Finite Group Databasebeta

← #24919087

Subgroups — #24919087

Order 10624.

498 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14581824C211yesmaximal, characteristic, complemented
2C2×#14581817C211yesmaximal, characteristic, complemented
3#19128358C211yesmaximal, characteristic, complemented
4#19128342C211yesmaximal, characteristic, complemented
5#19128082C211yesmaximal, characteristic, complemented
6#19127957C211yesmaximal, characteristic, complemented
7#19127953C211yesmaximal, characteristic, complemented
8#19127925C211yesmaximal, characteristic, complemented
9#19127915C211yesmaximal, characteristic, complemented
10#19127854C211yesmaximal, characteristic, complemented
11#19127845C211yesmaximal, characteristic, complemented
12#19127841C211yesmaximal, characteristic, complemented
13#19127786C211yesmaximal, characteristic, complemented
14#19127776C211yesmaximal, characteristic, complemented
15#452×C83C211yesmaximal, characteristic, complemented
16C2×#13050591C2211yescharacteristic
17C2×Q8×D83C2211yescharacteristic, complemented
18C22×D332C2211yescharacteristic
19#14581824—24no—
20#14581817—24no—
21C2×#13050580C2211yescharacteristic, complemented
22C2×#13050579C2211yescharacteristic
23C2×#13050579C2211yescharacteristic
24C2×#13050577C2211yescharacteristic
25C2×#13050577C2211yescharacteristic
26C2×#13050575C2211yescharacteristic
27C2×#13050575C2211yescharacteristic
28C2×#13050574C2211yescharacteristic
29C2×#13050573C2211yescharacteristic, complemented
30#14581781C2211yescharacteristic
31#14581779—21no—
32#14581779C2211yescharacteristic, complemented
33#14581777—21no—
34#14581771—21no—
35#14581771C2211yescharacteristic
36#14581767—21no—
37#14581767C2211yescharacteristic
38#14581763—21no—
39#14581763C2211yescharacteristic, complemented
40#14581762—21no—
41Q8×Dic83C2211yescharacteristic, complemented
42#14581754C2211yescharacteristic
43C4×C22⋊D83—21no—
44C4×C22⋊D83C2211yescharacteristic
45C22⋊C4×D83—21no—
46#14581723C2211yescharacteristic, complemented
47Dic83⋊C8C2211yescharacteristic, complemented
48#14581716C2211yescharacteristic, complemented
49#14581715C2211yescharacteristic, complemented
50#14581714C2211yescharacteristic
51#14581714C2211yescharacteristic
52(C2×D83)⋊C8C2211yescharacteristic, complemented
53C8×Dic83C2211yescharacteristic, complemented
54C2×#41×C83C2211yescharacteristic
55C2×Q16×C83C2211yescharacteristic, complemented
56C2×SD16×C83C2211yescharacteristic, complemented
57C22⋊Q8×C83C2211yescharacteristic
58#103×C83C2211yescharacteristic, complemented
59#102×C83C2211yescharacteristic, complemented
60C22⋊C8×C83C2211yescharacteristic
61C23×D83—21no—
62#13050591—22no—
63#13050591—41no—
64C2×Dic166—21no—
65C2×Dic166C2311yescharacteristic
66Q8×D83—22no—
67Q8×D83—41no—
68C2×D332—22no—
69C2×D332—21no—
70C2×D332—21no—
71C2×D332—21no—
72C2×D332—41no—
73C2×D332C2311yescharacteristic
74C2×D332C2311yescharacteristic
75C2×C22⋊D83—21no—
76C2×C22⋊D83D411yescharacteristic
77C2×C4×D83—21no—
78C2×C4×D83—21no—
79C2×C4×D83—21no—
80C2×C4×D83C2311yescharacteristic
81#13050580—22no—
82#13050579—22no—
83#13050579—41no—
84#13050577—22no—
85#13050577D414yescomplemented
86#13050575—22no—
87#13050575—22no—
88#13050574—22no—
89#13050573—22no—
90C2×C83⋊C8C2311yescharacteristic
91C2×C83⋊C8C2311yescharacteristic
92C4⋊Dic83—21no—
93C4⋊Dic83C2311yescharacteristic
94Dic83⋊C4—21no—
95Dic83⋊C4D411yescharacteristic
96C22⋊Dic83—21no—
97C22⋊Dic83—21no—
98C22⋊Dic83—21no—
99C22⋊Dic83—21no—
100C22⋊Dic83D411yescharacteristic
101(C2×D83)⋊C4—21no—
102(C2×D83)⋊C4—21no—
103(C2×D83)⋊C4—21no—
104(C2×D83)⋊C4—21no—
105(C2×D83)⋊C4D411yescharacteristic
106C4×Dic83—21no—
