Finite Group Databasebeta

← #25148706

Subgroups — #25148706

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#19144389C211yesmaximal, characteristic
3C2×#14583177C211yesmaximal, characteristic
4#19143539C211yesmaximal, characteristic, complemented
5#19136103C211yesmaximal, characteristic, complemented
6#19136102C211yesmaximal, characteristic, complemented
7#19135955C211yesmaximal, characteristic
8#19135953C211yesmaximal, characteristic
9#19135582C211yesmaximal, characteristic, complemented
10#19135380C211yesmaximal, characteristic, complemented
11#19135379C211yesmaximal, characteristic, complemented
12#19135369C211yesmaximal, characteristic, complemented
13#19135259C211yesmaximal, characteristic
14#100×Dic43C211yesmaximal, characteristic
15C43×#1931C211yesmaximal, characteristic
16#14583452C2211yescharacteristic
17C2×#13063324C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19#14583307—21no—
20#14583306—21no—
21#14583303—21no—
22#14583296—21no—
23#14583201—21no—
24#14583197—21no—
25#14583187—21no—
26#14583177—21no—
27#14583177—21no—
28#14583177—21no—
29#14583177—21no—
30#14583177—21no—
31#14583029—21no—
32#14583027—21no—
33#14583027—21no—
34C8×Dic86—21no—
35C2×#13063261C2211yescharacteristic
36C2×#13063260C2211yescharacteristic
37#14582942C2211yescharacteristic
38#14582942C2211yescharacteristic
39#14582941C2211yescharacteristic
40#14582941C2211yescharacteristic
41#14582939C2211yescharacteristic
42C2×#13063259C2211yescharacteristic
43C2×#13063258C2211yescharacteristic
44#14582926C2211yescharacteristic
45#14582925C2211yescharacteristic
46#14582922C2211yescharacteristic
47C2×Dic43⋊C8C2211yescharacteristic
48#14582904C2211yescharacteristic
49C2×#13063246C2211yescharacteristic
50C2×#13063242C2211yescharacteristic
51#14582857C2211yescharacteristic
52M16×Dic43C2211yescharacteristic
53M16×Dic43C2211yescharacteristic
54#14582668C2211yescharacteristic
55#14582667C2211yescharacteristic
56#14582667C2211yescharacteristic
57#14582667C2211yescharacteristic
58#14582667C2211yescharacteristic
59#14582663C2211yescharacteristic
60C43×#428C2211yescharacteristic
61C43×#418C2211yescharacteristic
62C2×#102×C43C2211yescharacteristic
63C2×#100×C43C2211yescharacteristic
64C43×#405C2211yescharacteristic
65C43×#343C2211yescharacteristic
66C43×#341C2211yescharacteristic
67C22×Dic86—21no—
68C23×Dic43—21no—
69C2×#10621877C2311yescharacteristic
70C2×#10621877C2311yescharacteristic
71C2×#10621877C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063324—21no—
74#13063324—21no—
75#13063324—21no—
76#13063324—21no—
77#13063324D411yescharacteristic
78#13063324D411yescharacteristic
79#13063316D411yescharacteristic
80#13063316D411yescharacteristic
81#13063302—21no—
82#13063302—21no—
83C4×Dic86—21no—
84C4×Dic86—21no—
85D4×Dic43—21no—
86D4×Dic43—21no—
87D4×Dic43—21no—
88D4×Dic43—21no—
89#13063284C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×Dic43⋊C4—21no—
93C2×C22⋊Dic43—21no—
94C2×C4×Dic43C2311yescharacteristic
95#13063261—22no—
96#13063260—22no—
97#13063259—21no—
98#13063259—21no—
99#13063259—21no—
100#13063259—21no—
101#13063258—21no—
102#13063258—21no—
103#13063258—21no—
104#13063258—21no—
105#13063258—21no—
106#13063257—21no—
107#13063257—21no—
108#13063256—21no—
109#13063256—21no—
110#13063256—21no—
111C4⋊(C43⋊C8)—21no—
112C4⋊(C43⋊C8)—21no—
113Dic43⋊C8—21no—
114Dic43⋊C8—21no—
115Dic43⋊C8—21no—
116Dic43⋊C8—21no—
117Dic43⋊C8D411yescharacteristic
118Dic43⋊C8D411yescharacteristic
119Dic43⋊C8D411yescharacteristic
120Dic43⋊C8D411yescharacteristic
121#13063246—21no—
122#13063246—21no—
123#13063246—21no—
124#13063246—21no—
125#13063242—22no—
126#13063235—21no—
127#13063235—21no—
128#13063235—21no—
129C8×Dic43—21no—
130C8×Dic43—21no—
131C8×Dic43—21no—
132C22×D4×C43C2311yescharacteristic
