Finite Group Databasebeta

← #25968905

Subgroups — #25968905

Order 11008.

2036 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D43C211yesmaximal, characteristic, complemented
2C2×#14583446C211yesmaximal, characteristic
3#19145792C212yesmaximal, complemented
4#19145791C212yesmaximal, complemented
5#19145783C214yesmaximal, complemented
6#19145730C214yesmaximal, complemented
7#19145722C212yesmaximal, complemented
8#19145715C212yesmaximal, complemented
9#19145139C212yesmaximal, complemented
10#19144967C212yesmaximal, complemented
11#19144537C212yesmaximal, complemented
12#19144533C212yesmaximal, complemented
13#19144394C211yesmaximal, characteristic, complemented
14#19144392C211yesmaximal, characteristic, complemented
15#19144388C211yesmaximal, characteristic, complemented
16#19143227C211yesmaximal, characteristic, complemented
17C43×#3077C211yesmaximal, characteristic, complemented
18C22×#10621898—21no—
19#14583456C2211yescharacteristic
20#14583455C2212yescomplemented
21#14583454C2211yescharacteristic, complemented
22#14583454C2211yescharacteristic, complemented
23#14583453—21no—
24#14583453—21no—
25#14583452C2212yes—
26#14583451—21no—
27#14583451—21no—
28#14583446—21no—
29#14583446—21no—
30#14583446—21no—
31#14583446—21no—
32#14583446C2212yes—
33#14583446C2212yes—
34#14583446C2212yes—
35#14583446C2212yes—
36C2×#13063324C2211yescharacteristic
37C4⋊Q8×D43C2211yescharacteristic, complemented
38C4⋊Q8×D43C2211yescharacteristic, complemented
39C2×#13063321C2211yescharacteristic
40#125×D43C2212yescomplemented
41C2×#13063311—21no—
42C22⋊Q8×D43—21no—
43C22⋊Q8×D43—21no—
44C2×#13063300C2211yescharacteristic
45C2×#13063298—21no—
46C2×#13063296C2211yescharacteristic
47C4×Q8×D43—21no—
48C4×Q8×D43—21no—
49C2×C4×D172C2211yescharacteristic
50C2×C4×C22⋊D43—21no—
51#117×D43C2212yes—
52C2×C42×D43C2211yescharacteristic
53#14583307C2214yescomplemented
54#14583306C2214yescomplemented
55#14583303C2214yescomplemented
56#14583296C2214yescomplemented
57#14583262C2214yescomplemented
58#14583262C2214yescomplemented
59#14583244C2214yescomplemented
60#14583244C2214yescomplemented
61#14583226C2214yescomplemented
62#14583225C2214yescomplemented
63#14583222C2214yescomplemented
64#14583221C2214yescomplemented
65#14583219C2214yescomplemented
66#14583216C2214yescomplemented
67#14583214C2214yescomplemented
68#14583211C2214yescomplemented
69#14583200C2214yescomplemented
70#14583199C2214yescomplemented
71#14583196C2214yescomplemented
72#14583190C2212yescomplemented
73#14583189C2212yescomplemented
74#14583186C2212yescomplemented
75#14583180C2212yescomplemented
76#14583179C2212yescomplemented
77#14583176C2212yescomplemented
78#14582955C2212yescomplemented
79#14582955C2212yescomplemented
80#14582951C2212yescomplemented
81#14582951C2212yescomplemented
82#14582942C2212yes—
83#14582941C2212yes—
84#14582939C2212yes—
85#14582923C2211yescharacteristic
86#14582905C2212yes—
87#14582904C2212yes—
88#14582903C2212yes—
89#14582862C2212yes—
