Finite Group Databasebeta

← #25084196

Subgroups — #25084196

Order 11008.

602 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145922C211yesmaximal, characteristic
2#19145725C211yesmaximal, characteristic, complemented
3#19145624C211yesmaximal, characteristic, complemented
4#19143757C211yesmaximal, characteristic, complemented
5#19134164C211yesmaximal, characteristic, complemented
6#19134157C211yesmaximal, characteristic, complemented
7#19134102C211yesmaximal, characteristic, complemented
8#19134095C211yesmaximal, characteristic, complemented
9#19134040C211yesmaximal, characteristic, complemented
10#19134033C211yesmaximal, characteristic, complemented
11#19133978C211yesmaximal, characteristic, complemented
12#19133971C211yesmaximal, characteristic, complemented
13#19133291C211yesmaximal, characteristic, complemented
14C2×#14582646C211yesmaximal, characteristic, complemented
15C43×#1573C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17C2×#13063325C2211yescharacteristic
18#14583433C2211yescharacteristic
19#14583297C2211yescharacteristic
20#14583297C2211yescharacteristic
21#14583293—21no—
22#14583268—21no—
23#14583246C2211yescharacteristic
24#14583246C2211yescharacteristic
25#14583218—21no—
26#14583218—21no—
27#14583200—21no—
28#14583195C2211yescharacteristic
29#14583190—21no—
30#14583190—21no—
31#14583190C2211yescharacteristic
32#14583135—21no—
33#14583128—21no—
34#14583115—21no—
35#14583110C2211yescharacteristic
36#14583110C2211yescharacteristic
37#14583105C2211yescharacteristic
38#14583105C2211yescharacteristic
39#14583100C2211yescharacteristic
40#14583095C2211yescharacteristic
41#14583057—21no—
42#14583040—21no—
43#14583029C2211yescharacteristic
44C8×Dic86C2211yescharacteristic
45#14582978C2211yescharacteristic
46#14582967—21no—
47C8×D172C2211yescharacteristic
48(C22⋊D43)⋊C8—21no—
49#14582959—21no—
50#14582924—21no—
51C2×C4⋊(C43⋊C8)C2211yescharacteristic
52#14582647C2211yescharacteristic
53#14582647C2211yescharacteristic
54#14582646C2211yescharacteristic
55#14582646C2211yescharacteristic
56#14582646C2211yescharacteristic
57#14582646C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#432C2211yescharacteristic
61C43×#431C2211yescharacteristic
62C2×C4⋊C8×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#334C2211yescharacteristic
66C43×#334C2211yescharacteristic
67C2×#10621898—21no—
68C22×Dic86—21no—
69C2×Dic172—21no—
70C2×Dic172—21no—
71C2×#10621873—21no—
72C2×#10621873—21no—
73C2×#10621873—21no—
74C2×D344—21no—
75C2×#10621872—21no—
76C22×C43⋊C8—21no—
77C2×C8×D43—21no—
78#13063325—21no—
79#13063325—21no—
80#13063325—21no—
81#13063325C2311yescharacteristic
82#13063325C2311yescharacteristic
83#13063325C2311yescharacteristic
84#13063322C2311yescharacteristic
85#13063319—21no—
86#13063317D411yescharacteristic
87#13063313—21no—
88#13063313D411yescharacteristic
89#13063308—21no—
90#13063304D411yescharacteristic
91#13063299—21no—
92#13063299—21no—
93#13063299D411yescharacteristic
94C4×Dic86C2311yescharacteristic
95C4×D172—21no—
96C4×D172—21no—
97C4×D172C2311yescharacteristic
98C4×C22⋊D43—21no—
99#13063282—21no—
100C2×C4⋊Dic43—21no—
101C2×C4⋊Dic43—21no—
102#13063259—21no—
103#13063257—21no—
104#13063257—21no—
105#13063257—21no—
106#13063257—21no—
107#13063257—21no—
108C4⋊(C43⋊C8)—21no—
