Finite Group Databasebeta

← #25097824

Subgroups — #25097824

Order 11008.

2258 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583411C211yesmaximal, characteristic
2C22×C4⋊C4×D43C211yesmaximal, characteristic, complemented
3C2×#14582901C211yesmaximal, characteristic, complemented
4C2×#14582898C211yesmaximal, characteristic, complemented
5C2×#14582862C211yesmaximal, characteristic, complemented
6#19134911C214yesmaximal, complemented
7#19134901C214yesmaximal, complemented
8#19134316C211yesmaximal, characteristic, complemented
9C43×#1736C211yesmaximal, characteristic, complemented
10C22×#10621898C2211yescharacteristic
11C23×C4×D43—21no—
12C23×C4×D43C2211yescharacteristic
13C22×#10621877C2211yescharacteristic
14#14583411—24no—
15#14583411C418yescomplemented
16C2×#13063309—21no—
17C2×#13063305C2212yes—
18C2×#13063300C2212yes—
19C2×#13063295—21no—
20C2×C4×D172—22no—
21C22×C4⋊Dic43C2211yescharacteristic
22C22×Dic43⋊C4—21no—
23C2×C4⋊C4×D43—22no—
24C2×C4⋊C4×D43—24no—
25C2×C4⋊C4×D43—24no—
26C2×C4⋊C4×D43C2214yes—
27#14582901—24no—
28#14582898—24no—
29C2×#13063250C2212yescomplemented
30C2×#13063248C2212yescomplemented
31C2×#13063247C2212yescomplemented
32C2×#13063245C2212yescomplemented
33#14582862—24no—
34C2×(C2×D43)⋊C8C2214yes—
35#14582661C2214yescomplemented
36C22×M16×C43C2211yescharacteristic
37C2×#117×C43C2211yescharacteristic
38C22×C4⋊C4×C43C2211yescharacteristic
39C43×#340C2214yescomplemented
40C24×D43D411yescharacteristic
41C2×#10621898—22no—
42C2×#10621898—22no—
43C2×#10621898—22no—
44C2×#10621898—22no—
45C2×#10621898—22no—
46C2×#10621898C2×C414yescomplemented
47C22×Dic86C2311yescharacteristic
48C22×D172—22no—
49C22×D172C2311yescharacteristic
50C22×C22⋊D43—21no—
51C23×Dic43—21no—
52C23×Dic43D411yescharacteristic
53C22×C4×D43—22no—
54C22×C4×D43—22no—
55C22×C4×D43—22no—
56C22×C4×D43—22no—
57C22×C4×D43—28no—
58C22×C4×D43—24no—
59C22×C4×D43—21no—
60C22×C4×D43—48no—
61C22×C4×D43C2×C414yes—
62C22×C4×D43D412yes—
63C22×C4×D43D414yes—
64C22×C4×D43C2312yes—
65C2×#10621877—22no—
66C2×#10621877—22no—
67C2×#10621877—22no—
68C22×C43⋊C8C2312yes—
69#13063309—28no—
70#13063305—24no—
71#13063305C2×C418yescomplemented
72#13063300—24no—
73#13063300C2×C418yescomplemented
74#13063295—28no—
75C4×D172—216no—
76C2×C4⋊Dic43—22no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—22no—
79C2×C4⋊Dic43D414yescomplemented
80C2×C4⋊Dic43C2312yes—
81C2×Dic43⋊C4—28no—
82C2×Dic43⋊C4—24no—
83C4⋊C4×D43—216no—
84C4⋊C4×D43—28no—
85C4⋊C4×D43—28no—
86C2×(C2×D43)⋊C4—22no—
87C2×(C2×D43)⋊C4—22no—
88#13063250—24no—
89#13063248—24no—
90#13063247—24no—
91#13063245—24no—
92(C2×D43)⋊C8—28no—
93C23×C4×C43—21no—
94C23×C4×C43C2311yescharacteristic
95C2×M16×C43—22no—
96C2×M16×C43—22no—
97C2×M16×C43—22no—
98C22×C8×C43C2312yes—
99#117×C43—22no—
100#117×C43C2×C414yescomplemented
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—22no—