90M16×Dic43C2212yes—
91C43×#533C2211yescharacteristic
92C2×C4×D4×C43C2211yescharacteristic
93C43×#478C2214yescomplemented
94C43×#476C2212yescomplemented
95C43×#474C2212yescomplemented
96C43×#428C2212yes—
97C43×#423C2211yescharacteristic
98C43×#418C2212yes—
99C2×#10621898—22no—
100C2×#10621898—22no—
101C2×#10621898—22no—
102C2×#10621898—22no—
103C2×#10621898—48no—
104C22×Dic86—21no—
105C2×Q8×D43—21no—
106C2×Q8×D43—21no—
107C22×D172—21no—
108C22×D172C2311yescharacteristic
109C22×C22⋊D43—21no—
110C22×C22⋊D43—21no—
111C22×C22⋊D43—21no—
112C22×C4×D43—21no—
113C22×C4×D43D411yescharacteristic
114C22×C4×D43D411yescharacteristic
115C22×C4×D43C2311yescharacteristic
116C2×#10621877C2312yes—
117#13063325C2311yescharacteristic
118#13063325C2311yescharacteristic
119#13063324—21no—
120#13063324—21no—
121#13063324—21no—
122#13063324—21no—
123#13063324C2312yes—
124#13063324C2312yes—
125#13063324C2312yes—
126#13063324C2312yes—
127#13063323—21no—
128#13063323—21no—
129#13063321—21no—
130#13063321—21no—
131#13063321C2312yes—
132#13063321C2312yes—
133#13063317C2312yes—
134#13063316C2312yes—
135#13063316C2312yes—
136#13063315—22no—
137#13063315—22no—
138#13063311—22no—
139#13063311—22no—
140#13063311—22no—
141#13063311—22no—
142#13063305—21no—
143#13063305—21no—
144#13063304—21no—
145#13063304—21no—
146#13063303—22no—
147#13063303—22no—
148#13063302—22no—
149#13063302—22no—
150#13063301—21no—
151#13063301—21no—
152#13063300—21no—
153#13063300—21no—
154#13063300C2312yes—
155#13063300C2312yes—
156#13063298—22no—
157#13063298—22no—
158#13063298—22no—
159#13063298—22no—
160#13063296—21no—
161#13063296—21no—
162#13063296C2312yes—
163#13063296C2312yes—
164Q8×Dic43—21no—
165Q8×Dic43—21no—
166C4×Dic86—21no—
167C4×Dic86—21no—
168C4×Dic86—22no—
169C4×Dic86—22no—
170#13063290—21no—
171#13063290—21no—
172#13063290—22no—
173#13063290—22no—
174C4×D172—21no—
175C4×D172—21no—
176C4×D172C2312yes—
177C4×D172C2312yes—
178C4×C22⋊D43—22no—
179C4×C22⋊D43—22no—
180C4×C22⋊D43—22no—
181C4×C22⋊D43—22no—
182#13063284C2312yes—
183#13063283C2312yes—
184#13063283C2312yes—
185#13063282—22no—
186#13063281—22no—
187C2×C4⋊Dic43C2311yescharacteristic
188C2×Dic43⋊C4—21no—
189C4⋊C4×D43—22no—
190C4⋊C4×D43—22no—
191C4⋊C4×D43—21no—
192C4⋊C4×D43—21no—
193C4⋊C4×D43C2312yes—
194C4⋊C4×D43C2312yes—
195C2×C22⋊Dic43—21no—
196C2×(C2×D43)⋊C4—21no—
197C2×(C2×D43)⋊C4—21no—
198C22⋊C4×D43—22no—
199C2×C4×Dic43D411yescharacteristic
200C2×C4×Dic43D411yescharacteristic
201C2×C4×Dic43C2311yescharacteristic
202C42×D43—22no—
203C42×D43D411yescharacteristic
204C42×D43D411yescharacteristic
205C42×D43D411yescharacteristic
206C42×D43D411yescharacteristic
207C42×D43C2311yescharacteristic
208C42×D43C2311yescharacteristic
209C42×D43C2311yescharacteristic
210C42×D43C2311yescharacteristic
211#13063259C2314yes—
212#13063258C2314yes—
213#13063258C2314yes—
214#13063257C2314yes—
215#13063256C2314yes—
216#13063256C2314yes—
217C4⋊(C43⋊C8)C2312yes—
218C4⋊(C43⋊C8)C2312yes—
