Finite Group Databasebeta

← #25110496

Subgroups — #25110496

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#19145065C211yesmaximal, characteristic
2#19143513C211yesmaximal, characteristic, complemented
3#19135500C211yesmaximal, characteristic, complemented
4#19135491C211yesmaximal, characteristic, complemented
5#19135132C211yesmaximal, characteristic, complemented
6#19135127C211yesmaximal, characteristic, complemented
7#19135119C211yesmaximal, characteristic, complemented
8#19135114C211yesmaximal, characteristic, complemented
9#19135089C211yesmaximal, characteristic, complemented
10#19135082C211yesmaximal, characteristic, complemented
11#19135072C211yesmaximal, characteristic, complemented
12#19135065C211yesmaximal, characteristic, complemented
13#19134718C211yesmaximal, characteristic, complemented
14#19134350C211yesmaximal, characteristic, complemented
15C43×#2949C211yesmaximal, characteristic, complemented
16C2×#13063356C2211yescharacteristic
17C2×#13063351C2211yescharacteristic
18C2×#13063347C2211yescharacteristic
19#14583665C2211yescharacteristic
20#14583665C2211yescharacteristic
21#14583473C2211yescharacteristic
22#14583466C2211yescharacteristic
23#14583290C412yescomplemented
24#14583285C412yescomplemented
25#14583280C412yescomplemented
26#14583270C412yescomplemented
27#14583022—22no—
28#14583017—22no—
29C2×#13063261C2211yescharacteristic
30#14582917C2211yescharacteristic
31#14582917C2211yescharacteristic
32#14582917C2211yescharacteristic
33#14582917C2211yescharacteristic
34#14582908C2211yescharacteristic
35#14582904C2211yescharacteristic
36C2×#13063244C2211yescharacteristic
37C2×#13063242C2211yescharacteristic
38#14582872C2211yescharacteristic
39#14582872C2211yescharacteristic
40#14582854C2211yescharacteristic
41#14582854C2211yescharacteristic
42#14582669C2211yescharacteristic
43#14582669C2211yescharacteristic
44C43⋊#338C2211yescharacteristic
45#14582656C2211yescharacteristic
46#14582655C2211yescharacteristic
47#14582655C2211yescharacteristic
48#14582655C2211yescharacteristic
49#14582655C2211yescharacteristic
50C22×SD16×C43C2211yescharacteristic
51C43×#519C2211yescharacteristic
52C43×#518C2211yescharacteristic
53C43×#440—22no—
54C4×SD16×C43—22no—
55C43×#427C2211yescharacteristic
56C43×#419C2211yescharacteristic
57C43×#418C2211yescharacteristic
58C43×#405C2211yescharacteristic
59C2×#10621898C2311yescharacteristic
60C2×#10621898C2311yescharacteristic
61#13063356—41no—
62#13063356—41no—
63#13063351—41no—
64#13063351—41no—
65#13063347—21no—
66#13063347—21no—
67#13063347—21no—
68#13063347—21no—
69C2×Dic172C2×C411yescharacteristic, complemented
70C2×#10621885C2×C412yescomplemented
71C2×#10621873C2×C411yescharacteristic, complemented
72C2×#10621873C2×C411yescharacteristic, complemented
73C2×#10621883C2×C412yes—
74C2×#10621884C2×C412yescomplemented
75C2×D344C2×C411yescharacteristic, complemented
76C2×#10621882C2×C412yes—
77#13063333—41no—
78#13063333—41no—
79#13063331—22no—
80#13063331—22no—
81C2×#10621877C2311yescharacteristic
82C2×#10621877C2311yescharacteristic
83C2×#10621877C2311yescharacteristic
84C2×#10621877C2311yescharacteristic
85M16×D43—41no—
86M16×D43—41no—
87#13063323C2×C412yescomplemented
88#13063321C2×C412yes—
89#13063314C2×C412yescomplemented
90#13063312C2×C412yes—
91#13063308—41no—
92#13063301—41no—
93#13063296—41no—
94#13063294—41no—
95#13063284C2311yescharacteristic
96#13063284C2311yescharacteristic
97#13063261—21no—
98#13063261—21no—
99#13063253—22no—
100#13063253—22no—
101#13063253—41no—
102#13063253—41no—
103#13063249—41no—
104#13063246—41no—
105#13063244—41no—
106#13063242—41no—
