Finite Group Databasebeta

← #25107785

Subgroups — #25107785

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×#14583044C211yesmaximal, characteristic
2#19137101C211yesmaximal, characteristic, complemented
3#19137086C211yesmaximal, characteristic, complemented
4#19135458C211yesmaximal, characteristic, complemented
5#19135446C211yesmaximal, characteristic, complemented
6#19135275C211yesmaximal, characteristic, complemented
7#19135268C211yesmaximal, characteristic, complemented
8#19135239C211yesmaximal, characteristic, complemented
9#19135225C211yesmaximal, characteristic, complemented
10#19134940C211yesmaximal, characteristic, complemented
11#19134926C211yesmaximal, characteristic, complemented
12#19134915C211yesmaximal, characteristic, complemented
13#19134792C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic43C211yesmaximal, characteristic, complemented
15C43×#1788C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×#13063299C2211yescharacteristic
19C2×#13063287C2211yescharacteristic
20C2×(C22⋊D43)⋊C4—21no—
21C2×#13063284C2211yescharacteristic
22C22×C4×Dic43C2211yescharacteristic
23#14583044C418yescomplemented
24C2×#13063258C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×C22⋊(C43⋊C8)C2211yescharacteristic
31C2×C8×Dic43C2211yescharacteristic
32C2×C8×Dic43C2211yescharacteristic
33#14582806C2211yescharacteristic
34#14582806C2211yescharacteristic
35#14582802C2211yescharacteristic
36#14582802C2211yescharacteristic
37#14582800C2211yescharacteristic
38#14582795C2211yescharacteristic
39#14582788—21no—
40#14582779—21no—
41#14582779—21no—
42#14582776—21no—
43C4⋊C4×Dic43C2211yescharacteristic
44C4×C22⋊Dic43—21no—
45C4×C22⋊Dic43—21no—
46#14582746—21no—
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×Dic43D411yescharacteristic
63C23×Dic43D411yescharacteristic
64C22×C4×D43—21no—
65C2×#10621884—41no—
66C2×#10621884—41no—
67C2×#10621884C2×C414yescomplemented
68C2×#10621882—41no—
69C2×#10621882—41no—
70C2×#10621882C2×C414yescomplemented
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063299—22no—
74#13063299C2×C414yes—
75#13063287—41no—
76#13063287—41no—
77(C22⋊D43)⋊C4—44no—
78#13063284—41no—
79#13063284—41no—
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×Dic43⋊C4—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43—41no—
96C2×C4×Dic43—41no—
97C2×C4×Dic43D411yescharacteristic
98C2×C4×Dic43D411yescharacteristic
99C2×C4×Dic43C2311yescharacteristic
100C2×C4×Dic43C2311yescharacteristic
101#13063258—41no—
102#13063256—41no—
103#13063249C2×C414yescomplemented
104#13063247—41no—
105#13063247—41no—
106#13063246C2×C414yescomplemented
107C22⋊(C43⋊C8)C2×C414yescomplemented
108C8×Dic43—41no—
109C8×Dic43—41no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C2×#41×C43—22no—
117C2×#41×C43—41no—
118C2×#41×C43—41no—
119C2×#41×C43—41no—
120C2×#41×C43—41no—
121C2×#41×C43C2×C414yescomplemented
122C22×Q8×C43C2311yescharacteristic
123C22×D4×C43—21no—
124C22×D4×C43C2311yescharacteristic
125C23×C4×C43—21no—
126C23×C4×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C22⋊C4×C43—21no—
132#103×C43—41no—
133#103×C43—41no—
134#102×C43—41no—
135#102×C43—41no—
136C22⋊C8×C43—22no—
137#95×C43—21no—
138C24×C43—21no—
139C24×C43C2×D411yescharacteristic
140C23×D43—21no—
141#41×C43—44no—
