Finite Group Databasebeta

← #25102522

Subgroups — #25102522

Order 11008.

1422 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
1C4×#13063371C211yesmaximal, characteristic
2C2×#14583075C211yesmaximal, characteristic
3C4×#13063356C211yesmaximal, characteristic, complemented
4#19137302C211yesmaximal, characteristic, complemented
5#19134980C211yesmaximal, characteristic, complemented
6#19134966C211yesmaximal, characteristic, complemented
7#19134961C211yesmaximal, characteristic, complemented
8#19134819C211yesmaximal, characteristic, complemented
9#19134818C211yesmaximal, characteristic, complemented
10#19134803C211yesmaximal, characteristic, complemented
11#19134547C211yesmaximal, characteristic
12#19134408C211yesmaximal, characteristic, complemented
13#19134405C211yesmaximal, characteristic, complemented
14C4×#13063241C211yesmaximal, characteristic, complemented
15C4×#137×C43C211yesmaximal, characteristic, complemented
16C2×#13063371C2211yescharacteristic
17C2×#13063356C2211yescharacteristic
18C2×#13063314C2211yescharacteristic
19#14583382C2211yescharacteristic
20#14583381—21no—
21#14583379—21no—
22#14583379C2211yescharacteristic
23#14583373—21no—
24#14583373C2211yescharacteristic
25#14583371—22no—
26#14583371—21no—
27C4×#10621902—21no—
28C4×#10621898—21no—
29C4×#10621898C2211yescharacteristic
30C2×C4×D172—21no—
31C2×C4×D172C2211yescharacteristic
32C4×D4×D43—22no—
33C4×D4×D43—21no—
34#14583075C418yescomplemented
35#14583004—21no—
36#14582997—21no—
37C4×#10621885—21no—
38C4×#10621884—21no—
39#14582939C2211yescharacteristic, complemented
40C2×#13063252C2211yescharacteristic
41C2×#13063252C2211yescharacteristic
42C2×#13063251C2211yescharacteristic
43C2×#13063251C2211yescharacteristic
44#14582908C2211yescharacteristic, complemented
45#14582898C2211yescharacteristic
46C2×#13063241C2211yescharacteristic
47C2×#13063241C2211yescharacteristic
48C4×#10621877C2211yescharacteristic, complemented
49#14582806C2211yescharacteristic, complemented
50#14582800C2211yescharacteristic
51#14582790—22no—
52#14582770—22no—
53#14582768C2211yescharacteristic, complemented
54#14582745C2211yescharacteristic, complemented
55#14582667C2211yescharacteristic, complemented
56#14582667C2211yescharacteristic, complemented
57#14582660C2211yescharacteristic, complemented
58#14582660C2211yescharacteristic, complemented
59#14582658C2211yescharacteristic, complemented
60#14582658C2211yescharacteristic, complemented
61C2×#137×C43C2211yescharacteristic
62C4×#41×C43C2211yescharacteristic
63C2×C4×Q8×C43C2211yescharacteristic, complemented
64C43×#441—21no—
65C43×#440—21no—
66C4×Q16×C43—21no—
67C4×SD16×C43—21no—
68C43×#428C2211yescharacteristic, complemented
69C43×#419C2211yescharacteristic, complemented
70C43×#417C2211yescharacteristic
71C4×M16×C43C2211yescharacteristic, complemented
72#13063371—22no—
73#13063371—22no—
74#13063371—22no—
75#13063371C2×C414yes—
76C2×#10621902—21no—
77C2×#10621898—21no—
78C2×#10621898C2311yescharacteristic
