Finite Group Databasebeta

← #25110500

Subgroups — #25110500

Order 11008.

796 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#19145072C211yesmaximal, characteristic
2#19143512C211yesmaximal, characteristic, complemented
3#19143453C211yesmaximal, characteristic, complemented
4#19135498C211yesmaximal, characteristic, complemented
5#19135129C211yesmaximal, characteristic, complemented
6#19135124C211yesmaximal, characteristic, complemented
7#19135120C211yesmaximal, characteristic, complemented
8#19135115C211yesmaximal, characteristic, complemented
9#19135092C211yesmaximal, characteristic, complemented
10#19135085C211yesmaximal, characteristic, complemented
11#19135073C211yesmaximal, characteristic, complemented
12#19135066C211yesmaximal, characteristic, complemented
13#19134718C211yesmaximal, characteristic, complemented
14#19134350C211yesmaximal, characteristic, complemented
15C43×#1976C211yesmaximal, characteristic, complemented
16C2×#13063355C2211yescharacteristic
17C2×#13063350C2211yescharacteristic
18C22×#10621873C2211yescharacteristic
19#14583666C2211yescharacteristic
20#14583666C2211yescharacteristic
21#14583470C2211yescharacteristic
22#14583463C2211yescharacteristic
23#14583376C2211yescharacteristic
24#14583373C2211yescharacteristic
25#14583292C412yescomplemented
26#14583287C412yescomplemented
27#14583280C412yescomplemented
28#14583270C412yescomplemented
29#14583021—22no—
30#14583016—22no—
31#14582998—22no—
32#14582986—22no—
33C2×#13063261C2211yescharacteristic
34#14582916C2211yescharacteristic
35#14582916C2211yescharacteristic
36#14582907C2211yescharacteristic
37#14582907C2211yescharacteristic
38#14582903C2211yescharacteristic
39#14582903C2211yescharacteristic
40C2×#13063243C2211yescharacteristic
41C2×#13063241C2211yescharacteristic
42#14582854C2211yescharacteristic
43#14582854C2211yescharacteristic
44#14582669C2211yescharacteristic
45#14582669C2211yescharacteristic
46C43⋊#338C2211yescharacteristic
47#14582656C2211yescharacteristic
48#14582655C2211yescharacteristic
49#14582655C2211yescharacteristic
50#14582655C2211yescharacteristic
51#14582655C2211yescharacteristic
52C2×#135×C43C2211yescharacteristic
53C43×#427C2211yescharacteristic
54C43×#421C2211yescharacteristic
55C43×#421C2211yescharacteristic
56C43×#410C2211yescharacteristic
57C43×#410C2211yescharacteristic
58C43×#405C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×D172C2311yescharacteristic
61#13063355—41no—
62#13063355—41no—
63#13063350—41no—
64#13063350—41no—
65C2×#10621885C2×C412yescomplemented
66C2×#10621873—21no—
67C2×#10621873—21no—
68C2×#10621873—21no—
69C2×#10621873—21no—
70C2×#10621873C2×C412yes—
71C2×#10621873C2×C412yes—
72C2×#10621883C2×C412yescomplemented
73C2×#10621884C2×C412yes—
74C2×#10621882C2×C412yes—
75#13063332—22no—
76#13063332—22no—
77#13063332—41no—
78#13063332—41no—
79C2×#10621877—41no—
80C2×#10621877—41no—
81C2×#10621877C2311yescharacteristic
82C2×#10621877C2311yescharacteristic
83C2×#10621877C2311yescharacteristic
84C2×#10621877C2311yescharacteristic
85#13063323C2×C412yescomplemented
86#13063321C2×C412yes—
87#13063314C2×C412yes—