219#13063247C2314yes—
220#13063247C2314yes—
221#13063246C2314yes—
222#13063246C2314yes—
223#13063245C2314yes—
224#13063245C2314yes—
225(C2×D43)⋊C8C2314yes—
226(C2×D43)⋊C8C2314yes—
227#13063235C2314yes—
228C8×Dic43C2314yes—
229C22×D4×C43C2311yescharacteristic
230C23×C4×C43—21no—
231C2×M16×C43C2312yes—
232C4⋊Q8×C43C2311yescharacteristic
233C4⋊Q8×C43C2311yescharacteristic
234#125×C43C2312yes—
235C22⋊Q8×C43—21no—
236C22⋊Q8×C43—21no—
237C4×Q8×C43—21no—
238C4×Q8×C43—21no—
239C4×D4×C43—21no—
240C4×D4×C43—21no—
241C4×D4×C43C2312yes—
242C4×D4×C43C2312yes—
243#117×C43C2312yes—
244C2×C4⋊C4×C43C2311yescharacteristic
245C2×C22⋊C4×C43—21no—
246C2×C42×C43C2311yescharacteristic
247#107×C43C2314yes—
248#106×C43C2314yes—
249C4⋊C8×C43C2312yes—
250C4⋊C8×C43C2312yes—
251#102×C43C2314yes—
252#102×C43C2314yes—
253C24×C43—21no—
254C23×D43—21no—
255C23×D43C2×D411yescharacteristic
256C2×Q8×C43—21no—
257C2×Q8×C43—21no—
258C2×D4×C43—21no—
259C2×D4×C43—22no—
260C2×D4×C43—22no—
261C2×D4×C43C2412yes—
262C22×C4×C43—22no—
263C22×C4×C43—22no—
264C22×C4×C43—21no—
265C22×C4×C43—44no—
266C22×C4×C43C2×D411yescharacteristic
267C22×C4×C43C2×D411yescharacteristic
268C22×C4×C43C2411yescharacteristic
269C2×C22⋊D43—22no—
270C2×C22⋊D43—22no—
271C2×C22⋊D43—22no—
272C2×C22⋊D43—22no—
273C2×C22⋊D43—22no—
274C2×C22⋊D43—22no—
275C2×C22⋊D43—44no—
276C2×C22⋊D43—44no—
277C2×C22⋊D43—44no—
278C22×Dic43—21no—
279C22×Dic43C2×D411yescharacteristic
280C22×Dic43C2×D411yescharacteristic
281C22×Dic43C2×D411yescharacteristic
282Q8×D43—44no—
283Q8×D43—44no—
284#10621898—48no—
285#10621898—48no—
286#10621898—48no—
287#10621898—48no—
288C2×D172—21no—
289C2×D172—22no—
290C2×D172—22no—
291C2×D172—22no—
292C2×D172—22no—
293C2×D172—44no—
294C2×D172C2412yes—
295C2×C4×D43—22no—
296C2×C4×D43—22no—
297C2×C4×D43—24no—
298C2×C4×D43—22no—
299C2×C4×D43—22no—
300C2×C4×D43—22no—
301C2×C4×D43—22no—
302C2×C4×D43—42no—
303C2×C4×D43—44no—
304C2×C4×D43C2×D411yescharacteristic
305C2×C4×D43C2×D411yescharacteristic
306C2×C4×D43C2×D411yescharacteristic
307C2×C4×D43C2×D411yescharacteristic
308C2×C4×D43C2×D411yescharacteristic
309C2×C4×D43C2×D411yescharacteristic
310C2×C4×D43C2×D411yescharacteristic
311C2×C4×D43C2×D411yescharacteristic
312C2×C4×D43C2×D411yescharacteristic
313C2×C4×D43C2×D411yescharacteristic
314C2×C4×D43C2411yescharacteristic
315C2×C4×D43C2411yescharacteristic
316C2×Dic86—21no—
317C2×Dic86—21no—
318C2×Dic86—22no—
319C2×Dic86—22no—
320C2×Dic86—22no—
321C2×Dic86—22no—
322C2×Dic86—44no—
323M16×C43—24no—
324C2×C8×C43C2414yes—
325C4⋊C4×C43—21no—
326C4⋊C4×C43—22no—
327C4⋊C4×C43—22no—
328C4⋊C4×C43—21no—
329C4⋊C4×C43—21no—
330C4⋊C4×C43C2412yes—
331C4⋊C4×C43C2412yes—
332C4⋊C4×C43C2412yes—
333C22⋊C4×C43—22no—
334C22⋊C4×C43—22no—
335C22⋊C4×C43—22no—
336C42×C43—22no—
337C42×C43C2×D411yescharacteristic
338C42×C43C2×D411yescharacteristic
339C42×C43C2411yescharacteristic
340C42×C43C2411yescharacteristic
341C22⋊Dic43—22no—
342C22⋊Dic43—22no—
343C22⋊Dic43—22no—
344(C2×D43)⋊C4—22no—
