Finite Group Databasebeta

← #25251239

Subgroups — #25251239

Order 11008.

546 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145107C211yesmaximal, characteristic, complemented
2#135×Dic43C211yesmaximal, characteristic
3#19136761C211yesmaximal, characteristic, complemented
4#19136757C211yesmaximal, characteristic, complemented
5#19136754C211yesmaximal, characteristic, complemented
6#19136750C211yesmaximal, characteristic, complemented
7#19136745C211yesmaximal, characteristic, complemented
8#19136740C211yesmaximal, characteristic, complemented
9#19136735C211yesmaximal, characteristic, complemented
10#19136730C211yesmaximal, characteristic, complemented
11#19136379C211yesmaximal, characteristic, complemented
12#19136377C211yesmaximal, characteristic, complemented
13C2×Dic43⋊C16C211yesmaximal, characteristic, complemented
14#19136302C211yesmaximal, characteristic
15C43×#2138C211yesmaximal, characteristic
16#14583452—21no—
17#41×Dic43—21no—
18C22×C43⋊C16C2211yescharacteristic
19#14583303C2211yescharacteristic
20#14583303C2211yescharacteristic
21#14583300C2211yescharacteristic
22#14583300C2211yescharacteristic
23#14583299—21no—
24#14583296—21no—
25Q16×Dic43C2211yescharacteristic
26Q16×Dic43C2211yescharacteristic
27SD16×Dic43—21no—
28SD16×Dic43—21no—
29D8×Dic43C2211yescharacteristic
30D8×Dic43C2211yescharacteristic
31#14582937C2211yescharacteristic
32#14582937C2211yescharacteristic
33#14582935—21no—
34#14582895—21no—
35C2×C8×Dic43C2211yescharacteristic
36#14582727C2211yescharacteristic
37#14582727C2211yescharacteristic
38#14582726C2211yescharacteristic
39#14582726C2211yescharacteristic
40#14582725C2211yescharacteristic
41#14582725C2211yescharacteristic
42#14582724C2211yescharacteristic
43#14582724C2211yescharacteristic
44Dic43⋊C16C2211yescharacteristic
45Dic43⋊C16C2211yescharacteristic
46Dic43⋊C16C2211yescharacteristic
47Dic43⋊C16C2211yescharacteristic
48#14582703C2211yescharacteristic
49#14582703C2211yescharacteristic
50#14582700C2211yescharacteristic
51#14582700C2211yescharacteristic
52C2×#135×C43C2211yescharacteristic
53C22×C16×C43C2211yescharacteristic
54C43×#427C2211yescharacteristic
55C43×#358C2211yescharacteristic
56C43×#358C2211yescharacteristic
57C43×#357C2211yescharacteristic
58C43×#357C2211yescharacteristic
59C22×C43⋊C8D411yescharacteristic
60#13063324—21no—
61#13063324—21no—
62#13063316—21no—
63#13063316—21no—
64#13063302—41no—
65#13063302—41no—
66Q8×Dic43—21no—
67Q8×Dic43—21no—
68C4×Dic86—41no—
69C4×Dic86—41no—
70D4×Dic43—21no—
71D4×Dic43—21no—
72D4×Dic43—41no—
73D4×Dic43—41no—
74#13063284—21no—
75#13063284—21no—
76#13063284—41no—
77C2×C4×Dic43—41no—
78C2×C4×Dic43D411yescharacteristic
79C2×C43⋊C16—22no—
80C2×C43⋊C16C2311yescharacteristic
81C2×C43⋊C16C2311yescharacteristic
82#13063259C2311yescharacteristic
83#13063259C2311yescharacteristic
84#13063259C2311yescharacteristic