133C2×M16×C43C2311yescharacteristic
134C2×M16×C43C2311yescharacteristic
135C2×M16×C43C2311yescharacteristic
136C22×C8×C43C2311yescharacteristic
137#117×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139#107×C43—21no—
140#106×C43—21no—
141#102×C43—21no—
142#102×C43—21no—
143#102×C43—21no—
144#102×C43—21no—
145#100×C43Q814yescomplemented
146#97×C43—21no—
147C4×C8×C43—21no—
148C24×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43C2×Q812yes—
155C22×C4×C43—21no—
156C22×C4×C43C2411yescharacteristic
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—41no—
160C22×Dic43—41no—
161C22×Dic43—82no—
162C22×Dic43#4111yescharacteristic
163C22×Dic43#4111yescharacteristic
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×C43C2×Q812yes—
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×C43C2×D411yescharacteristic
185C4⋊C4×C43C2×D411yescharacteristic
186C22⋊C4×C43—21no—
187C42×C43—21no—
188C22⋊Dic43—21no—
189C22⋊Dic43—41no—
190C22⋊Dic43—41no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
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#10621877—21no—
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×C43—22no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—81no—
227C23×C43—81no—
228C23×C43C2×#4111yescharacteristic
229D4×C43—22no—
230D4×C43—22no—
231D4×C43—41no—
232D4×C43—41no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—41no—
236C2×C4×C43—81no—
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C22×Q811yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C432−1+411yescharacteristic
242C2×C4×C432−1+411yescharacteristic
243C2×Dic43—22no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—82no—
250C2×Dic43—82no—
251C2×Dic43—81no—
252C2×Dic43—81no—
253C2×Dic43#12111yescharacteristic
254C2×Dic43#12111yescharacteristic
255C2×Dic43#12111yescharacteristic
256C2×Dic43#12111yescharacteristic
257Dic86—42no—
258Dic86—81no—
259Dic86—82no—
260Dic86—82no—
261C8×C43—21no—
262C8×C43—21no—
263C8×C43—22no—
264C8×C43—22no—
265C8×C43—41no—
266C43⋊C8—21no—
267C43⋊C8—21no—
268C43⋊C8—22no—
269C43⋊C8—41no—
270C43⋊C8—41no—
271#25489—431nomaximal, Sylow
272C22×C43—21no—
273C22×C43—21no—
274C22×C43—42no—
275C22×C43—82no—
276C22×C43—82no—
277C22×C43—81no—
278C22×C43—81no—
279C22×C43C2×#12111yescharacteristic
280C22×C43#53311yescharacteristic
281C22×C43#54111yescharacteristic
282C4×C43—41no—
283C4×C43—41no—
284C4×C43—81no—
285C4×C43#54711yescharacteristic
286C4×C43#54811yescharacteristic
287C4×C43D4×Q811yescharacteristic
288C4×C43D4×Q811yescharacteristic
289Dic43—21no—
290Dic43—21no—
291Dic43—21no—
292Dic43—41no—
293Dic43—41no—
294Dic43—81no—
295Dic43—81no—
296Dic43#47212yes—
297#3165—431no—
298#3077—431no—
299C2×#474—431no—
300#2962—431no—
301#2089—431no—
302#2089—431no—
303#2063—431no—
304#2063—431no—
305#1997—431no—
306#1952—431no—
307#1952—431no—
308#1950—431no—
309#1931—431no—
310#1931D4311yescharacteristic
311C4×#100—431no—
312C2×C43—21no—
313C2×C43—21no—
314C2×C43—82no—
315C2×C43#242911yescharacteristic
316C2×C43C2×#47211yescharacteristic
317C2×C43#306911yescharacteristic
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#428—431no—
344#428C2×D4311yescharacteristic
345C2×#107—431no—
346C2×#107—431no—
347#424—431no—
348#424—431no—
349#423—431no—
350C2×C4⋊C8—431no—
351#418—431no—
352#418C2×D4311yescharacteristic
353C2×#102—431no—
354C2×#102C2×D4311yescharacteristic
355C2×#100—431no—
356C2×#100C2×D4311yescharacteristic
357#405—431no—
358#405C2×D4311yescharacteristic
359C4×M16—431no—
360C4×M16—431no—
361#343—431no—
362#343—431no—
363#343—431no—
364#343—431no—
365#343—431no—
366#343C2×D4311yescharacteristic
367#341—431no—
368#341C2×D4311yescharacteristic
369C43#2548911yescharacteristic, complemented, Sylow
370C22×Q8—861no—
371C22×D4C22×D4311yescharacteristic
