2×#13063297—21no—
29C2×#13063296—21no—
30#14583380C2212yescomplemented
31#14583380C2212yescomplemented
32#14583379—21no—
33#14583379—21no—
34#14583376C2212yescomplemented
35#14583373C2212yescomplemented
36#14583372—21no—
37#14583372—21no—
38C4×#10621898—22no—
39#14583367C2212yes—
40#14583367C2212yes—
41C2×D4×Dic43C2211yescharacteristic, complemented
42C2×#13063287C2211yescharacteristic, complemented
43C2×#13063284C2211yescharacteristic
44#117×D43—22no—
45#14583223C2214yescomplemented
46#14583217C2212yescomplemented
47#14583212C2212yescomplemented
48#14583209C2214yescomplemented
49#14583205C2214yescomplemented
50#14583202C2214yescomplemented
51#14583198C2214yescomplemented
52#14583098C2214yescomplemented
53#14583098C2214yescomplemented
54#14583093C2214yescomplemented
55#14583093C2214yescomplemented
56#14583046C2214yescomplemented
57#14583042C2214yescomplemented
58#14583040C2212yescomplemented
59#14583037C2212yescomplemented
60#14583035C2212yescomplemented
61#14583032C2212yescomplemented
62#14583010C2214yescomplemented
63#14583008C2214yescomplemented
64#14582998C2214yescomplemented
65#14582996C2214yescomplemented
66#14582990C2214yescomplemented
67#14582986C2214yescomplemented
68#14582981C2214yescomplemented
69#14582979C2214yescomplemented
70#14582957C2214yescomplemented
71#14582957C2214yescomplemented
72#14582942C2212yescomplemented
73#14582922C2212yescomplemented
74#14582903C2212yescomplemented
75#14582901C2212yes—
76#14582898C2212yes—
77#14582863C2211yescharacteristic
78M16×Dic43C2212yescomplemented
79C2×#121×C43C2211yescharacteristic
80C2×#117×C43C2211yescharacteristic
81C43×#482C2214yescomplemented
82C43×#481C2212yescomplemented
83C43×#480C2212yescomplemented
84C43×#428C2212yescomplemented
85C43×#418C2212yescomplemented
86C43×#407C2211yescharacteristic
87C2×#10621898—21no—
88C2×#10621898—21no—
89C2×#10621898—28no—
90C2×#10621898C2312yes—
91C2×#10621898C2312yes—
92C22×Dic86C2311yescharacteristic
93C22×D172C2311yescharacteristic
94C22×D172C2311yescharacteristic
95C22×C22⋊D43—21no—
96C22×C22⋊D43—21no—
97C22×C22⋊D43—21no—
98C22×C22⋊D43—21no—
99C23×Dic43—21no—
100C22×C4×D43—21no—
101C22×C4×D43—21no—
102#13063353—28no—
103#13063351—28no—
104C2×#10621873C2314yes—
105C2×#10621883C2314yes—
106C2×D344C2314yes—
107C2×#10621882C2314yes—
108C2×#10621877C2312yes—
109#13063321—22no—
110#13063321C2314yes—
111#13063316—22no—
112#13063316C2314yes—
113#13063309—24no—
114#13063309—24no—
115#13063307—24no—
116#13063307—24no—
117#13063299—21no—
118#13063299—21no—
119#13063299C2312yes—
120#13063299C2312yes—
121#13063297—24no—
122#13063297—24no—
123#13063296—24no—
124#13063296—24no—
125C4×Dic86—22no—
126C4×Dic86—22no—
127#13063290C2312yes—
128#13063290C2312yes—
129#13063290C2312yes—
130#13063290C2312yes—
131C4×D172—22no—
