Finite Group Databasebeta

← #25107874

Subgroups — #25107874

Order 11008.

1080 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×#14583050C211yesmaximal, characteristic
2#19137273C211yesmaximal, characteristic, complemented
3#19137177C211yesmaximal, characteristic
4#19135477C211yesmaximal, characteristic, complemented
5#19135450C211yesmaximal, characteristic, complemented
6#19135289C211yesmaximal, characteristic, complemented
7#19135275C211yesmaximal, characteristic, complemented
8#19135225C211yesmaximal, characteristic, complemented
9#19135218C211yesmaximal, characteristic, complemented
10#19134947C211yesmaximal, characteristic, complemented
11#19134947C211yesmaximal, characteristic, complemented
12#19134905C211yesmaximal, characteristic, complemented
13#19134792C211yesmaximal, characteristic, complemented
14#19134363C211yesmaximal, characteristic, complemented
15C43×#1786C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C2×#13063304C2211yescharacteristic
19C2×#13063290C2211yescharacteristic, complemented
20C2×#13063284C2211yescharacteristic
21C2×#13063284C2211yescharacteristic
22#14583050C418yescomplemented
23C2×#13063258C2211yescharacteristic, complemented
24C2×#13063256C2211yescharacteristic, complemented
25C2×#13063250C2211yescharacteristic, complemented
26C2×#13063250C2211yescharacteristic, complemented
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C2×#13063235C2211yescharacteristic, complemented
31C2×C8×Dic43C2211yescharacteristic, complemented
32#14582804C2211yescharacteristic, complemented
33#14582802—21no—
34#14582802—21no—
35#14582802C2211yescharacteristic
36#14582802C2211yescharacteristic
37#14582802C2211yescharacteristic
38#14582802C2211yescharacteristic
39#14582796—21no—
40#14582795C2211yescharacteristic, complemented
41#14582793—21no—
42#14582787—21no—
43#14582786—21no—
44#14582755—21no—
45#14582755—21no—
46C4⋊C4×Dic43C2211yescharacteristic, complemented
47#14582662C2211yescharacteristic, complemented
48#14582662C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582653C2211yescharacteristic, complemented
52#14582653C2211yescharacteristic, complemented
53C23×D4×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C43×#380C2211yescharacteristic
60C22×Dic86C2311yescharacteristic
61C2×#10621883—41no—
62C2×#10621883—41no—
63C2×#10621883—41no—
64C2×#10621883—41no—
65C2×#10621883C2×C414yes—
66C2×#10621883C2×C414yes—
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063304—22no—
70#13063304C2×C414yes—
71#13063290—41no—
72#13063290—41no—
73#13063284—41no—
74#13063284—41no—
75#13063284—41no—
76#13063284—41no—
77C2×C4⋊Dic43D411yescharacteristic
78C2×C4⋊Dic43D411yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×C22⋊Dic43—21no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43D411yescharacteristic
96C2×C22⋊Dic43D411yescharacteristic
97C2×C4×Dic43—21no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43C2311yescharacteristic
101C2×C4×Dic43C2311yescharacteristic
102#13063258—41no—
103#13063256—41no—
104#13063250—41no—
105#13063250—41no—
106#13063246C2×C414yes—
107#13063246C2×C414yes—
108C22⋊(C43⋊C8)C2×C414yes—
109#13063235—41no—
110C8×Dic43—41no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C25×C43—21no—
116C22×D4×C43—21no—
117C22×D4×C43—22no—
118C22×D4×C43—41no—
119C22×D4×C43—41no—
120C22×D4×C43—41no—
121C22×D4×C43—41no—
122C22×D4×C43C2×C414yes—
123C22×D4×C43C2311yescharacteristic
124C22×D4×C43C2311yescharacteristic
125C23×C4×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C22⋊C4×C43—21no—
131#102×C43—41no—
132#102×C43—41no—
133#102×C43—41no—
134#102×C43—41no—
135C22⋊C8×C43—22no—
136#95×C43—21no—
137C24×C43—21no—
138C24×C43—21no—
139C24×C43—24no—
140C24×C43—42no—