109C4⋊(C43⋊C8)C2311yescharacteristic
110C4⋊(C43⋊C8)C2311yescharacteristic
111Dic43⋊C8—21no—
112Dic43⋊C8—21no—
113#13063250—21no—
114#13063250—21no—
115#13063250—21no—
116#13063250—21no—
117#13063250—21no—
118#13063247—21no—
119#13063247—21no—
120#13063247—21no—
121#13063247—21no—
122#13063247—21no—
123#13063247—21no—
124#13063247—21no—
125(C2×D43)⋊C8—21no—
126(C2×D43)⋊C8—21no—
127#13063235—21no—
128C8×Dic43—21no—
129C22×C8×C43—21no—
130C2×C42×C43C2311yescharacteristic
131C4⋊C8×C43—21no—
132C4⋊C8×C43D411yescharacteristic
133C4⋊C8×C43D411yescharacteristic
134C4⋊C8×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C22⋊C8×C43—21no—
139C22⋊C8×C43D411yescharacteristic
140C22⋊C8×C43D411yescharacteristic
141#97×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43#4111yescharacteristic
147C2×C22⋊D43—21no—
148C2×C22⋊D43—41no—
149C22×Dic43—41no—
150#10621898—82no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172C2×D411yescharacteristic
155C2×C4×D43—21no—
156C2×C4×D43—41no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—41no—
161C2×Dic86—81no—
162C2×Dic86—81no—
163C2×Dic86C2×D411yescharacteristic
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—81no—
169C2×C8×C43C2×D411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C42×C43C2×D411yescharacteristic
174C42×C43C2×D411yescharacteristic
175C42×C43#4111yescharacteristic
176C42×C43C2411yescharacteristic
177C22⋊Dic43—21no—
178(C2×D43)⋊C4—21no—
179(C2×D43)⋊C4—21no—
180(C2×D43)⋊C4—21no—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—41no—
183(C2×D43)⋊C4—41no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—41no—
191C4⋊Dic43—41no—
192C4⋊Dic43C2×D411yescharacteristic
193C4⋊Dic43C2×D411yescharacteristic
194Dic43⋊C4—21no—
195Dic43⋊C4—21no—
196Dic43⋊C4—21no—
197Dic43⋊C4—21no—
198C4×Dic43—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—81no—
202Dic172—81no—
203Dic172—81no—
204D344—81no—
205#10621873—81no—
206#10621873—81no—
207#10621873—81no—
208#10621872—81no—
209C8×D43—81no—
210C23×C43#12111yescharacteristic
211C22×D43—21no—
212C22×D43—41no—
213C2×C4×C43—22no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43#12111yescharacteristic
219C2×C4×C43#12111yescharacteristic
220C2×C4×C43#12111yescharacteristic
221C2×C4×C43C22×D411yescharacteristic
222C2×C4×C43C22×D411yescharacteristic
223C2×C4×C43C2×#4111yescharacteristic
224C22⋊D43—42no—
225C22⋊D43—82no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—41no—
230C2×Dic43—41no—
231C2×Dic43—41no—
232C2×Dic43—82no—
233D172—21no—
234D172—21no—
235D172—41no—
236D172—41no—
237D172—41no—
238D172—41no—
239D172—81no—
240C4×D43—41no—
241C4×D43—41no—
242C4×D43—82no—
243Dic86—21no—
244Dic86—21no—
245Dic86—41no—
246Dic86—41no—
247Dic86—41no—
248Dic86—41no—
249Dic86—82no—
250Dic86—81no—
251C8×C43—21no—
252C8×C43—21no—
253C8×C43—21no—
254C8×C43—21no—
255C8×C43—41no—
256C8×C43—41no—
257C8×C43—41no—
258C8×C43—41no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261#19589—431nomaximal, Sylow
262C22×C43—21no—
263C22×C43—21no—
264C22×C43#47112yes—
265C22×C43C2×#12111yescharacteristic
266C2×D43—41no—
267C2×D43—41no—
268C2×D43—41no—
269C2×D43—81no—
270C2×D43—81no—
271C2×D43—81no—
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—21no—
276C4×C43#57611yescharacteristic
277C4×C43#57711yescharacteristic