107#13063239—41no—
108#13063239—41no—
109#13063235—21no—
110#13063235C2×C412yescomplemented
111C8×Dic43—21no—
112C8×Dic43C2×C412yescomplemented
113C22×Q8×C43C2311yescharacteristic
114C22×D4×C43C2311yescharacteristic
115C2×SD16×C43—21no—
116C2×SD16×C43—21no—
117C2×SD16×C43—21no—
118C2×SD16×C43—21no—
119C2×SD16×C43C2×C412yes—
120C2×SD16×C43C2×C412yes—
121C2×M16×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123C4×Q8×C43—22no—
124C4×Q8×C43—41no—
125C4×D4×C43—22no—
126C4×D4×C43—41no—
127#117×C43—41no—
128#117×C43C2311yescharacteristic
129#117×C43C2311yescharacteristic
130#117×C43C2311yescharacteristic
131C2×C22⋊C4×C43—41no—
132#107×C43—21no—
133#106×C43—21no—
134#103×C43—22no—
135#102×C43—22no—
136#97×C43D412yescomplemented
137C4×C8×C43D412yescomplemented
138C24×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43C22×C412yes—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43C22×C412yes—
151C22×C4×C43—21no—
152C22×C4×C43—42no—
153C22×C4×C43C2411yescharacteristic
154C2×C22⋊D43—21no—
155C2×C22⋊D43—21no—
156C2×C22⋊D43—42no—
157#10621898—21no—
158#10621898—21no—
159#10621898—21no—
160#10621898—21no—
161#10621898—21no—
162#10621898—21no—
163#10621898—21no—
164#10621898—21no—
165C2×D172C22×C411yescharacteristic
166C2×D172C22×C411yescharacteristic
167C2×C4×D43—21no—
168C2×C4×D43—21no—
169C2×Dic86C22×C411yescharacteristic
170C2×Dic86C22×C411yescharacteristic
171SD16×C43—22no—
172SD16×C43—22no—
173SD16×C43—22no—
174SD16×C43—22no—
175M16×C43—21no—
176M16×C43—21no—
177C2×C8×C43C22×C411yescharacteristic
178C2×C8×C43C22×C411yescharacteristic
179C2×C8×C43C2×D412yes—
180C2×C8×C43C2×D411yescharacteristic
181C2×C8×C43C2×D411yescharacteristic
182C2×C8×C43#4111yescharacteristic
183C2×C8×C43#4111yescharacteristic
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—42no—
188C22⋊C4×C43—21no—
189C22⋊C4×C43—21no—
190C22⋊C4×C43—21no—
191C22⋊C4×C43—42no—
192C42×C43—21no—
193C42×C43—21no—
194C42×C43—42no—
195C42×C43C2×D412yes—
196C22⋊Dic43—21no—
197C22⋊Dic43—21no—
198C22⋊Dic43—42no—
199#10621885—42no—
200#10621884—42no—
201#10621883—42no—
202#10621882—42no—
203(C2×D43)⋊C4—42no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206Dic43⋊C4—42no—
207C4×Dic43—21no—
208C4×Dic43C22×C412yes—
209#10621877—21no—
210#10621877—21no—
211#10621877—21no—
212#10621877—21no—
213#10621877—21no—
214#10621877—21no—
215#10621877—21no—
216#10621877—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8C22×C412yes—
221Dic172—21no—
222Dic172—21no—
223D344—21no—
224D344—21no—
225#10621873—21no—
226#10621873—21no—
227#10621873—21no—
228#10621873—21no—
229#10621872—42no—
230#10621872—42no—
231C8×D43—42no—
232C8×D43—42no—
233C23×C43—22no—
234C23×C43—41no—
235C23×C43—41no—
236C23×C43—161no—
237C23×C43H(5,𝔽2)11yescharacteristic
238C22×D43—21no—
239C22×D43—21no—
240Q8×C43—22no—
241Q8×C43—22no—
242Q8×C43—41no—
243Q8×C43—41no—
244D4×C43—22no—
245D4×C43—22no—
246D4×C43—41no—
247D4×C43—41no—
248C2×C4×C43—22no—
249C2×C4×C43—22no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—162no—
255C2×C4×C43C23×C411yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43H(5,𝔽2)11yescharacteristic
259C2×C4×C43H(5,𝔽2)11yescharacteristic
260C2×C4×C43H(5,𝔽2)11yescharacteristic
261C22⋊D43—41no—
262C22⋊D43—41no—
263C22⋊D43—41no—
264C22⋊D43—41no—
265C22⋊D43—162no—
266C2×Dic43—22no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—41no—
270D172—21no—
271D172—21no—
272D172—21no—
273D172—21no—
274C4×D43—41no—
275C4×D43—41no—
276C4×D43—41no—
277C4×D43—41no—
278Dic86—21no—
279Dic86—21no—
280Dic86—21no—
281Dic86—21no—
282C8×C43—22no—
283C8×C43C4×D411yescharacteristic
