Finite Group Databasebeta

← #25965026

Subgroups — #25965026

Order 11008.

2428 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#532×D43C211yesmaximal, characteristic, complemented
2C2×C4×#10621902C211yesmaximal, characteristic, complemented
3#19144744C214yesmaximal, complemented
4#19144717C211yesmaximal, characteristic, complemented
5#19144687C211yesmaximal, characteristic, complemented
6#19144682C211yesmaximal, characteristic, complemented
7#19144658C212yesmaximal, complemented
8#19144654C212yesmaximal, complemented
9#19144621C212yesmaximal, complemented
10#19144592C212yesmaximal, complemented
11#19144530C212yesmaximal, complemented
12#19144409C212yesmaximal, complemented
13#19144072C212yesmaximal, complemented
14#19143846C212yesmaximal, complemented
15#19143400C214yesmaximal, complemented
16#19143225C211yesmaximal, characteristic, complemented
17C43×#3112C211yesmaximal, characteristic, complemented
18C22×#10621902C2211yescharacteristic
19C2×#41×D43—21no—
20C2×#13063352C2214yes—
21#14583450C2211yescharacteristic, complemented
22#14583449C2211yescharacteristic
23#14583448—21no—
24#14583447C2211yescharacteristic, complemented
25#14583446—21no—
26#14583446C2212yescomplemented
27#14583445—21no—
28#14583444—21no—
29#14583444C2212yes—
30C4⋊Q8×D43C2211yescharacteristic, complemented
31#127×D43C2211yescharacteristic, complemented
32#124×D43—21no—
33#121×D43—21no—
34#121×D43C2212yes—
35C4×#10621902—21no—
36C4×#10621902—21no—
37C4×#10621902—21no—
38C4×#10621902—21no—
39C4×#10621902C2212yes—
40C4×#10621902C2212yes—
41C4×#10621902C2212yescomplemented
42C4×#10621902C2212yescomplemented
43C2×Q8×Dic43C2211yescharacteristic, complemented
44C2×C4×D172—21no—
45C2×C4×D172C2211yescharacteristic, complemented
46C2×#13063287—21no—
47C2×#13063287C2211yescharacteristic, complemented
48C4×D4×D43—21no—
49C4×D4×D43C2212yescomplemented
50C2×#13063283—21no—
51C2×#13063283C2211yescharacteristic
52C2×C42×D43—21no—
53C2×C42×D43C2211yescharacteristic
54#14583226C2214yescomplemented
55#14583222C2214yescomplemented
56#14583218C2212yescomplemented
57#14583215C2212yescomplemented
58#14583212C2212yescomplemented
59#14583194C2212yescomplemented
60#14583190C2212yescomplemented
61#14583186C2212yescomplemented
62#14583182C2214yescomplemented
63#14583178C2214yescomplemented
64#14583099C2212yescomplemented
65#14583097C2214yescomplemented
66#14583095C2212yescomplemented
67#14583093C2214yescomplemented
68#14583091C2212yescomplemented
69#14583047C2214yescomplemented
70#14583043C2214yescomplemented
71#14583038C2212yescomplemented
72#14583035C2212yescomplemented
73#14583032C2212yescomplemented
74#14583012C2214yescomplemented
75#14583009C2214yescomplemented
76#14582997C2214yescomplemented
77SD16×Dic43C2214yescomplemented
78#14582984C2214yescomplemented
79#14582981C2214yescomplemented
80#14582979C2214yescomplemented
81#14582956C2211yescharacteristic, complemented
82#14582954C2212yescomplemented
83#14582951C2212yescomplemented
84#14582949C2212yescomplemented
85#14582940C2214yescomplemented
86#14582921C2212yescomplemented
87#14582902C2214yescomplemented
88#14582899C2214yes—
89#14582861C2212yes—
90#14582851C2212yescomplemented
