Finite Group Databasebeta

← #25097340

Subgroups — #25097340

Order 11008.

1630 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063283C211yesmaximal, characteristic
2C2×#14582940C212yesmaximal, complemented
3C2×#14582861C211yesmaximal, characteristic
4#380×D43C211yesmaximal, characteristic
5#19134795C212yesmaximal, complemented
6#19134791C212yesmaximal, complemented
7#19134790C211yesmaximal, characteristic, complemented
8#19134787C211yesmaximal, characteristic, complemented
9#19134783C211yesmaximal, characteristic, complemented
10#19134313C212yesmaximal, complemented
11C43×#1852C211yesmaximal, characteristic, complemented
12C23×C4×D43C2211yescharacteristic
13C22×#10621872C2212yes—
14C2×#13063283—21no—
15C2×#13063283—21no—
16C2×#13063283—28no—
17C2×#13063283C2212yes—
18C2×#13063283C2212yes—
19C22×C4⋊Dic43C2211yescharacteristic
20C2×C4⋊C4×D43C2211yescharacteristic
21C2×C4⋊C4×D43C2211yescharacteristic
22C22×(C2×D43)⋊C4—21no—
23C2×C22⋊C4×D43—21no—
24C22×C4×Dic43—21no—
25#14582940—28no—
26C2×#13063258C2212yescomplemented
27C2×#13063257C2212yescomplemented
28C2×#13063256C2212yescomplemented
29#14582861C418yescomplemented
30C2×C22⋊(C43⋊C8)C2211yescharacteristic
31C2×(C2×D43)⋊C8C2212yes—
32#14582759C2211yescharacteristic
33#14582758—21no—
34#14582757—21no—
35#14582756C2211yescharacteristic
36#14582756C2211yescharacteristic
37#95×D43—21no—
38#14582662C2212yescomplemented
39#14582661C2212yescomplemented
40#14582661C2212yescomplemented
41C22×C4⋊C4×C43C2211yescharacteristic
42C2×#107×C43C2212yescomplemented
43C2×C22⋊C8×C43C2211yescharacteristic
44C43×#380C2211yescharacteristic
45C43×#340C2212yescomplemented
46C24×D43D411yescharacteristic
47C23×Dic43—21no—
48C23×Dic43D411yescharacteristic
49C22×C4×D43—24no—
50C22×C4×D43—24no—
51C22×C4×D43—21no—
52C22×C4×D43—21no—
53C22×C4×D43C2×C414yes—
54C22×C4×D43D411yescharacteristic
55C22×C4×D43D411yescharacteristic
56C22×C4×D43Q814yes—
57C22×C4×D43C2311yescharacteristic
58C22×C4×D43C2311yescharacteristic
59C2×#10621872—24no—
60C2×#10621872—24no—
61C2×#10621872C2×C418yescomplemented
62C22×C43⋊C8C2312yes—
63#13063283—28no—
64#13063283—28no—
65#13063283—24no—
66#13063283—24no—
67#13063283—24no—
68#13063283D418yes—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—24no—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2312yes—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C4⋊C4×D43—24no—
77C4⋊C4×D43—24no—
78C2×C22⋊Dic43—21no—
79C2×(C2×D43)⋊C4—28no—
80C2×(C2×D43)⋊C4—22no—
81C2×(C2×D43)⋊C4—22no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C22⋊C4×D43—44no—
85C2×C4×Dic43—28no—
86C2×C4×Dic43—22no—
87C2×C4×Dic43—22no—
88#13063258—24no—
89#13063257—24no—
90#13063256—24no—
91C22⋊(C43⋊C8)C2×C414yescomplemented
92(C2×D43)⋊C8C2×C418yescomplemented
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C23×C4×C43—21no—
97C23×C4×C43C2311yescharacteristic
98C22×C8×C43C2312yes—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—24no—
101C2×C4⋊C4×C43C2311yescharacteristic
102C2×C4⋊C4×C43C2311yescharacteristic
103C2×C4⋊C4×C43C2312yes—
104C2×C22⋊C4×C43—21no—
105#107×C43—24no—
106C22⋊C8×C43C2×C414yescomplemented
107#95×C43—21no—
108C24×C43C2×D411yescharacteristic
109C23×D43—22no—
110C23×D43—22no—
111C23×D43—22no—
112C23×D43—22no—
113C23×D43—41no—
114C23×D43—41no—
115C23×D43C4⋊C414yes—
116C23×D43C2×D411yescharacteristic