132C4×D172—22no—
133D4×Dic43—22no—
134D4×Dic43C2314yes—
135#13063287—22no—
136#13063287C2312yes—
137#13063287C2312yes—
138#13063287C2314yes—
139#13063287C2312yes—
140#13063287C2312yes—
141C4×C22⋊D43—22no—
142C4×C22⋊D43—22no—
143C4×C22⋊D43—22no—
144C4×C22⋊D43—22no—
145(C22⋊D43)⋊C4—22no—
146(C22⋊D43)⋊C4—22no—
147(C22⋊D43)⋊C4—22no—
148(C22⋊D43)⋊C4—22no—
149#13063284D412yes—
150#13063284D412yes—
151#13063284C2312yes—
152#13063284C2312yes—
153#13063283—22no—
154#13063283—22no—
155#13063282—22no—
156#13063282—22no—
157#13063281—22no—
158#13063281—22no—
159C2×C4⋊Dic43—21no—
160C2×C4⋊Dic43D411yescharacteristic
161C2×C4⋊Dic43D411yescharacteristic
162C2×C4⋊Dic43C2311yescharacteristic
163C2×Dic43⋊C4—21no—
164C4⋊C4×D43—22no—
165C4⋊C4×D43—22no—
166C2×C22⋊Dic43—21no—
167C2×C22⋊Dic43D411yescharacteristic
168C2×C22⋊Dic43D411yescharacteristic
169C2×(C2×D43)⋊C4—21no—
170C2×(C2×D43)⋊C4—21no—
171C22⋊C4×D43—22no—
172C22⋊C4×D43—22no—
173C2×C4×Dic43C2311yescharacteristic
174C2×C4×Dic43C2311yescharacteristic
175C42×D43—22no—
176C42×D43—22no—
177#13063258C2314yes—
178#13063256C2314yes—
179Dic43⋊C8C2314yes—
180Dic43⋊C8C2314yes—
181#13063250C2314yes—
182#13063248C2314yes—
183#13063247C2314yes—
184#13063245C2314yes—
185#13063245C2314yes—
186#13063245C2314yes—
187C22⋊(C43⋊C8)C2312yes—
188C22⋊(C43⋊C8)C2312yes—
189#13063235C2314yes—
190C8×Dic43C2314yes—
191C22×D4×C43—21no—
192C22×D4×C43C2311yescharacteristic
193C23×C4×C43C2311yescharacteristic
194C2×M16×C43C2312yes—
195#121×C43—21no—
196#121×C43—21no—
197#121×C43C2312yes—
198#121×C43C2312yes—
199#117×C43—21no—
200#117×C43—21no—
201#117×C43C2312yes—
202#117×C43C2312yes—
203C2×C4⋊C4×C43C2311yescharacteristic
204C2×C4⋊C4×C43C2311yescharacteristic
205C2×C4⋊C4×C43C2311yescharacteristic
206C2×C22⋊C4×C43—21no—
207C2×C22⋊C4×C43—21no—
208C2×C42×C43—21no—
209#107×C43C2314yes—
210#106×C43C2314yes—
211#102×C43C2314yes—
212#102×C43C2314yes—
213C22⋊C8×C43C2312yes—
214C22⋊C8×C43C2312yes—
215C24×C43—21no—
216C24×C43C2×D411yescharacteristic
217C23×D43—21no—
218C23×D43—21no—
219C2×D4×C43—21no—
220C2×D4×C43—22no—
221C2×D4×C43—22no—
222C2×D4×C43—24no—
223C2×D4×C43—82no—
224C2×D4×C43C2412yes—
225C22×C4×C43—24no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43C2×D411yescharacteristic
230C22×C4×C43C2×D411yescharacteristic
231C22×C4×C43C2×D411yescharacteristic
232C22×C4×C43C2411yescharacteristic
233C22×C4×C43C2411yescharacteristic
234C22×C4×C43C2411yescharacteristic
235C2×C22⋊D43—28no—
236C2×C22⋊D43—24no—
237C2×C22⋊D43—24no—
238C2×C22⋊D43—22no—
239C2×C22⋊D43—22no—
240C2×C22⋊D43—22no—
241C2×C22⋊D43—22no—
242C2×C22⋊D43—82no—
243C2×C22⋊D43—82no—
244C2×C22⋊D43—82no—
245C22×Dic43—24no—
246C22×Dic43—21no—
247C22×Dic43—21no—
248C22×Dic43—82no—
249C22×Dic43C2×D411yescharacteristic
