Finite Group Databasebeta

← #25097823

Subgroups — #25097823

Order 11008.

2258 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583409C211yesmaximal, characteristic
2C22×C4⋊C4×D43C211yesmaximal, characteristic, complemented
3C2×#14582897C212yesmaximal, complemented
4C2×#14582861C211yesmaximal, characteristic, complemented
5#19134913C211yesmaximal, characteristic, complemented
6#19134909C212yesmaximal, complemented
7#19134902C211yesmaximal, characteristic, complemented
8#19134901C212yesmaximal, complemented
9#19134900C211yesmaximal, characteristic, complemented
10#19134313C212yesmaximal, complemented
11C43×#1874C211yesmaximal, characteristic, complemented
12C22×#10621900C2211yescharacteristic
13C23×C4×D43—21no—
14C23×C4×D43C2211yescharacteristic
15C22×#10621872C2212yes—
16#14583409—24no—
17#14583409C418yescomplemented
18C2×#13063307—21no—
19C2×#13063305C2211yescharacteristic
20C2×#13063304C2211yescharacteristic
21C2×#13063296C2211yescharacteristic
22C2×#13063293—21no—
23C2×D4×Dic43—21no—
24C2×(C22⋊D43)⋊C4—21no—
25C2×#13063283C2211yescharacteristic
26C22×C4⋊Dic43C2211yescharacteristic
27C22×Dic43⋊C4—21no—
28C2×C4⋊C4×D43—21no—
29C2×C4⋊C4×D43—21no—
30C2×C4⋊C4×D43—28no—
31C2×C4⋊C4×D43C2212yes—
32C2×C4⋊C4×D43C2212yes—
33#14582897—28no—
34C2×#13063250C2212yescomplemented
35C2×#13063248C2212yescomplemented
36C2×#13063246C2212yescomplemented
37#14582861—24no—
38C2×C22⋊(C43⋊C8)C2211yescharacteristic
39C2×(C2×D43)⋊C8C2212yes—
40#14582662C2212yescomplemented
41#14582661C2212yescomplemented
42#14582661C2212yescomplemented
43C2×#121×C43C2211yescharacteristic
44C22×C4⋊C4×C43C2211yescharacteristic
45C2×#102×C43C2212yescomplemented
46C2×C22⋊C8×C43C2211yescharacteristic
47C43×#340C2212yescomplemented
48C24×D43D411yescharacteristic
49C2×#10621900—24no—
50C2×#10621900—22no—
51C2×#10621900—24no—
52C2×#10621900C2×C414yescomplemented
53C22×Dic86C2311yescharacteristic
54C22×C22⋊D43—21no—
55C22×C22⋊D43—21no—
56C23×Dic43—21no—
57C23×Dic43—21no—
58C23×Dic43D411yescharacteristic
59C22×C4×D43—24no—
60C22×C4×D43—24no—
61C22×C4×D43—28no—
62C22×C4×D43—22no—
63C22×C4×D43—22no—
64C22×C4×D43—44no—
65C22×C4×D43—44no—
66C22×C4×D43C2×C414yes—
67C22×C4×D43D411yescharacteristic
68C22×C4×D43D411yescharacteristic
69C22×C4×D43D414yes—
70C22×C4×D43C2311yescharacteristic
71C22×C4×D43C2311yescharacteristic
72C2×#10621872—24no—
73C2×#10621872—24no—
74C2×#10621872—24no—
75C22×C43⋊C8C2312yes—
76#13063307—28no—
77#13063305—22no—
78#13063305C2×C414yescomplemented
79#13063304—22no—
80#13063304C2×C414yescomplemented
81#13063296—22no—
82#13063296C2×C414yescomplemented
83#13063293—28no—
84D4×Dic43—28no—
85(C22⋊D43)⋊C4—28no—
86#13063283—22no—
87#13063283C2×C414yescomplemented
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43—24no—
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2312yes—