103C2×C4⋊C4×C43D414yescomplemented
104C2×C4⋊C4×C43C2312yes—
105C2×C4⋊C4×C43C2312yes—
106C2×C22⋊C4×C43—21no—
107C2×C42×C43—21no—
108C24×C43C2×D411yescharacteristic
109C23×D43—22no—
110C23×D43—22no—
111C23×D43—24no—
112C23×D43—24no—
113C23×D43—21no—
114C23×D43C22⋊C414yes—
115C23×D43C2×D412yes—
116C22×C4×C43—24no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—44no—
120C22×C4×C43C22×C412yes—
121C22×C4×C43C2×D412yes—
122C22×C4×C43C2×D412yes—
123C22×C4×C43C2×D412yes—
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43#4112yes—
126C22×C4×C43#4112yes—
127C22×C4×C43C2411yescharacteristic
128C2×C22⋊D43—24no—
129C2×C22⋊D43—42no—
130C2×C22⋊D43—42no—
131C22×Dic43—22no—
132C22×Dic43—24no—
133C22×Dic43—22no—
134C22×Dic43—21no—
135C22×Dic43—22no—
136C22×Dic43—44no—
137C22×Dic43C22⋊C414yes—
138C22×Dic43C2×D412yes—
139#10621898—28no—
140#10621898—28no—
141#10621898—44no—
142#10621898—44no—
143C2×D172—21no—
144C2×D172—28no—
145C2×D172—21no—
146C2×D172—21no—
147C2×D172—21no—
148C2×D172—21no—
149C2×D172—44no—
150C2×D172—44no—
151C2×D172C22×C412yescomplemented
152C2×C4×D43—28no—
153C2×C4×D43—28no—
154C2×C4×D43—24no—
155C2×C4×D43—28no—
156C2×C4×D43—28no—
157C2×C4×D43—24no—
158C2×C4×D43—22no—
159C2×C4×D43—22no—
160C2×C4×D43—22no—
161C2×C4×D43—22no—
162C2×C4×D43—216no—
163C2×C4×D43—24no—
164C2×C4×D43—432no—
165C2×C4×D43—48no—
166C2×C4×D43—42no—
167C2×C4×D43—42no—
168C2×C4×D43—48no—
169C2×C4×D43C22⋊C418yes—
170C2×C4×D43C22×C414yes—
171C2×C4×D43C2×D414yes—
172C2×Dic86—21no—
173C2×Dic86—21no—
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86C22×C412yescomplemented
178M16×C43—44no—
179C2×C8×C43—22no—
180C2×C8×C43—22no—
181C2×C8×C43—22no—
182C4⋊C4×C43—24no—
183C4⋊C4×C43—22no—
184C4⋊C4×C43—22no—
185C4⋊C4×C43C22×C414yescomplemented
186C4⋊C4×C43C2×D414yes—
187C22⋊C4×C43—24no—
188C42×C43—24no—
189(C2×D43)⋊C4—28no—
190(C2×D43)⋊C4—28no—
191C4⋊Dic43—24no—
192C4⋊Dic43—22no—
193C4⋊Dic43—28no—
194C4⋊Dic43C2×D414yes—
195Dic43⋊C4—216no—
196#10621877—44no—
197C2×C43⋊C8—22no—
198C2×C43⋊C8—22no—
199C2×C43⋊C8—22no—
200C23×C43—22no—
201C23×C43—22no—
202C23×C43C2×C22⋊C412yes—
203C23×C43#12012yes—
204C23×C43#12312yes—
205C23×C43C22×D411yescharacteristic
206C22×D43—28no—
207C22×D43—216no—
208C22×D43—28no—
209C22×D43—22no—
210C22×D43—22no—
211C22×D43—22no—
212C22×D43—22no—
213C22×D43—28no—
214C22×D43—216no—
215C22×D43—22no—
216C22×D43—41no—
217C22×D43—41no—
218C22×D43—42no—
219C22×D43—42no—
220C22×D43C2×C22⋊C414yes—
221C22×D43AGL(1,ℤ/8)14yes—
222C22×D43#13714yes—
223C2×C4×C43—24no—
224C2×C4×C43—24no—
225C2×C4×C43—48no—
226C2×C4×C43—44no—
227C2×C4×C43—42no—
228C2×C4×C43—42no—
229C2×C4×C43C2×C22⋊C412yes—
230C2×C4×C43C4×D414yes—
231C2×C4×C43C4×D414yes—
232C2×C4×C43#12012yes—
233C2×C4×C43#12114yes—
234C2×C4×C43#12114yes—
235C2×C4×C43#12312yes—
236C2×C4×C43C23×C411yescharacteristic
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C22⋊D43—48no—
