Finite Group Databasebeta

← #25148704

Subgroups — #25148704

Order 11008.

664 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145139C211yesmaximal, characteristic, complemented
2#19144391C211yesmaximal, characteristic
3C2×#14583178C211yesmaximal, characteristic
4#19143541C211yesmaximal, characteristic, complemented
5#19136104C211yesmaximal, characteristic, complemented
6#19135956C211yesmaximal, characteristic
7#19135954C211yesmaximal, characteristic
8#19135582C211yesmaximal, characteristic, complemented
9#19135378C211yesmaximal, characteristic, complemented
10#19135377C211yesmaximal, characteristic, complemented
11#19135369C211yesmaximal, characteristic, complemented
12#19135258C211yesmaximal, characteristic
13#19135256C211yesmaximal, characteristic
14#19134386C211yesmaximal, characteristic
15C43×#2089C211yesmaximal, characteristic, complemented
16#14583452C2211yescharacteristic
17C2×#13063324C2211yescharacteristic
18C2×#13063287C2211yescharacteristic
19#14583307—21no—
20#14583306—21no—
21#14583303—21no—
22#14583296—21no—
23#14583202—21no—
24#14583198—21no—
25#14583188—21no—
26#14583178—21no—
27#14583178—21no—
28#14583178—21no—
29#14583178—21no—
30#14583178—21no—
31#14583028—21no—
32#14583028—21no—
33#14583026—21no—
34#14583023—21no—
35C2×#13063261C2211yescharacteristic
36C2×#13063260C2211yescharacteristic
37#14582942C2211yescharacteristic
38#14582941C2211yescharacteristic
39#14582939C2211yescharacteristic
40#14582939C2211yescharacteristic
41C2×#13063258C2211yescharacteristic
42#14582927C2211yescharacteristic
43#14582922C2211yescharacteristic
44C2×Dic43⋊C8C2211yescharacteristic
45#14582905C2211yescharacteristic
46#14582903C2211yescharacteristic
47C2×#13063247C2211yescharacteristic
48C2×#13063245C2211yescharacteristic
49C2×#13063241C2211yescharacteristic
50C2×#13063241C2211yescharacteristic
51#14582855C2211yescharacteristic
52#14582854C2211yescharacteristic
53M16×Dic43C2211yescharacteristic
54M16×Dic43C2211yescharacteristic
55#14582668C2211yescharacteristic
56#14582668C2211yescharacteristic
57#14582667C2211yescharacteristic
58#14582667C2211yescharacteristic
59#14582663C2211yescharacteristic
60C43×#428C2211yescharacteristic
61C43×#428C2211yescharacteristic
62C2×#107×C43C2211yescharacteristic
63C43×#424C2211yescharacteristic
64C43×#343C2211yescharacteristic
65C43×#343C2211yescharacteristic
66C43×#341C2211yescharacteristic
67C22×Dic86—21no—
68C22×D172C2311yescharacteristic
69C22×C4×D43—21no—
70C2×#10621877C2311yescharacteristic
71C2×#10621877C2311yescharacteristic
72C2×#10621877C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74#13063324—21no—
75#13063324—21no—
76#13063324—21no—
77#13063324—21no—
78#13063324D411yescharacteristic
79#13063324D411yescharacteristic
80#13063316D411yescharacteristic
81#13063316D411yescharacteristic
82#13063302—21no—
83#13063302—21no—
84C4×Dic86—21no—
85C4×Dic86—21no—
86#13063287—21no—
87#13063287—21no—
88#13063287—21no—
89#13063287—21no—
90#13063284C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×Dic43⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×C4×Dic43C2311yescharacteristic
95#13063261—22no—
96#13063260—22no—
97#13063259—21no—
98#13063258—21no—
99#13063258—21no—
100#13063258—21no—
101#13063258—21no—
102#13063258—21no—
103#13063257—21no—
104#13063256—21no—
105#13063256—21no—
106#13063256—21no—
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8D411yescharacteristic
