Finite Group Databasebeta

← #25252980

Subgroups — #25252980

Order 11008.

500 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145234C211yesmaximal, characteristic, complemented
2#19136756C211yesmaximal, characteristic, complemented
3#19136749C211yesmaximal, characteristic, complemented
4#19136742C211yesmaximal, characteristic, complemented
5#19136732C211yesmaximal, characteristic, complemented
6#19136706C211yesmaximal, characteristic, complemented
7#19136696C211yesmaximal, characteristic, complemented
8#19136689C211yesmaximal, characteristic, complemented
9#19136679C211yesmaximal, characteristic, complemented
10#19136650C211yesmaximal, characteristic, complemented
11#19136650C211yesmaximal, characteristic, complemented
12#19136632C211yesmaximal, characteristic, complemented
13#19136627C211yesmaximal, characteristic, complemented
14#19136354C211yesmaximal, characteristic, complemented
15C43×#3176C211yesmaximal, characteristic, complemented
16#14583520—21no—
17C2×#13063269C2211yescharacteristic
18C2×#13063269C2211yescharacteristic
19C2×#13063266C2211yescharacteristic
20C2×#13063266C2211yescharacteristic
21C2×#13063265C2211yescharacteristic
22C22×C43⋊C16C2211yescharacteristic
23#14583304C2211yescharacteristic
24#14583283C2211yescharacteristic
25#14583259—21no—
26#14583145—21no—
27#14583140C2211yescharacteristic
28#14583135C2211yescharacteristic
29#14583001—21no—
30C4×Dic172C2211yescharacteristic
31C4×D344C2211yescharacteristic
32#14582726C2211yescharacteristic
33#14582726C2211yescharacteristic
34#14582724C2211yescharacteristic
35#14582724C2211yescharacteristic
36C4⋊(C43⋊C16)C2211yescharacteristic
37C4⋊(C43⋊C16)C2211yescharacteristic
38C4⋊(C43⋊C16)C2211yescharacteristic
39C4⋊(C43⋊C16)C2211yescharacteristic
40#14582702C2211yescharacteristic
41#14582702C2211yescharacteristic
42#14582700C2211yescharacteristic
43#14582700C2211yescharacteristic
44#14582700C2211yescharacteristic
45#14582700C2211yescharacteristic
46#14582699C2211yescharacteristic
47#14582699C2211yescharacteristic
48C43×#540—21no—
49C43×#499C2211yescharacteristic
50C43×#493C2211yescharacteristic
51C43×#490—21no—
52C43×#469—21no—
53C43×#466C2211yescharacteristic
54C43×#466C2211yescharacteristic
55C43×#442—21no—
56C4×D8×C43C2211yescharacteristic
57C4×D8×C43C2211yescharacteristic
58C43×#405C2211yescharacteristic
59C2×Dic172C2311yescharacteristic
60C2×#10621873—21no—
61C2×D344C2311yescharacteristic
62#13063325—21no—
63#13063320—41no—
64#13063313—21no—
65#13063311—41no—
66#13063307—41no—
67#13063304—21no—
68#13063303—41no—
69#13063299—21no—
70C4×Dic86—21no—
71C4×D172—21no—
72#13063269—41no—
73#13063269—41no—
74#13063266—41no—
75#13063266—41no—
76#13063265—41no—
77C2×C43⋊C16—41no—
78C2×C43⋊C16C2311yescharacteristic
79C2×C43⋊C16C2311yescharacteristic
80C2×C43⋊C16C2311yescharacteristic
81C2×C43⋊C16C2311yescharacteristic
82#13063259—21no—
83#13063259C2311yescharacteristic
84#13063259C2311yescharacteristic
85#13063250—21no—
86#13063250—21no—
87#13063247—21no—
88#13063247—21no—
