Finite Group Databasebeta

← #25107791

Subgroups — #25107791

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×#14583046C211yesmaximal, characteristic
2C4×#13063299C211yesmaximal, characteristic, complemented
3#19137085C211yesmaximal, characteristic, complemented
4#19135461C211yesmaximal, characteristic, complemented
5#19135449C211yesmaximal, characteristic, complemented
6#19135278C211yesmaximal, characteristic, complemented
7#19135271C211yesmaximal, characteristic, complemented
8#19135237C211yesmaximal, characteristic, complemented
9#19135223C211yesmaximal, characteristic, complemented
10#19134942C211yesmaximal, characteristic, complemented
11#19134928C211yesmaximal, characteristic, complemented
12#19134915C211yesmaximal, characteristic, complemented
13#19134796C211yesmaximal, characteristic, complemented
14#19134536C211yesmaximal, characteristic, complemented
15C4×C22⋊C8×C43C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C22×D344C2211yescharacteristic
19C2×#13063299C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21C2×C4×C22⋊D43—21no—
22C2×#13063284C2211yescharacteristic
23#14583046C418yescomplemented
24C2×#13063259C2211yescharacteristic
25C2×#13063257C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063250C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×#13063247C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34#14582805C2211yescharacteristic
35#14582805C2211yescharacteristic
36#14582801C2211yescharacteristic
37#14582801C2211yescharacteristic
38#14582801C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582790—21no—
41#14582778—21no—
42#14582778—21no—
43#14582778—21no—
44#14582759C2211yescharacteristic
45C4×C4⋊Dic43C2211yescharacteristic
46C4×(C2×D43)⋊C4—21no—
47C4×(C2×D43)⋊C4—21no—
48C4×(C2×D43)⋊C4—21no—
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53C22×C42×C43C2211yescharacteristic
54C2×C22⋊C8×C43C2211yescharacteristic
55C2×C22⋊C8×C43C2211yescharacteristic
56C2×C4×C8×C43C2211yescharacteristic
57C2×C4×C8×C43C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C2×#10621898—22no—
61C2×#10621898—41no—
62C2×#10621898—41no—
63C2×#10621898—41no—
64C2×#10621898—41no—
65C2×#10621898C2×C414yescomplemented
66C22×Dic86C2311yescharacteristic
67C22×D172C2311yescharacteristic
68C22×D172C2311yescharacteristic
69C22×C22⋊D43—21no—
70C22×C22⋊D43—21no—
71C22×C4×D43—21no—
72C22×C4×D43—21no—
73C2×#10621873—41no—
74C2×#10621873—41no—
75C2×#10621873C2×C414yescomplemented
76C2×D344—41no—
77C2×D344—41no—
78C2×D344C2×C414yescomplemented
79#13063299—22no—
80#13063299C2×C414yes—
81C4×D172—41no—
82C4×D172—41no—
83C4×C22⋊D43—44no—
84#13063284—41no—
85#13063284—41no—
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×Dic43⋊C4—21no—
92C2×C22⋊Dic43—21no—
93C2×C22⋊Dic43—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)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×C4×Dic43—21no—
103C2×C4×Dic43—21no—
104#13063259—41no—
105#13063257—41no—
106#13063250—41no—
107#13063250—41no—
108#13063250C2×C414yescomplemented
109#13063247—41no—
110#13063247—41no—
111#13063247—41no—
112#13063247—41no—
113#13063247C2×C414yescomplemented
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C23×C4×C43D411yescharacteristic
122C23×C4×C43D411yescharacteristic
123C23×C4×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C2×C42×C43—41no—
129C2×C42×C43—41no—
130C2×C42×C43D411yescharacteristic
131C2×C42×C43D411yescharacteristic
132C2×C42×C43C2311yescharacteristic
133C2×C42×C43C2311yescharacteristic
134C22⋊C8×C43—22no—
135C22⋊C8×C43C2×C414yescomplemented
136C4×C8×C43—41no—
137C4×C8×C43—41no—
138C24×C43C2×D411yescharacteristic
139C23×D43—21no—
