Finite Group Databasebeta

← #25080368

Subgroups — #25080368

Order 11008.

590 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145915C211yesmaximal, characteristic
2#19145776C211yesmaximal, characteristic, complemented
3#19145309C211yesmaximal, characteristic, complemented
4#19143593C211yesmaximal, characteristic, complemented
5#19134180C211yesmaximal, characteristic, complemented
6#19134134C211yesmaximal, characteristic, complemented
7#19134117C211yesmaximal, characteristic, complemented
8#19134059C211yesmaximal, characteristic, complemented
9#19134049C211yesmaximal, characteristic, complemented
10#19134003C211yesmaximal, characteristic, complemented
11#19133998C211yesmaximal, characteristic, complemented
12#19133942C211yesmaximal, characteristic, complemented
13#19133348C211yesmaximal, characteristic, complemented
14#19133250C211yesmaximal, characteristic, complemented
15C43×#1543C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17#14583433C2211yescharacteristic
18#14583302C2211yescharacteristic
19#14583301—21no—
20#14583271C2211yescharacteristic
21#14583254—21no—
22#14583251C2211yescharacteristic
23#14583245C2211yescharacteristic
24#14583241—21no—
25#14583224—21no—
26#14583199—21no—
27#14583195C2211yescharacteristic
28#14583191C2211yescharacteristic
29#14583190C2211yescharacteristic
30#14583186C2211yescharacteristic
31#14583185C2211yescharacteristic
32#14583180C2211yescharacteristic
33#14583143—21no—
34#14583143—21no—
35#14583133—21no—
36#14583126—21no—
37#14583114—21no—
38#14583096C2211yescharacteristic
39#14583091C2211yescharacteristic
40#14583026C2211yescharacteristic
41#14583023C2211yescharacteristic
42#14582999—21no—
43#14582999—21no—
44#14582976C2211yescharacteristic
45#14582974—21no—
46#14582973—21no—
47#14582964C2211yescharacteristic
48#14582958—21no—
49C2×C4⋊(C43⋊C8)C2211yescharacteristic
50#14582853—21no—
51C4×#10621877C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582649C2211yescharacteristic
55#14582649C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582647C2211yescharacteristic
58#14582646C2211yescharacteristic
59#14582646C2211yescharacteristic
60C43×#532C2211yescharacteristic
61C43×#431C2211yescharacteristic
62C43×#431C2211yescharacteristic
63C43×#333C2211yescharacteristic
64C43×#333C2211yescharacteristic
65C43×#331C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C2×#10621883—21no—
68C2×#10621883—21no—
69C2×#10621883—21no—
70C2×#10621882—21no—
71C2×#10621877D411yescharacteristic
72C2×#10621877D411yescharacteristic
73C2×#10621872—21no—
74C22×C43⋊C8—21no—
75C2×C8×D43—21no—
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063319—21no—
79#13063317—21no—
80#13063317D411yescharacteristic
81#13063313D411yescharacteristic
82#13063308—21no—
83#13063304—21no—
84#13063304—21no—
85#13063304D411yescharacteristic
86#13063299D411yescharacteristic
87C4×Dic86—21no—
88C4×Dic86—21no—
89C4×Dic86C2311yescharacteristic
90C4×D172C2311yescharacteristic
91C4×C22⋊D43—21no—
92#13063284—21no—
93#13063282—21no—
94#13063259—21no—
95#13063259—21no—
96#13063258—21no—
97#13063258—21no—
98#13063258—21no—
99#13063257—21no—
100#13063257—21no—
101#13063256—21no—
102C4⋊(C43⋊C8)—21no—
103C4⋊(C43⋊C8)C2311yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107#13063250—21no—
108#13063250—21no—
109#13063248—21no—
110#13063248—21no—
111#13063248—21no—
112#13063247—21no—
113#13063247—21no—
114#13063246—21no—
115#13063246—21no—
116#13063246—21no—
117#13063246—21no—
118#13063245—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121#13063236D411yescharacteristic
122#13063236D411yescharacteristic
123#13063235—21no—
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C2×#41×C43—21no—
128C4⋊Q8×C43C2311yescharacteristic
129#127×C43C2311yescharacteristic
130#124×C43—21no—
131#121×C43—21no—
132#121×C43—21no—
133C4×D4×C43—21no—
134C4×D4×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140C22⋊C8×C43—21no—
141C22⋊C8×C43—21no—
142C4×C8×C43—21no—
143C4×C8×C43—21no—
144#41×C43—82no—
145C2×Q8×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—41no—
150C22×C4×C43—41no—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43#4111yescharacteristic
154C2×C22⋊D43—21no—
