Finite Group Databasebeta

← #25079852

Subgroups — #25079852

Order 11008.

570 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145939C211yesmaximal, characteristic
2#19145938C211yesmaximal, characteristic
3#19145104C211yesmaximal, characteristic
4#19143524C211yesmaximal, characteristic
5#19134122C211yesmaximal, characteristic, complemented
6#19134121C211yesmaximal, characteristic, complemented
7#19134112C211yesmaximal, characteristic, complemented
8#19134111C211yesmaximal, characteristic, complemented
9#19133978C211yesmaximal, characteristic, complemented
10#19133977C211yesmaximal, characteristic, complemented
11#19133974C211yesmaximal, characteristic, complemented
12#334×D43C211yesmaximal, characteristic
13#19133284C211yesmaximal, characteristic
14#19133282C211yesmaximal, characteristic
15C43×#1672C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583454C2211yescharacteristic
18#14583453C2211yescharacteristic
19#14583302C2211yescharacteristic
20#14583302C2211yescharacteristic
21#14583299—21no—
22#14583299—21no—
23#14583297C2211yescharacteristic
24#14583195C2211yescharacteristic
25#14583194C2211yescharacteristic
26#14583193—21no—
27#14583192—21no—
28#14583191C2211yescharacteristic
29#14583141—21no—
30#14583139—21no—
31#14583139—21no—
32#14583137—21no—
33#14583110C2211yescharacteristic
34#14583109C2211yescharacteristic
35#14583108—21no—
36#14583107—21no—
37#14583106C2211yescharacteristic
38#14583030C2211yescharacteristic
39#14583028—21no—
40#14583026C2211yescharacteristic
41C8×Dic86—21no—
42C8×Dic86C2211yescharacteristic
43#14582934—21no—
44#14582934—21no—
45#14582924—21no—
46#14582921C2211yescharacteristic
47C4⋊C8×D43C2211yescharacteristic
48C4⋊C8×D43C2211yescharacteristic
49#14582853—21no—
50C4×C8×D43C2211yescharacteristic
51#14582650C2211yescharacteristic
52#14582649C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582648C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582646C2211yescharacteristic
58#14582645C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#498C2211yescharacteristic
61C43×#477C2211yescharacteristic
62C43×#462C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic
65C43×#333C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×Dic172—21no—
68C2×#10621885—21no—
69C2×#10621885—21no—
70C2×#10621872—21no—
71C2×C8×D43—21no—
72C2×C8×D43—21no—
73C2×C8×D43D411yescharacteristic
74C2×C8×D43D411yescharacteristic
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063324D411yescharacteristic
78#13063323D411yescharacteristic
79#13063316—21no—
80#13063316—21no—
81#13063315—21no—
82#13063305—21no—
83#13063305—21no—
84#13063305D411yescharacteristic
85#13063303—21no—
86#13063301—21no—
87#13063301—21no—
88#13063301D411yescharacteristic
89Q8×Dic43—21no—
90Q8×Dic43—21no—
91C4×Dic86—21no—
92C4×Dic86C2311yescharacteristic
93#13063290—21no—
94#13063290—21no—
95#13063283—21no—
96#13063283—21no—
97#13063282—21no—
98C42×D43C2311yescharacteristic
99#13063259—21no—
100#13063258—21no—
101#13063258—21no—
102#13063258—21no—