91C43×#532C2211yescharacteristic
92C2×C4×Q8×C43C2211yescharacteristic, complemented
93C43×#480C2212yescomplemented
94C43×#477C2212yescomplemented
95C43×#460C2212yescomplemented
96C43×#448C2212yescomplemented
97C43×#440C2214yescomplemented
98C43×#432C2211yescharacteristic, complemented
99C2×#10621902—28no—
100C2×#10621902—21no—
101C2×#10621902—21no—
102C2×#10621902—21no—
103C2×#10621902C2312yes—
104C2×#10621902C2312yes—
105C2×#10621898—21no—
106C2×#10621898—22no—
107C2×#10621900—22no—
108C2×#10621900—21no—
109#41×D43—48no—
110C2×Q8×D43—21no—
111C22×D172—21no—
112C22×D172C2311yescharacteristic
113C2×D4×D43—22no—
114C2×D4×D43—21no—
115C2×D4×D43—21no—
116C2×D4×D43C2312yes—
117C22×C4×D43—21no—
118C22×C4×D43—21no—
119C22×C4×D43—21no—
120C22×C4×D43—22no—
121C22×C4×D43D411yescharacteristic
122C22×C4×D43D411yescharacteristic
123C22×C4×D43C2311yescharacteristic
124#13063352—216no—
125C2×#10621884C2314yes—
126C2×D344C2314yes—
127C2×#10621882C2314yes—
128C2×#10621872C2314yes—
129#13063325C2311yescharacteristic
130#13063324—21no—
131#13063324C2312yes—
132#13063323—21no—
133#13063322C2311yescharacteristic
134#13063321—21no—
135#13063321—21no—
136#13063321C2312yes—
137#13063314—21no—
138#13063313—21no—
139#13063312—21no—
140#13063311—22no—
141#13063311—22no—
142#13063300—21no—
143#13063300C2312yes—
144#13063299—21no—
145#13063299C2312yes—
146#13063298—22no—
147#13063298—22no—
148#13063297—22no—
149#13063297—22no—
150#13063296—21no—
151#13063296C2312yes—
152Q8×Dic43—21no—
153Q8×Dic43—21no—
154Q8×Dic43C2312yes—
155Q8×Dic43C2312yes—
156C4×D172—22no—
157C4×D172—22no—
158C4×D172—22no—
159C4×D172—22no—
160C4×D172—21no—
161C4×D172—21no—
162C4×D172—21no—
163C4×D172C2312yes—
164C4×D172C2312yes—
165C4×D172C2312yes—
166D4×Dic43—21no—
167D4×Dic43C2312yes—
168#13063287—22no—
169#13063287—22no—
170#13063287—22no—
171#13063287—22no—
172#13063287—21no—
173#13063287—21no—
174#13063287—21no—
175#13063287C2312yes—
176#13063287C2312yes—
177#13063287C2312yes—
178C4×C22⋊D43—22no—
179C4×C22⋊D43—22no—
180(C22⋊D43)⋊C4—22no—
181(C22⋊D43)⋊C4—22no—
182#13063283—21no—
183#13063283—21no—
184#13063283—22no—
185#13063283—22no—
186#13063283—22no—
187#13063283—22no—
188#13063283C2312yes—
189#13063283C2312yes—
190C2×C4⋊Dic43—21no—
191C2×C4⋊Dic43C2311yescharacteristic
192C4⋊C4×D43—21no—
193C4⋊C4×D43C2312yes—
194C2×(C2×D43)⋊C4—21no—
195C2×(C2×D43)⋊C4—21no—
196C2×(C2×D43)⋊C4—21no—
197C22⋊C4×D43—22no—
198C22⋊C4×D43—22no—
199C2×C4×Dic43—21no—
200C2×C4×Dic43—21no—
201C2×C4×Dic43D411yescharacteristic
202C2×C4×Dic43D411yescharacteristic
203C2×C4×Dic43C2311yescharacteristic
204C42×D43—22no—
205C42×D43—22no—
206C42×D43—22no—
207C42×D43—22no—
208C42×D43D411yescharacteristic
209C42×D43D411yescharacteristic
210C42×D43D411yescharacteristic
211C42×D43D411yescharacteristic
212C42×D43C2311yescharacteristic
213C42×D43C2311yescharacteristic
214C42×D43C2311yescharacteristic
215C42×D43C2311yescharacteristic
216#13063258C2314yes—
217#13063257C2314yes—
218#13063256C2314yes—
219C4⋊(C43⋊C8)C2312yes—
220Dic43⋊C8C2314yes—
221#13063249C2314yes—
222#13063247C2314yes—
223#13063247C2314yes—
224#13063246C2314yes—
225#13063245C2314yes—
226#13063245C2314yes—
