Finite Group Databasebeta

← #25251720

Subgroups — #25251720

Order 11008.

558 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145245C211yesmaximal, characteristic, complemented
2#19136780C211yesmaximal, characteristic, complemented
3#19136775C211yesmaximal, characteristic, complemented
4#19136759C211yesmaximal, characteristic, complemented
5#19136752C211yesmaximal, characteristic, complemented
6#19136635C211yesmaximal, characteristic, complemented
7#19136630C211yesmaximal, characteristic, complemented
8#19136518C211yesmaximal, characteristic, complemented
9#19136518C211yesmaximal, characteristic, complemented
10#19136469C211yesmaximal, characteristic, complemented
11#19136457C211yesmaximal, characteristic, complemented
12C4×#13063268C211yesmaximal, characteristic, complemented
13C4×#13063266C211yesmaximal, characteristic, complemented
14#19136402C211yesmaximal, characteristic, complemented
15C43×#2951C211yesmaximal, characteristic, complemented
16#14583504—21no—
17C2×#13063268C2211yescharacteristic
18C2×#13063268C2211yescharacteristic
19C2×#13063266C2211yescharacteristic
20C2×#13063266C2211yescharacteristic
21#14583301C2211yescharacteristic
22#14583276C2211yescharacteristic
23#14583264—21no—
24#14583152—21no—
25#14583135C2211yescharacteristic
26#14583135C2211yescharacteristic
27#14583012—21no—
28C4×D344C2211yescharacteristic
29C4×D344C2211yescharacteristic
30#14582726C2211yescharacteristic
31#14582726C2211yescharacteristic
32#14582724C2211yescharacteristic
33#14582724C2211yescharacteristic
34C4⋊(C43⋊C16)C2211yescharacteristic
35C4⋊(C43⋊C16)C2211yescharacteristic
36#14582703C2211yescharacteristic
37#14582703C2211yescharacteristic
38#14582700C2211yescharacteristic
39#14582700C2211yescharacteristic
40#14582699C2211yescharacteristic
41#14582699C2211yescharacteristic
42#14582699C2211yescharacteristic
43#14582699C2211yescharacteristic
44C22⋊(C43⋊C16)C2211yescharacteristic
45C22⋊(C43⋊C16)C2211yescharacteristic
46#14582675C2211yescharacteristic
47C4×C43⋊C16C2211yescharacteristic
48C2×#135×C43C2211yescharacteristic
49C43×#520—21no—
50C43×#440—21no—
51C43×#440—21no—
52C4×Q16×C43C2211yescharacteristic
53C4×Q16×C43C2211yescharacteristic
54C4×D8×C43C2211yescharacteristic
55C4×D8×C43C2211yescharacteristic
56C2×#107×C43C2211yescharacteristic
57C43×#417—21no—
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—22no—
73#13063268—22no—
74#13063266—22no—
75#13063266—22no—
76C2×C43⋊C16C2311yescharacteristic
77C2×C43⋊C16C2311yescharacteristic
78C2×C43⋊C16C2311yescharacteristic
79C2×C43⋊C16C2311yescharacteristic
80#13063259C2311yescharacteristic
81#13063259C2311yescharacteristic
82#13063257—21no—
83#13063247—21no—
84#13063247—21no—
85#13063247—21no—
86#13063247—21no—
87C2×#41×C43—21no—
88#135×C43—22no—
89#135×C43—22no—
90C2×Q16×C43C2311yescharacteristic
91C2×SD16×C43—21no—
92C2×D8×C43C2311yescharacteristic
93C2×M16×C43D411yescharacteristic
94C22×C8×C43C2311yescharacteristic