345(C2×D43)⋊C4—22no—
346(C2×D43)⋊C4—22no—
347(C2×D43)⋊C4—22no—
348(C2×D43)⋊C4—22no—
349(C2×D43)⋊C4—22no—
350C4⋊Dic43—21no—
351C4⋊Dic43—21no—
352C4⋊Dic43—21no—
353C4⋊Dic43—22no—
354C4⋊Dic43—22no—
355C4⋊Dic43C2412yes—
356C4⋊Dic43C2412yes—
357C4⋊Dic43C2412yes—
358Dic43⋊C4—22no—
359Dic43⋊C4—22no—
360Dic43⋊C4—22no—
361Dic43⋊C4—22no—
362Dic43⋊C4—22no—
363Dic43⋊C4—22no—
364Dic43⋊C4—22no—
365Dic43⋊C4—22no—
366Dic43⋊C4—22no—
367Dic43⋊C4—22no—
368C4×Dic43—22no—
369C4×Dic43—22no—
370C4×Dic43—22no—
371C4×Dic43C2×D411yescharacteristic
372C4×Dic43C2×D411yescharacteristic
373C4×Dic43C2×D411yescharacteristic
374C4×Dic43C2×D411yescharacteristic
375C4×Dic43C2×D411yescharacteristic
376C4×Dic43C2×D411yescharacteristic
377C4×Dic43C2×D411yescharacteristic
378C4×Dic43C2×D411yescharacteristic
379C4×Dic43C2×D411yescharacteristic
380C4×Dic43C2×D411yescharacteristic
381C4×Dic43C2411yescharacteristic
382C4×Dic43C2411yescharacteristic
383#10621877—24no—
384C2×C43⋊C8C2414yes—
385C23×C43—22no—
386C23×C43—42no—
387C23×C43—42no—
388C23×C43—42no—
389C23×C43C22×D411yescharacteristic
390C22×D43—22no—
391C22×D43—22no—
392C22×D43—22no—
393C22×D43—41no—
394C22×D43—42no—
395C22×D43—42no—
396C22×D43—42no—
397C22×D43C22×D411yescharacteristic
398C22×D43C22×D411yescharacteristic
399Q8×C43—42no—
400Q8×C43—42no—
401D4×C43—22no—
402D4×C43—22no—
403D4×C43—42no—
404C2×C4×C43—22no—
405C2×C4×C43—22no—
406C2×C4×C43—22no—
407C2×C4×C43—22no—
408C2×C4×C43—41no—
409C2×C4×C43—44no—
410C2×C4×C43—42no—
411C2×C4×C43—44no—
412C2×C4×C43C22×D411yescharacteristic
413C2×C4×C43C22×D411yescharacteristic
414C2×C4×C43C22×D411yescharacteristic
415C2×C4×C43C22×D411yescharacteristic
416C2×C4×C43C22×D411yescharacteristic
417C2×C4×C432−1+412yes—
418C2×C4×C432−1+412yes—
419C2×C4×C43C2511yescharacteristic
420C22⋊D43—44no—
421C22⋊D43—44no—
422C22⋊D43—44no—
423C22⋊D43—44no—
424C22⋊D43—44no—
425C22⋊D43—44no—
426C2×Dic43—22no—
427C2×Dic43—22no—
428C2×Dic43—22no—
429C2×Dic43—22no—
430C2×Dic43—22no—
431C2×Dic43—22no—
432C2×Dic43—42no—
433C2×Dic43C22×D411yescharacteristic
434C2×Dic43C22×D411yescharacteristic
435C2×Dic43C22×D411yescharacteristic
436C2×Dic43C22×D411yescharacteristic
437C2×Dic43C22×D411yescharacteristic
438C2×Dic43C22×D411yescharacteristic
439D172—22no—
440D172—22no—
441D172—44no—
442D172—44no—
443D172—42no—
444C4×D43—22no—
445C4×D43—22no—
446C4×D43—22no—
447C4×D43—22no—
448C4×D43—21no—
449C4×D43—21no—
450C4×D43—21no—
451C4×D43—21no—
452C4×D43—22no—
453C4×D43—22no—
454C4×D43—22no—
455C4×D43—41no—
456C4×D43—41no—
457C4×D43—44no—
458C4×D43—44no—
459C4×D43—44no—
460C4×D43—44no—
461C4×D43AGL(1,ℤ/8)14yes—
462Dic86—44no—
463Dic86—42no—
464Dic86—42no—
465Dic86—44no—
466Dic86—44no—
467Dic86—44no—
468C8×C43—24no—
469C43⋊C8—24no—
470#60864—431nomaximal, Sylow
471C22×C43—21no—
472C22×C43—21no—
473C22×C43—42no—
474C22×C43—42no—
475C22×C43—42no—
476C22×C43—84no—
477C22×C43#53612yes—
478C22×C43C23×D411yescharacteristic
479C2×D43—21no—
480C2×D43—21no—
481C2×D43—21no—
