Finite Group Databasebeta

← #25131433

Subgroups — #25131433

Order 11008.

1122 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583618C211yesmaximal, characteristic, complemented
2C2×C4×#10621883C211yesmaximal, characteristic, complemented
3#19139949C211yesmaximal, characteristic, complemented
4#19135839C211yesmaximal, characteristic, complemented
5#19135834C211yesmaximal, characteristic, complemented
6#19135676C211yesmaximal, characteristic, complemented
7#19135670C211yesmaximal, characteristic
8#19135530C211yesmaximal, characteristic, complemented
9#19135407C211yesmaximal, characteristic, complemented
10#19134952C211yesmaximal, characteristic, complemented
11#19134945C211yesmaximal, characteristic
12#19134861C211yesmaximal, characteristic, complemented
13#19134854C211yesmaximal, characteristic, complemented
14#19134611C211yesmaximal, characteristic, complemented
15C2×C43×#463C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17#14583618—24no—
18#14583618—24no—
19C2×#13063323C2211yescharacteristic
20C2×#13063318—21no—
21C2×#13063318—21no—
22C2×#13063312C2211yescharacteristic
23C2×#13063302—21no—
24C2×Q8×Dic43C2211yescharacteristic
25C2×C4×Dic86C2211yescharacteristic
26C2×C4×Dic86C2211yescharacteristic
27C2×D4×Dic43C2211yescharacteristic
28C2×#13063281—21no—
29C4×#10621883—24no—
30C2×#13063256C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063250C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063248C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×C4×C43⋊C8C2211yescharacteristic
40#14582835—21no—
41#14582811—21no—
42#14582802C2211yescharacteristic
43#14582802C2211yescharacteristic
44#14582795C2211yescharacteristic
45#14582795C2211yescharacteristic
46#14582772—21no—
47#14582772—21no—
48#14582765C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55C22×SD16×C43C2211yescharacteristic
56C22×D8×C43C2211yescharacteristic
57C2×#124×C43C2211yescharacteristic
58C2×C4×D4×C43C2211yescharacteristic
59C43×#463—24no—
60C2×C4⋊C8×C43C2211yescharacteristic
61C2×#103×C43C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic
63C22×Dic86D411yescharacteristic
64C22×Dic86C2311yescharacteristic
65C23×Dic43—21no—
66C2×#10621883—22no—
67C2×#10621883—22no—
68C2×#10621883—22no—
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71#13063323—22no—
72#13063323—22no—
73#13063318—28no—
74#13063318—28no—
75#13063312—22no—
76#13063312—22no—
77#13063302—28no—
78Q8×Dic43—22no—
79Q8×Dic43—22no—
80C4×Dic86—22no—
81C4×Dic86—22no—
82C4×Dic86—22no—
83C4×Dic86D414yes—
84D4×Dic43—22no—
85D4×Dic43—22no—
86#13063281—28no—
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43D411yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4D411yescharacteristic
98C2×Dic43⋊C4D411yescharacteristic
99C2×C22⋊Dic43—21no—
100C2×C22⋊Dic43—21no—
101C2×C22⋊Dic43—21no—
102C2×C22⋊Dic43—21no—
103C2×C22⋊Dic43—21no—
104C2×C22⋊Dic43—21no—
105C2×C22⋊Dic43—21no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43—21no—