227C22⋊(C43⋊C8)C2312yes—
228(C2×D43)⋊C8C2314yes—
229#13063236C2312yes—
230C8×Dic43C2314yes—
231C2×#41×C43—21no—
232C22×Q8×C43C2311yescharacteristic
233C2×SD16×C43C2314yes—
234C4⋊Q8×C43C2311yescharacteristic
235#127×C43C2311yescharacteristic
236#124×C43—21no—
237#121×C43—21no—
238#121×C43C2312yes—
239C4×Q8×C43—21no—
240C4×Q8×C43—21no—
241C4×Q8×C43C2312yes—
242C4×Q8×C43C2312yes—
243C4×D4×C43—21no—
244C4×D4×C43C2312yes—
245C2×C4⋊C4×C43—21no—
246C2×C4⋊C4×C43C2311yescharacteristic
247C2×C42×C43—21no—
248C2×C42×C43C2311yescharacteristic
249#107×C43C2314yes—
250C4⋊C8×C43C2312yes—
251#103×C43C2314yes—
252#102×C43C2314yes—
253C22⋊C8×C43C2312yes—
254#97×C43C2312yes—
255C23×D43—21no—
256C23×D43—22no—
257C23×D43C2×D411yescharacteristic
258#41×C43—44no—
259C2×Q8×C43—24no—
260C2×Q8×C43—21no—
261C2×Q8×C43—21no—
262C2×Q8×C43C2412yes—
263C2×D4×C43—21no—
264C2×D4×C43—21no—
265C2×D4×C43—22no—
266C2×D4×C43C2412yes—
267C22×C4×C43—22no—
268C22×C4×C43—21no—
269C22×C4×C43—21no—
270C22×C4×C43C2×D411yescharacteristic
271C22×C4×C43C2×D411yescharacteristic
272C22×C4×C43C2411yescharacteristic
273C2×C22⋊D43—22no—
274C2×C22⋊D43—22no—
275C2×C22⋊D43—22no—
276C2×C22⋊D43—22no—
277C2×C22⋊D43—22no—
278C22×Dic43—22no—
279C22×Dic43—21no—
280C22×Dic43C2×D411yescharacteristic
281C22×Dic43C2×D411yescharacteristic
282C22×Dic43C2×D411yescharacteristic
283#10621902—28no—
284#10621902—28no—
285#10621902—24no—
286#10621902—24no—
287#10621902—24no—
288#10621902—44no—
289#10621902#4118yescomplemented
290Q8×D43—44no—
291#10621900—44no—
292#10621900—48no—
293D4×D43—28no—
294D4×D43—48no—
295D4×D43—44no—
296D4×D43—44no—
297#10621898—48no—
298#10621898—44no—
299C2×D172—28no—
300C2×D172—21no—
301C2×D172—24no—
302C2×D172—21no—
303C2×D172—21no—
304C2×D172—22no—
305C2×D172—22no—
306C2×D172—22no—
307C2×D172C2412yes—
308C2×D172C2412yes—
309C2×C4×D43—28no—
310C2×C4×D43—24no—
311C2×C4×D43—22no—
312C2×C4×D43—22no—
313C2×C4×D43—24no—
314C2×C4×D43—22no—
315C2×C4×D43—22no—
316C2×C4×D43—22no—
317C2×C4×D43—22no—
318C2×C4×D43—22no—
319C2×C4×D43—22no—
320C2×C4×D43—22no—
321C2×C4×D43—42no—
322C2×C4×D43—48no—
323C2×C4×D43—44no—
324C2×C4×D43—44no—
325C2×C4×D43C2×D411yescharacteristic
326C2×C4×D43C2×D411yescharacteristic
327C2×C4×D43C2×D411yescharacteristic
328C2×C4×D43C2×D411yescharacteristic
329C2×C4×D43C2×D411yescharacteristic
330C2×C4×D43C2×D411yescharacteristic
331C2×C4×D43C2×D411yescharacteristic
332C2×C4×D43C2×D411yescharacteristic
333C2×C4×D43C2×D411yescharacteristic
334C2×C4×D43C2×D411yescharacteristic
335C2×C4×D43C2411yescharacteristic
336C2×C4×D43C2411yescharacteristic
337C2×Dic86—21no—
338C2×Dic86—22no—
339SD16×C43—28no—
340C2×C8×C43C2414yes—
341C4⋊C4×C43—22no—
342C4⋊C4×C43—22no—
343C4⋊C4×C43—21no—
344C4⋊C4×C43—21no—
345C4⋊C4×C43C2412yes—
346C4⋊C4×C43C2412yes—
347C22⋊C4×C43—22no—
348C22⋊C4×C43—22no—
349C42×C43—22no—
350C42×C43—22no—
351C42×C43C2×D411yescharacteristic
352C42×C43C2×D411yescharacteristic
353C42×C43C2411yescharacteristic
354C42×C43C2411yescharacteristic
355C22⋊Dic43—22no—
356C22⋊Dic43—22no—
357#10621884—28no—
358#10621882—28no—
359(C2×D43)⋊C4—22no—
360(C2×D43)⋊C4—22no—
361(C2×D43)⋊C4—22no—
362(C2×D43)⋊C4—22no—
363(C2×D43)⋊C4—22no—
