Finite Group Databasebeta

← #25126411

Subgroups — #25126411

Order 11008.

1098 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582940C211yesmaximal, characteristic
2C2×#14582938C211yesmaximal, characteristic
3C2×#14582906C211yesmaximal, characteristic
4C2×#14582906C211yesmaximal, characteristic
5#391×D43C211yesmaximal, characteristic
6#19137001C211yesmaximal, characteristic
7#19136146C211yesmaximal, characteristic, complemented
8#19136143C211yesmaximal, characteristic, complemented
9#19136142C211yesmaximal, characteristic, complemented
10#19136136C211yesmaximal, characteristic, complemented
11#19136135C211yesmaximal, characteristic, complemented
12#19136131C211yesmaximal, characteristic, complemented
13#19136130C211yesmaximal, characteristic, complemented
14#19134287C211yesmaximal, characteristic
15C43×#2097C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C2×#13063283C2211yescharacteristic
20C2×#13063283C2211yescharacteristic
21C2×C4⋊C4×D43C2211yescharacteristic
22C2×C42×D43C2211yescharacteristic
23#14582940—24no—
24#14582938—24no—
25C2×#13063259C2211yescharacteristic
26C2×#13063258C2211yescharacteristic
27C2×#13063258C2211yescharacteristic
28C2×#13063257C2211yescharacteristic
29C2×#13063256C2211yescharacteristic
30C2×#13063256C2211yescharacteristic
31#14582906—24no—
32#14582906—24no—
33C2×#13063250C2211yescharacteristic
34C2×#13063250C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39#14582806C2211yescharacteristic
40#14582805C2211yescharacteristic
41#14582804C2211yescharacteristic
42#14582803—22no—
43#14582768C2211yescharacteristic
44#14582768C2211yescharacteristic
45#14582765C2211yescharacteristic
46#14582758—22no—
47#14582750—22no—
48#95×D43—22no—
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#107×C43C2211yescharacteristic
53C2×#106×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C43×#391C2211yescharacteristic
57C43×#382C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86—21no—
60C22×Dic86C2311yescharacteristic
61C2×Q8×D43—22no—
62C2×Q8×D43—22no—
63C2×Q8×D43—22no—
64C2×Q8×D43—22no—
65C2×Q8×D43—22no—
66C2×Q8×D43Q814yes—
67C22×C4×D43—21no—
68C22×C4×D43—21no—
69C22×C4×D43D412yes—
70C22×C4×D43C2311yescharacteristic
71C2×#10621872—22no—
72C2×#10621872—22no—
73C2×#10621872—22no—
74C2×#10621872—22no—
75C2×#10621872D414yes—
76C2×#10621872D414yes—
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79#13063283—22no—
80#13063283—22no—
81#13063283—22no—
82#13063283—22no—
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—22no—
88C2×Dic43⋊C4—22no—
89C4⋊C4×D43—22no—
90C4⋊C4×D43—22no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43D412yes—
96C2×C4×Dic43C2311yescharacteristic
97C42×D43—22no—
98C42×D43—22no—
99#13063259—22no—
100#13063258—22no—
101#13063258—22no—
102#13063257—22no—
103#13063256—22no—
104#13063256—22no—
105#13063250—22no—
106#13063250—22no—
107#13063249—22no—
108#13063249—22no—
109#13063248—22no—
110#13063248—22no—
111C43⋊#95—22no—
112C43⋊#95—22no—
113C43⋊#95—22no—
114C43⋊#95—22no—
115C22×Q8×C43C2311yescharacteristic
116C22×C8×C43C2311yescharacteristic
