Finite Group Databasebeta

← #25097870

Subgroups — #25097870

Order 11008.

1842 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583480C211yesmaximal, characteristic
2C2×#14583380C211yesmaximal, characteristic, complemented
3C2×#14582898C211yesmaximal, characteristic, complemented
4C2×#14582896C211yesmaximal, characteristic, complemented
5C2×#14582865C211yesmaximal, characteristic, complemented
6#19134916C212yesmaximal, complemented
7#19134911C212yesmaximal, complemented
8#19134906C212yesmaximal, complemented
9#19134901C212yesmaximal, complemented
10#19134314C211yesmaximal, characteristic, complemented
11C2×C43×#340C211yesmaximal, characteristic, complemented
12C22×#10621898C2211yescharacteristic
13C22×#10621898C2211yescharacteristic
14C22×#10621877C2211yescharacteristic
15#14583480—24no—
16#14583480C418yescomplemented
17C2×#13063305—21no—
18C2×#13063305C2212yes—
19C2×#13063300—21no—
20C2×#13063300C2212yes—
21C2×#13063299—22no—
22#14583380—24no—
23#14583380—24no—
24C2×#13063290—21no—
25C2×#13063287—21no—
26C2×C4×C22⋊D43—22no—
27C2×#13063284C2211yescharacteristic
28C2×#13063283C2212yes—
29C2×C4⋊C4×D43C2212yes—
30#14582898—24no—
31#14582896—24no—
32C2×#13063250C2211yescharacteristic
33C2×#13063250C2211yescharacteristic
34C2×#13063248C2212yes—
35C2×#13063247C2211yescharacteristic
36C2×#13063247C2211yescharacteristic
37C2×#13063245C2212yes—
38#14582865—24no—
39C2×(C2×D43)⋊C8C2212yes—
40C2×(C2×D43)⋊C8C2212yes—
41#14582661C2212yes—
42#14582661C2212yes—
43C23×C8×C43C2211yescharacteristic
44C22×C4⋊C4×C43C2211yescharacteristic
45C22×C4⋊C4×C43C2211yescharacteristic
46C43×#340C2212yes—
47C43×#340C2212yes—
48C2×#10621898—22no—
49C2×#10621898—22no—
50C2×#10621898—22no—
51C2×#10621898—22no—
52C2×#10621898—22no—
53C2×#10621898—22no—
54C2×#10621898—22no—
55C2×#10621898—22no—
56C2×#10621898—22no—
57C2×#10621898C2×C414yes—
58C2×#10621898C2×C414yescomplemented
59C2×#10621898D414yes—
60C22×Dic86D411yescharacteristic
61C22×Dic86C2311yescharacteristic
62C22×D172—22no—
63C22×D172D411yescharacteristic
64C22×D172C2311yescharacteristic
65C22×C22⋊D43—21no—
66C22×C22⋊D43D412yes—
67C22×C4×D43—21no—
68C22×C4×D43—22no—
69C22×C4×D43C2312yes—
70C2×#10621877—22no—
71C2×#10621877—22no—
72C2×#10621877—22no—
73C22×C43⋊C8C2312yes—
74#13063305—24no—
75#13063305—28no—
76#13063305C2×C418yescomplemented
77#13063300—28no—
78#13063300—24no—
79#13063300C2×C418yescomplemented
80#13063299—216no—
81#13063290—28no—
82#13063287—28no—
83C4×C22⋊D43—216no—
84#13063284—22no—
85#13063284D414yescomplemented
86#13063283—24no—
87#13063283—24no—
88C2×C4⋊Dic43—22no—
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×Dic43⋊C4—22no—
92C4⋊C4×D43—24no—
93C4⋊C4×D43—24no—
94C2×C22⋊Dic43—21no—
95C2×(C2×D43)⋊C4—22no—
96C2×(C2×D43)⋊C4—22no—
97C2×(C2×D43)⋊C4—22no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43—22no—
100#13063250—22no—
101#13063250—22no—
102#13063248—24no—
103#13063247—22no—
104#13063247—22no—
105#13063245—24no—
106(C2×D43)⋊C8—24no—
107(C2×D43)⋊C8—24no—
108C23×C4×C43—21no—
109C23×C4×C43—21no—
110C23×C4×C43C2311yescharacteristic
