Finite Group Databasebeta

← #25965086

Subgroups — #25965086

Order 11008.

2078 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147985C211yesmaximal, characteristic, complemented
2#19144872C214yesmaximal, complemented
3#19144857C214yesmaximal, complemented
4#19144809C214yesmaximal, complemented
5#19144794C214yesmaximal, complemented
6#19144518C212yesmaximal, complemented
7#19144400C211yesmaximal, characteristic, complemented
8#19144392C211yesmaximal, characteristic, complemented
9#19144067C211yesmaximal, characteristic, complemented
10#19144059C211yesmaximal, characteristic, complemented
11#19143837C212yesmaximal, complemented
12C4×#13063356C212yesmaximal, complemented
13C4×#13063351C212yesmaximal, complemented
14#19143233C211yesmaximal, characteristic, complemented
15C2×C43×#520C211yesmaximal, characteristic, complemented
16C2×#13063356C2212yes—
17C2×#13063351C2212yes—
18#14583520C2212yescomplemented
19#14583520C2212yescomplemented
20#14583511C2212yescomplemented
21#14583504C2212yescomplemented
22#14583496—21no—
23#14583496—21no—
24#14583487—21no—
25#14583487—21no—
26#14583456C2211yescharacteristic
27#14583449C2211yescharacteristic
28#14583427—22no—
29#14583427—22no—
30#14583410C2212yes—
31C4×#10621898C2212yes—
32#14583234C2214yescomplemented
33#14583229C2214yescomplemented
34#14583217C2214yescomplemented
35#14583212C2214yescomplemented
36#14583206C2214yescomplemented
37#14583199C2214yescomplemented
38#14583194C2212yescomplemented
39#14583189C2212yescomplemented
40#14583184C2212yescomplemented
41#14583179C2212yescomplemented
42#14583121C2214yescomplemented
43#14583114C2214yescomplemented
44#14583109C2212yescomplemented
45#14583104C2212yescomplemented
46#14583099C2212yescomplemented
47#14583094C2212yescomplemented
48#14583061C2214yes—
49#14583061C2214yes—
50#14583044C2214yes—
51#14583044C2214yes—
52#14583009C2214yescomplemented
53#14583004C2214yescomplemented
54#14582999C2214yescomplemented
55#14582997C2214yescomplemented
56C4×#10621885C2214yescomplemented
57C4×#10621884C2214yescomplemented
58C4×#10621883C2214yescomplemented
59C4×#10621882C2214yescomplemented
60#14582960C2214yescomplemented
61#14582960C2214yescomplemented
62#14582939C2212yes—
63#14582939C2212yes—
64#14582923C2211yescharacteristic
65#14582923C2211yescharacteristic
66#14582908C2212yes—
67#14582904C2212yes—
68#14582898C2212yes—
69#14582898C2212yes—
70#14582863C2212yes—
71C4×#10621877C2212yes—
72C22×#41×C43C2211yescharacteristic
73C43×#520—22no—
74C43×#520—22no—
75C43×#520C2214yes—
76C43×#520C2214yes—
77C2×C4×Q8×C43C2211yescharacteristic
78C2×C4×Q8×C43C2211yescharacteristic
79C2×C4×D4×C43—21no—
80C2×C4×D4×C43—21no—
81C2×C4×D4×C43C2211yescharacteristic
82C2×C4×D4×C43C2211yescharacteristic
83C2×#117×C43—21no—
84C2×#117×C43C2211yescharacteristic
85C22×C4⋊C4×C43—21no—
86C22×C4⋊C4×C43C2211yescharacteristic
