Finite Group Databasebeta

← #25148751

Subgroups — #25148751

Order 11008.

648 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145147C211yesmaximal, characteristic, complemented
2#19144394C211yesmaximal, characteristic
3C2×#14583200C211yesmaximal, characteristic
4#19143538C211yesmaximal, characteristic, complemented
5#19136107C211yesmaximal, characteristic, complemented
6#19136102C211yesmaximal, characteristic, complemented
7#19135950C211yesmaximal, characteristic
8#19135950C211yesmaximal, characteristic
9#19135587C211yesmaximal, characteristic, complemented
10#19135381C211yesmaximal, characteristic, complemented
11#19135376C211yesmaximal, characteristic, complemented
12#19135258C211yesmaximal, characteristic
13#19135258C211yesmaximal, characteristic
14C4×#13063241C211yesmaximal, characteristic
15C43×#1950C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17C2×#13063317C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19#14583308—21no—
20#14583308—21no—
21#14583301—21no—
22#14583301—21no—
23#14583200—21no—
24#14583200—21no—
25#14583200—21no—
26#14583200—21no—
27#14583200—21no—
28#14583200—21no—
29#14583190—21no—
30#14583180—21no—
31#14583028—21no—
32#14583028—21no—
33#14583026—21no—
34#14583023—21no—
35#14582941C2211yescharacteristic
36#14582941C2211yescharacteristic
37#14582941C2211yescharacteristic
38#14582941C2211yescharacteristic
39#14582941C2211yescharacteristic
40#14582941C2211yescharacteristic
41C2×#13063259C2211yescharacteristic
42C2×#13063257C2211yescharacteristic
43#14582925C2211yescharacteristic
44#14582925C2211yescharacteristic
45#14582905C2211yescharacteristic
46#14582905C2211yescharacteristic
47C2×#13063247C2211yescharacteristic
48C2×#13063247C2211yescharacteristic
49C2×#13063241C2211yescharacteristic
50C2×#13063241C2211yescharacteristic
51#14582854C2211yescharacteristic
52#14582854C2211yescharacteristic
53C4×#10621877C2211yescharacteristic
54#14582667C2211yescharacteristic
55#14582667C2211yescharacteristic
56#14582667C2211yescharacteristic
57#14582667C2211yescharacteristic
58#14582667C2211yescharacteristic
59#14582667C2211yescharacteristic
60C2×#108×C43C2211yescharacteristic
61C2×#108×C43C2211yescharacteristic
62C43×#423C2211yescharacteristic
63C2×C4⋊C8×C43C2211yescharacteristic
64C4×M16×C43C2211yescharacteristic
65C43×#341C2211yescharacteristic
66C43×#341C2211yescharacteristic
67C22×D172C2311yescharacteristic
68C22×C4×D43—21no—
69C2×#10621877C2311yescharacteristic
70C2×#10621877C2311yescharacteristic
71#13063325D411yescharacteristic
72#13063325D411yescharacteristic
73#13063317—21no—
74#13063317—21no—
75#13063317—21no—
76#13063317—21no—
77#13063317D411yescharacteristic
78#13063317D411yescharacteristic
79#13063304—21no—
80#13063304—21no—
81C4×Dic86—21no—
82C4×Dic86—21no—
83C4×D172—21no—
84C4×D172—21no—
85C4×D172—21no—
86C4×D172—21no—
87#13063284C2311yescharacteristic
88#13063284C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95#13063259—21no—
96#13063259—21no—
97#13063259—21no—
98#13063259—21no—
99#13063259—21no—
100#13063259—21no—
101#13063259—21no—
102#13063259—21no—
103#13063257—21no—
104#13063257—21no—
105#13063257—21no—
106#13063257—21no—
107#13063257—21no—
108#13063257—21no—
109#13063257—21no—
110#13063257—21no—
111Dic43⋊C8—21no—
112Dic43⋊C8—21no—
113Dic43⋊C8—21no—
114Dic43⋊C8—21no—