141C24×C43—42no—
142C24×C43—81no—
143C24×C43—81no—
144C24×C43—81no—
145C24×C43—81no—
146C24×C43C2×D411yescharacteristic
147C2×D4×C43—24no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—44no—
159C2×D4×C43—44no—
160C2×D4×C43—44no—
161C2×D4×C43—44no—
162C2×D4×C43—42no—
163C2×D4×C43—42no—
164C2×D4×C43C22×C412yes—
165C2×D4×C43C22×C412yes—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43C22×C412yes—
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43#4112yes—
175C22×C4×C43C2411yescharacteristic
176C22×Dic43—21no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—21no—
180C22×Dic43C2×D411yescharacteristic
181C22×Dic43C2×D411yescharacteristic
182C22×Dic43C2×D411yescharacteristic
183C22×Dic43C2×D411yescharacteristic
184C2×Dic86—21no—
185C2×Dic86—21no—
186C2×Dic86—21no—
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86C22×C412yes—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C22⋊C4×C43—81no—
201C22⋊Dic43—24no—
202C22⋊Dic43—41no—
203C22⋊Dic43—41no—
204C22⋊Dic43—42no—
205C22⋊Dic43—81no—
206C22⋊Dic43—81no—
207C22⋊Dic43—81no—
208C22⋊Dic43—81no—
209C22⋊Dic43—81no—
210C22⋊Dic43—81no—
211C22⋊Dic43—81no—
212C22⋊Dic43—81no—
213#10621883—44no—
214#10621883—44no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—41no—
221C4⋊Dic43—41no—
222C4⋊Dic43C22×C412yes—
223Dic43⋊C4—24no—
224Dic43⋊C4—42no—
225Dic43⋊C4—81no—
226C4×Dic43—21no—
227C4×Dic43—21no—
228C4×Dic43—21no—
229C4×Dic43—21no—
230C4×Dic43—42no—
231C4×Dic43—42no—
232C4×Dic43—81no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8C22×C412yes—
238C2×C43⋊C8C22×C412yes—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—22no—
246C23×C43—22no—
247C23×C43—48no—
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×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—84no—
261C23×C43—84no—
262C23×C43—84no—
263C23×C43—84no—
264C23×C43—84no—
265C23×C43—84no—
266C23×C43C4×D412yes—
267C23×C43C22×D411yescharacteristic
268D4×C43—22no—
269D4×C43—22no—
270D4×C43—22no—
271D4×C43—22no—
272D4×C43—48no—
273D4×C43—41no—
274D4×C43—41no—
275D4×C43—41no—
276D4×C43—41no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43C4×D412yes—
290C2×C4×C43C23×C411yescharacteristic
291C2×C4×C43C2×#4111yescharacteristic
292C2×C4×C43H(5,𝔽2)11yescharacteristic
293C2×C4×C43H(5,𝔽2)11yescharacteristic
294C2×C4×C43H(5,𝔽2)11yescharacteristic
295C2×C4×C43H(5,𝔽2)11yescharacteristic
296C2×Dic43—22no—
297C2×Dic43—22no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320Dic86—22no—
321Dic86—22no—
322Dic86—41no—
323Dic86—41no—
324C8×C43—41no—
325C8×C43—41no—
326C43⋊C8—22no—
327C43⋊C8—22no—
328#22052—431nomaximal, Sylow
329C22×C43—22no—
330C22×C43—22no—
331C22×C43—22no—
332C22×C43—41no—
333C22×C43—41no—
334C22×C43—41no—
335C22×C43—41no—
336C22×C43—42no—
337C22×C43—42no—
338C22×C43—42no—
339C22×C43—42no—
340C22×C43—42no—
341C22×C43—42no—
342C22×C43—816no—
343C22×C43—81no—
344C22×C43—81no—
345C22×C43—81no—
346C22×C43—81no—
347C22×C43—81no—
348C22×C43—81no—
349C22×C43—81no—
350C22×C43—81no—
351C22×C43C2×C4×D411yescharacteristic
352C22×C43#53411yescharacteristic
353C22×C43#53511yescharacteristic
354C22×C43#57611yescharacteristic
355C22×C43#57711yescharacteristic
356C22×C43#57711yescharacteristic
357C22×C43#57711yescharacteristic
358C4×C43—22no—
359C4×C43—81no—
360C4×C43—81no—
361C4×C43#51811yescharacteristic
362C4×C43#51811yescharacteristic
363C4×C43#53811yescharacteristic
364C4×C43#53811yescharacteristic
365Dic43—42no—
366Dic43—41no—
367Dic43—41no—
368Dic43—41no—
369Dic43—41no—
370Dic43—42no—
371Dic43—81no—
372Dic43—81no—
373C2×#450—431no—
374#2323—431no—
375#2309—431no—
376#1973—431no—
377#1968—431no—
378#1936—431no—
379#1934—431no—
380#1926—431no—
381#1925—431no—
382#1880—431no—
383#1880—431no—
