Finite Group Databasebeta

← #25148752

Subgroups — #25148752

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#19145145C211yesmaximal, characteristic, complemented
2#19144391C211yesmaximal, characteristic
3C2×#14583202C211yesmaximal, characteristic
4#19143539C211yesmaximal, characteristic, complemented
5#19136108C211yesmaximal, characteristic, complemented
6#19136101C211yesmaximal, characteristic, complemented
7#19135952C211yesmaximal, characteristic
8#19135950C211yesmaximal, characteristic
9#19135586C211yesmaximal, characteristic, complemented
10#19135374C211yesmaximal, characteristic, complemented
11#19135367C211yesmaximal, characteristic, complemented
12#19135257C211yesmaximal, characteristic
13#19135255C211yesmaximal, characteristic
14#19134386C211yesmaximal, characteristic
15C43×#1952C211yesmaximal, characteristic, complemented
16#14583452C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×#13063287C2211yescharacteristic
19#14583307—21no—
20#14583306—21no—
21#14583300—21no—
22#14583299—21no—
23#14583202—21no—
24#14583202—21no—
25#14583202—21no—
26#14583202—21no—
27#14583202—21no—
28#14583198—21no—
29#14583188—21no—
30#14583178—21no—
31#14583029—21no—
32#14583027—21no—
33#14583027—21no—
34C8×Dic86—21no—
35C2×#13063260C2211yescharacteristic
36#14582942C2211yescharacteristic
37#14582941C2211yescharacteristic
38#14582939C2211yescharacteristic
39#14582939C2211yescharacteristic
40C2×#13063256C2211yescharacteristic
41#14582926C2211yescharacteristic
42#14582925C2211yescharacteristic
43#14582922C2211yescharacteristic
44C2×Dic43⋊C8C2211yescharacteristic
45#14582905C2211yescharacteristic
46#14582903C2211yescharacteristic
47C2×#13063247C2211yescharacteristic
48C2×#13063245C2211yescharacteristic
49C2×#13063241C2211yescharacteristic
50C2×#13063241C2211yescharacteristic
51#14582857C2211yescharacteristic
52M16×Dic43C2211yescharacteristic
53M16×Dic43C2211yescharacteristic
54#14582668C2211yescharacteristic
55#14582668C2211yescharacteristic
56#14582667C2211yescharacteristic
57#14582667C2211yescharacteristic
58#14582664C2211yescharacteristic
59#14582663C2211yescharacteristic
60C2×#108×C43C2211yescharacteristic
61C43×#428C2211yescharacteristic
62C43×#428C2211yescharacteristic
63C2×#107×C43C2211yescharacteristic
64C43×#405C2211yescharacteristic
65C43×#343C2211yescharacteristic
66C43×#343C2211yescharacteristic
67C22×D172C2311yescharacteristic
68C22×C4×D43—21no—
69C2×#10621877C2311yescharacteristic
70C2×#10621877C2311yescharacteristic
71C2×#10621877C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063324D411yescharacteristic
74#13063324D411yescharacteristic
75#13063316—21no—
76#13063316—21no—
77#13063316—21no—
78#13063316—21no—
79#13063316D411yescharacteristic
80#13063316D411yescharacteristic
81#13063302—21no—
82#13063302—21no—
83C4×Dic86—21no—
84C4×Dic86—21no—
85#13063287—21no—
86#13063287—21no—
87#13063287—21no—
88#13063287—21no—
89#13063284C2311yescharacteristic
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43C2311yescharacteristic
92C2×Dic43⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×C4×Dic43C2311yescharacteristic
95#13063260—22no—
96#13063259—21no—
97#13063258—21no—
98#13063258—21no—
99#13063258—21no—
100#13063257—21no—
101#13063256—21no—
102#13063256—21no—
103#13063256—21no—
104#13063256—21no—
105#13063256—21no—
106C4⋊(C43⋊C8)—21no—
107C4⋊(C43⋊C8)—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8—21no—
112Dic43⋊C8D411yescharacteristic
113Dic43⋊C8D411yescharacteristic
114Dic43⋊C8D411yescharacteristic
115Dic43⋊C8D411yescharacteristic
116#13063247—21no—
117#13063247—21no—
118#13063247—21no—
119#13063247—21no—
120#13063245—21no—
121#13063245—21no—
122#13063245—21no—
123#13063245—21no—
124#13063241—22no—
125#13063241Q814yescomplemented
126#13063235—21no—
127#13063235—21no—
