Finite Group Databasebeta

← #25126472

Subgroups — #25126472

Order 11008.

1098 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582938C211yesmaximal, characteristic, complemented
2C2×#106×D43C211yesmaximal, characteristic, complemented
3C2×#14582897C211yesmaximal, characteristic
4C2×#14582892C211yesmaximal, characteristic
5#19137216C211yesmaximal, characteristic, complemented
6#19137185C211yesmaximal, characteristic
7#19136144C211yesmaximal, characteristic, complemented
8#19136142C211yesmaximal, characteristic, complemented
9#19136139C211yesmaximal, characteristic, complemented
10#19136135C211yesmaximal, characteristic, complemented
11#19136126C211yesmaximal, characteristic, complemented
12#19136116C211yesmaximal, characteristic, complemented
13#19136114C211yesmaximal, characteristic, complemented
14#19134290C211yesmaximal, characteristic, complemented
15C43×#2094C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19C2×#13063283C2211yescharacteristic
20C2×#13063282C2211yescharacteristic
21C2×C4⋊C4×D43C2211yescharacteristic
22C2×C4⋊C4×D43C2211yescharacteristic
23#14582938—24no—
24C2×#13063259C2211yescharacteristic
25C2×#13063258C2211yescharacteristic
26C2×#13063257C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×#13063256C2211yescharacteristic
29C2×#13063256C2211yescharacteristic
30#106×D43—24no—
31#14582897—24no—
32#14582892—24no—
33C2×#13063250C2211yescharacteristic
34C2×#13063250C2211yescharacteristic
35C2×#13063248C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39#14582805C2211yescharacteristic
40#14582804C2211yescharacteristic
41#14582802C2211yescharacteristic
42#14582794—22no—
43#14582775—22no—
44#14582770—22no—
45#14582768C2211yescharacteristic
46#14582765C2211yescharacteristic
47#14582764C2211yescharacteristic
48#14582757—22no—
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#106×C43C2211yescharacteristic
53C2×#106×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C43×#384C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C2×#10621900—22no—
60C2×#10621900—22no—
61C2×#10621900—22no—
62C2×#10621900—22no—
63C2×#10621900—22no—
64C2×#10621900Q814yes—
65C22×Dic86C2311yescharacteristic
66C22×C22⋊D43—21no—
67C23×Dic43—21no—
68C22×C4×D43—21no—
69C22×C4×D43—21no—
70C22×C4×D43C2311yescharacteristic
71C2×#10621872—22no—
72C2×#10621872—22no—
73C2×#10621872D414yes—
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76C2×C8×D43—22no—
77C2×C8×D43—22no—
78C2×C8×D43D414yes—
79#13063283—22no—
80#13063283—22no—
81#13063282—22no—
82#13063282—22no—
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—22no—
89C2×Dic43⋊C4D412yes—
90C4⋊C4×D43—22no—
91C4⋊C4×D43—22no—
92C4⋊C4×D43—22no—
93C4⋊C4×D43—22no—
94C2×C22⋊Dic43—22no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4D412yes—
97C2×C4×Dic43—21no—
98C2×C4×Dic43C2311yescharacteristic
99#13063259—22no—
100#13063258—22no—
101#13063257—22no—
102#13063256—22no—
103#13063256—22no—
104#13063256—22no—
105#13063250—22no—
106#13063250—22no—
107#13063248—22no—
108#13063248—22no—
109#13063246—22no—
110#13063246—22no—
111C43⋊#95—22no—
112C43⋊#95—22no—
113C43⋊#95—22no—
114C43⋊#95—22no—
115C22×D4×C43C2311yescharacteristic
116C22×C8×C43C2311yescharacteristic
117C22×C8×C43C2311yescharacteristic
118C2×C4⋊C4×C43—22no—