79C22×D172—21no—
80C22×D172C2311yescharacteristic
81C2×D4×D43—22no—
82C2×D4×D43—21no—
83C22×C4×D43—22no—
84C22×C4×D43D412yes—
85#13063356—22no—
86#13063356C2×C414yescomplemented
87C2×#10621885—21no—
88C2×#10621884—21no—
89C2×#10621877C2311yescharacteristic
90C2×#10621877C2311yescharacteristic
91#13063314—22no—
92#13063314C2×C414yescomplemented
93Q8×Dic43—21no—
94C4×Dic86—21no—
95C4×Dic86D411yescharacteristic
96C4×Dic86D411yescharacteristic
97C4×D172—22no—
98C4×D172—22no—
99C4×D172—21no—
100C4×D172—21no—
101C4×D172—21no—
102C4×D172—21no—
103C4×D172—21no—
104C4×D172—21no—
105C4×D172—21no—
106C4×D172D411yescharacteristic
107C4×D172D411yescharacteristic
108D4×Dic43—21no—
109D4×Dic43—22no—
110#13063287—22no—
111#13063287—22no—
112#13063287—21no—
113#13063287—21no—
114C4×C22⋊D43—22no—
115C4×C22⋊D43—22no—
116C4×C22⋊D43—21no—
117C4×C22⋊D43—21no—
118(C22⋊D43)⋊C4—22no—
119(C22⋊D43)⋊C4—22no—
120(C22⋊D43)⋊C4—22no—
121#13063284—21no—
122#13063284C2311yescharacteristic
123#13063283—22no—
124#13063283—21no—
125#13063282—22no—
126#13063282—21no—
127C2×C4⋊Dic43—21no—
128C2×C4⋊Dic43C2311yescharacteristic
129C2×Dic43⋊C4—22no—
130C4⋊C4×D43—22no—
131C4⋊C4×D43—21no—
132C2×(C2×D43)⋊C4—22no—
133C2×(C2×D43)⋊C4—22no—
134C2×(C2×D43)⋊C4—22no—
135C2×(C2×D43)⋊C4D412yes—
136C22⋊C4×D43—22no—
137C22⋊C4×D43—22no—
138C22⋊C4×D43—22no—
139C2×C4×Dic43C2311yescharacteristic
140C2×C4×Dic43C2311yescharacteristic
141C42×D43—22no—
142C42×D43—21no—
143#13063258—21no—
144#13063256—21no—
145#13063252—22no—
146#13063252C2×C414yescomplemented
147#13063251—22no—
148#13063251C2×C414yescomplemented
149#13063249—21no—
150#13063249—21no—
151#13063248—21no—
152#13063245—21no—
153#13063241—22no—
154#13063241C2×C414yescomplemented
155#13063236—21no—
156C4×C43⋊C8—21no—
157C43⋊#95—21no—
158C43⋊#95—21no—
159C43⋊#95—22no—
160C2×#41×C43C2311yescharacteristic
161C22×Q8×C43C2311yescharacteristic
162#137×C43—22no—
163#137×C43C2×C414yescomplemented
164C2×Q16×C43—21no—
165C2×SD16×C43—21no—
166C2×M16×C43C2311yescharacteristic
167C2×M16×C43C2311yescharacteristic
168C4×Q8×C43—21no—
169C4×Q8×C43—21no—
170C4×Q8×C43—21no—
171C4×Q8×C43—21no—
172C4×Q8×C43D411yescharacteristic
173C4×Q8×C43D411yescharacteristic
174C4×D4×C43—21no—
175C4×D4×C43—21no—
176C4×D4×C43D411yescharacteristic
177C4×D4×C43D411yescharacteristic
178#117×C43—21no—
179#117×C43C2311yescharacteristic
180C2×C4⋊C4×C43—21no—
181C2×C4⋊C4×C43C2311yescharacteristic
182C2×C42×C43—21no—
183C2×C42×C43—21no—
184C2×C42×C43C2311yescharacteristic
185#107×C43—21no—
186#106×C43—21no—
187#103×C43—21no—
188#103×C43—21no—
189#103×C43—21no—
190#102×C43—21no—
191#97×C43—21no—
192C4×C8×C43—21no—
193C23×D43—22no—
194C23×D43C2×D412yes—
195#41×C43—21no—
196#41×C43—21no—
197#41×C43C22×C412yes—
198#41×C43#4112yes—
199C2×Q8×C43—21no—
200C2×Q8×C43—21no—
201C2×Q8×C43—21no—
202C2×Q8×C43—21no—
203C2×Q8×C43—21no—
204C2×Q8×C43C22×C412yescomplemented
205C2×Q8×C43C2×D411yescharacteristic
206C2×D4×C43—21no—
207C2×D4×C43C2×D411yescharacteristic