107C4×Dic83C2311yescharacteristic
108#41×C83—22no—
109#41×C83—41no—
110C2×Q8×C83C2311yescharacteristic
111C2×Q8×C83C2311yescharacteristic
112C2×D4×C83—21no—
113C2×D4×C83C2311yescharacteristic
114C22×C4×C83—21no—
115C22×C4×C83C2311yescharacteristic
116Q16×C83—22no—
117SD16×C83—41no—
118C2×C8×C83C2311yescharacteristic
119C2×C8×C83C2311yescharacteristic
120C4⋊C4×C83—21no—
121C4⋊C4×C83C2311yescharacteristic
122C22⋊C4×C83—21no—
123C23×C83—21no—
124C23×C83C2×D411yescharacteristic
125C22×D83—21no—
126C22×D83—21no—
127C22×D83—42no—
128C22×D83—42no—
129C22×D83—81no—
130C22×D83C2×D411yescharacteristic
131Q8×C83—21no—
132Q8×C83—21no—
133Q8×C83—21no—
134Q8×C83C2×D412yes—
135D4×C83—21no—
136D4×C83—21no—
137D4×C83—42no—
138C2×C4×C83—21no—
139C2×C4×C83—21no—
140C2×C4×C83—21no—
141C2×C4×C83—21no—
142C2×C4×C83—21no—
143C2×C4×C83—42no—
144C2×C4×C83C2×D411yescharacteristic
145C2×C4×C83C2411yescharacteristic
146C22⋊D83—41no—
147C22⋊D83—42no—
148C2×Dic83—21no—
149C2×Dic83—21no—
150C2×Dic83C2×D411yescharacteristic
151C2×Dic83C2×D411yescharacteristic
152C2×Dic83C2×D411yescharacteristic
153D332—21no—
154D332—21no—
155D332—21no—
156D332—42no—
157D332—42no—
158D332—81no—
159D332C2×D412yes—
160C4×D83—21no—
161C4×D83—21no—
162C4×D83—42no—
163C4×D83—42no—
164C4×D83—81no—
165Dic166—21no—
166Dic166—21no—
167Dic166—42no—
168C8×C83—21no—
169C8×C83—21no—
170C83⋊C8—21no—
171C83⋊C8C2×D412yes—
172C22×C83—21no—
173C22×C83—21no—
174C22×C83—21no—
175C22×C83—41no—
176C22×C83—41no—
177C22×C83—41no—
178C22×C83C22×D411yescharacteristic
179C2×D83—21no—
180C2×D83—22no—
181C2×D83—21no—
182C2×D83—21no—
183C2×D83—41no—
184C2×D83—41no—
185C2×D83—41no—
186C2×D83—41no—
187C2×D83—41no—
188C2×D83—84no—
189C4×C83—22no—
190C4×C83—21no—
191C4×C83—41no—
192C4×C83—41no—
193C4×C83C22×D411yescharacteristic
194C4×C83H(5,𝔽2)11yescharacteristic
195Dic83—21no—
196Dic83—21no—
197Dic83—21no—
198Dic83—41no—
199Dic83—41no—
200C2×C83—41no—
201C2×C83—81no—
202C2×C83D4211yescharacteristic
203C2×C83#57511yescharacteristic
204C2×C83#57711yescharacteristic
205D83—41no—
206D83—42no—
207D83—81no—
208#3275—831nomaximal, Sylow
209C83#327511yescharacteristic, complemented, Sylow
210C2×#137—831no—
211C2×AGL(1,ℤ/8)—831no—
212#548—831no—
213#546—831no—
214#495—831no—
215#470—831no—
216#469—831no—
217#464—831no—
218#463—831no—
219#452D8311yescharacteristic, complemented
220#450—831no—
221#449—831no—
222#448—831no—
223C4×SD16—831no—
224#436—831no—
225C2×#41—831no—
226C2×#41C2×D8311yescharacteristic
227C22×Q8—831no—
228C22×D4—831no—
229#137—1664no—
230AGL(1,ℤ/8)—1664no—
231C2×Q16—831no—
232C2×Q16C2×D8311yescharacteristic, complemented
233C2×SD16—831no—
234C2×SD16—831no—
235C2×SD16—831no—
236C2×SD16—831no—
237C2×SD16C2×D8311yescharacteristic, complemented
238C2×D8—831no—
239C2×D8—831no—
240C2×M16—831no—
241C2×M16—831no—
242#124—831no—
243#124—831no—
244#124—1661no—
245#123—1661no—
246C22⋊Q8—831no—
247C22⋊Q8—1661no—
248C22⋊Q8C2×D8311yescharacteristic
249#121—831no—
250#121—831no—
251#121—1661no—
252#121—1661no—
253#120—1661no—
254C4×Q8—831no—
255C4×D4—831no—
256C4×D4—831no—
257C4×D4—1661no—
258C2×C22⋊C4—1661no—
259#106—831no—
260C4⋊C8—831no—
261#103—831no—
262#103—831no—
263#103C2×D8311yescharacteristic, complemented
264#102—831no—
265#102—831no—
266#102C2×D8311yescharacteristic, complemented
267C22⋊C8—831no—
268C22⋊C8C2×D8311yescharacteristic
269C4×C8—831no—
270C24—1661no—
271#41—22no—
272#41—41no—
273#41—3321no—
274#41—1662no—
275C2×Q8—3321no—
276C2×Q8—831no—
277C2×Q8—1661no—
278C2×Q8—1662no—
279C2×Q8C22×D8311yescharacteristic
280C2×Q8C22×D8311yescharacteristic
281C2×D4—21no—
282C2×D4—3321no—
283C2×D4—831no—
284C2×D4—831no—
285C2×D4—831no—
