Finite Group Databasebeta

← #25107786

Subgroups — #25107786

Order 11008.

1096 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583041C211yesmaximal, characteristic
2C4×#13063296C211yesmaximal, characteristic, complemented
3#19137082C211yesmaximal, characteristic, complemented
4#19135462C211yesmaximal, characteristic, complemented
5#19135450C211yesmaximal, characteristic, complemented
6#19135275C211yesmaximal, characteristic, complemented
7#19135269C211yesmaximal, characteristic, complemented
8#19135237C211yesmaximal, characteristic, complemented
9#19135219C211yesmaximal, characteristic, complemented
10#19134929C211yesmaximal, characteristic, complemented
11#19134914C211yesmaximal, characteristic, complemented
12#19134797C211yesmaximal, characteristic, complemented
13#19134532C211yesmaximal, characteristic, complemented
14#19134352C211yesmaximal, characteristic, complemented
15C43×#1879C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C2×#13063296C2211yescharacteristic
19C2×C4×C22⋊D43—21no—
20C2×#13063283C2211yescharacteristic
21C2×C42×D43C2211yescharacteristic
22#14583041C418yescomplemented
23C2×#13063259C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32C2×(C2×D43)⋊C8C2211yescharacteristic
33C2×C8×Dic43C2211yescharacteristic
34C2×C8×Dic43C2211yescharacteristic
35#14582805C2211yescharacteristic
36#14582804C2211yescharacteristic
37#14582802C2211yescharacteristic
38#14582802C2211yescharacteristic
39#14582795C2211yescharacteristic
40#14582787—21no—
41#14582775—21no—
42#14582775—21no—
43#14582775—21no—
44#14582756C2211yescharacteristic
45C4×C4⋊Dic43C2211yescharacteristic
46C22⋊C4×Dic43—21no—
47C22⋊C4×Dic43—21no—
48C4×C22⋊Dic43—21no—
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582654C2211yescharacteristic
53C22×D8×C43C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C43×#390C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C2×#10621900—22no—
61C2×#10621900—41no—
62C2×#10621900—41no—
63C2×#10621900—41no—
64C2×#10621900—41no—
65C2×#10621900C2×C414yescomplemented
66C22×Dic86C2311yescharacteristic
67C22×C22⋊D43—21no—
68C22×C22⋊D43—21no—
69C23×Dic43—21no—
70C22×C4×D43D411yescharacteristic
71C22×C4×D43D411yescharacteristic
72C22×C4×D43C2311yescharacteristic
73C2×#10621883—41no—
74C2×#10621883—41no—
75C2×#10621883C2×C414yescomplemented
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78#13063296—22no—
79#13063296C2×C414yes—
80C4×C22⋊D43—44no—
81#13063283—41no—
82#13063283—41no—
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×Dic43⋊C4—21no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43D411yescharacteristic
97C2×C4×Dic43D411yescharacteristic
98C2×C4×Dic43C2311yescharacteristic
99C42×D43—41no—
100C42×D43—41no—
101#13063259—41no—
102#13063256—41no—
103#13063250—41no—
104#13063250C2×C414yescomplemented
105#13063248—41no—
106#13063246—41no—
107#13063246—41no—
108#13063246C2×C414yescomplemented
109(C2×D43)⋊C8—22no—
110(C2×D43)⋊C8C2×C414yescomplemented
111C8×Dic43—41no—
112C8×Dic43—41no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C22×D4×C43C2311yescharacteristic
