Finite Group Databasebeta

← #25107766

Subgroups — #25107766

Order 11008.

1224 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583048C211yesmaximal, characteristic
2#19137133C211yesmaximal, characteristic, complemented
3#390×D43C211yesmaximal, characteristic
4#19135452C211yesmaximal, characteristic, complemented
5#19135281C211yesmaximal, characteristic, complemented
6#19135278C211yesmaximal, characteristic, complemented
7#19135225C211yesmaximal, characteristic, complemented
8#19135221C211yesmaximal, characteristic, complemented
9#19134952C211yesmaximal, characteristic, complemented
10#19134948C211yesmaximal, characteristic, complemented
11#19134899C211yesmaximal, characteristic, complemented
12#19134786C211yesmaximal, characteristic, complemented
13#19134524C211yesmaximal, characteristic
14C4×(C2×D43)⋊C8C211yesmaximal, characteristic, complemented
15C43×#1968C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C2×#13063301C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic, complemented
20C2×C4⋊C4×D43C2211yescharacteristic
21C2×C22⋊C4×D43—21no—
22C2×C22⋊C4×D43—21no—
23C2×C42×D43C2211yescharacteristic
24#14583048C418yescomplemented
25C2×#13063256C2211yescharacteristic, complemented
26C2×#13063249C2211yescharacteristic, complemented
27C2×#13063247C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×(C2×D43)⋊C8C2211yescharacteristic
33C2×(C2×D43)⋊C8C2211yescharacteristic
34C2×C4×C43⋊C8C2211yescharacteristic, complemented
35#14582802C2211yescharacteristic
36#14582801C2211yescharacteristic
37#14582800C2211yescharacteristic
38#14582799—21no—
39#14582799—21no—
40#14582797C2211yescharacteristic, complemented
41#14582786—21no—
42#14582773—21no—
43#14582756C2211yescharacteristic
44C4⋊C4×Dic43C2211yescharacteristic, complemented
45#14582750—21no—
46#14582746—21no—
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×D43—21no—
70C22×C4×D43D411yescharacteristic
71C22×C4×D43D411yescharacteristic
72C22×C4×D43C2311yescharacteristic
73C2×#10621884—41no—
74C2×#10621884—41no—
75C2×#10621884C2×C414yescomplemented
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78#13063301—22no—
79#13063301C2×C414yes—
80Q8×Dic43—41no—
81Q8×Dic43—41no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C4⋊C4×D43—41no—
90C4⋊C4×D43—41no—
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—
99C22⋊C4×D43—44no—
100C22⋊C4×D43—44no—
101C2×C4×Dic43—21no—
102C2×C4×Dic43—21no—
103C2×C4×Dic43D411yescharacteristic
104C2×C4×Dic43D411yescharacteristic
105C2×C4×Dic43C2311yescharacteristic
106C42×D43—41no—
107C42×D43—41no—
108#13063256—41no—
109#13063249—41no—
110#13063247—41no—
111#13063247C2×C414yescomplemented
112#13063246—41no—
113#13063246C2×C414yescomplemented
114#13063245—41no—
115(C2×D43)⋊C8—22no—
116(C2×D43)⋊C8C2×C414yes—
117C4×C43⋊C8—41no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C22×Q8×C43C2311yescharacteristic
122C22×D4×C43C2311yescharacteristic
123C2×SD16×C43—41no—
124C2×SD16×C43—41no—
125C2×SD16×C43C2×C414yescomplemented
126C22×C8×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—21no—
132C2×C42×C43C2311yescharacteristic
133#106×C43—41no—
134#103×C43—41no—
135#102×C43—41no—
136C4×C8×C43—41no—
