Finite Group Databasebeta

← #25140307

Subgroups — #25140307

Order 11008.

1006 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583239C211yesmaximal, characteristic, complemented
2#19137934C211yesmaximal, characteristic
3#19137520C211yesmaximal, characteristic, complemented
4#19136114C211yesmaximal, characteristic, complemented
5#19136016C211yesmaximal, characteristic, complemented
6#19135789C211yesmaximal, characteristic, complemented
7#19135783C211yesmaximal, characteristic, complemented
8#19135231C211yesmaximal, characteristic, complemented
9#19135225C211yesmaximal, characteristic, complemented
10#19134914C211yesmaximal, characteristic, complemented
11#19134892C211yesmaximal, characteristic, complemented
12#19134788C211yesmaximal, characteristic, complemented
13#19134628C211yesmaximal, characteristic, complemented
14#19134535C211yesmaximal, characteristic, complemented
15C2×C43×#417C211yesmaximal, characteristic, complemented
16C2×#13063301C2211yescharacteristic
17C2×#13063296C2211yescharacteristic
18C2×C4×C22⋊D43C2211yescharacteristic
19C2×#13063283C2211yescharacteristic
20#14583239—24no—
21C2×#13063259C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32#14582813—21no—
33#14582807—21no—
34#14582806C2211yescharacteristic
35#14582802C2211yescharacteristic
36#14582789—21no—
37#14582780—21no—
38#14582778—21no—
39#14582778—21no—
40#14582772—21no—
41#14582764C2211yescharacteristic
42#14582759C2211yescharacteristic
43#14582759C2211yescharacteristic
44#14582756C2211yescharacteristic
45C4⋊C4×Dic43C2211yescharacteristic
46C4×C22⋊Dic43—21no—
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C22×#41×C43C2211yescharacteristic
54C22×M16×C43C2211yescharacteristic
55C22×C4⋊C4×C43C2211yescharacteristic
56C43×#417—24no—
57C2×#103×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C22×C22⋊D43—21no—
62C22×C22⋊D43D411yescharacteristic
63C22×C4×D43C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66#13063301—22no—
67#13063301—41no—
68#13063296—22no—
69#13063296—41no—
70C4×C22⋊D43—22no—
71C4×C22⋊D43—22no—
72#13063283—22no—
73#13063283—41no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4D411yescharacteristic
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43D411yescharacteristic
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4D411yescharacteristic
90C2×C4×Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43C2311yescharacteristic
93#13063259—22no—
94#13063257—41no—
95#13063256—22no—
96#13063256—41no—
97#13063249—22no—
98#13063249—41no—
99#13063246—22no—
100#13063246—41no—
101C22⋊(C43⋊C8)—22no—
102(C2×D43)⋊C8—22no—
103(C2×D43)⋊C8—41no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C2×#41×C43—22no—
113C2×#41×C43—22no—
114C2×#41×C43—22no—
115C2×#41×C43—22no—
116C2×#41×C43—41no—
117C2×#41×C43—41no—
118C22×Q8×C43C2311yescharacteristic
119C22×D4×C43—21no—
120C22×D4×C43C2311yescharacteristic
121C23×C4×C43—21no—
122C23×C4×C43—21no—
123C23×C4×C43C2311yescharacteristic
124C2×M16×C43—22no—
125C2×M16×C43—22no—
126C2×M16×C43—41no—
127C22×C8×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129C2×C4⋊C4×C43—22no—
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43—41no—
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134#103×C43—22no—
135#103×C43D414yescomplemented
136#102×C43—22no—
137#102×C43—22no—
138C24×C43—21no—
139C24×C43C2×D411yescharacteristic
140C23×D43C2×D411yescharacteristic
141#41×C43—28no—
142#41×C43—44no—
143#41×C43—44no—
144#41×C43—44no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43C2×D412yes—
151C2×D4×C43—21no—