115#13063247—21no—
116#13063247—21no—
117#13063247—21no—
118#13063247—21no—
119#13063247—21no—
120#13063247—21no—
121#13063247—21no—
122#13063247—21no—
123#13063241—22no—
124#13063241Q814yescomplemented
125#13063236—21no—
126#13063235—21no—
127#13063235—21no—
128C4×C43⋊C8—21no—
129C8×Dic43—21no—
130C8×Dic43—21no—
131C2×M16×C43C2311yescharacteristic
132C2×M16×C43C2311yescharacteristic
133C2×M16×C43C2311yescharacteristic
134C2×M16×C43C2311yescharacteristic
135C22×C8×C43C2311yescharacteristic
136C22×C8×C43C2311yescharacteristic
137C2×C42×C43C2311yescharacteristic
138#108×C43—22no—
139#108×C43—22no—
140C4⋊C8×C43—21no—
141C4⋊C8×C43—21no—
142C4⋊C8×C43D411yescharacteristic
143C4⋊C8×C43D411yescharacteristic
144C4⋊C8×C43D411yescharacteristic
145C4⋊C8×C43D411yescharacteristic
146#97×C43—21no—
147C4×C8×C43—21no—
148C23×D43—21no—
149C22×C4×C43#4111yescharacteristic
150C22×C4×C43#4111yescharacteristic
151C22×C4×C43C2411yescharacteristic
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
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—
166M16×C43—21no—
167M16×C43—21no—
168M16×C43—21no—
169M16×C43—21no—
170M16×C43—21no—
171M16×C43—21no—
172M16×C43C2×Q812yes—
173M16×C43#4112yes—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43C2×D411yescharacteristic
183C2×C8×C43C2×D411yescharacteristic
184C2×C8×C43C2×D411yescharacteristic
185C2×C8×C43C2×D411yescharacteristic
186C42×C43C2×D411yescharacteristic
187C42×C43C2×D411yescharacteristic
188C42×C43C2×D411yescharacteristic
189C42×C43C2×D411yescharacteristic
190C22⋊Dic43—21no—
191C22⋊Dic43—21no—
192(C2×D43)⋊C4—41no—
193(C2×D43)⋊C4—41no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43C2×D411yescharacteristic
203C4⋊Dic43C2×D411yescharacteristic
204C4⋊Dic43C2×D411yescharacteristic
205C4⋊Dic43C2×D411yescharacteristic
206Dic43⋊C4—21no—
207Dic43⋊C4—21no—
208Dic43⋊C4—21no—
209Dic43⋊C4—21no—
210Dic43⋊C4—41no—
211Dic43⋊C4—41no—
212Dic43⋊C4—41no—
213Dic43⋊C4—41no—
214C4×Dic43—21no—
215C4×Dic43—21no—
216#10621877—21no—
217#10621877—21no—
218#10621877—21no—
219#10621877C2×Q812yes—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C23×C43C2×#4111yescharacteristic
223C22×D43—22no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—81no—
227C22×D43—81no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43#12111yescharacteristic
231C2×C4×C43#12111yescharacteristic
232C2×C4×C43#12111yescharacteristic
233C2×C4×C43#12111yescharacteristic
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C22×Q811yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C432−1+411yescharacteristic
239C2×C4×C432−1+411yescharacteristic
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—81no—
248C2×Dic43—81no—
249C2×Dic43—81no—
250D172—22no—
251D172—22no—
252D172—41no—
253D172—41no—
254C4×D43—82no—
255C4×D43—82no—
256Dic86—42no—
257Dic86—81no—
258C8×C43—21no—
259C8×C43—21no—
260C8×C43—21no—
261C8×C43—21no—
262C8×C43—22no—
263C8×C43—22no—
264C8×C43—41no—
265C8×C43—41no—
266C43⋊C8—22no—
267C43⋊C8—41no—
268#25493—431nomaximal, Sylow
269C22×C43—21no—
270C22×C43—21no—
271C22×C43C2×#12111yescharacteristic
272C22×C43#53311yescharacteristic
273C22×C43#54111yescharacteristic
274C2×D43—42no—
275C2×D43—82no—
276C2×D43—81no—
277C2×D43—81no—
278C2×D43—82no—
279C4×C43—21no—
280C4×C43—21no—
281C4×C43—21no—
282C4×C43—21no—
