Finite Group Databasebeta

← #25126324

Subgroups — #25126324

Order 11008.

744 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#19143419C211yesmaximal, characteristic
2#137×Dic43C211yesmaximal, characteristic
3C2×#14583003C211yesmaximal, characteristic, complemented
4#19143242C211yesmaximal, characteristic
5#19136109C211yesmaximal, characteristic, complemented
6#19136043C211yesmaximal, characteristic
7#19135960C211yesmaximal, characteristic, complemented
8#19135957C211yesmaximal, characteristic, complemented
9#19135893C211yesmaximal, characteristic
10#19135861C211yesmaximal, characteristic, complemented
11#19135713C211yesmaximal, characteristic
12#19134503C211yesmaximal, characteristic, complemented
13#101×Dic43C211yesmaximal, characteristic, complemented
14#19134390C211yesmaximal, characteristic, complemented
15C43×#2052C211yesmaximal, characteristic
16C2×#13063355C2211yescharacteristic
17C22×#10621885C2211yescharacteristic
18#41×Dic43C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic
20C2×#13063290C2211yescharacteristic
21#14583006—21no—
22#14583003—21no—
23#14583003—22no—
24#14583003—22no—
25#14583000—21no—
26#14582996—21no—
27Q16×Dic43—21no—
28#14582991—21no—
29#14582990—21no—
30SD16×Dic43—21no—
31#14582957—22no—
32#14582953—22no—
33C2×#13063261C2211yescharacteristic
34#14582941C2211yescharacteristic
35#14582939C2211yescharacteristic
36C2×#13063256C2211yescharacteristic
37#14582927C2211yescharacteristic
38#14582925C2211yescharacteristic
39#14582909C2211yescharacteristic
40#14582908C2211yescharacteristic
41#14582900C2211yescharacteristic
42C2×#13063250C2211yescharacteristic
43C2×#13063244C2211yescharacteristic
44C2×#13063243C2211yescharacteristic
45C2×#13063243C2211yescharacteristic
46#14582866C2211yescharacteristic
47M16×Dic43C2211yescharacteristic
48M16×Dic43C2211yescharacteristic
49M16×Dic43C2211yescharacteristic
50C2×#13063235C2211yescharacteristic
51#14582668C2211yescharacteristic
52#14582667C2211yescharacteristic
53#14582667C2211yescharacteristic
54#14582663C2211yescharacteristic
55#14582663C2211yescharacteristic
56C2×#137×C43C2211yescharacteristic
57C2×#108×C43C2211yescharacteristic
58C43×#417C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#101×C43C2211yescharacteristic
61C43×#408C2211yescharacteristic
62C43×#343C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64#13063355—22no—
65#13063355—22no—
66C2×#10621885—21no—
67C2×#10621885—22no—
68C2×#10621885—22no—
69C2×#10621885—22no—
70C2×#10621883—21no—
71C2×#10621877C2311yescharacteristic
72C2×#10621877C2311yescharacteristic
73C2×#10621877C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75Q8×Dic43—21no—
76Q8×Dic43—21no—
77Q8×Dic43—21no—
78Q8×Dic43—21no—
79Q8×Dic43D411yescharacteristic
80Q8×Dic43D411yescharacteristic
81#13063290—21no—
82#13063290—21no—
83#13063290—21no—
84#13063290—21no—
85D4×Dic43—21no—
86D4×Dic43—21no—
87D4×Dic43D411yescharacteristic
88D4×Dic43D411yescharacteristic
89#13063284—21no—
90#13063284C2311yescharacteristic
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43C2311yescharacteristic
93C2×Dic43⋊C4—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43C2311yescharacteristic
98#13063261—22no—
99#13063259—21no—
100#13063258—21no—
101#13063257—21no—