117C23×D43C2×D411yescharacteristic
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—24no—
121C22×C4×C43—22no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—42no—
125C22×C4×C43—42no—
126C22×C4×C43C22×C412yes—
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×Q812yes—
129C22×C4×C43C2411yescharacteristic
130C22×Dic43—22no—
131C22×Dic43—22no—
132C22×Dic43—24no—
133C22×Dic43—22no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—42no—
137C22×Dic43—42no—
138C22×Dic43C4⋊C414yes—
139C22×Dic43C2×D411yescharacteristic
140C22×Dic43C2×D411yescharacteristic
141C2×C4×D43—22no—
142C2×C4×D43—22no—
143C2×C4×D43—22no—
144C2×C4×D43—22no—
145C2×C4×D43—216no—
146C2×C4×D43—216no—
147C2×C4×D43—22no—
148C2×C4×D43—22no—
149C2×C4×D43—42no—
150C2×C4×D43—42no—
151C2×C4×D43—42no—
152C2×C4×D43—42no—
153C2×C4×D43—42no—
154C2×C4×D43—42no—
155C2×C4×D43C4⋊C414yes—
156C2×C4×D43C4⋊C414yes—
157C2×C4×D43C22×C412yes—
158C2×C4×D43C22×C412yes—
159C2×C4×D43C2×D414yes—
160C2×C4×D43C2×Q812yes—
161C2×C4×D43C2×Q812yes—
162C2×C4×D43#4114yes—
163C2×C8×C43—22no—
164C2×C8×C43—22no—
165C2×C8×C43C22×C414yes—
166C4⋊C4×C43—24no—
167C4⋊C4×C43—22no—
168C4⋊C4×C43—22no—
169C4⋊C4×C43—22no—
170C4⋊C4×C43C2×D414yes—
171C22⋊C4×C43—42no—
172C22⋊Dic43—42no—
173(C2×D43)⋊C4—28no—
174(C2×D43)⋊C4—28no—
175(C2×D43)⋊C4—42no—
176(C2×D43)⋊C4—42no—
177C4⋊Dic43—24no—
178C4⋊Dic43—22no—
179C4⋊Dic43—22no—
180C4⋊Dic43—22no—
181C4⋊Dic43C2×D414yes—
182Dic43⋊C4—42no—
183Dic43⋊C4—42no—
184C4×Dic43—28no—
185C4×Dic43—28no—
186C2×C43⋊C8—22no—
187C2×C43⋊C8—22no—
188C2×C43⋊C8C22×C414yes—
189#10621872—216no—
190C23×C43—21no—
191C23×C43—21no—
192C23×C43—21no—
193C23×C43—21no—
194C23×C43C2×C4⋊C412yes—
195C23×C43AGL(1,ℤ/8)12yes—
196C23×C43#13712yes—
197C23×C43C22×D411yescharacteristic
198C22×D43—21no—
199C22×D43—21no—
200C22×D43—21no—
201C22×D43—21no—
202C22×D43—21no—
203C22×D43—21no—
204C22×D43—21no—
205C22×D43—21no—
206C22×D43—21no—
207C22×D43—21no—
208C22×D43—28no—
209C22×D43—28no—
210C22×D43—44no—
211C22×D43—44no—
212C22×D43—44no—
213C22×D43—44no—
214C22×D43—44no—
215C22×D43C2×C4⋊C412yes—
216C22×D43C2×C4⋊C412yes—
217C22×D43#12012yes—
218C22×D43#12312yes—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—24no—
222C2×C4×C43—24no—
223C2×C4×C43—24no—
224C2×C4×C43—48no—
225C2×C4×C43—42no—
226C2×C4×C43—42no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43C2×C4⋊C412yes—
234C2×C4×C43C23×C411yescharacteristic
235C2×C4×C43C22×D412yes—
236C2×C4×C43C22×Q811yescharacteristic
237C2×C4×C43C2×#4112yes—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—28no—
241C2×Dic43—24no—
242C2×Dic43—48no—
243C2×Dic43—42no—
244C2×Dic43—42no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43C2×C4⋊C412yes—
252C2×Dic43C2×C4⋊C412yes—
253C2×Dic43#12012yes—
254C2×Dic43#12312yes—
255C4×D43—28no—
256C4×D43—24no—
257C4×D43—24no—
258C4×D43—28no—
259C4×D43—84no—
260C4×D43—84no—
261C4×D43C4×D418yes—
262C4×D43C22⋊Q818yes—
263C8×C43—24no—
264C43⋊C8—24no—
265#20846—431nomaximal, Sylow
266C22×C43—22no—
267C22×C43—22no—
268C22×C43—22no—
269C22×C43—22no—
270C22×C43—22no—
271C22×C43—22no—
272C22×C43#42814yescomplemented
273C22×C43C22×C4⋊C411yescharacteristic
274C22×C43C2×#12011yescharacteristic
275C22×C43C2×#12311yescharacteristic
276C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
277C22×C43C2×#13711yescharacteristic