87C2×#10621898C2312yes—
88#13063356—28no—
89#13063351—28no—
90C2×#10621885C2314yes—
91C2×#10621883C2314yes—
92C2×#10621884C2314yes—
93C2×#10621882C2314yes—
94C2×#10621877C2312yes—
95C2×#10621877C2312yes—
96#13063325C2311yescharacteristic
97#13063325C2311yescharacteristic
98#13063325C2311yescharacteristic
99#13063322C2311yescharacteristic
100#13063320—22no—
101#13063320—22no—
102#13063318—22no—
103#13063318—22no—
104#13063317C2312yes—
105#13063315—22no—
106#13063315—22no—
107#13063313C2312yes—
108#13063311—22no—
109#13063311—22no—
110#13063310—22no—
111#13063310—22no—
112#13063308—22no—
113#13063307—22no—
114#13063307—22no—
115#13063304—21no—
116#13063304—21no—
117#13063304C2312yes—
118#13063304C2312yes—
119#13063303—22no—
120#13063303—22no—
121#13063299—21no—
122#13063299—21no—
123#13063299C2312yes—
124#13063299C2312yes—
125#13063298—22no—
126#13063298—22no—
127#13063294—22no—
128C4×Dic86—21no—
129C4×Dic86—21no—
130C4×Dic86C2312yes—
131C4×Dic86C2312yes—
132C4×D172—21no—
133C4×D172—21no—
134C4×D172C2312yes—
135C4×D172C2312yes—
136C4×C22⋊D43—22no—
137C4×C22⋊D43—22no—
138C4×C22⋊D43—22no—
139C4×C22⋊D43—22no—
140#13063284C2312yes—
141#13063282—22no—
142C42×D43—22no—
143#13063258C2314yes—
144#13063258C2314yes—
145#13063256C2314yes—
146#13063256C2314yes—
147C4⋊(C43⋊C8)C2312yes—
148C4⋊(C43⋊C8)C2312yes—
149C4⋊(C43⋊C8)C2312yes—
150C4⋊(C43⋊C8)C2312yes—
151#13063249C2314yes—
152#13063249C2314yes—
153#13063248C2314yes—
154#13063248C2314yes—
155#13063246C2314yes—
156#13063246C2314yes—
157#13063245C2314yes—
158#13063245C2314yes—
159C22⋊(C43⋊C8)C2314yes—
160C22⋊(C43⋊C8)C2314yes—
161#13063236C2314yes—
162C4×C43⋊C8C2314yes—
163C2×#41×C43—24no—
164C2×#41×C43—24no—
165C2×#41×C43—22no—
166C2×#41×C43C2314yes—
167C22×Q8×C43C2311yescharacteristic
168C22×D4×C43—21no—
169C22×D4×C43C2311yescharacteristic
170C23×C4×C43—21no—
171C23×C4×C43—21no—
172C23×C4×C43—21no—
173C23×C4×C43—21no—
174C23×C4×C43C2311yescharacteristic
175C4×Q8×C43—22no—
176C4×Q8×C43—21no—
177C4×Q8×C43—21no—
178C4×Q8×C43C2312yes—
179C4×Q8×C43C2312yes—
180C4×Q8×C43C2314yes—
181C4×D4×C43—24no—
182C4×D4×C43—24no—
183C4×D4×C43—24no—
184C4×D4×C43—24no—
185C4×D4×C43—22no—
186C4×D4×C43—21no—
187C4×D4×C43—21no—
188C4×D4×C43C2312yes—
189C4×D4×C43C2312yes—
190C4×D4×C43C2314yes—
191#117×C43—24no—
192#117×C43—24no—
193#117×C43D412yes—
194#117×C43D412yes—
195#117×C43C2312yes—
196#117×C43C2312yes—
197C2×C4⋊C4×C43—21no—
198C2×C4⋊C4×C43—21no—
199C2×C4⋊C4×C43—21no—
200C2×C4⋊C4×C43—22no—
201C2×C4⋊C4×C43—24no—
202C2×C4⋊C4×C43—24no—
203C2×C4⋊C4×C43D411yescharacteristic
204C2×C4⋊C4×C43D411yescharacteristic
205C2×C4⋊C4×C43C2311yescharacteristic
206C2×C4⋊C4×C43C2311yescharacteristic
207C2×C4⋊C4×C43C2314yes—
208C2×C22⋊C4×C43—21no—
209C2×C22⋊C4×C43—21no—
210C2×C22⋊C4×C43D411yescharacteristic
211C2×C22⋊C4×C43D411yescharacteristic