364(C2×D43)⋊C4—22no—
365(C2×D43)⋊C4—22no—
366(C2×D43)⋊C4—22no—
367(C2×D43)⋊C4—22no—
368(C2×D43)⋊C4—22no—
369C4⋊Dic43—21no—
370C4⋊Dic43—21no—
371C4⋊Dic43—22no—
372C4⋊Dic43—22no—
373C4⋊Dic43C2412yes—
374C4⋊Dic43C2412yes—
375Dic43⋊C4—22no—
376Dic43⋊C4—22no—
377C4×Dic43—22no—
378C4×Dic43—22no—
379C4×Dic43—22no—
380C4×Dic43—22no—
381C4×Dic43C2×D411yescharacteristic
382C4×Dic43C2×D411yescharacteristic
383C4×Dic43C2×D411yescharacteristic
384C4×Dic43C2×D411yescharacteristic
385C4×Dic43C2×D411yescharacteristic
386C4×Dic43C2×D411yescharacteristic
387C4×Dic43C2×D411yescharacteristic
388C4×Dic43C2×D411yescharacteristic
389C4×Dic43C2×D411yescharacteristic
390C4×Dic43C2×D411yescharacteristic
391C4×Dic43C2411yescharacteristic
392C4×Dic43C2411yescharacteristic
393C2×C43⋊C8C2414yes—
394D344—28no—
395#10621872—28no—
396C23×C43—22no—
397C23×C43C22×D411yescharacteristic
398C22×D43—24no—
399C22×D43—22no—
400C22×D43—22no—
401C22×D43—22no—
402C22×D43—22no—
403C22×D43—41no—
404C22×D43—44no—
405C22×D43—44no—
406C22×D43—42no—
407C22×D43—42no—
408C22×D43—44no—
409C22×D43C22×D411yescharacteristic
410C22×D43C22×D411yescharacteristic
411Q8×C43—24no—
412Q8×C43—22no—
413Q8×C43—42no—
414Q8×C43C2×#4114yescomplemented
415D4×C43—24no—
416D4×C43—42no—
417D4×C43—44no—
418D4×C43—42no—
419C2×C4×C43—24no—
420C2×C4×C43—22no—
421C2×C4×C43—22no—
422C2×C4×C43—22no—
423C2×C4×C43—22no—
424C2×C4×C43—22no—
425C2×C4×C43—22no—
426C2×C4×C43—44no—
427C2×C4×C43—42no—
428C2×C4×C43C22×D411yescharacteristic
429C2×C4×C43C22×D411yescharacteristic
430C2×C4×C43C22×D411yescharacteristic
431C2×C4×C43C22×D411yescharacteristic
432C2×C4×C43C22×D411yescharacteristic
433C2×C4×C43C2511yescharacteristic
434C22⋊D43—44no—
435C22⋊D43—44no—
436C22⋊D43—44no—
437C22⋊D43—44no—
438C22⋊D43—44no—
439C2×Dic43—22no—
440C2×Dic43—22no—
441C2×Dic43—22no—
442C2×Dic43—41no—
443C2×Dic43—42no—
444C2×Dic43—44no—
445C2×Dic43AGL(1,ℤ/8)14yescomplemented
446C2×Dic43C22×D411yescharacteristic
447C2×Dic43C22×D411yescharacteristic
448C2×Dic43C22×D411yescharacteristic
449C2×Dic43C22×D411yescharacteristic
450C2×Dic43C22×D411yescharacteristic
451C2×Dic43C22×D411yescharacteristic
452D172—28no—
453D172—24no—
454D172—28no—
455D172—22no—
456D172—24no—
457D172—42no—
458D172—44no—
459D172—42no—
460D172C2×#4114yescomplemented
461C4×D43—28no—
462C4×D43—22no—
463C4×D43—22no—
464C4×D43—22no—
465C4×D43—22no—
466C4×D43—28no—
467C4×D43—22no—
468C4×D43—22no—
469C4×D43—22no—
470C4×D43—22no—
471C4×D43—22no—
472C4×D43—41no—
473C4×D43—41no—
474C4×D43—44no—
475C4×D43—44no—
476C4×D43—44no—
477C4×D43—44no—
478C4×D43—44no—
479C4×D43—44no—
480C4×D43—44no—
481C4×D43C2×#4114yes—
482Dic86—42no—
483Dic86—44no—
484C8×C43—24no—
485C43⋊C8—24no—
486#60561—431nomaximal, Sylow
487C22×C43—21no—
488C22×C43—21no—
489C22×C43—42no—
490C22×C43—42no—
491C22×C43—42no—
492C22×C43C2×AGL(1,ℤ/8)12yes—
493C22×C43C23×D411yescharacteristic
494C2×D43—21no—
495C2×D43—21no—
496C2×D43—24no—
497C2×D43—21no—
498C2×D43—21no—
499C2×D43—21no—
500C2×D43—44no—
501C2×D43—48no—
502C2×D43—42no—
503C2×D43—42no—
504C2×D43—42no—
505C2×D43—42no—
506C2×D43—42no—
507C2×D43—88no—
508C2×D43#52512yes—
509C4×C43—24no—
510C4×C43—21no—
511C4×C43—21no—
