Finite Group Databasebeta

← #25138106

Subgroups — #25138106

Order 11008.

658 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144415C211yesmaximal, characteristic
2C2×#14583208C211yesmaximal, characteristic, complemented
3#137×Dic43C211yesmaximal, characteristic
4#19143257C211yesmaximal, characteristic
5#19136043C211yesmaximal, characteristic
6#19136035C211yesmaximal, characteristic
7#19135891C211yesmaximal, characteristic
8#19135586C211yesmaximal, characteristic, complemented
9#19135381C211yesmaximal, characteristic, complemented
10#19135374C211yesmaximal, characteristic, complemented
11#19135367C211yesmaximal, characteristic, complemented
12#19135252C211yesmaximal, characteristic, complemented
13#19135247C211yesmaximal, characteristic, complemented
14#19134589C211yesmaximal, characteristic, complemented
15C43×#2052C211yesmaximal, characteristic
16C2×#13063316C2211yescharacteristic
17#41×Dic43C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19#14583208—21no—
20#14583208—21no—
21#14583208—21no—
22#14583208—21no—
23#14583208—21no—
24#14583204—21no—
25#14583201—21no—
26#14583197—21no—
27#14583006—21no—
28#14583000—21no—
29Q16×Dic43—21no—
30SD16×Dic43—21no—
31#14582957—21no—
32#14582957—21no—
33#14582953—21no—
34#14582949—21no—
35C2×#13063260C2211yescharacteristic
36#14582941C2211yescharacteristic
37#14582941C2211yescharacteristic
38#14582939C2211yescharacteristic
39C2×#13063259C2211yescharacteristic
40C2×#13063256C2211yescharacteristic
41#14582922C2211yescharacteristic
42#14582922C2211yescharacteristic
43C2×Dic43⋊C8C2211yescharacteristic
44#14582908C2211yescharacteristic
45#14582900C2211yescharacteristic
46#14582900C2211yescharacteristic
47C2×#13063249C2211yescharacteristic
48C2×#13063244C2211yescharacteristic
49#14582866C2211yescharacteristic
50#14582857C2211yescharacteristic
51#14582854C2211yescharacteristic
52M16×Dic43C2211yescharacteristic
53#14582668C2211yescharacteristic
54#14582667C2211yescharacteristic
55#14582667C2211yescharacteristic
56#14582667C2211yescharacteristic
57#14582667C2211yescharacteristic
58#14582664C2211yescharacteristic
59#14582663C2211yescharacteristic
60C2×#137×C43C2211yescharacteristic
61C2×#108×C43C2211yescharacteristic
62C43×#417C2211yescharacteristic
63C2×#103×C43C2211yescharacteristic
64C2×#101×C43C2211yescharacteristic
65C43×#408C2211yescharacteristic
66C43×#343C2211yescharacteristic
67C2×#10621877C2311yescharacteristic
68C2×#10621877C2311yescharacteristic
69C2×#10621877C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71#13063316—21no—
72#13063316—21no—
73#13063316—21no—
74#13063316—21no—
75Q8×Dic43—21no—
76Q8×Dic43—21no—
77Q8×Dic43—21no—
78Q8×Dic43—21no—
79Q8×Dic43D411yescharacteristic
80Q8×Dic43D411yescharacteristic
81D4×Dic43—21no—
82D4×Dic43—21no—
83D4×Dic43D411yescharacteristic
84D4×Dic43D411yescharacteristic
85#13063284—21no—
86#13063284C2311yescharacteristic
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×Dic43⋊C4—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43C2311yescharacteristic
95#13063260—22no—
96#13063259—21no—
97#13063259—21no—
98#13063259—21no—
99#13063259—21no—
100#13063258—21no—
101#13063257—21no—
102#13063257—21no—
103#13063256—21no—
104#13063256—21no—
105#13063256—21no—
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8D411yescharacteristic
111Dic43⋊C8D411yescharacteristic