88#13063312C2×C412yescomplemented
89#13063306—41no—
90#13063304—41no—
91#13063299—41no—
92#13063293—41no—
93C4×Dic86—41no—
94#13063290—22no—
95C4×D172—41no—
96#13063287—22no—
97#13063284C2311yescharacteristic
98#13063284C2311yescharacteristic
99#13063281—41no—
100C22⋊C4×D43—41no—
101#13063261—21no—
102#13063261—21no—
103#13063252—22no—
104#13063252—22no—
105#13063248—22no—
106#13063248—41no—
107#13063245—22no—
108#13063245—41no—
109#13063243—41no—
110#13063241—41no—
111#13063235C2×C412yescomplemented
112#13063235D412yescomplemented
113C8×Dic43C2×C412yescomplemented
114C8×Dic43D412yescomplemented
115C2×#41×C43C2311yescharacteristic
116C2×#41×C43C2311yescharacteristic
117#135×C43—21no—
118#135×C43—21no—
119#135×C43—21no—
120#135×C43—21no—
121C2×Q16×C43C2×C411yescharacteristic, complemented
122C2×SD16×C43C2×C411yescharacteristic, complemented
123C2×SD16×C43C2×C411yescharacteristic, complemented
124C2×D8×C43C2×C411yescharacteristic, complemented
125C2×M16×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127#117×C43C2311yescharacteristic
128#117×C43C2311yescharacteristic
129#117×C43C2311yescharacteristic
130#107×C43—21no—
131#106×C43—21no—
132#104×C43—41no—
133#104×C43—41no—
134#99×C43—41no—
135#99×C43—41no—
136#97×C43—21no—
137C4×C8×C43—21no—
138C23×D43—21no—
139#41×C43—21no—
140#41×C43—21no—
141#41×C43—21no—
142#41×C43—21no—
143#41×C43—21no—
144#41×C43—21no—
145#41×C43—21no—
146#41×C43—21no—
147C2×Q8×C43C22×C411yescharacteristic
148C2×Q8×C43C22×C411yescharacteristic
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43C22×C411yescharacteristic
152C2×D4×C43C22×C411yescharacteristic
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43C2411yescharacteristic
156C2×C22⋊D43—42no—
157C22×Dic43—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172C22×C412yes—
164C2×C4×D43—42no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86C22×C412yes—
171Q16×C43—21no—
172Q16×C43—21no—
173SD16×C43—21no—
174SD16×C43—21no—
175SD16×C43—21no—
176SD16×C43—21no—
177D8×C43—21no—
178D8×C43—21no—
179M16×C43—21no—
180M16×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43C22×C411yescharacteristic
183C2×C8×C43C22×C411yescharacteristic
184C2×C8×C43C2×D411yescharacteristic
185C2×C8×C43C2×D411yescharacteristic
186C2×C8×C43#4111yescharacteristic
187C2×C8×C43#4111yescharacteristic
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C22⋊C4×C43—21no—
192C22⋊C4×C43—21no—
193C22⋊C4×C43—21no—
194C42×C43—21no—
195C42×C43—21no—
196C42×C43—21no—
197C22⋊Dic43—21no—
198C22⋊Dic43—21no—
199C22⋊Dic43—42no—
200#10621885—42no—
201#10621884—42no—
202#10621883—42no—
203#10621882—42no—
204(C2×D43)⋊C4—42no—
205(C2×D43)⋊C4—42no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208Dic43⋊C4—42no—
209Dic43⋊C4—42no—
210C4×Dic43—42no—
211C4×Dic43C22×C412yes—
212C4×Dic43C2×D412yes—
213#10621877—21no—
214#10621877—21no—
215#10621877—21no—
216#10621877—21no—
217#10621877—21no—
218#10621877—21no—
219#10621877—21no—
220#10621877—21no—
221#10621877—42no—
222#10621877—42no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—42no—
226C2×C43⋊C8—42no—
227C2×C43⋊C8C22×C412yes—
228C2×C43⋊C8C2×D412yes—