93C2×Dic43⋊C4—28no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—22no—
96C2×Dic43⋊C4—22no—
97C4⋊C4×D43—28no—
98C4⋊C4×D43—28no—
99C4⋊C4×D43—24no—
100C4⋊C4×D43—24no—
101C4⋊C4×D43—24no—
102C4⋊C4×D43D418yescomplemented
103C2×C22⋊Dic43—21no—
104C2×C22⋊Dic43—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×C4×Dic43—21no—
108#13063250—24no—
109#13063248—24no—
110#13063246—24no—
111C22⋊(C43⋊C8)—22no—
112(C2×D43)⋊C8—24no—
113C22×D4×C43—21no—
114C22×D4×C43C2311yescharacteristic
115C23×C4×C43—21no—
116C23×C4×C43C2311yescharacteristic
117C22×C8×C43C2312yes—
118#121×C43—22no—
119#121×C43C2×C414yescomplemented
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43—24no—
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2312yes—
124C2×C22⋊C4×C43—21no—
125#102×C43—24no—
126C22⋊C8×C43—22no—
127C24×C43—21no—
128C24×C43C2×D411yescharacteristic
129C23×D43—22no—
130C23×D43—22no—
131C23×D43—22no—
132C23×D43—22no—
133C23×D43—22no—
134C23×D43—22no—
135C23×D43C22⋊C414yes—
136C23×D43C2×D411yescharacteristic
137C23×D43C2×D411yescharacteristic
138C2×D4×C43—21no—
139C2×D4×C43—24no—
140C2×D4×C43—22no—
141C2×D4×C43—22no—
142C2×D4×C43—42no—
143C2×D4×C43—42no—
144C2×D4×C43C22×C412yescomplemented
145C22×C4×C43—22no—
146C22×C4×C43—22no—
147C22×C4×C43—24no—
148C22×C4×C43—21no—
149C22×C4×C43—22no—
150C22×C4×C43—42no—
151C22×C4×C43—42no—
152C22×C4×C43C22×C412yes—
153C22×C4×C43C2×D412yes—
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2411yescharacteristic
156C2×C22⋊D43—24no—
157C2×C22⋊D43—24no—
158C2×C22⋊D43—42no—
159C2×C22⋊D43—42no—
160C2×C22⋊D43—42no—
161C2×C22⋊D43—42no—
162C22×Dic43—22no—
163C22×Dic43—22no—
164C22×Dic43—24no—
165C22×Dic43—24no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—22no—
169C22×Dic43—42no—
170C22×Dic43—42no—
171C22×Dic43—42no—
172C22×Dic43—42no—
173C22×Dic43C22⋊C414yes—
174C22×Dic43C2×D411yescharacteristic
175C22×Dic43C2×D411yescharacteristic
176#10621900—216no—
177#10621900—48no—
178C2×C4×D43—22no—
179C2×C4×D43—22no—
180C2×C4×D43—22no—
181C2×C4×D43—22no—
182C2×C4×D43—216no—
183C2×C4×D43—216no—
184C2×C4×D43—28no—
185C2×C4×D43—22no—
186C2×C4×D43—28no—
187C2×C4×D43—22no—
188C2×C4×D43—432no—
189C2×C4×D43—44no—
190C2×C4×D43—44no—
191C2×C4×D43—44no—
192C2×C4×D43—44no—
193C2×C4×D43C22⋊C414yes—
194C2×C4×D43C22⋊C414yes—
195C2×C4×D43C22×C412yes—
196C2×C4×D43C22×C412yes—
197C2×C4×D43C2×D412yes—
198C2×C4×D43C2×D412yes—
199C2×C4×D43C2×D414yes—
200C2×C4×D43#4114yes—
201C2×Dic86—22no—
202C2×Dic86—22no—
203C2×Dic86—21no—
204C2×Dic86C22×C412yescomplemented
205C2×C8×C43—22no—
206C2×C8×C43—22no—
207C2×C8×C43—22no—
208C4⋊C4×C43—24no—
209C4⋊C4×C43—22no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43C22×C412yescomplemented
212C4⋊C4×C43C2×D414yes—
213C22⋊C4×C43—24no—
214C22⋊Dic43—24no—
215C22⋊Dic43—24no—
216(C2×D43)⋊C4—24no—
217(C2×D43)⋊C4—24no—
218C4⋊Dic43—24no—
219C4⋊Dic43—22no—