103#13063258—21no—
104#13063258—21no—
105#13063258—21no—
106#13063257—21no—
107#13063257—21no—
108C4⋊(C43⋊C8)—21no—
109C4⋊(C43⋊C8)C2311yescharacteristic
110C4⋊(C43⋊C8)C2311yescharacteristic
111C4⋊(C43⋊C8)C2311yescharacteristic
112Dic43⋊C8—21no—
113Dic43⋊C8—21no—
114Dic43⋊C8—21no—
115Dic43⋊C8—21no—
116Dic43⋊C8—21no—
117#13063250—21no—
118#13063250—21no—
119#13063249—21no—
120#13063249—21no—
121#13063248—21no—
122#13063248—21no—
123#13063236—21no—
124#13063235—21no—
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C8×Dic43D411yescharacteristic
128C8×Dic43D411yescharacteristic
129C2×Q16×C43—21no—
130C4⋊Q8×C43C2311yescharacteristic
131C4⋊Q8×C43C2311yescharacteristic
132C4×Q8×C43C2311yescharacteristic
133#107×C43—21no—
134#106×C43—21no—
135#106×C43—21no—
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#103×C43—21no—
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×C4×D43C2×D411yescharacteristic
148C2×C4×D43C2×D411yescharacteristic
149C2×C4×D43#4111yescharacteristic
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86C2×D411yescharacteristic
154Q16×C43—81no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43C2×D411yescharacteristic
159C2×C8×C43C2×D411yescharacteristic
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43C2×D411yescharacteristic
166C42×C43—21no—
167C42×C43C2411yescharacteristic
168#10621885—81no—
169#10621885—81no—
170(C2×D43)⋊C4—21no—
171(C2×D43)⋊C4—21no—
172(C2×D43)⋊C4—41no—
173(C2×D43)⋊C4—41no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—41no—
180C4⋊Dic43—41no—
181C4⋊Dic43C2×D411yescharacteristic
182Dic43⋊C4—21no—
183Dic43⋊C4—21no—
184Dic43⋊C4—21no—
185Dic43⋊C4—21no—
186Dic43⋊C4—21no—
187Dic43⋊C4—41no—
188Dic43⋊C4—41no—
189C4×Dic43—21no—
190C4×Dic43—41no—
191C4×Dic43—41no—
192C4×Dic43C2×D411yescharacteristic
193C4×Dic43C2×D411yescharacteristic
194C4×Dic43#4111yescharacteristic
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8C2×D411yescharacteristic
199C2×C43⋊C8C2×D411yescharacteristic
200Dic172—81no—
201#10621872—42no—
202C8×D43—22no—
203C8×D43—81no—
204C8×D43—81no—
205C8×D43Q1614yescomplemented
206C22×D43#12111yescharacteristic
207Q8×C43—21no—
208Q8×C43—21no—
209Q8×C43—41no—
210Q8×C43—41no—
211Q8×C43—81no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43C22×D411yescharacteristic
217C2×C4×C43C22×D411yescharacteristic
218C2×C4×C43C2×#4111yescharacteristic
219C2×Dic43—21no—
220C2×Dic43—21no—
221C2×Dic43—41no—
222C2×Dic43—41no—
223C2×Dic43#12111yescharacteristic
224C2×Dic43#12111yescharacteristic
225C2×Dic43#12111yescharacteristic
226C4×D43—21no—
227C4×D43—21no—
228C4×D43—41no—
229C4×D43C2×Q1612yes—
230C4×D43#13712yes—
231Dic86—21no—
232Dic86—21no—
233Dic86—42no—
234Dic86—41no—
235Dic86—41no—
236Dic86—81no—
237C8×C43—21no—
238C8×C43—41no—
239C8×C43—41no—
240C8×C43—41no—
241C8×C43C2×Q1612yes—
242C43⋊C8—21no—
243C43⋊C8—41no—
244C43⋊C8—41no—
245C43⋊C8—41no—
246C43⋊C8C2×Q1612yes—
247#19210—431nomaximal, Sylow
248C22×C43C2×#12111yescharacteristic
249C2×D43—21no—
250C2×D43—21no—
251C2×D43#46212yes—