229#10621873—22no—
230#10621873—22no—
231#10621873—22no—
232#10621873—22no—
233C23×C43—21no—
234C23×C43—21no—
235C23×C43H(5,𝔽2)11yescharacteristic
236C22×D43—22no—
237C22×D43—41no—
238C22×D43—41no—
239C22×D43—161no—
240Q8×C43—21no—
241Q8×C43—21no—
242Q8×C43—21no—
243Q8×C43—21no—
244D4×C43—21no—
245D4×C43—21no—
246D4×C43—21no—
247D4×C43—21no—
248D4×C43—41no—
249D4×C43—41no—
250D4×C43—41no—
251D4×C43—41no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43C23×C411yescharacteristic
262C2×C4×C43C22×D411yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C43H(5,𝔽2)11yescharacteristic
265C2×C4×C43H(5,𝔽2)11yescharacteristic
266C2×C4×C43H(5,𝔽2)11yescharacteristic
267C22⋊D43—162no—
268C2×Dic43—22no—
269C2×Dic43—22no—
270C2×Dic43—22no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273D172—22no—
274D172—22no—
275D172—41no—
276D172—41no—
277C4×D43—162no—
278Dic86—22no—
279Dic86—22no—
280Dic86—41no—
281Dic86—41no—
282C8×C43—41no—
283C8×C43C4×D411yescharacteristic
284C8×C43C4×D411yescharacteristic
285C8×C43C4×D411yescharacteristic
286C8×C43C4×D411yescharacteristic
287C43⋊C8—22no—
288C43⋊C8—22no—
289C43⋊C8—41no—
290C43⋊C8—41no—
291#22284—431nomaximal, Sylow
292C22×C43—41no—
293C22×C43—41no—
294C22×C43—41no—
295C22×C43—81no—
296C22×C43—81no—
297C22×C43#51811yescharacteristic
298C22×C43#53511yescharacteristic
299C22×C43#54011yescharacteristic
300C2×D43—42no—
301C2×D43—82no—
302C2×D43—82no—
303C2×D43—161no—
304C4×C43—41no—
305C4×C43—41no—
306C4×C43—81no—
307C4×C43—81no—
308C4×C43—81no—
309C4×C43C2×C4×D411yescharacteristic
310C4×C43#51811yescharacteristic
311C4×C43#53511yescharacteristic
312C4×C43#54011yescharacteristic
313Dic43—42no—
314Dic43—42no—
315Dic43—42no—
316#3154—431no—
317#2957—431no—
318#2949—431no—
319#1977—431no—
320#1976D4311yescharacteristic, complemented
321#1912—431no—
322#1911—431no—
323#1910—431no—
324#1909—431no—
325#1905—431no—
326#1904—431no—
327#1903—431no—
328#1902—431no—
329#1833—431no—
330#1747—431no—
331C2×C43—21no—
332C2×C43—21no—
333C2×C43—21no—
334C2×C43—81no—
335C2×C43—81no—
336C2×C43#232811yescharacteristic
337D43—82no—
338C2×#137—431no—
339C2×AGL(1,ℤ/8)—431no—
340C2×#135C2×D4311yescharacteristic
341C22×SD16—431no—
342#568—431no—
343#568—431no—
344#536—431no—
345#535—431no—
346#519—431no—
347#518—431no—
348#497—432no—
349#496—432no—
350#495—432no—
351#492—432no—
352#444—862no—
353#443—862no—
354#440—862no—
355C4×SD16—862no—
356C2×#108—431no—
357#427C2×D4311yescharacteristic
358#421—431no—
359#421—431no—
360#421C2×D4311yescharacteristic
361#421C2×D4311yescharacteristic
362#419—431no—
363#419—431no—
364#418—431no—
365#418—431no—
366C2×#101—431no—
367C2×#100—431no—
368#410C2×D4311yescharacteristic
369#410C2×D4311yescharacteristic
370#405—431no—
371#405—431no—
372#405C2×D4311yescharacteristic
373#344—431no—
374#344—431no—
375#338—431no—
376H(3,ℤ/4)—431no—
377H(3,ℤ/4)—431no—
378H(3,ℤ/4)—431no—
379H(3,ℤ/4)—431no—
380H(3,ℤ/4)—431no—
381C43#2228411yescharacteristic, complemented, Sylow
382C2×#41C22×D4311yescharacteristic
383C2×#41C22×D4311yescharacteristic
384C22×Q8—431no—
385C22×D4—431no—
386#137—1721no—