512C4×C43—21no—
513C4×C43—21no—
514C4×C43—42no—
515C4×C43—42no—
516C4×C43#57512yes—
517C4×C43C22×#4112yes—
518Dic43—21no—
519Dic43—21no—
520Dic43—21no—
521Dic43—42no—
522Dic43—42no—
523Dic43#52512yes—
524Dic43C2×AGL(1,ℤ/8)12yes—
525Dic43C2×AGL(1,ℤ/8)12yes—
526C2×#532—431no—
527C2×C4×#41—431no—
528#3115—434no—
529#3112—431no—
530#3112D4311yescharacteristic, complemented
531#3109—431no—
532#3109—431no—
533#3106—432no—
534#3106—432no—
535#3103—432no—
536#3100—432no—
537#3094—432no—
538#3079—432no—
539#3038—432no—
540#3006—432no—
541C4×AGL(1,ℤ/8)—434no—
542#2920—431no—
543C2×C43—22no—
544C2×C43—82no—
545C2×C43C2×#52511yescharacteristic
546C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
547C2×C43C2×#57511yescharacteristic
548D43—22no—
549D43—41no—
550D43—44no—
551D43—82no—
552C22×#41—431no—
553C22×#41—861no—
554C2×AGL(1,ℤ/8)—434no—
555#532—431no—
556#532—431no—
557#532—432no—
558#532—432no—
559#532—431no—
560#532—861no—
561#532—861no—
562#532—861no—
563#532—861no—
564#532C2×D4311yescharacteristic
565C2×C4⋊Q8—431no—
566C2×#127—431no—
567C2×#124—861no—
568C2×#121—432no—
569C2×#121—861no—
570C4×#41—432no—
571C4×#41—432no—
572C4×#41—432no—
573C4×#41—432no—
574C4×#41—861no—
575C4×#41—861no—
576C4×#41—861no—
577C4×#41—861no—
578C2×C4×Q8—431no—
579C2×C4×Q8C2×D4311yescharacteristic, complemented
580C2×C4×D4—432no—
581C2×C4×D4—431no—
582C2×C4×D4—431no—
583C2×C4×D4—861no—
584C2×C4×D4—861no—
585C2×C4×D4—861no—
586C2×#117—431no—
587C2×#117—861no—
588C22×C42—431no—
589C22×C42—861no—
590#482—434no—
591#482—434no—
592#481—432no—
593#481—432no—
594#480—432no—
595#480C2×D4312yescomplemented
596#477—432no—
597#477C2×D4312yescomplemented
598#476—432no—
599#476—432no—
600#475—434no—
601#474—434no—
602#460—434no—
603#460—432no—
604#460C2×D4312yescomplemented
605#459—432no—
606#459—432no—
607#459—434no—
608#449—434no—
609#449—434no—
610#448—432no—
611#448C2×D4312yescomplemented
612#447—432no—
613#447—432no—
614#442—434no—
615#442—434no—
616#440—434no—
617#440C2×D4314yescomplemented
618C4×SD16—434no—
619C4×SD16—434no—
620C4×D8—434no—
621C4×D8—434no—
622#432—431no—
623#432—432no—
624#432C2×D4311yescharacteristic, complemented
625#431—432no—
626#431—432no—
627#428—434no—
628#423—432no—
629#418—434no—
630#417—434no—
631#407—432no—
632C4×M16—432no—
633C43#6056111yescharacteristic, complemented, Sylow
634C2×#41—21no—
635C2×#41—432no—
636C2×#41—432no—
637C2×#41—862no—
638C2×#41—862no—
639C2×#41—861no—
640C2×#41—861no—
641C2×#41—861no—
642C2×#41—861no—
643C2×#41—868no—
644C2×#41—861no—
645C2×#41—1728no—
646C22×Q8—861no—
647C22×Q8C22×D4311yescharacteristic
648C22×D4—432no—
649C22×D4—431no—
650C22×D4—861no—
651C22×D4—861no—
652C22×D4—861no—
653C22×D4—862no—
654C23×C4—431no—
655C23×C4—431no—
656C23×C4—431no—
657C23×C4—861no—
658C23×C4—862no—
659C23×C4—861no—
660C23×C4—861no—
661AGL(1,ℤ/8)—8616no—
662C2×SD16—434no—
663C2×SD16C22×D4314yes—
664C2×D8—434no—
665C2×D8—434no—
666C2×M16—434no—
667C4⋊Q8—432no—
668C4⋊Q8—431no—
669C4⋊Q8—861no—
670C4⋊Q8—861no—
671C4⋊Q8C22×D4311yescharacteristic
672#127—432no—
673#127—431no—
674#127—861no—
675#127—861no—
676#127C22×D4311yescharacteristic
677#124—21no—
678#124—862no—