111C22×C8×C43—22no—
112C22×C8×C43—22no—
113C22×C8×C43—22no—
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43—22no—
118C2×C4⋊C4×C43—21no—
119C2×C4⋊C4×C43—22no—
120C2×C4⋊C4×C43C2×C414yescomplemented
121C2×C4⋊C4×C43D414yescomplemented
122C2×C4⋊C4×C43C2312yes—
123C2×C4⋊C4×C43C2312yes—
124C24×C43C2×D411yescharacteristic
125C23×D43—21no—
126C23×D43C2×D412yes—
127C22×C4×C43—24no—
128C22×C4×C43—24no—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43—81no—
132C22×C4×C43—81no—
133C22×C4×C43—81no—
134C22×C4×C43—81no—
135C22×C4×C43C22×C412yes—
136C22×C4×C43C2×D412yes—
137C22×C4×C43C2×D412yes—
138C22×C4×C43C2×D412yes—
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43#4112yes—
141C22×C4×C43#4112yes—
142C22×C4×C43C2411yescharacteristic
143C2×C22⋊D43—24no—
144C2×C22⋊D43—24no—
145C2×C22⋊D43—24no—
146C2×C22⋊D43—42no—
147C2×C22⋊D43—42no—
148C2×C22⋊D43C22⋊C418yes—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43C2×D412yes—
153#10621898—28no—
154#10621898—28no—
155#10621898—28no—
156#10621898—28no—
157#10621898—28no—
158#10621898—28no—
159#10621898—44no—
160#10621898—44no—
161C2×D172—22no—
162C2×D172—22no—
163C2×D172—21no—
164C2×D172—28no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172—82no—
170C2×D172—82no—
171C2×D172C22⋊C414yes—
172C2×D172C22×C412yes—
173C2×C4×D43—22no—
174C2×C4×D43—22no—
175C2×C4×D43—22no—
176C2×C4×D43—22no—
177C2×C4×D43—24no—
178C2×C4×D43—28no—
179C2×C4×D43—42no—
180C2×C4×D43—42no—
181C2×C4×D43—82no—
182C2×C4×D43—82no—
183C2×C4×D43C22×C414yes—
184C2×C4×D43C2×D414yes—
185C2×Dic86—22no—
186C2×Dic86—22no—
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86—21no—
190C2×Dic86—21no—
191C2×Dic86—21no—
192C2×Dic86C22⋊C414yes—
193C2×Dic86C22×C412yes—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—44no—
201C4⋊C4×C43—24no—
202C4⋊C4×C43—24no—
203C4⋊C4×C43—22no—
204C4⋊C4×C43—22no—
205C4⋊C4×C43C22×C414yes—
206C4⋊C4×C43C2×D414yes—
207C22⋊Dic43—24no—
208(C2×D43)⋊C4—28no—
209(C2×D43)⋊C4—28no—
210(C2×D43)⋊C4—28no—
211C4⋊Dic43—21no—
212C4⋊Dic43—21no—
213C4⋊Dic43—28no—
214C4⋊Dic43C2×D412yes—
215C4⋊Dic43C2×D412yes—
216Dic43⋊C4—28no—
217C4×Dic43—28no—
218C4×Dic43—24no—
219#10621877—44no—
220C2×C43⋊C8—22no—
221C2×C43⋊C8—22no—
222C2×C43⋊C8—22no—
223C23×C43—21no—
224C23×C43—21no—
225C23×C43—21no—
226C23×C43—21no—
227C23×C43C2×C22⋊C412yes—
228C23×C43#12012yes—
229C23×C43#12312yes—
230C23×C43C22×D411yescharacteristic
231C22×D43—22no—
232C22×D43—22no—
233C22×D43—22no—
234C22×D43—22no—
235C22×D43—22no—
236C22×D43—22no—
237C22×D43—22no—
238C22×D43—41no—
239C22×D43—41no—
240C22×D43—41no—
241C22×D43—41no—
242C22×D43—41no—
243C22×D43—41no—
244C22×D43C2×C22⋊C414yes—
245C2×C4×C43—24no—
246C2×C4×C43—24no—
247C2×C4×C43—42no—
248C2×C4×C43—42no—
249C2×C4×C43—42no—
250C2×C4×C43—42no—
251C2×C4×C43—84no—
252C2×C4×C43—84no—
253C2×C4×C43C2×C22⋊C412yes—
254C2×C4×C43C4×D414yes—
255C2×C4×C43C4×D414yes—
256C2×C4×C43#12012yes—
257C2×C4×C43#12114yes—
258C2×C4×C43#12114yes—
259C2×C4×C43#12312yes—
260C2×C4×C43C23×C411yescharacteristic
261C2×C4×C43C22×D411yescharacteristic