284C8×C43C4×D411yescharacteristic
285C8×C43C4×D411yescharacteristic
286C8×C43C4×D411yescharacteristic
287C43⋊C8—22no—
288C43⋊C8—41no—
289C43⋊C8—41no—
290C43⋊C8—41no—
291#22284—431nomaximal, Sylow
292C22×C43—41no—
293C22×C43—42no—
294C22×C43—82no—
295C22×C43—82no—
296C22×C43—161no—
297C22×C43#51811yescharacteristic
298C22×C43#53511yescharacteristic
299C22×C43#54011yescharacteristic
300C2×D43—41no—
301C2×D43—41no—
302C2×D43—81no—
303C2×D43—81no—
304C4×C43—42no—
305C4×C43—42no—
306C4×C43—81no—
307C4×C43—81no—
308C4×C43C2×C4×D411yescharacteristic
309C4×C43#51811yescharacteristic
310C4×C43#53511yescharacteristic
311C4×C43#54011yescharacteristic
312Dic43—42no—
313Dic43—41no—
314Dic43—41no—
315Dic43—81no—
316#3154—431no—
317#2957—431no—
318#2949D4311yescharacteristic, complemented
319#1977—431no—
320#1976—431no—
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—82no—
335C2×C43#232811yescharacteristic
336D43—81no—
337D43—81no—
338C2×#137—431no—
339C2×AGL(1,ℤ/8)—431no—
340C2×#135—431no—
341C22×SD16C2×D4311yescharacteristic
342#568—431no—
343#568—431no—
344#536—431no—
345#535—431no—
346#519C2×D4311yescharacteristic
347#518C2×D4311yescharacteristic
348#497—432no—
349#496—432no—
350#495—432no—
351#492—432no—
352#444—862no—
353#443—862no—
354#440—22no—
355C4×SD16—22no—
356C2×#108—431no—
357#427C2×D4311yescharacteristic
358#421—431no—
359#421—431no—
360#421—431no—
361#421—431no—
362#419—431no—
363#419C2×D4311yescharacteristic
364#418—431no—
365#418C2×D4311yescharacteristic
366C2×#101—431no—
367C2×#100—431no—
368#410—431no—
369#410—431no—
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×#41—431no—
383C2×#41—431no—
384C22×Q8C22×D4311yescharacteristic
385C22×D4C22×D4311yescharacteristic
386#137—1721no—
387#137—1721no—
388AGL(1,ℤ/8)—1721no—
389AGL(1,ℤ/8)—1721no—
390#135—861no—
391#135—861no—
392#135—861no—
393#135—861no—
394C2×Q16—432no—
395C2×Q16—431no—
396C2×SD16—21no—
397C2×SD16—21no—
398C2×SD16—21no—
399C2×SD16—21no—
400C2×SD16—432no—
401C2×SD16—432no—
402C2×SD16—431no—
403C2×SD16—431no—
404C2×SD16C4×D4312yes—
405C2×SD16C4×D4312yes—
406C2×D8—432no—
407C2×D8—431no—
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—22no—
429C4×Q8—41no—
430C4×D4—22no—
431C4×D4—41no—
432#117—41no—
433#117—431no—
434#117—431no—
435#117C22×D4311yescharacteristic
436#117C22×D4311yescharacteristic
437#117C22×D4311yescharacteristic
438C2×C22⋊C4—41no—
439#108—861no—
440#108—861no—
441#107—21no—
442#106—21no—
443#104—862no—
444#104—862no—
445#104—1721no—
446#104—1721no—
447#103—22no—
448#103—1721no—
449#102—22no—
450#102—1721no—
451#101—1721no—
452#100—1721no—
453#99—1721no—
454#99—1721no—
455#97—432no—
456#97—861no—
457#97C22⋊D4312yescomplemented
458C4×C8—432no—
459C4×C8—861no—
460C4×C8C22⋊D4312yescomplemented
461C24—21no—
462#41—861no—
463#41—861no—
464#41—861no—
465#41—861no—
466#41—861no—
467#41—861no—
468#41—861no—
469#41—861no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—431no—
476C2×Q8—431no—
477C2×Q8C2×C4×D4312yes—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—431no—
484C2×D4—431no—
485C2×D4—861no—
486C2×D4—861no—
487C2×D4—1722no—
488C2×D4C2×C4×D4312yes—
489C22×C4—21no—
490C22×C4—42no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4C23×D4311yescharacteristic
494Q16—861no—
495Q16—861no—
496Q16—1722no—
497SD16—22no—
498SD16—22no—
499SD16—22no—
500SD16—22no—
501SD16—861no—
502SD16—861no—
503SD16—861no—
504SD16—861no—
505SD16—1722no—
506SD16—1722no—
507D8—861no—
508D8—861no—
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—432no—
523C2×C8—861no—
524C2×C8—861no—
525C2×C8—861no—
526C2×C8—1722no—
527C2×C8—1722no—