89C2×D8×C43—21no—
90C2×D8×C43C2311yescharacteristic
91C2×D8×C43C2311yescharacteristic
92C2×M16×C43D411yescharacteristic
93C22×C8×C43C2311yescharacteristic
94#127×C43—21no—
95#125×C43—21no—
96#123×C43—41no—
97#123×C43—41no—
98#121×C43—21no—
99#121×C43—21no—
100#121×C43—41no—
101#121×C43—41no—
102C4×D4×C43—21no—
103C4×D4×C43—21no—
104#117×C43D411yescharacteristic
105#107×C43C2311yescharacteristic
106#107×C43C2311yescharacteristic
107#106×C43—21no—
108#102×C43—21no—
109#102×C43—21no—
110#102×C43—21no—
111#102×C43—21no—
112#97×C43D411yescharacteristic
113#97×C43D411yescharacteristic
114C4×C8×C43C2311yescharacteristic
115C4×C8×C43C2311yescharacteristic
116C2×D4×C43—21no—
117C2×D4×C43—21no—
118C2×D4×C43—41no—
119C2×D4×C43—41no—
120C2×D4×C43—41no—
121C2×D4×C43—41no—
122C22×C4×C43—41no—
123C22×C4×C43—41no—
124C22×C4×C43C2×D411yescharacteristic
125C2×C22⋊D43—41no—
126C2×D172—21no—
127C2×C4×D43—41no—
128C2×Dic86—21no—
129C2×Dic86—41no—
130D8×C43—21no—
131D8×C43—21no—
132D8×C43—21no—
133D8×C43—21no—
134D8×C43—42no—
135M16×C43—41no—
136C2×C8×C43—21no—
137C2×C8×C43—21no—
138C2×C8×C43C2×D411yescharacteristic
139C2×C8×C43C2×D411yescharacteristic
140C2×C8×C43C2×D411yescharacteristic
141C2×C8×C43C2411yescharacteristic
142C4⋊C4×C43—21no—
143C4⋊C4×C43—21no—
144C4⋊C4×C43—41no—
145C4⋊C4×C43—41no—
146C4⋊C4×C43D811yescharacteristic
147C4⋊C4×C43D811yescharacteristic
148C22⋊C4×C43—41no—
149C22⋊C4×C43—41no—
150C22⋊C4×C43—41no—
151C22⋊C4×C43—41no—
152C22⋊C4×C43D811yescharacteristic
153C22⋊C4×C43D811yescharacteristic
154C42×C43C2×D411yescharacteristic
155C42×C43C2×D411yescharacteristic
156C22⋊Dic43—41no—
157(C2×D43)⋊C4—41no—
158(C2×D43)⋊C4—41no—
159(C2×D43)⋊C4—41no—
160(C2×D43)⋊C4—41no—
161C4⋊Dic43—21no—
162C4⋊Dic43—21no—
163C4⋊Dic43—41no—
164Dic43⋊C4—41no—
165Dic43⋊C4—41no—
166C4×Dic43—41no—
167Dic172—21no—
168Dic172—21no—
169D344—21no—
170D344—21no—
171#10621873—42no—
172C43⋊C16—21no—
173C43⋊C16—21no—
174C43⋊C16—21no—
175C43⋊C16—21no—
176C23×C43—41no—
177C23×C43—41no—
178C23×C43C2×D811yescharacteristic
179C22×D43—41no—
180D4×C43—41no—
181D4×C43—41no—
182D4×C43—41no—
183D4×C43—41no—
184D4×C43—161no—
185D4×C43—161no—
186D4×C43—161no—
187D4×C43—161no—
188C2×C4×C43—21no—
189C2×C4×C43—21no—
190C2×C4×C43—41no—
191C2×C4×C43—41no—
192C2×C4×C43—161no—
193C2×C4×C43—161no—
194C2×C4×C43C2×D811yescharacteristic
195C2×C4×C43C2×D811yescharacteristic
196C2×C4×C43C2×D811yescharacteristic
197C2×C4×C43C2×D811yescharacteristic
198C2×C4×C43C2×D811yescharacteristic
199C2×C4×C43C22×D411yescharacteristic
200C22⋊D43—161no—
201C2×Dic43—41no—
202C2×Dic43—41no—
203C2×Dic43—41no—
204D172—41no—
205D172—41no—
206C4×D43—161no—
207Dic86—41no—
208Dic86—41no—
209Dic86—161no—
210C8×C43—21no—
211C8×C43—21no—
212C8×C43—21no—
213C8×C43H(5,𝔽2)11yescharacteristic
214C8×C432−1+411yescharacteristic
215#33823—431nomaximal, Sylow
216C22×C43—21no—
217C22×C43—21no—
218C22×C43—21no—
219C22×C43—81no—
220C22×C43—81no—
221C22×C43—81no—
222C22×C43—81no—
223C22×C43—81no—
224C22×C43—81no—
225C22×C43C22×D811yescharacteristic