482C2×D43—21no—
483C2×D43—21no—
484C2×D43—44no—
485C2×D43—42no—
486C2×D43—42no—
487C2×D43—42no—
488C2×D43—84no—
489C2×D43C2×AGL(1,ℤ/8)12yes—
490C4×C43—21no—
491C4×C43—21no—
492C4×C43—21no—
493C4×C43—42no—
494C4×C43—42no—
495C4×C43—42no—
496C4×C43#53612yes—
497C4×C43C2×AGL(1,ℤ/8)12yes—
498C4×C43C2×2−1+411yescharacteristic
499C4×C43C2×2−1+411yescharacteristic
500Dic43—21no—
501Dic43—21no—
502Dic43—21no—
503Dic43—21no—
504Dic43—42no—
505Dic43—42no—
506Dic43—42no—
507Dic43C2×AGL(1,ℤ/8)12yes—
508Dic43#57512yes—
509C2×#533—431no—
510C2×#532—431no—
511#3235—432no—
512#3235—432no—
513#3234—434no—
514#3228—434no—
515#3227—432no—
516#3226—432no—
517#3165—432no—
518#3138—432no—
519#3094—432no—
520#3094—432no—
521#3077—431no—
522#3077—431no—
523#3077—431no—
524#3077D4311yescharacteristic, complemented
525#2920—431no—
526C2×C43—22no—
527C2×C43—82no—
528C2×C43C2×#53611yescharacteristic
529C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
530C2×C43C2×#57511yescharacteristic
531D43—22no—
532D43—41no—
533D43—82no—
534C22×#41—861no—
535#533—431no—
536#533—431no—
537#533—432no—
538#533—432no—
539#533—431no—
540#533—861no—
541#533—861no—
542#533—861no—
543#533—861no—
544#533C2×D4311yescharacteristic
545#532—432no—
546#532—432no—
547#532—432no—
548#532—432no—
549#532—861no—
550#532—861no—
551#532—861no—
552#532—861no—
553C2×C4⋊Q8—431no—
554C2×C4⋊Q8—431no—
555C2×C4⋊Q8—431no—
556C2×#127—431no—
557C2×#125—432no—
558C2×#124—861no—
559C2×C22⋊Q8—861no—
560C2×C22⋊Q8—861no—
561C2×#121—431no—
562C2×#121—431no—
563C2×#121—861no—
564C2×C4×Q8—861no—
565C2×C4×Q8—861no—
566C2×C4×D4—431no—
567C2×C4×D4—861no—
568C2×C4×D4C2×D4311yescharacteristic
569C2×#117—432no—
570C22×C42—431no—
571#501—434no—
572#501—434no—
573#500—434no—
574#498—434no—
575#490—434no—
576#490—434no—
577#486—434no—
578#486—434no—
579#482—434no—
580#482—434no—
581#482—434no—
582#482—434no—
583#481—434no—
584#481—434no—
585#480—434no—
586#480—434no—
587#478—434no—
588#478—434no—
589#478—434no—
590#478C2×D4314yescomplemented
591#476—432no—
592#476—432no—
593#476—432no—
594#476C2×D4312yescomplemented
595#474—432no—
596#474—432no—
597#474—432no—
598#474C2×D4312yescomplemented
599#432—432no—
600#432—432no—
601#431—432no—
602#431—432no—
603#428—432no—
604#428—432no—
605#428—432no—
606#428C2×D4312yes—
607#423—431no—
608#423C2×D4311yescharacteristic
609#418—432no—
610#418—432no—
611#418—432no—
612#418C2×D4312yes—
613#407—432no—
614C4×M16—432no—
615C43#6086411yescharacteristic, complemented, Sylow
616C2×#41—862no—
617C2×#41—862no—
618C2×#41—862no—
619C2×#41—862no—
620C2×#41—1728no—
621C22×Q8—861no—
622C22×Q8—861no—
623C22×Q8—861no—
624C22×D4—431no—
625C22×D4—861no—
626C22×D4—861no—
627C22×D4—861no—
628C22×D4—861no—
629C22×D4C22×D4311yescharacteristic
630C23×C4—21no—
631C23×C4—431no—
632C23×C4—431no—
633C23×C4—431no—
634C23×C4—861no—
635C2×M16—432no—
636C2×M16C22×D4312yes—
637C4⋊Q8—432no—
638C4⋊Q8—432no—
639C4⋊Q8—432no—
640C4⋊Q8—432no—
641C4⋊Q8—431no—
