Finite Group Databasebeta

← #25252986

Subgroups — #25252986

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#19145245C211yesmaximal, characteristic, complemented
2#19136759C211yesmaximal, characteristic, complemented
3#19136752C211yesmaximal, characteristic, complemented
4#19136739C211yesmaximal, characteristic, complemented
5#19136729C211yesmaximal, characteristic, complemented
6#19136710C211yesmaximal, characteristic, complemented
7#19136696C211yesmaximal, characteristic, complemented
8#19136693C211yesmaximal, characteristic, complemented
9#19136679C211yesmaximal, characteristic, complemented
10#19136647C211yesmaximal, characteristic, complemented
11#19136647C211yesmaximal, characteristic, complemented
12#19136635C211yesmaximal, characteristic, complemented
13#19136630C211yesmaximal, characteristic, complemented
14#19136354C211yesmaximal, characteristic, complemented
15C43×#3175C211yesmaximal, characteristic, complemented
16#14583504—21no—
17C2×#13063268C2211yescharacteristic
18C2×#13063268C2211yescharacteristic
19C2×#13063266C2211yescharacteristic
20C2×#13063266C2211yescharacteristic
21C2×#13063265C2211yescharacteristic
22C22×C43⋊C16C2211yescharacteristic
23#14583301C2211yescharacteristic
24#14583276C2211yescharacteristic
25#14583264—21no—
26#14583152—21no—
27#14583135C2211yescharacteristic
28#14583135C2211yescharacteristic
29#14583012—21no—
30C4×D344C2211yescharacteristic
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#14582703C2211yescharacteristic
41#14582703C2211yescharacteristic
42#14582700C2211yescharacteristic
43#14582700C2211yescharacteristic
44#14582699C2211yescharacteristic
45#14582699C2211yescharacteristic
46#14582699C2211yescharacteristic
47#14582699C2211yescharacteristic
48C43×#542—21no—
49C43×#500C2211yescharacteristic
50C43×#495C2211yescharacteristic
51C43×#489—21no—
52C43×#468—21no—
53C43×#467C2211yescharacteristic
54C43×#466C2211yescharacteristic
55C43×#440—21no—
56C4×Q16×C43C2211yescharacteristic
57C4×D8×C43C2211yescharacteristic
58C43×#405C2211yescharacteristic
59C2×D344—21no—
60C2×D344C2311yescharacteristic
61C2×D344C2311yescharacteristic
62#13063322—21no—
63#13063317—21no—
64#13063310—41no—
65#13063310—41no—
66#13063299—21no—
67#13063299—21no—
68#13063298—41no—
69#13063298—41no—
70C4×D172—21no—
71C4×D172—21no—
72#13063268—41no—
73#13063268—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#13063259C2311yescharacteristic
83#13063259C2311yescharacteristic
84#13063257—21no—
85#13063247—21no—
86#13063247—21no—
87#13063247—21no—
88#13063247—21no—
89C2×Q16×C43C2311yescharacteristic
90C2×SD16×C43—21no—
91C2×D8×C43C2311yescharacteristic
92C2×M16×C43D411yescharacteristic
93C22×C8×C43C2311yescharacteristic
94C4⋊Q8×C43—21no—
95#126×C43—41no—
96#124×C43—21no—
97#124×C43—41no—
98#123×C43—41no—
99C22⋊Q8×C43—21no—
100C22⋊Q8×C43—41no—
101#121×C43—21no—
102C4×Q8×C43—21no—
103C4×D4×C43—21no—
104#117×C43D411yescharacteristic
105#107×C43—21no—
106#107×C43C2311yescharacteristic
107#107×C43C2311yescharacteristic
108#103×C43—21no—
109#103×C43—21no—
110#102×C43—21no—
111#102×C43—21no—
112#97×C43D411yescharacteristic
113#97×C43D411yescharacteristic
114C4×C8×C43C2311yescharacteristic
115C4×C8×C43C2311yescharacteristic