250C22×Dic43C2×D411yescharacteristic
251C22×Dic43C2×D411yescharacteristic
252C22×Dic43C2×D411yescharacteristic
253#10621898—28no—
254#10621898—28no—
255#10621898—24no—
256#10621898—24no—
257#10621898—24no—
258#10621898#4118yes—
259C2×D172—21no—
260C2×D172—24no—
261C2×D172—21no—
262C2×D172—24no—
263C2×D172C2412yes—
264C2×D172C2412yes—
265C2×C4×D43—28no—
266C2×C4×D43—22no—
267C2×C4×D43—22no—
268C2×C4×D43—22no—
269C2×C4×D43—22no—
270C2×C4×D43—22no—
271C2×C4×D43—22no—
272C2×C4×D43—24no—
273C2×C4×D43—82no—
274C2×Dic86—21no—
275C2×Dic86—24no—
276C2×Dic86C2412yes—
277M16×C43—24no—
278C2×C8×C43C2414yes—
279C4⋊C4×C43—21no—
280C4⋊C4×C43—21no—
281C4⋊C4×C43—21no—
282C4⋊C4×C43C2412yes—
283C4⋊C4×C43C2412yes—
284C4⋊C4×C43C2412yes—
285C22⋊C4×C43—22no—
286C22⋊C4×C43—22no—
287C22⋊C4×C43—22no—
288C22⋊C4×C43—22no—
289C42×C43—22no—
290C42×C43—22no—
291C22⋊Dic43—24no—
292C22⋊Dic43C2×D412yes—
293C22⋊Dic43C2×D412yes—
294C22⋊Dic43C2×D412yes—
295C22⋊Dic43C2×D412yes—
296#10621883—28no—
297#10621882—28no—
298(C2×D43)⋊C4—22no—
299(C2×D43)⋊C4—22no—
300(C2×D43)⋊C4—22no—
301(C2×D43)⋊C4—22no—
302(C2×D43)⋊C4—22no—
303(C2×D43)⋊C4—22no—
304(C2×D43)⋊C4—24no—
305C4⋊Dic43—21no—
306C4⋊Dic43—24no—
307C4⋊Dic43C2×D412yes—
308C4⋊Dic43C2×D412yes—
309C4⋊Dic43C2×D412yes—
310C4⋊Dic43C2×D412yes—
311C4⋊Dic43C2412yes—
312Dic43⋊C4—22no—
313Dic43⋊C4—22no—
314Dic43⋊C4—22no—
315Dic43⋊C4—22no—
316Dic43⋊C4—24no—
317C4×Dic43—22no—
318C4×Dic43—22no—
319C4×Dic43—22no—
320C4×Dic43—22no—
321C4×Dic43C2×D412yes—
322C4×Dic43C2×D412yes—
323C4×Dic43C2412yes—
324C4×Dic43C2412yes—
325#10621877—24no—
326C2×C43⋊C8C2414yes—
327D344—28no—
328#10621873—28no—
329C23×C43—22no—
330C23×C43—22no—
331C23×C43—41no—
332C23×C43—41no—
333C23×C43—42no—
334C23×C43—42no—
335C23×C43—42no—
336C23×C43C22×D411yescharacteristic
337C23×C43C22×D411yescharacteristic
338C23×C43C22×D411yescharacteristic
339C22×D43—22no—
340C22×D43—24no—
341C22×D43—22no—
342C22×D43—42no—
343C22×D43—42no—
344C22×D43—42no—
345C22×D43—81no—
346C22×D43—81no—
347D4×C43—24no—
348D4×C43—42no—
349D4×C43—82no—
350D4×C43—82no—
351C2×C4×C43—22no—
352C2×C4×C43—22no—
353C2×C4×C43—22no—
354C2×C4×C43—22no—
355C2×C4×C43—22no—
356C2×C4×C43—22no—
357C2×C4×C43—22no—
358C2×C4×C43—22no—
359C2×C4×C43—42no—
360C2×C4×C43—81no—
361C2×C4×C43—81no—
362C2×C4×C43C22×D411yescharacteristic
363C2×C4×C43C22×D411yescharacteristic
364C2×C4×C43C22×D411yescharacteristic
365C2×C4×C43C2×#4114yes—
366C2×C4×C43C2511yescharacteristic
367C22⋊D43—28no—
368C22⋊D43—28no—
369C22⋊D43—84no—
370C22⋊D43—84no—
371C22⋊D43—82no—
372C22⋊D43—82no—
373C2×Dic43—24no—
374C2×Dic43—22no—
375C2×Dic43—22no—
376C2×Dic43—41no—
377C2×Dic43—41no—
378C2×Dic43—41no—
379C2×Dic43—41no—
380C2×Dic43—42no—
381C2×Dic43—84no—
382C2×Dic43C22×D412yes—
383C2×Dic43C22×D412yes—
384C2×Dic43C22×D412yes—