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C22⋊C4×C43—22no—
123C2×C42×C43C2311yescharacteristic
124#106×C43—22no—
125#106×C43—22no—
126#102×C43—22no—
127#102×C43—22no—
128C24×C43—21no—
129C23×D43C2×D411yescharacteristic
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43C2×Q812yes—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43C2×D412yes—
140C22×C4×C43C2411yescharacteristic
141C2×C22⋊D43—24no—
142C2×C22⋊D43—42no—
143C2×C22⋊D43—42no—
144C22×Dic43—24no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—42no—
150C22×Dic43—42no—
151C22×Dic43C2×D412yes—
152C22×Dic43C2×D411yescharacteristic
153#10621900—28no—
154#10621900—28no—
155#10621900—44no—
156#10621900—44no—
157C2×C4×D43—42no—
158C2×C4×D43—42no—
159C2×C4×D43—82no—
160C2×C4×D43—82no—
161C2×C4×D43C2×D412yes—
162C2×C4×D43C2×D412yes—
163C2×C4×D43C2×Q812yes—
164C2×C4×D43#4112yes—
165C2×C4×D43#4112yes—
166C2×C4×D43#4112yes—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86C2×Q812yes—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43C2×D412yes—
178C2×C8×C43C2×D412yes—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—82no—
186C22⋊C4×C43—82no—
187C42×C43—21no—
188C42×C43—21no—
189C22⋊Dic43—82no—
190(C2×D43)⋊C4—24no—
191(C2×D43)⋊C4—42no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198Dic43⋊C4—24no—
199Dic43⋊C4—42no—
200Dic43⋊C4—42no—
201Dic43⋊C4—82no—
202C4×Dic43—21no—
203C4×Dic43—21no—
204C4×Dic43—42no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8C2×D412yes—
210C2×C43⋊C8C2×D412yes—
211#10621872—28no—
212C8×D43—28no—
213C23×C43—22no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—42no—
217C23×C43—42no—
218C23×C43C22×D411yescharacteristic
219C22×D43—22no—
220C22×D43—22no—
221C22×D43C22⋊Q812yes—
222C22×D43#12312yes—
223C22×D43#12712yes—
224D4×C43—22no—
225D4×C43—22no—
226D4×C43—41no—
227D4×C43—41no—
228C2×C4×C43—22no—
229C2×C4×C43—22no—
230C2×C4×C43—22no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C22×Q811yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C22⋊D43—48no—
244C2×Dic43—22no—
245C2×Dic43—22no—
246C2×Dic43—22no—
247C2×Dic43—22no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—48no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—42no—
255C2×Dic43—42no—
256C2×Dic43—42no—
257C2×Dic43C22⋊Q812yes—
258C2×Dic43#12312yes—
259C2×Dic43#12712yes—
260C4×D43—84no—
261C4×D43—84no—
262C4×D43C22⋊Q814yes—
263C4×D43C22⋊Q814yes—
264C4×D43#12314yes—
265C4×D43#12314yes—
266Dic86—22no—
267Dic86—22no—
268Dic86—41no—
269Dic86—41no—
270C8×C43—22no—
271C8×C43—22no—
272C43⋊C8—22no—
273C43⋊C8—22no—
274#23738—431nomaximal, Sylow
275C22×C43—44no—
276C22×C43—42no—
277C22×C43—82no—
278C22×C43—81no—
279C22×C43—81no—
280C22×C43C2×C22⋊Q811yescharacteristic
281C22×C43C2×#12311yescharacteristic
282C22×C43C2×#12711yescharacteristic
283C22×C43#57712yes—
284C22×C43#57712yes—
285C2×D43—24no—
286C2×D43—24no—
287C2×D43—22no—
288C2×D43—22no—
289C2×D43#39914yes—
290C4×C43—42no—
291C4×C43—81no—
292C4×C43—81no—
293C4×C43—81no—
294C4×C43C2×C22⋊Q811yescharacteristic
295C4×C43C2×C22⋊Q811yescharacteristic
296C4×C43C2×#12311yescharacteristic
297C4×C43C2×#12311yescharacteristic
298Dic43—42no—
299Dic43—42no—
300Dic43—81no—
301Dic43—81no—
302Dic43—81no—
303Dic43#39914yes—
304C2×#428—431no—