112Dic43⋊C8D411yescharacteristic
113Dic43⋊C8D411yescharacteristic
114#13063249—21no—
115#13063249—21no—
116#13063249—21no—
117#13063249—21no—
118#13063249—21no—
119#13063249—21no—
120#13063246—21no—
121#13063246—21no—
122#13063244—22no—
123C22⋊(C43⋊C8)—21no—
124C22⋊(C43⋊C8)—21no—
125#13063235—21no—
126#13063235—21no—
127#13063235—21no—
128C8×Dic43—21no—
129C8×Dic43—21no—
130C8×Dic43—21no—
131C2×#41×C43C2311yescharacteristic
132C22×Q8×C43C2311yescharacteristic
133#137×C43—22no—
134#137×C43—22no—
135C2×Q16×C43—21no—
136C2×SD16×C43—21no—
137C2×M16×C43C2311yescharacteristic
138C2×M16×C43C2311yescharacteristic
139C2×M16×C43C2311yescharacteristic
140C22×C8×C43C2311yescharacteristic
141C2×C4⋊C4×C43C2311yescharacteristic
142#108×C43—22no—
143#103×C43—21no—
144#103×C43—21no—
145#103×C43—21no—
146#102×C43—21no—
147#101×C43—22no—
148C22⋊C8×C43—21no—
149C22⋊C8×C43—21no—
150#41×C43—21no—
151#41×C43—21no—
152#41×C43—21no—
153#41×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43C2×D411yescharacteristic
160C2×Q8×C43#4112yes—
161C2×D4×C43—21no—
162C2×D4×C43C2×D411yescharacteristic
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43C2411yescharacteristic
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43#4111yescharacteristic
172C22×Dic43#4111yescharacteristic
173Q16×C43—24no—
174SD16×C43—24no—
175M16×C43—21no—
176M16×C43—21no—
177M16×C43—21no—
178M16×C43—21no—
179M16×C43—21no—
180M16×C43#4112yes—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43C2×D411yescharacteristic
187C2×C8×C43C2×D411yescharacteristic
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C22⋊Dic43—21no—
191C22⋊Dic43—21no—
192C22⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—41no—
200C4⋊Dic43—41no—
201C4⋊Dic43—41no—
202C4⋊Dic43—41no—
203C4⋊Dic43C2×D411yescharacteristic
204C4⋊Dic43C2×D411yescharacteristic
205Dic43⋊C4—41no—
206Dic43⋊C4—41no—
207C4×Dic43—21no—
208C4×Dic43—21no—
209C4×Dic43—21no—
210C4×Dic43—41no—
211C4×Dic43—41no—
212C4×Dic43C2×D411yescharacteristic
213C4×Dic43C2×D411yescharacteristic
214C4×Dic43C2×D411yescharacteristic
215C4×Dic43C2×D411yescharacteristic
216#10621877—21no—
217#10621877—21no—
218#10621877—21no—
219#10621877—21no—
220#10621877—21no—
221#10621877—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8C2×D411yescharacteristic
228C2×C43⋊C8C2×D411yescharacteristic
229C23×C43—21no—
230C23×C43C2×#4111yescharacteristic
231Q8×C43—22no—
232Q8×C43—21no—
233Q8×C43—21no—
234Q8×C43—22no—
235Q8×C43—41no—
236Q8×C43—41no—
237D4×C43—21no—
238D4×C43—21no—
239D4×C43—41no—
240D4×C43—41no—
241C2×C4×C43—21no—
242C2×C4×C43—22no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—81no—
249C2×C4×C43C22×D411yescharacteristic
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C432−1+411yescharacteristic
254C2×C4×C432−1+411yescharacteristic
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—42no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—81no—
263C2×Dic43—81no—
264C2×Dic43—81no—
265C2×Dic43#12111yescharacteristic
266C2×Dic43#12111yescharacteristic
267C2×Dic43#12111yescharacteristic
268C2×Dic43#12111yescharacteristic
269C8×C43—22no—
270C8×C43—21no—
271C8×C43—21no—
272C8×C43—41no—
273C8×C43—41no—
274C43⋊C8—21no—
275C43⋊C8—21no—
276C43⋊C8—41no—
277C43⋊C8—41no—
278C43⋊C8—41no—
279#24725—431nomaximal, Sylow
280C22×C43—21no—
281C22×C43—21no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43C2×#12111yescharacteristic