385C2×Dic43C22×D412yes—
386D172—24no—
387D172—22no—
388D172—24no—
389D172—42no—
390D172C2×#4114yes—
391C4×D43—28no—
392C4×D43—28no—
393C4×D43—82no—
394C4×D43—82no—
395C4×D43—82no—
396C4×D43—82no—
397C4×D43—84no—
398Dic86—24no—
399Dic86—22no—
400Dic86C2×#4114yes—
401C8×C43—24no—
402C43⋊C8—24no—
403#60568—431nomaximal, Sylow
404C22×C43—21no—
405C22×C43—21no—
406C22×C43—21no—
407C22×C43—21no—
408C22×C43—21no—
409C22×C43—21no—
410C22×C43—21no—
411C22×C43—21no—
412C22×C43—42no—
413C22×C43—42no—
414C22×C43—42no—
415C22×C43—82no—
416C22×C43—84no—
417C22×C43#52512yes—
418C22×C43C23×D411yescharacteristic
419C2×D43—24no—
420C2×D43—42no—
421C2×D43—42no—
422C2×D43—42no—
423C2×D43—42no—
424C2×D43—42no—
425C2×D43—84no—
426C2×D43—84no—
427C4×C43—21no—
428C4×C43—21no—
429C4×C43—42no—
430C4×C43—42no—
431C4×C43—42no—
432C4×C43#52512yes—
433C4×C43C22×#4112yes—
434Dic43—22no—
435Dic43—22no—
436Dic43—22no—
437Dic43—22no—
438Dic43—24no—
439Dic43—42no—
440C2×#540—431no—
441#3428—431no—
442#3126—434no—
443#3122—434no—
444#3119—434no—
445#3119—434no—
446#3094—431no—
447#3094D4311yescharacteristic, complemented
448#3080—432no—
449#3038—432no—
450#3006—431no—
451#3006—431no—
452C4×AGL(1,ℤ/8)—432no—
453C4×AGL(1,ℤ/8)—432no—
454#2921—431no—
455C2×C43—22no—
456C2×C43—41no—
457C2×C43—41no—
458C2×C43—82no—
459C2×C43C2×#52511yescharacteristic
460C2×C43#358511yescharacteristic
461C2×C43#358511yescharacteristic
462D43—44no—
463D43—82no—
464C22×#41—431no—
465C2×AGL(1,ℤ/8)—432no—
466C2×AGL(1,ℤ/8)—432no—
467#540—434no—
468#540—434no—
469#540—862no—
470#540—862no—
471C2×#127—431no—
472C2×#125—431no—
473C2×#123—861no—
474C2×#123—861no—
475C2×#121—431no—
476C2×#121—861no—
477C2×#121—861no—
478C2×#121C2×D4311yescharacteristic
479#520—432no—
480#520—432no—
481#520—861no—
482#520—861no—
483#519—432no—
484#518—432no—
485#518—861no—
486#518—861no—
487C4×#41—432no—
488C4×#41—432no—
489C4×#41—862no—
490C2×C4×D4—431no—
491C2×C4×D4—431no—
492C2×#117—431no—
493C2×#117—862no—
494C2×#117C2×D4311yescharacteristic
495#482—434no—
496#482C2×D4314yescomplemented
497#481—432no—
498#481C2×D4312yescomplemented
499#480—432no—
500#480C2×D4312yescomplemented
501#479—434no—
502#479—434no—
503#478—434no—
504#478—434no—
505#460—434no—
506#460—434no—
507#459—434no—
508#459—434no—
509#449—434no—
510#449—434no—
511#448—432no—
512#448—432no—
513#447—432no—
514#447—432no—
515#442—434no—
516#442—434no—
517#440—434no—
518#440—434no—
519C4×SD16—434no—
520C4×SD16—434no—
521C4×D8—434no—
522C4×D8—434no—
523#433—434no—
524#433—434no—
525#428—432no—
526#428C2×D4312yescomplemented
527#423—432no—
528#418—432no—
529#418C2×D4312yescomplemented
530#417—432no—
531#417—432no—
532#407—431no—
533#407C2×D4311yescharacteristic
534C4×M16—432no—
535C43#6056811yescharacteristic, complemented, Sylow