283C4×C43#54711yescharacteristic
284C4×C43#54811yescharacteristic
285C4×C43D4×Q811yescharacteristic
286C4×C43D4×Q811yescharacteristic
287Dic43—41no—
288Dic43—41no—
289Dic43—41no—
290Dic43—41no—
291Dic43—81no—
292Dic43—81no—
293Dic43—81no—
294#3166—431no—
295#3077—431no—
296C2×#478—431no—
297#2962—431no—
298#2090—431no—
299#2089—431no—
300#2063—431no—
301#2063—431no—
302#1998—431no—
303#1952—431no—
304#1951—431no—
305#1950D4311yescharacteristic, complemented
306#1931—431no—
307#1931—431no—
308C4×#100—431no—
309C2×C43—21no—
310C2×C43—21no—
311C2×C43#242911yescharacteristic
312C2×C43#306711yescharacteristic
313C2×C43#306811yescharacteristic
314D43—82no—
315#533—431no—
316C2×#125—431no—
317C2×C4×D4—431no—
318#501—861no—
319#501—861no—
320#499—861no—
321#499—861no—
322#478—861no—
323#478—861no—
324#478—861no—
325#478—861no—
326#478—861no—
327#478—861no—
328#476—861no—
329#474—861no—
330#446—861no—
331#446—861no—
332#446—861no—
333C8×Q8—861no—
334C2×#108C2×D4311yescharacteristic
335C2×#108C2×D4311yescharacteristic
336#428—431no—
337#428—431no—
338#428—431no—
339#428—431no—
340#428—431no—
341#428—431no—
342C2×#107—431no—
343C2×#106—431no—
344#424—431no—
345#424—431no—
346#423C2×D4311yescharacteristic
347C2×C4⋊C8C2×D4311yescharacteristic
348#418—431no—
349#418—431no—
350C2×#102—431no—
351C2×#102—431no—
352C2×#100—431no—
353C2×#100—431no—
354#405—431no—
355#405—431no—
356C4×M16—431no—
357C4×M16C2×D4311yescharacteristic
358#343—431no—
359#343—431no—
360#343—431no—
361#343—431no—
362#343—431no—
363#343—431no—
364#341C2×D4311yescharacteristic
365#341C2×D4311yescharacteristic
366C43#2549311yescharacteristic, complemented, Sylow
367C22×D4—431no—
368C23×C4—861no—
369C2×M16—431no—
370C2×M16—431no—
371C2×M16C22×D4311yescharacteristic
372C2×M16C22×D4311yescharacteristic
373C2×M16C22×D4311yescharacteristic
374C2×M16C22×D4311yescharacteristic
375C22×C8C22×D4311yescharacteristic
376C22×C8C22×D4311yescharacteristic
377C4⋊Q8—431no—
378C4⋊Q8—431no—
379#125—431no—
380#125—431no—
381#125—861no—
382#125—861no—
383#125—861no—
384#125—861no—
385C22⋊Q8—861no—
386C22⋊Q8—861no—
387C4×Q8—861no—
388C4×Q8—861no—
389C4×D4—861no—
390C4×D4—861no—
391C4×D4—861no—
392C4×D4—861no—
393#117—431no—
394#117—431no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C22⋊C4—861no—
401C2×C42C22×D4311yescharacteristic
402#108—22no—
403#108—22no—
404#107—861no—
405#107—861no—
406#107—861no—
407#107—861no—
408#107—861no—
409#107—861no—
410#107—861no—
411#107—861no—
412#106—861no—
413#106—861no—
414#106—861no—
415#106—861no—
416#106—861no—
417#106—861no—
418#106—861no—
419#106—861no—
420C4⋊C8—21no—
421C4⋊C8—21no—
422C4⋊C8—861no—
423C4⋊C8—861no—
424C4⋊C8—861no—
425C4⋊C8—861no—
426C4⋊C8D17211yescharacteristic
427C4⋊C8D17211yescharacteristic
428C4⋊C8D17211yescharacteristic
429C4⋊C8D17211yescharacteristic
430#102—861no—
431#102—861no—
432#102—861no—
433#102—861no—
434#102—861no—
435#102—861no—
436#102—861no—
437#102—861no—
438#100—434no—
439#100—862no—
440#97—21no—
441#97—861no—
442#97—861no—
443#97—861no—
444C4×C8—21no—
445C4×C8—861no—
446C4×C8—861no—
447C4×C8—861no—
448C24—861no—
449C2×Q8—861no—
450C2×Q8—861no—
451C2×D4—432no—
452C2×D4—861no—
453C2×D4—861no—
454C2×D4—861no—
455C2×D4—861no—
456C2×D4—861no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—3442no—
461C22×C4—1721no—