212C2×C42×C43—21no—
213C2×C42×C43—21no—
214C2×C42×C43C2311yescharacteristic
215C2×C42×C43C2311yescharacteristic
216C24×C43—21no—
217C24×C43C2×D411yescharacteristic
218#41×C43—216no—
219#41×C43—28no—
220#41×C43—28no—
221C2×Q8×C43—21no—
222C2×Q8×C43—22no—
223C2×Q8×C43#4114yes—
224C2×Q8×C43C2412yes—
225C2×D4×C43—28no—
226C2×D4×C43—21no—
227C2×D4×C43—22no—
228C2×D4×C43—24no—
229C2×D4×C43#4114yes—
230C2×D4×C43C2412yes—
231C22×C4×C43—28no—
232C22×C4×C43—24no—
233C22×C4×C43—22no—
234C22×C4×C43—22no—
235C22×C4×C43—24no—
236C22×C4×C43—22no—
237C22×C4×C43—22no—
238C22×C4×C43—21no—
239C22×C4×C43—21no—
240C22×C4×C43—21no—
241C22×C4×C43—24no—
242C22×C4×C43—82no—
243C22×C4×C43—82no—
244C22×C4×C43—82no—
245C22×C4×C43C2×D411yescharacteristic
246C22×C4×C43C2×D412yes—
247C22×C4×C43C2×D411yescharacteristic
248C22×C4×C43C2×D411yescharacteristic
249C22×C4×C43C2×D411yescharacteristic
250C22×C4×C43C2×D411yescharacteristic
251C22×C4×C43C2412yes—
252C22×C4×C43C2411yescharacteristic
253C2×C22⋊D43—22no—
254C2×C22⋊D43—22no—
255C2×C22⋊D43—22no—
256#10621898—24no—
257#10621898—24no—
258C2×D172—21no—
259C2×D172—21no—
260C2×D172C2412yes—
261C2×C4×D43—22no—
262C2×C4×D43—22no—
263C2×C4×D43—22no—
264C2×Dic86—21no—
265C2×Dic86—21no—
266C2×Dic86C2412yes—
267C4⋊C4×C43—24no—
268C4⋊C4×C43—24no—
269C4⋊C4×C43—22no—
270C4⋊C4×C43—22no—
271C4⋊C4×C43—21no—
272C4⋊C4×C43—21no—
273C4⋊C4×C43C2×D412yes—
274C4⋊C4×C43C2×D412yes—
275C4⋊C4×C43C2×D412yes—
276C4⋊C4×C43C2×D412yes—
277C4⋊C4×C43C2412yes—
278C4⋊C4×C43C2412yes—
279C22⋊C4×C43—24no—
280C22⋊C4×C43—22no—
281C22⋊C4×C43—22no—
282C22⋊C4×C43C2×D412yes—
283C22⋊C4×C43C2×D412yes—
284C22⋊C4×C43C2×D412yes—
285C22⋊C4×C43C2×D412yes—
286C42×C43—24no—
287C42×C43—22no—
288C42×C43—22no—
289C42×C43C2×D412yes—
290C42×C43C2×D411yescharacteristic
291C42×C43C2×D411yescharacteristic
292C42×C43C2412yes—
293C42×C43C2411yescharacteristic
294C42×C43C2411yescharacteristic
295C22⋊Dic43—22no—
296C22⋊Dic43—22no—
297C22⋊Dic43—22no—
298#10621885—28no—
299#10621884—28no—
300#10621883—28no—
301#10621882—28no—
302(C2×D43)⋊C4—22no—
303(C2×D43)⋊C4—22no—
304(C2×D43)⋊C4—22no—
305(C2×D43)⋊C4—22no—
306(C2×D43)⋊C4—22no—
307(C2×D43)⋊C4—22no—
308C4⋊Dic43—21no—
309C4⋊Dic43—21no—
310C4⋊Dic43—21no—
311C4⋊Dic43—21no—
312C4⋊Dic43C2412yes—
313C4⋊Dic43C2412yes—
314Dic43⋊C4—22no—
315Dic43⋊C4—22no—
316Dic43⋊C4—22no—
317Dic43⋊C4—22no—
318Dic43⋊C4—22no—
319Dic43⋊C4—22no—
320C4×Dic43—22no—
321C4×Dic43—22no—
322C4×Dic43—22no—
323#10621877—24no—
324#10621877—24no—
325C2×C43⋊C8C2414yes—
326C2×C43⋊C8C2414yes—
327C23×C43—22no—
328C23×C43—24no—
329C23×C43—22no—
330C23×C43—41no—
331C23×C43—41no—
332C23×C43—42no—
333C23×C43—42no—
334C23×C43C22×D412yes—
335C23×C43C22×D411yescharacteristic
336C22×D43—22no—
337Q8×C43—24no—
338Q8×C43—22no—
339Q8×C43C2×#4114yes—
340D4×C43—216no—
341D4×C43—24no—
342D4×C43—22no—
343D4×C43C2×#4114yes—