536C2×#41—432no—
537C2×#41—432no—
538C2×#41—868no—
539C2×#41—861no—
540C2×#41—861no—
541C22×Q8—431no—
542C22×D4—21no—
543C22×D4—431no—
544C22×D4—431no—
545C22×D4—861no—
546C22×D4—861no—
547C22×D4—861no—
548C22×D4—861no—
549C22×D4C22×D4311yescharacteristic
550C23×C4—861no—
551C23×C4—861no—
552C23×C4—861no—
553C23×C4C22×D4311yescharacteristic
554AGL(1,ℤ/8)—868no—
555AGL(1,ℤ/8)—868no—
556C2×SD16—434no—
557C2×SD16—434no—
558C2×D8—434no—
559C2×D8—434no—
560C2×M16—432no—
561C2×M16C22×D4312yes—
562#127—434no—
563#127—862no—
564#125—434no—
565#125—862no—
566#123—864no—
567#123—864no—
568#123—864no—
569#123—864no—
570#121—21no—
571#121—21no—
572#121—432no—
573#121—432no—
574#121—864no—
575#121—864no—
576#121—864no—
577#121—864no—
578#121—861no—
579#121—861no—
580#121C22×D4312yes—
581#121C22×D4312yes—
582C4×Q8—432no—
583C4×Q8—432no—
584C4×Q8—432no—
585C4×Q8—432no—
586C4×Q8—862no—
587C4×Q8—862no—
588C4×D4—434no—
589C4×D4—434no—
590C4×D4—432no—
591C4×D4—432no—
592C4×D4—432no—
593C4×D4—432no—
594C4×D4—862no—
595C4×D4—862no—
596C4×D4—862no—
597C4×D4—862no—
598C4×D4—862no—
599C4×D4—862no—
600C4×D4—862no—
601C4×D4—862no—
602C4×D4—862no—
603C4×D4—862no—
604C4×D4—862no—
605C4×D4—862no—
606#117—21no—
607#117—21no—
608#117—432no—
609#117—432no—
610#117—432no—
611#117—432no—
612#117—862no—
613#117—862no—
614#117—862no—
615#117—862no—
616#117—862no—
617#117—862no—
618#117C22×D4312yes—
619#117C22×D4312yes—
620C2×C4⋊C4—431no—
621C2×C4⋊C4—431no—
622C2×C4⋊C4—431no—
623C2×C4⋊C4—862no—
624C2×C4⋊C4—862no—
625C2×C4⋊C4—861no—
626C2×C4⋊C4—861no—
627C2×C4⋊C4C22×D4311yescharacteristic
628C2×C4⋊C4C22×D4311yescharacteristic
629C2×C4⋊C4C22×D4311yescharacteristic
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—431no—
633C2×C22⋊C4—431no—
634C2×C22⋊C4—862no—
635C2×C22⋊C4—862no—
636C2×C22⋊C4—861no—
637C2×C22⋊C4—861no—
638C2×C22⋊C4—861no—
639C2×C42—21no—
640C2×C42—431no—
641C2×C42—431no—
642C2×C42—862no—
643C2×C42—862no—
644#107—434no—
645#107C22×D4314yes—
646#106—434no—
647#106C22×D4314yes—
648C4⋊C8—434no—
649C4⋊C8—434no—
650#103—434no—
651#103—434no—
652#102—434no—
653#102—434no—
654#102—434no—
655#102—434no—
656#102C22×D4314yes—
657#102C22×D4314yes—
658C22⋊C8—432no—
659C22⋊C8—432no—
660C22⋊C8C22×D4312yes—
661C22⋊C8C22×D4312yes—
662#97—434no—
663C4×C8—434no—
664C24—21no—
665C24—861no—
666C24—861no—
667C24D4×D4311yescharacteristic
668#41—438no—
669#41—864no—
670#41—864no—
671#41—868no—
672#41—868no—
673#41—864no—
674C2×Q8—432no—
675C2×Q8—864no—
676C2×Q8—861no—
677C2×D4—22no—
678C2×D4—22no—
679C2×D4—21no—
680C2×D4—24no—
681C2×D4—82no—
682C2×D4—432no—
683C2×D4—432no—
684C2×D4—864no—
685C2×D4—864no—
686C2×D4—864no—
687C2×D4—868no—
688C2×D4—862no—
689C2×D4—862no—
690C2×D4—862no—
691C2×D4—862no—
692C2×D4—861no—