384#1873—431no—
385#1854—431no—
386#1786D4311yescharacteristic
387#1750—431no—
388C2×C43—42no—
389C2×C43—82no—
390C2×C43—82no—
391C2×C43#232111yescharacteristic
392C2×C43#294611yescharacteristic
393C2×C43#294911yescharacteristic
394C2×C43#319811yescharacteristic
395C2×C43#320011yescharacteristic
396C2×C43#322211yescharacteristic
397C2×C43#322411yescharacteristic
398C23×D4C2×D4311yescharacteristic
399C22×SD16—431no—
400C22×SD16—431no—
401C2×C22⋊Q8—431no—
402C2×C4×Q8—431no—
403C2×#117—431no—
404C2×#117—431no—
405#450—438no—
406C2×#107—431no—
407C2×#106—431no—
408C2×#103—431no—
409C2×#103—431no—
410C2×#102—431no—
411C2×#102—431no—
412C2×#102C2×D4311yescharacteristic
413C2×#102C2×D4311yescharacteristic
414C2×#102C2×D4311yescharacteristic
415C2×#102C2×D4311yescharacteristic
416C2×C22⋊C8—431no—
417C2×C22⋊C8C2×D4311yescharacteristic
418C2×#97—431no—
419C2×C4×C8—431no—
420#391—431no—
421#390—431no—
422#390—431no—
423#390—431no—
424#390—431no—
425#390—861no—
426#390—861no—
427#389—431no—
428#389—861no—
429#388—861no—
430#388—861no—
431#387—861no—
432#380C2×D4311yescharacteristic
433#379—861no—
434#379—861no—
435C4×C4⋊C4—431no—
436#340—431no—
437#340—431no—
438#340—431no—
439#340—431no—
440#336—431no—
441#336—431no—
442C43#2205211yescharacteristic, complemented, Sylow
443C25—21no—
444C22×Q8—431no—
445C22×D4—21no—
446C22×D4—22no—
447C22×D4—41no—
448C22×D4—41no—
449C22×D4—41no—
450C22×D4—41no—
451C22×D4C4×D4314yes—
452C22×D4C22×D4311yescharacteristic
453C22×D4C22×D4311yescharacteristic
454C23×C4C22×D4311yescharacteristic
455C2×SD16—434no—
456C2×SD16—434no—
457C2×SD16—1721no—
458C2×SD16—1721no—
459C2×SD16—1721no—
460C2×SD16—1721no—
461C22×C8—431no—
462C22×C8—431no—
463C22×C8C22×D4311yescharacteristic
464C22×C8C22×D4311yescharacteristic
465C22⋊Q8—434no—
466C22⋊Q8—862no—
467C4×Q8—1721no—
468C4×Q8—1721no—
469#117—1721no—
470#117—1721no—
471#117—1721no—
472#117—1721no—
473C2×C4⋊C4—431no—
474C2×C4⋊C4—431no—
475C2×C4⋊C4—431no—
476C2×C4⋊C4—431no—
477C2×C4⋊C4—431no—
478C2×C4⋊C4—861no—
479C2×C4⋊C4—861no—
480C2×C4⋊C4—861no—
481C2×C4⋊C4C22×D4311yescharacteristic
482C2×C4⋊C4C22×D4311yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—431no—
485C2×C22⋊C4—431no—
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×C22⋊C4—861no—
493C2×C22⋊C4—861no—
494C2×C22⋊C4—861no—
495C2×C22⋊C4—861no—
496C2×C42—431no—
497C2×C42—431no—
498C2×C42—861no—
499C2×C42—861no—
500C2×C42—861no—
501#107—1721no—
502#106—1721no—
503#103—1721no—
504#103—1721no—
505#102—41no—
506#102—41no—
507#102—41no—
508#102—41no—
509#102—434no—
510#102—434no—
511C22⋊C8—22no—
512C22⋊C8—434no—
513#97—1721no—
514C4×C8—1721no—
515#95—21no—
516#95—861no—
517#95—861no—
518#95—861no—
519#95—861no—
520C24—21no—
521C24—21no—
522C24—24no—
523C24—42no—
524C24—42no—
525C24—81no—
526C24—81no—
527C24—81no—
528C24—81no—
529C24D4×D4311yescharacteristic
530C2×Q8—432no—
531C2×Q8—861no—
532C2×Q8—861no—
533C2×Q8—861no—
534C2×Q8—861no—
535C2×Q8—861no—
536C2×D4—24no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—42no—
550C2×D4—42no—
551C2×D4—44no—
552C2×D4—44no—
553C2×D4C2×C4×D4312yes—
554C2×D4C2×C4×D4312yes—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—431no—
562C22×C4—431no—
563C22×C4—431no—
564C22×C4—431no—
565C22×C4—861no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—861no—
569C22×C4C2×C4×D4312yes—
570C22×C4D4×D4311yescharacteristic
571C22×C4#1062190012yes—
572C22×C4C23×D4311yescharacteristic
573SD16—1724no—
574SD16—1724no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—432no—
582C2×C8—432no—
583C2×C8—861no—
584C2×C8—861no—
585C2×C8—861no—
586C2×C8—861no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—432no—
592C4⋊C4—864no—
593C4⋊C4—861no—
594C4⋊C4—861no—
595C4⋊C4—861no—