278C4×C43#57711yescharacteristic
279C4×C43#57811yescharacteristic
280Dic43—41no—
281Dic43—41no—
282Dic43—41no—
283Dic43—81no—
284Dic43—81no—
285Dic43—81no—
286#3247—431no—
287#3227—431no—
288#3218—431no—
289#2994—431no—
290#1702—431no—
291#1701—431no—
292#1692—431no—
293#1691—431no—
294#1682—431no—
295#1681—431no—
296#1672—431no—
297#1671—431no—
298#1573D4311yescharacteristic, complemented
299#1551—431no—
300C2×#332—431no—
301C2×C43—22no—
302C2×C43#304611yescharacteristic
303C2×C43#306211yescharacteristic
304C2×C43C2×#47111yescharacteristic
305D43—81no—
306D43—161no—
307#532—431no—
308C2×C4⋊Q8—431no—
309#529—431no—
310#498—431no—
311#498—431no—
312#497—861no—
313#491—861no—
314#486—431no—
315#486—431no—
316#481—861no—
317#481—861no—
318#478—861no—
319#477—431no—
320#476—431no—
321#476—861no—
322#476—861no—
323#466—861no—
324#465—861no—
325#463—861no—
326#462—431no—
327#462—431no—
328#461—431no—
329#461—431no—
330#460—431no—
331#459—431no—
332#451—861no—
333#448—861no—
334#446—431no—
335C8×Q8—431no—
336#436—431no—
337#435—861no—
338C8×D4—431no—
339C8×D4—861no—
340#433—861no—
341#432C2×D4311yescharacteristic
342#431C2×D4311yescharacteristic
343#424—861no—
344C2×C4⋊C8—431no—
345C2×C4⋊C8C2×D4311yescharacteristic
346#335C2×D4311yescharacteristic
347#335C2×D4311yescharacteristic
348#334C2×D4311yescharacteristic
349#334C2×D4311yescharacteristic
350#333—431no—
351#333—431no—
352#332—431no—
353#332—431no—
354#332—431no—
355#332—431no—
356#331—431no—
357#331—431no—
358C43#1958911yescharacteristic, complemented, Sylow
359C2×#41—861no—
360C22×Q8—861no—
361C2×Q16—861no—
362C2×Q16—861no—
363C2×SD16—861no—
364C2×SD16—861no—
365C2×SD16—861no—
366C2×D8—861no—
367C2×M16—861no—
368C22×C8—21no—
369C22×C8—861no—
370C22×C8—861no—
371C4⋊Q8—431no—
372C4⋊Q8—431no—
373C4⋊Q8—431no—
374C4⋊Q8—861no—
375C4⋊Q8—861no—
376C4⋊Q8—861no—
377#127—431no—
378#126—861no—
379#125—431no—
380#124—431no—
381#124—861no—
382#123—861no—
383C22⋊Q8—431no—
384#121—431no—
385#121—861no—
386#121—861no—
387C4×Q8—431no—
388C4×D4—431no—
389C4×D4—861no—
390C4×D4—861no—
391C4×D4—861no—
392#117—861no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C42C22×D4311yescharacteristic
396#107—861no—
397#106—861no—
398#106—861no—
399#106—861no—
400#106—861no—
401#106—861no—
402C4⋊C8—21no—
403C4⋊C8—431no—
404C4⋊C8—431no—
405C4⋊C8—861no—
406C4⋊C8—861no—
407C4⋊C8—861no—
408C4⋊C8D17211yescharacteristic
409C4⋊C8D17211yescharacteristic
410C4⋊C8C22×D4311yescharacteristic
411C4⋊C8C22×D4311yescharacteristic
412C4⋊C8C22×D4311yescharacteristic
413C4⋊C8C22×D4311yescharacteristic
414#103—861no—
415#103—861no—
416#103—861no—
417#103—861no—
418#103—861no—
419#102—861no—
420#102—861no—
421#102—861no—
422#102—861no—
423#102—861no—
424#102—861no—
425#102—861no—
426C22⋊C8—21no—
427C22⋊C8—861no—
428C22⋊C8—861no—
429C22⋊C8D17211yescharacteristic
430C22⋊C8D17211yescharacteristic
431#97—21no—
432#97—861no—
433C4×C8—861no—
434C4×C8C22×D4311yescharacteristic
435C4×C8C22×D4311yescharacteristic
436#41—3442no—
437C2×Q8—431no—
438C2×Q8—861no—
439C2×Q8—861no—
440C2×Q8—861no—
441C2×Q8—3441no—
442C2×Q8—3441no—
443C2×Q8—1721no—
444C2×D4—431no—
445C2×D4—861no—
446C2×D4—861no—
447C2×D4—861no—
448C2×D4—861no—
449C2×D4—1721no—
450C22×C4—861no—
451C22×C4—1721no—
452C22×C4—1721no—
