Finite Group Databasebeta

← #25138104

Subgroups — #25138104

Order 11008.

690 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144413C211yesmaximal, characteristic, complemented
2C2×#14583196C211yesmaximal, characteristic, complemented
3C4×#13063353C211yesmaximal, characteristic
4#19143263C211yesmaximal, characteristic, complemented
5#19136044C211yesmaximal, characteristic, complemented
6#19136039C211yesmaximal, characteristic, complemented
7#19135890C211yesmaximal, characteristic
8#19135890C211yesmaximal, characteristic
9#19135379C211yesmaximal, characteristic, complemented
10#19135374C211yesmaximal, characteristic, complemented
11#19135370C211yesmaximal, characteristic, complemented
12#19135255C211yesmaximal, characteristic, complemented
13#19135255C211yesmaximal, characteristic, complemented
14#19134584C211yesmaximal, characteristic, complemented
15C43×#1998C211yesmaximal, characteristic, complemented
16C2×#13063353C2211yescharacteristic
17C4×#10621898C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19#14583203—21no—
20#14583203—21no—
21#14583196—21no—
22#14583196—21no—
23#14583196—21no—
24#14583196—21no—
25#14583196—21no—
26#14583196—21no—
27#14583012—21no—
28#14583001—21no—
29C4×#10621873—21no—
30C4×D344—21no—
31#14582959—21no—
32#14582959—21no—
33#14582955—21no—
34#14582951—21no—
35C2×#13063260C2211yescharacteristic
36C2×#13063260C2211yescharacteristic
37#14582941C2211yescharacteristic
38#14582939C2211yescharacteristic
39#14582939C2211yescharacteristic
40C2×#13063258C2211yescharacteristic
41C2×#13063256C2211yescharacteristic
42#14582923C2211yescharacteristic
43C2×C4⋊(C43⋊C8)C2211yescharacteristic
44#14582905C2211yescharacteristic
45#14582901C2211yescharacteristic
46#14582898C2211yescharacteristic
47#14582898C2211yescharacteristic
48C2×#13063245C2211yescharacteristic
49C2×#13063245C2211yescharacteristic
50C2×#13063241C2211yescharacteristic
51C2×#13063241C2211yescharacteristic
52#14582867C2211yescharacteristic
53#14582867C2211yescharacteristic
54#14582857C2211yescharacteristic
55#14582857C2211yescharacteristic
56#14582667C2211yescharacteristic
57#14582667C2211yescharacteristic
58#14582663C2211yescharacteristic
59#14582663C2211yescharacteristic
60C2×#125×C43C2211yescharacteristic
61C43×#423C2211yescharacteristic
62C4×M16×C43C2211yescharacteristic
63C43×#343C2211yescharacteristic
64C43×#343C2211yescharacteristic
65C43×#343C2211yescharacteristic
66C43×#343C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68C22×D172C2311yescharacteristic
69C22×C4×D43—21no—
70#13063353—22no—
71#13063353—22no—
72C2×#10621873—21no—
73C2×D344—21no—
74C2×#10621877C2311yescharacteristic
75C2×#10621877C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C4×Dic86D411yescharacteristic
79C4×Dic86D411yescharacteristic
80C4×D172—21no—
81C4×D172—21no—
82C4×D172—21no—
83C4×D172—21no—
84C4×D172D411yescharacteristic
85C4×D172D411yescharacteristic
86C4×C22⋊D43—21no—
87C4×C22⋊D43—21no—
88#13063284C2311yescharacteristic
89#13063282—21no—
90C2×C4⋊Dic43C2311yescharacteristic
91C2×(C2×D43)⋊C4—21no—
92C42×D43—21no—
93#13063260—22no—
94#13063260—22no—
95#13063259—21no—
96#13063258—21no—
97#13063258—21no—
98#13063258—21no—
99#13063258—21no—
100#13063257—21no—
101#13063256—21no—
102#13063256—21no—
103#13063256—21no—
104#13063256—21no—
105C4⋊(C43⋊C8)—21no—
106C4⋊(C43⋊C8)—21no—
107C4⋊(C43⋊C8)D411yescharacteristic
108C4⋊(C43⋊C8)D411yescharacteristic
109C4⋊(C43⋊C8)D411yescharacteristic
110C4⋊(C43⋊C8)D411yescharacteristic
111#13063250—21no—
112#13063248—21no—