137#95×C43—21no—
138#95×C43—21no—
139C24×C43—21no—
140C23×D43—21no—
141C23×D43—24no—
142C23×D43—42no—
143C23×D43—42no—
144C23×D43—42no—
145C23×D43—42no—
146C23×D43—42no—
147C23×D43—42no—
148C23×D43C2×D411yescharacteristic
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43C22×C412yes—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43C22×C412yes—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2411yescharacteristic
167C2×C22⋊D43—24no—
168C2×C22⋊D43—42no—
169C2×C22⋊D43—42no—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43—21no—
173C22×Dic43C2×D411yescharacteristic
174C22×Dic43C2×D411yescharacteristic
175C22×Dic43C2×D411yescharacteristic
176D4×D43—44no—
177D4×D43—44no—
178D4×D43—44no—
179D4×D43—44no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172—21no—
184C2×D172—21no—
185C2×D172C22×C412yes—
186C2×C4×D43—21no—
187C2×C4×D43—21no—
188C2×C4×D43—21no—
189C2×C4×D43—21no—
190C2×C4×D43—22no—
191C2×C4×D43—22no—
192C2×C4×D43—41no—
193C2×C4×D43—41no—
194C2×C4×D43—41no—
195C2×C4×D43—42no—
196C2×C4×D43—42no—
197C2×C4×D43—42no—
198C2×C4×D43SD1614yescomplemented
199C2×C4×D43C22×C412yes—
200C2×C4×D43#4112yes—
201SD16×C43—44no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43C22×C412yes—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C22⋊C4×C43—42no—
213C22⋊C4×C43—42no—
214C42×C43—21no—
215C42×C43—21no—
216C22⋊Dic43—42no—
217C22⋊Dic43—42no—
218#10621884—44no—
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—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—42no—
231C4⋊Dic43C22×C412yes—
232Dic43⋊C4—24no—
233Dic43⋊C4—42no—
234Dic43⋊C4—42no—
235C4×Dic43—21no—
236C4×Dic43—21no—
237C4×Dic43—41no—
238C4×Dic43—41no—
239C4×Dic43—42no—
240C4×Dic43—42no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8C22×C412yes—
247C23×C43—22no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43C22×D411yescharacteristic
255C22×D43—21no—
256C22×D43—21no—
257C22×D43—21no—
258C22×D43—21no—
259C22×D43—22no—
260C22×D43—48no—
261C22×D43—48no—
262C22×D43—41no—
263C22×D43—41no—
264C22×D43—41no—
265C22×D43—41no—
266C22×D43—41no—
267C22×D43—41no—
268C22×D43—48no—
269C22×D43—84no—
270C22×D43—84no—
271C22×D43—84no—
272C22×D43—84no—
273C22×D43C4×D412yes—
274C22×D43C2×SD1612yes—
275C22×D43#13512yes—
276Q8×C43—22no—
277Q8×C43—22no—
278Q8×C43—41no—
279Q8×C43—41no—
280D4×C43—22no—
281D4×C43—22no—
282D4×C43—41no—
283D4×C43—41no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—22no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43C2×SD1612yes—
298C2×C4×C43AGL(1,ℤ/8)12yes—
299C2×C4×C43C23×C411yescharacteristic
300C2×C4×C43C2×#4111yescharacteristic
301C2×C4×C43H(5,𝔽2)11yescharacteristic
302C2×C4×C43H(5,𝔽2)11yescharacteristic
303C2×C4×C43H(5,𝔽2)11yescharacteristic
304C2×C4×C43H(5,𝔽2)11yescharacteristic
305C22⋊D43—48no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—22no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43C4×D412yes—
323C2×Dic43C2×SD1612yes—
324D172—22no—
325D172—22no—
326D172—41no—
327D172—41no—
328C4×D43—22no—
329C4×D43—22no—
330C4×D43—22no—
331C4×D43—22no—
332C4×D43—44no—
333C4×D43—44no—
334C4×D43—84no—
335C8×C43—22no—
336C8×C43—41no—
337C43⋊C8—22no—
338C43⋊C8—41no—
339#22043—431nomaximal, Sylow