140C23×D43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—22no—
146C22×C4×C43—22no—
147C22×C4×C43—22no—
148C22×C4×C43—41no—
149C22×C4×C43—41no—
150C22×C4×C43—41no—
151C22×C4×C43C22×C412yes—
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43#4112yes—
158C22×C4×C43C2411yescharacteristic
159C2×C22⋊D43—24no—
160C2×C22⋊D43—24no—
161C2×C22⋊D43—42no—
162C2×C22⋊D43—42no—
163C2×C22⋊D43—42no—
164C2×C22⋊D43—42no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171#10621898—44no—
172#10621898—44no—
173#10621898—44no—
174#10621898—44no—
175C2×D172—21no—
176C2×D172—21no—
177C2×D172—21no—
178C2×D172—21no—
179C2×D172—21no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172—21no—
184C2×D172—21no—
185C2×D172C22×C412yes—
186C2×D172C22×C412yes—
187C2×C4×D43—24no—
188C2×C4×D43—42no—
189C2×C4×D43—42no—
190C2×C4×D43—42no—
191C2×C4×D43—42no—
192C2×C4×D43—42no—
193C2×Dic86—21no—
194C2×Dic86—21no—
195C2×Dic86—21no—
196C2×Dic86—21no—
197C2×Dic86—21no—
198C2×Dic86C22×C412yes—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43C22×C412yes—
210C2×C8×C43C22×C412yes—
211C42×C43—21no—
212C42×C43—21no—
213C42×C43—21no—
214C42×C43—21no—
215C42×C43—41no—
216C42×C43—41no—
217C22⋊Dic43—42no—
218C22⋊Dic43—42no—
219(C2×D43)⋊C4—24no—
220(C2×D43)⋊C4—42no—
221(C2×D43)⋊C4—42no—
222(C2×D43)⋊C4—42no—
223(C2×D43)⋊C4—42no—
224(C2×D43)⋊C4—42no—
225(C2×D43)⋊C4—42no—
226(C2×D43)⋊C4—42no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236C4⋊Dic43C22×C412yes—
237Dic43⋊C4—42no—
238C4×Dic43—42no—
239C4×Dic43—42no—
240D344—44no—
241#10621873—44no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43C4×D412yes—
249C23×C43C22×D411yescharacteristic
250C22×D43—22no—
251C22×D43—22no—
252C22×D43—41no—
253C22×D43—41no—
254C22×D43—41no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—41no—
259C22×D43—41no—
260C22×D43—41no—
261C22×D43—41no—
262C22×D43—41no—
263C22×D43—41no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
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—21no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—44no—
280C2×C4×C43—44no—
281C2×C4×C43C4×D412yes—
282C2×C4×C43#13512yes—
283C2×C4×C43#13512yes—
284C2×C4×C43AGL(1,ℤ/8)12yes—
285C2×C4×C43C23×C411yescharacteristic
286C2×C4×C43C2×#4111yescharacteristic
287C2×C4×C43H(5,𝔽2)11yescharacteristic
288C2×C4×C43H(5,𝔽2)11yescharacteristic
289C2×C4×C43H(5,𝔽2)11yescharacteristic
290C2×C4×C43H(5,𝔽2)11yescharacteristic
291C22⋊D43—48no—
292C22⋊D43—48no—
293C2×Dic43—22no—
294C2×Dic43—22no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311D172—22no—
312D172—22no—
313D172—22no—
314D172—22no—
315D172—41no—
316D172—41no—
317D172—41no—
318D172—41no—
319C4×D43—48no—
320C4×D43—84no—
321Dic86—22no—
322Dic86—22no—
323Dic86—41no—
324Dic86—41no—
325C8×C43—22no—
326C8×C43—22no—
327C8×C43—41no—
328C8×C43—41no—
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×C43C2×C4×D411yescharacteristic
338C22×C43#53411yescharacteristic
339C22×C43#53511yescharacteristic
340C22×C43C2×#13511yescharacteristic
341C22×C43C2×#13511yescharacteristic
342C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
343C22×C43#57511yescharacteristic
344C2×D43—42no—
345C2×D43—42no—
346C2×D43—42no—
347C2×D43—42no—
348C2×D43—42no—
349C2×D43—42no—
350C2×D43—81no—
351C2×D43—81no—
352C2×D43—81no—
353C2×D43—81no—
354C2×D43—81no—
355C2×D43—81no—
356C2×D43—81no—
357C2×D43—81no—
358C4×C43—22no—
359C4×C43—22no—
360C4×C43—22no—
361C4×C43—22no—
362C4×C43—41no—
363C4×C43#51811yescharacteristic
364C4×C43#51811yescharacteristic
365C4×C43#53811yescharacteristic
366C4×C43#53811yescharacteristic
367Dic43—42no—
368Dic43—42no—
369Dic43—81no—
370Dic43—81no—
