Finite Group Databasebeta

← #25107881

Subgroups — #25107881

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×#14583048C211yesmaximal, characteristic
2#19137280C211yesmaximal, characteristic, complemented
3#19137174C211yesmaximal, characteristic
4#19135479C211yesmaximal, characteristic, complemented
5#19135295C211yesmaximal, characteristic, complemented
6#19135278C211yesmaximal, characteristic, complemented
7#19135221C211yesmaximal, characteristic, complemented
8#19135218C211yesmaximal, characteristic, complemented
9#19134952C211yesmaximal, characteristic, complemented
10#19134948C211yesmaximal, characteristic, complemented
11#19134904C211yesmaximal, characteristic, complemented
12#19134793C211yesmaximal, characteristic, complemented
13#19134524C211yesmaximal, characteristic
14#19134362C211yesmaximal, characteristic, complemented
15C43×#1968C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C2×#13063301C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic, complemented
20C2×#13063283C2211yescharacteristic
21C2×#13063282C2211yescharacteristic
22#14583048C418yescomplemented
23C2×#13063258C2211yescharacteristic, complemented
24C2×#13063249C2211yescharacteristic, complemented
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32C2×#13063236C2211yescharacteristic, complemented
33#14582802C2211yescharacteristic
34#14582801C2211yescharacteristic
35#14582800C2211yescharacteristic
36#14582799—21no—
37#14582799—21no—
38#14582797C2211yescharacteristic, complemented
39#14582796—21no—
40#14582791—21no—
41#14582788—21no—
42#14582781—21no—
43#14582756C2211yescharacteristic
44#14582754—21no—
45#14582754—21no—
46C4⋊C4×Dic43C2211yescharacteristic, complemented
47#14582662C2211yescharacteristic, complemented
48#14582662C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582653C2211yescharacteristic, complemented
52#14582653C2211yescharacteristic, complemented
53C22×SD16×C43C2211yescharacteristic
54C2×#106×C43C2211yescharacteristic, complemented
55C2×#103×C43C2211yescharacteristic, complemented
56C2×#102×C43C2211yescharacteristic
57C2×C4×C8×C43C2211yescharacteristic, complemented
58C43×#391C2211yescharacteristic, complemented
59C43×#390C2211yescharacteristic
60C24×D43—21no—
61C22×D172C2311yescharacteristic
62C22×C22⋊D43—21no—
63C2×D4×D43—22no—
64C2×D4×D43—41no—
65C2×D4×D43—41no—
66C2×D4×D43—41no—
67C2×D4×D43—41no—
68C2×D4×D43C2×C414yes—
69C22×C4×D43C2311yescharacteristic
70C2×#10621884—41no—
71C2×#10621884—41no—
72C2×#10621884C2×C414yes—
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063301—22no—
76#13063301C2×C414yes—
77Q8×Dic43—41no—
78Q8×Dic43—41no—
79#13063283—41no—
80#13063283—41no—
81#13063282—41no—
82#13063282—41no—
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4D411yescharacteristic
90C2×Dic43⋊C4D411yescharacteristic
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4D411yescharacteristic
101C2×(C2×D43)⋊C4D411yescharacteristic
102C2×C4×Dic43—21no—
103C2×C4×Dic43—21no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43C2311yescharacteristic
106#13063258—41no—
107#13063249—41no—
108#13063247—41no—
109#13063247C2×C414yes—
110#13063246—41no—
111#13063246C2×C414yes—
112#13063245—41no—
113(C2×D43)⋊C8—22no—
114(C2×D43)⋊C8C2×C414yes—
115#13063236—41no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C22×Q8×C43C2311yescharacteristic
120C22×D4×C43C2311yescharacteristic
121C2×SD16×C43—41no—
122C2×SD16×C43—41no—
123C2×SD16×C43C2×C414yes—
124C22×C8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43—21no—
130C2×C42×C43C2311yescharacteristic
131#106×C43—41no—
132#103×C43—41no—
133#102×C43—41no—
134C4×C8×C43—41no—
135#95×C43—21no—
136#95×C43—21no—
137C24×C43—21no—
138C23×D43—21no—
139C23×D43—24no—
140C23×D43—42no—
141C23×D43—42no—
142C23×D43—81no—
143C23×D43—81no—
144C23×D43—81no—
145C23×D43—81no—
146C23×D43C2×D411yescharacteristic
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43C22×C412yes—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43C22×C412yes—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2411yescharacteristic
165C2×C22⋊D43—24no—
166C2×C22⋊D43—42no—
167C2×C22⋊D43—42no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43C2×D411yescharacteristic
172C22×Dic43C2×D411yescharacteristic
173C22×Dic43C2×D411yescharacteristic
174D4×D43—44no—
175D4×D43—44no—
176D4×D43—44no—
177D4×D43—44no—
178C2×D172—21no—
179C2×D172—21no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172C22×C412yes—
184C2×C4×D43—21no—
185C2×C4×D43—21no—
186C2×C4×D43—21no—
