Finite Group Databasebeta

← #25084166

Subgroups — #25084166

Order 11008.

550 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145969C211yesmaximal, characteristic
2#19145776C211yesmaximal, characteristic
3#19145756C211yesmaximal, characteristic, complemented
4#19143757C211yesmaximal, characteristic
5#19134171C211yesmaximal, characteristic, complemented
6#19134150C211yesmaximal, characteristic, complemented
7#19134124C211yesmaximal, characteristic, complemented
8#19134095C211yesmaximal, characteristic, complemented
9#19134054C211yesmaximal, characteristic, complemented
10#19134019C211yesmaximal, characteristic, complemented
11#19133995C211yesmaximal, characteristic, complemented
12#19133978C211yesmaximal, characteristic, complemented
13#19133286C211yesmaximal, characteristic, complemented
14#19133250C211yesmaximal, characteristic, complemented
15C43×#1574C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17#14583456C2211yescharacteristic
18#14583433C2211yescharacteristic
19#14583304C2211yescharacteristic
20#14583301—21no—
21#14583297C2211yescharacteristic
22#14583254—21no—
23#14583250C2211yescharacteristic
24#14583250C2211yescharacteristic
25#14583241—21no—
26#14583241—21no—
27#14583241—21no—
28#14583224—21no—
29#14583207—21no—
30#14583207—21no—
31#14583207—21no—
32#14583195C2211yescharacteristic
33#14583195C2211yescharacteristic
34#14583190C2211yescharacteristic
35#14583190C2211yescharacteristic
36#14583185C2211yescharacteristic
37#14583180C2211yescharacteristic
38#14583157—21no—
39#14583145—21no—
40#14583122—21no—
41#14583110C2211yescharacteristic
42#14583105C2211yescharacteristic
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#14582647C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582646C2211yescharacteristic
57#14582646C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#431C2211yescharacteristic
61C43×#431C2211yescharacteristic
62C43×#423C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#334C2211yescharacteristic
66C43×#334C2211yescharacteristic
67C2×Dic172—21no—
68C2×#10621873—21no—
69C2×#10621872—21no—
70C22×C43⋊C8—21no—
71C2×C8×D43—21no—
72#13063325C2311yescharacteristic
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063319—21no—
77#13063317—21no—
78#13063317—21no—
79#13063317D411yescharacteristic
80#13063313D411yescharacteristic
81#13063308—21no—
82#13063304—21no—
83#13063304—21no—
84#13063304—21no—
85#13063304—21no—
86#13063304D411yescharacteristic
87#13063299D411yescharacteristic
88C4×Dic86—21no—
89C4×Dic86—21no—
90C4×Dic86—21no—
91C4×Dic86—21no—
92C4×Dic86C2311yescharacteristic
93C4×D172C2311yescharacteristic
94C4×C22⋊D43—21no—
95#13063284—21no—
96#13063284—21no—
97#13063282—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—
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#13063250—21no—
119#13063250—21no—
120#13063250—21no—
121#13063250—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—
129C2×M16×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
141C4×C8×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×D172C2×D411yescharacteristic
149C2×C4×D43—21no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86C2×D411yescharacteristic
155M16×C43—81no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43C2×D411yescharacteristic
161C2×C8×C43C2×D411yescharacteristic
162C2×C8×C43C2×D411yescharacteristic
163C2×C8×C43C2×D411yescharacteristic
164C42×C43C2×D411yescharacteristic
165C42×C43C2×D411yescharacteristic
166C42×C43#4111yescharacteristic
167C42×C43C2411yescharacteristic
168C22⋊Dic43—21no—
169C22⋊Dic43—41no—
170C22⋊Dic43—41no—
171(C2×D43)⋊C4—21no—
172(C2×D43)⋊C4—21no—
173(C2×D43)⋊C4—21no—
174(C2×D43)⋊C4—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43C2×D411yescharacteristic
184C4⋊Dic43C2×D411yescharacteristic
185Dic43⋊C4—21no—
186Dic43⋊C4—21no—
