Finite Group Databasebeta

← #25160025

Subgroups — #25160025

Order 11008.

740 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144442C211yesmaximal, characteristic, complemented
2#19143427C211yesmaximal, characteristic
3#19143192C211yesmaximal, characteristic, complemented
4#19136121C211yesmaximal, characteristic, complemented
5#19136100C211yesmaximal, characteristic, complemented
6#19135955C211yesmaximal, characteristic, complemented
7#19135937C211yesmaximal, characteristic, complemented
8#19135377C211yesmaximal, characteristic, complemented
9#19135196C211yesmaximal, characteristic, complemented
10#19135106C211yesmaximal, characteristic
11#19134968C211yesmaximal, characteristic
12#19134869C211yesmaximal, characteristic, complemented
13#19134818C211yesmaximal, characteristic, complemented
14#19134805C211yesmaximal, characteristic, complemented
15C43×#3081C211yesmaximal, characteristic, complemented
16C2×#13063351C2211yescharacteristic
17C2×#13063331C2211yescharacteristic
18#14583379C2211yescharacteristic
19#14583379C2211yescharacteristic
20#14583203—21no—
21#14583196—21no—
22#14583191—21no—
23#14583176—21no—
24#14583009—21no—
25#14582999—21no—
26C4×#10621883—21no—
27C4×#10621882—21no—
28C2×#13063260C2211yescharacteristic
29#14582942C2211yescharacteristic
30#14582942C2211yescharacteristic
31#14582942C2211yescharacteristic
32#14582942C2211yescharacteristic
33#14582938—21no—
34#14582938—21no—
35#14582936—21no—
36C2×#13063259C2211yescharacteristic
37C2×#13063258C2211yescharacteristic
38#107×D43—21no—
39#14582926C2211yescharacteristic
40C2×#13063251C2211yescharacteristic
41#14582898C2211yescharacteristic
42#14582893C2211yescharacteristic
43C2×#13063246C2211yescharacteristic
44C2×#13063242C2211yescharacteristic
45#14582855C2211yescharacteristic
46#14582802C2211yescharacteristic
47#14582768C2211yescharacteristic
48#14582668C2211yescharacteristic
49#14582667C2211yescharacteristic
50#14582667C2211yescharacteristic
51#14582664C2211yescharacteristic
52#14582658C2211yescharacteristic
53#14582658C2211yescharacteristic
54#14582658C2211yescharacteristic
55#14582653C2211yescharacteristic
56C43×#544C2211yescharacteristic
57C43×#518C2211yescharacteristic
58C43×#478—21no—
59C43×#478—21no—
60C43×#476—21no—
61C43×#474—21no—
62C43×#428C2211yescharacteristic
63C43×#427C2211yescharacteristic
64C43×#424C2211yescharacteristic
65C43×#418C2211yescharacteristic
66C2×#102×C43C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68#13063351—22no—
69#13063351Q814yescomplemented
70C2×#10621883—21no—
71C2×#10621882—21no—
72#13063331—22no—
73#13063331—22no—
74C2×#10621877C2311yescharacteristic
75C2×#10621877C2311yescharacteristic
76C2×#10621877C2311yescharacteristic
77C2×#10621872—21no—
78C22×C43⋊C8C2311yescharacteristic
79C2×C8×D43—21no—
80C4×Dic86—21no—
81C4×Dic86—21no—
82C4×D172—21no—
83C4×D172—21no—
84(C22⋊D43)⋊C4—41no—
85(C22⋊D43)⋊C4—41no—
86#13063283—21no—
87#13063283—21no—
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×Dic43⋊C4—41no—
91C4⋊C4×D43—21no—
92C4⋊C4×D43—21no—
93C2×C22⋊Dic43—41no—
94C2×C4×Dic43C2311yescharacteristic
95#13063260—22no—
96#13063259—21no—
97#13063259—21no—
98#13063258—21no—
99#13063258—21no—
100#13063258—21no—
101#13063258—21no—
102#13063258—21no—
103#13063258—21no—
104#13063256—21no—
105#13063256—21no—
106#13063256—21no—
107#13063256—21no—
108C4⋊(C43⋊C8)—21no—
109C4⋊(C43⋊C8)—21no—
110#13063251—22no—
111#13063248—21no—
112#13063248D411yescharacteristic
113#13063248D411yescharacteristic
114#13063246—21no—
115#13063246—21no—
116#13063245—21no—
117#13063245D411yescharacteristic