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×C43—42no—
159C2×D4×C43#4112yes—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—42no—
168C22×C4×C43—42no—
169C22×C4×C43—42no—
170C22×C4×C43—42no—
171C22×C4×C43—42no—
172C22×C4×C43—81no—
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43#4112yes—
175C22×C4×C43#4112yes—
176C22×C4×C43C2411yescharacteristic
177C2×C22⋊D43—22no—
178C2×C22⋊D43—41no—
179C2×C22⋊D43—41no—
180C2×C22⋊D43—42no—
181C2×C22⋊D43—42no—
182C2×C22⋊D43—81no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—21no—
187C22×Dic43C2×D411yescharacteristic
188C22×Dic43C2×D411yescharacteristic
189C22×Dic43C2×D411yescharacteristic
190C2×C4×D43—21no—
191C2×C4×D43—21no—
192C2×C4×D43—21no—
193C2×C4×D43—21no—
194C2×C4×D43—21no—
195C2×C4×D43—21no—
196M16×C43—44no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43C2×D412yes—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—42no—
207C4⋊C4×C43C2×D412yes—
208C22⋊Dic43—22no—
209C22⋊Dic43—42no—
210C22⋊Dic43—42no—
211C22⋊Dic43—42no—
212C22⋊Dic43—81no—
213C22⋊Dic43—81no—
214(C2×D43)⋊C4—22no—
215(C2×D43)⋊C4—42no—
216(C2×D43)⋊C4—42no—
217(C2×D43)⋊C4—81no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226Dic43⋊C4—22no—
227Dic43⋊C4—42no—
228C4×Dic43—21no—
229C4×Dic43—21no—
230C4×Dic43—42no—
231C4×Dic43—81no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—22no—
245C23×C43—41no—
246C23×C43—41no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43#12312yes—
252C23×C43C22×D411yescharacteristic
253C22×D43—21no—
254C22×D43—21no—
255C22×D43—21no—
256C22×D43—21no—
257C22×D43—21no—
258C22×D43—21no—
259C22×D43—21no—
260Q8×C43—22no—
261Q8×C43—22no—
262Q8×C43—41no—
263Q8×C43—41no—
264D4×C43—22no—
265D4×C43—22no—
266D4×C43—48no—
267D4×C43—41no—
268D4×C43—41no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—22no—
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—84no—
286C2×C4×C43#12312yes—
287C2×C4×C43C22×D411yescharacteristic
288C2×C4×C43C2×#4111yescharacteristic
289C2×C4×C43C2×#4111yescharacteristic
290C2×C4×C43C2×#4111yescharacteristic
291C2×C4×C43H(5,𝔽2)11yescharacteristic
292C2×C4×C43H(5,𝔽2)11yescharacteristic
293C22⋊D43—44no—
294C22⋊D43—84no—
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—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
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—41no—
316C4×D43—41no—
317C4×D43—41no—
318C4×D43—41no—
319C4×D43—41no—
320C8×C43—22no—
321C8×C43—41no—
322C43⋊C8—41no—
323C43⋊C8—41no—
324#24891—431nomaximal, Sylow
325C22×C43—22no—
326C22×C43—22no—
327C22×C43—22no—
328C22×C43—41no—
329C22×C43—41no—
330C22×C43—41no—
331C22×C43—41no—
332C22×C43—42no—
333C22×C43—42no—
334C22×C43—42no—
335C22×C43—81no—
336C22×C43—81no—
337C22×C43—81no—
338C22×C43—81no—
339C22×C43C2×#12311yescharacteristic
340C22×C43D4211yescharacteristic
341C22×C43#54611yescharacteristic
342C22×C43#57511yescharacteristic
343C22×C43#57511yescharacteristic
344C22×C43#57711yescharacteristic
345C22×C43#57711yescharacteristic
346C2×D43—41no—
347C2×D43—41no—
348C2×D43—41no—
349C2×D43—41no—
350C2×D43—41no—
351C2×D43—41no—
352C2×D43—41no—
353C4×C43—22no—
354C4×C43—42no—
355C4×C43—42no—
356C4×C43—81no—
357C4×C43#52511yescharacteristic
358C4×C43#53811yescharacteristic
359C4×C43#54611yescharacteristic
360C4×C43#55111yescharacteristic
361Dic43—41no—
362Dic43—41no—
363Dic43—41no—
364Dic43—81no—
365Dic43—81no—
366Dic43—81no—
367Dic43—81no—
368C2×#485—431no—
369C2×#417D4311yescharacteristic, complemented
370#2407—431no—
371#2352—431no—
372#2092—431no—
373#2074—431no—
374#2035—431no—
375#2034—431no—
376#1927—431no—
377#1926—431no—
378#1875—431no—