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×C43C22×C412yes—
151C2×D4×C43—21no—
152C2×D4×C43—24no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—42no—
158C2×D4×C43—42no—
159C2×D4×C43C22×C412yes—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—24no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—42no—
169C22×C4×C43—42no—
170C22×C4×C43C22×C412yes—
171C22×C4×C43C2×D411yescharacteristic
172C22×C4×C43#4112yes—
173C22×C4×C43C2411yescharacteristic
174C2×C22⋊D43—24no—
175C2×C22⋊D43—42no—
176C2×C22⋊D43—42no—
177C22×Dic43—22no—
178C22×Dic43—22no—
179C22×Dic43—22no—
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43—21no—
183C22×Dic43—41no—
184C22×Dic43—41no—
185C22×Dic43—41no—
186C22×Dic43C2×D411yescharacteristic
187C22×Dic43C2×D411yescharacteristic
188C22×Dic43C2×D411yescharacteristic
189C22×Dic43C2×D411yescharacteristic
190C2×D172—21no—
191C2×D172—21no—
192C2×D172—21no—
193C2×D172—21no—
194C2×D172—21no—
195C2×D172C22×C412yes—
196C2×C4×D43—42no—
197C2×C4×D43—42no—
198C2×C4×D43—42no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C22⋊C4×C43—42no—
210C22⋊Dic43—42no—
211C22⋊Dic43—42no—
212C22⋊Dic43—42no—
213C22⋊Dic43—42no—
214C22⋊Dic43—42no—
215#10621884—44no—
216#10621882—44no—
217(C2×D43)⋊C4—24no—
218(C2×D43)⋊C4—42no—
219(C2×D43)⋊C4—42no—
220(C2×D43)⋊C4—42no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43C22×C412yes—
227Dic43⋊C4—42no—
228C4×Dic43—21no—
229C4×Dic43—21no—
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⋊C8C22×C412yes—
241C2×C43⋊C8C22×C412yes—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—22no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43C4×D412yes—
256C23×C43C22×D411yescharacteristic
257C22×D43—22no—
258C22×D43—41no—
259C22×D43—41no—
260C22×D43—41no—
261C22×D43—41no—
262C22×D43—41no—
263C22×D43—41no—
264Q8×C43—22no—
265Q8×C43—22no—
266Q8×C43—41no—
267Q8×C43—41no—
268D4×C43—22no—
269D4×C43—22no—
270D4×C43—48no—
271D4×C43—41no—
272D4×C43—41no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—48no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
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
296C22⋊D43—48no—
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—22no—
304C2×Dic43—21no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—44no—
308C2×Dic43—44no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43#13512yes—
318C2×Dic43#13512yes—
319C2×Dic43AGL(1,ℤ/8)12yes—
320D172—22no—
321D172—22no—
322D172—41no—
323D172—41no—
324C4×D43—84no—
325C8×C43—41no—
326C8×C43—41no—
327C43⋊C8—22no—
328C43⋊C8—22no—
329#22045—431nomaximal, Sylow
330C22×C43—22no—
331C22×C43—22no—
332C22×C43—22no—
333C22×C43—41no—
334C22×C43—41no—
335C22×C43—41no—
336C22×C43—41no—
337C22×C43—42no—
338C22×C43—42no—
339C22×C43—42no—
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—42no—
352C2×D43—42no—
353C2×D43—42no—
354C2×D43—81no—
355C2×D43—81no—
356C2×D43—81no—
357C2×D43—81no—
358C4×C43—22no—
359C4×C43—42no—
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—41no—
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#1879—431no—
383#1877—431no—
384#1875—431no—
385#1854—431no—
386#1788D4311yescharacteristic, complemented
387C4×C22⋊C8—431no—
388C2×C43—42no—
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—82no—
398C22×#41C2×D4311yescharacteristic