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43C2×D411yescharacteristic
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2411yescharacteristic
216C2×C22⋊D43—22no—
217C2×C22⋊D43—21no—
218C22×Dic43—22no—
219C22×Dic43—21no—
220C22×Dic43—21no—
221C22×Dic43C2×D412yes—
222#10621902—24no—
223#10621902—24no—
224D4×D43—24no—
225D4×D43—28no—
226D4×D43—24no—
227D4×D43—28no—
228#10621898—24no—
229#10621898—21no—
230#10621898—21no—
231#10621898—24no—
232#10621898C22×C412yes—
233#10621898#4112yes—
234C2×D172—22no—
235C2×D172—24no—
236C2×D172—21no—
237C2×D172—21no—
238C2×D172—21no—
239C2×D172—21no—
240C2×D172—24no—
241C2×D172C22×C412yes—
242C2×D172C2×D411yescharacteristic
243C2×D172#4112yes—
244C2×C4×D43—22no—
245C2×C4×D43—21no—
246C2×C4×D43—22no—
247C2×C4×D43—21no—
248C2×C4×D43—22no—
249C2×C4×D43—22no—
250C2×C4×D43—22no—
251C2×C4×D43—21no—
252C2×C4×D43—22no—
253C2×C4×D43—82no—
254C2×C4×D43—84no—
255C2×Dic86C2×D411yescharacteristic
256Q16×C43—24no—
257SD16×C43—24no—
258M16×C43—21no—
259M16×C43—21no—
260M16×C43—21no—
261M16×C43C22×C412yescomplemented
262C2×C8×C43—21no—
263C2×C8×C43—21no—
264C4⋊C4×C43—21no—
265C4⋊C4×C43—21no—
266C4⋊C4×C43—21no—
267C4⋊C4×C43—21no—
268C4⋊C4×C43—41no—
269C4⋊C4×C43—41no—
270C4⋊C4×C43C2×D411yescharacteristic
271C4⋊C4×C43C2×D411yescharacteristic
272C22⋊C4×C43—21no—
273C22⋊C4×C43—21no—
274C22⋊C4×C43—21no—
275C42×C43—21no—
276C42×C43—21no—
277C42×C43—21no—
278C42×C43—41no—
279C42×C43—41no—
280C42×C43C2×D411yescharacteristic
281C42×C43C2×D411yescharacteristic
282C42×C43C2×D411yescharacteristic
283C42×C43C2×D411yescharacteristic
284C22⋊Dic43—22no—
285C22⋊Dic43—21no—
286#10621885—24no—
287#10621884—24no—
288(C2×D43)⋊C4—22no—
289(C2×D43)⋊C4—22no—
290(C2×D43)⋊C4—22no—
291(C2×D43)⋊C4—21no—
292(C2×D43)⋊C4—22no—
293(C2×D43)⋊C4—21no—
294(C2×D43)⋊C4—22no—
295(C2×D43)⋊C4—28no—
296(C2×D43)⋊C4—82no—
297C4⋊Dic43—22no—
298C4⋊Dic43—21no—
299C4⋊Dic43—21no—
300C4⋊Dic43C2×D411yescharacteristic
301C4⋊Dic43C2×D411yescharacteristic
302Dic43⋊C4—22no—
303Dic43⋊C4—21no—
304Dic43⋊C4—21no—
305Dic43⋊C4—82no—
306C4×Dic43—22no—
307C4×Dic43—22no—
308C4×Dic43—21no—
309C4×Dic43—21no—
310C4×Dic43—21no—
311C4×Dic43—21no—
312C4×Dic43—21no—
313C4×Dic43—21no—
314C4×Dic43C22×C412yescomplemented
315#10621877—21no—
316#10621877—21no—
317#10621877—21no—
318#10621877C22×C412yescomplemented
319C2×C43⋊C8—21no—
320C2×C43⋊C8—21no—
321C23×C43—21no—
322C23×C43C22×D411yescharacteristic
323C22×D43—22no—
324C22×D43—21no—
325C22×D43—28no—
326C22×D43—22no—
327C22×D43—42no—
328C22×D43—42no—
329C22×D43—82no—
330C22×D43—82no—
331C22×D43C4×D414yes—
332Q8×C43—21no—
333Q8×C43—22no—
334Q8×C43—22no—
335Q8×C43—41no—
336Q8×C43—41no—
337Q8×C43C4×D412yes—
338D4×C43—22no—
339D4×C43—22no—
340D4×C43—21no—
341D4×C43C4×D412yes—
342C2×C4×C43—21no—
343C2×C4×C43—22no—
344C2×C4×C43—22no—
345C2×C4×C43—22no—
346C2×C4×C43—21no—
347C2×C4×C43—21no—
348C2×C4×C43—41no—
349C2×C4×C43—41no—
350C2×C4×C43—42no—
351C2×C4×C43—41no—
352C2×C4×C43—41no—
353C2×C4×C43—42no—