344C2×C4×C43—216no—
345C2×C4×C43—22no—
346C2×C4×C43—24no—
347C2×C4×C43—22no—
348C2×C4×C43—24no—
349C2×C4×C43—22no—
350C2×C4×C43—22no—
351C2×C4×C43—22no—
352C2×C4×C43—22no—
353C2×C4×C43—41no—
354C2×C4×C43—41no—
355C2×C4×C43—41no—
356C2×C4×C43—41no—
357C2×C4×C43—42no—
358C2×C4×C43—42no—
359C2×C4×C43—82no—
360C2×C4×C43—84no—
361C2×C4×C43—82no—
362C2×C4×C43—84no—
363C2×C4×C43C22×D412yes—
364C2×C4×C43C22×D412yes—
365C2×C4×C43C22×D411yescharacteristic
366C2×C4×C43C22×D411yescharacteristic
367C2×C4×C43C22×D412yes—
368C2×C4×C43C22×D411yescharacteristic
369C2×C4×C43C22×D411yescharacteristic
370C2×C4×C43C22×D411yescharacteristic
371C2×C4×C43C2×#4112yes—
372C2×C4×C43C2×#4112yes—
373C2×C4×C43C2511yescharacteristic
374C22⋊D43—44no—
375C22⋊D43—82no—
376C22⋊D43—82no—
377C2×Dic43—22no—
378C2×Dic43—22no—
379C2×Dic43—22no—
380D172—22no—
381D172—22no—
382D172—81no—
383D172—81no—
384C4×D43—44no—
385C4×D43—82no—
386C4×D43—82no—
387Dic86—22no—
388Dic86—22no—
389Dic86—81no—
390Dic86—81no—
391C43⋊C8—24no—
392C43⋊C8—24no—
393#60565—431nomaximal, Sylow
394C22×C43—21no—
395C22×C43—21no—
396C22×C43—22no—
397C22×C43—22no—
398C22×C43—24no—
399C22×C43—22no—
400C22×C43—44no—
401C22×C43—48no—
402C22×C43—42no—
403C22×C43—42no—
404C22×C43#52512yes—
405C22×C43C23×D411yescharacteristic
406C2×D43—42no—
407C2×D43—42no—
408C2×D43—42no—
409C4×C43—21no—
410C4×C43—22no—
411C4×C43—21no—
412C4×C43—21no—
413C4×C43—22no—
414C4×C43—21no—
415C4×C43—22no—
416C4×C43—24no—
417C4×C43—42no—
418C4×C43—42no—
419C4×C43#52512yes—
420C4×C43C22×#4111yescharacteristic
421C4×C43C22×#4111yescharacteristic
422Dic43—42no—
423Dic43—42no—
424Dic43—42no—
425#3455—431no—
426C2×#520D4311yescharacteristic, complemented
427#3125—434no—
428#3124—434no—
429#3120—434no—
430#3119—434no—
431#3092—432no—
432#3078—431no—
433#3077—431no—
434#3037—431no—
435#3036—431no—
436#3005—432no—
437C4×#137—432no—
438C4×AGL(1,ℤ/8)—432no—
439#2921—431no—
440C2×C43—22no—
441C2×C43—42no—
442C2×C43—44no—
443C2×C43C2×#52511yescharacteristic
444C2×C43#358511yescharacteristic
445C2×C43#358611yescharacteristic
446D43—82no—
447C22×#41C2×D4311yescharacteristic
448C2×#137—432no—
449C2×AGL(1,ℤ/8)—432no—
450#542—432no—
451#542—432no—
452#541—432no—
453#540—432no—
454#539—861no—
455#539—861no—
456#538—861no—
457#538—861no—
458#533—431no—
459#532—431no—
460#529—862no—
461#529—862no—
462#525—432no—
463#520—22no—
464#520—22no—
465#520C2×D4314yes—
466#520C2×D4314yes—
467C4×#41—432no—
468C2×C4×Q8C2×D4311yescharacteristic
469C2×C4×Q8C2×D4311yescharacteristic
470C2×C4×D4—21no—
471C2×C4×D4—21no—
472C2×C4×D4C2×D4311yescharacteristic
473C2×C4×D4C2×D4311yescharacteristic
474C2×#117—21no—
475C2×#117C2×D4311yescharacteristic
476C22×C4⋊C4—21no—
477C22×C4⋊C4C2×D4311yescharacteristic
478#484—434no—
479#483—434no—
480#481—434no—
481#480—434no—
482#479—434no—
483#478—434no—