187C2×C4×D43—21no—
188C2×C4×D43C22×C412yes—
189C2×C4×D43#4112yes—
190SD16×C43—44no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43C22×C412yes—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C22⋊C4×C43—81no—
202C22⋊C4×C43—81no—
203C42×C43—21no—
204C42×C43—21no—
205C22⋊Dic43—81no—
206C22⋊Dic43—81no—
207#10621884—44no—
208(C2×D43)⋊C4—24no—
209(C2×D43)⋊C4—41no—
210(C2×D43)⋊C4—41no—
211(C2×D43)⋊C4—42no—
212(C2×D43)⋊C4—81no—
213(C2×D43)⋊C4—81no—
214(C2×D43)⋊C4—81no—
215(C2×D43)⋊C4—81no—
216(C2×D43)⋊C4—81no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—42no—
223C4⋊Dic43C22×C412yes—
224Dic43⋊C4—24no—
225Dic43⋊C4—41no—
226Dic43⋊C4—41no—
227Dic43⋊C4—81no—
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⋊C8—21no—
238C2×C43⋊C8C22×C412yes—
239C23×C43—22no—
240C23×C43—41no—
241C23×C43—41no—
242C23×C43—41no—
243C23×C43—41no—
244C23×C43—41no—
245C23×C43—41no—
246C23×C43C22×D411yescharacteristic
247C22×D43—21no—
248C22×D43—21no—
249C22×D43—21no—
250C22×D43—21no—
251C22×D43—21no—
252C22×D43—21no—
253C22×D43—22no—
254C22×D43—48no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—41no—
259C22×D43—41no—
260C22×D43—41no—
261C22×D43—84no—
262C22×D43—84no—
263C22×D43—84no—
264C22×D43—84no—
265C22×D43—84no—
266C22×D43—84no—
267C22×D43C4×D412yes—
268Q8×C43—22no—
269Q8×C43—22no—
270Q8×C43—41no—
271Q8×C43—41no—
272D4×C43—22no—
273D4×C43—22no—
274D4×C43—41no—
275D4×C43—41no—
276C2×C4×C43—22no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
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×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43C23×C411yescharacteristic
292C2×C4×C43C2×#4111yescharacteristic
293C2×C4×C43H(5,𝔽2)11yescharacteristic
294C2×C4×C43H(5,𝔽2)11yescharacteristic
295C2×C4×C43H(5,𝔽2)11yescharacteristic
296C2×C4×C43H(5,𝔽2)11yescharacteristic
297C22⋊D43—48no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—22no—
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×Dic43C4×D412yes—
316D172—22no—
317D172—22no—
318D172—41no—
319D172—41no—
320C4×D43—22no—
321C4×D43—22no—
322C4×D43—22no—
323C4×D43—22no—
324C8×C43—22no—
325C8×C43—41no—
326C43⋊C8—22no—
327C43⋊C8—41no—
328#22052—431nomaximal, Sylow
329C22×C43—42no—
330C22×C43—42no—
331C22×C43—42no—
332C22×C43—81no—
333C22×C43—81no—
334C22×C43—81no—
335C22×C43—81no—
336C22×C43C2×C4×D411yescharacteristic
337C22×C43#53411yescharacteristic
338C22×C43#53511yescharacteristic
339C22×C43#57611yescharacteristic
340C22×C43#57711yescharacteristic
341C22×C43#57711yescharacteristic
342C22×C43#57711yescharacteristic
343C2×D43—22no—
344C2×D43—22no—
345C2×D43—22no—
346C2×D43—41no—
347C2×D43—41no—
348C2×D43—41no—
349C2×D43—41no—
350C2×D43—42no—
351C2×D43—42no—
352C2×D43—42no—
353C2×D43—816no—
354C2×D43—81no—
355C2×D43—81no—
356C2×D43—81no—
357C2×D43—81no—
358C4×C43—42no—
359C4×C43—41no—
360C4×C43—41no—
361C4×C43—81no—
362C4×C43—81no—
363C4×C43#51811yescharacteristic
364C4×C43#51811yescharacteristic
365C4×C43#53811yescharacteristic
366C4×C43#53811yescharacteristic
367Dic43—22no—
368Dic43—41no—
369Dic43—41no—
370Dic43—42no—
371Dic43—81no—
372Dic43—81no—
373C2×#450—431no—
374#2323—431no—
375#2309—431no—
376#1973—431no—
377#1968D4311yescharacteristic, complemented
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#1786—431no—
387#1750—431no—
388C2×C43—82no—
389C2×C43#232111yescharacteristic
390C2×C43#294611yescharacteristic
391C2×C43#294911yescharacteristic
392C2×C43#319811yescharacteristic
393C2×C43#320011yescharacteristic
394C2×C43#322211yescharacteristic
395C2×C43#322411yescharacteristic
396D43—42no—
397D43—82no—
398C23×D4—431no—
399C22×SD16—431no—
400C22×SD16C2×D4311yescharacteristic
401C2×C22⋊Q8—431no—
402C2×C4×Q8—431no—
403C2×#117—431no—
404C2×#117—431no—
405#450—438no—
406C2×#107—431no—
407C2×#106C2×D4311yescharacteristic, complemented
408C2×#103—431no—
409C2×#103C2×D4311yescharacteristic, complemented
410C2×#102—431no—
411C2×#102—431no—
412C2×#102—431no—
413C2×#102—431no—
414C2×#102—431no—
415C2×#102C2×D4311yescharacteristic
416C2×C22⋊C8—431no—
417C2×C22⋊C8—431no—
418C2×#97—431no—
419C2×C4×C8C2×D4311yescharacteristic, complemented
420#391C2×D4311yescharacteristic, complemented
421#390—431no—
422#390—431no—
423#390—431no—
424#390—861no—
425#390—861no—
426#390C2×D4311yescharacteristic
427#389—431no—
428#389—861no—
429#388—861no—
430#388—861no—
431#387—861no—
432#380—431no—
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—861no—
444C22×Q8C22×D4311yescharacteristic
445C22×D4—434no—
446C22×D4—431no—
447C22×D4—862no—