108C2×C4×Dic43C2311yescharacteristic
109C2×C4×Dic43C2311yescharacteristic
110#13063256—22no—
111#13063250—41no—
112#13063250—41no—
113#13063249—22no—
114#13063249—41no—
115#13063248—22no—
116#13063246—22no—
117#13063246—22no—
118#13063246—41no—
119C4×C43⋊C8—22no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C22×Q8×C43C2311yescharacteristic
125C22×D4×C43C2311yescharacteristic
126C22×D4×C43C2311yescharacteristic
127C23×C4×C43—21no—
128C2×SD16×C43—22no—
129C2×SD16×C43—22no—
130C2×SD16×C43—41no—
131C2×D8×C43—22no—
132C2×D8×C43—22no—
133C2×D8×C43—41no—
134C22×C8×C43C2311yescharacteristic
135C22×C8×C43C2311yescharacteristic
136#124×C43—22no—
137#124×C43D414yes—
138C4×D4×C43—22no—
139C4×D4×C43—22no—
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43—21no—
144C2×C42×C43C2311yescharacteristic
145C4⋊C8×C43—22no—
146#103×C43—22no—
147#102×C43—22no—
148C24×C43—21no—
149C24×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43C2×D412yes—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43C2×D412yes—
167C2×D4×C43#4112yes—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—42no—
171C22×C4×C43—81no—
172C22×C4×C43—81no—
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2411yescharacteristic
176C22×Dic43—24no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—42no—
182C22×Dic43—42no—
183C22×Dic43C2×D411yescharacteristic
184C22×Dic43C2×D411yescharacteristic
185C22×Dic43C2×D411yescharacteristic
186C22×Dic43C2×D411yescharacteristic
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86—21no—
190C2×Dic86—21no—
191C2×Dic86—22no—
192C2×Dic86—21no—
193C2×Dic86—22no—
194C2×Dic86—41no—
195C2×Dic86C2×D412yes—
196SD16×C43—44no—
197D8×C43—44no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C22⋊C4×C43—24no—
207C22⋊C4×C43—24no—
208C22⋊C4×C43—42no—
209C42×C43C2×D412yes—
210C42×C43C2×D412yes—
211C22⋊Dic43—24no—
212C22⋊Dic43—24no—
213C22⋊Dic43—24no—
214C22⋊Dic43—42no—
215C22⋊Dic43—42no—
216C22⋊Dic43—81no—
217C22⋊Dic43—81no—
218#10621883—28no—
219C4⋊Dic43—24no—
220C4⋊Dic43—22no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43C2×D412yes—
227Dic43⋊C4—24no—
228Dic43⋊C4—24no—
229Dic43⋊C4—24no—
230Dic43⋊C4—22no—
231Dic43⋊C4—22no—
232Dic43⋊C4—81no—
233Dic43⋊C4—81no—
234C4×Dic43—24no—
235C4×Dic43—24no—
236C4×Dic43—21no—
237C4×Dic43—21no—
238C4×Dic43—21no—
239C4×Dic43—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8#4112yes—
246C23×C43—22no—
247C23×C43—22no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43C22×D411yescharacteristic
261Q8×C43—22no—
262Q8×C43—22no—
263Q8×C43—41no—
264Q8×C43—41no—
265D4×C43—22no—
266D4×C43—22no—
267D4×C43—22no—
268D4×C43—22no—
269D4×C43—41no—
270D4×C43—41no—
271D4×C43—41no—
272D4×C43—41no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—22no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—84no—
284C2×C4×C43#12012yes—
285C2×C4×C43#12012yes—
286C2×C4×C43C22×D411yescharacteristic