128#13063235—21no—
129C8×Dic43—21no—
130C8×Dic43—21no—
131C8×Dic43—21no—
132C2×M16×C43C2311yescharacteristic
133C2×M16×C43C2311yescharacteristic
134C2×M16×C43C2311yescharacteristic
135C22×C8×C43C2311yescharacteristic
136#117×C43C2311yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139#108×C43—22no—
140#107×C43—21no—
141#107×C43—21no—
142#107×C43—21no—
143#107×C43—21no—
144#106×C43—21no—
145#106×C43—21no—
146#97×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—
166M16×C43—21no—
167M16×C43—21no—
168M16×C43—21no—
169M16×C43—21no—
170M16×C43C2×Q812yes—
171M16×C43#4112yes—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43C2×D411yescharacteristic
178C2×C8×C43C2×D411yescharacteristic
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43C2×D411yescharacteristic
184C4⋊C4×C43C2×D411yescharacteristic
185C22⋊C4×C43—21no—
186C42×C43—21no—
187C22⋊Dic43—21no—
188(C2×D43)⋊C4—41no—
189(C2×D43)⋊C4—41no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—41no—
195C4⋊Dic43—41no—
196C4⋊Dic43C2×D411yescharacteristic
197C4⋊Dic43C2×D411yescharacteristic
198Dic43⋊C4—21no—
199Dic43⋊C4—21no—
200Dic43⋊C4—21no—
201Dic43⋊C4—21no—
202Dic43⋊C4—41no—
203Dic43⋊C4—41no—
204C4×Dic43—21no—
205C4×Dic43C2×D411yescharacteristic
206C4×Dic43C2×D411yescharacteristic
207C4×Dic43C2×D411yescharacteristic
208C4×Dic43C2×D411yescharacteristic
209#10621877—21no—
210#10621877—21no—
211#10621877—21no—
212#10621877—21no—
213#10621877—21no—
214#10621877C2×Q812yes—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8C2×D411yescharacteristic
221C2×C43⋊C8C2×D411yescharacteristic
222C23×C43C2×#4111yescharacteristic
223C22×D43—22no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—81no—
227C22×D43—81no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—81no—
233C2×C4×C43—81no—
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—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—81no—
246C2×Dic43#12111yescharacteristic
247C2×Dic43#12111yescharacteristic
248C2×Dic43#12111yescharacteristic
249C2×Dic43#12111yescharacteristic
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—22no—
261C8×C43—22no—
262C8×C43—41no—
263C43⋊C8—21no—
264C43⋊C8—21no—
265C43⋊C8—22no—
266C43⋊C8—41no—
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—41no—
280C4×C43—41no—
281C4×C43—81no—
282C4×C43—81no—
283C4×C43#54711yescharacteristic
284C4×C43#54811yescharacteristic
285C4×C43D4×Q811yescharacteristic
286C4×C43D4×Q811yescharacteristic
287Dic43—21no—
288Dic43—21no—
289Dic43—21no—
290Dic43—21no—
291Dic43—41no—
292Dic43—41no—
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#1952D4311yescharacteristic, complemented
304#1951—431no—
305#1950—431no—
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×#108—431no—
335C2×#108C2×D4311yescharacteristic
336#428—431no—
337#428—431no—
338#428—431no—
339#428—431no—
340#428C2×D4311yescharacteristic
341#428C2×D4311yescharacteristic
342C2×#107C2×D4311yescharacteristic
343C2×#106—431no—
344#424—431no—
345#424—431no—
346#423—431no—
347C2×C4⋊C8—431no—
348#418—431no—
349#418—431no—
350C2×#102—431no—
351C2×#102—431no—
352C2×#100—431no—
353C2×#100—431no—
354#405—431no—
355#405C2×D4311yescharacteristic
356C4×M16—431no—
357C4×M16—431no—
358#343—431no—
359#343—431no—
360#343—431no—
361#343—431no—
362#343C2×D4311yescharacteristic
363#343C2×D4311yescharacteristic
364#341—431no—
365#341—431no—
366C43#2549311yescharacteristic, complemented, Sylow
367C22×D4—431no—
368C23×C4—861no—
369C2×M16—431no—
370C2×M16—431no—
371C2×M16—431no—
372C2×M16C22×D4311yescharacteristic
373C2×M16C22×D4311yescharacteristic
374C2×M16C22×D4311yescharacteristic
375C22×C8—431no—
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#117C22×D4311yescharacteristic
395C2×C4⋊C4—431no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4C22×D4311yescharacteristic