118#13063245D411yescharacteristic
119#13063242—22no—
120#13063236—21no—
121C4×C43⋊C8—21no—
122C22×D4×C43C2311yescharacteristic
123C2×M16×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125C4⋊Q8×C43—21no—
126C4⋊Q8×C43—21no—
127#125×C43—21no—
128#125×C43—21no—
129C22⋊Q8×C43—41no—
130C4×D4×C43—21no—
131C4×D4×C43—21no—
132C4×D4×C43—21no—
133C4×D4×C43—21no—
134#117×C43C2311yescharacteristic
135#117×C43C2311yescharacteristic
136#117×C43C2311yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C22⋊C4×C43—41no—
139#107×C43—21no—
140#107×C43D411yescharacteristic
141#107×C43D411yescharacteristic
142#106×C43—21no—
143#106×C43D411yescharacteristic
144#106×C43D411yescharacteristic
145C4⋊C8×C43—21no—
146C4⋊C8×C43—21no—
147#102×C43—21no—
148#102×C43—21no—
149#102×C43—21no—
150#102×C43—21no—
151C24×C43—21no—
152C2×Q8×C43—41no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43C2×Q812yes—
159C22×C4×C43—21no—
160C22×C4×C43—41no—
161C22×C4×C43—41no—
162C22×C4×C43C2411yescharacteristic
163C2×C22⋊D43—21no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167#10621898—21no—
168#10621898—21no—
169#10621898C2×Q812yes—
170#10621898#4112yes—
171C2×D172C2×D411yescharacteristic
172C2×C4×D43—21no—
173C2×C4×D43—41no—
174C2×C4×D43—41no—
175C2×Dic86C2×D411yescharacteristic
176M16×C43—21no—
177M16×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43C2×D411yescharacteristic
182C2×C8×C43C2×D411yescharacteristic
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—41no—
186C4⋊C4×C43—41no—
187C4⋊C4×C43—41no—
188C4⋊C4×C43C2×D411yescharacteristic
189C4⋊C4×C43C2×D411yescharacteristic
190C4⋊C4×C43C2×D411yescharacteristic
191C4⋊C4×C43C2×D411yescharacteristic
192C4⋊C4×C43C2×D411yescharacteristic
193C4⋊C4×C43C2×D411yescharacteristic
194C22⋊C4×C43—21no—
195C22⋊C4×C43—21no—
196C22⋊C4×C43—21no—
197C22⋊C4×C43—41no—
198C22⋊C4×C43—41no—
199C42×C43—21no—
200C42×C43—21no—
201C42×C43—21no—
202C22⋊Dic43—82no—
203#10621883—24no—
204#10621882—24no—
205(C2×D43)⋊C4—41no—
206(C2×D43)⋊C4—41no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211Dic43⋊C4—41no—
212Dic43⋊C4—41no—
213Dic43⋊C4—82no—
214C4×Dic43—21no—
215C4×Dic43—21no—
216C4×Dic43—41no—
217C4×Dic43—41no—
218#10621877—21no—
219#10621877—21no—
220#10621877—21no—
221#10621877—21no—
222#10621877C2×Q812yes—
223#10621877#4112yes—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8C2×D411yescharacteristic
230C2×C43⋊C8C2×D411yescharacteristic
231#10621872—24no—
232C8×D43—24no—
233C23×C43—22no—
234C23×C43—41no—
235C23×C43—41no—
236C23×C43—81no—
237C23×C43—81no—
238C23×C43H(5,𝔽2)11yescharacteristic
239C22×D43—21no—
240Q8×C43—161no—
241D4×C43—22no—
242D4×C43—22no—
243D4×C43—41no—
244D4×C43—41no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—41no—
252C2×C4×C43—81no—
253C2×C4×C43—161no—
254C2×C4×C43—161no—
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43C22×Q811yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43C2×#4111yescharacteristic
260C2×C4×C432−1+411yescharacteristic
261C22⋊D43—22no—
262C22⋊D43—22no—
263C2×Dic43—21no—
264C2×Dic43—22no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—81no—
270C2×Dic43—81no—
271D172—21no—
272D172C22⋊Q812yes—
273C4×D43—22no—
274C4×D43—22no—
275C4×D43—161no—
276C4×D43—161no—
277Dic86—21no—
278Dic86C22⋊Q812yes—
279C8×C43—21no—
280C8×C43—21no—
281C8×C43—41no—
282C43⋊C8—22no—
283C43⋊C8—22no—
284C43⋊C8—21no—
285C43⋊C8—21no—
286C43⋊C8—41no—
287#26400—431nomaximal, Sylow
288C22×C43—21no—
289C22×C43—21no—
290C22×C43—42no—
291C22×C43—82no—
292C22×C43—81no—
293C22×C43—81no—
294C22×C43—161no—
295C22×C43#53911yescharacteristic
296C22×C43D4211yescharacteristic