340C22×C43—42no—
341C22×C43—42no—
342C22×C43—42no—
343C22×C43—81no—
344C22×C43—81no—
345C22×C43—81no—
346C22×C43—81no—
347C22×C43C2×C4×D411yescharacteristic
348C22×C43#53411yescharacteristic
349C22×C43#53511yescharacteristic
350C22×C43C22×SD1611yescharacteristic
351C22×C43C2×#13511yescharacteristic
352C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
353C22×C43#57511yescharacteristic
354C2×D43—22no—
355C2×D43—22no—
356C2×D43—22no—
357C2×D43—22no—
358C2×D43—22no—
359C2×D43—22no—
360C2×D43—42no—
361C2×D43—42no—
362C2×D43—42no—
363C2×D43—816no—
364C2×D43—81no—
365C2×D43—81no—
366C2×D43—81no—
367C2×D43—81no—
368C2×D43C4×SD1614yes—
369C4×C43—22no—
370C4×C43—22no—
371C4×C43—42no—
372C4×C43—81no—
373C4×C43—81no—
374C4×C43#51811yescharacteristic
375C4×C43#51811yescharacteristic
376C4×C43#53811yescharacteristic
377C4×C43#53811yescharacteristic
378Dic43—22no—
379Dic43—22no—
380Dic43—41no—
381Dic43—42no—
382Dic43—81no—
383Dic43—81no—
384C2×#450—431no—
385C4×C22⋊Q8—431no—
386C2×#390—431no—
387#1968—431no—
388#1968D4311yescharacteristic, complemented
389#1934—431no—
390#1934—431no—
391#1926—431no—
392#1926—431no—
393#1880—431no—
394#1880—431no—
395#1872—431no—
396#1853—431no—
397#1786—431no—
398C4×C22⋊C8—431no—
399C2×C43—82no—
400C2×C43#232111yescharacteristic
401C2×C43C2×C4×SD1611yescharacteristic
402C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
403C2×C43#318711yescharacteristic
404C2×C43#318811yescharacteristic
405C2×C43#320811yescharacteristic
406C2×C43#321111yescharacteristic
407D43—24no—
408D43—82no—
409C23×D4—431no—
410C22×SD16—431no—
411C22×SD16C2×D4311yescharacteristic
412C2×C22⋊Q8—431no—
413C2×C4×Q8—431no—
414C22×C4⋊C4—431no—
415C22×C22⋊C4—861no—
416C22×C22⋊C4—861no—
417C22×C42—431no—
418#450—438no—
419C2×#106—431no—
420C2×#106C2×D4311yescharacteristic, complemented
421C2×#103—431no—
422C2×#103C2×D4311yescharacteristic, complemented
423C2×#102—431no—
424C2×#102—431no—
425C2×#102—431no—
426C2×#102—431no—
427C2×#102—431no—
428C2×#102C2×D4311yescharacteristic
429C2×C22⋊C8—431no—
430C2×C22⋊C8—431no—
431C2×C4×C8—431no—
432C2×C4×C8C2×D4311yescharacteristic, complemented
433#391C2×D4311yescharacteristic, complemented
434#390—431no—
435#390—431no—
436#390—431no—
437#390—861no—
438#390—861no—
439#390C2×D4311yescharacteristic
440#389—431no—
441#387—861no—
442#385—861no—
443#380—431no—
444C4×C4⋊C4—431no—
445C4×C4⋊C4—861no—
446C4×C22⋊C4—861no—
447#340—431no—
448#340—431no—
449#340—431no—
450#340—431no—
451#336—431no—
452#336—431no—
453C43#2204311yescharacteristic, complemented, Sylow
454C25—861no—
455C22×Q8C22×D4311yescharacteristic
456C22×D4—434no—
457C22×D4—431no—
458C22×D4—862no—
459C22×D4—861no—
460C22×D4—1721no—
461C22×D4—1721no—
462C22×D4—1721no—
463C22×D4—1721no—
464C22×D4C22×D4311yescharacteristic
465C23×C4—431no—
466C23×C4—431no—
467C23×C4—431no—
468C23×C4—861no—
469C2×SD16—41no—
470C2×SD16—41no—
471C2×SD16—434no—
472C2×SD16—1721no—
473C2×SD16—1721no—
474C2×SD16C4×D4314yescomplemented
475C22×C8—431no—
476C22×C8—431no—
477C22×C8C22×D4311yescharacteristic
478C22×C8C22×D4311yescharacteristic
479C22⋊Q8—434no—
480C22⋊Q8—862no—
481C4×Q8—1721no—
482C4×Q8—1721no—
483C2×C4⋊C4—431no—