305C22×#106—431no—
306C2×#417—431no—
307C2×#416—431no—
308#2317—431no—
309#2311—431no—
310#2097—431no—
311#2097—431no—
312#2096—431no—
313#2096—431no—
314#2094—431no—
315#2094D4311yescharacteristic, complemented
316#2092—431no—
317#2092—431no—
318#1729—431no—
319C2×C43—82no—
320C2×C43C2×#39911yescharacteristic
321C2×C43#308412yes—
322C2×C43#309912yes—
323C2×C43#315411yescharacteristic
324C2×C43#315411yescharacteristic
325D43—24no—
326C22×#41—431no—
327C22×M16—431no—
328C23×C8—431no—
329C2×#117—431no—
330C2×#117—431no—
331C22×C4⋊C4—431no—
332C22×C4⋊C4—431no—
333#428—864no—
334C2×#107—431no—
335C2×#107—431no—
336C2×#106—431no—
337C2×#106—431no—
338C2×#106—431no—
339C2×#106—431no—
340C2×#106—864no—
341C2×#106C2×D4311yescharacteristic
342C2×#106C2×D4311yescharacteristic
343#417—864no—
344#416—864no—
345C2×#103—431no—
346C2×#103—431no—
347C2×#103—431no—
348C2×#103—431no—
349C2×#102—431no—
350C2×#102—431no—
351C2×#102C2×D4311yescharacteristic
352C2×#102C2×D4311yescharacteristic
353#391—431no—
354#391—431no—
355#390—431no—
356#390C2×D4311yescharacteristic
357#389—862no—
358#386—862no—
359#385—862no—
360#384—431no—
361#384C2×D4311yescharacteristic
362#382—431no—
363#382—431no—
364#380—862no—
365#336—431no—
366#336—431no—
367#336—431no—
368#336C2×D4311yescharacteristic
369C43#2373811yescharacteristic, complemented, Sylow
370C2×#41—434no—
371C2×#41—862no—
372C2×#41—862no—
373C2×#41—862no—
374C2×#41—862no—
375C2×#41—862no—
376C22×Q8—431no—
377C22×D4—861no—
378C22×D4C22×D4311yescharacteristic
379C23×C4—431no—
380C23×C4—861no—
381C23×C4—861no—
382C23×C4—861no—
383C2×M16—434no—
384C2×M16—862no—
385C2×M16—862no—
386C22×C8—431no—
387C22×C8—431no—
388C22×C8—434no—
389C22×C8—862no—
390C22×C8—862no—
391C22×C8C22×D4311yescharacteristic
392C22×C8C22×D4311yescharacteristic
393#117—862no—
394#117—862no—
395#117—862no—
396#117—862no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—432no—
399C2×C4⋊C4—431no—
400C2×C4⋊C4—431no—
401C2×C4⋊C4—431no—
402C2×C4⋊C4—862no—
403C2×C4⋊C4—862no—
404C2×C4⋊C4—862no—
405C2×C4⋊C4—862no—
406C2×C4⋊C4—862no—
407C2×C4⋊C4—861no—
408C2×C4⋊C4—861no—
409C2×C4⋊C4C22×D4311yescharacteristic
410C2×C4⋊C4C22×D4311yescharacteristic
411C2×C4⋊C4C22×D4311yescharacteristic
412C2×C22⋊C4—22no—
413C2×C22⋊C4—432no—
414C2×C22⋊C4—862no—
415C2×C22⋊C4—861no—
416C2×C42—431no—
417C2×C42—861no—
418C2×C42C22×D4311yescharacteristic
419#107—862no—
420#107—862no—
421#106—22no—
422#106—22no—
423#106—862no—
424#106—862no—
425#106—862no—
426#106—862no—
427#103—862no—
428#103—862no—
429#103—862no—
430#103—862no—
431#102—22no—
432#102—22no—
433#102—862no—
434#102—862no—
435#95—862no—
436#95—862no—
437#95—862no—
438#95—862no—
439C24—21no—
440C24—431no—
441#41—868no—
442#41—868no—
443#41—1724no—
444#41—1724no—
445C2×Q8—432no—
446C2×Q8—861no—
447C2×Q8—861no—
448C2×Q8—861no—
449C2×Q8—861no—
450C2×Q8—861no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—864no—
457C2×D4—1722no—
458C2×D4—1722no—
459C2×D4Q8×D4312yes—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—431no—
464C22×C4—432no—
465C22×C4—432no—
466C22×C4—432no—
467C22×C4—432no—
468C22×C4—432no—
469C22×C4—432no—
470C22×C4—432no—
471C22×C4—864no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—3442no—
477C22×C4—3442no—