297C22×C43#55411yescharacteristic
298C2×D43—22no—
299C2×D43—41no—
300C2×D43—41no—
301C4×C43—41no—
302C4×C43—41no—
303C4×C43—41no—
304C4×C43—41no—
305C4×C43—41no—
306C4×C43—41no—
307C4×C43—81no—
308C4×C43C2×C22⋊Q811yescharacteristic
309C4×C43#52511yescharacteristic
310C4×C43#54711yescharacteristic
311C4×C43D4×Q811yescharacteristic
312Dic43—22no—
313Dic43—42no—
314Dic43—81no—
315Dic43—81no—
316#3083—431no—
317#3081D4311yescharacteristic, complemented
318#2946—431no—
319#2913—431no—
320#2093—431no—
321#2089—431no—
322#2063—431no—
323#2060—431no—
324#1952—431no—
325#1922—431no—
326#1907—431no—
327#1883—431no—
328#1866—431no—
329#1859—431no—
330#1856—431no—
331C2×C43—21no—
332C2×C43—21no—
333C2×C43—82no—
334C2×C43#244911yescharacteristic
335C2×C43#328911yescharacteristic
336C2×C43#329211yescharacteristic
337D43—42no—
338C2×AGL(1,ℤ/8)—431no—
339C2×#131—431no—
340#544C2×D4311yescharacteristic
341#520—431no—
342#520—431no—
343#518C2×D4311yescharacteristic
344#479—861no—
345#478—21no—
346#478—21no—
347#478—861no—
348#477—861no—
349#476—21no—
350#474—21no—
351#474—861no—
352#442—861no—
353#440—861no—
354C4×SD16—861no—
355C4×D8—861no—
356C2×#108—431no—
357#428—431no—
358#428—431no—
359#428—431no—
360#428—431no—
361#428—861no—
362#428—861no—
363#428C2×D4311yescharacteristic
364#427—861no—
365#427C2×D4311yescharacteristic
366C2×#107—431no—
367C2×#107—431no—
368C2×#107—861no—
369#424—431no—
370#424C2×D4311yescharacteristic
371C2×#104—431no—
372#418C2×D4311yescharacteristic
373#417—431no—
374#416—431no—
375C2×#102—431no—
376C2×#102C2×D4311yescharacteristic
377C2×#100—431no—
378#405—431no—
379#390—431no—
380#384—431no—
381#343—431no—
382#343—431no—
383#343—431no—
384#341—431no—
385#339—431no—
386#339—431no—
387#339—431no—
388#336—431no—
389C43#2640011yescharacteristic, complemented, Sylow
390C2×#41—431no—
391C22×D4C22×D4311yescharacteristic
392AGL(1,ℤ/8)—434no—
393AGL(1,ℤ/8)—862no—
394C2×SD16—861no—
395C2×D8—861no—
396#131—862no—
397#131—862no—
398C2×M16—431no—
399C2×M16—431no—
400C2×M16—431no—
401C2×M16—861no—
402C2×M16C22×D4311yescharacteristic
403C22×C8—431no—
404C22×C8—861no—
405C22×C8C22×D4311yescharacteristic
406C4⋊Q8—21no—
407C4⋊Q8—21no—
408#125—21no—
409#125—21no—
410C22⋊Q8—41no—
411C4×Q8—861no—
412C4×Q8—861no—
413C4×D4—21no—
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—21no—
417C4×D4—861no—
418C4×D4—861no—
419C4×D4—1721no—
420C4×D4—1721no—
421#117—861no—
422#117—861no—
423#117C22×D4311yescharacteristic
424#117C22×D4311yescharacteristic
425#117C22×D4311yescharacteristic
426C2×C4⋊C4—431no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—1721no—
431C2×C4⋊C4C22×D4311yescharacteristic
432C2×C22⋊C4—41no—
433C2×C22⋊C4—1721no—
434C2×C42—431no—
435#108—862no—
436#107—21no—
437#107—861no—
438#107—861no—
439#107—861no—
440#107—861no—
441#107—861no—
442#107—861no—
443#107—861no—
444#107—861no—
445#107C22⋊D4311yescharacteristic
446#107C22⋊D4311yescharacteristic
447#106—21no—
448#106—861no—
449#106—861no—
450#106—861no—
451#106—861no—
452#106C22⋊D4311yescharacteristic
453#106C22⋊D4311yescharacteristic
454C4⋊C8—21no—
455C4⋊C8—21no—
456C4⋊C8—861no—
457C4⋊C8—861no—
458#104—862no—
459#103—431no—
460#103—431no—
461#103—861no—
462#102—21no—
463#102—21no—
464#102—21no—
465#102—21no—
466#102—431no—
467#102—431no—
468#102—861no—
469#102—861no—
470#102—861no—
471#100—862no—
472#97—861no—
473C4×C8—861no—
474C24—21no—
475#41—432no—
476#41—432no—
477#41—861no—
478#41—861no—
479C2×Q8—41no—
480C2×Q8—431no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—431no—
487C2×D4—861no—
488C2×D4Q8×D4312yes—