113#13063248—21no—
114#13063247—21no—
115#13063247—21no—
116#13063247—21no—
117#13063245—21no—
118#13063245—21no—
119#13063245—21no—
120#13063245—21no—
121#13063245—21no—
122#13063245—21no—
123#13063241—22no—
124#13063241—22no—
125(C2×D43)⋊C8—21no—
126(C2×D43)⋊C8—21no—
127(C2×D43)⋊C8—21no—
128(C2×D43)⋊C8—21no—
129#13063235—21no—
130#13063235—21no—
131C8×Dic43—21no—
132C8×Dic43—21no—
133C2×M16×C43C2311yescharacteristic
134C2×M16×C43C2311yescharacteristic
135C2×M16×C43C2311yescharacteristic
136C2×M16×C43C2311yescharacteristic
137#125×C43—21no—
138#125×C43—21no—
139#125×C43—21no—
140#125×C43—21no—
141C2×C4⋊C4×C43—21no—
142C2×C4⋊C4×C43—21no—
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C42×C43C2311yescharacteristic
146C4⋊C8×C43—21no—
147C4⋊C8×C43—21no—
148#97×C43—21no—
149C4×C8×C43—21no—
150C23×D43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43#4111yescharacteristic
154C22×C4×C43#4111yescharacteristic
155C22×C4×C43C2411yescharacteristic
156C2×C22⋊D43—21no—
157C22×Dic43—21no—
158#10621898—21no—
159#10621898—21no—
160#10621898—21no—
161#10621898—21no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172C2×D411yescharacteristic
168C2×D172#4112yes—
169C2×C4×D43—21no—
170C2×C4×D43—21no—
171C2×C4×D43—21no—
172C2×C4×D43—41no—
173C2×C4×D43—41no—
174C2×C4×D43—82no—
175C2×Dic86C2×D411yescharacteristic
176M16×C43—21no—
177M16×C43—21no—
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—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—41no—
193C4⋊C4×C43—41no—
194C4⋊C4×C43—41no—
195C4⋊C4×C43—41no—
196C42×C43C2×D411yescharacteristic
197C42×C43C2×D411yescharacteristic
198C42×C43C2×D411yescharacteristic
199C42×C43C2×D411yescharacteristic
200C22⋊Dic43—21no—
201(C2×D43)⋊C4—21no—
202(C2×D43)⋊C4—21no—
203(C2×D43)⋊C4—41no—
204(C2×D43)⋊C4—41no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43C2×D411yescharacteristic
208C4⋊Dic43C2×D411yescharacteristic
209Dic43⋊C4—21no—
210Dic43⋊C4—21no—
211C4×Dic43—21no—
212C4×Dic43—21no—
213C4×Dic43—21no—
214#10621877—21no—
215#10621877—21no—
216#10621877—21no—
217#10621877—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8C2×D411yescharacteristic
225C2×C43⋊C8C2×D411yescharacteristic
226C2×C43⋊C8C2×D411yescharacteristic
227C2×C43⋊C8C2×D411yescharacteristic
228D344—24no—
229#10621873—24no—
230C23×C43C2×#4111yescharacteristic
231C22×D43—21no—
232C22×D43—22no—
233C22×D43—41no—
234C22×D43—41no—
235C22×D43—81no—
236C22×D43—81no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—81no—
242C2×C4×C43—81no—
243C2×C4×C43#12111yescharacteristic
244C2×C4×C43#12111yescharacteristic
245C2×C4×C43#12111yescharacteristic
246C2×C4×C43#12111yescharacteristic
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C432−1+411yescharacteristic
252C2×C4×C432−1+411yescharacteristic
253C22⋊D43—41no—
254C22⋊D43—41no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—41no—
259C2×Dic43—81no—
260D172—22no—
261D172—21no—
262D172—21no—
263D172—22no—
264D172—41no—
265D172—41no—
266C4×D43—42no—
267C4×D43—41no—
268C4×D43—41no—
269C4×D43—81no—
270C4×D43—82no—
271C4×D43—82no—
272Dic86—21no—
273Dic86—21no—
274C8×C43—22no—
275C8×C43—41no—
276C8×C43—41no—
277C8×C43—41no—
278C43⋊C8—21no—
279C43⋊C8—21no—
280C43⋊C8—21no—
281C43⋊C8—21no—
282C43⋊C8—41no—
283C43⋊C8—41no—
284#24724—431nomaximal, Sylow
285C22×C43—21no—
286C22×C43—21no—
287C22×C43C2×#12111yescharacteristic
288C22×C43#55211yescharacteristic
289C22×C43#55611yescharacteristic
290C2×D43—42no—
291C2×D43—41no—
292C2×D43—41no—
293C2×D43—41no—
294C2×D43—82no—
295C2×D43—81no—
