Finite Group Databasebeta

← #25107769

Subgroups — #25107769

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×#14583051C211yesmaximal, characteristic
2C4×#13063305C211yesmaximal, characteristic, complemented
3#390×D43C211yesmaximal, characteristic
4#19135450C211yesmaximal, characteristic, complemented
5#19135447C211yesmaximal, characteristic, complemented
6#19135280C211yesmaximal, characteristic, complemented
7#19135279C211yesmaximal, characteristic, complemented
8#19135222C211yesmaximal, characteristic, complemented
9#19134953C211yesmaximal, characteristic, complemented
10#19134949C211yesmaximal, characteristic, complemented
11#19134901C211yesmaximal, characteristic, complemented
12#19134786C211yesmaximal, characteristic, complemented
13#19134524C211yesmaximal, characteristic
14#19134352C211yesmaximal, characteristic, complemented
15C43×#1926C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C22×#10621883C2211yescharacteristic
19C2×#13063305C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic, complemented
21C2×C4⋊C4×D43C2211yescharacteristic
22C2×C22⋊C4×D43—21no—
23C2×C22⋊C4×D43—21no—
24C2×C42×D43C2211yescharacteristic
25#14583051C418yescomplemented
26C2×#13063256C2211yescharacteristic, complemented
27C2×#13063250C2211yescharacteristic, complemented
28C2×#13063248C2211yescharacteristic, complemented
29C2×#13063247C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×(C2×D43)⋊C8C2211yescharacteristic
34C2×(C2×D43)⋊C8C2211yescharacteristic
35C2×C8×Dic43C2211yescharacteristic, complemented
36C2×C8×Dic43C2211yescharacteristic, complemented
37#14582804C2211yescharacteristic, complemented
38#14582802C2211yescharacteristic
39#14582801C2211yescharacteristic
40#14582800C2211yescharacteristic
41#14582799—21no—
42#14582799—21no—
43#14582798C2211yescharacteristic, complemented
44#14582784—21no—
45#14582773—21no—
46#14582756C2211yescharacteristic
47C4×C4⋊Dic43—21no—
48C4×(C2×D43)⋊C4—21no—
49#14582662C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582661C2211yescharacteristic, complemented
52#14582654C2211yescharacteristic, complemented
53C2×#106×C43C2211yescharacteristic, complemented
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic, complemented
58C43×#340C2211yescharacteristic, complemented
59C43×#336C2211yescharacteristic, complemented
60C24×D43—21no—
61C22×Dic86C2311yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C22⋊D43—21no—
64C2×D4×D43—22no—
65C2×D4×D43—41no—
66C2×D4×D43—41no—
67C2×D4×D43—41no—
68C2×D4×D43—41no—
69C2×D4×D43C2×C414yes—
70C22×C4×D43—21no—
71C22×C4×D43D411yescharacteristic
72C22×C4×D43D411yescharacteristic
73C22×C4×D43C2311yescharacteristic
74C2×#10621873—41no—
75C2×#10621873—41no—
76C2×#10621873C2×C414yescomplemented
77C2×#10621883—41no—
78C2×#10621883—41no—
79C2×#10621883C2×C414yescomplemented
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82#13063305—22no—
83#13063305C2×C414yes—
84C4×Dic86—41no—
85C4×Dic86—41no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C4⋊C4×D43—41no—
93C4⋊C4×D43—41no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—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—
102C22⋊C4×D43—44no—
103C22⋊C4×D43—44no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43D411yescharacteristic
106C2×C4×Dic43D411yescharacteristic
107C2×C4×Dic43C2311yescharacteristic
108C42×D43—41no—
109C42×D43—41no—
110#13063256—41no—
111#13063250—41no—
112#13063248—41no—
113#13063247—41no—
114#13063246—41no—
115#13063245—41no—
116#13063245C2×C414yescomplemented
117(C2×D43)⋊C8—22no—
118(C2×D43)⋊C8C2×C414yes—
119C8×Dic43—41no—
120C8×Dic43—41no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C22×D4×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43—21no—
133C2×C42×C43—21no—
134C2×C42×C43C2311yescharacteristic
135#106×C43—41no—
136#102×C43—41no—
137#102×C43C2×C414yescomplemented
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×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43C22×C412yes—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2411yescharacteristic
161C2×C22⋊D43—24no—
162C2×C22⋊D43—42no—
163C2×C22⋊D43—42no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43C2×D411yescharacteristic
168C22×Dic43C2×D411yescharacteristic
169C22×Dic43C2×D411yescharacteristic
170D4×D43—44no—
171D4×D43—44no—
172D4×D43—44no—
173D4×D43—44no—
174C2×D172—21no—
175C2×D172—21no—
176C2×D172—21no—
177C2×D172—21no—
178C2×D172—21no—
179C2×D172C22×C412yes—
180C2×C4×D43—21no—
181C2×C4×D43—21no—
182C2×C4×D43—21no—
183C2×C4×D43—21no—
184C2×C4×D43—22no—
185C2×C4×D43—22no—
186C2×C4×D43—41no—
187C2×C4×D43—41no—
188C2×C4×D43—41no—
189C2×C4×D43—42no—
190C2×C4×D43—42no—
191C2×C4×D43—42no—
192C2×C4×D43SD1614yescomplemented
193C2×C4×D43C22×C412yes—
194C2×C4×D43#4112yes—
195C2×Dic86—21no—
196C2×Dic86—21no—
197C2×Dic86—21no—
198C2×Dic86—21no—
199C2×Dic86—21no—
200C2×Dic86C22×C412yes—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43C22×C412yes—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43C22×C412yes—
213C22⋊C4×C43—42no—
214C22⋊C4×C43—42no—
215C42×C43—21no—
216C42×C43—21no—
217C42×C43—42no—
218C22⋊Dic43—42no—
219C22⋊Dic43—42no—
220#10621883—44no—
221(C2×D43)⋊C4—24no—
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—24no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—42no—
233Dic43⋊C4—42no—
234Dic43⋊C4—42no—
235C4×Dic43—21no—
236C4×Dic43—21no—
237C4×Dic43—41no—
238C4×Dic43—41no—
239C4×Dic43—42no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8C22×C412yes—
246#10621873—44no—