112Dic43⋊C8D411yescharacteristic
113Dic43⋊C8D411yescharacteristic
114Dic43⋊C8D411yescharacteristic
115#13063247—21no—
116#13063247—21no—
117#13063247—21no—
118#13063247—21no—
119#13063245—21no—
120#13063245—21no—
121#13063245—21no—
122#13063245—21no—
123#13063241—22no—
124#13063241Q814yescomplemented
125#13063236—21no—
126#13063235—21no—
127#13063235—21no—
128#13063235—21no—
129C4×C43⋊C8—21no—
130C8×Dic43—21no—
131C8×Dic43—21no—
132C8×Dic43—21no—
133C2×M16×C43C2311yescharacteristic
134C2×M16×C43C2311yescharacteristic
135C2×M16×C43C2311yescharacteristic
136C22×C8×C43C2311yescharacteristic
137#117×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140#107×C43—21no—
141#107×C43—21no—
142#107×C43—21no—
143#107×C43—21no—
144#106×C43—21no—
145#106×C43—21no—
146C4⋊C8×C43—21no—
147C4⋊C8×C43—21no—
148C23×D43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43C2411yescharacteristic
152C22×Dic43—21no—
153C22×Dic43#4111yescharacteristic
154C22×Dic43#4111yescharacteristic
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172C2×Q812yes—
161C2×C4×D43—41no—
162C2×C4×D43—41no—
163C2×C4×D43—82no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—41no—
167C2×Dic86—41no—
168C2×Dic86—82no—
169M16×C43—21no—
170M16×C43—21no—
171M16×C43—21no—
172M16×C43—21no—
173M16×C43—21no—
174M16×C43C2×Q812yes—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43C2×D411yescharacteristic
181C2×C8×C43C2×D411yescharacteristic
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43C2×D411yescharacteristic
187C4⋊C4×C43C2×D411yescharacteristic
188C22⋊C4×C43—21no—
189C42×C43—21no—
190C22⋊Dic43—21no—
191(C2×D43)⋊C4—41no—
192(C2×D43)⋊C4—41no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43C2×D411yescharacteristic
198C4⋊Dic43C2×D411yescharacteristic
199Dic43⋊C4—21no—
200Dic43⋊C4—21no—
201Dic43⋊C4—21no—
202Dic43⋊C4—21no—
203Dic43⋊C4—41no—
204Dic43⋊C4—41no—
205C4×Dic43—21no—
206C4×Dic43C2×D411yescharacteristic
207C4×Dic43C2×D411yescharacteristic
208C4×Dic43C2×D411yescharacteristic
209C4×Dic43C2×D411yescharacteristic
210#10621877—21no—
211#10621877—21no—
212#10621877—21no—
213#10621877—21no—
214#10621877C2×Q812yes—
215#10621877#4112yes—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8C2×D411yescharacteristic
222C2×C43⋊C8C2×D411yescharacteristic
223C23×C43C2×#4111yescharacteristic
224C22×D43—22no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—81no—
228C22×D43—81no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—81no—
234C2×C4×C43—81no—
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43C22×Q811yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×C4×C432−1+411yescharacteristic
240C2×C4×C432−1+411yescharacteristic
241C2×Dic43—22no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—81no—
247C2×Dic43#12111yescharacteristic
248C2×Dic43#12111yescharacteristic
249C2×Dic43#12111yescharacteristic
250C2×Dic43#12111yescharacteristic
251D172—22no—
252D172—22no—
253D172—41no—
254D172—41no—
255C4×D43—82no—
256C4×D43—82no—
257Dic86—42no—
258Dic86—81no—
259Dic86—82no—
260Dic86—82no—
261C8×C43—21no—
262C8×C43—21no—
263C8×C43—22no—
264C8×C43—41no—
265C8×C43—41no—
266C43⋊C8—21no—
267C43⋊C8—21no—
268C43⋊C8—22no—
269C43⋊C8—22no—
270C43⋊C8—41no—
271#25489—431nomaximal, Sylow
272C22×C43—21no—
273C22×C43—21no—
274C22×C43C2×#12111yescharacteristic
275C22×C43#53311yescharacteristic