262C2×C4×C43C22×D411yescharacteristic
263C2×C4×C43C22×D411yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C22⋊D43—216no—
267C22⋊D43—48no—
268C2×Dic43—22no—
269C2×Dic43—22no—
270C2×Dic43—22no—
271C2×Dic43—22no—
272C2×Dic43—22no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43C2×C22⋊C414yes—
280D172—22no—
281D172—22no—
282D172—28no—
283D172—41no—
284D172—41no—
285D172—88no—
286C4×D43—24no—
287C4×D43—24no—
288C4×D43—24no—
289C4×D43—24no—
290C4×D43—48no—
291C4×D43—88no—
292Dic86—28no—
293Dic86—22no—
294Dic86—22no—
295Dic86—41no—
296Dic86—41no—
297C8×C43—41no—
298C8×C43—41no—
299C43⋊C8—42no—
300#20915—431nomaximal, Sylow
301C22×C43—22no—
302C22×C43—22no—
303C22×C43—22no—
304C22×C43—22no—
305C22×C43—22no—
306C22×C43—22no—
307C22×C43#38614yes—
308C22×C43C22×C22⋊C411yescharacteristic
309C22×C43C2×#12011yescharacteristic
310C22×C43C2×#12311yescharacteristic
311C22×C43#57611yescharacteristic
312C22×C43#57711yescharacteristic
313C22×C43#57711yescharacteristic
314C22×C43#57811yescharacteristic
315C2×D43—24no—
316C2×D43—24no—
317C2×D43—24no—
318C2×D43—42no—
319C2×D43—42no—
320C2×D43—42no—
321C2×D43—42no—
322C2×D43—42no—
323C2×D43—42no—
324C2×D43—42no—
325C2×D43—81no—
326C2×D43—81no—
327C2×D43—81no—
328C2×D43—81no—
329C4×C43—44no—
330C4×C43—44no—
331C4×C43#38614yes—
332C4×C43C2×C4×D411yescharacteristic
333C4×C43C2×C4×D411yescharacteristic
334C4×C43C2×#12111yescharacteristic
335C4×C43C2×#12111yescharacteristic
336Dic43—24no—
337Dic43—42no—
338Dic43—42no—
339Dic43—42no—
340C2×#537—431no—
341C2×#520—431no—
342C2×#417—431no—
343C2×#416—431no—
344C2×#408—431no—
345#1875—432no—
346#1874—432no—
347#1873—432no—
348#1872—432no—
349#1736—431no—
350C2×#340D4311yescharacteristic, complemented
351C2×C43—24no—
352C2×C43C2×#38611yescharacteristic
353C2×C43#289711yescharacteristic
354C2×C43#289811yescharacteristic
355C2×C43#301211yescharacteristic
356C2×C43#301311yescharacteristic
357C2×C43#309811yescharacteristic
358C2×C43#309911yescharacteristic
359D43—44no—
360D43—82no—
361C22×#41—431no—
362C22×#41—431no—
363C22×M16—431no—
364C23×C8C2×D4311yescharacteristic
365#537—438no—
366#537—864no—
367C2×C22⋊Q8—432no—
368C2×C22⋊Q8—861no—
369C2×#121—432no—
370C2×#121—861no—
371C2×#121—862no—
372#520—864no—
373#520—864no—
374C2×C4×Q8—861no—
375C2×C4×D4—861no—
376C2×C4×D4—862no—
377C2×#117—431no—
378C2×#117—432no—
379C22×C4⋊C4—432no—
380C22×C4⋊C4C2×D4311yescharacteristic
381C22×C4⋊C4C2×D4311yescharacteristic
382#417—864no—
383#416—864no—
384C2×#103—431no—
385C2×#103—431no—
386C2×#103—432no—
387C2×#102—431no—
388C2×#102—431no—
389C2×#102—432no—
390#408—864no—
391C2×C22⋊C8—432no—
392C2×C22⋊C8—432no—
393#340—432no—
394#340—432no—
395#340C2×D4312yes—
396#340C2×D4312yes—
397C43#2091511yescharacteristic, complemented, Sylow
398C2×#41—434no—
399C2×#41—434no—
400C2×#41—434no—
401C2×#41—862no—
402C2×#41—862no—
403C2×#41—862no—
404C2×#41—862no—
405C2×#41—862no—
406C2×#41—862no—
407C2×#41—862no—
408C2×#41—862no—
409C2×#41—862no—
410C22×Q8—431no—
411C22×Q8—431no—
412C22×D4—432no—
413C22×D4—431no—
414C22×D4—431no—
415C22×D4—862no—