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—
276D4×C43—22no—
277D4×C43—22no—
278D4×C43—41no—
279D4×C43—41no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—22no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43C2×SD1612yes—
295C2×C4×C43C23×C411yescharacteristic
296C2×C4×C43C2×#4111yescharacteristic
297C2×C4×C43H(5,𝔽2)11yescharacteristic
298C2×C4×C43H(5,𝔽2)11yescharacteristic
299C2×C4×C43H(5,𝔽2)11yescharacteristic
300C2×C4×C43H(5,𝔽2)11yescharacteristic
301C22⋊D43—48no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—22no—
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×Dic43C4×D412yes—
318C2×Dic43C2×SD1612yes—
319C2×Dic43AGL(1,ℤ/8)12yes—
320D172—22no—
321D172—22no—
322D172—41no—
323D172—41no—
324C4×D43—22no—
325C4×D43—22no—
326C4×D43—22no—
327C4×D43—22no—
328C4×D43—44no—
329C4×D43—44no—
330C4×D43—84no—
331Dic86—22no—
332Dic86—22no—
333Dic86—41no—
334Dic86—41no—
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—41no—
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—22no—
381Dic43—42no—
382Dic43—81no—
383Dic43—81no—
384C2×#450—431no—
385C4×C22⋊Q8—431no—
386C2×#390—431no—
387#1968—431no—
388#1968—431no—
389#1934—431no—
390#1934—431no—
391#1926—431no—
392#1926D4311yescharacteristic, complemented
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×SD16—431no—
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×#103—431no—
423C2×#102—431no—
424C2×#102—431no—
425C2×#102—431no—
426C2×#102—431no—
427C2×#102C2×D4311yescharacteristic
428C2×#102C2×D4311yescharacteristic
429C2×C22⋊C8—431no—
430C2×C22⋊C8—431no—
431C2×C4×C8—431no—
432C2×C4×C8—431no—
433#391—431no—
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—861no—
445C4×C4⋊C4C2×D4311yescharacteristic, complemented
446C4×C22⋊C4—861no—
447#340—431no—
448#340—431no—
449#340—431no—
450#340C2×D4311yescharacteristic, complemented
451#336—431no—
452#336C2×D4311yescharacteristic, complemented
453C43#2204311yescharacteristic, complemented, Sylow
454C25—861no—
455C22×Q8—431no—
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—434no—
470C2×SD16—434no—
471C2×SD16—1721no—
472C2×SD16—1721no—
473C2×SD16—1721no—
474C2×SD16—1721no—
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—861no—
486C2×C4⋊C4—861no—
487C2×C4⋊C4—861no—
488C2×C4⋊C4—861no—
489C2×C4⋊C4—1721no—
490C2×C4⋊C4—1721no—
491C2×C4⋊C4C22×D4311yescharacteristic
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—21no—
507C2×C42—431no—
508C2×C42—431no—
509C2×C42—431no—
510C2×C42—861no—
511C2×C42—1721no—
512C2×C42—1721no—
513C2×C42C22×D4311yescharacteristic
514#106—41no—
515#106—1721no—
516#103—1721no—
517#103—1721no—
518#102—41no—
519#102—434no—
520#102—1721no—
521#102—1721no—
522#102—1721no—
523#102C4×D4314yescomplemented
524C22⋊C8—434no—
525C22⋊C8—862no—
526C4×C8—1721no—
527C4×C8—1721no—
528#95—21no—
529#95—861no—
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—432no—
544C2×Q8—861no—
545C2×Q8—861no—
546C2×Q8—861no—
547C2×Q8—861no—
548C2×Q8—861no—
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—431no—
574C22×C4—432no—
575C22×C4—432no—
576C22×C4—434no—
577C22×C4—862no—
578C22×C4—862no—
579C22×C4—861no—
580C22×C4—861no—
581C22×C4—861no—
582C22×C4—861no—
583C22×C4—861no—
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—1724no—
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—21no—
614C4⋊C4—864no—
615C4⋊C4—861no—
616C4⋊C4—861no—
617C4⋊C4—861no—
618C4⋊C4—861no—
619C4⋊C4—1722no—
620C4⋊C4—1722no—
621C4⋊C4—1722no—
622C4⋊C4C2×C4×D4312yes—
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—42no—
636C42—861no—
637C42—861no—
638C42—1721no—
639C42—1721no—
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—862no—
671Q8—862no—
672Q8—1721no—
673Q8—1721no—
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—22no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—432no—
698C2×C4—432no—
699C2×C4—432no—
700C2×C4—861no—
701C2×C4—861no—
702C2×C4—861no—
703C2×C4—861no—
704C2×C4—861no—
705C2×C4—861no—
706C2×C4—862no—
707C2×C4—862no—
708C2×C4—862no—
709C2×C4—862no—
710C2×C4—862no—
711C2×C4—3444no—
712C2×C4—1724no—
713C2×C4—1724no—
714C2×C4—1721no—
715C2×C4—1721no—
716C2×C4—1721no—
717C2×C4—1721no—
718C2×C4—1721no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4—1721no—
722C2×C4SD16×D4312yes—
723C2×C4C22×C4×D4311yescharacteristic
724C2×C4#41×D4311yescharacteristic
725C2×C4#1306337011yescharacteristic
726C2×C4#1306337111yescharacteristic
727C2×C4#1306337111yescharacteristic
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#1458346011yescharacteristic
757C22#1458346511yescharacteristic
758C22C2×SD16×D4311yescharacteristic
759C22#135×D4311yescharacteristic
760C22AGL(1,ℤ/8)×D4311yescharacteristic
761C22#1458369511yescharacteristic
762C4—22no—
763C4—41no—
764C4—42no—
765C4—81no—
766C4—81no—
767C4—862no—
768C4—862no—
769C4—862no—
770C4—3441no—
771C4—3441no—
772C4—1722no—
773C4#1458337111yescharacteristic
774C4#1458337311yescharacteristic
775C4#1458348311yescharacteristic
776C4#1458348811yescharacteristic
777C2—82no—
778C2—864no—
779C2—3442no—
780C2#1913725711yescharacteristic
781C2C4×SD16×D4311yescharacteristic
782C2#1914340611yescharacteristic
783C2#1914535411yescharacteristic
784C2#1914536411yescharacteristic
785C2#1914553511yescharacteristic
786C2#1914555811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1926C2
socleC23×C43C22×D4
prime radicalC22×D4×D43C22
cosocleC22×C4×C43C24
hypercenter#1926D43
hypocenterC43#22043
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1926