243C2×Dic43—22no—
244C2×Dic43—22no—
245C2×Dic43—28no—
246C2×Dic43—22no—
247C2×Dic43—24no—
248C2×Dic43—48no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—44no—
252C2×Dic43C2×C22⋊C414yes—
253D172—22no—
254D172—22no—
255D172—416no—
256D172—41no—
257D172—41no—
258C4×D43—24no—
259C4×D43—24no—
260C4×D43—24no—
261C4×D43—24no—
262C4×D43—216no—
263C4×D43—432no—
264C4×D43—48no—
265Dic86—22no—
266Dic86—22no—
267Dic86—41no—
268Dic86—41no—
269C8×C43—42no—
270C43⋊C8—42no—
271#20909—431nomaximal, Sylow
272C22×C43—24no—
273C22×C43—24no—
274C22×C43—22no—
275C22×C43—22no—
276C22×C43#38614yes—
277C22×C43C22×C22⋊C411yescharacteristic
278C22×C43C2×#12011yescharacteristic
279C22×C43C2×#12311yescharacteristic
280C22×C43C2×AGL(1,ℤ/8)12yes—
281C22×C43C2×#13712yes—
282C2×D43—232no—
283C2×D43—24no—
284C2×D43—24no—
285C2×D43—24no—
286C2×D43—24no—
287C2×D43—24no—
288C2×D43—24no—
289C2×D43—44no—
290C2×D43—42no—
291C2×D43—82no—
292C2×D43—81no—
293C2×D43—81no—
294C2×D43#41718yescomplemented
295C4×C43—44no—
296C4×C43—44no—
297C4×C43#38614yes—
298C4×C43C2×C4×D411yescharacteristic
299C4×C43C2×C4×D411yescharacteristic
300C4×C43C2×#12111yescharacteristic
301C4×C43C2×#12111yescharacteristic
302Dic43—24no—
303Dic43—44no—
304Dic43—42no—
305C2×#525—431no—
306C23×C4⋊C4—431no—
307C2×#417—431no—
308C2×#417—431no—
309C2×#407—431no—
310#1874—434no—
311#1872—434no—
312#1736—431no—
313#1736D4311yescharacteristic, complemented
314C2×C43—24no—
315C2×C43C2×#38611yescharacteristic
316C2×C43C2×#41712yes—
317C2×C43#300311yescharacteristic
318C2×C43#300411yescharacteristic
319C2×C43#309212yes—
320D43—28no—
321D43—82no—
322C22×#41—431no—
323C24×C4—431no—
324C24×C4—861no—
325C22×M16—431no—
326C22×M16C2×D4311yescharacteristic
327#525—438no—
328#525—864no—
329C2×#123—861no—
330C2×C22⋊Q8—432no—
331C2×#121—432no—
332C2×#120—861no—
333C2×C4×D4—862no—
334C2×#117C2×D4311yescharacteristic
335C22×C4⋊C4—431no—
336C22×C4⋊C4—434no—
337C22×C4⋊C4—864no—
338C22×C4⋊C4—862no—
339C22×C4⋊C4—861no—
340C22×C4⋊C4—864no—
341C22×C4⋊C4C2×D4311yescharacteristic
342#417—864no—
343#417—864no—
344C2×#103—432no—
345C2×#103—432no—
346C2×#102—432no—
347C2×#102—432no—
348#407—864no—
349C2×C22⋊C8—434no—
350#340—434no—
351#340C2×D4314yescomplemented
352C43#2090911yescharacteristic, complemented, Sylow
353C25—431no—
354C2×#41—434no—
355C2×#41—862no—
356C2×#41—862no—
357C2×#41—862no—
358C2×#41—862no—
359C2×#41—862no—
360C22×Q8—431no—
361C22×D4—431no—
362C22×D4—862no—
363C22×D4—861no—
364C23×C4—21no—
365C23×C4—431no—
366C23×C4—434no—
367C23×C4—432no—
368C23×C4—434no—
369C23×C4—432no—
370C23×C4—864no—
371C23×C4—868no—
372C23×C4—862no—
373C23×C4—862no—
374C23×C4—862no—
375C23×C4—862no—
376C23×C4—861no—
377C23×C4—861no—
378C23×C4—1728no—
379C23×C4C22×D4311yescharacteristic
380C2×M16—22no—
381C2×M16—22no—
382C2×M16—22no—
383C2×M16—862no—
384C2×M16—862no—
385C2×M16—862no—
386C22×C8—432no—