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189Dic43⋊C4—41no—
190Dic43⋊C4—41no—
191Dic43⋊C4—41no—
192Dic43⋊C4—41no—
193C4×Dic43—21no—
194C4×Dic43—41no—
195C4×Dic43—41no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—81no—
199Dic172—81no—
200#10621873—81no—
201#10621872—81no—
202C8×D43—81no—
203C23×C43#12111yescharacteristic
204C22×D43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—41no—
210C2×C4×C43#12111yescharacteristic
211C2×C4×C43#12111yescharacteristic
212C2×C4×C43#12111yescharacteristic
213C2×C4×C43C22×D411yescharacteristic
214C2×C4×C43C22×D411yescharacteristic
215C2×C4×C43C2×#4111yescharacteristic
216C22⋊D43—42no—
217C2×Dic43—21no—
218C2×Dic43—21no—
219C2×Dic43—21no—
220C2×Dic43—41no—
221C2×Dic43—41no—
222C2×Dic43—41no—
223C2×Dic43—41no—
224D172—21no—
225D172—21no—
226C4×D43—41no—
227C4×D43—41no—
228Dic86—21no—
229Dic86—21no—
230Dic86—41no—
231Dic86—41no—
232Dic86—41no—
233Dic86—41no—
234Dic86—81no—
235Dic86—81no—
236C8×C43—21no—
237C8×C43—21no—
238C8×C43—21no—
239C8×C43—21no—
240C8×C43—41no—
241C8×C43—41no—
242C8×C43—41no—
243C8×C43—41no—
244C43⋊C8—41no—
245C43⋊C8—41no—
246#19587—431nomaximal, Sylow
247C22×C43—21no—
248C22×C43—21no—
249C22×C43—21no—
250C22×C43C2×#12111yescharacteristic
251C2×D43—41no—
252C2×D43—41no—
253C2×D43—41no—
254C4×C43—21no—
255C4×C43—21no—
256C4×C43—21no—
257C4×C43—21no—
258C4×C43#57711yescharacteristic
259C4×C43#57711yescharacteristic
260C4×C43#57811yescharacteristic
261C4×C43#57811yescharacteristic
262Dic43—41no—
263Dic43—41no—
264Dic43—41no—
265Dic43—81no—
266Dic43—81no—
267Dic43—81no—
268Dic43—81no—
269#3252—431no—
270#3233—431no—
271#3231—431no—
272#2994—431no—
273#1703—431no—
274#1700—431no—
275#1696—431no—
276#1691—431no—
277#1684—431no—
278#1679—431no—
279#1675—431no—
280#1672—431no—
281#1574D4311yescharacteristic, complemented
282#1550—431no—
283#1542—431no—
284C2×C43—41no—
285C2×C43#304611yescharacteristic
286C2×C43#306311yescharacteristic
287C2×C43#306711yescharacteristic
288D43—81no—
289#533—431no—
290#533—431no—
291#529—431no—
292#500—431no—
293#499—861no—
294#498—431no—
295#488—861no—
296#487—431no—
297#487—431no—
298#485—861no—
299#485—861no—
300#485—861no—
301#482—861no—
302#479—861no—
303#479—861no—
304#479—861no—
305#477—431no—
306#477—431no—
307#476—431no—
308#476—431no—
309#475—431no—
310#474—431no—
311#470—861no—
312#468—861no—
313#464—861no—
314#462—431no—
315#461—431no—
316#446—431no—
317C8×Q8—431no—
318#436—431no—
319#435—861no—
320C8×D4—431no—
321C8×D4—861no—
322#433—861no—
323#431C2×D4311yescharacteristic
324#431C2×D4311yescharacteristic
325#424—861no—
326#423C2×D4311yescharacteristic
327C2×C4⋊C8—431no—
328#335C2×D4311yescharacteristic
329#335C2×D4311yescharacteristic
330#334C2×D4311yescharacteristic
331#334C2×D4311yescharacteristic
332#333—431no—
333#333—431no—
334#333—431no—
335#333—431no—
336#332—431no—
337#332—431no—
338#332—431no—
339#332—431no—
340C43#1958711yescharacteristic, complemented, Sylow
341C2×Q16—861no—
342C2×SD16—861no—
343C2×M16—21no—
344C2×M16—861no—
345C22×C8—861no—
346C22×C8—861no—
347C4⋊Q8—431no—
348C4⋊Q8—431no—
349C4⋊Q8—431no—
350C4⋊Q8—431no—
351#126—861no—
352#125—431no—
353#125—861no—
354#125—861no—
355#124—431no—
356#123—861no—
357C22⋊Q8—431no—
358C22⋊Q8—861no—
359C22⋊Q8—861no—
360C22⋊Q8—861no—
361C22⋊Q8—861no—
362#121—431no—
363C4×Q8—431no—
364C4×Q8—861no—
365C4×Q8—861no—
366C4×Q8—861no—
367C4×Q8—861no—
368C4×D4—431no—
369C4×D4—861no—
370#117—861no—
371#117—861no—
372#117—861no—
373C2×C42C22×D4311yescharacteristic
374#107—861no—
375#107—861no—
376#107—861no—
377#107—861no—
378#107—861no—
379#106—861no—
380#106—861no—
381#106—861no—
382#106—861no—
383#106—861no—
384C4⋊C8—21no—
385C4⋊C8—431no—
386C4⋊C8—431no—
387C4⋊C8—861no—
388C4⋊C8—861no—
389C4⋊C8—861no—
390C4⋊C8D17211yescharacteristic
391C4⋊C8D17211yescharacteristic
392C4⋊C8C22×D4311yescharacteristic