679#124—862no—
680#124—861no—
681#124—861no—
682#124—861no—
683#121—21no—
684#121—432no—
685#121—432no—
686#121—432no—
687#121—862no—
688#121—862no—
689#121—861no—
690#121—862no—
691#121—861no—
692#121—862no—
693#121—861no—
694#121C22×D4312yes—
695C4×Q8—21no—
696C4×Q8—21no—
697C4×Q8—432no—
698C4×Q8—432no—
699C4×Q8—861no—
700C4×Q8—861no—
701C4×Q8C22×D4312yes—
702C4×Q8C22×D4312yes—
703C4×D4—21no—
704C4×D4—432no—
705C4×D4—432no—
706C4×D4—432no—
707C4×D4—432no—
708C4×D4—432no—
709C4×D4—432no—
710C4×D4—432no—
711C4×D4—862no—
712C4×D4—862no—
713C4×D4—862no—
714C4×D4—862no—
715C4×D4—862no—
716C4×D4—862no—
717C4×D4—861no—
718C4×D4—861no—
719C4×D4—861no—
720C4×D4—862no—
721C4×D4—862no—
722C4×D4—861no—
723C4×D4—862no—
724C4×D4—862no—
725C4×D4—862no—
726C4×D4—862no—
727C4×D4—861no—
728C4×D4—861no—
729C4×D4—861no—
730C4×D4C22×D4312yes—
731#117—432no—
732#117—432no—
733#117—862no—
734#117—862no—
735#117—862no—
736#117—862no—
737#117—861no—
738#117—861no—
739C2×C4⋊C4—21no—
740C2×C4⋊C4—431no—
741C2×C4⋊C4—432no—
742C2×C4⋊C4—861no—
743C2×C4⋊C4—861no—
744C2×C4⋊C4C22×D4311yescharacteristic
745C2×C22⋊C4—862no—
746C2×C22⋊C4—862no—
747C2×C22⋊C4—861no—
748C2×C22⋊C4—861no—
749C2×C22⋊C4—861no—
750C2×C42—21no—
751C2×C42—431no—
752C2×C42—431no—
753C2×C42—431no—
754C2×C42—431no—
755C2×C42—431no—
756C2×C42—431no—
757C2×C42—431no—
758C2×C42—431no—
759C2×C42—431no—
760C2×C42—431no—
761C2×C42—431no—
762C2×C42—862no—
763C2×C42—862no—
764C2×C42—862no—
765C2×C42—862no—
766C2×C42—861no—
767C2×C42—861no—
768C2×C42C22×D4311yescharacteristic
769#107—434no—
770#107C22×D4314yes—
771#106—434no—
772#106—434no—
773C4⋊C8—434no—
774C4⋊C8—432no—
775C4⋊C8C22×D4312yes—
776#103—434no—
777#103C22×D4314yes—
778#102—434no—
779#102—434no—
780#102—434no—
781#102—434no—
782#102—434no—
783#102C22×D4314yes—
784C22⋊C8—432no—
785C22⋊C8—434no—
786C22⋊C8C22×D4312yes—
787#97—432no—
788#97C22×D4312yes—
789C4×C8—434no—
790C24—431no—
791C24—862no—
792C24—861no—
793#41—44no—
794#41—438no—
795#41—864no—
796#41—864no—
797#41—868no—
798#41—868no—
799#41—864no—
800#41—1724no—
801#41—1728no—
802#41—1728no—
803#41—1724no—
804#41—1724no—
805C2×Q8—24no—
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—862no—
809C2×Q8—861no—
810C2×Q8—1724no—
811C2×Q8C23×D4312yes—
812C2×D4—22no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—432no—
816C2×D4—432no—
817C2×D4—864no—
818C2×D4—862no—
819C2×D4—862no—
820C2×D4—868no—
821C2×D4—862no—
822C2×D4—868no—
823C2×D4—862no—
824C2×D4—862no—
825C2×D4—862no—
826C2×D4—862no—
827C2×D4—862no—
828C2×D4—861no—
829C2×D4—861no—
830C2×D4—861no—
831C2×D4—1724no—
832C2×D4—1724no—
833C2×D4—1728no—
834C2×D4C23×D4312yes—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—22no—
838C22×C4—431no—
839C22×C4—431no—
840C22×C4—431no—
841C22×C4—431no—
842C22×C4—431no—
843C22×C4—431no—
844C22×C4—431no—
845C22×C4—431no—
846C22×C4—431no—
847C22×C4—431no—
848C22×C4—431no—
849C22×C4—431no—
850C22×C4—431no—
851C22×C4—431no—
852C22×C4—431no—
853C22×C4—862no—
854C22×C4—862no—
855C22×C4—864no—
856C22×C4—864no—
857C22×C4—862no—
858C22×C4—862no—
859C22×C4—862no—
860C22×C4—868no—
861C22×C4—862no—
862C22×C4—862no—
863C22×C4—861no—
864C22×C4—862no—