296C2×D43—81no—
297C2×D43—82no—
298C4×C43—21no—
299C4×C43—21no—
300C4×C43—21no—
301C4×C43—21no—
302C4×C43—81no—
303C4×C43—81no—
304C4×C43#52511yescharacteristic
305C4×C43#53611yescharacteristic
306C4×C43#54711yescharacteristic
307C4×C43#54811yescharacteristic
308Dic43—41no—
309Dic43—41no—
310Dic43—41no—
311Dic43—81no—
312#3080—431no—
313C2×#478—431no—
314C4×AGL(1,ℤ/8)—431no—
315#2925—431no—
316#2079—431no—
317#2078—431no—
318#2051—431no—
319#2051—431no—
320#1998D4311yescharacteristic, complemented
321#1952—431no—
322#1951—431no—
323#1950—431no—
324#1931—431no—
325#1931—431no—
326#1800—431no—
327C2×C43—21no—
328C2×C43—21no—
329C2×C43#241511yescharacteristic
330C2×C43#306711yescharacteristic
331C2×C43#306811yescharacteristic
332D43—81no—
333D43—82no—
334C2×AGL(1,ℤ/8)—431no—
335C2×#125C2×D4311yescharacteristic
336C4×#41—431no—
337C2×C4×D4—431no—
338#479—861no—
339#479—861no—
340#478—861no—
341#478—861no—
342#478—861no—
343#478—861no—
344#478—861no—
345#478—861no—
346#442—861no—
347#440—861no—
348C4×SD16—861no—
349C4×D8—861no—
350#433—861no—
351#433—861no—
352#432—861no—
353#431—861no—
354C2×#108—431no—
355C2×#108—431no—
356#428—431no—
357#428—431no—
358#428—431no—
359C2×#107—431no—
360C2×#106—431no—
361#423—431no—
362#423C2×D4311yescharacteristic
363C2×C4⋊C8—431no—
364#418—431no—
365#417—431no—
366#417—431no—
367#417—431no—
368C2×#102—431no—
369C2×#102—431no—
370C2×#100—431no—
371C2×#100—431no—
372#408—431no—
373#408—431no—
374#405—431no—
375#405—431no—
376C4×M16C2×D4311yescharacteristic
377#343—431no—
378#343—431no—
379#343C2×D4311yescharacteristic
380#343C2×D4311yescharacteristic
381#343C2×D4311yescharacteristic
382#343C2×D4311yescharacteristic
383#341—431no—
384#341—431no—
385C43#2472411yescharacteristic, complemented, Sylow
386C2×#41—431no—
387C22×D4—431no—
388C23×C4—861no—
389AGL(1,ℤ/8)—862no—
390AGL(1,ℤ/8)—862no—
391C2×SD16—861no—
392C2×D8—861no—
393C2×M16—431no—
394C2×M16—431no—
395C2×M16C22×D4311yescharacteristic
396C2×M16C22×D4311yescharacteristic
397C2×M16C22×D4311yescharacteristic
398C2×M16C22×D4311yescharacteristic
399C22×C8—431no—
400C22×C8—431no—
401#125—21no—
402#125—21no—
403#125—21no—
404#125—21no—
405C4×Q8—431no—
406C4×Q8—431no—
407C4×D4—431no—
408C4×D4—431no—
409C4×D4—861no—
410C4×D4—861no—
411C4×D4—861no—
412C4×D4—861no—
413C4×D4—861no—
414C4×D4—861no—
415#117—431no—
416#117—861no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4C22×D4311yescharacteristic
421C2×C4⋊C4C22×D4311yescharacteristic
422C2×C22⋊C4—861no—
423C2×C42—861no—
424C2×C42C22×D4311yescharacteristic
425#108—862no—
426#108—862no—
427#107—861no—
428#107—861no—
429#107—861no—
430#107—861no—
431#107—861no—
432#106—861no—
433#106—861no—
434#106—861no—
435#106—861no—
436#106—861no—
437C4⋊C8—21no—
438C4⋊C8—21no—
439C4⋊C8—431no—
440C4⋊C8—431no—
441C4⋊C8—431no—
442C4⋊C8—431no—
443C4⋊C8—861no—
444C4⋊C8—861no—
445#103—861no—
446#103—861no—
447#103—861no—
448#102—861no—
449#102—861no—
450#102—861no—
451#102—861no—
452#102—861no—
453#102—861no—
454#102—861no—
455#102—861no—
456#102—861no—
457#100—862no—
458#100—862no—
459C22⋊C8—861no—
460C22⋊C8—861no—
461C22⋊C8—861no—
462C22⋊C8—861no—
463#97—21no—
464#97—861no—
465#97—861no—
466C4×C8—21no—
467C4×C8—861no—
468C4×C8—861no—
469C24—861no—
470#41—861no—
471#41—861no—
472#41—861no—
473#41—861no—
474C2×Q8—431no—
475C2×D4—431no—
476C2×D4—432no—
477C2×D4—861no—
478C2×D4—861no—
479C2×D4—861no—
480C2×D4—861no—
481C2×D4—861no—
482C2×D4—861no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—3442no—
490C22×C4—1721no—