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#1788—431no—
387C4×C22⋊C8D4311yescharacteristic, complemented
388C2×C43—42no—
389C2×C43#232111yescharacteristic
390C2×C43C4×#13511yescharacteristic
391C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
392C2×C43#318811yescharacteristic
393C2×C43#319111yescharacteristic
394C2×C43#320711yescharacteristic
395C2×C43#321211yescharacteristic
396D43—82no—
397D43—82no—
398C22×#41—431no—
399C22×SD16—431no—
400C22×D8—431no—
401C2×#121—431no—
402C2×C4×D4—431no—
403C2×C4×D4—861no—
404C2×#117—431no—
405C22×C42C2×D4311yescharacteristic
406#449—438no—
407C2×#107—431no—
408C2×#106—431no—
409C2×#103—431no—
410C2×#103—431no—
411C2×#103—431no—
412C2×#102—431no—
413C2×#102—431no—
414C2×#102—431no—
415C2×#102—431no—
416C2×#102—431no—
417C2×C22⋊C8C2×D4311yescharacteristic
418C2×C22⋊C8C2×D4311yescharacteristic
419C2×C4×C8C2×D4311yescharacteristic
420C2×C4×C8C2×D4311yescharacteristic
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#380—431no—
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#336C2×D4311yescharacteristic
441#336C2×D4311yescharacteristic
442C43#2204511yescharacteristic, complemented, Sylow
443C2×#41—434no—
444C2×#41—862no—
445C2×#41—1721no—
446C2×#41—1721no—
447C2×#41—1721no—
448C2×#41—1721no—
449C22×Q8—431no—
450C22×D4—431no—
451C22×D4—431no—
452C22×D4—861no—
453C22×D4—861no—
454C23×C4—861no—
455C23×C4—861no—
456C23×C4D17211yescharacteristic
457C23×C4D17211yescharacteristic
458C23×C4C22×D4311yescharacteristic
459C2×SD16—434no—
460C2×SD16—1721no—
461C2×SD16—1721no—
462C2×D8—434no—
463C2×D8—1721no—
464C2×D8—1721no—
465C22×C8C22×D4311yescharacteristic
466C22×C8C22×D4311yescharacteristic
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—431no—
480C2×C4⋊C4—431no—
481C2×C4⋊C4—861no—
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×C22⋊C4—861no—
491C2×C22⋊C4—861no—
492C2×C42—41no—
493C2×C42—41no—
494C2×C42—861no—
495C2×C42—861no—
496C2×C42D17211yescharacteristic
497C2×C42D17211yescharacteristic
498C2×C42C22×D4311yescharacteristic
499C2×C42C22×D4311yescharacteristic
500#107—1721no—
501#106—1721no—
502#103—434no—
503#103—1721no—
504#103—1721no—
505#102—434no—
506#102—1721no—
507#102—1721no—
508#102—1721no—
509#102—1721no—
510C22⋊C8—22no—
511C22⋊C8C4×D4314yescomplemented
512C4×C8—41no—
513C4×C8—41no—
514#95—861no—
515#95—861no—
516#95—861no—
517#95—861no—
518#95—861no—
519#95—861no—
520#95—861no—
521C24—861no—
522C24—861no—
523C24C2×D17211yescharacteristic
524#41—1724no—
525#41—1724no—
526#41—1724no—
527#41—1724no—
528C2×Q8—432no—
529C2×Q8—861no—
530C2×Q8—861no—
531C2×Q8—861no—
532C2×Q8—861no—
533C2×Q8—861no—
534C2×D4—432no—
535C2×D4—432no—
536C2×D4—864no—
537C2×D4—864no—
538C2×D4—861no—
539C2×D4—861no—
540C2×D4—861no—
541C2×D4—861no—
542C2×D4—861no—
543C2×D4—861no—
544C2×D4—861no—
545C2×D4—861no—
546C2×D4—861no—
547C2×D4—861no—
548C2×D4—1722no—
549C2×D4—1722no—
550C2×D4—1722no—
551C2×D4—1722no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—861no—
563C22×C4—861no—
564C22×C4—864no—
565C22×C4—861no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—861no—
569C22×C4—1722no—
570C22×C4—1722no—
571C22×C4—1722no—
572C22×C4—1722no—
573C22×C4—1722no—
574C22×C4C2×C4×D4312yes—
575C22×C4C2×D17211yescharacteristic
576C22×C4C2×D17211yescharacteristic
577C22×C4C2×D17211yescharacteristic
578C22×C4C2×D17211yescharacteristic
579C22×C4C2×D17211yescharacteristic
580C22×C4#1062189812yes—
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—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8C2×C4×D4312yes—
595C2×C8C2×C4×D4312yes—
596C4⋊C4—432no—
597C4⋊C4—861no—
598C4⋊C4—861no—
599C4⋊C4—861no—
600C4⋊C4—861no—