642C4⋊Q8—431no—
643C4⋊Q8—861no—
644C4⋊Q8—861no—
645C4⋊Q8—861no—
646C4⋊Q8—861no—
647C4⋊Q8—861no—
648C4⋊Q8—861no—
649C4⋊Q8C22×D4311yescharacteristic
650C4⋊Q8C22×D4311yescharacteristic
651#127—432no—
652#127—432no—
653#127—861no—
654#127—861no—
655#125—432no—
656#125—432no—
657#125—432no—
658#125—862no—
659#125—862no—
660#125C22×D4312yes—
661#124—862no—
662#124—862no—
663#124—862no—
664#124—862no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8—862no—
668C22⋊Q8—862no—
669C22⋊Q8—862no—
670C22⋊Q8—862no—
671C22⋊Q8—861no—
672C22⋊Q8—861no—
673C22⋊Q8—861no—
674C22⋊Q8—861no—
675C22⋊Q8—861no—
676C22⋊Q8—861no—
677#121—432no—
678#121—432no—
679#121—432no—
680#121—432no—
681#121—862no—
682#121—862no—
683#121—862no—
684#121—862no—
685#121—861no—
686#121—861no—
687#121—861no—
688#121—861no—
689C4×Q8—21no—
690C4×Q8—21no—
691C4×Q8—862no—
692C4×Q8—862no—
693C4×Q8—862no—
694C4×Q8—861no—
695C4×Q8—862no—
696C4×Q8—861no—
697C4×Q8—861no—
698C4×Q8—861no—
699C4×Q8—861no—
700C4×Q8—861no—
701C4×D4—21no—
702C4×D4—21no—
703C4×D4—432no—
704C4×D4—432no—
705C4×D4—862no—
706C4×D4—862no—
707C4×D4—862no—
708C4×D4—862no—
709C4×D4—861no—
710C4×D4—861no—
711C4×D4C22×D4312yes—
712C4×D4C22×D4312yes—
713#117—432no—
714#117—432no—
715#117—432no—
716#117—862no—
717#117—862no—
718#117C22×D4312yes—
719C2×C4⋊C4—431no—
720C2×C4⋊C4—432no—
721C2×C4⋊C4—432no—
722C2×C4⋊C4—862no—
723C2×C4⋊C4—862no—
724C2×C4⋊C4—861no—
725C2×C4⋊C4—861no—
726C2×C4⋊C4—861no—
727C2×C4⋊C4C22×D4311yescharacteristic
728C2×C22⋊C4—21no—
729C2×C22⋊C4—862no—
730C2×C22⋊C4—861no—
731C2×C22⋊C4—861no—
732C2×C22⋊C4—861no—
733C2×C42—431no—
734C2×C42—431no—
735C2×C42—431no—
736C2×C42—431no—
737C2×C42—431no—
738C2×C42—431no—
739C2×C42—431no—
740C2×C42—431no—
741C2×C42—431no—
742C2×C42—431no—
743C2×C42—431no—
744C2×C42—862no—
745C2×C42C22×D4311yescharacteristic
746#107—434no—
747#107—434no—
748#107—434no—
749#107C22×D4314yes—
750#106—434no—
751#106—434no—
752#106—434no—
753#106C22×D4314yes—
754C4⋊C8—432no—
755C4⋊C8—432no—
756C4⋊C8C22×D4312yes—
757C4⋊C8C22×D4312yes—
758#102—434no—
759#102—434no—
760#102—434no—
761#102—434no—
762#102—434no—
763#102—434no—
764#102C22×D4314yes—
765#102C22×D4314yes—
766C22⋊C8—434no—
767C22⋊C8—434no—
768#97—434no—
769C4×C8—434no—
770C24—21no—
771C24—431no—
772C24—861no—
773#41—1728no—
774#41—1728no—
775#41—1728no—
776#41—1728no—
777C2×Q8—21no—
778C2×Q8—21no—
779C2×Q8—862no—
780C2×Q8—862no—
781C2×Q8—862no—
782C2×Q8—862no—
783C2×Q8—861no—
784C2×Q8—861no—
785C2×Q8—1724no—
786C2×Q8—1724no—
787C2×Q8—1724no—
788C2×D4—21no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—432no—
792C2×D4—862no—
793C2×D4—862no—
794C2×D4—862no—
795C2×D4—862no—
796C2×D4—862no—
797C2×D4—862no—
798C2×D4—862no—
799C2×D4—862no—
800C2×D4—861no—
801C2×D4—862no—
802C2×D4—862no—
803C2×D4—1724no—
804C2×D4—1724no—
805C2×D4—1724no—
806C2×D4—1724no—
807C2×D4C23×D4312yes—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—44no—
812C22×C4—431no—
813C22×C4—431no—
814C22×C4—431no—