484C2×C4⋊C4—431no—
485C2×C4⋊C4—431no—
486C2×C4⋊C4—861no—
487C2×C4⋊C4—861no—
488C2×C4⋊C4—861no—
489C2×C4⋊C4—861no—
490C2×C4⋊C4—1721no—
491C2×C4⋊C4—1721no—
492C2×C4⋊C4C22×D4311yescharacteristic
493C2×C4⋊C4C22×D4311yescharacteristic
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—861no—
497C2×C22⋊C4—861no—
498C2×C22⋊C4—861no—
499C2×C22⋊C4—861no—
500C2×C22⋊C4—861no—
501C2×C22⋊C4—861no—
502C2×C22⋊C4—861no—
503C2×C22⋊C4—861no—
504C2×C22⋊C4—1724no—
505C2×C22⋊C4—1724no—
506C2×C42—431no—
507C2×C42—431no—
508C2×C42—431no—
509C2×C42—861no—
510C2×C42—861no—
511C2×C42—1721no—
512C2×C42—1721no—
513C2×C42C22×D4311yescharacteristic
514#106—41no—
515#106—1721no—
516#103—41no—
517#103—1721no—
518#102—41no—
519#102—434no—
520#102—434no—
521#102—1721no—
522#102—1721no—
523#102—1721no—
524C22⋊C8—434no—
525C22⋊C8—862no—
526C4×C8—41no—
527C4×C8—1721no—
528#95—21no—
529#95—21no—
530#95—861no—
531#95—861no—
532#95—861no—
533C24—21no—
534C24—431no—
535C24—864no—
536C24—861no—
537C24—1722no—
538C24—1722no—
539C24—1722no—
540C24—1722no—
541C24—1722no—
542C24—1722no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8C2×C4×D4312yes—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—432no—
555C2×D4—864no—
556C2×D4—861no—
557C2×D4—861no—
558C2×D4—861no—
559C2×D4—861no—
560C2×D4—861no—
561C2×D4—1724no—
562C2×D4—1724no—
563C2×D4—1724no—
564C2×D4—1724no—
565C2×D4—1722no—
566C2×D4—1722no—
567C2×D4C2×C4×D4312yes—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—431no—
572C22×C4—431no—
573C22×C4—432no—
574C22×C4—432no—
575C22×C4—434no—
576C22×C4—431no—
577C22×C4—862no—
578C22×C4—861no—
579C22×C4—861no—
580C22×C4—861no—
581C22×C4—861no—
582C22×C4—861no—
583C22×C4—862no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—1721no—
587C22×C4—1721no—
588C22×C4—1721no—
589C22×C4—1722no—
590C22×C4—1722no—
591C22×C4—1722no—
592C22×C4D4×D4311yescharacteristic
593C22×C4D4×D4311yescharacteristic
594C22×C4C23×D4311yescharacteristic
595SD16—44no—
596SD16—1724no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—432no—
603C2×C8—861no—
604C2×C8—861no—
605C2×C8—861no—
606C2×C8—861no—
607C2×C8—861no—
608C2×C8C2×C4×D4312yes—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—432no—
614C4⋊C4—864no—
615C4⋊C4—861no—
616C4⋊C4—861no—
617C4⋊C4—861no—
618C4⋊C4—861no—
619C4⋊C4—861no—
620C4⋊C4—1722no—
621C4⋊C4—1722no—
622C4⋊C4—1722no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—864no—
626C22⋊C4—1722no—
627C22⋊C4—1722no—
628C22⋊C4—1722no—
629C22⋊C4—1722no—
630C22⋊C4—1722no—
631C22⋊C4—1722no—
632C22⋊C4—1722no—
633C42—21no—
634C42—21no—
635C42—861no—
636C42—861no—
637C42—1721no—
638C42—1721no—
639C42—1722no—
640C42—1722no—
641C23—22no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—432no—
649C23—432no—
650C23—432no—
651C23—861no—
652C23—861no—
653C23—861no—
654C23—861no—
655C23—862no—
656C23—3444no—
657C23—3444no—
658C23—3444no—
659C23—3444no—
660C23—1728no—
661C23—1728no—
662C23—1728no—
663C23—1721no—
664C23—1721no—
665C23—1721no—
666C23—1721no—
667C23—1721no—
668C23—1721no—
669C23C2×D4×D4311yescharacteristic
670Q8—22no—
671Q8—22no—
672Q8—41no—
673Q8—41no—
674D4—22no—
675D4—22no—
676D4—41no—
677D4—41no—
678D4—862no—
679D4—862no—
680D4—1728no—