102#13063256—21no—
103#13063256—22no—
104Dic43⋊C8—22no—
105Dic43⋊C8—22no—
106#13063250—22no—
107#13063250—21no—
108#13063250—21no—
109#13063249—21no—
110#13063249—21no—
111#13063249—21no—
112#13063246—21no—
113#13063244—22no—
114#13063243—22no—
115#13063243—22no—
116C22⋊(C43⋊C8)—22no—
117#13063235—21no—
118#13063235—21no—
119#13063235—21no—
120#13063235D412yes—
121#13063235D412yes—
122C8×Dic43—21no—
123C8×Dic43—21no—
124C8×Dic43—21no—
125C2×#41×C43C2311yescharacteristic
126C22×Q8×C43C2311yescharacteristic
127#137×C43—22no—
128#137×C43—22no—
129C2×Q16×C43—21no—
130C2×SD16×C43—21no—
131C2×M16×C43C2311yescharacteristic
132C2×M16×C43C2311yescharacteristic
133C2×M16×C43C2311yescharacteristic
134C22×C8×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136#108×C43—22no—
137#103×C43—21no—
138#103×C43—22no—
139#102×C43—21no—
140#101×C43—22no—
141C22⋊C8×C43—22no—
142#41×C43—21no—
143#41×C43—21no—
144#41×C43—21no—
145#41×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43C2×D411yescharacteristic
152C2×Q8×C43#4112yes—
153C2×D4×C43—21no—
154C2×D4×C43C2×D411yescharacteristic
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43C2411yescharacteristic
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43#4111yescharacteristic
164C22×Dic43#4111yescharacteristic
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86#4112yes—
171Q16×C43—24no—
172SD16×C43—24no—
173M16×C43—21no—
174M16×C43—21no—
175M16×C43—21no—
176M16×C43—21no—
177M16×C43—21no—
178M16×C43#4112yes—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43C2×D412yes—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C22⋊Dic43—21no—
188C22⋊Dic43—21no—
189C22⋊Dic43—21no—
190#10621885—28no—
191#10621885—24no—
192#10621883—24no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—41no—
198C4⋊Dic43—41no—
199C4⋊Dic43C2×D411yescharacteristic
200C4⋊Dic43C2×D411yescharacteristic
201Dic43⋊C4—41no—
202Dic43⋊C4—41no—
203C4×Dic43—21no—
204C4×Dic43—21no—
205C4×Dic43—21no—
206C4×Dic43—41no—
207C4×Dic43—41no—
208C4×Dic43—41no—
209C4×Dic43—41no—
210C4×Dic43C2×D411yescharacteristic
211C4×Dic43C2×D411yescharacteristic
212C4×Dic43C2×D411yescharacteristic
213C4×Dic43C2×D411yescharacteristic
214#10621877—21no—
215#10621877—21no—
216#10621877—21no—
217#10621877—21no—
218#10621877—21no—
219#10621877#4112yes—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8C2×D412yes—
226C23×C43—21no—
227C23×C43C2×#4111yescharacteristic
228Q8×C43—22no—
229Q8×C43—21no—
230Q8×C43—22no—
231Q8×C43—21no—
232Q8×C43—41no—
233Q8×C43—41no—
234D4×C43—21no—
235D4×C43—21no—
236D4×C43—41no—
237D4×C43—41no—
238C2×C4×C43—21no—
239C2×C4×C43—22no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—81no—
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—22no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—81no—
261C2×Dic43—81no—
262C2×Dic43—81no—
263C2×Dic43#12111yescharacteristic
264C2×Dic43#12111yescharacteristic
265C2×Dic43#12111yescharacteristic
266C2×Dic43#12111yescharacteristic
267Dic86—22no—
268Dic86—22no—
269Dic86—41no—
270Dic86—41no—
271C8×C43—22no—
272C8×C43—22no—
273C8×C43—41no—
274C8×C43—41no—
275C43⋊C8—22no—
276C43⋊C8—22no—
277C43⋊C8—41no—
278C43⋊C8—41no—
279#23720—431nomaximal, Sylow
280C22×C43—21no—
281C22×C43—21no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43C2×#12111yescharacteristic