95C4×Q8×C43—21no—
96C4×Q8×C43—21no—
97C4×D4×C43—21no—
98C4×D4×C43—21no—
99C4×D4×C43—41no—
100C4×D4×C43—41no—
101#117×C43—41no—
102#117×C43D411yescharacteristic
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—41no—
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
116#41×C43—24no—
117#41×C43—42no—
118C2×Q8×C43—21no—
119C2×D4×C43—21no—
120C2×D4×C43—41no—
121C22×C4×C43—41no—
122C22×C4×C43—41no—
123C22×C4×C43—41no—
124C22×C4×C43—41no—
125C22×C4×C43C2×D411yescharacteristic
126C2×C22⋊D43—41no—
127C2×C22⋊D43—41no—
128C2×D172—21no—
129C2×D172—21no—
130C2×D172—41no—
131C2×D172—41no—
132C2×C4×D43—41no—
133C2×C4×D43—41no—
134Q16×C43—21no—
135Q16×C43#4112yes—
136SD16×C43—24no—
137D8×C43—21no—
138D8×C43#4112yes—
139M16×C43—41no—
140C2×C8×C43—21no—
141C2×C8×C43—21no—
142C2×C8×C43C2×D411yescharacteristic
143C2×C8×C43C2×D411yescharacteristic
144C2×C8×C43C2×D411yescharacteristic
145C2×C8×C43C2411yescharacteristic
146C4⋊C4×C43—21no—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—41no—
149C4⋊C4×C43—41no—
150C4⋊C4×C43—41no—
151C4⋊C4×C43D811yescharacteristic
152C4⋊C4×C43D811yescharacteristic
153C22⋊C4×C43—41no—
154C22⋊C4×C43—41no—
155C22⋊C4×C43D811yescharacteristic
156C22⋊C4×C43D811yescharacteristic
157C42×C43—41no—
158C42×C43—41no—
159C42×C43C2×D411yescharacteristic
160C42×C43C2×D411yescharacteristic
161(C2×D43)⋊C4—41no—
162(C2×D43)⋊C4—41no—
163(C2×D43)⋊C4—41no—
164(C2×D43)⋊C4—41no—
165C4⋊Dic43—21no—
166C4⋊Dic43—21no—
167Dic43⋊C4—41no—
168Dic43⋊C4—41no—
169D344—21no—
170D344—21no—
171D344—21no—
172D344—21no—
173D344—42no—
174C43⋊C16—21no—
175C43⋊C16—21no—
176C43⋊C16—21no—
177C43⋊C16—21no—
178C23×C43—41no—
179C23×C43C2×D811yescharacteristic
180C22×D43—41no—
181C22×D43—41no—
182Q8×C43—22no—
183Q8×C43—41no—
184D4×C43—22no—
185D4×C43—44no—
186D4×C43—41no—
187C2×C4×C43—21no—
188C2×C4×C43—21no—
189C2×C4×C43—44no—
190C2×C4×C43—41no—
191C2×C4×C43—41no—
192C2×C4×C43—41no—
193C2×C4×C43—161no—
194C2×C4×C43—161no—
195C2×C4×C43—161no—
196C2×C4×C43C2×D811yescharacteristic
197C2×C4×C43C2×D811yescharacteristic
198C2×C4×C43C2×D811yescharacteristic
199C2×C4×C43C2×D811yescharacteristic
200C2×C4×C43C2×D811yescharacteristic
201C2×C4×C43C22×D411yescharacteristic
202C22⋊D43—161no—
203C22⋊D43—161no—
204C2×Dic43—41no—
205C2×Dic43—41no—
206D172—41no—
207D172—41no—
208D172—41no—
209D172—41no—
210D172—161no—
211D172—161no—
212C4×D43—161no—
213C4×D43—161no—
214C8×C43—21no—
215C8×C43—21no—
216C8×C43—21no—
217C8×C43C2×#4111yescharacteristic
218C8×C43C2×#4111yescharacteristic
219#33679—431nomaximal, Sylow
220C22×C43—21no—
221C22×C43—21no—
222C22×C43—21no—
223C22×C43—42no—
224C22×C43—81no—
225C22×C43—81no—
226C22×C43C22×D811yescharacteristic
227C2×D43—81no—
228C2×D43—81no—
229C2×D43—81no—
230C2×D43—81no—
231C2×D43—81no—
232C2×D43—81no—
233C4×C43—21no—
234C4×C43—21no—
235C4×C43—21no—
236C4×C43—21no—
237C4×C43—21no—
238C4×C43—42no—
239C4×C43—81no—
240C4×C43—81no—
241C4×C43#52511yescharacteristic