155C2×D172C2×D411yescharacteristic
156C2×C4×D43—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86C2×D411yescharacteristic
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C22⋊C4×C43—41no—
167C22⋊C4×C43—41no—
168C42×C43C2×D411yescharacteristic
169C42×C43C2×D411yescharacteristic
170C42×C43#4111yescharacteristic
171C42×C43C2411yescharacteristic
172C22⋊Dic43—21no—
173C22⋊Dic43—41no—
174#10621883—42no—
175#10621883—42no—
176#10621883—81no—
177#10621882—81no—
178(C2×D43)⋊C4—21no—
179(C2×D43)⋊C4—21no—
180(C2×D43)⋊C4—21no—
181(C2×D43)⋊C4—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43C2×D411yescharacteristic
187C4⋊Dic43C2×D411yescharacteristic
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192Dic43⋊C4—41no—
193Dic43⋊C4—41no—
194C4×Dic43—21no—
195C4×Dic43—41no—
196#10621877—22no—
197#10621877—41no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—81no—
201C2×C43⋊C8C2×D411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205#10621872—42no—
206C8×D43—42no—
207C23×C43—41no—
208C23×C43#12111yescharacteristic
209C22×D43—21no—
210Q8×C43—81no—
211D4×C43—41no—
212D4×C43—41no—
213D4×C43—41no—
214D4×C43—41no—
215D4×C43—81no—
216D4×C43—82no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—82no—
224C2×C4×C43#12111yescharacteristic
225C2×C4×C43#12111yescharacteristic
226C2×C4×C43#12111yescharacteristic
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C22⋊D43—81no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236D172—21no—
237D172—21no—
238C4×D43—41no—
239C4×D43—41no—
240Dic86—21no—
241Dic86—21no—
242Dic86—41no—
243Dic86—41no—
244Dic86—81no—
245C8×C43—41no—
246C8×C43—41no—
247C8×C43—41no—
248C8×C43—41no—
249C43⋊C8—21no—
250C43⋊C8—21no—
251C43⋊C8—21no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254C43⋊C8#13512yes—
255#19253—431nomaximal, Sylow
256C22×C43—21no—
257C22×C43—21no—
258C22×C43—21no—
259C22×C43—81no—
260C22×C43—81no—
261C22×C43—81no—
262C22×C43C2×#12111yescharacteristic
263C2×D43—41no—
264C2×D43—41no—
265C2×D43—41no—
266C4×C43—21no—
267C4×C43—21no—
268C4×C43—21no—
269C4×C43—21no—
270C4×C43—81no—
271C4×C43C2×#13511yescharacteristic
272C4×C43#57511yescharacteristic
273C4×C43#57711yescharacteristic
274C4×C43#57811yescharacteristic
275Dic43—41no—
276Dic43—41no—
277Dic43—41no—
278Dic43—81no—
279Dic43—81no—
280#3247—431no—
281#3233—431no—
282#3182—431no—
283#2969—431no—
284#1704—431no—
285#1698—431no—
286#1695—431no—
287#1685—431no—
288#1683—431no—
289#1677—431no—
290#1676—431no—
291#1666—431no—
292#1565—431no—
293#1543D4311yescharacteristic, complemented
294#1542—431no—
295C2×C43—41no—
296C2×C43—161no—
297C2×C43#303511yescharacteristic
298C2×C43#306311yescharacteristic
299C2×C43#306811yescharacteristic
300D43—81no—
301#533—431no—
302#532C2×D4311yescharacteristic
303#529—431no—
304#500—431no—
305#499—861no—
306#492—431no—
307#488—861no—
308#487—431no—
309#486—431no—
310#485—861no—
311#482—861no—
312#478—861no—
313#477—431no—
314#477—431no—
315#476—431no—
316#476—431no—
317#475—431no—
318#474—431no—
319#468—861no—
320#468—861no—
321#466—861no—
322#465—861no—
323#463—861no—
324#460—431no—
325#459—431no—
326#446—431no—
327C8×Q8—431no—
328#440—861no—
329#440—861no—
330#436—431no—
331#436—861no—
332#435—861no—
333C8×D4—431no—
334#433—861no—
335#431C2×D4311yescharacteristic
336#431C2×D4311yescharacteristic
337C2×C4⋊C8—431no—
338#405—861no—
339C4×M16—431no—
340#335—431no—
341#335—431no—
342#334—431no—
343#334—431no—
344#333—431no—
345#333—431no—
346#333C2×D4311yescharacteristic
347#333C2×D4311yescharacteristic
348#332—431no—
349#332—431no—
350#331C2×D4311yescharacteristic
351#331C2×D4311yescharacteristic
352C43#1925311yescharacteristic, complemented, Sylow
353C2×#41—21no—
354C2×SD16—861no—
355C2×SD16—861no—
356C2×SD16—861no—
357C2×D8—861no—
358C2×M16—431no—
359C2×M16—431no—
360C2×M16—861no—
361C22×C8—861no—
362C22×C8—861no—
363C4⋊Q8—431no—
364C4⋊Q8—431no—
365C4⋊Q8C22×D4311yescharacteristic
366#127C22×D4311yescharacteristic
367#126—861no—
368#125—431no—
369#125—861no—
370#124—21no—
371#124—431no—
372#123—861no—
373C22⋊Q8—431no—
374C22⋊Q8—861no—
375C22⋊Q8—861no—
376#121—21no—
377#121—21no—
378#121—431no—
379C4×Q8—431no—
380C4×Q8—861no—