286C22×C43#55211yescharacteristic
287C22×C43#55611yescharacteristic
288C4×C43—41no—
289C4×C43—42no—
290C4×C43—81no—
291C4×C43#52511yescharacteristic
292C4×C43#53611yescharacteristic
293C4×C43#54711yescharacteristic
294C4×C43#54811yescharacteristic
295Dic43—21no—
296Dic43—21no—
297Dic43—21no—
298Dic43—21no—
299Dic43—41no—
300Dic43—41no—
301Dic43—81no—
302Dic43—81no—
303#3080—431no—
304C2×#479—431no—
305C4×#137—431no—
306#2925—431no—
307#2079—431no—
308#2078—431no—
309#2052—431no—
310#2052D4311yescharacteristic
311#1998—431no—
312#1952—431no—
313#1951—431no—
314#1950—431no—
315#1930—431no—
316#1930—431no—
317#1801—431no—
318C2×C43—21no—
319C2×C43—21no—
320C2×C43—81no—
321C2×C43#241511yescharacteristic
322C2×C43#306711yescharacteristic
323C2×C43#306911yescharacteristic
324C2×#137C2×D4311yescharacteristic
325C2×#125—431no—
326C4×#41—431no—
327C2×C4×Q8—431no—
328#479—861no—
329#479—861no—
330#479—861no—
331#479—861no—
332#479—861no—
333#479—861no—
334#478—861no—
335#478—861no—
336#441—861no—
337#440—861no—
338C4×Q16—861no—
339C4×SD16—861no—
340#433—861no—
341#433—861no—
342#432—861no—
343#431—861no—
344C2×#108—431no—
345C2×#108C2×D4311yescharacteristic
346#428—431no—
347#428—431no—
348#428—431no—
349C2×#107—431no—
350C2×#106—431no—
351#423—431no—
352#423—431no—
353C2×C4⋊C8—431no—
354#419—431no—
355#417—431no—
356#417—431no—
357#417C2×D4311yescharacteristic
358C2×#103—431no—
359C2×#103C2×D4311yescharacteristic
360C2×#101—431no—
361C2×#101C2×D4311yescharacteristic
362#408—431no—
363#408C2×D4311yescharacteristic
364#405—431no—
365#405—431no—
366C4×M16—431no—
367#343—431no—
368#343—431no—
369#343—431no—
370#343—431no—
371#343—431no—
372#343C2×D4311yescharacteristic
373#341—431no—
374#341—431no—
375C43#2472511yescharacteristic, complemented, Sylow
376C2×#41C22×D4311yescharacteristic
377C22×Q8C22×D4311yescharacteristic
378#137—22no—
379#137—22no—
380C2×Q16—21no—
381C2×SD16—21no—
382C2×M16—431no—
383C2×M16—431no—
384C2×M16—431no—
385C2×M16C22×D4311yescharacteristic
386C2×M16C22×D4311yescharacteristic
387C2×M16C22×D4311yescharacteristic
388C22×C8—431no—
389C22×C8C22×D4311yescharacteristic
390#125—861no—
391#125—861no—
392#125—861no—
393#125—861no—
394C4×Q8—431no—
395C4×Q8—431no—
396C4×Q8—861no—
397C4×Q8—861no—
398C4×Q8—861no—
399C4×Q8—861no—
400C4×D4—431no—
401C4×D4—431no—
402C4×D4—861no—
403C4×D4—861no—
404#117—431no—
405#117—861no—
406C2×C4⋊C4—431no—
407C2×C4⋊C4—431no—
408C2×C4⋊C4—861no—
409C2×C4⋊C4—861no—
410C2×C4⋊C4—861no—
411C2×C4⋊C4C22×D4311yescharacteristic
412C2×C42—431no—
413C2×C42—861no—
414C2×C42—861no—
415#108—22no—
416#108—862no—
417#107—861no—
418#107—861no—
419#107—861no—
420#107—861no—
421#107—861no—
422#106—861no—
423#106—861no—
424#106—861no—
425#106—861no—
426#106—861no—
427C4⋊C8—431no—
428C4⋊C8—431no—
429C4⋊C8—431no—
430C4⋊C8—431no—
431C4⋊C8—861no—
432C4⋊C8—861no—
433C4⋊C8—861no—
434C4⋊C8—861no—
435#103—21no—
436#103—21no—
437#103—21no—
438#103—861no—
439#103—861no—
440#103—861no—
441#103—861no—
442#103—861no—
443#103—861no—
444#102—21no—
445#102—861no—
446#102—861no—
447#101—22no—
448#101—862no—
449C22⋊C8—21no—
450C22⋊C8—21no—
451C22⋊C8—861no—
452C22⋊C8—861no—
453#97—861no—
454#97—861no—
455#97—861no—
456C4×C8—861no—
457C4×C8—861no—
458C4×C8—861no—
459#41—21no—
460#41—21no—
461#41—21no—
