Finite Group Databasebeta

← #25138080

Subgroups — #25138080

Order 11008.

674 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144406C211yesmaximal, characteristic
2C2×#14583182C211yesmaximal, characteristic, complemented
3#137×Dic43C211yesmaximal, characteristic
4#19143257C211yesmaximal, characteristic
5#19136043C211yesmaximal, characteristic
6#19136040C211yesmaximal, characteristic
7#19135891C211yesmaximal, characteristic
8#19135582C211yesmaximal, characteristic, complemented
9#19135376C211yesmaximal, 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×#13063324C2211yescharacteristic
17#41×Dic43C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19#14583192—21no—
20#14583187—21no—
21#14583182—21no—
22#14583182—21no—
23#14583182—21no—
24#14583182—21no—
25#14583182—21no—
26#14583177—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×#13063257C2211yescharacteristic
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
67C22×Dic86—21no—
68C2×#10621877C2311yescharacteristic
69C2×#10621877C2311yescharacteristic
70C2×#10621877C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72#13063324—21no—
73#13063324—21no—
74#13063324—21no—
75#13063324—21no—
76Q8×Dic43—21no—
77Q8×Dic43—21no—
78Q8×Dic43—21no—
79Q8×Dic43—21no—
80Q8×Dic43D411yescharacteristic
81Q8×Dic43D411yescharacteristic
82D4×Dic43—21no—
83D4×Dic43—21no—
84D4×Dic43D411yescharacteristic
85D4×Dic43D411yescharacteristic
86#13063284—21no—
87#13063284C2311yescharacteristic
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#13063258—21no—
99#13063257—21no—
100#13063257—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
173C2×Dic86—41no—
174C2×Dic86—41no—
175C2×Dic86—82no—
176Q16×C43—24no—
177SD16×C43—24no—
178M16×C43—21no—
179M16×C43—21no—
180M16×C43—21no—
181M16×C43—21no—
182M16×C43—21no—
183M16×C43#4112yes—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43C2×D411yescharacteristic
190C2×C8×C43C2×D411yescharacteristic
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C22⋊Dic43—21no—
194C22⋊Dic43—21no—
195C22⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—41no—
203C4⋊Dic43—41no—
204C4⋊Dic43C2×D411yescharacteristic
205C4⋊Dic43C2×D411yescharacteristic
206Dic43⋊C4—41no—
207Dic43⋊C4—41no—
208C4×Dic43—21no—
209C4×Dic43—21no—
210C4×Dic43—21no—
211C4×Dic43—41no—
212C4×Dic43—41no—
213C4×Dic43C2×D411yescharacteristic
214C4×Dic43C2×D411yescharacteristic
215C4×Dic43C2×D411yescharacteristic
216C4×Dic43C2×D411yescharacteristic
217#10621877—21no—
218#10621877—21no—
219#10621877—21no—
220#10621877—21no—
221#10621877—21no—
222#10621877—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8C2×D411yescharacteristic
229C2×C43⋊C8C2×D411yescharacteristic
230C23×C43—21no—
231C23×C43C2×#4111yescharacteristic
232Q8×C43—22no—
233Q8×C43—21no—
234Q8×C43—21no—
235Q8×C43—22no—
236Q8×C43—41no—
237Q8×C43—41no—
238D4×C43—21no—
239D4×C43—21no—
240D4×C43—41no—
241D4×C43—41no—
242C2×C4×C43—21no—
243C2×C4×C43—22no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—81no—
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C22×D411yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C432−1+411yescharacteristic
255C2×C4×C432−1+411yescharacteristic
256C2×Dic43—22no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—41no—
260C2×Dic43—42no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—81no—