85#13063259C2311yescharacteristic
86#13063258—21no—
87#13063258—21no—
88#13063257—21no—
89#13063257—21no—
90#13063256—21no—
91#13063256—21no—
92#13063249—21no—
93#13063249—21no—
94#13063246—21no—
95#13063246—21no—
96C8×Dic43D411yescharacteristic
97C8×Dic43D411yescharacteristic
98C8×Dic43C2311yescharacteristic
99C8×Dic43C2311yescharacteristic
100C2×#41×C43—21no—
101#135×C43—22no—
102#135×C43Q814yescomplemented
103C2×Q16×C43C2311yescharacteristic
104C2×SD16×C43—21no—
105C2×D8×C43C2311yescharacteristic
106C22×C8×C43C2311yescharacteristic
107#117×C43—21no—
108C2×C16×C43—22no—
109C2×C16×C43C2311yescharacteristic
110C2×C16×C43C2311yescharacteristic
111#107×C43C2311yescharacteristic
112#107×C43C2311yescharacteristic
113#106×C43—21no—
114#41×C43—24no—
115#41×C43—42no—
116C2×Q8×C43—21no—
117C2×D4×C43—21no—
118C2×D4×C43—41no—
119C22×C4×C43—41no—
120C22×C4×C43C2×D411yescharacteristic
121C22×Dic43—41no—
122C22×Dic43—41no—
123C22×Dic43D811yescharacteristic
124C22×Dic43D811yescharacteristic
125C2×Dic86—41no—
126C2×Dic86—41no—
127Q16×C43—21no—
128Q16×C43C2×Q812yes—
129SD16×C43—24no—
130D8×C43—21no—
131D8×C43C2×Q812yes—
132C2×C8×C43C2×D411yescharacteristic
133C2×C8×C43C2×Q812yes—
134C2×C8×C43#4112yes—
135C2×C8×C43C2411yescharacteristic
136C4⋊C4×C43—21no—
137C4⋊C4×C43—21no—
138C22⋊C4×C43—41no—
139C42×C43—41no—
140C22⋊Dic43—41no—
141C22⋊Dic43—41no—
142C22⋊Dic43—41no—
143C22⋊Dic43—41no—
144C4⋊Dic43—21no—
145C4⋊Dic43—21no—
146C4⋊Dic43—21no—
147C4⋊Dic43—21no—
148C4⋊Dic43—41no—
149C4⋊Dic43—41no—
150C4⋊Dic43—41no—
151C4⋊Dic43—41no—
152Dic43⋊C4—41no—
153Dic43⋊C4—41no—
154Dic43⋊C4—41no—
155Dic43⋊C4—41no—
156C4×Dic43—41no—
157C4×Dic43—41no—
158C4×Dic43—41no—
159C4×Dic43—41no—
160C4×Dic43D811yescharacteristic
161C4×Dic43D811yescharacteristic
162C4×Dic43C2×D411yescharacteristic
163C4×Dic43C2×D411yescharacteristic
164C2×C43⋊C8—22no—
165C2×C43⋊C8C2×D411yescharacteristic
166C2×C43⋊C8C2×D411yescharacteristic
167C16×C43—21no—
168C16×C43—21no—
169C43⋊C16—21no—
170C43⋊C16—21no—
171C23×C43—41no—
172C23×C43C2×D811yescharacteristic
173Q8×C43—22no—
174Q8×C43—41no—
175D4×C43—22no—
176D4×C43—44no—
177D4×C43—41no—
178C2×C4×C43—41no—
179C2×C4×C43—44no—
180C2×C4×C43—41no—
181C2×C4×C43—41no—
182C2×C4×C43C22⋊Q812yes—
183C2×C4×C43C2×D811yescharacteristic
184C2×C4×C43#13712yes—
185C2×C4×C43C22×D411yescharacteristic
186C2×Dic43—22no—
187C2×Dic43—41no—
188C2×Dic43—41no—
189C2×Dic43—41no—
190C2×Dic43—41no—
191C2×Dic43—41no—
192C2×Dic43—82no—
193C2×Dic43—82no—
194C2×Dic43C2×D811yescharacteristic
195C2×Dic43C2×D811yescharacteristic
196C2×Dic43C2×D811yescharacteristic
197C2×Dic43C2×D811yescharacteristic
198Dic86—82no—
199Dic86—82no—
200C8×C43C22⋊Q812yes—
201C8×C43C22×Q811yescharacteristic
202C8×C43C2×#4111yescharacteristic
203C43⋊C8—21no—
204C43⋊C8—21no—
205#33626—431nomaximal, Sylow
206C22×C43—21no—
207C22×C43—21no—
208C22×C43—42no—
209C22×C43—81no—