491C22×C4—1721no—
492C22×C4#1062189811yescharacteristic
493C22×C4#1062189811yescharacteristic
494C22×C4C23×D4311yescharacteristic
495SD16—864no—
496D8—864no—
497M16—21no—
498M16—21no—
499M16—21no—
500M16—21no—
501M16—21no—
502M16—21no—
503M16—21no—
504M16—861no—
505M16—861no—
506M16—861no—
507M16—861no—
508M16#1062190212yes—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—431no—
514C2×C8—431no—
515C2×C8—431no—
516C2×C8—431no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—861no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—41no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—431no—
532C4⋊C4—431no—
533C4⋊C4—861no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C22⋊C4—861no—
538C22⋊C4—861no—
539C22⋊C4—861no—
540C22⋊C4—1721no—
541C22⋊C4—1721no—
542C42—861no—
543C42—861no—
544C42—861no—
545C42D4×D4311yescharacteristic
546C42D4×D4311yescharacteristic
547C42D4×D4311yescharacteristic
548C42D4×D4311yescharacteristic
549C23—862no—
550C23—861no—
551C23—3441no—
552C23—3441no—
553C23—1721no—
554C23—1721no—
555C23C2×#1062189811yescharacteristic
556Q8—861no—
557Q8—861no—
558D4—862no—
559D4—861no—
560D4—862no—
561D4—861no—
562D4—1721no—
563D4—1721no—
564D4—1721no—
565D4—1721no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—81no—
571C2×C4—81no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—3442no—
576C2×C4—3442no—
577C2×C4—3441no—
578C2×C4—3441no—
579C2×C4—1722no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4#1306329811yescharacteristic
584C2×C4#1306329811yescharacteristic
585C2×C4#1306329811yescharacteristic
586C2×C4#1306329811yescharacteristic
587C2×C4C2×D4×D4311yescharacteristic
588C2×C4C2×D4×D4311yescharacteristic
589C2×C4#41×D4311yescharacteristic
590C2×C4C2×#1062190211yescharacteristic
591C2×C4#1306337211yescharacteristic
592C2×C4#1306337311yescharacteristic
593C8—22no—
594C8—41no—
595C8—41no—
596C8—41no—
597C8—861no—
598C8—861no—
599C8—861no—
600C8—861no—
601C8—1721no—
602C8—1721no—
603C22—21no—
604C22—21no—
605C22—3442no—
606C22—3442no—
607C22—3441no—
608C22—3441no—
609C22—1721no—
610C22—1721no—
611C22—1721no—
612C22—1722no—
613C22C2×#1306329811yescharacteristic
614C22#1458359011yescharacteristic
615C22#1458362211yescharacteristic
616C4—21no—
617C4—21no—
618C4—21no—
619C4—21no—
620C4—81no—
621C4—81no—
622C4—3441no—
623C4—1721no—
624C4—1721no—
625C4—1721no—
626C4#1458341211yescharacteristic
627C4#1458347211yescharacteristic
628C4#1458355211yescharacteristic
629C4#1458355711yescharacteristic
630C2—21no—
631C2—21no—
632C2—3442no—
633C2—3441no—
634C2#1913802711yescharacteristic
635C2#1914431411yescharacteristic
636C2#1914432611yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1998C2
socleC22×C43C2×#121
prime radicalC2×#13063353C22
hypercenter#1998D43
hypocenterC43#24724
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1998

Complements

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

NH ≅ G/Ntype
1. #19144413C2semidirect
2. C2×#14583196C2semidirect
4. #19143263C2semidirect
5. #19136044C2semidirect
6. #19136039C2semidirect
9. #19135379C2semidirect
10. #19135374C2semidirect
11. #19135370C2semidirect
12. #19135255C2semidirect
13. #19135255C2semidirect
14. #19134584C2semidirect
15. C43×#1998C2semidirect
320. #1998D43semidirect
385. C43#24724semidirect

Maximal subgroups

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

subgroupindex
#191444132
C2×#145831962
C4×#130633532
#191432632
#191360442
#191360392
#191358902
#191353792
#191353742
#191353702
#191352552
#191345842
C43×#19982
#2472443