276C22×C43#54111yescharacteristic
277C2×D43—42no—
278C2×D43—82no—
279C2×D43—81no—
280C2×D43—81no—
281C2×D43—82no—
282C4×C43—41no—
283C4×C43—41no—
284C4×C43—81no—
285C4×C43—81no—
286C4×C43#54711yescharacteristic
287C4×C43#54811yescharacteristic
288C4×C43D4×Q811yescharacteristic
289C4×C43D4×Q811yescharacteristic
290Dic43—21no—
291Dic43—21no—
292Dic43—21no—
293Dic43—41no—
294Dic43—41no—
295Dic43—81no—
296Dic43#47212yes—
297#3165—431no—
298#3077—431no—
299C2×#474—431no—
300#2962—431no—
301#2089—431no—
302#2089D4311yescharacteristic, complemented
303#2063—431no—
304#2063—431no—
305#1997—431no—
306#1952—431no—
307#1952—431no—
308#1950—431no—
309#1931—431no—
310#1931—431no—
311C4×#100—431no—
312C2×C43—21no—
313C2×C43—21no—
314C2×C43#242911yescharacteristic
315C2×C43C2×#47211yescharacteristic
316C2×C43#306911yescharacteristic
317D43—82no—
318#533—431no—
319C2×C4⋊Q8—431no—
320C2×C4×D4—431no—
321#501—861no—
322#501—861no—
323#500—861no—
324#498—861no—
325#478—861no—
326#478—861no—
327#476—861no—
328#474—861no—
329#474—861no—
330#474—861no—
331#474—861no—
332#474—861no—
333#446—861no—
334#446—861no—
335#446—861no—
336C8×Q8—861no—
337C2×#108—431no—
338C2×#108—431no—
339#428—431no—
340#428—431no—
341#428—431no—
342#428—431no—
343#428C2×D4311yescharacteristic
344#428C2×D4311yescharacteristic
345C2×#107—431no—
346C2×#107C2×D4311yescharacteristic
347#424—431no—
348#424C2×D4311yescharacteristic
349#423—431no—
350C2×C4⋊C8—431no—
351#418—431no—
352#418—431no—
353C2×#102—431no—
354C2×#102—431no—
355C2×#100—431no—
356C2×#100—431no—
357#405—431no—
358#405—431no—
359C4×M16—431no—
360C4×M16—431no—
361#343—431no—
362#343—431no—
363#343—431no—
364#343—431no—
365#343C2×D4311yescharacteristic
366#343C2×D4311yescharacteristic
367#341—431no—
368#341C2×D4311yescharacteristic
369C43#2548911yescharacteristic, complemented, Sylow
370C22×Q8—861no—
371C22×D4—431no—
372C23×C4—861no—
373C2×M16—431no—
374C2×M16—431no—
375C2×M16—431no—
376C2×M16C22×D4311yescharacteristic
377C2×M16C22×D4311yescharacteristic
378C2×M16C22×D4311yescharacteristic
379C22×C8—431no—
380C22×C8C22×D4311yescharacteristic
381C4⋊Q8—431no—
382C4⋊Q8—431no—
383C4⋊Q8—861no—
384C4⋊Q8—861no—
385C4⋊Q8—861no—
386C4⋊Q8—861no—
387#125—431no—
388#125—431no—
389C22⋊Q8—861no—
390C22⋊Q8—861no—
391C4×Q8—861no—
392C4×Q8—861no—
393C4×D4—861no—
394C4×D4—861no—
395C4×D4—861no—
396C4×D4—861no—
397#117—431no—
398#117C22×D4311yescharacteristic
399C2×C4⋊C4—431no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4C22×D4311yescharacteristic
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C22⋊C4—861no—
404C2×C42—431no—
405#108—862no—
406#108—862no—
407#107—21no—
408#107—21no—
409#107—21no—
410#107—21no—
411#107—861no—
412#107—861no—
413#107—861no—
414#107—861no—
415#107—861no—
416#107—861no—
417#106—21no—
418#106—21no—
419#106—861no—
420#106—861no—
421#106—861no—
422#106—861no—
423C4⋊C8—21no—
424C4⋊C8—21no—
425C4⋊C8—431no—
426C4⋊C8—431no—
427C4⋊C8—431no—
428C4⋊C8—431no—
429C4⋊C8—861no—
430C4⋊C8—861no—
431C4⋊C8—861no—
432C4⋊C8—861no—
433#102—861no—
434#102—861no—
435#102—861no—
436#102—861no—
437#102—861no—
438#102—861no—
439#102—861no—
440#102—861no—
441#100—434no—
442#100—862no—
443#97—861no—
444#97—861no—
445#97—861no—
446#97—861no—
447C4×C8—861no—
448C4×C8—861no—
449C4×C8—861no—
450C4×C8—861no—
451C24—861no—
452C2×Q8—861no—
453C2×Q8—861no—
454C2×Q8—3442no—
455C2×Q8—1721no—
456C2×Q8—1721no—