226C2×D43—81no—
227C2×D43—81no—
228C2×D43—81no—
229C4×C43—21no—
230C4×C43—21no—
231C4×C43—21no—
232C4×C43—21no—
233C4×C43—21no—
234C4×C43—81no—
235C4×C43—81no—
236C4×C43#53711yescharacteristic
237C4×C43#57511yescharacteristic
238Dic43—81no—
239Dic43—81no—
240Dic43—81no—
241#3176D4311yescharacteristic, complemented
242#3175—431no—
243#2229—431no—
244#2228—431no—
245#2226—431no—
246#2224—431no—
247#2220—431no—
248#2218—431no—
249#2217—431no—
250#2215—431no—
251#2210—431no—
252#2210—431no—
253#2207—431no—
254#2206—431no—
255#2151—431no—
256C2×C43—41no—
257C2×C43—161no—
258C2×C43—161no—
259C2×C43#324511yescharacteristic
260C2×C43#341511yescharacteristic
261C2×C43#341611yescharacteristic
262D43—161no—
263#542—861no—
264#540—21no—
265C2×SD32—431no—
266C2×SD32—431no—
267C2×D16—431no—
268C2×D16—431no—
269C2×M32—431no—
270C22×C16—431no—
271#500—431no—
272#499C2×D4311yescharacteristic
273#495—431no—
274#493C2×D4311yescharacteristic
275#490—21no—
276#489—861no—
277#469—21no—
278#468—861no—
279#467—431no—
280#466—431no—
281#466C2×D4311yescharacteristic
282#466C2×D4311yescharacteristic
283#442—21no—
284#440—861no—
285C4×Q16—431no—
286C4×D8—431no—
287C4×D8C2×D4311yescharacteristic
288C4×D8C2×D4311yescharacteristic
289#405C2×D4311yescharacteristic
290#367—431no—
291#367—431no—
292#366—431no—
293#366—431no—
294C4⋊C16—431no—
295C4⋊C16—431no—
296C4⋊C16—431no—
297C4⋊C16—431no—
298#358—431no—
299#358—431no—
300#357—431no—
301#357—431no—
302#357—431no—
303#357—431no—
304#357—431no—
305#357—431no—
306C43#3382311yescharacteristic, complemented, Sylow
307C2×Q16—431no—
308C2×SD16—861no—
309C2×D8—21no—
310C2×D8—431no—
311C2×D8C22×D4311yescharacteristic
312C2×D8C22×D4311yescharacteristic
313C2×M16C22⋊D4311yescharacteristic
314C22×C8C22×D4311yescharacteristic
315C4⋊Q8—861no—
316#127—21no—
317#126—1721no—
318#125—21no—
319#124—861no—
320#124—1721no—
321#123—41no—
322#123—41no—
323#123—1721no—
324C22⋊Q8—861no—
325C22⋊Q8—1721no—
326#121—21no—
327#121—21no—
328#121—41no—
329#121—41no—
330#121—861no—
331C4×Q8—861no—
332C4×D4—21no—
333C4×D4—21no—
334C4×D4—861no—
335#117C22⋊D4311yescharacteristic
336SD32—1721no—
337SD32—1721no—
338D16—1721no—
339D16—1721no—
340M32—1721no—
341C2×C16—431no—
342C2×C16—431no—
343C2×C16—431no—
344C2×C16—431no—
345C2×C16—1721no—
346#107—431no—
347#107—431no—
348#107—861no—
349#107C22×D4311yescharacteristic
350#107C22×D4311yescharacteristic
351#106—21no—
352#103—861no—
353#103—861no—
354#102—21no—
355#102—21no—
356#102—21no—
357#102—21no—
358#102—861no—
359#102—861no—
360#97C22⋊D4311yescharacteristic
361#97C22⋊D4311yescharacteristic
362C4×C8C22×D4311yescharacteristic
363C4×C8C22×D4311yescharacteristic
364C2×Q8—861no—
365C2×Q8—1721no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—861no—
373C2×D4—1721no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—1721no—
377C22×C4C2×C22⋊D4311yescharacteristic
378Q16—861no—
379Q16—861no—
380SD16—1722no—
381D8—21no—
382D8—21no—
383D8—21no—
384D8—21no—
385D8—42no—
386D8—861no—
387D8—861no—