264C2×Dic43—81no—
265C2×Dic43—81no—
266C2×Dic43#12111yescharacteristic
267C2×Dic43#12111yescharacteristic
268C2×Dic43#12111yescharacteristic
269C2×Dic43#12111yescharacteristic
270Dic86—82no—
271Dic86—82no—
272C8×C43—22no—
273C8×C43—21no—
274C8×C43—21no—
275C8×C43—41no—
276C8×C43—41no—
277C43⋊C8—21no—
278C43⋊C8—21no—
279C43⋊C8—41no—
280C43⋊C8—41no—
281C43⋊C8—41no—
282#24723—431nomaximal, Sylow
283C22×C43—21no—
284C22×C43—21no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43—41no—
288C22×C43C2×#12111yescharacteristic
289C22×C43#55211yescharacteristic
290C22×C43#55611yescharacteristic
291C4×C43—41no—
292C4×C43—42no—
293C4×C43—81no—
294C4×C43#52511yescharacteristic
295C4×C43#53611yescharacteristic
296C4×C43#54711yescharacteristic
297C4×C43#54811yescharacteristic
298Dic43—21no—
299Dic43—21no—
300Dic43—21no—
301Dic43—41no—
302Dic43—41no—
303Dic43—81no—
304Dic43—81no—
305Dic43#47112yes—
306#3079—431no—
307C2×#475—431no—
308C4×#137—431no—
309#2925—431no—
310#2079—431no—
311#2079—431no—
312#2052—431no—
313#2052D4311yescharacteristic
314#1997—431no—
315#1951—431no—
316#1951—431no—
317#1950—431no—
318#1930—431no—
319#1930—431no—
320#1801—431no—
321C2×C43—21no—
322C2×C43—21no—
323C2×C43—81no—
324C2×C43#241511yescharacteristic
325C2×C43C2×#47111yescharacteristic
326C2×C43#306911yescharacteristic
327C2×#137C2×D4311yescharacteristic
328C2×C4⋊Q8—431no—
329C4×#41—431no—
330C2×C4×Q8—431no—
331#477—861no—
332#476—861no—
333#475—861no—
334#475—861no—
335#475—861no—
336#475—861no—
337#475—861no—
338#474—861no—
339#441—861no—
340#440—861no—
341C4×Q16—861no—
342C4×SD16—861no—
343#433—861no—
344#433—861no—
345#432—861no—
346#431—861no—
347C2×#108—431no—
348C2×#108C2×D4311yescharacteristic
349#428—431no—
350#428—431no—
351#428—431no—
352C2×#106—431no—
353C2×#106—431no—
354#423—431no—
355#423—431no—
356C2×C4⋊C8—431no—
357#419—431no—
358#417—431no—
359#417—431no—
360#417C2×D4311yescharacteristic
361C2×#103—431no—
362C2×#103C2×D4311yescharacteristic
363C2×#101—431no—
364C2×#101C2×D4311yescharacteristic
365#408—431no—
366#408C2×D4311yescharacteristic
367#405—431no—
368#405—431no—
369C4×M16—431no—
370#343—431no—
371#343—431no—
372#343—431no—
373#343—431no—
374#343—431no—
375#343C2×D4311yescharacteristic
376#341—431no—
377#341—431no—
378C43#2472311yescharacteristic, complemented, Sylow
379C2×#41C22×D4311yescharacteristic
380C22×Q8—861no—
381C22×Q8C22×D4311yescharacteristic
382#137—22no—
383#137—22no—
384C2×Q16—21no—
385C2×SD16—21no—
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—861no—
395C4⋊Q8—861no—
396C4⋊Q8—861no—
397C4⋊Q8—861no—
398C4×Q8—431no—
399C4×Q8—431no—
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—431no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4C22×D4311yescharacteristic
415C2×C42—431no—
416C2×C42—861no—
417C2×C42—861no—
418#108—22no—
419#108—862no—
420#107—861no—
421#107—861no—
422#107—861no—
423#106—861no—
424#106—861no—
425#106—861no—
426#106—861no—
427#106—861no—
428#106—861no—
429#106—861no—
430C4⋊C8—431no—
431C4⋊C8—431no—
432C4⋊C8—431no—
433C4⋊C8—431no—
434C4⋊C8—861no—
435C4⋊C8—861no—
436C4⋊C8—861no—
437C4⋊C8—861no—
438#103—21no—
439#103—21no—
440#103—21no—
441#103—861no—
442#103—861no—
443#103—861no—
444#103—861no—
445#103—861no—
446#103—861no—
447#102—21no—
448#102—861no—
449#102—861no—
450#101—22no—