121C22×D4×C43C2311yescharacteristic
122C23×C4×C43—21no—
123C2×D8×C43—41no—
124C2×D8×C43—41no—
125C2×D8×C43C2×C414yescomplemented
126C22×C8×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C4×D4×C43—41no—
129C4×D4×C43—41no—
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C22⋊C4×C43—21no—
133C2×C22⋊C4×C43—21no—
134C2×C22⋊C4×C43—21no—
135C2×C42×C43C2311yescharacteristic
136#102×C43—41no—
137#102×C43—41no—
138C24×C43—21no—
139C24×C43—21no—
140C23×D43C2×D411yescharacteristic
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43C22×C412yes—
152C2×D4×C43C22×C412yes—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—42no—
156C22×C4×C43—42no—
157C22×C4×C43—42no—
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2411yescharacteristic
161C2×C22⋊D43—24no—
162C2×C22⋊D43—24no—
163C2×C22⋊D43—42no—
164C2×C22⋊D43—42no—
165C2×C22⋊D43—42no—
166C2×C22⋊D43—42no—
167C22×Dic43—24no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43—42no—
173C22×Dic43—42no—
174C22×Dic43C2×D411yescharacteristic
175C22×Dic43C2×D411yescharacteristic
176C22×Dic43C2×D411yescharacteristic
177#10621900—44no—
178#10621900—44no—
179#10621900—44no—
180#10621900—44no—
181C2×C4×D43—21no—
182C2×C4×D43—21no—
183C2×C4×D43—21no—
184C2×C4×D43—21no—
185C2×C4×D43—22no—
186C2×C4×D43—22no—
187C2×C4×D43—22no—
188C2×C4×D43—41no—
189C2×C4×D43—41no—
190C2×C4×D43—41no—
191C2×C4×D43C22×C412yes—
192C2×C4×D43#4112yes—
193C2×Dic86—21no—
194C2×Dic86—21no—
195C2×Dic86—21no—
196C2×Dic86—21no—
197C2×Dic86—21no—
198C2×Dic86C22×C412yes—
199D8×C43—44no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43C22×C412yes—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C22⋊C4×C43—42no—
211C22⋊C4×C43—42no—
212C22⋊C4×C43—42no—
213C42×C43—21no—
214C42×C43—21no—
215C22⋊Dic43—24no—
216C22⋊Dic43—42no—
217C22⋊Dic43—42no—
218C22⋊Dic43—42no—
219C22⋊Dic43—42no—
220#10621883—44no—
221(C2×D43)⋊C4—42no—
222(C2×D43)⋊C4—42no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43C22×C412yes—
229Dic43⋊C4—42no—
230C4×Dic43—21no—
231C4×Dic43—21no—
232C4×Dic43—41no—
233C4×Dic43—41no—
234C4×Dic43—42no—
235C4×Dic43—42no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8C22×C412yes—
242C23×C43—22no—
243C23×C43—22no—
244C23×C43—41no—
245C23×C43—41no—
246C23×C43—41no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43C22×D411yescharacteristic
257C22×D43—21no—
258C22×D43—21no—
259C22×D43—21no—
260C22×D43—21no—
261C22×D43—21no—
262C22×D43—21no—
263C22×D43C4×D412yes—
264D4×C43—22no—
265D4×C43—22no—
266D4×C43—22no—
267D4×C43—22no—
268D4×C43—41no—
269D4×C43—41no—
270D4×C43—41no—
271D4×C43—41no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—84no—
284C2×C4×C43#13512yes—
285C2×C4×C43C23×C411yescharacteristic
286C2×C4×C43C2×#4111yescharacteristic
287C2×C4×C43H(5,𝔽2)11yescharacteristic
288C2×C4×C43H(5,𝔽2)11yescharacteristic
289C2×C4×C43H(5,𝔽2)11yescharacteristic
290C2×C4×C43H(5,𝔽2)11yescharacteristic
291C22⋊D43—48no—
292C22⋊D43—48no—
293C2×Dic43—21no—
294C2×Dic43—21no—
295C2×Dic43—21no—
296C2×Dic43—21no—