116C2×Q8×C43—21no—
117C2×Q8×C43—41no—
118C2×D4×C43—21no—
119C2×D4×C43—41no—
120C22×C4×C43—41no—
121C22×C4×C43C2×D411yescharacteristic
122C2×C22⋊D43—41no—
123C2×C22⋊D43—41no—
124C2×D172—21no—
125C2×D172—21no—
126C2×D172—41no—
127C2×D172—41no—
128C2×C4×D43—41no—
129C2×C4×D43—41no—
130Q16×C43—21no—
131Q16×C43—21no—
132SD16×C43—42no—
133D8×C43—21no—
134D8×C43—21no—
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×C43—41no—
147C4⋊C4×C43D811yescharacteristic
148C4⋊C4×C43D811yescharacteristic
149C22⋊C4×C43—41no—
150C22⋊C4×C43—41no—
151C22⋊C4×C43—41no—
152C22⋊C4×C43—41no—
153C22⋊C4×C43—41no—
154C22⋊C4×C43D811yescharacteristic
155C22⋊C4×C43D811yescharacteristic
156C42×C43—41no—
157C42×C43C2×D411yescharacteristic
158C42×C43C2×D411yescharacteristic
159(C2×D43)⋊C4—41no—
160(C2×D43)⋊C4—41no—
161(C2×D43)⋊C4—41no—
162(C2×D43)⋊C4—41no—
163C4⋊Dic43—21no—
164C4⋊Dic43—21no—
165Dic43⋊C4—41no—
166Dic43⋊C4—41no—
167D344—21no—
168D344—21no—
169D344—21no—
170D344—21no—
171D344—42no—
172C43⋊C16—21no—
173C43⋊C16—21no—
174C43⋊C16—21no—
175C43⋊C16—21no—
176C23×C43—41no—
177C23×C43C2×D811yescharacteristic
178C22×D43—41no—
179C22×D43—41no—
180Q8×C43—41no—
181Q8×C43—41no—
182Q8×C43—161no—
183D4×C43—41no—
184D4×C43—41no—
185D4×C43—161no—
186C2×C4×C43—21no—
187C2×C4×C43—21no—
188C2×C4×C43—41no—
189C2×C4×C43—41no—
190C2×C4×C43—41no—
191C2×C4×C43—161no—
192C2×C4×C43C2×D811yescharacteristic
193C2×C4×C43C2×D811yescharacteristic
194C2×C4×C43C2×D811yescharacteristic
195C2×C4×C43C2×D811yescharacteristic
196C2×C4×C43C2×D811yescharacteristic
197C2×C4×C43C22×D411yescharacteristic
198C22⋊D43—161no—
199C22⋊D43—161no—
200C2×Dic43—41no—
201C2×Dic43—41no—
202D172—41no—
203D172—41no—
204D172—41no—
205D172—41no—
206D172—161no—
207D172—161no—
208C4×D43—161no—
209C4×D43—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×C43C22×D811yescharacteristic
223C2×D43—81no—
224C2×D43—81no—
225C2×D43—81no—
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—81no—
237C4×C43#53711yescharacteristic
238C4×C43#57511yescharacteristic
239Dic43—81no—
240Dic43—81no—
241#3176—431no—
242#3175D4311yescharacteristic, complemented
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#324511yescharacteristic
259C2×C43#341511yescharacteristic
260C2×C43#341611yescharacteristic
261D43—161no—
262D43—161no—
263#542—21no—
264#540—861no—
265C2×SD32—431no—
266C2×SD32—431no—
267C2×D16—431no—
268C2×D16—431no—
269C2×M32—431no—
270C22×C16—431no—
271#500C2×D4311yescharacteristic
272#499—431no—
273#495C2×D4311yescharacteristic
274#493—431no—
275#490—861no—
276#489—21no—
277#469—861no—
278#468—21no—
279#467C2×D4311yescharacteristic
280#466—431no—
281#466—431no—
282#466C2×D4311yescharacteristic
283#442—861no—
284#440—21no—
285C4×Q16C2×D4311yescharacteristic
286C4×D8—431no—
287C4×D8—431no—
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×Q16C22×D4311yescharacteristic
308C2×SD16—21no—
309C2×D8—431no—
310C2×D8—431no—
311C2×D8—861no—
312C2×D8C22×D4311yescharacteristic
313C2×M16C22⋊D4311yescharacteristic
314C22×C8C22×D4311yescharacteristic
315C4⋊Q8—21no—
316#127—861no—
317#126—41no—
318#125—861no—
319#124—21no—
320#124—41no—
321#123—41no—
322#123—1721no—
323#123—1721no—
324C22⋊Q8—21no—