252C4×C43—21no—
253C4×C43—41no—
254C4×C43—41no—
255C4×C43—81no—
256C4×C43—81no—
257C4×C43C22×Q1611yescharacteristic
258C4×C43C2×#13711yescharacteristic
259C4×C43#57711yescharacteristic
260C4×C43#57711yescharacteristic
261Dic43—21no—
262Dic43—21no—
263Dic43—41no—
264Dic43—41no—
265Dic43—81no—
266Dic43—81no—
267Dic43#46212yes—
268#3249—431no—
269#3249—431no—
270#3160—431no—
271#2960—431no—
272#1696—431no—
273#1696—431no—
274#1694—431no—
275#1694—431no—
276#1672—431no—
277#1672—431no—
278#1672—431no—
279#1672D4311yescharacteristic, complemented
280C2×#334—431no—
281#1550—431no—
282#1550—431no—
283C2×C43C2×#46211yescharacteristic
284C2×C43#306011yescharacteristic
285C2×C43#306711yescharacteristic
286D43—22no—
287#533—431no—
288#533—431no—
289#533—431no—
290#500—431no—
291#500—431no—
292#499—861no—
293#499—861no—
294#498—431no—
295#498C2×D4311yescharacteristic
296#477—431no—
297#477—431no—
298#477—431no—
299#477—861no—
300#477—861no—
301#477C2×D4311yescharacteristic
302#467—861no—
303#467—861no—
304#467—861no—
305#467—861no—
306#462—431no—
307#462—431no—
308#462—431no—
309#462—861no—
310#462—861no—
311#462C2×D4311yescharacteristic
312#446—431no—
313#446—431no—
314#446—861no—
315C8×Q8—431no—
316C8×Q8—861no—
317C8×Q8C2×D4311yescharacteristic
318#427—861no—
319#427—861no—
320#424—861no—
321#423—431no—
322C2×C4⋊C8—431no—
323C2×C4⋊C8—431no—
324#405—861no—
325C2×C4×C8—431no—
326#334—431no—
327#334—431no—
328#334—431no—
329#334C2×D4311yescharacteristic
330#333—431no—
331#333—431no—
332#333—431no—
333#333C2×D4311yescharacteristic
334#332—431no—
335#332—431no—
336#332—431no—
337#332C2×D4311yescharacteristic
338C43#1921011yescharacteristic, complemented, Sylow
339C2×Q16—21no—
340C2×Q16—861no—
341C2×Q16—861no—
342C2×Q16—861no—
343C2×M16—861no—
344C22×C8—431no—
345C22×C8—431no—
346C22×C8—861no—
347C22×C8—861no—
348C4⋊Q8—431no—
349C4⋊Q8—431no—
350C4⋊Q8—431no—
351C4⋊Q8—431no—
352C4⋊Q8C22×D4311yescharacteristic
353C4⋊Q8C22×D4311yescharacteristic
354#125—861no—
355#125—861no—
356#125—861no—
357C22⋊Q8—431no—
358C22⋊Q8—431no—
359C22⋊Q8—861no—
360C22⋊Q8—861no—
361C22⋊Q8—861no—
362C22⋊Q8—861no—
363C22⋊Q8—861no—
364C4×Q8—431no—
365C4×Q8—861no—
366C4×Q8—861no—
367C4×Q8—861no—
368C4×Q8—861no—
369C4×Q8—861no—
370C4×Q8C22×D4311yescharacteristic
371#117—861no—
372#117—861no—
373#117—861no—
374C2×C42—431no—
375#107—21no—
376#107—861no—
377#107—861no—
378#107—861no—
379#107—861no—
380#107—861no—
381#107—861no—
382#107—861no—
383#106—21no—
384#106—21no—
385#106—861no—
386#106—861no—
387C4⋊C8—21no—
388C4⋊C8—431no—
389C4⋊C8—431no—
390C4⋊C8—431no—
391C4⋊C8—861no—
392C4⋊C8—861no—
393C4⋊C8—861no—
394C4⋊C8—861no—
395C4⋊C8—861no—
396C4⋊C8—861no—
397C4⋊C8C22×D4311yescharacteristic
398C4⋊C8C22×D4311yescharacteristic
399C4⋊C8C22×D4311yescharacteristic
400#103—21no—
401#103—21no—
402#103—861no—
403#103—861no—
404#103—861no—
405#103—861no—
406#103—861no—
407#103—861no—
408#97—861no—
409#97—861no—
410C4×C8—21no—
411C4×C8—431no—
412C4×C8—431no—
413C4×C8—431no—
414C4×C8—861no—