388M16—41no—
389C2×C8—21no—
390C2×C8—21no—
391C2×C8C2×C22⋊D4311yescharacteristic
392C2×C8C2×C22⋊D4311yescharacteristic
393C2×C8C2×C22⋊D4311yescharacteristic
394C2×C8C23×D4311yescharacteristic
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—41no—
398C4⋊C4—41no—
399C4⋊C4—861no—
400C4⋊C4—861no—
401C4⋊C4—1721no—
402C4⋊C4—1721no—
403C4⋊C4—1721no—
404C4⋊C4#1062188211yescharacteristic
405C4⋊C4#1062188211yescharacteristic
406C22⋊C4—41no—
407C22⋊C4—41no—
408C22⋊C4—41no—
409C22⋊C4—41no—
410C22⋊C4—1721no—
411C22⋊C4—1721no—
412C22⋊C4—1721no—
413C22⋊C4—1721no—
414C22⋊C4—1721no—
415C22⋊C4#1062188211yescharacteristic
416C22⋊C4#1062188211yescharacteristic
417C42—1721no—
418C42C2×C22⋊D4311yescharacteristic
419C42C2×C22⋊D4311yescharacteristic
420C16—861no—
421C16—861no—
422C16—861no—
423C16—861no—
424C23—41no—
425C23—41no—
426C23—1721no—
427C23C2×#1062188211yescharacteristic
428Q8—1721no—
429Q8—1721no—
430Q8—6881no—
431D4—41no—
432D4—41no—
433D4—41no—
434D4—41no—
435D4—161no—
436D4—161no—
437D4—161no—
438D4—161no—
439D4—1721no—
440D4—1721no—
441D4—6881no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—161no—
447C2×C4—161no—
448C2×C4—1721no—
449C2×C4—1721no—
450C2×C4—1721no—
451C2×C4—6881no—
452C2×C4C2×#1062188211yescharacteristic
453C2×C4C2×#1062188211yescharacteristic
454C2×C4C2×#1062188211yescharacteristic
455C2×C4C2×#1062188211yescharacteristic
456C2×C4C2×#1062188211yescharacteristic
457C2×C4C22×C22⋊D4311yescharacteristic
458C8—21no—
459C8—21no—
460C8—21no—
461C8#1306337111yescharacteristic
462C8#1306337211yescharacteristic
463C22—21no—
464C22—21no—
465C22—21no—
466C22—81no—
467C22—81no—
468C22—81no—
469C22—81no—
470C22—81no—
471C22—81no—
472C22—3441no—
473C22—3441no—
474C22—3441no—
475C22C22×#1062188211yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—81no—
482C4—81no—
483C4—3441no—
484C4—3441no—
485C4—3441no—
486C4#1458347711yescharacteristic
487C4#1458369711yescharacteristic
488C2—41no—
489C2—161no—
490C2—161no—
491C2—6881no—
492C2#1914590211yescharacteristic
493C2#1914773411yescharacteristic
494C2#1914774211yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3176C2
socleC22×C43C22×D8
hypercenter#3176D43
hypocenterC43#33823
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3176

Complements

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

NH ≅ G/Ntype
1. #19145234C2semidirect
2. #19136756C2semidirect
3. #19136749C2semidirect
4. #19136742C2semidirect
5. #19136732C2semidirect
6. #19136706C2semidirect
7. #19136696C2semidirect
8. #19136689C2semidirect
9. #19136679C2semidirect
10. #19136650C2semidirect
11. #19136650C2semidirect
12. #19136632C2semidirect
13. #19136627C2semidirect
14. #19136354C2semidirect
15. C43×#3176C2semidirect
241. #3176D43semidirect
306. C43#33823semidirect

Maximal subgroups

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

subgroupindex
#191452342
#191367562
#191367492
#191367422
#191367322
#191367062
#191366962
#191366892
#191366792
#191366502
#191366322
#191366272
#191363542
C43×#31762
#3382343