448C22×D4—861no—
449C22×D4—1721no—
450C22×D4—1721no—
451C22×D4—1721no—
452C22×D4—1721no—
453C22×D4C22×D4311yescharacteristic
454C23×C4—431no—
455C2×SD16—41no—
456C2×SD16—41no—
457C2×SD16—434no—
458C2×SD16—1721no—
459C2×SD16—1721no—
460C2×SD16C4×D4314yes—
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—21no—
485C2×C22⋊C4—431no—
486C2×C22⋊C4—431no—
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—861no—
498C2×C42—861no—
499C2×C42—861no—
500C2×C42C22×D4311yescharacteristic
501#107—1721no—
502#106—41no—
503#103—41no—
504#103—1721no—
505#102—41no—
506#102—434no—
507#102—434no—
508#102—1721no—
509#102—1721no—
510#102—1721no—
511C22⋊C8—434no—
512C22⋊C8—862no—
513#97—1721no—
514C4×C8—41no—
515#95—21no—
516#95—21no—
517#95—861no—
518#95—861no—
519#95—861no—
520C24—21no—
521C24—431no—
522C24—864no—
523C24—861no—
524C24—3441no—
525C24—3441no—
526C24—3441no—
527C24—3441no—
528C24—1722no—
529C24—1722no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8C2×C4×D4312yes—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—432no—
542C2×D4—864no—
543C2×D4—861no—
544C2×D4—861no—
545C2×D4—861no—
546C2×D4—861no—
547C2×D4—861no—
548C2×D4—1724no—
549C2×D4—1724no—
550C2×D4—1724no—
551C2×D4—1724no—
552C2×D4—1722no—
553C2×D4—1722no—
554C2×D4C2×C4×D4312yes—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—431no—
559C22×C4—432no—
560C22×C4—432no—
561C22×C4—431no—
562C22×C4—431no—
563C22×C4—861no—
564C22×C4—861no—
565C22×C4—861no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—861no—
569C22×C4—861no—
570C22×C4D4×D4311yescharacteristic
571C22×C4D4×D4311yescharacteristic
572C22×C4C23×D4311yescharacteristic
573SD16—44no—
574SD16—1724no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—432no—
581C2×C8—861no—
582C2×C8—861no—
583C2×C8—861no—
584C2×C8—861no—
585C2×C8—861no—
586C2×C8C2×C4×D4312yes—
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—81no—
604C22⋊C4—864no—
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—21no—
616C42—21no—
617C42—861no—
618C42—861no—
619C42—3441no—
620C42—1722no—
621C42—1722no—
622C23—22no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—432no—
630C23—861no—
631C23—861no—
632C23—861no—
633C23—861no—
634C23—861no—
635C23—861no—
636C23—862no—
637C23—3444no—
638C23—3444no—
639C23—3444no—
640C23—3444no—
641C23—3444no—
642C23—3444no—
643C23—1728no—
644C23—1721no—
645C23—1721no—
646C23—1721no—
647C23—1721no—
648C23—1721no—
649C23—1721no—
650C23C2×D4×D4311yescharacteristic
651Q8—22no—
652Q8—22no—
653Q8—41no—
654Q8—41no—
655D4—22no—
656D4—22no—
657D4—41no—
658D4—41no—
659D4—862no—
660D4—862no—
661D4—1728no—
662D4—1721no—
663D4—1721no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—432no—
680C2×C4—861no—
681C2×C4—861no—
682C2×C4—862no—
683C2×C4—862no—
684C2×C4—862no—
685C2×C4—862no—
686C2×C4—862no—
687C2×C4—861no—
688C2×C4—861no—
689C2×C4—861no—
690C2×C4—861no—
691C2×C4—861no—
692C2×C4—861no—
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×C4C22×C4×D4311yescharacteristic
702C2×C4#41×D4311yescharacteristic
703C2×C4#1306337011yescharacteristic
704C2×C4#1306337011yescharacteristic
705C2×C4#1306337011yescharacteristic
706C2×C4#1306337111yescharacteristic
707C8—22no—
708C8—41no—
709C8—862no—
710C8—1721no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—862no—
719C22—862no—
720C22—862no—
721C22—34416no—
722C22—3441no—
723C22—3441no—
724C22—3441no—
725C22—3441no—
726C22—1722no—
727C22—1722no—
728C22—1722no—
729C22—1721no—
730C22—1721no—
731C22—1721no—
732C22—1721no—
733C22C4×D4×D4311yescharacteristic
734C22#1458345711yescharacteristic
735C22#1458346211yescharacteristic
736C22#1458370111yescharacteristic
737C22#1458370511yescharacteristic
738C22#1458370511yescharacteristic
739C22#1458370611yescharacteristic
740C4—42no—
741C4—41no—
742C4—41no—
743C4—81no—
744C4—81no—
745C4—862no—
746C4—3441no—
747C4—3441no—
748C4—1721no—
749C4—1721no—
750C4—1722no—
751C4#1458337111yescharacteristic
752C4#1458337211yescharacteristic
753C4#1458348111yescharacteristic
754C4#1458348311yescharacteristic
755C2—82no—
756C2—3442no—
757C2—1722no—
758C2#1913725411yescharacteristic
759C2#1914342211yescharacteristic
760C2#1914344911yescharacteristic
761C2#1914545011yescharacteristic
762C2#1914546111yescharacteristic
763C2#1914566011yescharacteristic
764C2#1914568211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1968C2
socleC23×C43C22×D4
prime radicalC22×D4×D43C22
cosocleC22×C4×C43C24
hypercenter#1968D43
hypocenterC43#22052
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1968