528C2×C8C2×C4×D4311yescharacteristic
529C2×C8C2×C4×D4311yescharacteristic
530C2×C8#1062189811yescharacteristic
531C2×C8#1062189811yescharacteristic
532C2×C8C2×C22⋊D4312yes—
533C2×C8C2×C22⋊D4311yescharacteristic
534C2×C8C2×C22⋊D4311yescharacteristic
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—42no—
539C4⋊C4—861no—
540C4⋊C4—861no—
541C4⋊C4—1722no—
542C22⋊C4—21no—
543C22⋊C4—21no—
544C22⋊C4—21no—
545C22⋊C4—42no—
546C22⋊C4—861no—
547C22⋊C4—861no—
548C22⋊C4—1722no—
549C22⋊C4—1722no—
550C42—21no—
551C42—21no—
552C42—42no—
553C42—432no—
554C42—861no—
555C42C2×C22⋊D4312yes—
556C23—22no—
557C23—41no—
558C23—41no—
559C23—161no—
560C23—861no—
561C23—861no—
562C23#1306337011yescharacteristic
563Q8—22no—
564Q8—22no—
565Q8—41no—
566Q8—41no—
567Q8—861no—
568Q8—861no—
569Q8—861no—
570Q8—861no—
571D4—22no—
572D4—22no—
573D4—41no—
574D4—41no—
575D4—861no—
576D4—861no—
577D4—861no—
578D4—861no—
579D4—1721no—
580D4—1721no—
581D4—1721no—
582D4—1721no—
583D4—6882no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—162no—
591C2×C4—862no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4C22×C4×D4311yescharacteristic
600C2×C4C22×C22⋊D4311yescharacteristic
601C2×C4C2×#1062189811yescharacteristic
602C2×C4#1306337011yescharacteristic
603C2×C4#1306337111yescharacteristic
604C2×C4#1306337111yescharacteristic
605C8—22no—
606C8—862no—
607C8—1721no—
608C8—1721no—
609C8—1721no—
610C8C4×C22⋊D4311yescharacteristic
611C8C4×C22⋊D4311yescharacteristic
612C8C4×C22⋊D4311yescharacteristic
613C8C4×C22⋊D4311yescharacteristic
614C22—41no—
615C22—42no—
616C22—82no—
617C22—82no—
618C22—161no—
619C22—3441no—
620C22—3441no—
621C22—1721no—
622C22—1721no—
623C22#1458337111yescharacteristic
624C22#1458346611yescharacteristic
625C22#1458350011yescharacteristic
626C4—42no—
627C4—42no—
628C4—81no—
629C4—81no—
630C4—3441no—
631C4—1722no—
632C4—1721no—
633C4—1721no—
634C4C2×C4×C22⋊D4311yescharacteristic
635C4#1458337111yescharacteristic
636C4#1458346311yescharacteristic
637C4#1458350011yescharacteristic
638C2—21no—
639C2—21no—
640C2—21no—
641C2—82no—
642C2—3441no—
643C2—3441no—
644C2#1913731711yescharacteristic
subgroupG/H
centerC2#19137317
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2949C2
socleC2×C43#2328
prime radical#19145065C2
cosocleC22×C4×C43C24
hypercenter#2949D43
hypocenterC43#22284
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ #2949

Complements

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

NH ≅ G/Ntype
2. #19143513C2semidirect
3. #19135500C2semidirect
4. #19135491C2semidirect
5. #19135132C2semidirect
6. #19135127C2semidirect
7. #19135119C2semidirect
8. #19135114C2semidirect
9. #19135089C2semidirect
10. #19135082C2semidirect
11. #19135072C2semidirect
12. #19135065C2semidirect
13. #19134718C2semidirect
14. #19134350C2semidirect
15. C43×#2949C2semidirect
23. #14583290C4semidirect
24. #14583285C4semidirect
25. #14583280C4semidirect
26. #14583270C4semidirect
69. C2×Dic172C2×C4semidirect
70. C2×#10621885C2×C4semidirect
71. C2×#10621873C2×C4semidirect
72. C2×#10621873C2×C4semidirect
74. C2×#10621884C2×C4semidirect
75. C2×D344C2×C4semidirect
87. #13063323C2×C4semidirect
89. #13063314C2×C4semidirect
110. #13063235C2×C4semidirect
112. C8×Dic43C2×C4semidirect
136. #97×C43D4semidirect
137. C4×C8×C43D4semidirect
318. #2949D43semidirect
381. C43#22284semidirect
457. #97C22⋊D43semidirect
460. C4×C8C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191450652
#191435132
#191355002
#191354912
#191351322
#191351272
#191351192
#191351142
#191350892
#191350822
#191350722
#191350652
#191347182
#191343502
C43×#29492
#2228443