354C2×C4×C43—41no—
355C2×C4×C43—81no—
356C2×C4×C43#12011yescharacteristic
357C2×C4×C43#12011yescharacteristic
358C2×C4×C43#12011yescharacteristic
359C2×C4×C43#12011yescharacteristic
360C2×C4×C43C23×C411yescharacteristic
361C2×C4×C43C22×D411yescharacteristic
362C2×C4×C43C22×D411yescharacteristic
363C2×C4×C43C2×#4111yescharacteristic
364C2×C4×C43C2×#4111yescharacteristic
365C2×C4×C43C2×#4111yescharacteristic
366C22⋊D43—28no—
367C22⋊D43—22no—
368C22⋊D43—22no—
369C2×Dic43—21no—
370C2×Dic43—22no—
371C2×Dic43—21no—
372C2×Dic43—22no—
373C2×Dic43—21no—
374C2×Dic43—41no—
375C2×Dic43—41no—
376C2×Dic43—42no—
377C2×Dic43—41no—
378C2×Dic43—41no—
379C2×Dic43—41no—
380C2×Dic43—82no—
381D172—28no—
382D172—22no—
383D172—22no—
384D172—21no—
385D172—22no—
386D172—22no—
387D172C4×D412yes—
388C4×D43—28no—
389C4×D43—22no—
390C4×D43—22no—
391C4×D43—44no—
392C4×D43—42no—
393C4×D43—81no—
394C4×D43—82no—
395C4×D43—82no—
396C4×D43—82no—
397C4×D43—82no—
398Dic86—21no—
399Dic86C4×D412yes—
400C8×C43—22no—
401C8×C43—41no—
402C43⋊C8—22no—
403C43⋊C8—41no—
404#21474—431nomaximal, Sylow
405C22×C43—21no—
406C22×C43—21no—
407C22×C43—22no—
408C22×C43—41no—
409C22×C43—41no—
410C22×C43C2×C4×D411yescharacteristic
411C22×C43C2×#12011yescharacteristic
412C22×C43#52511yescharacteristic
413C2×D43—22no—
414C2×D43—24no—
415C2×D43—42no—
416C2×D43—41no—
417C2×D43—42no—
418C2×D43—41no—
419C2×D43—44no—
420C2×D43—82no—
421C2×D43—88no—
422C4×C43—21no—
423C4×C43—21no—
424C4×C43—21no—
425C4×C43—21no—
426C4×C43—22no—
427C4×C43—41no—
428C4×C43—41no—
429C4×C43—42no—
430C4×C43—81no—
431C4×C43C2×C4×D411yescharacteristic
432C4×C43C2×C4×D411yescharacteristic
433C4×C43#52511yescharacteristic
434C4×C43#52511yescharacteristic
435Dic43—22no—
436Dic43—42no—
437Dic43—42no—
438Dic43—41no—
439Dic43—41no—
440Dic43—81no—
441C4×H(5,𝔽2)—431no—
442C2×#455—431no—
443C4×#137—431no—
444C4×#137D4311yescharacteristic, complemented
445#2326—431no—
446#1885—431no—
447#1882—431no—
448#1882—431no—
449#1859—431no—
450#1859—431no—
451#1856—431no—
452#1792—431no—
453#1759—431no—
454#1759—431no—
455C4×#100—431no—
456C2×C43—21no—
457C2×C43—21no—
458C2×C43—42no—
459C2×C43C4×#12011yescharacteristic
460C2×C43#301911yescharacteristic
461C2×C43#302211yescharacteristic
462D43—44no—
463D43—42no—
464C2×H(5,𝔽2)—431no—
465C2×#137—431no—
466C2×#137C2×D4311yescharacteristic
467C2×#124—431no—
468#520—431no—
469#520—431no—
470#520—861no—
471#520—861no—
472#518—431no—
473#518—862no—
474#518—861no—
475#518—861no—
476C4×#41—431no—
477C4×#41—861no—
478C4×#41—861no—
479C4×#41C2×D4311yescharacteristic
480C2×C4×Q8C2×D4311yescharacteristic, complemented
481C2×C4×D4—431no—
482C2×C4×D4—861no—
483C2×C4×D4—862no—
484C2×C4×D4—861no—
485#455—438no—
486#441—21no—
487#441—861no—
488#440—21no—
489#440—861no—
490C4×Q16—21no—
491C4×Q16—861no—
492C4×SD16—21no—
493C4×SD16—861no—
494#428—431no—
495#428C2×D4311yescharacteristic, complemented
496C2×#104—431no—
497C2×#104—431no—
498C2×#104—431no—
499C2×#104—431no—