220C4⋊Dic43—21no—
221C4⋊Dic43—24no—
222C4⋊Dic43C22×C412yescomplemented
223C4⋊Dic43C2×D414yes—
224Dic43⋊C4—28no—
225Dic43⋊C4—24no—
226Dic43⋊C4—28no—
227C4×Dic43—24no—
228C2×C43⋊C8—22no—
229C2×C43⋊C8—22no—
230C2×C43⋊C8—22no—
231#10621872—48no—
232C23×C43—21no—
233C23×C43—21no—
234C23×C43—21no—
235C23×C43—21no—
236C23×C43—22no—
237C23×C43—41no—
238C23×C43—41no—
239C23×C43—41no—
240C23×C43—41no—
241C23×C43—41no—
242C23×C43—41no—
243C23×C43C2×C22⋊C412yes—
244C23×C43AGL(1,ℤ/8)12yes—
245C23×C43#13712yes—
246C23×C43C22×D411yescharacteristic
247C22×D43—28no—
248C22×D43—28no—
249C22×D43—28no—
250C22×D43—28no—
251C22×D43—21no—
252C22×D43—21no—
253C22×D43—21no—
254C22×D43—21no—
255C22×D43—21no—
256C22×D43—21no—
257C22×D43—21no—
258C22×D43—21no—
259C22×D43—28no—
260C22×D43—28no—
261C22×D43—28no—
262C22×D43C2×C22⋊C412yes—
263C22×D43C2×C22⋊C412yes—
264C22×D43#12012yes—
265C22×D43#12312yes—
266C22×D43AGL(1,ℤ/8)12yes—
267C22×D43#13712yes—
268D4×C43—24no—
269D4×C43—48no—
270D4×C43—42no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—24no—
274C2×C4×C43—24no—
275C2×C4×C43—22no—
276C2×C4×C43—24no—
277C2×C4×C43—48no—
278C2×C4×C43—42no—
279C2×C4×C43—42no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43C2×C22⋊C412yes—
283C2×C4×C43C23×C411yescharacteristic
284C2×C4×C43C22×D412yes—
285C2×C4×C43C22×D411yescharacteristic
286C2×C4×C43C2×#4112yes—
287C22⋊D43—48no—
288C22⋊D43—48no—
289C2×Dic43—21no—
290C2×Dic43—21no—
291C2×Dic43—28no—
292C2×Dic43—22no—
293C2×Dic43—22no—
294C2×Dic43—24no—
295C2×Dic43—48no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—42no—
299C2×Dic43—42no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—48no—
303C2×Dic43C2×C22⋊C412yes—
304C2×Dic43C2×C22⋊C412yes—
305C2×Dic43#12012yes—
306C2×Dic43#12312yes—
307C4×D43—28no—
308C4×D43—24no—
309C4×D43—24no—
310C4×D43—28no—
311C4×D43—416no—
312C4×D43—416no—
313C4×D43C4×D418yes—
314C4×D43#12118yes—
315Dic86—24no—
316Dic86—42no—
317C8×C43—42no—
318C43⋊C8—42no—
319#20909—431nomaximal, Sylow
320C22×C43—22no—
321C22×C43—22no—
322C22×C43—22no—
323C22×C43—22no—
324C22×C43—22no—
325C22×C43—22no—
326C22×C43—42no—
327C22×C43—42no—
328C22×C43—42no—
329C22×C43—81no—
330C22×C43—81no—
331C22×C43—81no—
332C22×C43—81no—
333C22×C43#41714yescomplemented
334C22×C43C22×C22⋊C411yescharacteristic
335C22×C43C2×#12011yescharacteristic
336C22×C43C2×#12311yescharacteristic
337C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
338C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
339C22×C43C2×#13711yescharacteristic
340C22×C43C2×#13711yescharacteristic
341C2×D43—232no—
342C2×D43—22no—
343C2×D43—22no—
344C2×D43—22no—
345C2×D43—22no—
346C2×D43—22no—
347C2×D43—22no—
348C2×D43—22no—
349C2×D43—22no—
350C2×D43—22no—
351C2×D43—22no—
352C2×D43—22no—
353C2×D43—22no—
354C2×D43#38614yes—
355C2×D43#41714yescomplemented
356C4×C43—22no—
357C4×C43—42no—