865C22×C4—862no—
866C22×C4—862no—
867C22×C4—1722no—
868C22×C4—1724no—
869C22×C4—1724no—
870C22×C4—1728no—
871C22×C4D4×D4311yescharacteristic
872C22×C4D4×D4311yescharacteristic
873C22×C4C23×D4311yescharacteristic
874SD16—28no—
875SD16—868no—
876D8—868no—
877D8—868no—
878M16—868no—
879C2×C8—434no—
880C2×C8C23×D4314yes—
881C4⋊C4—22no—
882C4⋊C4—22no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—432no—
886C4⋊C4—432no—
887C4⋊C4—862no—
888C4⋊C4—862no—
889C4⋊C4—862no—
890C4⋊C4—862no—
891C4⋊C4—861no—
892C4⋊C4—861no—
893C4⋊C4C23×D4312yes—
894C4⋊C4C23×D4312yes—
895C22⋊C4—22no—
896C22⋊C4—22no—
897C22⋊C4—862no—
898C22⋊C4—862no—
899C22⋊C4—862no—
900C22⋊C4—862no—
901C22⋊C4—862no—
902C22⋊C4—862no—
903C22⋊C4—862no—
904C22⋊C4—862no—
905C22⋊C4—862no—
906C22⋊C4—862no—
907C22⋊C4—862no—
908C22⋊C4—862no—
909C42—22no—
910C42—22no—
911C42—431no—
912C42—431no—
913C42—431no—
914C42—431no—
915C42—431no—
916C42—431no—
917C42—431no—
918C42—431no—
919C42—431no—
920C42—431no—
921C42—431no—
922C42—431no—
923C42—862no—
924C42—862no—
925C42—862no—
926C42—862no—
927C42D4×D4311yescharacteristic
928C42D4×D4311yescharacteristic
929C42C23×D4311yescharacteristic
930C42C23×D4311yescharacteristic
931C23—22no—
932C23—431no—
933C23—431no—
934C23—862no—
935C23—864no—
936C23—862no—
937C23—862no—
938C23—862no—
939C23—1721no—
940C23—1722no—
941C23—1724no—
942C23—1724no—
943C23—1724no—
944C23—1722no—
945C23C2×D4×D4311yescharacteristic
946Q8—24no—
947Q8—22no—
948Q8—42no—
949Q8—1722no—
950Q8—1724no—
951Q8#41×D4314yescomplemented
952D4—24no—
953D4—42no—
954D4—44no—
955D4—42no—
956D4—434no—
957D4—868no—
958D4—868no—
959D4—864no—
960D4—862no—
961D4—864no—
962D4—1722no—
963D4—1724no—
964D4—1724no—
965D4—1724no—
966D4—1724no—
967D4—1724no—
968D4—1724no—
969D4—1722no—
970C2×C4—24no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—44no—
978C2×C4—42no—
979C2×C4—434no—
980C2×C4—431no—
981C2×C4—431no—
982C2×C4—431no—
983C2×C4—434no—
984C2×C4—431no—
985C2×C4—431no—
986C2×C4—431no—
987C2×C4—862no—
988C2×C4—862no—
989C2×C4—862no—
990C2×C4—862no—
991C2×C4—862no—
992C2×C4—868no—
993C2×C4—862no—
994C2×C4—868no—
995C2×C4—862no—
996C2×C4—862no—
997C2×C4—862no—
998C2×C4—862no—
999C2×C4—862no—
1000C2×C4—862no—
1001C2×C4—1721no—
1002C2×C4—1721no—
1003C2×C4—1724no—
1004C2×C4—1724no—
1005C2×C4—1724no—
1006C2×C4—1724no—
1007C2×C4—1724no—
1008C2×C4—1724no—
1009C2×C4—1724no—
1010C2×C4—1721no—
1011C2×C4—1722no—
1012C2×C4—1724no—
1013C2×C4C2×D4×D4311yescharacteristic
1014C2×C4C2×D4×D4311yescharacteristic
1015C2×C4C2×D4×D4311yescharacteristic
1016C2×C4C2×D4×D4311yescharacteristic
1017C2×C4C2×D4×D4311yescharacteristic
1018C2×C4C24×D4311yescharacteristic
1019C8—24no—
1020C8—864no—
1021C22—21no—
1022C22—21no—
1023C22—42no—
1024C22—42no—
1025C22—42no—
1026C22—432no—
1027C22—861no—
1028C22—861no—
1029C22—861no—
1030C22—861no—
1031C22—864no—
1032C22—861no—
1033C22—3448no—
1034C22—1724no—
1035C22—1728no—
1036C22—1722no—
1037C22—1722no—
1038C22—1722no—
1039C22—1722no—
1040C22—1722no—
1041C22AGL(1,ℤ/8)×D4312yes—
1042C22C22×D4×D4311yescharacteristic
1043C4—21no—
1044C4—21no—
1045C4—21no—
1046C4—24no—
1047C4—21no—
1048C4—42no—
1049C4—42no—
1050C4—432no—
1051C4—432no—