693C2×D4—861no—
694C2×D4—864no—
695C2×D4—3442no—
696C2×D4—3442no—
697C2×D4—3442no—
698C2×D4C23×D4312yes—
699C22×C4—24no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—431no—
704C22×C4—431no—
705C22×C4—431no—
706C22×C4—431no—
707C22×C4—862no—
708C22×C4—862no—
709C22×C4—862no—
710C22×C4—862no—
711C22×C4—864no—
712C22×C4—868no—
713C22×C4—864no—
714C22×C4—861no—
715C22×C4—862no—
716C22×C4—862no—
717C22×C4—861no—
718C22×C4—3442no—
719C22×C4—3442no—
720C22×C4D4×D4311yescharacteristic
721C22×C4D4×D4311yescharacteristic
722C22×C4D4×D4311yescharacteristic
723C22×C4C23×D4311yescharacteristic
724C22×C4C23×D4311yescharacteristic
725C22×C4C23×D4311yescharacteristic
726SD16—868no—
727SD16—868no—
728D8—868no—
729D8—868no—
730M16—24no—
731M16—864no—
732C2×C8—434no—
733C2×C8C23×D4314yes—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—432no—
738C4⋊C4—432no—
739C4⋊C4—432no—
740C4⋊C4—432no—
741C4⋊C4—432no—
742C4⋊C4—862no—
743C4⋊C4—862no—
744C4⋊C4—862no—
745C4⋊C4—862no—
746C4⋊C4—864no—
747C4⋊C4—864no—
748C4⋊C4—861no—
749C4⋊C4C23×D4312yes—
750C4⋊C4C23×D4312yes—
751C4⋊C4C23×D4312yes—
752C22⋊C4—22no—
753C22⋊C4—22no—
754C22⋊C4—22no—
755C22⋊C4—22no—
756C22⋊C4—432no—
757C22⋊C4—432no—
758C22⋊C4—432no—
759C22⋊C4—432no—
760C22⋊C4—862no—
761C22⋊C4—862no—
762C22⋊C4—862no—
763C22⋊C4—862no—
764C22⋊C4—864no—
765C22⋊C4—864no—
766C22⋊C4—862no—
767C22⋊C4—862no—
768C42—22no—
769C42—22no—
770C42—432no—
771C42—432no—
772C42—432no—
773C42—432no—
774C42—862no—
775C42—862no—
776C42—862no—
777C42—862no—
778C23—22no—
779C23—22no—
780C23—41no—
781C23—41no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—864no—
786C23—862no—
787C23—862no—
788C23—3441no—
789C23—3441no—
790C23—1722no—
791C23—1722no—
792C23—1722no—
793C23C2×D4×D4311yescharacteristic
794C23C2×D4×D4311yescharacteristic
795C23C2×D4×D4311yescharacteristic
796Q8—434no—
797Q8—864no—
798Q8—862no—
799D4—24no—
800D4—42no—
801D4—82no—
802D4—82no—
803D4—434no—
804D4—864no—
805D4—868no—
806D4—868no—
807D4—862no—
808D4—864no—
809D4—3444no—
810D4—3444no—
811D4—3442no—
812D4—3442no—
813D4—1722no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—42no—
823C2×C4—81no—
824C2×C4—81no—
825C2×C4—432no—
826C2×C4—432no—
827C2×C4—432no—
828C2×C4—432no—
829C2×C4—868no—
830C2×C4—864no—
831C2×C4—862no—
832C2×C4—868no—
833C2×C4—862no—
834C2×C4—3444no—
835C2×C4—3442no—
836C2×C4—3442no—
837C2×C4—3442no—
838C2×C4—3442no—
839C2×C4—3444no—
840C2×C4—1721no—
841C2×C4—1721no—
842C2×C4—1721no—
843C2×C4—1721no—
844C2×C4—1722no—
845C2×C4C2×D4×D4311yescharacteristic
846C2×C4C2×D4×D4311yescharacteristic
847C2×C4C2×D4×D4311yescharacteristic
848C2×C4#41×D4314yes—
849C2×C4C24×D4311yescharacteristic
850C8—24no—
851C8—864no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—82no—
864C22—84no—