358C4×C43—44no—
359C4×C43C2×C4×D412yes—
360C4×C43C2×#12112yes—
361Dic43—22no—
362Dic43—42no—
363Dic43—44no—
364Dic43—42no—
365Dic43#38614yes—
366C2×#525—431no—
367C23×C4⋊C4—431no—
368C2×#417—432no—
369C2×#407—431no—
370#1874—432no—
371#1874—431no—
372#1874D4311yescharacteristic, complemented
373#1872—431no—
374#1872—432no—
375#1872—431no—
376#1736—432no—
377C2×C43—24no—
378C2×C43—82no—
379C2×C43C2×#38611yescharacteristic
380C2×C43C2×#41711yescharacteristic
381C2×C43C2×#41711yescharacteristic
382C2×C43#300311yescharacteristic
383C2×C43#300411yescharacteristic
384C2×C43#309211yescharacteristic
385C2×C43#309211yescharacteristic
386D43—24no—
387D43—24no—
388C22×#41—431no—
389C24×C4—431no—
390C24×C4—861no—
391C22×M16—432no—
392#525—438no—
393#525—864no—
394C2×#123—861no—
395C2×C22⋊Q8—431no—
396C2×C22⋊Q8—431no—
397C2×#121—431no—
398C2×#121C2×D4311yescharacteristic
399C2×#120—861no—
400C2×C4×D4—861no—
401C2×C4×D4—861no—
402C2×#117—431no—
403C22×C4⋊C4—432no—
404C22×C4⋊C4—431no—
405C22×C4⋊C4—432no—
406C22×C4⋊C4—868no—
407C22×C4⋊C4—861no—
408C22×C4⋊C4—861no—
409C22×C4⋊C4—861no—
410C22×C4⋊C4C2×D4311yescharacteristic
411#417—868no—
412C2×#103—432no—
413C2×#103—432no—
414C2×#102—432no—
415C2×#102C2×D4312yescomplemented
416#407—864no—
417C2×C22⋊C8—431no—
418C2×C22⋊C8—432no—
419C2×C22⋊C8C2×D4311yescharacteristic
420#340—432no—
421#340—432no—
422#340—432no—
423#340C2×D4312yescomplemented
424C43#2090911yescharacteristic, complemented, Sylow
425C25—431no—
426C2×#41—434no—
427C2×#41—862no—
428C2×#41—864no—
429C2×#41—864no—
430C22×Q8—431no—
431C22×D4—21no—
432C22×D4—861no—
433C22×D4—861no—
434C22×D4C22×D4311yescharacteristic
435C23×C4—21no—
436C23×C4—431no—
437C23×C4—431no—
438C23×C4—434no—
439C23×C4—431no—
440C23×C4—431no—
441C23×C4—434no—
442C23×C4—431no—
443C23×C4—864no—
444C23×C4—864no—
445C23×C4—862no—
446C23×C4—862no—
447C23×C4—868no—
448C23×C4—861no—
449C23×C4—861no—
450C23×C4—1724no—
451C23×C4—1724no—
452C23×C4C22×D4311yescharacteristic
453C2×M16—864no—
454C2×M16—864no—
455C2×M16—864no—
456C22×C8—432no—
457C22×C8C22×D4312yes—
458#123—868no—
459C22⋊Q8—434no—
460C22⋊Q8—434no—
461C22⋊Q8—862no—
462C22⋊Q8—862no—
463#121—22no—
464#121—434no—
465#121—862no—
466#121C4×D4314yescomplemented
467#120—868no—
468C4×D4—868no—
469C4×D4—868no—
470#117—434no—
471#117—862no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—432no—
475C2×C4⋊C4—431no—
476C2×C4⋊C4—438no—
477C2×C4⋊C4—864no—
478C2×C4⋊C4—864no—
479C2×C4⋊C4—868no—
480C2×C4⋊C4—868no—
481C2×C4⋊C4—864no—
482C2×C4⋊C4—862no—
483C2×C4⋊C4—862no—
484C2×C4⋊C4—861no—
485C2×C4⋊C4—868no—
486C2×C4⋊C4—861no—
487C2×C4⋊C4—861no—
488C2×C4⋊C4—864no—
489C2×C4⋊C4C22×D4311yescharacteristic
490C2×C4⋊C4C22×D4312yes—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—861no—
493C2×C22⋊C4—861no—
494C2×C22⋊C4—861no—
495C2×C22⋊C4—861no—
496C2×C42—861no—
497#103—864no—