286C22×C43#52911yescharacteristic
287C22×C43#52911yescharacteristic
288C4×C43—41no—
289C4×C43—42no—
290C4×C43—81no—
291C4×C43#52511yescharacteristic
292C4×C43#52511yescharacteristic
293C4×C43#52511yescharacteristic
294C4×C43#53211yescharacteristic
295Dic43—21no—
296Dic43—21no—
297Dic43—21no—
298Dic43—21no—
299Dic43—42no—
300Dic43—41no—
301Dic43—41no—
302Dic43—81no—
303C4×#137—431no—
304C4×#137—431no—
305C2×#441—431no—
306#2923—431no—
307#2090—431no—
308#2079—431no—
309#2064—431no—
310#2064—431no—
311#2052—431no—
312#2052D4311yescharacteristic
313#2047—431no—
314#2020—431no—
315#1778—431no—
316C4×#101—431no—
317C4×#101—431no—
318C2×C43—21no—
319C2×C43—21no—
320C2×C43—81no—
321C2×C43#239211yescharacteristic
322C2×C43#306911yescharacteristic
323C2×C43#306911yescharacteristic
324C2×#137—431no—
325C2×#137C2×D4311yescharacteristic
326C22×Q16—431no—
327C4×#41—431no—
328C2×C4×Q8—431no—
329C2×C4×Q8—431no—
330#441—862no—
331#441—862no—
332#441—861no—
333#441—861no—
334#440—861no—
335#440—861no—
336C4×Q16—861no—
337C4×Q16—861no—
338C4×SD16—861no—
339C4×SD16—861no—
340#433—862no—
341#432—862no—
342C2×#108—431no—
343C2×#108C2×D4311yescharacteristic
344#428—431no—
345#428—431no—
346C2×#106—431no—
347#424—431no—
348#424—431no—
349#419—431no—
350#419—431no—
351#417—431no—
352#417C2×D4311yescharacteristic
353C2×#103—431no—
354C2×#103C2×D4311yescharacteristic
355C2×#101—431no—
356C2×#101—431no—
357C2×#101—431no—
358C2×#101C2×D4311yescharacteristic
359#408—431no—
360#408C2×D4311yescharacteristic
361C4×M16—431no—
362C4×M16—431no—
363C4×M16—431no—
364C2×#97—431no—
365#343—431no—
366#343—431no—
367#343—431no—
368#343C2×D4311yescharacteristic
369#341—431no—
370#341—431no—
371C43#2372011yescharacteristic, complemented, Sylow
372C2×#41C22×D4311yescharacteristic
373C22×Q8—431no—
374C22×Q8C22×D4311yescharacteristic
375#137—22no—
376#137—22no—
377#137—862no—
378#137—862no—
379C2×Q16—21no—
380C2×Q16—862no—
381C2×Q16—862no—
382C2×Q16—861no—
383C2×Q16—862no—
384C2×SD16—21no—
385C2×SD16—861no—
386C2×M16—431no—
387C2×M16—431no—
388C2×M16—431no—
389C2×M16C22×D4311yescharacteristic
390C2×M16C22×D4311yescharacteristic
391C2×M16C22×D4311yescharacteristic
392C22×C8—431no—
393C22×C8C22×D4311yescharacteristic
394C4×Q8—431no—
395C4×Q8—431no—
396C4×Q8—861no—
397C4×Q8—861no—
398C4×Q8—861no—
399C4×Q8—861no—
400C4×Q8—861no—
401C4×Q8—861no—
402C4×Q8—861no—
403C4×Q8—861no—
404C4×D4—431no—
405C4×D4—431no—
406C4×D4—861no—
407C4×D4—861no—
408#117—431no—
409#117—861no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—861no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4C22×D4311yescharacteristic
414C2×C42—431no—
415C2×C42—861no—
416C2×C42—861no—
417C2×C42—861no—
418#108—22no—
419#108—862no—
420#107—861no—
421#107—861no—
422#106—861no—
423#106—862no—
424#106—861no—
425C4⋊C8—862no—
426C4⋊C8—862no—
427#103—21no—
428#103—22no—
429#103—861no—
430#103—861no—
431#103—861no—
432#103—861no—
433#103—861no—
434#103—862no—
435#102—21no—
436#102—861no—
437#101—22no—
438#101—862no—
439#101—862no—
440#101—862no—
441C22⋊C8—22no—
442C22⋊C8—862no—
443#97—432no—
444#97—432no—
445#97—861no—
446#97—861no—
447#97—861no—
448C4×C8—861no—
449C4×C8—861no—
450C4×C8—861no—
451#41—21no—