117C22×C8×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C42×C43C2311yescharacteristic
122#107×C43—22no—
123#106×C43—22no—
124#103×C43—22no—
125#103×C43—22no—
126#95×C43—22no—
127#95×C43—22no—
128C23×D43C2×D411yescharacteristic
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43C2×Q812yes—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43C2×D412yes—
140C22×C4×C43C2411yescharacteristic
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43C2×D412yes—
146C22×Dic43C2×D411yescharacteristic
147Q8×D43—28no—
148Q8×D43—28no—
149Q8×D43—44no—
150Q8×D43—44no—
151C2×C4×D43—24no—
152C2×C4×D43—24no—
153C2×C4×D43—24no—
154C2×C4×D43—42no—
155C2×C4×D43—44no—
156C2×C4×D43—42no—
157C2×C4×D43—42no—
158C2×C4×D43—42no—
159C2×C4×D43C2×D412yes—
160C2×C4×D43C2×D412yes—
161C2×C4×D43C2×Q812yes—
162C2×C4×D43#4112yes—
163C2×C4×D43#4112yes—
164C2×C4×D43#4112yes—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—24no—
171C2×Dic86—42no—
172C2×Dic86—42no—
173C2×Dic86C2×Q812yes—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43C2×D412yes—
179C2×C8×C43C2×D412yes—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C42×C43—21no—
187C42×C43—21no—
188(C2×D43)⋊C4—42no—
189(C2×D43)⋊C4—42no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196Dic43⋊C4—44no—
197Dic43⋊C4—42no—
198Dic43⋊C4—44no—
199C4×Dic43—21no—
200C4×Dic43—21no—
201C4×Dic43—24no—
202C4×Dic43—42no—
203C4×Dic43—42no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8C2×D412yes—
209C2×C43⋊C8C2×D412yes—
210#10621872—28no—
211#10621872—28no—
212C23×C43C22×D411yescharacteristic
213C22×D43—22no—
214C22×D43—22no—
215C22×D43C22⋊Q812yes—
216C22×D43#12312yes—
217C22×D43#12712yes—
218Q8×C43—22no—
219Q8×C43—22no—
220Q8×C43—41no—
221Q8×C43—41no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—22no—
225C2×C4×C43—22no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—42no—
232C2×C4×C43—42no—
233C2×C4×C43—42no—
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C22×Q811yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×Dic43—22no—
241C2×Dic43—22no—
242C2×Dic43—22no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—42no—
249C2×Dic43—42no—
250C2×Dic43—42no—
251C2×Dic43C22⋊Q812yes—
252C2×Dic43#12312yes—
253C2×Dic43#12712yes—
254C2×Dic43#13714yes—
255C4×D43—48no—
256C4×D43—48no—
257C4×D43—84no—
258C4×D43C22⋊Q814yes—
259C4×D43C22⋊Q814yes—
260C4×D43#12314yes—
261C4×D43#12314yes—
262Dic86—22no—
263Dic86—22no—
264Dic86—41no—
265Dic86—41no—
266Dic86—48no—
267C8×C43—22no—
268C8×C43—22no—
269C43⋊C8—22no—
270C43⋊C8—22no—
271#23732—431nomaximal, Sylow
272C22×C43C2×C22⋊Q811yescharacteristic
273C22×C43C2×#12311yescharacteristic
274C22×C43C2×#12711yescharacteristic
275C22×C43C2×#13712yes—
276C22×C43#57512yes—
277C2×D43—24no—
278C2×D43—24no—
279C2×D43—22no—
280C2×D43—22no—
281C2×D43#39914yes—
282C4×C43—42no—
283C4×C43—42no—
284C4×C43—81no—
285C4×C43—81no—
286C4×C43—81no—
287C4×C43C2×C22⋊Q811yescharacteristic
288C4×C43C2×C22⋊Q811yescharacteristic
289C4×C43C2×#12311yescharacteristic
290C4×C43C2×#12311yescharacteristic
291Dic43—24no—
292Dic43—42no—
293Dic43—81no—
294Dic43—81no—
295Dic43—81no—