498#103—864no—
499#102—24no—
500#102—864no—
501C22⋊C8—22no—
502C22⋊C8—864no—
503C22⋊C8—862no—
504C24—21no—
505C24—431no—
506C24—431no—
507C24—434no—
508C24—862no—
509C24—862no—
510C24—862no—
511C24—862no—
512C24—862no—
513C24—862no—
514C24D4×D4311yescharacteristic
515#41—8616no—
516#41—1728no—
517C2×Q8—432no—
518C2×Q8—861no—
519C2×Q8—862no—
520C2×Q8—862no—
521C2×D4—24no—
522C2×D4—22no—
523C2×D4—21no—
524C2×D4—22no—
525C2×D4—42no—
526C2×D4—42no—
527C2×D4—864no—
528C2×D4—864no—
529C2×D4—1722no—
530C2×D4—1722no—
531C2×D4—1722no—
532C2×D4—1722no—
533C2×D4C2×C4×D4312yescomplemented
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—431no—
542C22×C4—432no—
543C22×C4—434no—
544C22×C4—432no—
545C22×C4—434no—
546C22×C4—434no—
547C22×C4—431no—
548C22×C4—434no—
549C22×C4—434no—
550C22×C4—432no—
551C22×C4—432no—
552C22×C4—862no—
553C22×C4—862no—
554C22×C4—8616no—
555C22×C4—8616no—
556C22×C4—862no—
557C22×C4—862no—
558C22×C4—868no—
559C22×C4—868no—
560C22×C4—862no—
561C22×C4—862no—
562C22×C4—864no—
563C22×C4—862no—
564C22×C4—862no—
565C22×C4—864no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—862no—
569C22×C4—1724no—
570C22×C4—17232no—
571C22×C4—1724no—
572C22×C4—1724no—
573C22×C4—1724no—
574C22×C4—1722no—
575C22×C4—1722no—
576C22×C4—1722no—
577C22×C4—1722no—
578C22×C4C2×C4×D4312yes—
579C22×C4D4×D4311yescharacteristic
580C22×C4D4×D4312yes—
581C22×C4C23×D4311yescharacteristic
582M16—1728no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—862no—
587C2×C8—862no—
588C2×C8—862no—
589C4⋊C4—24no—
590C4⋊C4—22no—
591C4⋊C4—21no—
592C4⋊C4—432no—
593C4⋊C4—434no—
594C4⋊C4—868no—
595C4⋊C4—864no—
596C4⋊C4—868no—
597C4⋊C4—864no—
598C4⋊C4—864no—
599C4⋊C4—862no—
600C4⋊C4—861no—
601C4⋊C4C2×C4×D4312yescomplemented
602C4⋊C4D4×D4314yes—
603C22⋊C4—24no—
604C22⋊C4—864no—
605C22⋊C4—864no—
606C22⋊C4—864no—
607C22⋊C4—864no—
608C42—864no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—22no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—432no—
621C23—432no—
622C23—432no—
623C23—432no—
624C23—432no—
625C23—432no—
626C23—868no—
627C23—868no—
628C23—868no—
629C23—868no—
630C23—868no—
631C23—868no—
632C23—861no—
633C23—861no—
634C23—868no—
635C23—861no—
636C23—861no—
637C23—861no—
638C23—861no—
639C23—861no—
640C23—861no—
641C23C22⋊C4×D4312yes—
642C23#1306334912yes—
643C23#1306335412yes—
644C23C2×D4×D4311yescharacteristic
645Q8—864no—
646Q8—1722no—
647D4—24no—
648D4—48no—
649D4—42no—
650D4—1728no—
651D4—1728no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—48no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—432no—
664C2×C4—432no—
665C2×C4—432no—
666C2×C4—438no—
667C2×C4—438no—
668C2×C4—432no—
669C2×C4—868no—
670C2×C4—868no—
671C2×C4—868no—
672C2×C4—861no—
673C2×C4—861no—
674C2×C4—864no—
675C2×C4—864no—
676C2×C4—862no—
677C2×C4—862no—
678C2×C4—864no—
679C2×C4—17216no—
680C2×C4—17216no—