500#419—431no—
501#419C2×D4311yescharacteristic, complemented
502#417—431no—
503#417C2×D4311yescharacteristic
504C2×#100—431no—
505C2×#100—431no—
506C4×M16—431no—
507C4×M16C2×D4311yescharacteristic, complemented
508#391—431no—
509#390—431no—
510#388—862no—
511#385—862no—
512#384—431no—
513#376—431no—
514#343—431no—
515#343—431no—
516#339—431no—
517#339—431no—
518#339—431no—
519#339—431no—
520C43#2147411yescharacteristic, complemented, Sylow
521H(5,𝔽2)—434no—
522H(5,𝔽2)—862no—
523H(5,𝔽2)—862no—
524H(5,𝔽2)—862no—
525C2×#41—431no—
526C2×#41—861no—
527C2×#41—861no—
528C2×#41C22×D4311yescharacteristic
529C22×Q8C22×D4311yescharacteristic
530C22×D4—431no—
531C22×D4—861no—
532C22×D4—862no—
533C22×D4—861no—
534C23×C4—432no—
535C23×C4—862no—
536#137—22no—
537#137—434no—
538#137—862no—
539#137C4×D4314yescomplemented
540C2×Q16—21no—
541C2×Q16—861no—
542C2×SD16—21no—
543C2×SD16—861no—
544C2×M16—431no—
545C2×M16—431no—
546C2×M16C22×D4311yescharacteristic
547C2×M16C22×D4311yescharacteristic
548#124—434no—
549#124—862no—
550C4×Q8—21no—
551C4×Q8—21no—
552C4×Q8—21no—
553C4×Q8—21no—
554C4×Q8—431no—
555C4×Q8—431no—
556C4×Q8—861no—
557C4×Q8—861no—
558C4×Q8C22⋊D4311yescharacteristic
559C4×Q8C22⋊D4311yescharacteristic
560C4×D4—21no—
561C4×D4—21no—
562C4×D4—431no—
563C4×D4—431no—
564C4×D4—861no—
565C4×D4—861no—
566C4×D4—861no—
567C4×D4—862no—
568C4×D4—862no—
569C4×D4—862no—
570C4×D4—862no—
571C4×D4—862no—
572C4×D4—862no—
573C4×D4—862no—
574C4×D4—862no—
575C4×D4—862no—
576C4×D4—862no—
577C4×D4—861no—
578C4×D4—861no—
579C4×D4—861no—
580C4×D4—861no—
581C4×D4—861no—
582C4×D4—861no—
583C4×D4—861no—
584C4×D4—861no—
585C4×D4—861no—
586C4×D4C22⋊D4311yescharacteristic
587C4×D4C22⋊D4311yescharacteristic
588#117—21no—
589#117—431no—
590#117—862no—
591#117—862no—
592#117—861no—
593#117—861no—
594#117—861no—
595#117C22×D4311yescharacteristic
596C2×C4⋊C4—21no—
597C2×C4⋊C4—431no—
598C2×C4⋊C4—862no—
599C2×C4⋊C4—861no—
600C2×C4⋊C4—861no—
601C2×C4⋊C4—862no—
602C2×C4⋊C4C22×D4311yescharacteristic
603C2×C22⋊C4—432no—
604C2×C22⋊C4—862no—
605C2×C22⋊C4—862no—
606C2×C22⋊C4—862no—
607C2×C22⋊C4—862no—
608C2×C22⋊C4—862no—
609C2×C22⋊C4—862no—
610C2×C42—21no—
611C2×C42—21no—
612C2×C42—431no—
613C2×C42—431no—
614C2×C42—862no—
615C2×C42—861no—
616C2×C42C22×D4311yescharacteristic
617#107—21no—
618#107—861no—
619#106—21no—
620#106—861no—
621#104—434no—
622#104—434no—
623#104—862no—
624#104—862no—
625#103—21no—
626#103—21no—
627#103—21no—
628#103—861no—
629#103—861no—
630#103—861no—
631#102—21no—
632#102—861no—
633#100—434no—
634#100—862no—
635#97—21no—
636#97—861no—
637C4×C8—21no—
638C4×C8—861no—
639#95—862no—
640#95—861no—
641#95—861no—
642C24—432no—
643C24—862no—
644#41—21no—
645#41—21no—
646#41—432no—
647#41—432no—
648#41—864no—
649#41—864no—
650#41—864no—
651#41—864no—
652#41—861no—
653#41—861no—
654#41C2×C4×D4312yes—
655#41#1062189812yes—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—431no—
662C2×Q8C2×C4×D4312yescomplemented
