Finite Group Databasebeta

← #25107889

Subgroups — #25107889

Order 11008.

1024 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583044C211yesmaximal, characteristic
2#19137284C211yesmaximal, characteristic, complemented
3#19137187C211yesmaximal, characteristic, complemented
4#19135468C211yesmaximal, characteristic, complemented
5#19135446C211yesmaximal, characteristic, complemented
6#19135282C211yesmaximal, characteristic, complemented
7#19135275C211yesmaximal, characteristic, complemented
8#19135232C211yesmaximal, characteristic, complemented
9#19135225C211yesmaximal, characteristic, complemented
10#19134940C211yesmaximal, characteristic, complemented
11#19134926C211yesmaximal, characteristic, complemented
12#19134910C211yesmaximal, characteristic, complemented
13#19134787C211yesmaximal, characteristic, complemented
14#19134363C211yesmaximal, characteristic, complemented
15C43×#1788C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×#13063299C2211yescharacteristic
19C2×#13063287C2211yescharacteristic
20C2×#13063284C2211yescharacteristic
21C22×C4⋊Dic43C2211yescharacteristic
22#14583044C418yescomplemented
23C2×#13063256C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C2×#13063235C2211yescharacteristic
31C2×C8×Dic43C2211yescharacteristic
32#14582806C2211yescharacteristic
33#14582806C2211yescharacteristic
34#14582802C2211yescharacteristic
35#14582802C2211yescharacteristic
36#14582800C2211yescharacteristic
37#14582799—21no—
38#14582795C2211yescharacteristic
39#14582791—21no—
40#14582779—21no—
41#14582779—21no—
42#14582775—21no—
43#14582773—21no—
44#14582759—21no—
45#14582759—21no—
46C4⋊C4×Dic43C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C22×#41×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C43×#380C2211yescharacteristic
60C22×D172C2311yescharacteristic
61C22×C22⋊D43—21no—
62C23×Dic43—21no—
63C22×C4×D43—21no—
64C2×#10621884—41no—
65C2×#10621884—41no—
66C2×#10621884C2×C414yescomplemented
67C2×#10621882—41no—
68C2×#10621882—41no—
69C2×#10621882C2×C414yescomplemented
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72#13063299—22no—
73#13063299C2×C414yes—
74#13063287—41no—
75#13063287—41no—
76#13063284—41no—
77#13063284—41no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43—41no—
80C2×C4⋊Dic43—41no—
81C2×C4⋊Dic43D411yescharacteristic
82C2×C4⋊Dic43D411yescharacteristic
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⋊Dic43D411yescharacteristic
92C2×C22⋊Dic43D411yescharacteristic
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43C2311yescharacteristic
99C2×C4×Dic43C2311yescharacteristic
100#13063256—41no—
101#13063256—41no—
102#13063249C2×C414yescomplemented
103#13063247—41no—
104#13063247—41no—
105#13063246C2×C414yescomplemented
106C22⋊(C43⋊C8)C2×C414yescomplemented
107#13063235—41no—
108C8×Dic43—41no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C2×#41×C43—22no—
116C2×#41×C43—41no—
117C2×#41×C43—41no—
118C2×#41×C43—41no—
119C2×#41×C43—41no—
120C2×#41×C43C2×C414yescomplemented
121C22×Q8×C43C2311yescharacteristic
122C22×D4×C43—21no—
123C22×D4×C43C2311yescharacteristic
124C23×C4×C43—21no—
125C23×C4×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C22⋊C4×C43—21no—
131#103×C43—41no—
132#103×C43—41no—
133#102×C43—41no—
134#102×C43—41no—
135C22⋊C8×C43—22no—
136#95×C43—21no—
137C24×C43—21no—
138C24×C43C2×D411yescharacteristic
139C23×D43—21no—
140#41×C43—44no—
141#41×C43—44no—
142#41×C43—44no—
143#41×C43—44no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43C22×C412yes—
150C2×D4×C43—21no—
151C2×D4×C43—24no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—42no—