681C2×C4—1728no—
682C2×C4—1728no—
683C2×C4—1721no—
684C2×C4—1721no—
685C2×C4—1722no—
686C2×C4—1721no—
687C2×C4—1722no—
688C2×C4—1721no—
689C2×C4C22⋊C4×D4312yes—
690C2×C4C22×C4×D4311yescharacteristic
691C2×C4C2×D4×D4312yes—
692C2×C4C2×D4×D4311yescharacteristic
693C2×C4#41×D4312yes—
694C8—42no—
695C8—1722no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22—434no—
710C22—434no—
711C22—8632no—
712C22—862no—
713C22—862no—
714C22—862no—
715C22—862no—
716C22—862no—
717C22—862no—
718C22—862no—
719C22—862no—
720C22—862no—
721C22—862no—
722C22—862no—
723C22—862no—
724C22#1458289714yescomplemented
725C22C2×C22⋊C4×D4311yescharacteristic
726C22#120×D4311yescharacteristic
727C22#123×D4311yescharacteristic
728C22AGL(1,ℤ/8)×D4311yescharacteristic
729C22C2×#1306334911yescharacteristic
730C22#137×D4311yescharacteristic
731C22C2×#1306335411yescharacteristic
732C4—22no—
733C4—44no—
734C4—42no—
735C4—434no—
736C4—862no—
737C4—1724no—
738C4—1722no—
739C4—1722no—
740C4C4×D4×D4312yes—
741C4#121×D4312yes—
742C2—24no—
743C2—82no—
744C2—864no—
745C2—864no—
746C2#386×D4311yescharacteristic
747C2#417×D4311yescharacteristic
748C2C2×#1458289711yescharacteristic
749C2#1914381911yescharacteristic
750C2#1914382611yescharacteristic
751C2#1914451411yescharacteristic
752C2#1914451711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1874C2
socleC23×C43C22×D4
prime radicalC2×#14583409C2
cosocleC22×C4×C43C24
hypercenter#1874D43
hypocenterC43#20909
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D43C2semidirect
3. C2×#14582897C2semidirect
4. C2×#14582861C2semidirect
5. #19134913C2semidirect
6. #19134909C2semidirect
7. #19134902C2semidirect
8. #19134901C2semidirect
9. #19134900C2semidirect
10. #19134313C2semidirect
11. C43×#1874C2semidirect
17. #14583409C4semidirect
34. C2×#13063250C22semidirect
35. C2×#13063248C22semidirect
36. C2×#13063246C22semidirect
40. #14582662C22semidirect
41. #14582661C22semidirect
42. #14582661C22semidirect
45. C2×#102×C43C22semidirect
47. C43×#340C22semidirect
52. C2×#10621900C2×C4semidirect
78. #13063305C2×C4semidirect
80. #13063304C2×C4semidirect
82. #13063296C2×C4semidirect
87. #13063283C2×C4semidirect
102. C4⋊C4×D43D4semidirect
119. #121×C43C2×C4semidirect
144. C2×D4×C43C22×C4semidirect
204. C2×Dic86C22×C4semidirect
211. C4⋊C4×C43C22×C4semidirect
222. C4⋊Dic43C22×C4semidirect
333. C22×C43#417semidirect
355. C2×D43#417semidirect
372. #1874D43semidirect
415. C2×#102C2×D43semidirect
423. #340C2×D43semidirect
424. C43#20909semidirect
466. #121C4×D43semidirect
533. C2×D4C2×C4×D43semidirect
601. C4⋊C4C2×C4×D43semidirect
724. C22#14582897semidirect

Maximal subgroups

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

subgroupindex
C2×#145834092
C22×C4⋊C4×D432
C2×#145828972
C2×#145828612
#191349132
#191349092
#191349022
#191349012
#191349002
#191343132
C43×#18742
#2090943