393C4⋊C8C22×D4311yescharacteristic
394C4⋊C8C22×D4311yescharacteristic
395C4⋊C8C22×D4311yescharacteristic
396#103—861no—
397#103—861no—
398#103—861no—
399#103—861no—
400#103—861no—
401#103—861no—
402#103—861no—
403#103—861no—
404#103—861no—
405#102—861no—
406#102—861no—
407#102—861no—
408C22⋊C8—21no—
409C22⋊C8—861no—
410C22⋊C8—861no—
411C22⋊C8D17211yescharacteristic
412C22⋊C8D17211yescharacteristic
413#97—861no—
414C4×C8—21no—
415C4×C8—861no—
416C4×C8C22×D4311yescharacteristic
417C4×C8C22×D4311yescharacteristic
418C2×Q8—431no—
419C2×Q8—861no—
420C2×Q8—861no—
421C2×Q8—861no—
422C2×Q8—861no—
423C2×D4—431no—
424C2×D4—861no—
425C22×C4—861no—
426C22×C4C2×D17211yescharacteristic
427C22×C4D4×D4311yescharacteristic
428C22×C4#1062190211yescharacteristic
429Q16—3441no—
430SD16—3441no—
431M16—81no—
432M16—3441no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—861no—
438C2×C8—861no—
439C2×C8—3441no—
440C2×C8—3441no—
441C2×C8C2×D17211yescharacteristic
442C2×C8C2×D17211yescharacteristic
443C2×C8C2×D17211yescharacteristic
444C2×C8C2×D17211yescharacteristic
445C4⋊C4—431no—
446C4⋊C4—431no—
447C4⋊C4—861no—
448C4⋊C4—861no—
449C4⋊C4—861no—
450C4⋊C4—861no—
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—1721no—
460C4⋊C4—1721no—
461C4⋊C4—1721no—
462C4⋊C4—1721no—
463C22⋊C4—861no—
464C22⋊C4—861no—
465C22⋊C4—861no—
466C22⋊C4—861no—
467C22⋊C4—861no—
468C22⋊C4—1721no—
469C22⋊C4—1721no—
470C42—861no—
471C42—1721no—
472C42—1721no—
473C42C2×D17211yescharacteristic
474C42D4×D4311yescharacteristic
475C42#1062190211yescharacteristic
476C42C23×D4311yescharacteristic
477C23—861no—
478C23#1306330011yescharacteristic
479Q8—861no—
480Q8—861no—
481Q8—3441no—
482Q8—3441no—
483Q8—1721no—
484Q8—1721no—
485Q8—1721no—
486Q8—1721no—
487D4—861no—
488D4—861no—
489D4—1722no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—41no—
495C2×C4—861no—
496C2×C4—861no—
497C2×C4—861no—
498C2×C4—1721no—
499C2×C4—1721no—
500C2×C4—1721no—
501C2×C4—1721no—
502C2×C4—1721no—
503C2×C4—1721no—
504C2×C4#1306330011yescharacteristic
505C2×C4#1306330011yescharacteristic
506C2×C4#1306330011yescharacteristic
507C2×C4C2×D4×D4311yescharacteristic
508C2×C4C22×D17211yescharacteristic
509C2×C4C2×#1062190211yescharacteristic
510C8—21no—
511C8—21no—
512C8—21no—
513C8—21no—
514C8—41no—
515C8—41no—
516C8—41no—
517C8—41no—
518C8—1721no—
519C8—1721no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—1721no—
524C22—1721no—
525C22—1721no—
526C22C2×#1306330011yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—3441no—
532C4—3441no—
533C4—3441no—
534C4—3441no—
535C4—1721no—
536C4—1721no—
537C4—1721no—
538C4#1458370911yescharacteristic
539C4#1458371111yescharacteristic
540C4#1458371511yescharacteristic
541C4#1458371611yescharacteristic
542C2—41no—
543C2—3441no—
544C2#1914414711yescharacteristic
545C2#1914428711yescharacteristic
546C2#1914431611yescharacteristic
subgroupG/H
centerC22C2×#13063300
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1574C2
socleC22×C43C2×#121
prime radical#13063299D4
hypercenter#1574D43
hypocenterC43#19587
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1574

Complements

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

NH ≅ G/Ntype
3. #19145756C2semidirect
5. #19134171C2semidirect
6. #19134150C2semidirect
7. #19134124C2semidirect
8. #19134095C2semidirect
9. #19134054C2semidirect
10. #19134019C2semidirect
11. #19133995C2semidirect
12. #19133978C2semidirect
13. #19133286C2semidirect
14. #19133250C2semidirect
15. C43×#1574C2semidirect
281. #1574D43semidirect
340. C43#19587semidirect

Maximal subgroups

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

subgroupindex
#191459692
#191457762
#191457562
#191437572
#191341712
#191341502
#191341242
#191340952
#191340542
#191340192
#191339952
#191339782
#191332862
#191332502
C43×#15742
#1958743