416C22×D4—861no—
417C23×C4—21no—
418C23×C4—21no—
419C23×C4—432no—
420C23×C4—862no—
421C23×C4—861no—
422C23×C4C22×D4311yescharacteristic
423C2×M16—862no—
424C2×M16—862no—
425C2×M16—862no—
426C22×C8—22no—
427C22×C8—22no—
428C22×C8—22no—
429C22×C8—432no—
430C22×C8C22×D4311yescharacteristic
431C22×C8C22×D4311yescharacteristic
432C22⋊Q8—438no—
433C22⋊Q8—864no—
434C22⋊Q8—868no—
435#121—438no—
436#121—864no—
437#121—868no—
438#121—8616no—
439C4×Q8—868no—
440C4×D4—868no—
441C4×D4—8616no—
442#117—434no—
443#117—864no—
444#117—862no—
445#117—864no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—431no—
451C2×C4⋊C4—431no—
452C2×C4⋊C4—864no—
453C2×C4⋊C4—862no—
454C2×C4⋊C4—862no—
455C2×C4⋊C4—864no—
456C2×C4⋊C4C4×D4314yescomplemented
457C2×C4⋊C4D17214yescomplemented
458C2×C4⋊C4C22×D4312yes—
459C2×C4⋊C4C22×D4312yes—
460C2×C22⋊C4—862no—
461C2×C22⋊C4—862no—
462C2×C22⋊C4—862no—
463C2×C22⋊C4—861no—
464C2×C42—862no—
465C2×C42—861no—
466#103—862no—
467#103—862no—
468#103—864no—
469#102—862no—
470#102—862no—
471#102—864no—
472C22⋊C8—864no—
473C22⋊C8—864no—
474C24—432no—
475C24—861no—
476C24D4×D4311yescharacteristic
477#41—868no—
478#41—868no—
479#41—868no—
480#41—868no—
481#41—868no—
482#41—868no—
483#41—1724no—
484#41—1724no—
485C2×Q8—434no—
486C2×Q8—432no—
487C2×Q8—862no—
488C2×Q8—862no—
489C2×Q8—861no—
490C2×Q8—861no—
491C2×Q8—861no—
492C2×Q8—861no—
493C2×Q8—861no—
494C2×D4—438no—
495C2×D4—434no—
496C2×D4—432no—
497C2×D4—868no—
498C2×D4—864no—
499C2×D4—864no—
500C2×D4—864no—
501C2×D4—862no—
502C2×D4—862no—
503C2×D4—861no—
504C2×D4—861no—
505C2×D4—861no—
506C2×D4—861no—
507C2×D4—861no—
508C2×D4—3442no—
509C2×D4—3442no—
510C2×D4—1722no—
511C2×D4—1722no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—81no—
517C22×C4—81no—
518C22×C4—81no—
519C22×C4—81no—
520C22×C4—432no—
521C22×C4—434no—
522C22×C4—434no—
523C22×C4—868no—
524C22×C4—862no—
525C22×C4—862no—
526C22×C4—862no—
527C22×C4—862no—
528C22×C4—861no—
529C22×C4—861no—
530C22×C4—861no—
531C22×C4—864no—
532C22×C4—3442no—
533C22×C4—3442no—
534C22×C4—1722no—
535C22×C4—1722no—
536C22×C4C2×C4×D4312yes—
537C22×C4C2×D17212yes—
538C22×C4#1062189812yes—
539C22×C4D4×D4311yescharacteristic
540C22×C4D4×D4312yes—
541C22×C4D4×D4312yes—
542C22×C4#1062190212yes—
543C22×C4C23×D4311yescharacteristic
544M16—1724no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—44no—
552C2×C8—862no—
553C2×C8—862no—
554C2×C8—862no—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—22no—
558C4⋊C4—22no—
559C4⋊C4—432no—
560C4⋊C4—432no—
561C4⋊C4—868no—
562C4⋊C4—868no—
563C4⋊C4—861no—
564C4⋊C4—861no—
565C4⋊C4C2×C4×D4314yes—
566C4⋊C4C2×D17214yes—
567C22⋊C4—868no—
568C22⋊C4—868no—
569C22⋊C4—868no—
570C22⋊C4—864no—
571C42—868no—
572C42—864no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—434no—
578C23—862no—
579C23—862no—
580C23—862no—
581C23—862no—
582C23—862no—
583C23—862no—
584C23—862no—
585C23—1721no—
586C23—1721no—
587C23—1721no—
588C23—1721no—
589C23—1721no—
590C23—1721no—
591C23C22⋊C4×D4312yes—
592C23#1306329512yes—
593C23#1306331012yes—
594C23C2×D4×D4311yescharacteristic