596C4⋊C4—861no—
597C4⋊C4—861no—
598C4⋊C4—3441no—
599C4⋊C4—1721no—
600C4⋊C4—1721no—
601C4⋊C4—1722no—
602C22⋊C4—81no—
603C22⋊C4—864no—
604C22⋊C4—3441no—
605C22⋊C4—3441no—
606C22⋊C4—3441no—
607C22⋊C4—3441no—
608C22⋊C4—3441no—
609C22⋊C4—3441no—
610C22⋊C4—3441no—
611C22⋊C4—3441no—
612C22⋊C4—1721no—
613C22⋊C4—1721no—
614C22⋊C4—1722no—
615C42—861no—
616C42—861no—
617C42—861no—
618C42—861no—
619C42—3441no—
620C42—1722no—
621C42—1722no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—22no—
629C23—22no—
630C23—48no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—84no—
644C23—84no—
645C23—84no—
646C23—84no—
647C23—84no—
648C23—84no—
649C23(C22⋊D43)⋊C412yes—
650C23C2×D4×D4311yescharacteristic
651Q8—862no—
652Q8—862no—
653Q8—1721no—
654Q8—1721no—
655D4—22no—
656D4—22no—
657D4—22no—
658D4—22no—
659D4—48no—
660D4—41no—
661D4—41no—
662D4—41no—
663D4—41no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—862no—
677C2×C4—862no—
678C2×C4—861no—
679C2×C4—861no—
680C2×C4—861no—
681C2×C4—861no—
682C2×C4—861no—
683C2×C4—861no—
684C2×C4—861no—
685C2×C4—861no—
686C2×C4—861no—
687C2×C4—861no—
688C2×C4—861no—
689C2×C4—861no—
690C2×C4—1721no—
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(C22⋊D43)⋊C412yes—
701C2×C4C22×C4×D4311yescharacteristic
702C2×C4C2×#1062190011yescharacteristic
703C2×C4#1306337011yescharacteristic
704C2×C4#1306337011yescharacteristic
705C2×C4#1306337011yescharacteristic
706C2×C4#1306337011yescharacteristic
707C8—41no—
708C8—41no—
709C8—862no—
710C8—862no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—816no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22C2×(C22⋊D43)⋊C411yescharacteristic
734C22#1458345911yescharacteristic
735C22#1458346411yescharacteristic
736C22#1458370011yescharacteristic
737C22#1458370511yescharacteristic
738C22#1458370911yescharacteristic
739C22#1458370911yescharacteristic
740C4—22no—
741C4—81no—
742C4—81no—
743C4—3441no—
744C4—3441no—
745C4—1722no—
746C4—1721no—
747C4—1721no—
748C4—1721no—
749C4—1721no—
750C4—1722no—
751C4#1458337211yescharacteristic
752C4#1458337211yescharacteristic
753C4#1458348411yescharacteristic
754C4#1458348411yescharacteristic
755C2—42no—
756C2—82no—
757C2—82no—
758C2#1913725011yescharacteristic
759C2#1914342111yescharacteristic
760C2#1914345711yescharacteristic
761C2#1914544311yescharacteristic
762C2#1914546411yescharacteristic
763C2#1914566311yescharacteristic
764C2#1914568511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1786C2
socleC23×C43C22×D4
prime radicalC23×D4×C43C22
cosocleC22×C4×C43C24
hypercenter#1786D43
hypocenterC43#22052
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
2. #19137273C2semidirect
4. #19135477C2semidirect
5. #19135450C2semidirect
6. #19135289C2semidirect
7. #19135275C2semidirect
8. #19135225C2semidirect
9. #19135218C2semidirect
10. #19134947C2semidirect
11. #19134947C2semidirect
12. #19134905C2semidirect
13. #19134792C2semidirect
14. #19134363C2semidirect
19. C2×#13063290C22semidirect
22. #14583050C4semidirect
23. C2×#13063258C22semidirect
24. C2×#13063256C22semidirect
25. C2×#13063250C22semidirect
26. C2×#13063250C22semidirect
30. C2×#13063235C22semidirect
31. C2×C8×Dic43C22semidirect
32. #14582804C22semidirect
40. #14582795C22semidirect
46. C4⋊C4×Dic43C22semidirect
47. #14582662C22semidirect
48. #14582662C22semidirect
49. #14582661C22semidirect
50. #14582661C22semidirect
51. #14582653C22semidirect
52. #14582653C22semidirect
442. C43#22052semidirect

Maximal subgroups

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

subgroupindex
C2×#145830502
#191372732
#191371772
#191354772
#191354502
#191352892
#191352752
#191352252
#191352182
#191349472
#191349052
#191347922
#191343632
C43×#17862
#2205243