663C2×Q8C2×C22⋊D4311yescharacteristic
664C2×D4—21no—
665C2×D4—432no—
666C2×D4—431no—
667C2×D4—432no—
668C2×D4—864no—
669C2×D4—862no—
670C2×D4—864no—
671C2×D4—868no—
672C2×D4—868no—
673C2×D4—864no—
674C2×D4—862no—
675C2×D4—861no—
676C2×D4—864no—
677C2×D4—861no—
678C2×D4—861no—
679C2×D4—861no—
680C2×D4—861no—
681C2×D4C2×C22⋊D4311yescharacteristic
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—432no—
688C22×C4—862no—
689C22×C4—862no—
690C22×C4—862no—
691C22×C4—862no—
692C22×C4—861no—
693C22×C4—862no—
694C22×C4—861no—
695C22×C4—861no—
696C22×C4—862no—
697C22×C4—861no—
698C22×C4—862no—
699C22×C4—861no—
700C22×C4—3444no—
701C22×C4—3442no—
702C22×C4D4×D4311yescharacteristic
703C22×C4D4×D4311yescharacteristic
704C22×C4C23×D4311yescharacteristic
705Q16—24no—
706Q16—864no—
707SD16—24no—
708SD16—864no—
709M16—21no—
710M16—21no—
711M16—21no—
712M16—432no—
713M16—861no—
714M16—861no—
715M16—861no—
716M16C2×C4×D4312yescomplemented
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—861no—
720C2×C8—861no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—41no—
726C4⋊C4—41no—
727C4⋊C4—431no—
728C4⋊C4—431no—
729C4⋊C4—862no—
730C4⋊C4—862no—
731C4⋊C4—861no—
732C4⋊C4—861no—
733C4⋊C4—861no—
734C4⋊C4—861no—
735C4⋊C4—3442no—
736C4⋊C4C2×C22⋊D4311yescharacteristic
737C4⋊C4C2×C22⋊D4311yescharacteristic
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—868no—
742C22⋊C4—862no—
743C22⋊C4—862no—
744C22⋊C4—862no—
745C22⋊C4—862no—
746C22⋊C4—861no—
747C22⋊C4—862no—
748C22⋊C4—862no—
749C22⋊C4—861no—
750C22⋊C4—861no—
751C22⋊C4—3442no—
752C42—21no—
753C42—21no—
754C42—21no—
755C42—41no—
756C42—41no—
757C42—432no—
758C42—862no—
759C42—862no—
760C42—861no—
761C42—861no—
762C42—861no—
763C42—861no—
764C42—861no—
765C42—861no—
766C42D4×D4311yescharacteristic
767C42D4×D4311yescharacteristic
768C42C2×C22⋊D4311yescharacteristic
769C42C2×C22⋊D4311yescharacteristic
770C23—21no—
771C23—434no—
772C23—868no—
773C23—862no—
774C23—861no—
775C23—862no—
776C23—3442no—
777C23—3442no—
778C23—1722no—
779C23—1722no—
780C23C2×D4×D4311yescharacteristic
781Q8—21no—
782Q8—22no—
783Q8—22no—
784Q8—41no—
785Q8—41no—
786Q8—432no—
787Q8—861no—
788Q8C4×C22⋊D4312yes—
789D4—22no—
790D4—22no—
791D4—21no—
792D4—432no—
793D4—868no—
794D4—868no—
795D4—862no—
796D4—862no—
797D4—862no—
798D4—862no—
799D4—862no—
800D4—861no—
801D4—862no—
802D4C4×C22⋊D4312yes—
803C2×C4—21no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—41no—
816C2×C4—81no—
817C2×C4—868no—
818C2×C4—861no—
819C2×C4—862no—
820C2×C4—862no—
821C2×C4—862no—
822C2×C4—861no—
823C2×C4—861no—
824C2×C4—862no—
825C2×C4—3442no—
826C2×C4—3441no—
827C2×C4—3442no—
828C2×C4—3442no—
829C2×C4—3442no—
830C2×C4—3442no—
831C2×C4—1722no—
832C2×C4—1724no—
833C2×C4—1721no—
834C2×C4—1721no—
835C2×C4—1721no—
836C2×C4—1721no—
837C2×C4—1721no—
838C2×C4—1722no—
839C2×C4#1306329311yescharacteristic
840C2×C4#1306329311yescharacteristic
841C2×C4#1306329311yescharacteristic
842C2×C4#1306329311yescharacteristic
843C2×C4C22×C4×D4311yescharacteristic