286C2×D4—1661no—
287C2×D4—1662no—
288C2×D4—1661no—
289C2×D4—1661no—
290C2×D4—1661no—
291C2×D4C22×D8311yescharacteristic
292C22×C4—21no—
293C22×C4—831no—
294C22×C4—1661no—
295C22×C4—1661no—
296C22×C4—1661no—
297C22×C4C22×D8311yescharacteristic
298Q16—22no—
299Q16—1662no—
300SD16—41no—
301SD16—3321no—
302SD16—834no—
303SD16—1662no—
304SD16—1662no—
305D8—1662no—
306D8—1662no—
307M16—1662no—
308M16—1662no—
309C2×C8—831no—
310C2×C8—831no—
311C2×C8C22×D8311yescharacteristic
312C2×C8C22×D8311yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—831no—
315C4⋊C4—831no—
316C4⋊C4—1661no—
317C4⋊C4—1661no—
318C4⋊C4C22×D8311yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—831no—
321C22⋊C4—831no—
322C22⋊C4—1661no—
323C22⋊C4—1661no—
324C22⋊C4—1661no—
325C22⋊C4—1661no—
326C22⋊C4—1661no—
327C22⋊C4—1661no—
328C22⋊C4—1661no—
329C22⋊C4—1661no—
330C42—831no—
331C42—1661no—
332C23—21no—
333C23—3322no—
334C23—3322no—
335C23—831no—
336C23—6641no—
337C23—1661no—
338C23—1661no—
339C23D4×D8311yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—3322no—
344Q8—1661no—
345Q8—1661no—
346Q8D4×D8312yes—
347D4—21no—
348D4—21no—
349D4—42no—
350D4—3322no—
351D4—3322no—
352D4—3322no—
353D4—3321no—
354D4—832no—
355D4—6641no—
356D4—1661no—
357D4—1661no—
358D4—1661no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—42no—
365C2×C4—3322no—
366C2×C4—3322no—
367C2×C4—831no—
368C2×C4—831no—
369C2×C4—831no—
370C2×C4—6641no—
371C2×C4—1661no—
372C2×C4—1661no—
373C2×C4—1661no—
374C2×C4—1661no—
375C2×C4D4×D8311yescharacteristic
376C2×C4C23×D8311yescharacteristic
377C8—21no—
378C8—21no—
379C8—832no—
380C8—1661no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—3321no—
388C22—3321no—
389C22—3321no—
390C22—3321no—
391C22—3321no—
392C22—6644no—
393C22—1661no—
394C22—1662no—
395C22—1661no—
396C22—1661no—
397C22C2×D4×D8311yescharacteristic
398C4—21no—
399C4—22no—
400C4—41no—
401C4—41no—
402C4—3321no—
403C4—3321no—
404C4—1661no—
405C4—1661no—
406C4—1661no—
407C4C2×D4×D8311yescharacteristic
408C4#1458183711yescharacteristic
409C2—41no—
410C2—81no—
411C2—3322no—
412C2—3321no—
413C2—6641no—
414C2#1912833311yescharacteristic
415C2#1912850011yescharacteristic
416C2#1912850811yescharacteristic
subgroupG/H
centerC22C2×D4×D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting#452×C83C2
socleC22×C83C22×D4
hypercenter#452D83
hypocenterC83#3275
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. C2×#14581824C2semidirect
2. C2×#14581817C2semidirect
3. #19128358C2semidirect
4. #19128342C2semidirect
5. #19128082C2semidirect
6. #19127957C2semidirect
7. #19127953C2semidirect
8. #19127925C2semidirect
9. #19127915C2semidirect
10. #19127854C2semidirect
11. #19127845C2semidirect
12. #19127841C2semidirect
13. #19127786C2semidirect
14. #19127776C2semidirect
15. #452×C83C2semidirect
17. C2×Q8×D83C22semidirect
21. C2×#13050580C22semidirect
29. C2×#13050573C22semidirect
32. #14581779C22semidirect
39. #14581763C22semidirect
41. Q8×Dic83C22semidirect
46. #14581723C22semidirect
47. Dic83⋊C8C22semidirect
48. #14581716C22semidirect
49. #14581715C22semidirect
52. (C2×D83)⋊C8C22semidirect
53. C8×Dic83C22semidirect
55. C2×Q16×C83C22semidirect
56. C2×SD16×C83C22semidirect
58. #103×C83C22semidirect
59. #102×C83C22semidirect
85. #13050577D4semidirect
209. C83#3275semidirect
219. #452D83semidirect
232. C2×Q16C2×D83semidirect
237. C2×SD16C2×D83semidirect
263. #103C2×D83semidirect
266. #102C2×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#145818242
C2×#145818172
#191283582
#191283422
#191280822
#191279572
#191279532
#191279252
#191279152
#191278542
#191278452
#191278412
#191277862
#191277762
#452×C832
#327583