815C22×C4—431no—
816C22×C4—431no—
817C22×C4—431no—
818C22×C4—431no—
819C22×C4—431no—
820C22×C4—431no—
821C22×C4—431no—
822C22×C4—431no—
823C22×C4—431no—
824C22×C4—431no—
825C22×C4—431no—
826C22×C4—431no—
827C22×C4—864no—
828C22×C4—862no—
829C22×C4—862no—
830C22×C4—862no—
831C22×C4—862no—
832C22×C4—861no—
833C22×C4—862no—
834C22×C4—862no—
835C22×C4—1724no—
836C22×C4—1722no—
837C22×C4D4×D4311yescharacteristic
838C22×C4D4×D4311yescharacteristic
839C22×C4C23×D4311yescharacteristic
840M16—24no—
841M16—864no—
842C2×C8—434no—
843C2×C8C23×D4314yes—
844C4⋊C4—22no—
845C4⋊C4—22no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—432no—
850C4⋊C4—432no—
851C4⋊C4—432no—
852C4⋊C4—862no—
853C4⋊C4—862no—
854C4⋊C4—862no—
855C4⋊C4—862no—
856C4⋊C4—862no—
857C4⋊C4—862no—
858C4⋊C4—862no—
859C4⋊C4—862no—
860C4⋊C4—862no—
861C4⋊C4—862no—
862C4⋊C4—861no—
863C4⋊C4—862no—
864C4⋊C4—862no—
865C4⋊C4—861no—
866C4⋊C4—861no—
867C4⋊C4C23×D4312yes—
868C4⋊C4C23×D4312yes—
869C4⋊C4C23×D4312yes—
870C22⋊C4—22no—
871C22⋊C4—22no—
872C22⋊C4—22no—
873C22⋊C4—862no—
874C22⋊C4—862no—
875C22⋊C4—862no—
876C22⋊C4—862no—
877C22⋊C4—862no—
878C22⋊C4—862no—
879C22⋊C4—862no—
880C22⋊C4—862no—
881C22⋊C4—862no—
882C42—22no—
883C42—431no—
884C42—431no—
885C42—431no—
886C42—431no—
887C42—431no—
888C42—431no—
889C42—431no—
890C42—431no—
891C42—431no—
892C42—431no—
893C42—431no—
894C42—431no—
895C42—862no—
896C42—862no—
897C42—862no—
898C42D4×D4311yescharacteristic
899C42D4×D4311yescharacteristic
900C42C23×D4311yescharacteristic
901C42C23×D4311yescharacteristic
902C23—22no—
903C23—42no—
904C23—42no—
905C23—42no—
906C23—431no—
907C23—431no—
908C23—862no—
909C23—862no—
910C23—862no—
911C23—1721no—
912C23—1722no—
913C23—1722no—
914C23—1722no—
915C23C2×D4×D4311yescharacteristic
916Q8—42no—
917Q8—42no—
918Q8—1722no—
919Q8—1724no—
920Q8—1724no—
921Q8—1724no—
922Q8—1724no—
923Q8—1722no—
924D4—22no—
925D4—22no—
926D4—42no—
927D4—862no—
928D4—862no—
929D4—1724no—
930D4—1724no—
931D4—1724no—
932D4—1724no—
933D4—1724no—
934D4—1724no—
935D4—1724no—
936D4—1724no—
937D4—1722no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—41no—
943C2×C4—44no—
944C2×C4—42no—
945C2×C4—44no—
946C2×C4—431no—
947C2×C4—431no—
948C2×C4—434no—
949C2×C4—431no—
950C2×C4—431no—
951C2×C4—431no—
952C2×C4—431no—
953C2×C4—862no—
954C2×C4—862no—
955C2×C4—862no—
956C2×C4—862no—
957C2×C4—862no—
958C2×C4—862no—
959C2×C4—862no—
960C2×C4—862no—
961C2×C4—862no—
962C2×C4—862no—
963C2×C4—861no—
964C2×C4—861no—
965C2×C4—861no—
966C2×C4—861no—
967C2×C4—862no—
968C2×C4—862no—
969C2×C4—862no—
970C2×C4—1721no—
971C2×C4—1721no—
972C2×C4—1724no—
973C2×C4—1724no—
974C2×C4—1724no—
975C2×C4—1722no—
976C2×C4—1724no—
977C2×C4C2×D4×D4311yescharacteristic
978C2×C4C2×D4×D4311yescharacteristic
979C2×C4C2×D4×D4311yescharacteristic
980C2×C4C2×D4×D4311yescharacteristic
981C2×C4C2×D4×D4311yescharacteristic
982C2×C4#1306337212yes—
983C2×C4#1306337312yes—
984C2×C4C24×D4311yescharacteristic
985C8—24no—
986C8—864no—