452#41—21no—
453#41—21no—
454#41—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—432no—
461C2×Q8—861no—
462C2×Q8—861no—
463C2×Q8—861no—
464C2×Q8—861no—
465C2×Q8—861no—
466C2×Q8D4×D4311yescharacteristic
467C2×Q8#1062190012yes—
468C2×D4—21no—
469C2×D4D4×D4311yescharacteristic
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4C23×D4311yescharacteristic
480Q16—24no—
481Q16—868no—
482Q16—864no—
483SD16—24no—
484SD16—864no—
485M16—21no—
486M16—21no—
487M16—21no—
488M16—21no—
489M16—21no—
490M16—432no—
491M16—861no—
492M16—861no—
493M16—861no—
494M16—861no—
495M16—861no—
496M16#1062190012yes—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—432no—
503C2×C8—861no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8D4×D4312yes—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—431no—
512C4⋊C4—431no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—1721no—
518C4⋊C4—1721no—
519C4⋊C4—1721no—
520C4⋊C4—1721no—
521C22⋊C4—861no—
522C22⋊C4—861no—
523C22⋊C4—861no—
524C42—431no—
525C42—431no—
526C42—431no—
527C42—431no—
528C42—861no—
529C42—861no—
530C42—861no—
531C42—1721no—
532C42—1721no—
533C42—1721no—
534C42—1721no—
535C23—21no—
536C23#41×D4311yescharacteristic
537Q8—22no—
538Q8—21no—
539Q8—21no—
540Q8—22no—
541Q8—41no—
542Q8—41no—
543Q8—862no—
544Q8—862no—
545Q8—1721no—
546Q8—1721no—
547D4—21no—
548D4—21no—
549D4—41no—
550D4—41no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—81no—
559C2×C4—431no—
560C2×C4—431no—
561C2×C4—431no—
562C2×C4—431no—
563C2×C4—861no—
564C2×C4—861no—
565C2×C4—862no—
566C2×C4—3441no—
567C2×C4—3441no—
568C2×C4—3441no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4C2×D4×D4311yescharacteristic
575C2×C4C2×D4×D4311yescharacteristic
576C2×C4#41×D4311yescharacteristic
577C2×C4#41×D4311yescharacteristic
578C2×C4C2×#1062190011yescharacteristic
579C2×C4C2×#1062190011yescharacteristic
580C8—22no—
581C8—22no—
582C8—41no—
583C8—41no—
584C8—862no—
585C8—862no—
586C8—1721no—
587C8—1721no—
588C22—21no—
589C22—21no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22#121×D4311yescharacteristic
594C22#1458342611yescharacteristic
595C22#1458342811yescharacteristic
596C4—41no—
597C4—42no—
598C4—81no—
599C4—861no—
600C4—861no—
601C4—861no—
602C4—861no—
603C4—3441no—
604C4—1722no—
605C4—1721no—
606C4—1721no—
607C4#1458340511yescharacteristic
608C4#1458340711yescharacteristic
609C4#1458340911yescharacteristic
610C4#1458344411yescharacteristic
611C2—21no—
612C2—21no—
613C2—81no—
614C2#1913783811yescharacteristic
615C2#1914432711yescharacteristic
616C2#1914433011yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2052C2
socleC22×C43C2×#121
prime radicalC2×#41×C43C23
hypercenter#2052D43
hypocenterC43#23720
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
3. C2×#14583003C2semidirect
5. #19136109C2semidirect
7. #19135960C2semidirect
8. #19135957C2semidirect
10. #19135861C2semidirect
12. #19134503C2semidirect
13. #101×Dic43C2semidirect
14. #19134390C2semidirect
371. C43#23720semidirect

Maximal subgroups

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

subgroupindex
#191434192
#137×Dic432
C2×#145830032
#191432422
#191361092
#191360432
#191359602
#191359572
#191358932
#191358612
#191357132
#191345032
#101×Dic432
#191343902
C43×#20522
#2372043