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—48no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43C4×D412yes—
313C2×Dic43#13512yes—
314C2×Dic43AGL(1,ℤ/8)12yes—
315C4×D43—22no—
316C4×D43—22no—
317C4×D43—22no—
318C4×D43—22no—
319C4×D43—44no—
320C4×D43—44no—
321Dic86—22no—
322Dic86—22no—
323Dic86—41no—
324Dic86—41no—
325C8×C43—22no—
326C8×C43—41no—
327C43⋊C8—22no—
328C43⋊C8—41no—
329#22045—431nomaximal, Sylow
330C22×C43—42no—
331C22×C43—42no—
332C22×C43—42no—
333C22×C43—42no—
334C22×C43—42no—
335C22×C43—42no—
336C22×C43—81no—
337C22×C43—81no—
338C22×C43—81no—
339C22×C43—81no—
340C22×C43—81no—
341C22×C43—81no—
342C22×C43—81no—
343C22×C43—81no—
344C22×C43C2×C4×D411yescharacteristic
345C22×C43#53411yescharacteristic
346C22×C43#53511yescharacteristic
347C22×C43C2×#13511yescharacteristic
348C22×C43C2×#13511yescharacteristic
349C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
350C22×C43#57511yescharacteristic
351C2×D43—22no—
352C2×D43—22no—
353C2×D43—22no—
354C2×D43—41no—
355C2×D43—41no—
356C2×D43—41no—
357C2×D43—41no—
358C4×C43—22no—
359C4×C43—41no—
360C4×C43—81no—
361C4×C43—81no—
362C4×C43#51811yescharacteristic
363C4×C43#51811yescharacteristic
364C4×C43#53811yescharacteristic
365C4×C43#53811yescharacteristic
366Dic43—22no—
367Dic43—22no—
368Dic43—22no—
369Dic43—42no—
370Dic43—42no—
371Dic43—81no—
372Dic43—81no—
373C2×#449—431no—
374C4×#121—431no—
375#2297—431no—
376#1970—431no—
377#1968—431no—
378#1934—431no—
379#1933—431no—
380#1928—431no—
381#1926—431no—
382#1879D4311yescharacteristic, complemented
383#1877—431no—
384#1875—431no—
385#1854—431no—
386#1788—431no—
387C4×C22⋊C8—431no—
388C2×C43—82no—
389C2×C43—82no—
390C2×C43#232111yescharacteristic
391C2×C43C4×#13511yescharacteristic
392C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
393C2×C43#318811yescharacteristic
394C2×C43#319111yescharacteristic
395C2×C43#320711yescharacteristic
396C2×C43#321211yescharacteristic
397D43—42no—
398C22×#41—431no—
399C22×SD16—431no—
400C22×D8C2×D4311yescharacteristic
401C2×#121—431no—
402C2×C4×D4—861no—
403C2×C4×D4C2×D4311yescharacteristic
404C2×#117—431no—
405C22×C42—431no—
406#449—438no—
407C2×#107—431no—
408C2×#106—431no—
409C2×#103—431no—
410C2×#103—431no—
411C2×#103—431no—
412C2×#102—431no—
413C2×#102—431no—
414C2×#102—431no—
415C2×#102C2×D4311yescharacteristic
416C2×#102C2×D4311yescharacteristic
417C2×C22⋊C8—431no—
418C2×C22⋊C8—431no—
419C2×C4×C8—431no—
420C2×C4×C8—431no—
421#391—431no—
422#391—431no—
423#390—431no—
424#390—431no—
425#390C2×D4311yescharacteristic
426#389—431no—
427#388—861no—
428#386—861no—
429#386—861no—
430#386—861no—
431#380—431no—
432C4×C4⋊C4—431no—
433C4×C22⋊C4—861no—
434C4×C22⋊C4—861no—
435C4×C22⋊C4—861no—
436#340—431no—
437#340—431no—
438#340—431no—
439#340C2×D4311yescharacteristic
440#336—431no—
441#336C2×D4311yescharacteristic
442C43#2204511yescharacteristic, complemented, Sylow
443C2×#41—434no—
444C2×#41—862no—
445C2×#41—1721no—
446C2×#41—1721no—
447C2×#41—1721no—
448C2×#41—1721no—
449C22×Q8—431no—
450C22×D4—861no—
451C22×D4—861no—