987C22—21no—
988C22—21no—
989C22—42no—
990C22—42no—
991C22—42no—
992C22—84no—
993C22—432no—
994C22—861no—
995C22—861no—
996C22—861no—
997C22—861no—
998C22—861no—
999C22—3444no—
1000C22—1724no—
1001C22—1722no—
1002C22—1722no—
1003C22—1722no—
1004C22#1458347212yes—
1005C22C22×D4×D4311yescharacteristic
1006C4—21no—
1007C4—21no—
1008C4—21no—
1009C4—42no—
1010C4—42no—
1011C4—42no—
1012C4—432no—
1013C4—432no—
1014C4—861no—
1015C4—861no—
1016C4—861no—
1017C4—861no—
1018C4—1722no—
1019C4—1722no—
1020C4—1722no—
1021C4#1458347212yes—
1022C4AGL(1,ℤ/8)×D4312yes—
1023C4C2×#1306337211yescharacteristic
1024C4C2×#1306337311yescharacteristic
1025C2—22no—
1026C2—82no—
1027C2—862no—
1028C2—3442no—
1029C2—1721no—
1030C2C2×#1458347211yescharacteristic
1031C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
1032C2#575×D4311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3077C2
socleC22×C43C23×D4
prime radicalC2×#14583446C2
hypercenter#3077D43
hypocenterC43#60864
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3077

Complements

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

NH ≅ G/Ntype
1. #533×D43C2semidirect
3. #19145792C2semidirect
4. #19145791C2semidirect
5. #19145783C2semidirect
6. #19145730C2semidirect
7. #19145722C2semidirect
8. #19145715C2semidirect
9. #19145139C2semidirect
10. #19144967C2semidirect
11. #19144537C2semidirect
12. #19144533C2semidirect
13. #19144394C2semidirect
14. #19144392C2semidirect
15. #19144388C2semidirect
16. #19143227C2semidirect
17. C43×#3077C2semidirect
20. #14583455C22semidirect
21. #14583454C22semidirect
22. #14583454C22semidirect
37. C4⋊Q8×D43C22semidirect
38. C4⋊Q8×D43C22semidirect
40. #125×D43C22semidirect
53. #14583307C22semidirect
54. #14583306C22semidirect
55. #14583303C22semidirect
56. #14583296C22semidirect
57. #14583262C22semidirect
58. #14583262C22semidirect
59. #14583244C22semidirect
60. #14583244C22semidirect
61. #14583226C22semidirect
62. #14583225C22semidirect
63. #14583222C22semidirect
64. #14583221C22semidirect
65. #14583219C22semidirect
66. #14583216C22semidirect
67. #14583214C22semidirect
68. #14583211C22semidirect
69. #14583200C22semidirect
70. #14583199C22semidirect
71. #14583196C22semidirect
72. #14583190C22semidirect
73. #14583189C22semidirect
74. #14583186C22semidirect
75. #14583180C22semidirect
76. #14583179C22semidirect
77. #14583176C22semidirect
78. #14582955C22semidirect
79. #14582955C22semidirect
80. #14582951C22semidirect
81. #14582951C22semidirect
93. C43×#478C22semidirect
94. C43×#476C22semidirect
95. C43×#474C22semidirect
524. #3077D43semidirect
590. #478C2×D43semidirect
594. #476C2×D43semidirect
598. #474C2×D43semidirect
615. C43#60864semidirect

Maximal subgroups

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

subgroupindex
#533×D432
C2×#145834462
#191457922
#191457912
#191457832
#191457302
#191457222
#191457152
#191451392
#191449672
#191445372
#191445332
#191443942
#191443922
#191443882
#191432272
C43×#30772
#6086443