489C22×C4—21no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—1721no—
497C22×C4—1721no—
498C22×C4C23×D4311yescharacteristic
499SD16—864no—
500D8—864no—
501M16—21no—
502M16—21no—
503M16—432no—
504M16—432no—
505M16—864no—
506M16—861no—
507M16—861no—
508M16—861no—
509M16—861no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—431no—
514C2×C8—431no—
515C2×C8—864no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8C2×C22⋊D4311yescharacteristic
522C2×C8C2×C22⋊D4311yescharacteristic
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—41no—
526C4⋊C4—41no—
527C4⋊C4—41no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—3442no—
533C4⋊C4—1721no—
534C4⋊C4—1721no—
535C4⋊C4D4×D4311yescharacteristic
536C4⋊C4D4×D4311yescharacteristic
537C4⋊C4C2×C22⋊D4311yescharacteristic
538C4⋊C4C2×C22⋊D4311yescharacteristic
539C4⋊C4C2×C22⋊D4311yescharacteristic
540C4⋊C4C2×C22⋊D4311yescharacteristic
541C22⋊C4—21no—
542C22⋊C4—21no—
543C22⋊C4—21no—
544C22⋊C4—41no—
545C22⋊C4—41no—
546C22⋊C4—3442no—
547C22⋊C4—1721no—
548C22⋊C4—1721no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—861no—
553C42—861no—
554C42—1721no—
555C42—1721no—
556C23—22no—
557C23—41no—
558C23—41no—
559C23—81no—
560C23—81no—
561C23—861no—
562C23#1306337011yescharacteristic
563Q8—161no—
564Q8—432no—
565Q8—861no—
566D4—22no—
567D4—22no—
568D4—41no—
569D4—41no—
570D4—432no—
571D4—862no—
572D4—862no—
573D4—861no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—41no—
581C2×C4—81no—
582C2×C4—161no—
583C2×C4—161no—
584C2×C4—861no—
585C2×C4—862no—
586C2×C4—862no—
587C2×C4—862no—
588C2×C4—3441no—
589C2×C4—3441no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—6881no—
595C2×C4—6881no—
596C2×C4C2×D4×D4311yescharacteristic
597C2×C4C22×C22⋊D4311yescharacteristic
598C2×C4C2×Q8×D4311yescharacteristic
599C2×C4#41×D4311yescharacteristic
600C2×C4#41×D4311yescharacteristic
601C2×C4#1306337311yescharacteristic
602C8—21no—
603C8—21no—
604C8—41no—
605C8—862no—
606C8—862no—
607C8—861no—
608C8—861no—
609C8—1721no—
610C22—21no—
611C22—21no—
612C22—42no—
613C22—82no—
614C22—81no—
615C22—81no—
616C22—161no—
617C22—862no—
618C22—1721no—
619C22—1721no—
620C22#1458349511yescharacteristic
621C22D4×C22⋊D4311yescharacteristic
622C22#1458360311yescharacteristic
623C4—41no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—41no—
628C4—41no—
629C4—81no—
630C4—862no—
631C4—3441no—
632C4—3441no—
633C4—1722no—
634C4C22⋊Q8×D4311yescharacteristic
635C4#1458340611yescharacteristic
636C4#1458355111yescharacteristic
637C4Q8×C22⋊D4311yescharacteristic
638C2—21no—
639C2—21no—
640C2—82no—
641C2—1722no—
642C2#1913840111yescharacteristic
643C2#1914636811yescharacteristic
644C2#1914639211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#3081C2
socleC22×C43D42
prime radicalC2×#13063351C22
hypercenter#3081D43
hypocenterC43#26400
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #3081

Complements

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

NH ≅ G/Ntype
1. #19144442C2semidirect
3. #19143192C2semidirect
4. #19136121C2semidirect
5. #19136100C2semidirect
6. #19135955C2semidirect
7. #19135937C2semidirect
8. #19135377C2semidirect
9. #19135196C2semidirect
12. #19134869C2semidirect
13. #19134818C2semidirect
14. #19134805C2semidirect
15. C43×#3081C2semidirect
69. #13063351Q8semidirect
317. #3081D43semidirect
389. C43#26400semidirect

Maximal subgroups

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

subgroupindex
#191444422
#191434272
#191431922
#191361212
#191361002
#191359552
#191359372
#191353772
#191351962
#191351062
#191349682
#191348692
#191348182
#191348052
C43×#30812
#2640043