452C22×D4C22×D4311yescharacteristic
453C22×D4C22×D4311yescharacteristic
454C23×C4—21no—
455C23×C4—431no—
456C23×C4—431no—
457C23×C4—431no—
458C23×C4—861no—
459C2×SD16—434no—
460C2×SD16—1721no—
461C2×SD16—1721no—
462C2×D8—41no—
463C2×D8—41no—
464C2×D8C4×D4314yescomplemented
465C22×C8—431no—
466C22×C8—431no—
467C22×C8C22×D4311yescharacteristic
468C22×C8C22×D4311yescharacteristic
469#121—434no—
470#121—862no—
471C4×D4—41no—
472C4×D4—41no—
473C4×D4—1724no—
474#117—1721no—
475#117—1721no—
476C2×C4⋊C4—431no—
477C2×C4⋊C4—431no—
478C2×C4⋊C4—431no—
479C2×C4⋊C4—861no—
480C2×C4⋊C4C22×D4311yescharacteristic
481C2×C4⋊C4C22×D4311yescharacteristic
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—861no—
486C2×C22⋊C4—861no—
487C2×C22⋊C4—861no—
488C2×C22⋊C4—861no—
489C2×C22⋊C4—861no—
490C2×C22⋊C4—861no—
491C2×C22⋊C4—861no—
492C2×C42—431no—
493C2×C42—431no—
494C2×C42—431no—
495C2×C42—861no—
496C2×C42—861no—
497C2×C42—1721no—
498C2×C42—1721no—
499C2×C42C22×D4311yescharacteristic
500#107—1721no—
501#106—1721no—
502#103—434no—
503#103—1721no—
504#103—1721no—
505#102—41no—
506#102—41no—
507#102—434no—
508#102—1721no—
509#102—1721no—
510C22⋊C8—434no—
511C22⋊C8—862no—
512C4×C8—1721no—
513C4×C8—1721no—
514#95—861no—
515#95—861no—
516#95—861no—
517#95—861no—
518#95—861no—
519#95—861no—
520#95—861no—
521C24—21no—
522C24—21no—
523C24—431no—
524#41—1724no—
525#41—1724no—
526#41—1724no—
527#41—1724no—
528C2×Q8—432no—
529C2×Q8—861no—
530C2×Q8—861no—
531C2×Q8—861no—
532C2×Q8—861no—
533C2×Q8—861no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—864no—
545C2×D4—864no—
546C2×D4—1722no—
547C2×D4—1722no—
548C2×D4—1722no—
549C2×D4—1722no—
550C2×D4C2×C4×D4312yes—
551C2×D4C2×C4×D4312yes—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—431no—
558C22×C4—431no—
559C22×C4—431no—
560C22×C4—432no—
561C22×C4—432no—
562C22×C4—862no—
563C22×C4—862no—
564C22×C4—864no—
565C22×C4—861no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—861no—
569C22×C4—861no—
570C22×C4—861no—
571C22×C4—862no—
572C22×C4—861no—
573C22×C4—861no—
574C22×C4—1721no—
575C22×C4—1721no—
576C22×C4—1721no—
577C22×C4—1722no—
578C22×C4—1722no—
579C22×C4D4×D4311yescharacteristic
580C22×C4D4×D4311yescharacteristic
581C22×C4C23×D4311yescharacteristic
582SD16—1724no—
583D8—44no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—432no—
590C2×C8—861no—
591C2×C8—861no—
592C2×C8—861no—
593C2×C8—861no—
594C2×C8—861no—
595C2×C8C2×C4×D4312yes—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—432no—
601C4⋊C4—861no—
602C4⋊C4—861no—
603C4⋊C4—861no—
604C4⋊C4—861no—
605C4⋊C4—861no—
606C4⋊C4—1722no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—864no—
611C22⋊C4—1722no—
612C22⋊C4—1722no—
613C22⋊C4—1722no—
614C22⋊C4—1722no—
615C22⋊C4—1722no—
616C22⋊C4—1722no—
617C42—21no—
618C42—21no—
619C42—861no—
620C42—861no—
621C42—1721no—
622C42—1721no—
623C42—1722no—
624C42—1722no—
625C23—22no—
626C23—22no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—432no—
640C23—861no—
641C23—861no—
642C23—861no—
643C23—861no—
644C23—861no—
645C23—861no—
646C23C2×D4×D4311yescharacteristic