844C2×C4C2×D4×D4311yescharacteristic
845C2×C4C22×C22⋊D4311yescharacteristic
846C2×C4#41×D4311yescharacteristic
847C2×C4#41×D4311yescharacteristic
848C2×C4C2×#1062189811yescharacteristic
849C8—22no—
850C8—41no—
851C8—862no—
852C8—1721no—
853C22—21no—
854C22—21no—
855C22—22no—
856C22—41no—
857C22—41no—
858C22—862no—
859C22—864no—
860C22—3442no—
861C22—3448no—
862C22—1724no—
863C22—1721no—
864C22—1722no—
865C22—1721no—
866C22—1722no—
867C22C4×D4×D4311yescharacteristic
868C22C2×#1306329311yescharacteristic
869C22#1458340811yescharacteristic
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—22no—
875C4—41no—
876C4—41no—
877C4—42no—
878C4—81no—
879C4—862no—
880C4—3441no—
881C4—1722no—
882C4—1721no—
883C4—1722no—
884C4—1721no—
885C4C4×D4×D4311yescharacteristic
886C4C2×C4×C22⋊D4311yescharacteristic
887C4#1458340611yescharacteristic
888C4#1458340811yescharacteristic
889C2—21no—
890C2—21no—
891C2—42no—
892C2—1722no—
893C2—1724no—
894C2C4×#1306329311yescharacteristic
895C2#1914395011yescharacteristic
896C2#1914397111yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#137×C43C2
socleC22×C43C2×#120
prime radicalC2×#13063371C22
cosocleC22×C4×C43C24
hypercenterC4×#137D43
hypocenterC43#21474
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#137

Complements

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

NH ≅ G/Ntype
3. C4×#13063356C2semidirect
4. #19137302C2semidirect
5. #19134980C2semidirect
6. #19134966C2semidirect
7. #19134961C2semidirect
8. #19134819C2semidirect
9. #19134818C2semidirect
10. #19134803C2semidirect
12. #19134408C2semidirect
13. #19134405C2semidirect
14. C4×#13063241C2semidirect
15. C4×#137×C43C2semidirect
34. #14583075C4semidirect
39. #14582939C22semidirect
44. #14582908C22semidirect
48. C4×#10621877C22semidirect
49. #14582806C22semidirect
53. #14582768C22semidirect
54. #14582745C22semidirect
55. #14582667C22semidirect
56. #14582667C22semidirect
57. #14582660C22semidirect
58. #14582660C22semidirect
59. #14582658C22semidirect
60. #14582658C22semidirect
63. C2×C4×Q8×C43C22semidirect
68. C43×#428C22semidirect
69. C43×#419C22semidirect
71. C4×M16×C43C22semidirect
86. #13063356C2×C4semidirect
92. #13063314C2×C4semidirect
146. #13063252C2×C4semidirect
148. #13063251C2×C4semidirect
154. #13063241C2×C4semidirect
163. #137×C43C2×C4semidirect
204. C2×Q8×C43C22×C4semidirect
261. M16×C43C22×C4semidirect
314. C4×Dic43C22×C4semidirect
318. #10621877C22×C4semidirect
444. C4×#137D43semidirect
480. C2×C4×Q8C2×D43semidirect
495. #428C2×D43semidirect
501. #419C2×D43semidirect
507. C4×M16C2×D43semidirect
520. C43#21474semidirect
539. #137C4×D43semidirect
662. C2×Q8C2×C4×D43semidirect
716. M16C2×C4×D43semidirect

Maximal subgroups

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

subgroupindex
C4×#130633712
C2×#145830752
C4×#130633562
#191373022
#191349802
#191349662
#191349612
#191348192
#191348182
#191348032
#191345472
#191344082
#191344052
C4×#130632412
C4×#137×C432
#2147443