399C22×SD16—431no—
400C22×D8—431no—
401C2×#121—431no—
402C2×C4×D4—431no—
403C2×C4×D4—861no—
404C2×#117—431no—
405C22×C42—431no—
406#449—438no—
407C2×#107—431no—
408C2×#106—431no—
409C2×#103—431no—
410C2×#103C2×D4311yescharacteristic
411C2×#103C2×D4311yescharacteristic
412C2×#102—431no—
413C2×#102—431no—
414C2×#102—431no—
415C2×#102C2×D4311yescharacteristic
416C2×#102C2×D4311yescharacteristic
417C2×C22⋊C8—431no—
418C2×C22⋊C8C2×D4311yescharacteristic
419C2×C4×C8—431no—
420C2×C4×C8—431no—
421#391—431no—
422#391—431no—
423#390—431no—
424#390—431no—
425#390—431no—
426#389—431no—
427#388—861no—
428#386—861no—
429#386—861no—
430#386—861no—
431#380C2×D4311yescharacteristic
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#340—431no—
440#336—431no—
441#336—431no—
442C43#2204511yescharacteristic, complemented, Sylow
443C2×#41—22no—
444C2×#41—41no—
445C2×#41—41no—
446C2×#41—41no—
447C2×#41—41no—
448C2×#41C4×D4314yescomplemented
449C22×Q8C22×D4311yescharacteristic
450C22×D4—21no—
451C22×D4—431no—
452C22×D4—861no—
453C22×D4C22×D4311yescharacteristic
454C23×C4—21no—
455C23×C4—431no—
456C23×C4—431no—
457C23×C4—861no—
458C23×C4C22×D4311yescharacteristic
459C2×SD16—434no—
460C2×SD16—1721no—
461C2×SD16—1721no—
462C2×D8—434no—
463C2×D8—1721no—
464C2×D8—1721no—
465C22×C8—431no—
466C22×C8—431no—
467C22×C8C22×D4311yescharacteristic
468C22×C8C22×D4311yescharacteristic
469#121—434no—
470#121—862no—
471C4×D4—1721no—
472C4×D4—1721no—
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—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×C22⋊C4—861no—
491C2×C22⋊C4—861no—
492C2×C42—431no—
493C2×C42—431no—
494C2×C42—431no—
495C2×C42—431no—
496C2×C42—861no—
497C2×C42—861no—
498C2×C42—1721no—
499C2×C42—1721no—
500#107—1721no—
501#106—1721no—
502#103—41no—
503#103—41no—
504#103—434no—
505#102—41no—
506#102—41no—
507#102—434no—
508#102—1721no—
509#102—1721no—
510C22⋊C8—22no—
511C22⋊C8—434no—
512C4×C8—1721no—
513C4×C8—1721no—
514#95—21no—
515#95—861no—
516#95—861no—
517#95—861no—
518#95—861no—
519#95—861no—
520#95—861no—
521C24—21no—
522C24—861no—
523C24D4×D4311yescharacteristic
524#41—44no—
525#41—44no—
526#41—44no—
527#41—44no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8C2×C4×D4312yes—
534C2×D4—24no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—432no—
543C2×D4—864no—
544C2×D4—861no—
545C2×D4—861no—
546C2×D4—861no—
547C2×D4—861no—
548C2×D4—861no—
549C2×D4—1722no—
550C2×D4—1722no—
551C2×D4C2×C4×D4312yes—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—24no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—431no—
563C22×C4—431no—
564C22×C4—431no—
565C22×C4—431no—
566C22×C4—862no—
567C22×C4—862no—
568C22×C4—862no—
569C22×C4—861no—
570C22×C4—861no—
571C22×C4—861no—
572C22×C4—1722no—
573C22×C4—1722no—
574C22×C4—1722no—
575C22×C4—1721no—
576C22×C4—1721no—
577C22×C4—1721no—
578C22×C4C2×C4×D4312yes—
579C22×C4D4×D4311yescharacteristic
580C22×C4#1062190012yes—
581C22×C4C23×D4311yescharacteristic
582SD16—1724no—
583D8—1724no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—432no—
591C2×C8—432no—
592C2×C8—861no—
593C2×C8—861no—
594C2×C8—861no—
595C2×C8—861no—
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—864no—
609C22⋊C4—1722no—
610C22⋊C4—1722no—
611C22⋊C4—1722no—
612C22⋊C4—1722no—