457C2×D4—432no—
458C2×D4—861no—
459C2×D4—861no—
460C2×D4—861no—
461C2×D4—861no—
462C2×D4—861no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—431no—
466C22×C4—431no—
467C22×C4—861no—
468C22×C4—3442no—
469C22×C4—1721no—
470C22×C4—1721no—
471C22×C4C23×D4311yescharacteristic
472M16—21no—
473M16—21no—
474M16—21no—
475M16—21no—
476M16—21no—
477M16—432no—
478M16—432no—
479M16—861no—
480M16—861no—
481M16—861no—
482M16—861no—
483M16Q8×D4312yes—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—431no—
490C2×C8—431no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—861no—
496C2×C8D4×D4311yescharacteristic
497C2×C8D4×D4311yescharacteristic
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—431no—
503C4⋊C4—431no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—1721no—
513C4⋊C4—1721no—
514C4⋊C4D4×D4311yescharacteristic
515C4⋊C4D4×D4311yescharacteristic
516C22⋊C4—21no—
517C22⋊C4—861no—
518C22⋊C4—1721no—
519C22⋊C4—1721no—
520C42—21no—
521C42—431no—
522C42—431no—
523C42—431no—
524C42—431no—
525C42—861no—
526C23—862no—
527C23—3441no—
528C23—3441no—
529C23—1721no—
530C23—1721no—
531C23#41×D4311yescharacteristic
532Q8—3441no—
533Q8—3442no—
534Q8—3442no—
535Q8—1722no—
536D4—862no—
537D4—862no—
538D4—1721no—
539D4—1721no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—81no—
545C2×C4—81no—
546C2×C4—431no—
547C2×C4—431no—
548C2×C4—431no—
549C2×C4—431no—
550C2×C4—862no—
551C2×C4—861no—
552C2×C4—861no—
553C2×C4—3442no—
554C2×C4—3442no—
555C2×C4—3441no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4C2×D4×D4311yescharacteristic
559C2×C4C2×D4×D4311yescharacteristic
560C2×C4C2×Q8×D4311yescharacteristic
561C2×C4#41×D4311yescharacteristic
562C2×C4#1306337211yescharacteristic
563C2×C4#1306337311yescharacteristic
564C8—22no—
565C8—21no—
566C8—21no—
567C8—41no—
568C8—41no—
569C8—862no—
570C8—862no—
571C8—861no—
572C8—861no—
573C8—1721no—
574C22—21no—
575C22—21no—
576C22—3442no—
577C22—3442no—
578C22—3441no—
579C22—3441no—
580C22—1722no—
581C22#121×D4311yescharacteristic
582C22#1458345511yescharacteristic
583C22#1458350811yescharacteristic
584C4—41no—
585C4—41no—
586C4—81no—
587C4—81no—
588C4—432no—
589C4—861no—
590C4—861no—
591C4—861no—
592C4—3441no—
593C4—1721no—
594C4—1721no—
595C4#1458354711yescharacteristic
596C4#1458355911yescharacteristic
597C4#1458356211yescharacteristic
598C4#1458356411yescharacteristic
599C2—21no—
600C2—21no—
601C2—3442no—
602C2#1913818911yescharacteristic
603C2#472×D4311yescharacteristic
604C2#1914433011yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2089C2
socleC22×C43C2×#121
prime radicalC22×D172C23
hypercenter#2089D43
hypocenterC43#25489
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #2089

Complements

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

NH ≅ G/Ntype
1. #19145139C2semidirect
4. #19143541C2semidirect
5. #19136104C2semidirect
8. #19135582C2semidirect
9. #19135378C2semidirect
10. #19135377C2semidirect
11. #19135369C2semidirect
15. C43×#2089C2semidirect
124. #13063241Q8semidirect
302. #2089D43semidirect
369. C43#25489semidirect

Maximal subgroups

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

subgroupindex
#191451392
#191443912
C2×#145831782
#191435412
#191361042
#191359562
#191359542
#191355822
#191353782
#191353772
#191353692
#191352582
#191352562
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C43×#20892
#2548943