399C2×C4⋊C4C22×D4311yescharacteristic
400C2×C22⋊C4—861no—
401C2×C42—431no—
402#108—22no—
403#108—862no—
404#107—21no—
405#107—21no—
406#107—21no—
407#107—21no—
408#107—861no—
409#107—861no—
410#107—861no—
411#107—861no—
412#106—21no—
413#106—21no—
414#106—861no—
415#106—861no—
416#106—861no—
417#106—861no—
418#106—861no—
419#106—861no—
420C4⋊C8—431no—
421C4⋊C8—431no—
422C4⋊C8—431no—
423C4⋊C8—431no—
424C4⋊C8—861no—
425C4⋊C8—861no—
426C4⋊C8—861no—
427C4⋊C8—861no—
428C4⋊C8—861no—
429C4⋊C8—861no—
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—21no—
458C22×C4—21no—
459C22×C4—431no—
460C22×C4—431no—
461C22×C4—861no—
462C22×C4—3442no—
463C22×C4—1721no—
464C22×C4—1721no—
465C22×C4C23×D4311yescharacteristic
466M16—21no—
467M16—21no—
468M16—21no—
469M16—21no—
470M16—432no—
471M16—861no—
472M16—861no—
473M16—861no—
474M16—861no—
475M16—861no—
476M16#1062189812yes—
477M16Q8×D4312yes—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—431no—
484C2×C8—431no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8D4×D4311yescharacteristic
491C2×C8D4×D4311yescharacteristic
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—431no—
497C4⋊C4—431no—
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—1721no—
507C4⋊C4—1721no—
508C4⋊C4—1721no—
509C4⋊C4—1721no—
510C4⋊C4D4×D4311yescharacteristic
511C4⋊C4D4×D4311yescharacteristic
512C22⋊C4—21no—
513C22⋊C4—861no—
514C22⋊C4—1721no—
515C22⋊C4—1721no—
516C42—21no—
517C42—431no—
518C42—431no—
519C42—431no—
520C42—431no—
521C42—861no—
522C23—862no—
523C23—3441no—
524C23—3441no—
525C23—1721no—
526C23—1721no—
527C23#41×D4311yescharacteristic
528Q8—3441no—
529Q8—1722no—
530D4—862no—
531D4—862no—
532D4—1721no—
533D4—1721no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—81no—
539C2×C4—81no—
540C2×C4—431no—
541C2×C4—431no—
542C2×C4—431no—
543C2×C4—431no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—3442no—
547C2×C4—3442no—
548C2×C4—3441no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4C2×D4×D4311yescharacteristic
553C2×C4C2×D4×D4311yescharacteristic
554C2×C4C2×Q8×D4311yescharacteristic
555C2×C4C2×#1062189811yescharacteristic
556C2×C4#1306337211yescharacteristic
557C2×C4#1306337311yescharacteristic
558C8—22no—
559C8—22no—
560C8—21no—
561C8—21no—
562C8—41no—
563C8—862no—
564C8—861no—
565C8—861no—
566C8—1721no—
567C8—1721no—
568C22—21no—
569C22—21no—
570C22—3442no—
571C22—3442no—
572C22—3441no—
573C22—3441no—
574C22—1722no—
575C22#121×D4311yescharacteristic
576C22#1458345311yescharacteristic
577C22#1458350811yescharacteristic
578C4—41no—
579C4—41no—
580C4—81no—
581C4—81no—
582C4—861no—
583C4—861no—
584C4—861no—
585C4—861no—
586C4—3441no—
587C4—1721no—
588C4—1721no—
589C4#1458355011yescharacteristic
590C4#1458355811yescharacteristic
591C4#1458356211yescharacteristic
592C4#1458356411yescharacteristic
593C2—21no—
594C2—21no—
595C2—3442no—
596C2#1913819311yescharacteristic
597C2#1914431711yescharacteristic
598C2#1914432111yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1952C2
socleC22×C43C2×#121
prime radicalC22×D172C23
hypercenter#1952D43
hypocenterC43#25493
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1952

Complements

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

NH ≅ G/Ntype
1. #19145145C2semidirect
4. #19143539C2semidirect
5. #19136108C2semidirect
6. #19136101C2semidirect
9. #19135586C2semidirect
10. #19135374C2semidirect
11. #19135367C2semidirect
15. C43×#1952C2semidirect
125. #13063241Q8semidirect
303. #1952D43semidirect
366. C43#25493semidirect

Maximal subgroups

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

subgroupindex
#191451452
#191443912
C2×#145832022
#191435392
#191361082
#191361012
#191359522
#191359502
#191355862
#191353742
#191353672
#191352572
#191352552
#191343862
C43×#19522
#2549343