681D4—1721no—
682D4—1721no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—432no—
697C2×C4—432no—
698C2×C4—861no—
699C2×C4—861no—
700C2×C4—861no—
701C2×C4—861no—
702C2×C4—862no—
703C2×C4—862no—
704C2×C4—862no—
705C2×C4—862no—
706C2×C4—862no—
707C2×C4—861no—
708C2×C4—861no—
709C2×C4—861no—
710C2×C4—3444no—
711C2×C4—1724no—
712C2×C4—1724no—
713C2×C4—1721no—
714C2×C4—1721no—
715C2×C4—1721no—
716C2×C4—1721no—
717C2×C4—1721no—
718C2×C4—1721no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4SD16×D4312yes—
722C2×C4#1306335212yes—
723C2×C4C22×C4×D4311yescharacteristic
724C2×C4#41×D4311yescharacteristic
725C2×C4#1306337011yescharacteristic
726C2×C4#1306337011yescharacteristic
727C2×C4#1306337011yescharacteristic
728C2×C4#1306337111yescharacteristic
729C8—22no—
730C8—41no—
731C8—862no—
732C8—1721no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—81no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—434no—
741C22—862no—
742C22—862no—
743C22—862no—
744C22—862no—
745C22—862no—
746C22—862no—
747C22—34416no—
748C22—3441no—
749C22—3441no—
750C22—3441no—
751C22—3441no—
752C22—1722no—
753C22—1722no—
754C22—1722no—
755C22C4×D4×D4311yescharacteristic
756C22#1458345711yescharacteristic
757C22#1458346211yescharacteristic
758C22C2×SD16×D4311yescharacteristic
759C22#135×D4311yescharacteristic
760C22C2×#1306335211yescharacteristic
761C22#1458369611yescharacteristic
762C4—22no—
763C4—22no—
764C4—42no—
765C4—81no—
766C4—81no—
767C4—862no—
768C4—862no—
769C4—3441no—
770C4—3441no—
771C4—1721no—
772C4—1722no—
773C4#1458337111yescharacteristic
774C4#1458337211yescharacteristic
775C4#1458348111yescharacteristic
776C4#1458348311yescharacteristic
777C2—82no—
778C2—864no—
779C2—3442no—
780C2#1913725411yescharacteristic
781C2C4×SD16×D4311yescharacteristic
782C2C4×#1306335211yescharacteristic
783C2#1914534711yescharacteristic
784C2#1914536111yescharacteristic
785C2#1914553211yescharacteristic
786C2#1914555511yescharacteristic
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#22043
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. #19137133C2semidirect
4. #19135452C2semidirect
5. #19135281C2semidirect
6. #19135278C2semidirect
7. #19135225C2semidirect
8. #19135221C2semidirect
9. #19134952C2semidirect
10. #19134948C2semidirect
11. #19134899C2semidirect
12. #19134786C2semidirect
14. C4×(C2×D43)⋊C8C2semidirect
15. C43×#1968C2semidirect
19. C2×Q8×Dic43C22semidirect
24. #14583048C4semidirect
25. C2×#13063256C22semidirect
26. C2×#13063249C22semidirect
34. C2×C4×C43⋊C8C22semidirect
40. #14582797C22semidirect
44. 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
75. C2×#10621884C2×C4semidirect
111. #13063247C2×C4semidirect
113. #13063246C2×C4semidirect
125. C2×SD16×C43C2×C4semidirect
198. C2×C4×D43SD16semidirect
388. #1968D43semidirect
420. C2×#106C2×D43semidirect
422. C2×#103C2×D43semidirect
432. C2×C4×C8C2×D43semidirect
433. #391C2×D43semidirect
453. C43#22043semidirect
474. C2×SD16C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830482
#191371332
#390×D432
#191354522
#191352812
#191352782
#191352252
#191352212
#191349522
#191349482
#191348992
#191347862
#191345242
C4×(C2×D43)⋊C82
C43×#19682
#2204343