278C22×C43#57511yescharacteristic
279C22×C43#57511yescharacteristic
280C2×D43—22no—
281C2×D43—22no—
282C2×D43—22no—
283C2×D43—22no—
284C2×D43—22no—
285C2×D43—22no—
286C2×D43—22no—
287C2×D43—22no—
288C2×D43—22no—
289C2×D43—416no—
290C2×D43—41no—
291C2×D43—41no—
292C2×D43—41no—
293C2×D43—41no—
294C2×D43#38514yes—
295C4×C43—22no—
296C4×C43—44no—
297C4×C43—81no—
298C4×C43—81no—
299C4×C43C2×C4×D412yes—
300C4×C43C2×C22⋊Q812yes—
301Dic43—22no—
302Dic43—44no—
303Dic43—81no—
304Dic43—81no—
305Dic43#38514yes—
306C22×#117—431no—
307C2×#428—432no—
308C2×#407—431no—
309C2×#380—431no—
310#1854—432no—
311#1854—432no—
312#1853—431no—
313#1853—431no—
314#1852—431no—
315#1852D4311yescharacteristic, complemented
316#1736—432no—
317C2×C43—24no—
318C2×C43C2×#38511yescharacteristic
319C2×C43C2×#42811yescharacteristic
320C2×C43#291111yescharacteristic
321C2×C43#300611yescharacteristic
322C2×C43#300711yescharacteristic
323C2×C43#309411yescharacteristic
324C2×C43#309511yescharacteristic
325D43—24no—
326D43—42no—
327C24×C4—431no—
328C22×M16—432no—
329C2×#117—432no—
330C2×#117—432no—
331C2×#117—868no—
332C2×#117—861no—
333C2×#117—861no—
334C22×C4⋊C4—431no—
335C22×C4⋊C4—431no—
336C22×C4⋊C4—431no—
337C22×C4⋊C4C2×D4311yescharacteristic
338C22×C22⋊C4—861no—
339C22×C22⋊C4—861no—
340C22×C42—861no—
341#428—868no—
342C2×#107—432no—
343C2×#107C2×D4312yescomplemented
344C2×#106—432no—
345C2×#106—432no—
346#407—438no—
347C2×C22⋊C8—431no—
348C2×C22⋊C8—432no—
349C2×C22⋊C8C2×D4311yescharacteristic
350#380—431no—
351#380—431no—
352#380—431no—
353#380—861no—
354#380—861no—
355#380C2×D4311yescharacteristic
356C2×#95—861no—
357#340—432no—
358#340—432no—
359#340—432no—
360#340C2×D4312yescomplemented
361C43#2084611yescharacteristic, complemented, Sylow
362C25—431no—
363C23×C4—21no—
364C23×C4—431no—
365C23×C4—431no—
366C23×C4—434no—
367C23×C4—431no—
368C23×C4—431no—
369C23×C4—434no—
370C23×C4—431no—
371C23×C4—864no—
372C23×C4—864no—
373C23×C4—861no—
374C23×C4—861no—
375C23×C4—861no—
376C23×C4C22×D4311yescharacteristic
377C2×M16—438no—
378C2×M16—864no—
379C2×M16—864no—
380C22×C8—432no—
381C22×C8C22×D4312yes—
382#117—438no—
383#117—864no—
384#117—864no—
385#117—868no—
386#117—868no—
387#117—864no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—432no—
391C2×C4⋊C4—431no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—864no—
394C2×C4⋊C4—864no—
395C2×C4⋊C4—864no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4C22×D4311yescharacteristic
400C2×C4⋊C4C22×D4311yescharacteristic
401C2×C4⋊C4C22×D4312yes—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—862no—
404C2×C22⋊C4—862no—
405C2×C22⋊C4—868no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4—861no—
409C2×C22⋊C4—1724no—
410C2×C42—862no—
411C2×C42—862no—
412C2×C42—868no—
413#107—24no—
414#107—864no—
415#106—864no—
416#106—864no—
417C22⋊C8—434no—
418C22⋊C8—438no—
419C22⋊C8C4×D4314yescomplemented
420#95—21no—
421#95—861no—
422#95—861no—
423#95—861no—
424C24—431no—
425C24—431no—
426C24—434no—
427C24—862no—
428C24—862no—
429C24—862no—
430C24—862no—
431C24—1721no—
432C24—1721no—
433C24D4×D4311yescharacteristic
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—431no—
443C22×C4—432no—
444C22×C4—434no—
445C22×C4—432no—
446C22×C4—434no—
447C22×C4—434no—
448C22×C4—431no—
449C22×C4—434no—
450C22×C4—434no—
451C22×C4—432no—