462#41—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8D4×D4311yescharacteristic
469C2×Q8#1062190012yes—
470C2×D4—21no—
471C2×D4D4×D4311yescharacteristic
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—431no—
476C22×C4—431no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4—861no—
480C22×C4—861no—
481C22×C4C23×D4311yescharacteristic
482Q16—24no—
483SD16—24no—
484M16—21no—
485M16—21no—
486M16—21no—
487M16—21no—
488M16—21no—
489M16—861no—
490M16—861no—
491M16—861no—
492M16—861no—
493M16—861no—
494M16—861no—
495M16#1062190012yes—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—431no—
502C2×C8—431no—
503C2×C8—861no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8D4×D4311yescharacteristic
509C2×C8D4×D4311yescharacteristic
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—431no—
513C4⋊C4—431no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—1721no—
521C4⋊C4—1721no—
522C4⋊C4—1721no—
523C4⋊C4—1721no—
524C4⋊C4—1721no—
525C4⋊C4—1721no—
526C22⋊C4—861no—
527C22⋊C4—861no—
528C22⋊C4—861no—
529C42—431no—
530C42—431no—
531C42—431no—
532C42—431no—
533C42—861no—
534C42—861no—
535C42—861no—
536C42—1721no—
537C42—1721no—
538C23—21no—
539C23#41×D4311yescharacteristic
540Q8—22no—
541Q8—22no—
542Q8—21no—
543Q8—21no—
544Q8—41no—
545Q8—41no—
546D4—21no—
547D4—21no—
548D4—41no—
549D4—41no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—81no—
558C2×C4—431no—
559C2×C4—431no—
560C2×C4—431no—
561C2×C4—431no—
562C2×C4—861no—
563C2×C4—861no—
564C2×C4—3441no—
565C2×C4—3441no—
566C2×C4—3441no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1722no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4C2×D4×D4311yescharacteristic
573C2×C4C2×D4×D4311yescharacteristic
574C2×C4C2×#1062190011yescharacteristic
575C2×C4C2×#1062190011yescharacteristic
576C2×C4#1306337211yescharacteristic
577C2×C4#1306337211yescharacteristic
578C8—22no—
579C8—21no—
580C8—21no—
581C8—41no—
582C8—41no—
583C8—861no—
584C8—861no—
585C8—1721no—
586C8—1721no—
587C8—1721no—
588C22—21no—
589C22—21no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22#121×D4311yescharacteristic
594C22#1458358611yescharacteristic
595C22#1458361811yescharacteristic
596C4—41no—
597C4—42no—
598C4—81no—
599C4—861no—
600C4—861no—
601C4—861no—
602C4—861no—
603C4—3441no—
604C4—3441no—
605C4—1721no—
606C4—1721no—
607C4#1458340511yescharacteristic
608C4#1458347111yescharacteristic
609C4#1458354911yescharacteristic
610C4#1458355511yescharacteristic
611C2—21no—
612C2—21no—
613C2—81no—
614C2#1913801711yescharacteristic
615C2#1914431711yescharacteristic
616C2#1914432711yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2052C2
socleC22×C43C2×#121
prime radicalC2×#41×C43C23
hypercenter#2052D43
hypocenterC43#24725
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2052

Complements

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

NH ≅ G/Ntype
2. C2×#14583208C2semidirect
8. #19135586C2semidirect
9. #19135381C2semidirect
10. #19135374C2semidirect
11. #19135367C2semidirect
12. #19135252C2semidirect
13. #19135247C2semidirect
14. #19134589C2semidirect
375. C43#24725semidirect

Maximal subgroups

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

subgroupindex
#191444152
C2×#145832082
#137×Dic432
#191432572
#191360432
#191360352
#191358912
#191355862
#191353812
#191353742
#191353672
#191352522
#191352472
#191345892
C43×#20522
#2472543