157C2×D4×C43—42no—
158C2×D4×C43C22×C412yes—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—24no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—42no—
168C22×C4×C43—42no—
169C22×C4×C43C22×C412yes—
170C22×C4×C43C2×D411yescharacteristic
171C22×C4×C43#4112yes—
172C22×C4×C43C2411yescharacteristic
173C2×C22⋊D43—24no—
174C2×C22⋊D43—81no—
175C2×C22⋊D43—81no—
176C22×Dic43—21no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—42no—
180C22×Dic43—81no—
181C22×Dic43—81no—
182C22×Dic43C2×D411yescharacteristic
183C22×Dic43C2×D411yescharacteristic
184C22×Dic43C2×D411yescharacteristic
185C22×Dic43C2×D411yescharacteristic
186C2×D172—21no—
187C2×D172—21no—
188C2×D172—21no—
189C2×D172—21no—
190C2×D172—21no—
191C2×D172C22×C412yes—
192C2×C4×D43—42no—
193C2×C4×D43—81no—
194C2×C4×D43—81no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C22⋊C4×C43—81no—
206C22⋊Dic43—41no—
207C22⋊Dic43—41no—
208C22⋊Dic43—81no—
209C22⋊Dic43—81no—
210C22⋊Dic43—81no—
211C22⋊Dic43—81no—
212#10621884—44no—
213#10621882—44no—
214(C2×D43)⋊C4—24no—
215(C2×D43)⋊C4—42no—
216(C2×D43)⋊C4—81no—
217(C2×D43)⋊C4—81no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—41no—
224C4⋊Dic43—41no—
225C4⋊Dic43—42no—
226C4⋊Dic43C22×C412yes—
227Dic43⋊C4—81no—
228C4×Dic43—21no—
229C4×Dic43—21no—
230C4×Dic43—21no—
231C4×Dic43—21no—
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—41no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43C4×D412yes—
253C23×C43C22×D411yescharacteristic
254C22×D43—22no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—41no—
259C22×D43—41no—
260C22×D43—41no—
261Q8×C43—22no—
262Q8×C43—22no—
263Q8×C43—41no—
264Q8×C43—41no—
265D4×C43—22no—
266D4×C43—22no—
267D4×C43—48no—
268D4×C43—41no—
269D4×C43—41no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—48no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43C4×D412yes—
287C2×C4×C43C23×C411yescharacteristic
288C2×C4×C43C2×#4111yescharacteristic
289C2×C4×C43H(5,𝔽2)11yescharacteristic
290C2×C4×C43H(5,𝔽2)11yescharacteristic
291C2×C4×C43H(5,𝔽2)11yescharacteristic
292C2×C4×C43H(5,𝔽2)11yescharacteristic
293C22⋊D43—84no—
294C2×Dic43—22no—
295C2×Dic43—21no—
296C2×Dic43—21no—
297C2×Dic43—21no—
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—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—84no—
316D172—22no—
317D172—22no—
318D172—41no—
319D172—41no—
320C4×D43—84no—
321C8×C43—41no—
322C8×C43—41no—
323C43⋊C8—22no—
324C43⋊C8—22no—
325#22053—431nomaximal, Sylow
326C22×C43—22no—
327C22×C43—22no—
328C22×C43—22no—
329C22×C43—41no—
330C22×C43—41no—
331C22×C43—41no—
332C22×C43—41no—
333C22×C43—42no—
334C22×C43—42no—
335C22×C43—42no—
336C22×C43—81no—
337C22×C43—81no—
338C22×C43—81no—
339C22×C43—81no—
340C22×C43C2×C4×D411yescharacteristic
341C22×C43#53411yescharacteristic
342C22×C43#53511yescharacteristic
343C22×C43#57611yescharacteristic
344C22×C43#57711yescharacteristic
345C22×C43#57711yescharacteristic
346C22×C43#57711yescharacteristic
347C2×D43—42no—
348C2×D43—42no—
349C2×D43—42no—
350C2×D43—81no—
351C2×D43—81no—
352C2×D43—81no—
353C2×D43—81no—
354C4×C43—22no—
355C4×C43—42no—
356C4×C43—81no—
357C4×C43—81no—
358C4×C43#51811yescharacteristic
359C4×C43#51811yescharacteristic
360C4×C43#53811yescharacteristic
361C4×C43#53811yescharacteristic
362Dic43—41no—
363Dic43—41no—
364Dic43—42no—
365Dic43—41no—
366Dic43—41no—
367Dic43—81no—
368Dic43—81no—
369C2×#449—431no—
370#2324—431no—
371#2311—431no—
372#1972—431no—
373#1968—431no—
374#1935—431no—
375#1934—431no—
376#1927—431no—
377#1926—431no—
378#1879—431no—
379#1877—431no—
380#1874—431no—