287C2×C4×C43C22×D411yescharacteristic
288C2×C4×C43C2×#4111yescharacteristic
289C2×C4×C43C2×#4111yescharacteristic
290C2×C4×C43H(5,𝔽2)11yescharacteristic
291C2×C4×C432−1+411yescharacteristic
292C2×Dic43—21no—
293C2×Dic43—21no—
294C2×Dic43—21no—
295C2×Dic43—22no—
296C2×Dic43—21no—
297C2×Dic43—22no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—48no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43#13512yes—
317Dic86—22no—
318Dic86—22no—
319Dic86—44no—
320Dic86—41no—
321Dic86—41no—
322C8×C43—41no—
323C8×C43—41no—
324C43⋊C8—22no—
325C43⋊C8—41no—
326#24193—431nomaximal, Sylow
327C22×C43—42no—
328C22×C43—42no—
329C22×C43—42no—
330C22×C43—42no—
331C22×C43—42no—
332C22×C43—42no—
333C22×C43—81no—
334C22×C43—81no—
335C22×C43—81no—
336C22×C43—81no—
337C22×C43—81no—
338C22×C43—81no—
339C22×C43—81no—
340C22×C43—81no—
341C22×C43C2×#12011yescharacteristic
342C22×C43#54811yescharacteristic
343C22×C43#55011yescharacteristic
344C22×C43C2×#13511yescharacteristic
345C22×C43#57511yescharacteristic
346C22×C43#57711yescharacteristic
347C22×C43#57711yescharacteristic
348C4×C43—22no—
349C4×C43—22no—
350C4×C43—42no—
351C4×C43—81no—
352C4×C43#52511yescharacteristic
353C4×C43#53711yescharacteristic
354C4×C43#54611yescharacteristic
355C4×C43#54711yescharacteristic
356Dic43—22no—
357Dic43—42no—
358Dic43—41no—
359Dic43—42no—
360Dic43—41no—
361Dic43—41no—
362Dic43—81no—
363Dic43—81no—
364C2×#556—431no—
365C2×#463D4311yescharacteristic
366C2×C4×SD16—431no—
367#2580—431no—
368#2043—431no—
369#2042—431no—
370#2013—431no—
371#2012—431no—
372#1984—431no—
373#1958—431no—
374#1880—431no—
375#1879—431no—
376#1865—431no—
377#1864—431no—
378#1805—431no—
379C2×C43—82no—
380C2×C43—82no—
381C2×C43#240711yescharacteristic
382C2×C43#300211yescharacteristic
383C2×C43#301011yescharacteristic
384C2×C43#336011yescharacteristic
385C2×C43#337611yescharacteristic
386C2×C43#339411yescharacteristic
387C2×C43#340111yescharacteristic
388C22×SD16—431no—
389C22×SD16C2×D4311yescharacteristic
390C22×D8C2×D4311yescharacteristic
391#556—864no—
392#556—864no—
393C2×C4⋊Q8—431no—
394C2×#126—861no—
395C2×#126—861no—
396C2×#124—431no—
397C2×#124C2×D4311yescharacteristic
398C2×C22⋊Q8—861no—
399C2×C4×Q8—431no—
400C2×C4×Q8—431no—
401C2×C4×Q8—431no—
402C2×C4×D4—431no—
403C2×C4×D4C2×D4311yescharacteristic
404C2×#117—861no—
405#463—24no—
406C4×SD16—864no—
407C2×#106—431no—
408C2×C4⋊C8C2×D4311yescharacteristic
409C2×#103—431no—
410C2×#103—431no—
411C2×#103—431no—
412C2×#103—431no—
413C2×#103—431no—
414C2×#103C2×D4311yescharacteristic
415C2×#102—431no—
416C2×#102—431no—
417C2×#102—431no—
418C2×#102C2×D4311yescharacteristic
419C2×C4×C8—431no—
420#399—861no—
421#393—861no—
422#390—431no—
423#390—431no—
424#389—431no—
425#389—431no—
426#385—861no—
427#385—861no—
428#382—431no—
429#340—431no—
430#340—431no—
431#336—431no—
432#336—431no—
433#336—431no—
434#336—431no—
435C43#2419311yescharacteristic, complemented, Sylow
436C22×Q8—431no—