Complements

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

NH ≅ G/Ntype
2. C4×#13063305C2semidirect
4. #19135450C2semidirect
5. #19135447C2semidirect
6. #19135280C2semidirect
7. #19135279C2semidirect
8. #19135222C2semidirect
9. #19134953C2semidirect
10. #19134949C2semidirect
11. #19134901C2semidirect
12. #19134786C2semidirect
14. #19134352C2semidirect
15. C43×#1926C2semidirect
20. C2×C4×Dic86C22semidirect
25. #14583051C4semidirect
26. C2×#13063256C22semidirect
27. C2×#13063250C22semidirect
28. C2×#13063248C22semidirect
35. C2×C8×Dic43C22semidirect
36. C2×C8×Dic43C22semidirect
37. #14582804C22semidirect
43. #14582798C22semidirect
49. #14582662C22semidirect
50. #14582661C22semidirect
51. #14582661C22semidirect
52. #14582654C22semidirect
53. C2×#106×C43C22semidirect
57. C4×C4⋊C4×C43C22semidirect
58. C43×#340C22semidirect
59. C43×#336C22semidirect
76. C2×#10621873C2×C4semidirect
79. C2×#10621883C2×C4semidirect
116. #13063245C2×C4semidirect
137. #102×C43C2×C4semidirect
192. C2×C4×D43SD16semidirect
392. #1926D43semidirect
420. C2×#106C2×D43semidirect
445. C4×C4⋊C4C2×D43semidirect
450. #340C2×D43semidirect
452. #336C2×D43semidirect
453. C43#22043semidirect
523. #102C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830512
C4×#130633052
#390×D432
#191354502
#191354472
#191352802
#191352792
#191352222
#191349532
#191349492
#191349012
#191347862
#191345242
#191343522
C43×#19262
#2204343