865C22—864no—
866C22—3444no—
867C22—3444no—
868C22—1722no—
869C22—1722no—
870C22—1722no—
871C22—1722no—
872C22—1722no—
873C22#1458340712yes—
874C22C22×D4×D4311yescharacteristic
875C4—21no—
876C4—21no—
877C4—42no—
878C4—42no—
879C4—42no—
880C4—864no—
881C4—862no—
882C4—862no—
883C4—862no—
884C4—862no—
885C4—1722no—
886C4#1458340712yes—
887C4C2×#41×D4312yes—
888C2—22no—
889C2—41no—
890C2—41no—
891C2—82no—
892C2—3442no—
893C2—1724no—
894C2C2×#1458340711yescharacteristic
895C2#1914937111yescharacteristic
896C2#1914937211yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3094C2
socleC22×C43C23×D4
hypercenter#3094D43
hypocenterC43#60568
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. C2×#14583502C2semidirect
2. #19147796C2semidirect
3. #19144882C2semidirect
4. #19144834C2semidirect
5. #19144797C2semidirect
6. #19144789C2semidirect
7. #19144535C2semidirect
8. #19144416C2semidirect
9. #19144074C2semidirect
10. #19143849C2semidirect
11. #19143845C2semidirect
12. #19143402C2semidirect
13. #19143399C2semidirect
14. #19143230C2semidirect
15. C43×#3094C2semidirect
22. #14583502C22semidirect
23. C2×#13063321C22semidirect
24. C2×#13063316C22semidirect
30. #14583380C22semidirect
31. #14583380C22semidirect
34. #14583376C22semidirect
35. #14583373C22semidirect
41. C2×D4×Dic43C22semidirect
42. C2×#13063287C22semidirect
45. #14583223C22semidirect
46. #14583217C22semidirect
47. #14583212C22semidirect
48. #14583209C22semidirect
49. #14583205C22semidirect
50. #14583202C22semidirect
51. #14583198C22semidirect
52. #14583098C22semidirect
53. #14583098C22semidirect
54. #14583093C22semidirect
55. #14583093C22semidirect
56. #14583046C22semidirect
57. #14583042C22semidirect
58. #14583040C22semidirect
59. #14583037C22semidirect
60. #14583035C22semidirect
61. #14583032C22semidirect
62. #14583010C22semidirect
63. #14583008C22semidirect
64. #14582998C22semidirect
65. #14582996C22semidirect
66. #14582990C22semidirect
67. #14582986C22semidirect
68. #14582981C22semidirect
69. #14582979C22semidirect
70. #14582957C22semidirect
71. #14582957C22semidirect
72. #14582942C22semidirect
73. #14582922C22semidirect
74. #14582903C22semidirect
78. M16×Dic43C22semidirect
81. C43×#482C22semidirect
82. C43×#481C22semidirect
83. C43×#480C22semidirect
84. C43×#428C22semidirect
85. C43×#418C22semidirect
447. #3094D43semidirect
496. #482C2×D43semidirect
498. #481C2×D43semidirect
500. #480C2×D43semidirect
526. #428C2×D43semidirect
529. #418C2×D43semidirect
535. C43#60568semidirect

Maximal subgroups

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

subgroupindex
C2×#145835022
#191477962
#191448822
#191448342
#191447972
#191447892
#191445352
#191444162
#191440742
#191438492
#191438452
#191434022
#191433992
#191432302
C43×#30942
#6056843