453C22×C4C2×D17211yescharacteristic
454C22×C4D4×D4311yescharacteristic
455C22×C4#1062190211yescharacteristic
456Q16—3441no—
457Q16—3441no—
458SD16—3441no—
459SD16—3441no—
460SD16—3441no—
461D8—3441no—
462M16—3441no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—81no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8—3441no—
471C2×C8—3441no—
472C2×C8C2×D17211yescharacteristic
473C2×C8C2×D17211yescharacteristic
474C2×C8C2×D17211yescharacteristic
475C2×C8C2×D17211yescharacteristic
476C4⋊C4—431no—
477C4⋊C4—431no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—1721no—
489C4⋊C4—1721no—
490C22⋊C4—861no—
491C22⋊C4—861no—
492C22⋊C4—861no—
493C22⋊C4—861no—
494C22⋊C4—861no—
495C22⋊C4—1721no—
496C22⋊C4—1721no—
497C42—861no—
498C42C2×D17211yescharacteristic
499C42D4×D4311yescharacteristic
500C42#1062190211yescharacteristic
501C42C23×D4311yescharacteristic
502C23—861no—
503C23—1721no—
504C23#1306330011yescharacteristic
505Q8—861no—
506Q8—861no—
507Q8—3441no—
508Q8—3442no—
509Q8—1721no—
510Q8—1721no—
511Q8—1721no—
512Q8—1721no—
513D4—861no—
514D4—861no—
515D4—3441no—
516D4—3442no—
517D4—1722no—
518D4—1721no—
519D4—1721no—
520D4—1721no—
521D4—1721no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—861no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—3442no—
531C2×C4—3442no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4#1306330011yescharacteristic
538C2×C4#1306330011yescharacteristic
539C2×C4#1306330011yescharacteristic
540C2×C4C2×D4×D4311yescharacteristic
541C2×C4C22×D17211yescharacteristic
542C2×C4C2×#1062190211yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—21no—
547C8—41no—
548C8—41no—
549C8—41no—
550C8—41no—
551C8—1721no—
552C8—1721no—
553C22—21no—
554C22—21no—
555C22—3441no—
556C22—3441no—
557C22—3441no—
558C22—1721no—
559C22—1721no—
560C22—1721no—
561C22#1458316312yes—
562C22C2×#1306330011yescharacteristic
563C4—21no—
564C4—21no—
565C4—21no—
566C4—21no—
567C4—3441no—
568C4—3441no—
569C4—3441no—
570C4—1721no—
571C4—1721no—
572C4—1721no—
573C4#1458370311yescharacteristic
574C4#1458370811yescharacteristic
575C4#1458371111yescharacteristic
576C4#1458371611yescharacteristic
577C2—22no—
578C2—3441no—
579C2—6881no—
580C2#1914414711yescharacteristic
581C2#1914427611yescharacteristic
582C2C2×#1458316311yescharacteristic
subgroupG/H
centerC22C2×#13063300
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1573C2
socleC22×C43C2×#121
prime radical#19145922C2
hypercenter#1573D43
hypocenterC43#19589
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1573

Complements

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

NH ≅ G/Ntype
2. #19145725C2semidirect
3. #19145624C2semidirect
4. #19143757C2semidirect
5. #19134164C2semidirect
6. #19134157C2semidirect
7. #19134102C2semidirect
8. #19134095C2semidirect
9. #19134040C2semidirect
10. #19134033C2semidirect
11. #19133978C2semidirect
12. #19133971C2semidirect
13. #19133291C2semidirect
14. C2×#14582646C2semidirect
15. C43×#1573C2semidirect
298. #1573D43semidirect
358. C43#19589semidirect

Maximal subgroups

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

subgroupindex
#191459222
#191457252
#191456242
#191437572
#191341642
#191341572
#191341022
#191340952
#191340402
#191340332
#191339782
#191339712
#191332912
C2×#145826462
C43×#15732
#1958943