296Dic43#39914yes—
297C2×#428—431no—
298C2×#428—431no—
299C2×#419—431no—
300C2×#419—431no—
301C2×#391—431no—
302#2285—431no—
303#2097—431no—
304#2097—431no—
305#2097—431no—
306#2097D4311yescharacteristic, complemented
307#2096—431no—
308#2096—431no—
309#2095—431no—
310#2095—431no—
311#1728—431no—
312C2×C43C2×#39911yescharacteristic
313C2×C43#307812yes—
314C2×C43#309512yes—
315C2×C43#315211yescharacteristic
316C2×C43#315311yescharacteristic
317D43—24no—
318C23×Q8—431no—
319C22×M16—431no—
320C22×M16—431no—
321C2×#117—431no—
322C2×#117—431no—
323C22×C4⋊C4—431no—
324C22×C42—431no—
325#428—864no—
326#428—864no—
327C2×#107—431no—
328C2×#107—431no—
329C2×#107—431no—
330C2×#107C2×D4311yescharacteristic
331C2×#106—431no—
332C2×#106—431no—
333C2×#106—431no—
334C2×#106C2×D4311yescharacteristic
335#419—864no—
336#419—864no—
337C2×#103—431no—
338C2×#103—431no—
339C2×#103—431no—
340C2×#103—431no—
341C2×#103—431no—
342C2×#103—431no—
343C2×#103C2×D4311yescharacteristic
344C2×#103C2×D4311yescharacteristic
345#391—431no—
346#391—431no—
347#391—431no—
348#391—862no—
349#391C2×D4311yescharacteristic
350#384—431no—
351#384—431no—
352#382—431no—
353#382C2×D4311yescharacteristic
354#380—862no—
355C4×C4⋊C4—862no—
356C2×#95—862no—
357#336—431no—
358#336—431no—
359#336—431no—
360#336C2×D4311yescharacteristic
361C43#2373211yescharacteristic, complemented, Sylow
362C22×Q8—434no—
363C22×Q8—431no—
364C22×Q8—861no—
365C22×Q8—862no—
366C22×Q8—862no—
367C22×Q8—862no—
368C22×Q8—862no—
369C22×Q8—862no—
370C22×Q8C22×D4311yescharacteristic
371C23×C4—431no—
372C23×C4—432no—
373C23×C4—861no—
374C23×C4—861no—
375C2×M16—434no—
376C2×M16—434no—
377C2×M16—862no—
378C2×M16—862no—
379C2×M16—862no—
380C2×M16—862no—
381C22×C8—431no—
382C22×C8—431no—
383C22×C8C22×D4311yescharacteristic
384C22×C8C22×D4311yescharacteristic
385#117—862no—
386#117—862no—
387#117—862no—
388#117—862no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—431no—
391C2×C4⋊C4—431no—
392C2×C4⋊C4—862no—
393C2×C4⋊C4—862no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—862no—
396C2×C4⋊C4—862no—
397C2×C4⋊C4C22×D4311yescharacteristic
398C2×C4⋊C4C22×D4311yescharacteristic
399C2×C4⋊C4C22×D4311yescharacteristic
400C2×C22⋊C4—861no—
401C2×C22⋊C4—861no—
402C2×C42—432no—
403C2×C42—431no—
404C2×C42—862no—
405C2×C42—862no—
406C2×C42—861no—
407C2×C42—861no—
408C2×C42C22×D4311yescharacteristic
409#107—22no—
410#107—862no—
411#107—862no—
412#107—862no—
413#106—22no—
414#106—862no—
415#106—862no—
416#106—862no—
417#103—22no—
418#103—22no—
419#103—862no—
420#103—862no—
421#103—862no—
422#103—862no—
423#103—862no—
424#103—862no—
425#95—22no—
426#95—22no—
427#95—862no—
428#95—862no—
429#95—862no—
430#95—862no—
431C24—431no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—432no—
438C2×Q8—864no—
439C2×Q8—868no—
440C2×Q8—868no—
441C2×Q8—861no—
442C2×Q8—861no—
443C2×Q8—861no—
444C2×Q8—861no—
445C2×Q8—861no—
446C2×Q8—1722no—
447C2×Q8—1722no—
448C2×Q8—1724no—
449C2×Q8—1724no—
450C2×Q8Q8×D4312yes—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—431no—
456C22×C4—432no—
457C22×C4—432no—
458C22×C4—432no—