601C4⋊C4—861no—
602C4⋊C4—861no—
603C4⋊C4—861no—
604C4⋊C4—861no—
605C4⋊C4—861no—
606C4⋊C4—1722no—
607C22⋊C4—864no—
608C22⋊C4—1722no—
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—21no—
618C42—21no—
619C42—21no—
620C42—21no—
621C42—41no—
622C42—41no—
623C42—1722no—
624C42—1722no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—862no—
632C23—862no—
633C23—1721no—
634C23—1721no—
635C23—1721no—
636C23—1721no—
637C23—1721no—
638C23—1721no—
639C23—1721no—
640C23—1721no—
641C23—1721no—
642C23—1721no—
643C23—1721no—
644C23—1721no—
645C23C4×D17212yes—
646C23C22×D17211yescharacteristic
647Q8—862no—
648Q8—862no—
649Q8—1721no—
650Q8—1721no—
651D4—862no—
652D4—862no—
653D4—862no—
654D4—862no—
655D4—1728no—
656D4—1728no—
657D4—1721no—
658D4—1721no—
659D4—1721no—
660D4—1721no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—44no—
677C2×C4—44no—
678C2×C4—862no—
679C2×C4—862no—
680C2×C4—3444no—
681C2×C4—1728no—
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—1721no—
692C2×C4—1721no—
693C2×C4—1721no—
694C2×C4—1721no—
695C2×C4—1721no—
696C2×C4—1721no—
697C2×C4—1721no—
698C2×C4C4×D17212yes—
699C2×C4#1306334712yes—
700C2×C4#1306334712yes—
701C2×C4#1306335312yes—
702C2×C4C22×C4×D4311yescharacteristic
703C2×C4C2×#1062189811yescharacteristic
704C2×C4#1306337011yescharacteristic
705C2×C4#1306337011yescharacteristic
706C2×C4#1306337111yescharacteristic
707C2×C4#1306337111yescharacteristic
708C8—22no—
709C8—22no—
710C8—41no—
711C8—41no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—3441no—
720C22—3441no—
721C22—3441no—
722C22—3441no—
723C22—3441no—
724C22—3441no—
725C22—3441no—
726C22—3441no—
727C22—1722no—
728C22—1722no—
729C22—1722no—
730C22—1722no—
731C22—1722no—
732C22—1722no—
733C22C2×C4×D17211yescharacteristic
734C22#1458346111yescharacteristic
735C22#1458346811yescharacteristic
736C22C2×#1306334711yescharacteristic
737C22C2×#1306334711yescharacteristic
738C22C2×#1306335311yescharacteristic
739C22#1458369911yescharacteristic
740C4—22no—
741C4—22no—
742C4—22no—
743C4—22no—
744C4—41no—
745C4—3441no—
746C4—3441no—
747C4—3441no—
748C4—3441no—
749C4—1722no—
750C4—1722no—
751C4#1458337111yescharacteristic
752C4#1458337111yescharacteristic
753C4#1458348211yescharacteristic
754C4#1458348211yescharacteristic
755C2—42no—
756C2—3442no—
757C2—3442no—
758C2#1913725511yescharacteristic
759C2C4×#1306334711yescharacteristic
760C2C4×#1306335311yescharacteristic
761C2#1914536211yescharacteristic
762C2#1914538811yescharacteristic
763C2#1914553011yescharacteristic
764C2#1914557311yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×C22⋊C8×C43C2
socleC23×C43C22×D4
prime radicalC2×#14583046C2
cosocleC22×C4×C43C24
hypercenterC4×C22⋊C8D43
hypocenterC43#22045
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C4×#13063299C2semidirect
3. #19137085C2semidirect
4. #19135461C2semidirect
5. #19135449C2semidirect
6. #19135278C2semidirect
7. #19135271C2semidirect
8. #19135237C2semidirect
9. #19135223C2semidirect
10. #19134942C2semidirect
11. #19134928C2semidirect
12. #19134915C2semidirect
13. #19134796C2semidirect
14. #19134536C2semidirect
15. C4×C22⋊C8×C43C2semidirect
23. #14583046C4semidirect
65. C2×#10621898C2×C4semidirect
75. C2×#10621873C2×C4semidirect
78. C2×D344C2×C4semidirect
108. #13063250C2×C4semidirect
113. #13063247C2×C4semidirect
135. C22⋊C8×C43C2×C4semidirect
387. C4×C22⋊C8D43semidirect
442. C43#22045semidirect
511. C22⋊C8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830462
C4×#130632992
#191370852
#191354612
#191354492
#191352782
#191352712
#191352372
#191352232
#191349422
#191349282
#191349152
#191347962
#191345362
C4×C22⋊C8×C432
#2204543