242C4×C43#57511yescharacteristic
243Dic43—81no—
244Dic43—81no—
245#3176—431no—
246#2951D4311yescharacteristic, complemented
247#2233—431no—
248#2232—431no—
249#2229—431no—
250#2228—431no—
251#2207—431no—
252#2206—431no—
253#2186—431no—
254#2186—431no—
255#2177—431no—
256#2175—431no—
257C4×SD32—431no—
258C4×D16—431no—
259#2164—431no—
260C2×C43—41no—
261C2×C43—82no—
262C2×C43#310011yescharacteristic
263C2×C43#341511yescharacteristic
264C2×C43#341611yescharacteristic
265D43—161no—
266D43—161no—
267C2×#135C2×D4311yescharacteristic
268#540—861no—
269#520—21no—
270C2×SD32—431no—
271C2×SD32—431no—
272C2×D16—431no—
273C2×D16—431no—
274#499—431no—
275#493—431no—
276#490—861no—
277#469—861no—
278#466—431no—
279#466—431no—
280#442—861no—
281#440—21no—
282#440—21no—
283C4×Q16C2×D4311yescharacteristic
284C4×Q16C2×D4311yescharacteristic
285C4×D8—431no—
286C4×D8—431no—
287C4×D8C2×D4311yescharacteristic
288C4×D8C2×D4311yescharacteristic
289C2×#107C2×D4311yescharacteristic
290#417—21no—
291#405C2×D4311yescharacteristic
292#367—431no—
293#367—431no—
294#366—431no—
295#366—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—
306C22⋊C16—431no—
307C22⋊C16—431no—
308#346—431no—
309C4×C16—431no—
310C43#3367911yescharacteristic, complemented, Sylow
311C2×#41—21no—
312#135—22no—
313#135—22no—
314C2×Q16C22×D4311yescharacteristic
315C2×SD16—21no—
316C2×D8—431no—
317C2×D8—431no—
318C2×D8—861no—
319C2×D8C22×D4311yescharacteristic
320C2×M16C22⋊D4311yescharacteristic
321C22×C8C22×D4311yescharacteristic
322#127—861no—
323#125—861no—
324#123—1721no—
325#123—1721no—
326#121—861no—
327#121—861no—
328#121—1721no—
329#121—1721no—
330C4×Q8—21no—
331C4×Q8—21no—
332C4×D4—21no—
333C4×D4—21no—
334C4×D4—41no—
335C4×D4—41no—
336C4×D4—861no—
337C4×D4—861no—
338#117—41no—
339#117C22⋊D4311yescharacteristic
340C2×C4⋊C4—21no—
341C2×C4⋊C4—41no—
342SD32—862no—
343SD32—862no—
344D16—862no—
345D16—862no—
346C2×C16—431no—
347C2×C16—431no—
348C2×C16—431no—
349C2×C16—431no—
350#107—21no—
351#107—431no—
352#107—431no—
353#107C22×D4311yescharacteristic
354#107C22×D4311yescharacteristic
355#106—861no—
356#103—21no—
357#103—21no—
358#102—21no—
359#102—21no—
360#102—861no—
361#102—861no—
362#102—861no—
363#102—861no—
364#97C22⋊D4311yescharacteristic
365#97C22⋊D4311yescharacteristic
366C4×C8C22×D4311yescharacteristic
367C4×C8C22×D4311yescharacteristic
368#41—24no—
369#41—42no—
370C2×Q8—21no—
371C2×D4—21no—
372C2×D4—41no—
373C2×D4—861no—
374C2×D4—861no—
375C2×D4—1721no—
376C2×D4—1721no—
377C2×D4—1721no—
378C2×D4—1721no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—1721no—
384C22×C4—1721no—
385C22×C4C2×C22⋊D4311yescharacteristic
386Q16—21no—
387Q16#1062189812yes—
388SD16—24no—
389D8—21no—
390D8—861no—
391D8—861no—
392D8—861no—
393D8—861no—
394D8—1722no—
395D8#1062189812yes—
396M16—41no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8C2×C22⋊D4311yescharacteristic
400C2×C8C2×C22⋊D4311yescharacteristic