387C22×C8C22×D4312yes—
388#123—868no—
389C22⋊Q8—438no—
390C22⋊Q8—864no—
391#121—438no—
392#121—864no—
393#120—868no—
394C4×D4—8616no—
395#117—22no—
396#117C4×D4314yescomplemented
397C2×C4⋊C4—21no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—434no—
400C2×C4⋊C4—432no—
401C2×C4⋊C4—868no—
402C2×C4⋊C4—8616no—
403C2×C4⋊C4—864no—
404C2×C4⋊C4—862no—
405C2×C4⋊C4—868no—
406C2×C4⋊C4—862no—
407C2×C4⋊C4—861no—
408C2×C4⋊C4—868no—
409C2×C4⋊C4D17214yescomplemented
410C2×C4⋊C4C22×D4312yes—
411C2×C4⋊C4C22×D4312yes—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—862no—
414C2×C22⋊C4—862no—
415C2×C42—21no—
416#103—864no—
417#103—864no—
418#102—864no—
419#102—864no—
420C22⋊C8—868no—
421C24—432no—
422C24—434no—
423C24—864no—
424C24—864no—
425C24—862no—
426C24—862no—
427C24—861no—
428C24D4×D4311yescharacteristic
429#41—868no—
430#41—868no—
431#41—1724no—
432#41—1724no—
433C2×Q8—432no—
434C2×Q8—861no—
435C2×Q8—861no—
436C2×Q8—861no—
437C2×Q8—861no—
438C2×Q8—861no—
439C2×D4—432no—
440C2×D4—868no—
441C2×D4—864no—
442C2×D4—861no—
443C2×D4—861no—
444C2×D4—861no—
445C2×D4—861no—
446C2×D4—861no—
447C2×D4—1724no—
448C2×D4—1724no—
449C2×D4—1722no—
450C2×D4—1722no—
451C22×C4—24no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—44no—
455C22×C4—434no—
456C22×C4—432no—
457C22×C4—438no—
458C22×C4—434no—
459C22×C4—434no—
460C22×C4—8616no—
461C22×C4—862no—
462C22×C4—862no—
463C22×C4—868no—
464C22×C4—868no—
465C22×C4—864no—
466C22×C4—868no—
467C22×C4—868no—
468C22×C4—864no—
469C22×C4—862no—
470C22×C4—862no—
471C22×C4—862no—
472C22×C4—862no—
473C22×C4—864no—
474C22×C4—861no—
475C22×C4—862no—
476C22×C4—864no—
477C22×C4—1728no—
478C22×C4—17232no—
479C22×C4—1728no—
480C22×C4—1724no—
481C22×C4—1722no—
482C22×C4—1722no—
483C22×C4C2×C4×D4312yes—
484C22×C4C2×D17212yes—
485C22×C4#1062189812yes—
486C22×C4D4×D4311yescharacteristic
487C22×C4D4×D4312yes—
488C22×C4D4×D4312yes—
489C22×C4#1062190212yes—
490C22×C4C23×D4311yescharacteristic
491M16—44no—
492M16—1724no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—862no—
497C2×C8—862no—
498C2×C8—862no—
499C4⋊C4—24no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—434no—
503C4⋊C4—868no—
504C4⋊C4—8616no—
505C4⋊C4—864no—
506C4⋊C4—862no—
507C4⋊C4C2×C4×D4314yescomplemented
508C4⋊C4C2×D17214yes—
509C22⋊C4—24no—
510C22⋊C4—868no—
511C22⋊C4—868no—
512C42—24no—
513C23—22no—
514C23—22no—
515C23—434no—
516C23—434no—
517C23—434no—
518C23—8616no—
519C23—868no—
520C23—8616no—
521C23—868no—
522C23—862no—
523C23—862no—
524C23—862no—
525C23—862no—
526C23—868no—
527C23—862no—
528C23—1721no—
529C23—1721no—
530C23—1722no—
531C23—1722no—
532C23C22⋊C4×D4312yes—
533C23#1306329512yes—
534C23#1306331012yes—
535C23C2×D4×D4311yescharacteristic
536Q8—862no—
537Q8—862no—
538Q8—1721no—
539Q8—1721no—
540D4—862no—
541D4—862no—
542D4—17216no—
543D4—1728no—
544D4—1721no—
545D4—1721no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—48no—