415C4×C8C22×D4311yescharacteristic
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—431no—
419C2×Q8—861no—
420C2×Q8—861no—
421C2×Q8—861no—
422C2×Q8D4×D4311yescharacteristic
423C22×C4—431no—
424C22×C4—431no—
425C22×C4—431no—
426Q16—81no—
427Q16—3441no—
428Q16—3441no—
429Q16—3441no—
430M16—1722no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—431no—
435C2×C8—434no—
436C2×C8—431no—
437C2×C8—862no—
438C2×C8—861no—
439C2×C8—861no—
440C2×C8—861no—
441C2×C8—3441no—
442C2×C8—3441no—
443C2×C8D4×D4311yescharacteristic
444C2×C8D4×D4311yescharacteristic
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—431no—
451C4⋊C4—861no—
452C4⋊C4—861no—
453C4⋊C4—861no—
454C4⋊C4—861no—
455C4⋊C4—861no—
456C4⋊C4—861no—
457C4⋊C4—861no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—1721no—
462C4⋊C4—1721no—
463C4⋊C4—1721no—
464C4⋊C4—1721no—
465C4⋊C4D4×D4311yescharacteristic
466C22⋊C4—861no—
467C22⋊C4—861no—
468C22⋊C4—1721no—
469C22⋊C4—1721no—
470C42—21no—
471C42—431no—
472C42—431no—
473C42—431no—
474C42—861no—
475C42—1721no—
476C42—1721no—
477C42C23×D4311yescharacteristic
478C23—431no—
479Q8—21no—
480Q8—21no—
481Q8—41no—
482Q8—41no—
483Q8—81no—
484Q8—861no—
485Q8—861no—
486Q8—3441no—
487Q8—1722no—
488Q8—1721no—
489Q8—1721no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—431no—
495C2×C4—432no—
496C2×C4—432no—
497C2×C4—431no—
498C2×C4—431no—
499C2×C4—861no—
500C2×C4—861no—
501C2×C4—861no—
502C2×C4—861no—
503C2×C4—1721no—
504C2×C4—1721no—
505C2×C4—1721no—
506C2×C4C2×D4×D4311yescharacteristic
507C2×C4C2×D4×D4311yescharacteristic
508C2×C4#41×D4311yescharacteristic
509C8—21no—
510C8—41no—
511C8—41no—
512C8—41no—
513C8—432no—
514C8—861no—
515C8—1721no—
516C8—1721no—
517C8—1721no—
518C8Q16×D4312yes—
519C22—432no—
520C22—861no—
521C22—861no—
522C22#121×D4311yescharacteristic
523C4—21no—
524C4—41no—
525C4—41no—
526C4—81no—
527C4—81no—
528C4—432no—
529C4—861no—
530C4—861no—
531C4—3441no—
532C4—3441no—
533C4—1721no—
534C4—1721no—
535C4C2×Q16×D4311yescharacteristic
536C4#137×D4311yescharacteristic
537C4#1458370511yescharacteristic
538C4#1458370611yescharacteristic
539C2—862no—
540C2#462×D4311yescharacteristic
541C2#1914425211yescharacteristic
542C2#1914431011yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1672C2
socleC22×C43C2×#121
prime radicalC22×D43#121
hypercenter#1672D43
hypocenterC43#19210
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1672

Complements

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

NH ≅ G/Ntype
5. #19134122C2semidirect
6. #19134121C2semidirect
7. #19134112C2semidirect
8. #19134111C2semidirect
9. #19133978C2semidirect
10. #19133977C2semidirect
11. #19133974C2semidirect
15. C43×#1672C2semidirect
205. C8×D43Q16semidirect
279. #1672D43semidirect
338. C43#19210semidirect

Maximal subgroups

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

subgroupindex
#191459392
#191459382
#191451042
#191435242
#191341222
#191341212
#191341122
#191341112
#191339782
#191339772
#191339742
#334×D432
#191332842
#191332822
C43×#16722
#1921043