387#137—1721no—
388AGL(1,ℤ/8)—1721no—
389AGL(1,ℤ/8)—1721no—
390#135—21no—
391#135—21no—
392#135—21no—
393#135—21no—
394C2×Q16—432no—
395C2×Q16C4×D4311yescharacteristic, complemented
396C2×SD16—432no—
397C2×SD16—432no—
398C2×SD16—432no—
399C2×SD16—432no—
400C2×SD16—861no—
401C2×SD16—861no—
402C2×SD16—861no—
403C2×SD16—861no—
404C2×SD16C4×D4311yescharacteristic, complemented
405C2×SD16C4×D4311yescharacteristic, complemented
406C2×D8—432no—
407C2×D8C4×D4311yescharacteristic, complemented
408#131—862no—
409#131—862no—
410#131—1721no—
411#131—1721no—
412C2×M16—431no—
413C2×M16—431no—
414C2×M16—431no—
415C2×M16—431no—
416C2×M16—1721no—
417C2×M16—1721no—
418C2×M16C22×D4311yescharacteristic
419C22×C8C22×D4311yescharacteristic
420C4⋊Q8—432no—
421#127—432no—
422#124—432no—
423#124—432no—
424#123—1721no—
425C22⋊Q8—1721no—
426#121—1721no—
427#120—1721no—
428C4×Q8—862no—
429C4×Q8—1721no—
430C4×D4—862no—
431C4×D4—1721no—
432#117—431no—
433#117—431no—
434#117—1721no—
435#117C22×D4311yescharacteristic
436#117C22×D4311yescharacteristic
437#117C22×D4311yescharacteristic
438C2×C22⋊C4—1721no—
439#108—861no—
440#108—861no—
441#107—21no—
442#106—21no—
443#104—41no—
444#104—41no—
445#104—862no—
446#104—862no—
447#103—862no—
448#103—1721no—
449#102—862no—
450#102—1721no—
451#101—1721no—
452#100—1721no—
453#99—41no—
454#99—41no—
455#97—21no—
456#97—432no—
457#97—432no—
458C4×C8—21no—
459C4×C8—432no—
460C4×C8—432no—
461C24—861no—
462#41—21no—
463#41—21no—
464#41—21no—
465#41—21no—
466#41—21no—
467#41—21no—
468#41—21no—
469#41—21no—
470C2×Q8—432no—
471C2×Q8—861no—
472C2×Q8—861no—
473C2×Q8—861no—
474C2×Q8—861no—
475C2×Q8—861no—
476C2×Q8C2×C4×D4311yescharacteristic
477C2×Q8C2×C4×D4311yescharacteristic
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—432no—
481C2×D4—861no—
482C2×D4—861no—
483C2×D4—861no—
484C2×D4—861no—
485C2×D4—861no—
486C2×D4—1722no—
487C2×D4C2×C4×D4311yescharacteristic
488C2×D4C2×C4×D4311yescharacteristic
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—861no—
492C22×C4—1722no—
493C22×C4C23×D4311yescharacteristic
494Q16—21no—
495Q16—21no—
496Q16—1722no—
497SD16—21no—
498SD16—21no—
499SD16—21no—
500SD16—21no—
501SD16—862no—
502SD16—862no—
503SD16—862no—
504SD16—862no—
505SD16—1722no—
506SD16—1722no—
507D8—21no—
508D8—21no—
509D8—1722no—
510M16—21no—
511M16—21no—
512M16—861no—
513M16—861no—
514M16—861no—
515M16—861no—
516M16—861no—
517M16—861no—
518M16—861no—
519M16—861no—
520M16—1722no—
521M16—1722no—
522C2×C8—21no—
523C2×C8—432no—
524C2×C8—432no—
525C2×C8—861no—
526C2×C8—861no—
527C2×C8—1722no—
528C2×C8—1722no—
529C2×C8C2×C4×D4311yescharacteristic
530C2×C8C2×C4×D4311yescharacteristic
531C2×C8D4×D4311yescharacteristic
532C2×C8D4×D4311yescharacteristic
533C2×C8#1062190011yescharacteristic
534C2×C8#1062190011yescharacteristic
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—861no—
539C4⋊C4—861no—
540C4⋊C4—1722no—
541C4⋊C4—1722no—
542C22⋊C4—21no—
543C22⋊C4—21no—
544C22⋊C4—21no—
545C22⋊C4—861no—
546C22⋊C4—861no—
547C22⋊C4—1722no—
548C22⋊C4—1722no—
549C22⋊C4—1722no—
550C42—21no—
551C42—21no—
552C42—21no—
553C42—432no—
554C42—432no—
555C42—1722no—