401C2×C8C2×C22⋊D4311yescharacteristic
402C2×C8C23×D4311yescharacteristic
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—861no—
409C4⋊C4—861no—
410C4⋊C4—1721no—
411C4⋊C4—1721no—
412C4⋊C4#1062188211yescharacteristic
413C4⋊C4#1062188211yescharacteristic
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—1721no—
417C22⋊C4—1721no—
418C22⋊C4—1721no—
419C22⋊C4—1721no—
420C22⋊C4#1062188211yescharacteristic
421C22⋊C4#1062188211yescharacteristic
422C42—41no—
423C42—41no—
424C42C2×C22⋊D4311yescharacteristic
425C42C2×C22⋊D4311yescharacteristic
426C16—861no—
427C16—861no—
428C16—861no—
429C16—861no—
430C23—41no—
431C23—1721no—
432C23—1721no—
433C23C2×#1062188211yescharacteristic
434Q8—22no—
435Q8—41no—
436D4—22no—
437D4—44no—
438D4—41no—
439D4—1721no—
440D4—1721no—
441D4—1721no—
442D4—1721no—
443D4—6881no—
444D4—6881no—
445D4—6881no—
446D4—6881no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—44no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—161no—
454C2×C4—161no—
455C2×C4—161no—
456C2×C4—1721no—
457C2×C4—1721no—
458C2×C4—6881no—
459C2×C4—6881no—
460C2×C4C2×#1062188211yescharacteristic
461C2×C4C2×#1062188211yescharacteristic
462C2×C4C2×#1062188211yescharacteristic
463C2×C4C2×#1062188211yescharacteristic
464C2×C4C2×#1062188211yescharacteristic
465C2×C4C22×C22⋊D4311yescharacteristic
466C8—21no—
467C8—21no—
468C8—21no—
469C8C2×#1062189811yescharacteristic
470C8C2×#1062189811yescharacteristic
471C22—21no—
472C22—21no—
473C22—21no—
474C22—42no—
475C22—81no—
476C22—81no—
477C22—3441no—
478C22—3441no—
479C22—3441no—
480C22—3441no—
481C22—3441no—
482C22—3441no—
483C22C22×#1062188211yescharacteristic
484C4—21no—
485C4—21no—
486C4—21no—
487C4—21no—
488C4—21no—
489C4—42no—
490C4—81no—
491C4—81no—
492C4—3441no—
493C4—3441no—
494C4#1458341011yescharacteristic
495C4#1458369711yescharacteristic
496C2—41no—
497C2—82no—
498C2—6881no—
499C2—6881no—
500C2#1914459511yescharacteristic
501C2#1914773411yescharacteristic
502C2#1914773911yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2951C2
socleC22×C43C22×D8
hypercenter#2951D43
hypocenterC43#33679
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2951

Complements

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

NH ≅ G/Ntype
1. #19145245C2semidirect
2. #19136780C2semidirect
3. #19136775C2semidirect
4. #19136759C2semidirect
5. #19136752C2semidirect
6. #19136635C2semidirect
7. #19136630C2semidirect
8. #19136518C2semidirect
9. #19136518C2semidirect
10. #19136469C2semidirect
11. #19136457C2semidirect
12. C4×#13063268C2semidirect
13. C4×#13063266C2semidirect
14. #19136402C2semidirect
15. C43×#2951C2semidirect
246. #2951D43semidirect
310. C43#33679semidirect

Maximal subgroups

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

subgroupindex
#191452452
#191367802
#191367752
#191367592
#191367522
#191366352
#191366302
#191365182
#191364692
#191364572
C4×#130632682
C4×#130632662
#191364022
C43×#29512
#3367943