437C22×Q8—431no—
438C22×Q8C22×D4311yescharacteristic
439C22×D4C22×D4311yescharacteristic
440C22×D4C22×D4311yescharacteristic
441C23×C4—21no—
442C23×C4—861no—
443C2×SD16—22no—
444C2×SD16—22no—
445C2×SD16—41no—
446C2×SD16—862no—
447C2×SD16—862no—
448C2×SD16—862no—
449C2×D8—22no—
450C2×D8—22no—
451C2×D8—41no—
452C22×C8—431no—
453C22×C8—431no—
454C22×C8C22×D4311yescharacteristic
455C22×C8C22×D4311yescharacteristic
456C4⋊Q8—862no—
457C4⋊Q8—862no—
458#126—868no—
459#126—868no—
460#124—22no—
461#124—862no—
462#124—862no—
463#124C22⋊D4314yes—
464C22⋊Q8—868no—
465C4×Q8—434no—
466C4×Q8—862no—
467C4×Q8—862no—
468C4×Q8—862no—
469C4×Q8—862no—
470C4×Q8—862no—
471C4×D4—22no—
472C4×D4—22no—
473C4×D4—862no—
474C4×D4—862no—
475#117—868no—
476C2×C4⋊C4—431no—
477C2×C4⋊C4—431no—
478C2×C4⋊C4—431no—
479C2×C4⋊C4—431no—
480C2×C4⋊C4—431no—
481C2×C4⋊C4—431no—
482C2×C4⋊C4—861no—
483C2×C4⋊C4—861no—
484C2×C4⋊C4—861no—
485C2×C4⋊C4—861no—
486C2×C4⋊C4—861no—
487C2×C4⋊C4—861no—
488C2×C4⋊C4C22×D4311yescharacteristic
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—861no—
493C2×C22⋊C4—861no—
494C2×C22⋊C4—861no—
495C2×C22⋊C4—861no—
496C2×C22⋊C4—861no—
497C2×C22⋊C4—861no—
498C2×C22⋊C4—861no—
499C2×C42—431no—
500C2×C42—431no—
501C2×C42—861no—
502C2×C42—861no—
503C2×C42C22×D4311yescharacteristic
504#106—862no—
505C4⋊C8—22no—
506#103—22no—
507#103—862no—
508#103—862no—
509#103—1721no—
510#103—1721no—
511#103—1721no—
512#102—22no—
513#102—862no—
514#102—862no—
515#102—1721no—
516C4×C8—862no—
517#95—861no—
518#95—861no—
519#95—861no—
520#95—861no—
521C24—21no—
522C24—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—432no—
529C2×Q8—862no—
530C2×Q8—862no—
531C2×Q8—861no—
532C2×Q8—861no—
533C2×Q8—861no—
534C2×Q8—861no—
535C2×Q8—861no—
536C2×Q8—1721no—
537C2×Q8C2×C22⋊D4312yes—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4#1062190012yes—
549C2×D4C2×C22⋊D4312yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—42no—
553C22×C4—81no—
554C22×C4—81no—
555C22×C4—431no—
556C22×C4—431no—
557C22×C4—431no—
558C22×C4—431no—
559C22×C4—864no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4—861no—
563C22×C4—861no—
564C22×C4—1722no—
565C22×C4—1722no—
566C22×C4D4×D4311yescharacteristic
567C22×C4D4×D4311yescharacteristic
568C22×C4C23×D4311yescharacteristic
569SD16—44no—
570SD16—868no—
571D8—44no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—432no—
579C2×C8—861no—
580C2×C8—861no—
581C2×C8—861no—
582C2×C8—861no—
583C2×C8—861no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—432no—
587C4⋊C4—864no—
588C4⋊C4—864no—
589C4⋊C4—864no—
590C4⋊C4—862no—
591C4⋊C4—862no—
592C4⋊C4—862no—
593C4⋊C4—864no—
594C4⋊C4—861no—
595C4⋊C4—861no—
596C4⋊C4—861no—
597C4⋊C4—861no—
598C4⋊C4—861no—
599C4⋊C4—3441no—
600C4⋊C4—3441no—
601C22⋊C4—24no—
602C22⋊C4—24no—
603C22⋊C4—42no—
604C22⋊C4—864no—
605C22⋊C4—864no—
606C22⋊C4—864no—
607C22⋊C4—3441no—
608C22⋊C4—3441no—
609C22⋊C4—1722no—
610C22⋊C4—1722no—
611C42—864no—
612C42—864no—