462C22×C4—1721no—
463C22×C4#1062190211yescharacteristic
464C22×C4#1062190211yescharacteristic
465C22×C4C23×D4311yescharacteristic
466M16—21no—
467M16—21no—
468M16—21no—
469M16—21no—
470M16—21no—
471M16—21no—
472M16—432no—
473M16—861no—
474M16—861no—
475M16—861no—
476M16#1062190012yes—
477M16Q8×D4312yes—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8C2×D17211yescharacteristic
489C2×C8C2×D17211yescharacteristic
490C2×C8C2×D17211yescharacteristic
491C2×C8C2×D17211yescharacteristic
492C4⋊C4—431no—
493C4⋊C4—431no—
494C4⋊C4—431no—
495C4⋊C4—431no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—1721no—
509C4⋊C4—1721no—
510C4⋊C4—1721no—
511C4⋊C4—1721no—
512C22⋊C4—861no—
513C22⋊C4—861no—
514C22⋊C4—1721no—
515C22⋊C4—1721no—
516C42—861no—
517C42—861no—
518C42C2×D17211yescharacteristic
519C42C2×D17211yescharacteristic
520C42D4×D4311yescharacteristic
521C42D4×D4311yescharacteristic
522C23—862no—
523C23—3441no—
524C23—3441no—
525C23—1721no—
526C23—1721no—
527C23C2×#1062190211yescharacteristic
528Q8—3441no—
529Q8—1722no—
530D4—862no—
531D4—862no—
532D4—1721no—
533D4—1721no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—3442no—
541C2×C4—3442no—
542C2×C4—3441no—
543C2×C4—3441no—
544C2×C4—3441no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4#1306330011yescharacteristic
549C2×C4#1306330011yescharacteristic
550C2×C4#1306330011yescharacteristic
551C2×C4#1306330011yescharacteristic
552C2×C4C2×D4×D4311yescharacteristic
553C2×C4C22×D17211yescharacteristic
554C2×C4C2×Q8×D4311yescharacteristic
555C2×C4C2×#1062190011yescharacteristic
556C2×C4#1306337211yescharacteristic
557C2×C4#1306337211yescharacteristic
558C8—21no—
559C8—21no—
560C8—21no—
561C8—21no—
562C8—22no—
563C8—22no—
564C8—41no—
565C8—41no—
566C8—862no—
567C8—1721no—
568C22—21no—
569C22—21no—
570C22—3442no—
571C22—3442no—
572C22—3441no—
573C22—3441no—
574C22—1722no—
575C22C2×#1306330011yescharacteristic
576C22#1458345411yescharacteristic
577C22#1458351211yescharacteristic
578C4—21no—
579C4—21no—
580C4—21no—
581C4—21no—
582C4—3441no—
583C4—3441no—
584C4—3441no—
585C4—1721no—
586C4—1721no—
587C4—1721no—
588C4—1721no—
589C4#1458355311yescharacteristic
590C4#1458355511yescharacteristic
591C4#1458356211yescharacteristic
592C4Q8×D17211yescharacteristic
593C2—21no—
594C2—21no—
595C2—3442no—
596C2#1913819211yescharacteristic
597C2#1914431611yescharacteristic
598C2#1914432411yescharacteristic
subgroupG/H
centerC22C2×#13063300
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1950C2
socleC22×C43C2×#121
prime radicalC22×D172C23
hypercenter#1950D43
hypocenterC43#25493
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1950

Complements

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

NH ≅ G/Ntype
1. #19145147C2semidirect
4. #19143538C2semidirect
5. #19136107C2semidirect
6. #19136102C2semidirect
9. #19135587C2semidirect
10. #19135381C2semidirect
11. #19135376C2semidirect
15. C43×#1950C2semidirect
124. #13063241Q8semidirect
305. #1950D43semidirect
366. C43#25493semidirect

Maximal subgroups

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

subgroupindex
#191451472
#191443942
C2×#145832002
#191435382
#191361072
#191361022
#191359502
#191355872
#191353812
#191353762
#191352582
C4×#130632412
C43×#19502
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