210C22×C43—81no—
211C22×C43#47412yes—
212C22×C43C22×D811yescharacteristic
213C4×C43—42no—
214C4×C43—81no—
215C4×C43—81no—
216C4×C43#47412yes—
217C4×C43C2×C22⋊Q811yescharacteristic
218C4×C43C2×#13711yescharacteristic
219Dic43—21no—
220Dic43—21no—
221Dic43—21no—
222Dic43—81no—
223Dic43—81no—
224Dic43—81no—
225Dic43—81no—
226Dic43#50812yes—
227#3160—431no—
228C4×#135—431no—
229#2229—431no—
230#2229—431no—
231#2228—431no—
232#2228—431no—
233#2227—431no—
234#2226—431no—
235#2225—431no—
236#2224—431no—
237#2158—431no—
238#2158—431no—
239C2×C4⋊C16—431no—
240#2138—431no—
241#2138D4311yescharacteristic
242C2×C43—22no—
243C2×C43—82no—
244C2×C43C2×#47411yescharacteristic
245C2×C43C2×#50811yescharacteristic
246C2×C43#341411yescharacteristic
247C2×#135C2×D4311yescharacteristic
248#533—861no—
249C4×#41—861no—
250C22×C16—431no—
251C22×C16C2×D4311yescharacteristic
252#500—431no—
253#500—431no—
254#499—431no—
255#499—431no—
256#499—861no—
257#498—861no—
258C4×Q16—431no—
259C4×Q16—431no—
260C4×SD16—861no—
261C4×SD16—861no—
262C4×D8—431no—
263C4×D8—431no—
264#427—431no—
265#427—431no—
266#427—861no—
267#427C2×D4311yescharacteristic
268#416—861no—
269C2×C4×C8—431no—
270#367—431no—
271#367—431no—
272#367—431no—
273#367—431no—
274#366—431no—
275#366—431no—
276#366—431no—
277#366—431no—
278C4⋊C16—431no—
279C4⋊C16—431no—
280C4⋊C16—431no—
281C4⋊C16—431no—
282#358—431no—
283#358—431no—
284#358C2×D4311yescharacteristic
285#358C2×D4311yescharacteristic
286#357—431no—
287#357—431no—
288#357C2×D4311yescharacteristic
289#357C2×D4311yescharacteristic
290C43#3362611yescharacteristic, complemented, Sylow
291C2×#41—21no—
292#135—22no—
293#135Dic8614yescomplemented
294C2×Q16C22×D4311yescharacteristic
295C2×SD16—21no—
296C2×D8C22×D4311yescharacteristic
297C22×C8—431no—
298C22×C8C22×D4311yescharacteristic
299C4⋊Q8—861no—
300C4⋊Q8—861no—
301#125—861no—
302#125—861no—
303C22⋊Q8—1721no—
304C22⋊Q8—1721no—
305C4×Q8—861no—
306C4×Q8—861no—
307C4×Q8—1721no—
308C4×Q8—1721no—
309C4×D4—861no—
310C4×D4—861no—
311C4×D4—1721no—
312C4×D4—1721no—
313#117—21no—
314#117—861no—
315#117—861no—
316#117—1721no—
317C2×C42—431no—
318C2×C42—1721no—
319C2×C16—22no—
320C2×C16—431no—
321C2×C16—431no—
322C2×C16—862no—
323C2×C16C22×D4311yescharacteristic
324C2×C16C22×D4311yescharacteristic
325#107—431no—
326#107—431no—
327#107—431no—
328#107—431no—
329#107—861no—
330#107—861no—
331#107C22×D4311yescharacteristic
332#107C22×D4311yescharacteristic
333#106—21no—
334#106—861no—
335#106—861no—
336#106—861no—
337#106—861no—
338#103—861no—
339#103—861no—
340#102—861no—
341#102—861no—
342C4×C8—431no—
343C4×C8—431no—
344C4×C8—431no—
345C4×C8—431no—
346#41—24no—
347#41—42no—
348C2×Q8—21no—
349C2×Q8—1721no—
350C2×Q8—1721no—
351C2×D4—21no—
352C2×D4—41no—
353C22×C4—41no—
354C22×C4—431no—
355C22×C4—431no—
356C22×C4—1721no—
357C22×C4—1721no—
358C22×C4D4×D4311yescharacteristic