379#1870—431no—
380#1853—431no—
381#1809—431no—
382#1788—431no—
383C2×C43—42no—
384C2×C43—82no—
385C2×C43#241811yescharacteristic
386C2×C43#309311yescharacteristic
387C2×C43#309911yescharacteristic
388C2×C43#327111yescharacteristic
389C2×C43#327511yescharacteristic
390C2×C43#330711yescharacteristic
391C2×C43#332311yescharacteristic
392D43—81no—
393C22×#41C2×D4311yescharacteristic
394C22×M16C2×D4311yescharacteristic
395C2×C22⋊Q8—431no—
396C2×#121—431no—
397C2×C4×D4—431no—
398C2×#117—431no—
399C22×C4⋊C4C2×D4311yescharacteristic
400#485—864no—
401C2×#107—431no—
402C2×#106—431no—
403C2×#106—431no—
404C2×#106—431no—
405#417—24no—
406C2×#103—431no—
407C2×#103—431no—
408C2×#103C2×D4311yescharacteristic
409C2×#103C2×D4311yescharacteristic
410C2×#102—431no—
411C2×#102—431no—
412C2×#102C2×D4311yescharacteristic
413C2×#102C2×D4311yescharacteristic
414C2×C22⋊C8—431no—
415C2×C22⋊C8—431no—
416C2×C22⋊C8—431no—
417#394—861no—
418#392—861no—
419#391—431no—
420#390—431no—
421#388—861no—
422#387—861no—
423#386—861no—
424#386—861no—
425#385—861no—
426#382—431no—
427#380—431no—
428#380—431no—
429#380—431no—
430C4×C4⋊C4—431no—
431C4×C22⋊C4—861no—
432#340—431no—
433#340—431no—
434#340—431no—
435#340—431no—
436#336—431no—
437#336—431no—
438C43#2489111yescharacteristic, complemented, Sylow
439C2×#41—22no—
440C2×#41—22no—
441C2×#41—22no—
442C2×#41—22no—
443C2×#41—41no—
444C2×#41—41no—
445C22×Q8C22×D4311yescharacteristic
446C22×D4—21no—
447C22×D4—431no—
448C22×D4—861no—
449C22×D4C22×D4311yescharacteristic
450C23×C4—21no—
451C23×C4—21no—
452C23×C4—431no—
453C23×C4C22×D4311yescharacteristic
454C2×M16—22no—
455C2×M16—22no—
456C2×M16—41no—
457C22×C8—431no—
458C22×C8—431no—
459C22×C8C22×D4311yescharacteristic
460C22×C8C22×D4311yescharacteristic
461C22⋊Q8—862no—
462C22⋊Q8—1721no—
463#121—862no—
464#121—1721no—
465C4×D4—862no—
466C4×D4—862no—
467#117—862no—
468#117—1721no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—41no—
472C2×C4⋊C4—431no—
473C2×C4⋊C4—431no—
474C2×C4⋊C4—431no—
475C2×C4⋊C4—431no—
476C2×C4⋊C4—431no—
477C2×C4⋊C4—861no—
478C2×C4⋊C4C22×D4311yescharacteristic
479C2×C4⋊C4C22×D4311yescharacteristic
480C2×C22⋊C4—431no—
481C2×C22⋊C4—431no—
482C2×C22⋊C4—861no—
483C2×C22⋊C4—861no—
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×C42—431no—
491C2×C42—861no—
492C2×C42—861no—
493#107—862no—
494#106—862no—
495#106—1721no—
496#106—1721no—
497#103—22no—
498#103—862no—
499#103—1721no—
500#103C22⋊D4314yescomplemented
501#102—22no—
502#102—22no—
503#102—862no—
504#102—1721no—
505C22⋊C8—862no—
506C22⋊C8—862no—
507C22⋊C8—1721no—
508#95—861no—
509#95—861no—
510#95—861no—
511#95—861no—
512#95—861no—
513#95—861no—
514#95—861no—
515#95—861no—
516C24—21no—
517C24—431no—
518C24D4×D4311yescharacteristic
519#41—28no—
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×C22⋊D4312yes—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—862no—
538C2×D4—3441no—
539C2×D4—1721no—
540C2×D4—1721no—
541C2×D4—1722no—
542C2×D4—1722no—
543C2×D4#1062189812yes—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—81no—
557C22×C4—431no—
558C22×C4—431no—
559C22×C4—431no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4—861no—
563C22×C4—861no—
564C22×C4—861no—
565C22×C4—861no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—861no—
569C22×C4—861no—
570C22×C4#1062189812yes—
571C22×C4D4×D4311yescharacteristic
572C22×C4#1062190012yes—
573C22×C4C23×D4311yescharacteristic
574M16—44no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—861no—
581C2×C8—861no—
582C2×C8—861no—
583C2×C8—861no—
584C2×C8—861no—
585C2×C8—861no—