484#477—432no—
485#476—432no—
486#475—432no—
487#474—432no—
488#464—434no—
489#463—434no—
490#462—432no—
491#461—432no—
492#460—432no—
493#459—432no—
494#452—434no—
495#452—434no—
496#449—434no—
497#449—434no—
498#442—434no—
499#441—434no—
500#440—434no—
501#440—434no—
502C4×Q16—434no—
503C4×SD16—434no—
504C4×SD16—434no—
505C4×D8—434no—
506#433—434no—
507#433—434no—
508#428—432no—
509#428—432no—
510#423—431no—
511#423—431no—
512#419—432no—
513#418—432no—
514#417—432no—
515#417—432no—
516#407—432no—
517C4×M16—432no—
518C43#6056511yescharacteristic, complemented, Sylow
519C2×#41—24no—
520C2×#41—24no—
521C2×#41—22no—
522C2×#41—432no—
523C2×#41C22×D4314yes—
524C22×Q8C22×D4311yescharacteristic
525C22×D4—21no—
526C22×D4C22×D4311yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C22×D4311yescharacteristic
532#137—868no—
533AGL(1,ℤ/8)—868no—
534C2×Q16—434no—
535C2×SD16—434no—
536C2×SD16—434no—
537C2×D8—434no—
538C2×M16—432no—
539C2×M16—432no—
540C4⋊Q8—431no—
541C4⋊Q8—431no—
542C4⋊Q8—431no—
543#127—431no—
544#126—862no—
545#126—862no—
546#126—862no—
547#126—862no—
548#125—432no—
549#125—862no—
550#125—862no—
551#124—432no—
552#124—862no—
553#124—862no—
554#123—862no—
555#123—862no—
556#123—862no—
557#123—862no—
558#123—862no—
559C22⋊Q8—432no—
560C22⋊Q8—432no—
561C22⋊Q8—861no—
562C22⋊Q8—861no—
563C22⋊Q8—862no—
564C22⋊Q8—862no—
565#121—432no—
566#121—432no—
567#121—861no—
568#121—861no—
569#121—862no—
570#121—862no—
571#120—862no—
572C4×Q8—22no—
573C4×Q8—21no—
574C4×Q8—21no—
575C4×Q8—432no—
576C4×Q8—432no—
577C4×Q8—861no—
578C4×Q8—861no—
579C4×Q8C22×D4314yes—
580C4×Q8C22×D4312yes—
581C4×Q8C22×D4312yes—
582C4×D4—24no—
583C4×D4—24no—
584C4×D4—24no—
585C4×D4—24no—
586C4×D4—22no—
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—432no—
590C4×D4—432no—
591C4×D4—862no—
592C4×D4—862no—
593C4×D4—862no—
594C4×D4—862no—
595C4×D4—861no—
596C4×D4—861no—
597C4×D4C22×D4314yes—
598C4×D4C22×D4312yes—
599C4×D4C22×D4312yes—
600#117—24no—
601#117—24no—
602#117—432no—
603#117—862no—
604#117C22⋊D4312yes—
605#117C22⋊D4312yes—
606#117C22×D4312yes—
607#117C22×D4312yes—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—24no—
613C2×C4⋊C4—24no—
614C2×C4⋊C4C22⋊D4311yescharacteristic
615C2×C4⋊C4C22⋊D4311yescharacteristic
616C2×C4⋊C4C22×D4311yescharacteristic
617C2×C4⋊C4C22×D4311yescharacteristic
618C2×C4⋊C4C22×D4314yes—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4C22⋊D4311yescharacteristic
622C2×C22⋊C4C22⋊D4311yescharacteristic
623C2×C42—21no—
624C2×C42—21no—
625C2×C42—862no—
626C2×C42C22×D4311yescharacteristic
627C2×C42C22×D4311yescharacteristic
628#107—434no—
629#107—434no—
630#106—434no—
631#106—434no—
632C4⋊C8—432no—
633C4⋊C8—432no—
634C4⋊C8—432no—
635C4⋊C8—432no—
636#103—434no—
637#103—434no—
638#103—434no—
639#103—434no—
640#102—434no—
641#102—434no—
642#102—434no—
643#102—434no—