452C22×C4—432no—
453C22×C4—862no—
454C22×C4—862no—
455C22×C4—8616no—
456C22×C4—8616no—
457C22×C4—862no—
458C22×C4—862no—
459C22×C4—862no—
460C22×C4—862no—
461C22×C4—862no—
462C22×C4—862no—
463C22×C4—864no—
464C22×C4—862no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—1722no—
468C22×C4—1722no—
469C22×C4—1722no—
470C22×C4—1722no—
471C22×C4—1722no—
472C22×C4—1722no—
473C22×C4—1722no—
474C22×C4—1722no—
475C22×C4C2×C4×D4312yes—
476C22×C4D4×D4311yescharacteristic
477C22×C4Q8×D4312yes—
478C22×C4C23×D4311yescharacteristic
479M16—8616no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—434no—
483C2×C8—862no—
484C2×C8—862no—
485C2×C8C2×C4×D4314yes—
486C4⋊C4—24no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—434no—
491C4⋊C4—864no—
492C4⋊C4—862no—
493C4⋊C4—862no—
494C4⋊C4—862no—
495C4⋊C4—1722no—
496C4⋊C4—1722no—
497C4⋊C4D4×D4314yes—
498C22⋊C4—42no—
499C22⋊C4—868no—
500C22⋊C4—868no—
501C22⋊C4—1722no—
502C22⋊C4—1722no—
503C22⋊C4—1722no—
504C42—868no—
505C42—868no—
506C23—21no—
507C23—21no—
508C23—21no—
509C23—21no—
510C23—432no—
511C23—432no—
512C23—432no—
513C23—432no—
514C23—868no—
515C23—861no—
516C23—861no—
517C23—861no—
518C23—861no—
519C23—861no—
520C23—861no—
521C23—861no—
522C23—861no—
523C23—861no—
524C23—861no—
525C23—868no—
526C23—1724no—
527C23—1724no—
528C23—1724no—
529C23—1724no—
530C23—1724no—
531C23C4⋊C4×D4312yes—
532C23#1306334912yes—
533C23#1306335712yes—
534C23C2×D4×D4311yescharacteristic
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—48no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—432no—
550C2×C4—432no—
551C2×C4—432no—
552C2×C4—438no—
553C2×C4—438no—
554C2×C4—432no—
555C2×C4—868no—
556C2×C4—868no—
557C2×C4—868no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—864no—
561C2×C4—864no—
562C2×C4—864no—
563C2×C4—3444no—
564C2×C4—3444no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1728no—
572C2×C4—1722no—
573C2×C4—1722no—
574C2×C4C4⋊C4×D4312yes—
575C2×C4C22×C4×D4311yescharacteristic
576C2×C4C2×D4×D4312yes—
577C2×C4C2×Q8×D4311yescharacteristic
578C2×C4#41×D4312yes—
579C8—24no—
580C8—864no—
581C22—22no—
582C22—22no—
583C22—22no—
584C22—22no—
585C22—22no—
586C22—22no—
587C22—434no—
588C22—862no—
589C22—862no—
590C22—862no—
591C22—862no—
592C22—862no—
593C22—862no—
594C22—862no—
595C22—862no—
596C22—862no—
597C22—17216no—
598C22—1721no—
599C22—1721no—
600C22—1721no—
601C22—1721no—
602C22#1458294014yescomplemented
603C22C2×C4⋊C4×D4311yescharacteristic
604C22#120×D4311yescharacteristic
605C22#123×D4311yescharacteristic
606C22C2×#1306334911yescharacteristic
607C22C2×#1306335711yescharacteristic
608C22#1458369511yescharacteristic
609C22#1458369811yescharacteristic
610C4—22no—
611C4—44no—
612C4—81no—
613C4—81no—
614C4—434no—
615C4—862no—
616C4—3441no—
617C4—3441no—
618C4—1724no—
619C4C4×D4×D4312yes—
620C4C22⋊Q8×D4312yes—
621C2—24no—
622C2—864no—
623C2—1722no—
624C2#385×D4311yescharacteristic
625C2C2×#1458294011yescharacteristic
626C2#1914318211yescharacteristic
627C2#1914384211yescharacteristic
628C2#1914385411yescharacteristic
629C2#1914453011yescharacteristic
630C2#1914454011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1852C2
socleC23×C43C22×D4
prime radicalC24×D43D4
cosocleC22×C4×C43C24
hypercenter#1852D43
hypocenterC43#20846
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1852