647Q8—862no—
648Q8—862no—
649Q8—1721no—
650Q8—1721no—
651D4—22no—
652D4—22no—
653D4—22no—
654D4—22no—
655D4—41no—
656D4—41no—
657D4—41no—
658D4—41no—
659D4—1728no—
660D4—1728no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—84no—
673C2×C4—432no—
674C2×C4—432no—
675C2×C4—432no—
676C2×C4—861no—
677C2×C4—861no—
678C2×C4—861no—
679C2×C4—861no—
680C2×C4—861no—
681C2×C4—861no—
682C2×C4—862no—
683C2×C4—862no—
684C2×C4—862no—
685C2×C4—862no—
686C2×C4—862no—
687C2×C4—862no—
688C2×C4—1724no—
689C2×C4—1724no—
690C2×C4—1728no—
691C2×C4—1721no—
692C2×C4—1721no—
693C2×C4—1721no—
694C2×C4—1721no—
695C2×C4—1721no—
696C2×C4—1721no—
697C2×C4—1721no—
698C2×C4—1721no—
699C2×C4—1721no—
700C2×C4—1721no—
701C2×C4#1306334412yes—
702C2×C4C22×C4×D4311yescharacteristic
703C2×C4#41×D4311yescharacteristic
704C2×C4#1306337011yescharacteristic
705C2×C4#1306337011yescharacteristic
706C2×C4#1306337011yescharacteristic
707C2×C4#1306337111yescharacteristic
708C8—22no—
709C8—41no—
710C8—862no—
711C8—1721no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—862no—
727C22—862no—
728C22—862no—
729C22—1721no—
730C22—1721no—
731C22—1721no—
732C22—1721no—
733C22C4×D4×D4311yescharacteristic
734C22#1458345911yescharacteristic
735C22#1458346511yescharacteristic
736C22#135×D4311yescharacteristic
737C22C2×#1306334411yescharacteristic
738C22AGL(1,ℤ/8)×D4311yescharacteristic
739C22#1458369511yescharacteristic
740C4—22no—
741C4—41no—
742C4—81no—
743C4—81no—
744C4—862no—
745C4—862no—
746C4—862no—
747C4—3441no—
748C4—3441no—
749C4—1722no—
750C4—1722no—
751C4#1458337111yescharacteristic
752C4#1458337211yescharacteristic
753C4#1458348111yescharacteristic
754C4#1458348511yescharacteristic
755C2—82no—
756C2—82no—
757C2—1722no—
758C2#1913725111yescharacteristic
759C2C4×#1306334411yescharacteristic
760C2#1914340611yescharacteristic
761C2#1914535711yescharacteristic
762C2#1914538511yescharacteristic
763C2#1914552711yescharacteristic
764C2#1914556911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1879C2
socleC23×C43C22×D4
prime radicalC2×#14583041C2
cosocleC22×C4×C43C24
hypercenter#1879D43
hypocenterC43#22045
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
2. C4×#13063296C2semidirect
3. #19137082C2semidirect
4. #19135462C2semidirect
5. #19135450C2semidirect
6. #19135275C2semidirect
7. #19135269C2semidirect
8. #19135237C2semidirect
9. #19135219C2semidirect
10. #19134929C2semidirect
11. #19134914C2semidirect
12. #19134797C2semidirect
13. #19134532C2semidirect
14. #19134352C2semidirect
15. C43×#1879C2semidirect
22. #14583041C4semidirect
65. C2×#10621900C2×C4semidirect
75. C2×#10621883C2×C4semidirect
104. #13063250C2×C4semidirect
108. #13063246C2×C4semidirect
110. (C2×D43)⋊C8C2×C4semidirect
125. C2×D8×C43C2×C4semidirect
382. #1879D43semidirect
442. C43#22045semidirect
464. C2×D8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830412
C4×#130632962
#191370822
#191354622
#191354502
#191352752
#191352692
#191352372
#191352192
#191349292
#191349142
#191347972
#191345322
#191343522
C43×#18792
#2204543