1052C4—432no—
1053C4—861no—
1054C4—861no—
1055C4—861no—
1056C4—1722no—
1057C4—1722no—
1058C4#1458369812yes—
1059C4C2×#41×D4312yes—
1060C2—22no—
1061C2—82no—
1062C2—862no—
1063C2—3442no—
1064C2—1721no—
1065C2—1724no—
1066C2#525×D4311yescharacteristic
1067C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
1068C2C2×#1458369811yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3112C2
socleC22×C43C23×D4
hypercenter#3112D43
hypocenterC43#60561
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3112

Complements

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

NH ≅ G/Ntype
1. #532×D43C2semidirect
2. C2×C4×#10621902C2semidirect
3. #19144744C2semidirect
4. #19144717C2semidirect
5. #19144687C2semidirect
6. #19144682C2semidirect
7. #19144658C2semidirect
8. #19144654C2semidirect
9. #19144621C2semidirect
10. #19144592C2semidirect
11. #19144530C2semidirect
12. #19144409C2semidirect
13. #19144072C2semidirect
14. #19143846C2semidirect
15. #19143400C2semidirect
16. #19143225C2semidirect
17. C43×#3112C2semidirect
21. #14583450C22semidirect
24. #14583447C22semidirect
26. #14583446C22semidirect
30. C4⋊Q8×D43C22semidirect
31. #127×D43C22semidirect
41. C4×#10621902C22semidirect
42. C4×#10621902C22semidirect
43. C2×Q8×Dic43C22semidirect
45. C2×C4×D172C22semidirect
47. C2×#13063287C22semidirect
49. C4×D4×D43C22semidirect
54. #14583226C22semidirect
55. #14583222C22semidirect
56. #14583218C22semidirect
57. #14583215C22semidirect
58. #14583212C22semidirect
59. #14583194C22semidirect
60. #14583190C22semidirect
61. #14583186C22semidirect
62. #14583182C22semidirect
63. #14583178C22semidirect
64. #14583099C22semidirect
65. #14583097C22semidirect
66. #14583095C22semidirect
67. #14583093C22semidirect
68. #14583091C22semidirect
69. #14583047C22semidirect
70. #14583043C22semidirect
71. #14583038C22semidirect
72. #14583035C22semidirect
73. #14583032C22semidirect
74. #14583012C22semidirect
75. #14583009C22semidirect
76. #14582997C22semidirect
77. SD16×Dic43C22semidirect
78. #14582984C22semidirect
79. #14582981C22semidirect
80. #14582979C22semidirect
81. #14582956C22semidirect
82. #14582954C22semidirect
83. #14582951C22semidirect
84. #14582949C22semidirect
85. #14582940C22semidirect
86. #14582921C22semidirect
87. #14582902C22semidirect
90. #14582851C22semidirect
92. C2×C4×Q8×C43C22semidirect
93. C43×#480C22semidirect
94. C43×#477C22semidirect
95. C43×#460C22semidirect
96. C43×#448C22semidirect
97. C43×#440C22semidirect
98. C43×#432C22semidirect
289. #10621902#41semidirect
414. Q8×C43C2×#41semidirect
445. C2×Dic43AGL(1,ℤ/8)semidirect
460. D172C2×#41semidirect
530. #3112D43semidirect
579. C2×C4×Q8C2×D43semidirect
595. #480C2×D43semidirect
597. #477C2×D43semidirect
604. #460C2×D43semidirect
611. #448C2×D43semidirect
617. #440C2×D43semidirect
624. #432C2×D43semidirect
633. C43#60561semidirect
951. Q8#41×D43semidirect

Maximal subgroups

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

subgroupindex
#532×D432
C2×C4×#106219022
#191447442
#191447172
#191446872
#191446822
#191446582
#191446542
#191446212
#191445922
#191445302
#191444092
#191440722
#191438462
#191434002
#191432252
C43×#31122
#6056143