459C22×C4—432no—
460C22×C4—432no—
461C22×C4—432no—
462C22×C4—432no—
463C22×C4—864no—
464C22×C4—864no—
465C22×C4—864no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—1722no—
471C22×C4—1722no—
472C22×C4—1724no—
473C22×C4—1722no—
474C22×C4—1722no—
475C22×C4D4×D4312yes—
476C22×C4C23×D4311yescharacteristic
477M16—868no—
478M16—868no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—432no—
484C2×C8—432no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8D4×D4312yes—
490C2×C8D4×D4312yes—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—1722no—
504C4⋊C4—1724no—
505C4⋊C4—1724no—
506C22⋊C4—1722no—
507C22⋊C4—1722no—
508C42—21no—
509C42—21no—
510C42—864no—
511C42—861no—
512C42—861no—
513C42—1722no—
514C42—1722no—
515C23—432no—
516C23—432no—
517C23—432no—
518C23—862no—
519C23—862no—
520C23C2×D4×D4311yescharacteristic
521Q8—22no—
522Q8—22no—
523Q8—41no—
524Q8—41no—
525Q8—862no—
526Q8—862no—
527Q8—1728no—
528Q8—1721no—
529Q8—1721no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—432no—
543C2×C4—432no—
544C2×C4—432no—
545C2×C4—434no—
546C2×C4—434no—
547C2×C4—434no—
548C2×C4—434no—
549C2×C4—434no—
550C2×C4—862no—
551C2×C4—862no—
552C2×C4—862no—
553C2×C4—3444no—
554C2×C4—1728no—
555C2×C4—1728no—
556C2×C4—1722no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1722no—
561C2×C4—1722no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4C2×D4×D4311yescharacteristic
565C2×C4C2×D4×D4311yescharacteristic
566C2×C4C2×Q8×D4311yescharacteristic
567C2×C4#41×D4311yescharacteristic
568C2×C4#41×D4311yescharacteristic
569C2×C4#41×D4311yescharacteristic
570C8—22no—
571C8—22no—
572C8—862no—
573C8—862no—
574C22—434no—
575C22—862no—
576C22—864no—
577C22—862no—
578C22—864no—
579C22C22⋊Q8×D4311yescharacteristic
580C22#123×D4311yescharacteristic
581C22#127×D4311yescharacteristic
582C22#137×D4312yes—
583C22#1458369612yes—
584C4—42no—
585C4—42no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4—434no—
590C4—864no—
591C4—3441no—
592C4—3441no—
593C4—3441no—
594C4—1722no—
595C4C22⋊Q8×D4311yescharacteristic
596C4C22⋊Q8×D4311yescharacteristic
597C4#123×D4311yescharacteristic
598C4#123×D4311yescharacteristic
599C2—864no—
600C2#399×D4311yescharacteristic
601C2#1914439812yes—
602C2#1914454212yes—
603C2#1914505111yescharacteristic
604C2#1914505611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2097C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#2097D43
hypocenterC43#23732
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2097

Complements

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

NH ≅ G/Ntype
7. #19136146C2semidirect
8. #19136143C2semidirect
9. #19136142C2semidirect
10. #19136136C2semidirect
11. #19136135C2semidirect
12. #19136131C2semidirect
13. #19136130C2semidirect
15. C43×#2097C2semidirect
306. #2097D43semidirect
361. C43#23732semidirect

Maximal subgroups

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

subgroupindex
C2×#145829402
C2×#145829382
C2×#145829062
#391×D432
#191370012
#191361462
#191361432
#191361422
#191361362
#191361352
#191361312
#191361302
#191342872
C43×#20972
#2373243