644C22⋊C8—434no—
645C22⋊C8—434no—
646#97—434no—
647C4×C8—434no—
648C24—21no—
649C24C2×C22⋊D4311yescharacteristic
650#41—216no—
651#41—28no—
652#41—28no—
653#41—864no—
654#41—864no—
655C2×Q8—21no—
656C2×Q8—22no—
657C2×Q8—432no—
658C2×Q8—861no—
659C2×Q8—861no—
660C2×Q8#1062189814yes—
661C2×Q8C23×D4312yes—
662C2×D4—28no—
663C2×D4—24no—
664C2×D4—21no—
665C2×D4—22no—
666C2×D4—432no—
667C2×D4—862no—
668C2×D4—862no—
669C2×D4—862no—
670C2×D4—861no—
671C2×D4—861no—
672C2×D4#1062189814yes—
673C2×D4C23×D4312yes—
674C22×C4—28no—
675C22×C4—21no—
676C22×C4—24no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—24no—
682C22×C4—24no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—82no—
686C22×C4—82no—
687C22×C4—82no—
688C22×C4—862no—
689C22×C4—862no—
690C22×C4—862no—
691C22×C4C2×C22⋊D4311yescharacteristic
692C22×C4C2×C22⋊D4312yes—
693C22×C4C2×C22⋊D4311yescharacteristic
694C22×C4C2×C22⋊D4311yescharacteristic
695C22×C4C2×C22⋊D4311yescharacteristic
696C22×C4C2×C22⋊D4311yescharacteristic
697C22×C4C23×D4312yes—
698C22×C4C23×D4311yescharacteristic
699Q16—868no—
700SD16—868no—
701SD16—868no—
702D8—868no—
703M16—864no—
704M16—864no—
705C2×C8—434no—
706C2×C8—434no—
707C4⋊C4—24no—
708C4⋊C4—24no—
709C4⋊C4—22no—
710C4⋊C4—22no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—432no—
714C4⋊C4—432no—
715C4⋊C4—862no—
716C4⋊C4—862no—
717C4⋊C4—861no—
718C4⋊C4—861no—
719C4⋊C4—862no—
720C4⋊C4—862no—
721C4⋊C4—862no—
722C4⋊C4—862no—
723C4⋊C4—861no—
724C4⋊C4—861no—
725C4⋊C4C2×C22⋊D4312yes—
726C4⋊C4C2×C22⋊D4312yes—
727C4⋊C4C2×C22⋊D4312yes—
728C4⋊C4C2×C22⋊D4312yes—
729C4⋊C4C23×D4312yes—
730C4⋊C4C23×D4312yes—
731C22⋊C4—24no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—862no—
735C22⋊C4—862no—
736C22⋊C4—862no—
737C22⋊C4—862no—
738C22⋊C4—862no—
739C22⋊C4—862no—
740C22⋊C4—862no—
741C22⋊C4—862no—
742C22⋊C4—862no—
743C22⋊C4C2×C22⋊D4312yes—
744C22⋊C4C2×C22⋊D4312yes—
745C22⋊C4C2×C22⋊D4312yes—
746C22⋊C4C2×C22⋊D4312yes—
747C42—24no—
748C42—22no—
749C42—22no—
750C42—862no—
751C42—862no—
752C42—862no—
753C42C2×C22⋊D4312yes—
754C42C2×C22⋊D4311yescharacteristic
755C42C2×C22⋊D4311yescharacteristic
756C42C23×D4312yes—
757C42C23×D4311yescharacteristic
758C42C23×D4311yescharacteristic
759C23—22no—
760C23—24no—
761C23—22no—
762C23—41no—
763C23—41no—
764C23—42no—
765C23—42no—
766C23—862no—
767C23C22×C22⋊D4312yes—
768C23C22×C22⋊D4311yescharacteristic
769Q8—24no—
770Q8—22no—
771Q8—862no—
772Q8—862no—
773Q8—3441no—
774Q8—3441no—
775Q8C2×#1062189814yes—
776D4—216no—
777D4—24no—
778D4—22no—
779D4—862no—
780D4—862no—
781D4—3441no—
782D4—3441no—
783D4—3442no—
784D4—3442no—
785D4—1724no—
786D4C2×#1062189814yes—
787C2×C4—216no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—22no—
791C2×C4—24no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—84no—
803C2×C4—82no—
804C2×C4—82no—
805C2×C4—84no—
806C2×C4—862no—