451#101—862no—
452C22⋊C8—21no—
453C22⋊C8—21no—
454C22⋊C8—861no—
455C22⋊C8—861no—
456#97—861no—
457#97—861no—
458#97—861no—
459C4×C8—861no—
460C4×C8—861no—
461C4×C8—861no—
462#41—21no—
463#41—21no—
464#41—21no—
465#41—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—3442no—
472C2×Q8—1721no—
473C2×Q8—1721no—
474C2×Q8D4×D4311yescharacteristic
475C2×Q8#1062190012yes—
476C2×D4—21no—
477C2×D4D4×D4311yescharacteristic
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4C23×D4311yescharacteristic
488Q16—24no—
489SD16—24no—
490M16—21no—
491M16—21no—
492M16—21no—
493M16—21no—
494M16—21no—
495M16—861no—
496M16—861no—
497M16—861no—
498M16—861no—
499M16—861no—
500M16—861no—
501M16#1062190012yes—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—431no—
508C2×C8—431no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8D4×D4311yescharacteristic
515C2×C8D4×D4311yescharacteristic
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—431no—
519C4⋊C4—431no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—1721no—
527C4⋊C4—1721no—
528C4⋊C4—1721no—
529C4⋊C4—1721no—
530C22⋊C4—861no—
531C22⋊C4—861no—
532C22⋊C4—861no—
533C42—431no—
534C42—431no—
535C42—431no—
536C42—431no—
537C42—861no—
538C42—861no—
539C42—861no—
540C42—1721no—
541C42—1721no—
542C23—21no—
543C23#41×D4311yescharacteristic
544Q8—22no—
545Q8—22no—
546Q8—21no—
547Q8—21no—
548Q8—41no—
549Q8—41no—
550Q8—3442no—
551Q8—3442no—
552D4—21no—
553D4—21no—
554D4—41no—
555D4—41no—
556C2×C4—22no—
557C2×C4—21no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—81no—
564C2×C4—431no—
565C2×C4—431no—
566C2×C4—431no—
567C2×C4—431no—
568C2×C4—862no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—3441no—
572C2×C4—3441no—
573C2×C4—3441no—
574C2×C4—1722no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4C2×D4×D4311yescharacteristic
579C2×C4C2×D4×D4311yescharacteristic
580C2×C4C2×#1062190011yescharacteristic
581C2×C4C2×#1062190011yescharacteristic
582C2×C4#1306337211yescharacteristic
583C2×C4#1306337211yescharacteristic
584C8—22no—
585C8—21no—
586C8—21no—
587C8—41no—
588C8—41no—
589C8—861no—
590C8—861no—
591C8—1721no—
592C8—1721no—
593C8—1721no—
594C22—21no—
595C22—21no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22#121×D4311yescharacteristic
600C22#1458358611yescharacteristic
601C22#1458361811yescharacteristic
602C4—41no—
603C4—42no—
604C4—81no—
605C4—432no—
606C4—861no—
607C4—861no—
608C4—861no—
609C4—3441no—
610C4—3441no—
611C4—1721no—
612C4—1721no—
613C4#1458340511yescharacteristic
614C4#1458347111yescharacteristic
615C4#1458354911yescharacteristic
616C4#1458355511yescharacteristic
617C2—21no—
618C2—21no—
619C2—81no—
620C2#1913801711yescharacteristic
621C2#471×D4311yescharacteristic
622C2#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#24723
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×#14583182C2semidirect
8. #19135582C2semidirect
9. #19135376C2semidirect
10. #19135374C2semidirect
11. #19135367C2semidirect
12. #19135252C2semidirect
13. #19135247C2semidirect
14. #19134589C2semidirect
378. C43#24723semidirect

Maximal subgroups

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

subgroupindex
#191444062
C2×#145831822
#137×Dic432
#191432572
#191360432
#191360402
#191358912
#191355822
#191353762
#191353742
#191353672
#191352522
#191352472
#191345892
C43×#20522
#2472343