556C23—21no—
557C23—21no—
558C23—862no—
559C23—1721no—
560C23—1721no—
561C23—6881no—
562C23#1306337011yescharacteristic
563Q8—21no—
564Q8—21no—
565Q8—21no—
566Q8—21no—
567Q8—862no—
568Q8—862no—
569Q8—1721no—
570Q8—1721no—
571D4—21no—
572D4—21no—
573D4—21no—
574D4—21no—
575D4—41no—
576D4—41no—
577D4—41no—
578D4—41no—
579D4—862no—
580D4—862no—
581D4—1721no—
582D4—1721no—
583D4—6882no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—862no—
594C2×C4—862no—
595C2×C4—862no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—6882no—
599C2×C4C22×C4×D4311yescharacteristic
600C2×C4C2×D4×D4311yescharacteristic
601C2×C4C2×#1062190011yescharacteristic
602C2×C4#1306337011yescharacteristic
603C2×C4#1306337111yescharacteristic
604C2×C4#1306337111yescharacteristic
605C8—41no—
606C8—862no—
607C8—862no—
608C8—1721no—
609C8—1721no—
610C8(C22⋊D43)⋊C411yescharacteristic
611C8(C22⋊D43)⋊C411yescharacteristic
612C8(C22⋊D43)⋊C411yescharacteristic
613C8(C22⋊D43)⋊C411yescharacteristic
614C22—41no—
615C22—41no—
616C22—41no—
617C22—81no—
618C22—81no—
619C22—3442no—
620C22—3442no—
621C22—1722no—
622C22—6881no—
623C22#1458337111yescharacteristic
624C22#1458346211yescharacteristic
625C22#1458350211yescharacteristic
626C4—41no—
627C4—41no—
628C4—81no—
629C4—81no—
630C4—81no—
631C4—1722no—
632C4—1722no—
633C4—1722no—
634C4C2×(C22⋊D43)⋊C411yescharacteristic
635C4#1458337111yescharacteristic
636C4#1458346711yescharacteristic
637C4#1458350211yescharacteristic
638C2—21no—
639C2—21no—
640C2—21no—
641C2—81no—
642C2—81no—
643C2—3442no—
644C2#1913731911yescharacteristic
subgroupG/H
centerC2#19137319
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1976C2
socleC2×C43#2328
prime radical#19145072C2
cosocleC22×C4×C43C24
hypercenter#1976D43
hypocenterC43#22284
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ #1976

Complements

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

NH ≅ G/Ntype
2. #19143512C2semidirect
3. #19143453C2semidirect
4. #19135498C2semidirect
5. #19135129C2semidirect
6. #19135124C2semidirect
7. #19135120C2semidirect
8. #19135115C2semidirect
9. #19135092C2semidirect
10. #19135085C2semidirect
11. #19135073C2semidirect
12. #19135066C2semidirect
13. #19134718C2semidirect
14. #19134350C2semidirect
15. C43×#1976C2semidirect
25. #14583292C4semidirect
26. #14583287C4semidirect
27. #14583280C4semidirect
28. #14583270C4semidirect
65. C2×#10621885C2×C4semidirect
72. C2×#10621883C2×C4semidirect
85. #13063323C2×C4semidirect
88. #13063312C2×C4semidirect
111. #13063235C2×C4semidirect
112. #13063235D4semidirect
113. C8×Dic43C2×C4semidirect
114. C8×Dic43D4semidirect
121. C2×Q16×C43C2×C4semidirect
122. C2×SD16×C43C2×C4semidirect
123. C2×SD16×C43C2×C4semidirect
124. C2×D8×C43C2×C4semidirect
320. #1976D43semidirect
381. C43#22284semidirect
395. C2×Q16C4×D43semidirect
404. C2×SD16C4×D43semidirect
405. C2×SD16C4×D43semidirect
407. C2×D8C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191450722
#191435122
#191434532
#191354982
#191351292
#191351242
#191351202
#191351152
#191350922
#191350852
#191350732
#191350662
#191347182
#191343502
C43×#19762
#2228443