807C2×C4—862no—
808C2×C4—862no—
809C2×C4—3442no—
810C2×C4—3442no—
811C2×C4—1724no—
812C2×C4C22×C22⋊D4312yes—
813C2×C4C22×C22⋊D4311yescharacteristic
814C2×C4C22×C22⋊D4311yescharacteristic
815C2×C4C22×C22⋊D4312yes—
816C2×C4C22×C22⋊D4311yescharacteristic
817C2×C4C22×C22⋊D4311yescharacteristic
818C2×C4C22×C22⋊D4312yes—
819C2×C4C22×C22⋊D4311yescharacteristic
820C2×C4C2×#1062189812yes—
821C2×C4C2×#1062189812yes—
822C2×C4C24×D4311yescharacteristic
823C8—864no—
824C8—864no—
825C22—21no—
826C22—21no—
827C22—22no—
828C22—24no—
829C22—22no—
830C22—22no—
831C22—44no—
832C22—48no—
833C22—42no—
834C22—42no—
835C22—1722no—
836C22—1722no—
837C22—1722no—
838C22#1458341012yes—
839C22C23×C22⋊D4311yescharacteristic
840C4—22no—
841C4—24no—
842C4—22no—
843C4—21no—
844C4—21no—
845C4—22no—
846C4—21no—
847C4—21no—
848C4—42no—
849C4—42no—
850C4—1722no—
851C4—1722no—
852C4—1722no—
853C4#1458341012yes—
854C4C22×#1062189811yescharacteristic
855C4C22×#1062189811yescharacteristic
856C2—22no—
857C2—42no—
858C2—44no—
859C2—3442no—
860C2C2×#1458341011yescharacteristic
861C2#1914937511yescharacteristic
862C2#1914938211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#520C2
socleC22×C43C23×D4
hypercenterC2×#520D43
hypocenterC43#60565
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #19147985C2semidirect
2. #19144872C2semidirect
3. #19144857C2semidirect
4. #19144809C2semidirect
5. #19144794C2semidirect
6. #19144518C2semidirect
7. #19144400C2semidirect
8. #19144392C2semidirect
9. #19144067C2semidirect
10. #19144059C2semidirect
11. #19143837C2semidirect
12. C4×#13063356C2semidirect
13. C4×#13063351C2semidirect
14. #19143233C2semidirect
15. C2×C43×#520C2semidirect
18. #14583520C22semidirect
19. #14583520C22semidirect
20. #14583511C22semidirect
21. #14583504C22semidirect
32. #14583234C22semidirect
33. #14583229C22semidirect
34. #14583217C22semidirect
35. #14583212C22semidirect
36. #14583206C22semidirect
37. #14583199C22semidirect
38. #14583194C22semidirect
39. #14583189C22semidirect
40. #14583184C22semidirect
41. #14583179C22semidirect
42. #14583121C22semidirect
43. #14583114C22semidirect
44. #14583109C22semidirect
45. #14583104C22semidirect
46. #14583099C22semidirect
47. #14583094C22semidirect
52. #14583009C22semidirect
53. #14583004C22semidirect
54. #14582999C22semidirect
55. #14582997C22semidirect
56. C4×#10621885C22semidirect
57. C4×#10621884C22semidirect
58. C4×#10621883C22semidirect
59. C4×#10621882C22semidirect
60. #14582960C22semidirect
61. #14582960C22semidirect
426. C2×#520D43semidirect
518. C43#60565semidirect

Maximal subgroups

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

subgroupindex
#191479852
#191448722
#191448572
#191448092
#191447942
#191445182
#191444002
#191443922
#191440672
#191440592
#191438372
C4×#130633562
C4×#130633512
#191432332
C2×C43×#5202
#6056543