Complements

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

NH ≅ G/Ntype
2. C2×#14582940C2semidirect
5. #19134795C2semidirect
6. #19134791C2semidirect
7. #19134790C2semidirect
8. #19134787C2semidirect
9. #19134783C2semidirect
10. #19134313C2semidirect
11. C43×#1852C2semidirect
26. C2×#13063258C22semidirect
27. C2×#13063257C22semidirect
28. C2×#13063256C22semidirect
29. #14582861C4semidirect
38. #14582662C22semidirect
39. #14582661C22semidirect
40. #14582661C22semidirect
42. C2×#107×C43C22semidirect
45. C43×#340C22semidirect
61. C2×#10621872C2×C4semidirect
91. C22⋊(C43⋊C8)C2×C4semidirect
92. (C2×D43)⋊C8C2×C4semidirect
106. C22⋊C8×C43C2×C4semidirect
272. C22×C43#428semidirect
315. #1852D43semidirect
343. C2×#107C2×D43semidirect
360. #340C2×D43semidirect
361. C43#20846semidirect
419. C22⋊C8C4×D43semidirect
602. C22#14582940semidirect

Maximal subgroups

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

subgroupindex
C22×#130632832
C2×#145829402
C2×#145828612
#380×D432
#191347952
#191347912
#191347902
#191347872
#191347832
#191343132
C43×#18522
#2084643