381#1853—431no—
382#1788D4311yescharacteristic, complemented
383#1750—431no—
384C2×C43—42no—
385C2×C43—82no—
386C2×C43#232111yescharacteristic
387C2×C43#294611yescharacteristic
388C2×C43#295211yescharacteristic
389C2×C43#319811yescharacteristic
390C2×C43#320411yescharacteristic
391C2×C43#322111yescharacteristic
392C2×C43#322411yescharacteristic
393D43—82no—
394C22×#41C2×D4311yescharacteristic
395C22×SD16—431no—
396C22×D8—431no—
397C2×#121—431no—
398C2×C4×D4—431no—
399C2×#117—431no—
400C22×C4⋊C4—431no—
401#449—438no—
402C2×#106—431no—
403C2×#106—431no—
404C2×#103—431no—
405C2×#103C2×D4311yescharacteristic
406C2×#103C2×D4311yescharacteristic
407C2×#102—431no—
408C2×#102—431no—
409C2×#102—431no—
410C2×#102C2×D4311yescharacteristic
411C2×#102C2×D4311yescharacteristic
412C2×C22⋊C8—431no—
413C2×C22⋊C8C2×D4311yescharacteristic
414C2×#97—431no—
415C2×C4×C8—431no—
416#391—431no—
417#391—431no—
418#390—431no—
419#390—431no—
420#390—431no—
421#390—861no—
422#389—431no—
423#388—861no—
424#386—861no—
425#386—861no—
426#386—861no—
427#385—861no—
428#380—861no—
429#380—861no—
430#380C2×D4311yescharacteristic
431C4×C4⋊C4—431no—
432#340—431no—
433#340—431no—
434#340—431no—
435#340—431no—
436#336—431no—
437#336—431no—
438C43#2205311yescharacteristic, complemented, Sylow
439C2×#41—22no—
440C2×#41—41no—
441C2×#41—41no—
442C2×#41—41no—
443C2×#41—41no—
444C2×#41C4×D4314yescomplemented
445C22×Q8C22×D4311yescharacteristic
446C22×D4—21no—
447C22×D4—431no—
448C22×D4—861no—
449C22×D4C22×D4311yescharacteristic
450C23×C4—21no—
451C23×C4—861no—
452C23×C4—861no—
453C23×C4C22×D4311yescharacteristic
454C2×SD16—434no—
455C2×SD16—1721no—
456C2×SD16—1721no—
457C2×D8—434no—
458C2×D8—1721no—
459C2×D8—1721no—
460C22×C8—431no—
461C22×C8—431no—
462C22×C8C22×D4311yescharacteristic
463C22×C8C22×D4311yescharacteristic
464#121—434no—
465#121—862no—
466C4×D4—1721no—
467C4×D4—1721no—
468#117—1721no—
469#117—1721no—
470C2×C4⋊C4—431no—
471C2×C4⋊C4—431no—
472C2×C4⋊C4—431no—
473C2×C4⋊C4—431no—
474C2×C4⋊C4—431no—
475C2×C4⋊C4—861no—
476C2×C4⋊C4—861no—
477C2×C4⋊C4—1721no—
478C2×C4⋊C4—1721no—
479C2×C4⋊C4C22×D4311yescharacteristic
480C2×C4⋊C4C22×D4311yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—431no—
483C2×C22⋊C4—431no—
484C2×C22⋊C4—861no—
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—861no—
495#106—1721no—
496#106—1721no—
497#103—41no—
498#103—41no—
499#103—434no—
500#102—41no—
501#102—41no—
502#102—434no—
503#102—1721no—
504#102—1721no—
505C22⋊C8—22no—
506C22⋊C8—434no—
507#97—1721no—
508C4×C8—1721no—
509#95—21no—
510#95—861no—
511#95—861no—
512#95—861no—
513#95—861no—
514#95—861no—
515#95—861no—
516C24—21no—
517C24—861no—
518C24D4×D4311yescharacteristic
519#41—44no—
520#41—44no—
521#41—44no—
522#41—44no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8C2×C4×D4312yes—
529C2×D4—24no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—432no—
538C2×D4—864no—
539C2×D4—861no—
540C2×D4—861no—
541C2×D4—861no—
542C2×D4—861no—
543C2×D4—861no—
544C2×D4—3441no—
545C2×D4—3441no—
546C2×D4C2×C4×D4312yes—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—24no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—431no—
558C22×C4—431no—
559C22×C4—431no—
560C22×C4—431no—
561C22×C4—861no—
562C22×C4—861no—
563C22×C4—861no—
564C22×C4—3441no—
565C22×C4—3441no—
566C22×C4—3441no—
567C22×C4—3441no—
568C22×C4—1722no—
569C22×C4—1722no—
570C22×C4C2×C4×D4312yes—
571C22×C4D4×D4311yescharacteristic
572C22×C4#1062190012yes—
573C22×C4C23×D4311yescharacteristic
574SD16—1724no—
575D8—1724no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—432no—