613C42—861no—
614C42—861no—
615C42—861no—
616C42—861no—
617C42D4×D4312yes—
618C42C2×C22⋊D4312yes—
619C23—22no—
620C23—22no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23C2×D4×D4311yescharacteristic
634Q8—22no—
635Q8—22no—
636Q8—41no—
637Q8—41no—
638Q8—862no—
639Q8—862no—
640Q8—1724no—
641Q8—1721no—
642Q8—1721no—
643D4—22no—
644D4—22no—
645D4—22no—
646D4—22no—
647D4—41no—
648D4—41no—
649D4—41no—
650D4—41no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—22no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—84no—
662C2×C4—432no—
663C2×C4—861no—
664C2×C4—861no—
665C2×C4—861no—
666C2×C4—862no—
667C2×C4—861no—
668C2×C4—861no—
669C2×C4—862no—
670C2×C4—861no—
671C2×C4—861no—
672C2×C4—861no—
673C2×C4—861no—
674C2×C4—861no—
675C2×C4—861no—
676C2×C4—1728no—
677C2×C4—1721no—
678C2×C4—1721no—
679C2×C4—1721no—
680C2×C4—1721no—
681C2×C4—1721no—
682C2×C4—1721no—
683C2×C4—1721no—
684C2×C4—1721no—
685C2×C4—1721no—
686C2×C4—1721no—
687C2×C4#1306329312yes—
688C2×C4#1306329312yes—
689C2×C4C2×D4×D4311yescharacteristic
690C2×C4C22×C22⋊D4311yescharacteristic
691C2×C4#41×D4311yescharacteristic
692C2×C4C2×#1062190011yescharacteristic
693C2×C4#1306337011yescharacteristic
694C2×C4#1306337211yescharacteristic
695C8—41no—
696C8—41no—
697C8—862no—
698C8—1721no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22C2×#1306329311yescharacteristic
714C22#1458355511yescharacteristic
715C22#1458356711yescharacteristic
716C22#135×D4311yescharacteristic
717C22#1458369611yescharacteristic
718C22#1458370911yescharacteristic
719C22#1458370911yescharacteristic
720C4—22no—
721C4—22no—
722C4—42no—
723C4—81no—
724C4—862no—
725C4—3441no—
726C4—3441no—
727C4—1721no—
728C4—1722no—
729C4—1722no—
730C4—1721no—
731C4—1721no—
732C4#1458340911yescharacteristic
733C4#1458347811yescharacteristic
734C4#1458354311yescharacteristic
735C4#1458354811yescharacteristic
736C2—82no—
737C2—82no—
738C2#1913793611yescharacteristic
739C2#1914380911yescharacteristic
740C2#1914388011yescharacteristic
741C2#1914723911yescharacteristic
742C2#1914742611yescharacteristic
743C2#1914759411yescharacteristic
744C2#1914765911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#463C2
socleC23×C43C22×D4
prime radicalC22×D8×C43C22
hypercenterC2×#463D43
hypocenterC43#24193
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#14583618C2semidirect
2. C2×C4×#10621883C2semidirect
3. #19139949C2semidirect
4. #19135839C2semidirect
5. #19135834C2semidirect
6. #19135676C2semidirect
8. #19135530C2semidirect
9. #19135407C2semidirect
10. #19134952C2semidirect
12. #19134861C2semidirect
13. #19134854C2semidirect
14. #19134611C2semidirect
435. C43#24193semidirect

Maximal subgroups

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

subgroupindex
C2×#145836182
C2×C4×#106218832
#191399492
#191358392
#191358342
#191356762
#191356702
#191355302
#191354072
#191349522
#191349452
#191348612
#191348542
#191346112
C2×C43×#4632
#2419343