549C2×C4—44no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—434no—
553C2×C4—862no—
554C2×C4—862no—
555C2×C4—868no—
556C2×C4—864no—
557C2×C4—864no—
558C2×C4—864no—
559C2×C4—864no—
560C2×C4—8616no—
561C2×C4—862no—
562C2×C4—864no—
563C2×C4—17232no—
564C2×C4—1728no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1724no—
568C2×C4—1728no—
569C2×C4C22⋊C4×D4312yes—
570C2×C4#1306328714yes—
571C2×C4C4×D17214yes—
572C2×C4#1306329512yes—
573C2×C4#1306329814yes—
574C2×C4#1306330014yes—
575C2×C4#1306331012yes—
576C2×C4C22×C4×D4311yescharacteristic
577C2×C4C2×D4×D4311yescharacteristic
578C2×C4C2×D4×D4311yescharacteristic
579C2×C4C22×D17211yescharacteristic
580C2×C4C2×#1062189811yescharacteristic
581C2×C4C2×#1062190211yescharacteristic
582C8—42no—
583C8—1722no—
584C22—24no—
585C22—22no—
586C22—22no—
587C22—24no—
588C22—438no—
589C22—8632no—
590C22—864no—
591C22—864no—
592C22—864no—
593C22—864no—
594C22—864no—
595C22—864no—
596C22—3442no—
597C22—3441no—
598C22—3441no—
599C22—1724no—
600C22—1722no—
601C22#1458277714yes—
602C22C2×C22⋊C4×D4311yescharacteristic
603C22C2×#1306329511yescharacteristic
604C22C2×#1306331011yescharacteristic
605C22AGL(1,ℤ/8)×D4312yes—
606C22#137×D4312yes—
607C4—44no—
608C4—44no—
609C4—864no—
610C4—1724no—
611C4—1722no—
612C4#1458277714yes—
613C4C2×#1306328711yescharacteristic
614C4C2×C4×D17211yescharacteristic
615C4C2×#1306329811yescharacteristic
616C4C2×#1306330011yescharacteristic
617C2—24no—
618C2—868no—
619C2—3442no—
620C2C2×#1458277711yescharacteristic
621C2#417×D4312yes—
622C2#1914382411yescharacteristic
623C2#1914383111yescharacteristic
624C2#1914452112yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1736C2
socleC23×C43C22×D4
prime radicalC2×#14583411C2
cosocleC22×C4×C43C24
hypercenter#1736D43
hypocenterC43#20909
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D43C2semidirect
3. C2×#14582901C2semidirect
4. C2×#14582898C2semidirect
5. C2×#14582862C2semidirect
6. #19134911C2semidirect
7. #19134901C2semidirect
8. #19134316C2semidirect
9. C43×#1736C2semidirect
15. #14583411C4semidirect
29. C2×#13063250C22semidirect
30. C2×#13063248C22semidirect
31. C2×#13063247C22semidirect
32. C2×#13063245C22semidirect
35. #14582661C22semidirect
39. C43×#340C22semidirect
46. C2×#10621898C2×C4semidirect
71. #13063305C2×C4semidirect
73. #13063300C2×C4semidirect
79. C2×C4⋊Dic43D4semidirect
100. #117×C43C2×C4semidirect
103. C2×C4⋊C4×C43D4semidirect
151. C2×D172C22×C4semidirect
177. C2×Dic86C22×C4semidirect
185. C4⋊C4×C43C22×C4semidirect
294. C2×D43#417semidirect
313. #1736D43semidirect
351. #340C2×D43semidirect
352. C43#20909semidirect
396. #117C4×D43semidirect
409. C2×C4⋊C4D172semidirect
507. C4⋊C4C2×C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834112
C22×C4⋊C4×D432
C2×#145829012
C2×#145828982
C2×#145828622
#191349112
#191349012
#191343162
C43×#17362
#2090943