325C22⋊Q8—41no—
326#121—21no—
327#121—861no—
328#121—861no—
329#121—1721no—
330#121—1721no—
331C4×Q8—21no—
332C4×D4—21no—
333C4×D4—861no—
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—21no—
347#107—431no—
348#107—431no—
349#107C22×D4311yescharacteristic
350#107C22×D4311yescharacteristic
351#106—861no—
352#103—21no—
353#103—21no—
354#102—21no—
355#102—21no—
356#102—861no—
357#102—861no—
358#102—861no—
359#102—861no—
360#97C22⋊D4311yescharacteristic
361#97C22⋊D4311yescharacteristic
362C4×C8C22×D4311yescharacteristic
363C4×C8C22×D4311yescharacteristic
364C2×Q8—21no—
365C2×Q8—41no—
366C2×D4—21no—
367C2×D4—41no—
368C2×D4—861no—
369C2×D4—861no—
370C2×D4—1721no—
371C2×D4—1721no—
372C2×D4—1721no—
373C2×D4—1721no—
374C22×C4—41no—
375C22×C4—1721no—
376C22×C4—1721no—
377C22×C4C2×C22⋊D4311yescharacteristic
378Q16—21no—
379Q16—21no—
380SD16—42no—
381D8—21no—
382D8—21no—
383D8—861no—
384D8—861no—
385D8—861no—
386D8—861no—
387D8—1722no—
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—41no—
400C4⋊C4—861no—
401C4⋊C4—861no—
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—41no—
411C22⋊C4—1721no—
412C22⋊C4—1721no—
413C22⋊C4—1721no—
414C22⋊C4—1721no—
415C22⋊C4#1062188211yescharacteristic
416C22⋊C4#1062188211yescharacteristic
417C42—41no—
418C42C2×C22⋊D4311yescharacteristic
419C42C2×C22⋊D4311yescharacteristic
420C16—861no—
421C16—861no—
422C16—861no—
423C16—861no—
424C23—41no—
425C23—1721no—
426C23—1721no—
427C23C2×#1062188211yescharacteristic
428Q8—41no—
429Q8—41no—
430Q8—161no—
431D4—41no—
432D4—41no—
433D4—161no—
434D4—1721no—
435D4—1721no—
436D4—1721no—
437D4—1721no—
438D4—6881no—
439D4—6881no—
440D4—6881no—
441D4—6881no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—161no—
448C2×C4—1721no—
449C2×C4—1721no—
450C2×C4—6881no—
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—3441no—
470C22—3441no—
471C22—3441no—
472C22—3441no—
473C22—3441no—
474C22—3441no—
475C22C22×#1062188211yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—81no—
482C4—81no—
483C4—81no—
484C4—3441no—
485C4—3441no—
486C4#1458347711yescharacteristic
487C4#1458369711yescharacteristic
488C2—41no—
489C2—161no—
490C2—6881no—
491C2—6881no—
492C2#1914590211yescharacteristic
493C2#1914773411yescharacteristic
494C2#1914773911yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3175C2
socleC22×C43C22×D8
hypercenter#3175D43
hypocenterC43#33823
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3175

Complements

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

NH ≅ G/Ntype
1. #19145245C2semidirect
2. #19136759C2semidirect
3. #19136752C2semidirect
4. #19136739C2semidirect
5. #19136729C2semidirect
6. #19136710C2semidirect
7. #19136696C2semidirect
8. #19136693C2semidirect
9. #19136679C2semidirect
10. #19136647C2semidirect
11. #19136647C2semidirect
12. #19136635C2semidirect
13. #19136630C2semidirect
14. #19136354C2semidirect
15. C43×#3175C2semidirect
242. #3175D43semidirect
306. C43#33823semidirect

Maximal subgroups

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

subgroupindex
#191452452
#191367592
#191367522
#191367392
#191367292
#191367102
#191366962
#191366932
#191366792
#191366472
#191366352
#191366302
#191363542
C43×#31752
#3382343