359Q16—21no—
360Q16C2×Dic8612yes—
361SD16—24no—
362D8—21no—
363D8C2×Dic8612yes—
364C2×C8—431no—
365C2×C8—431no—
366C2×C8—862no—
367C2×C8C2×Dic8612yes—
368C2×C8D4×D4311yescharacteristic
369C2×C8#1062190012yes—
370C2×C8C23×D4311yescharacteristic
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—861no—
374C4⋊C4—861no—
375C4⋊C4—861no—
376C4⋊C4—861no—
377C4⋊C4—1721no—
378C4⋊C4—1721no—
379C4⋊C4—1721no—
380C4⋊C4—1721no—
381C4⋊C4—1721no—
382C4⋊C4—1721no—
383C4⋊C4—1721no—
384C4⋊C4—1721no—
385C22⋊C4—41no—
386C22⋊C4—1721no—
387C22⋊C4—1721no—
388C22⋊C4—1721no—
389C22⋊C4—1721no—
390C42—41no—
391C42—431no—
392C42—431no—
393C42—431no—
394C42—431no—
395C42—1721no—
396C42—1721no—
397C42—1721no—
398C42—1721no—
399C16—21no—
400C16—21no—
401C16—861no—
402C16—861no—
403C23—41no—
404C23D8×D4311yescharacteristic
405Q8—22no—
406Q8—41no—
407Q8—3442no—
408Q8—3442no—
409D4—22no—
410D4—44no—
411D4—41no—
412C2×C4—41no—
413C2×C4—44no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—431no—
417C2×C4—431no—
418C2×C4—431no—
419C2×C4—431no—
420C2×C4—862no—
421C2×C4—3442no—
422C2×C4—3442no—
423C2×C4—1721no—
424C2×C4—1721no—
425C2×C4—1721no—
426C2×C4—1721no—
427C2×C4—1721no—
428C2×C4#1306330212yes—
429C2×C4D8×D4311yescharacteristic
430C2×C4#1306335412yes—
431C2×C4C2×D4×D4311yescharacteristic
432C8—861no—
433C8—861no—
434C8#1306330212yes—
435C8C22×Dic8611yescharacteristic
436C8C2×#1062190011yescharacteristic
437C22—21no—
438C22—21no—
439C22—42no—
440C22—81no—
441C22—81no—
442C22#1458317712yes—
443C22C2×D8×D4311yescharacteristic
444C4—42no—
445C4—81no—
446C4—81no—
447C4—432no—
448C4—861no—
449C4—861no—
450C4—861no—
451C4—3441no—
452C4—3441no—
453C4—3441no—
454C4—3441no—
455C4#1458317712yes—
456C4C2×#1306330211yescharacteristic
457C4C2×#1306335411yescharacteristic
458C2—22no—
459C2—82no—
460C2C2×#1458317711yescharacteristic
461C2#508×D4311yescharacteristic
462C2#1914772811yescharacteristic
subgroupG/H
centerC2×C4D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2138C2
socleC22×C43C22×D8
prime radicalC2×#135×C43C22
hypercenter#2138D43
hypocenterC43#33626
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #2138

Complements

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

NH ≅ G/Ntype
1. #19145107C2semidirect
3. #19136761C2semidirect
4. #19136757C2semidirect
5. #19136754C2semidirect
6. #19136750C2semidirect
7. #19136745C2semidirect
8. #19136740C2semidirect
9. #19136735C2semidirect
10. #19136730C2semidirect
11. #19136379C2semidirect
12. #19136377C2semidirect
13. C2×Dic43⋊C16C2semidirect
102. #135×C43Q8semidirect
290. C43#33626semidirect
293. #135Dic86semidirect

Maximal subgroups

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

subgroupindex
#191451072
#135×Dic432
#191367612
#191367572
#191367542
#191367502
#191367452
#191367402
#191367352
#191367302
#191363792
#191363772
C2×Dic43⋊C162
#191363022
C43×#21382
#3362643