613C22⋊C4—1722no—
614C22⋊C4—1722no—
615C22⋊C4—1722no—
616C22⋊C4—1722no—
617C42—861no—
618C42—861no—
619C42—861no—
620C42—861no—
621C42—1721no—
622C42—1721no—
623C42—1722no—
624C42—1722no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—22no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—862no—
639C23—1721no—
640C23—1721no—
641C23—1721no—
642C23—1721no—
643C23—1721no—
644C23—1721no—
645C23(C22⋊D43)⋊C412yes—
646C23C2×D4×D4311yescharacteristic
647Q8—22no—
648Q8—22no—
649Q8—41no—
650Q8—41no—
651D4—22no—
652D4—22no—
653D4—48no—
654D4—41no—
655D4—41no—
656D4—862no—
657D4—862no—
658D4—1728no—
659D4—1721no—
660D4—1721no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—48no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—432no—
678C2×C4—432no—
679C2×C4—432no—
680C2×C4—861no—
681C2×C4—861no—
682C2×C4—861no—
683C2×C4—861no—
684C2×C4—861no—
685C2×C4—861no—
686C2×C4—862no—
687C2×C4—861no—
688C2×C4—861no—
689C2×C4—861no—
690C2×C4—3444no—
691C2×C4—1724no—
692C2×C4—1724no—
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(C22⋊D43)⋊C412yes—
702C2×C4C22×C4×D4311yescharacteristic
703C2×C4C2×#1062190011yescharacteristic
704C2×C4#1306337011yescharacteristic
705C2×C4#1306337011yescharacteristic
706C2×C4#1306337011yescharacteristic
707C2×C4#1306337011yescharacteristic
708C8—41no—
709C8—41no—
710C8—862no—
711C8—862no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—3441no—
727C22—3441no—
728C22—3441no—
729C22—3441no—
730C22—1722no—
731C22—1722no—
732C22—1722no—
733C22C2×(C22⋊D43)⋊C411yescharacteristic
734C22#1458345911yescharacteristic
735C22#1458346411yescharacteristic
736C22#135×D4311yescharacteristic
737C22#135×D4311yescharacteristic
738C22AGL(1,ℤ/8)×D4311yescharacteristic
739C22#1458369811yescharacteristic
740C4—22no—
741C4—42no—
742C4—81no—
743C4—81no—
744C4—862no—
745C4—862no—
746C4—862no—
747C4—3441no—
748C4—3441no—
749C4—1721no—
750C4—1722no—
751C4#1458337211yescharacteristic
752C4#1458337211yescharacteristic
753C4#1458348411yescharacteristic
754C4#1458348411yescharacteristic
755C2—42no—
756C2—82no—
757C2—3442no—
758C2#1913725011yescharacteristic
759C2#1914336311yescharacteristic
760C2#1914340811yescharacteristic
761C2#1914535811yescharacteristic
762C2#1914538711yescharacteristic
763C2#1914552611yescharacteristic
764C2#1914557411yescharacteristic
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#22045
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. #19137101C2semidirect
3. #19137086C2semidirect
4. #19135458C2semidirect
5. #19135446C2semidirect
6. #19135275C2semidirect
7. #19135268C2semidirect
8. #19135239C2semidirect
9. #19135225C2semidirect
10. #19134940C2semidirect
11. #19134926C2semidirect
12. #19134915C2semidirect
13. #19134792C2semidirect
14. C22⋊C8×Dic43C2semidirect
15. C43×#1788C2semidirect
23. #14583044C4semidirect
67. C2×#10621884C2×C4semidirect
70. C2×#10621882C2×C4semidirect
103. #13063249C2×C4semidirect
106. #13063246C2×C4semidirect
107. C22⋊(C43⋊C8)C2×C4semidirect
121. C2×#41×C43C2×C4semidirect
386. #1788D43semidirect
442. C43#22045semidirect
448. 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
#191371012
#191370862
#191354582
#191354462
#191352752
#191352682
#191352392
#191352252
#191349402
#191349262
#191349152
#191347922
C22⋊C8×Dic432
C43×#17882
#2204543