583C2×C8—432no—
584C2×C8—861no—
585C2×C8—861no—
586C2×C8—861no—
587C2×C8—861no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—432no—
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—1722no—
611C22⋊C4—1721no—
612C22⋊C4—1721no—
613C42—861no—
614C42—861no—
615C42—861no—
616C42—861no—
617C42—3441no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—22no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—862no—
632C23—1721no—
633C23—1721no—
634C23—1721no—
635C23—1721no—
636C23—1721no—
637C23—1721no—
638C23(C22⋊D43)⋊C412yes—
639C23C2×D4×D4311yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—41no—
643Q8—41no—
644D4—22no—
645D4—22no—
646D4—48no—
647D4—41no—
648D4—41no—
649D4—862no—
650D4—862no—
651D4—3444no—
652D4—1721no—
653D4—1721no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—48no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—862no—
671C2×C4—861no—
672C2×C4—861no—
673C2×C4—861no—
674C2×C4—861no—
675C2×C4—861no—
676C2×C4—861no—
677C2×C4—861no—
678C2×C4—861no—
679C2×C4—861no—
680C2×C4—861no—
681C2×C4—861no—
682C2×C4—861no—
683C2×C4—3444no—
684C2×C4—3444no—
685C2×C4—1721no—
686C2×C4—1721no—
687C2×C4—1721no—
688C2×C4—1721no—
689C2×C4—1721no—
690C2×C4—1721no—
691C2×C4—1721no—
692C2×C4—1721no—
693C2×C4(C22⋊D43)⋊C412yes—
694C2×C4C22×C4×D4311yescharacteristic
695C2×C4C2×#1062190011yescharacteristic
696C2×C4#1306337011yescharacteristic
697C2×C4#1306337011yescharacteristic
698C2×C4#1306337011yescharacteristic
699C2×C4#1306337011yescharacteristic
700C8—41no—
701C8—41no—
702C8—862no—
703C8—862no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—3441no—
719C22—3441no—
720C22—3441no—
721C22—3441no—
722C22—1722no—
723C22—1722no—
724C22—1722no—
725C22C2×(C22⋊D43)⋊C411yescharacteristic
726C22#1458345911yescharacteristic
727C22#1458346411yescharacteristic
728C22#1458370111yescharacteristic
729C22#1458370611yescharacteristic
730C22#1458370811yescharacteristic
731C22#1458370911yescharacteristic
732C4—22no—
733C4—42no—
734C4—81no—
735C4—81no—
736C4—3441no—
737C4—3441no—
738C4—1722no—
739C4—1721no—
740C4—1721no—
741C4—1721no—
742C4—1721no—
743C4#1458337211yescharacteristic
744C4#1458337211yescharacteristic
745C4#1458348411yescharacteristic
746C4#1458348411yescharacteristic
747C2—42no—
748C2—82no—
749C2—3442no—
750C2#1913725011yescharacteristic
751C2#1914343011yescharacteristic
752C2#1914347411yescharacteristic
753C2#1914544411yescharacteristic
754C2#1914550311yescharacteristic
755C2#1914565411yescharacteristic
756C2#1914569511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1788C2
socleC23×C43C22×D4
prime radicalC2×#14583044C2
cosocleC22×C4×C43C24
hypercenter#1788D43
hypocenterC43#22053
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. #19137284C2semidirect
3. #19137187C2semidirect
4. #19135468C2semidirect
5. #19135446C2semidirect
6. #19135282C2semidirect
7. #19135275C2semidirect
8. #19135232C2semidirect
9. #19135225C2semidirect
10. #19134940C2semidirect
11. #19134926C2semidirect
12. #19134910C2semidirect
13. #19134787C2semidirect
14. #19134363C2semidirect
15. C43×#1788C2semidirect
22. #14583044C4semidirect
66. C2×#10621884C2×C4semidirect
69. C2×#10621882C2×C4semidirect
102. #13063249C2×C4semidirect
105. #13063246C2×C4semidirect
106. C22⋊(C43⋊C8)C2×C4semidirect
120. C2×#41×C43C2×C4semidirect
382. #1788D43semidirect
438. C43#22053semidirect
444. C2×#41C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830442
#191372842
#191371872
#191354682
#191354462
#191352822
#191352752
#191352322
#191352252
#191349402
#191349262
#191349102
#191347872
#191343632
C43×#17882
#2205343