595Q8—868no—
596Q8—862no—
597Q8—862no—
598Q8—1721no—
599Q8—1721no—
600D4—8616no—
601D4—862no—
602D4—862no—
603D4—868no—
604D4—3448no—
605D4—1728no—
606D4—1721no—
607D4—1721no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—84no—
615C2×C4—84no—
616C2×C4—434no—
617C2×C4—862no—
618C2×C4—862no—
619C2×C4—864no—
620C2×C4—864no—
621C2×C4—864no—
622C2×C4—864no—
623C2×C4—862no—
624C2×C4—862no—
625C2×C4—862no—
626C2×C4—3448no—
627C2×C4—1721no—
628C2×C4—1721no—
629C2×C4—1721no—
630C2×C4—1721no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4—1728no—
634C2×C4C22⋊C4×D4312yes—
635C2×C4#1306328714yes—
636C2×C4C4×D17214yes—
637C2×C4#1306329512yes—
638C2×C4#1306329814yes—
639C2×C4#1306330014yes—
640C2×C4#1306331012yes—
641C2×C4C22×C4×D4311yescharacteristic
642C2×C4C2×D4×D4311yescharacteristic
643C2×C4C2×D4×D4311yescharacteristic
644C2×C4C22×D17211yescharacteristic
645C2×C4C2×#1062189811yescharacteristic
646C2×C4C2×#1062190211yescharacteristic
647C8—41no—
648C8—41no—
649C8—1722no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—22no—
656C22—864no—
657C22—864no—
658C22—864no—
659C22—3441no—
660C22—3441no—
661C22—3441no—
662C22—3441no—
663C22—1722no—
664C22—1722no—
665C22—1722no—
666C22—1722no—
667C22—1722no—
668C22—1722no—
669C22—1722no—
670C22#1458277714yes—
671C22C2×C22⋊C4×D4311yescharacteristic
672C22C2×#1306329511yescharacteristic
673C22C2×#1306331011yescharacteristic
674C22#1458370011yescharacteristic
675C22#1458370511yescharacteristic
676C22#1458370511yescharacteristic
677C22#1458371211yescharacteristic
678C4—44no—
679C4—44no—
680C4—864no—
681C4—1722no—
682C4—1722no—
683C4—1722no—
684C4#1458277714yes—
685C4C2×#1306328711yescharacteristic
686C4C2×C4×D17211yescharacteristic
687C4C2×#1306329811yescharacteristic
688C4C2×#1306330011yescharacteristic
689C2—24no—
690C2—3442no—
691C2—1724no—
692C2C2×#1458277711yescharacteristic
693C2#1914311611yescharacteristic
694C2#1914312311yescharacteristic
695C2#1914390411yescharacteristic
696C2#1914391511yescharacteristic
697C2#1914457811yescharacteristic
698C2#1914458911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#340C2
socleC23×C43C22×D4
prime radicalC2×#14583480C2
cosocleC22×C4×C43C24
hypercenterC2×#340D43
hypocenterC43#20915
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
2. C2×#14583380C2semidirect
3. C2×#14582898C2semidirect
4. C2×#14582896C2semidirect
5. C2×#14582865C2semidirect
6. #19134916C2semidirect
7. #19134911C2semidirect
8. #19134906C2semidirect
9. #19134901C2semidirect
10. #19134314C2semidirect
11. C2×C43×#340C2semidirect
16. #14583480C4semidirect
58. C2×#10621898C2×C4semidirect
76. #13063305C2×C4semidirect
79. #13063300C2×C4semidirect
85. #13063284D4semidirect
120. C2×C4⋊C4×C43C2×C4semidirect
121. C2×C4⋊C4×C43D4semidirect
350. C2×#340D43semidirect
397. C43#20915semidirect
456. C2×C4⋊C4C4×D43semidirect
457. C2×C4⋊C4D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145834802
C2×#145833802
C2×#145828982
C2×#145828962
C2×#145828652
#191349162
#191349112
#191349062
#191349012
#191343142
C2×C43×#3402
#2091543