381C4×Q8—861no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—431no—
385C4×D4—861no—
386#117—861no—
387#117—861no—
388C2×C42C22×D4311yescharacteristic
389#107—861no—
390#107—861no—
391#107—861no—
392#107—861no—
393#107—861no—
394#106—861no—
395#106—861no—
396#106—861no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—861no—
400C4⋊C8—861no—
401C4⋊C8—861no—
402C4⋊C8C22×D4311yescharacteristic
403C4⋊C8C22×D4311yescharacteristic
404C4⋊C8C22×D4311yescharacteristic
405C4⋊C8C22×D4311yescharacteristic
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#102—861no—
412#102—861no—
413#102—861no—
414#102—861no—
415#102—861no—
416#102—861no—
417#102—861no—
418C22⋊C8—21no—
419C22⋊C8—21no—
420C22⋊C8—861no—
421C22⋊C8—861no—
422#97—431no—
423#97—431no—
424#97—861no—
425C4×C8—21no—
426C4×C8—21no—
427C4×C8—431no—
428C4×C8—431no—
429C4×C8—861no—
430#41—82no—
431C2×Q8—21no—
432C2×Q8—431no—
433C2×Q8—861no—
434C2×Q8—861no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—41no—
439C2×D4—431no—
440C2×D4—861no—
441C22×C4—41no—
442C22×C4—861no—
443C22×C4#1062189811yescharacteristic
444C22×C4D4×D4311yescharacteristic
445C22×C4D4×D4311yescharacteristic
446SD16—3441no—
447SD16—1722no—
448SD16—1722no—
449D8—3441no—
450M16—862no—
451M16—1722no—
452M16—1721no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—431no—
458C2×C8—431no—
459C2×C8—431no—
460C2×C8—431no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—3441no—
464C2×C8—1722no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—431no—
468C4⋊C4—431no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—1721no—
478C4⋊C4—1721no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—861no—
482C22⋊C4—861no—
483C22⋊C4—861no—
484C22⋊C4—861no—
485C22⋊C4—861no—
486C22⋊C4—1721no—
487C42—861no—
488C42—1721no—
489C42#1062189811yescharacteristic
490C42D4×D4311yescharacteristic
491C42D4×D4311yescharacteristic
492C42C23×D4311yescharacteristic
493C23—41no—
494C23—861no—
495C23#1306329811yescharacteristic
496Q8—81no—
497Q8—861no—
498Q8—861no—
499Q8—3441no—
500Q8—1721no—
501Q8—1721no—
502D4—41no—
503D4—41no—
504D4—41no—
505D4—41no—
506D4—81no—
507D4—82no—
508D4—861no—
509D4—861no—
510D4—3441no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—82no—
518C2×C4—861no—
519C2×C4—861no—
520C2×C4—861no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4—1721no—
524C2×C4—1721no—
525C2×C4#1306329811yescharacteristic
526C2×C4#1306329811yescharacteristic
527C2×C4#1306329811yescharacteristic
528C2×C4C2×D4×D4311yescharacteristic
529C2×C4C2×D4×D4311yescharacteristic
530C2×C4C2×#1062189811yescharacteristic
531C8—41no—
532C8—41no—
533C8—41no—
534C8—41no—
535C8—432no—
536C8—861no—
537C8—861no—
538C8—861no—
539C8—1721no—
540C8—1721no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22—1721no—
548C22—1721no—
549C22—1721no—
550C22C2×#1306329811yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—81no—
556C4—3441no—
557C4—3441no—
558C4—1721no—
559C4—1721no—
560C4—1721no—
561C4#135×D4311yescharacteristic
562C4#1458369611yescharacteristic
563C4#1458370611yescharacteristic
564C4#1458371311yescharacteristic
565C2—41no—
566C2—161no—
567C2—3441no—
568C2#1914404811yescharacteristic
569C2#1914428911yescharacteristic
570C2#1914432211yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1543C2
socleC22×C43C2×#121
prime radical#19145915C2
hypercenter#1543D43
hypocenterC43#19253
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1543

Complements

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

NH ≅ G/Ntype
2. #19145776C2semidirect
3. #19145309C2semidirect
4. #19143593C2semidirect
5. #19134180C2semidirect
6. #19134134C2semidirect
7. #19134117C2semidirect
8. #19134059C2semidirect
9. #19134049C2semidirect
10. #19134003C2semidirect
11. #19133998C2semidirect
12. #19133942C2semidirect
13. #19133348C2semidirect
14. #19133250C2semidirect
15. C43×#1543C2semidirect
293. #1543D43semidirect
352. C43#19253semidirect

Maximal subgroups

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

subgroupindex
#191459152
#191457762
#191453092
#191435932
#191341802
#191341342
#191341172
#191340592
#191340492
#191340032
#191339982
#191339422
#191333482
#191332502
C43×#15432
#1925343