586C2×C8C2×C22⋊D4312yes—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—42no—
591C4⋊C4—862no—
592C4⋊C4—861no—
593C4⋊C4—861no—
594C4⋊C4—861no—
595C4⋊C4—861no—
596C4⋊C4—861no—
597C4⋊C4—861no—
598C4⋊C4—861no—
599C4⋊C4—861no—
600C4⋊C4—1722no—
601C4⋊C4C2×C22⋊D4312yes—
602C22⋊C4—862no—
603C22⋊C4—862no—
604C22⋊C4—3441no—
605C22⋊C4—3441no—
606C22⋊C4—3441no—
607C22⋊C4—1722no—
608C22⋊C4—1722no—
609C22⋊C4—1722no—
610C22⋊C4—1722no—
611C22⋊C4—1722no—
612C42—861no—
613C42—861no—
614C42—3441no—
615C42—1722no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—22no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—861no—
630C23—861no—
631C23—861no—
632C23—861no—
633C23—861no—
634C23—861no—
635C23—861no—
636C23#1306330712yes—
637C23C2×D4×D4311yescharacteristic
638Q8—22no—
639Q8—22no—
640Q8—41no—
641Q8—41no—
642D4—22no—
643D4—22no—
644D4—48no—
645D4—41no—
646D4—41no—
647D4—3444no—
648D4—1724no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—48no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—84no—
666C2×C4—861no—
667C2×C4—861no—
668C2×C4—861no—
669C2×C4—861no—
670C2×C4—861no—
671C2×C4—861no—
672C2×C4—861no—
673C2×C4—861no—
674C2×C4—861no—
675C2×C4—1721no—
676C2×C4—1721no—
677C2×C4—1721no—
678C2×C4—1721no—
679C2×C4—1721no—
680C2×C4—1721no—
681C2×C4—1721no—
682C2×C4—1721no—
683C2×C4—1721no—
684C2×C4—1721no—
685C2×C4—1721no—
686C2×C4—1721no—
687C2×C4—1721no—
688C2×C4—1721no—
689C2×C4—1721no—
690C2×C4—1721no—
691C2×C4#1306330712yes—
692C2×C4C22×C22⋊D4311yescharacteristic
693C2×C4C2×#1062190011yescharacteristic
694C2×C4C2×#1062189811yescharacteristic
695C2×C4C2×#1062189811yescharacteristic
696C2×C4#1306337011yescharacteristic
697C2×C4#1306337011yescharacteristic
698C8—22no—
699C8—41no—
700C8—1721no—
701C8—1721no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—1721no—
717C22—1721no—
718C22—1721no—
719C22—1721no—
720C22—1721no—
721C22—1721no—
722C22—1721no—
723C22C2×#1306330711yescharacteristic
724C22D4×C22⋊D4311yescharacteristic
725C22#1458353911yescharacteristic
726C22#1458369511yescharacteristic
727C22#1458369811yescharacteristic
728C22#1458370811yescharacteristic
729C22#1458370911yescharacteristic
730C4—22no—
731C4—42no—
732C4—42no—
733C4—81no—
734C4—3441no—
735C4—3441no—
736C4—3441no—
737C4—3441no—
738C4—1721no—
739C4—1721no—
740C4—1721no—
741C4#1458341011yescharacteristic
742C4#1458348711yescharacteristic
743C4#1458354311yescharacteristic
744C4#1458357511yescharacteristic
745C2—42no—
746C2—82no—
747C2—3441no—
748C2#1913805711yescharacteristic
749C2#1914452511yescharacteristic
750C2#1914458311yescharacteristic
751C2#1914617411yescharacteristic
752C2#1914622611yescharacteristic
753C2#1914657211yescharacteristic
754C2#1914681211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#417C2
socleC23×C43C22×D4
prime radical#19137934C2
hypercenterC2×#417D43
hypocenterC43#24891
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#14583239C2semidirect
3. #19137520C2semidirect
4. #19136114C2semidirect
5. #19136016C2semidirect
6. #19135789C2semidirect
7. #19135783C2semidirect
8. #19135231C2semidirect
9. #19135225C2semidirect
10. #19134914C2semidirect
11. #19134892C2semidirect
12. #19134788C2semidirect
13. #19134628C2semidirect
14. #19134535C2semidirect
15. C2×C43×#417C2semidirect
135. #103×C43D4semidirect
369. C2×#417D43semidirect
438. C43#24891semidirect
500. #103C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145832392
#191379342
#191375202
#191361142
#191360162
#191357892
#191357832
#191352312
#191352252
#191349142
#191348922
#191347882
#191346282
#191345352
C2×C43×#4172
#2489143