Complements

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

NH ≅ G/Ntype
2. #19137280C2semidirect
4. #19135479C2semidirect
5. #19135295C2semidirect
6. #19135278C2semidirect
7. #19135221C2semidirect
8. #19135218C2semidirect
9. #19134952C2semidirect
10. #19134948C2semidirect
11. #19134904C2semidirect
12. #19134793C2semidirect
14. #19134362C2semidirect
15. C43×#1968C2semidirect
19. C2×Q8×Dic43C22semidirect
22. #14583048C4semidirect
23. C2×#13063258C22semidirect
24. C2×#13063249C22semidirect
32. C2×#13063236C22semidirect
38. #14582797C22semidirect
46. C4⋊C4×Dic43C22semidirect
47. #14582662C22semidirect
48. #14582662C22semidirect
49. #14582661C22semidirect
50. #14582661C22semidirect
51. #14582653C22semidirect
52. #14582653C22semidirect
54. C2×#106×C43C22semidirect
55. C2×#103×C43C22semidirect
57. C2×C4×C8×C43C22semidirect
58. C43×#391C22semidirect
377. #1968D43semidirect
407. C2×#106C2×D43semidirect
409. C2×#103C2×D43semidirect
419. C2×C4×C8C2×D43semidirect
420. #391C2×D43semidirect
442. C43#22052semidirect

Maximal subgroups

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

subgroupindex
C2×#145830482
#191372802
#191371742
#191354792
#191352952
#191352782
#191352212
#191352182
#191349522
#191349482
#191349042
#191347932
#191345242
#191343622
C43×#19682
#2205243