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—431no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C22⋊C4—861no—
404C2×C42—431no—
405#108—862no—
406#108—862no—
407#107—21no—
408#107—861no—
409#107—861no—
410#107—861no—
411#107—861no—
412#107—861no—
413#107—861no—
414#107—861no—
415#107—861no—
416#107—861no—
417#106—21no—
418#106—861no—
419#106—861no—
420#106—861no—
421#106—861no—
422#106—861no—
423C4⋊C8—431no—
424C4⋊C8—431no—
425C4⋊C8—431no—
426C4⋊C8—431no—
427C4⋊C8—861no—
428C4⋊C8—861no—
429C4⋊C8—861no—
430C4⋊C8—861no—
431C4⋊C8—861no—
432C4⋊C8—861no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—861no—
438#102—861no—
439#102—861no—
440#102—861no—
441#100—862no—
442#100Dic8614yescomplemented
443#97—21no—
444#97—861no—
445#97—861no—
446#97—861no—
447C4×C8—21no—
448C4×C8—861no—
449C4×C8—861no—
450C4×C8—861no—
451C24—21no—
452C2×Q8—861no—
453C2×Q8—861no—
454C2×Q8—3442no—
455C2×Q8—1721no—
456C2×Q8—1721no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4C2×Dic8612yes—
463C22×C4—21no—
464C22×C4—431no—
465C22×C4—431no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—3442no—
469C22×C4—1721no—
470C22×C4—1721no—
471C22×C4C23×D4311yescharacteristic
472M16—21no—
473M16—21no—
474M16—21no—
475M16—21no—
476M16—432no—
477M16—861no—
478M16—861no—
479M16—861no—
480M16—861no—
481M16—861no—
482M16C2×Dic8612yes—
483M16C2×Dic8612yes—
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—431no—
501C4⋊C4—431no—
502C4⋊C4—861no—
503C4⋊C4—861no—
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—22no—
527C23—41no—
528C23—41no—
529C23—81no—
530C23—81no—
531C23#41×D4311yescharacteristic
532Q8—3441no—
533Q8—3442no—
534Q8—3442no—
535Q8—1722no—
536D4—22no—
537D4—22no—
538D4—41no—
539D4—41no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—81no—
544C2×C4—431no—
545C2×C4—431no—
546C2×C4—431no—
547C2×C4—431no—
548C2×C4—862no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—3442no—
552C2×C4—3442no—
553C2×C4—3441no—
554C2×C4—3441no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4C2×D4×D4311yescharacteristic
559C2×C4C2×D4×D4311yescharacteristic
560C2×C4C22×Dic8611yescharacteristic
561C2×C4#41×D4311yescharacteristic
562C2×C4#1306337211yescharacteristic
563C2×C4#1306337211yescharacteristic
564C8—22no—
565C8—22no—
566C8—21no—
567C8—21no—
568C8—41no—
569C8—862no—
570C8—861no—
571C8—861no—
572C8—1721no—
573C8—1721no—
574C22—21no—
575C22—21no—
576C22—42no—
577C22—82no—
578C22—82no—
579C22—81no—
580C22—81no—
581C22#121×D4311yescharacteristic
582C22#1458345211yescharacteristic
583C22#1458350611yescharacteristic
584C4—41no—
585C4—41no—
586C4—81no—
587C4—432no—
588C4—861no—
589C4—861no—
590C4—861no—
591C4—3441no—
592C4—3441no—
593C4—1721no—
594C4—1721no—
595C4#1458354711yescharacteristic
596C4#1458355711yescharacteristic
597C4D4×Dic8611yescharacteristic
598C4D4×Dic8611yescharacteristic
599C2—21no—
600C2—21no—
601C2—82no—
602C2#1913819111yescharacteristic
603C2#472×D4311yescharacteristic
604C2#1914432711yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1931C2
socleC22×C43C2×#121
prime radicalC22×D4×C43C23
hypercenter#1931D43
hypocenterC43#25489
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1931

Complements

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

NH ≅ G/Ntype
1. #19145139C2semidirect
4. #19143539C2semidirect
5. #19136103C2semidirect
6. #19136102C2semidirect
9. #19135582C2semidirect
10. #19135380C2semidirect
11. #19135379C2semidirect
12. #19135369C2semidirect
145. #100×C43Q8semidirect
369. C43#25489semidirect
442. #100Dic86semidirect

Maximal subgroups

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

subgroupindex
#191451392
#191443892
C2×#145831772
#191435392
#191361032
#191361022
#191359552
#191359532
#191355822
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