478C22×C4—1722no—
479C22×C4—1722no—
480C22×C4—1722no—
481C22×C4—1722no—
482C22×C4D4×D4312yes—
483C22×C4C23×D4311yescharacteristic
484M16—868no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—432no—
490C2×C8—432no—
491C2×C8—868no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—861no—
496C2×C8D4×D4312yes—
497C2×C8D4×D4312yes—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—82no—
505C4⋊C4—864no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—3442no—
513C4⋊C4—1722no—
514C4⋊C4—1722no—
515C22⋊C4—82no—
516C22⋊C4—864no—
517C22⋊C4—3442no—
518C22⋊C4—1722no—
519C42—21no—
520C42—21no—
521C42—861no—
522C42—861no—
523C42—1722no—
524C23—22no—
525C23—41no—
526C23—41no—
527C23—42no—
528C23—42no—
529C23—432no—
530C23—432no—
531C23—432no—
532C23—862no—
533C23—862no—
534C23C2×D4×D4311yescharacteristic
535Q8—862no—
536Q8—862no—
537Q8—1721no—
538Q8—1721no—
539D4—22no—
540D4—22no—
541D4—41no—
542D4—41no—
543D4—1728no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—432no—
554C2×C4—432no—
555C2×C4—432no—
556C2×C4—434no—
557C2×C4—434no—
558C2×C4—434no—
559C2×C4—434no—
560C2×C4—862no—
561C2×C4—862no—
562C2×C4—862no—
563C2×C4—862no—
564C2×C4—3444no—
565C2×C4—3444no—
566C2×C4—1728no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1722no—
571C2×C4—1722no—
572C2×C4—1722no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4C2×D4×D4311yescharacteristic
576C2×C4C2×D4×D4311yescharacteristic
577C2×C4C2×Q8×D4311yescharacteristic
578C2×C4#41×D4311yescharacteristic
579C2×C4#41×D4311yescharacteristic
580C2×C4#41×D4311yescharacteristic
581C8—22no—
582C8—22no—
583C8—862no—
584C8—862no—
585C22—44no—
586C22—42no—
587C22—81no—
588C22—81no—
589C22—82no—
590C22—434no—
591C22—864no—
592C22—862no—
593C22—862no—
594C22—864no—
595C22C22⋊Q8×D4311yescharacteristic
596C22#123×D4311yescharacteristic
597C22#127×D4311yescharacteristic
598C22#1458370512yes—
599C22#1458370912yes—
600C4—42no—
601C4—81no—
602C4—81no—
603C4—81no—
604C4—434no—
605C4—3441no—
606C4—3441no—
607C4—3441no—
608C4—1722no—
609C4—1722no—
610C4C22⋊Q8×D4311yescharacteristic
611C4C22⋊Q8×D4311yescharacteristic
612C4#123×D4311yescharacteristic
613C4#123×D4311yescharacteristic
614C2—82no—
615C2—864no—
616C2#399×D4311yescharacteristic
617C2#1914445212yes—
618C2#1914458512yes—
619C2#1914506411yescharacteristic
620C2#1914506811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2094C2
socleC23×C43C22×D4
prime radicalC22×#10621900C22
hypercenter#2094D43
hypocenterC43#23738
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2094

Complements

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

NH ≅ G/Ntype
1. C2×#14582938C2semidirect
2. C2×#106×D43C2semidirect
5. #19137216C2semidirect
7. #19136144C2semidirect
8. #19136142C2semidirect
9. #19136139C2semidirect
10. #19136135C2semidirect
11. #19136126C2semidirect
12. #19136116C2semidirect
13. #19136114C2semidirect
14. #19134290C2semidirect
15. C43×#2094C2semidirect
315. #2094D43semidirect
369. C43#23738semidirect

Maximal subgroups

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

subgroupindex
C2×#145829382
C2×#106×D432
C2×#145828972
C2×#145828922
#191372162
#191371852
#191361442
#191361422
#191361392
#191361352
#191361262
#191361162
#191361142
#191342902
C43×#20942
#2373843