Finite Group Databasebeta

← #24918990

Subgroups — #24918990

Order 10624.

500 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×#14581816C211yesmaximal, characteristic, complemented
2C2×#14581811C211yesmaximal, characteristic, complemented
3#19128355C211yesmaximal, characteristic, complemented
4#19128346C211yesmaximal, characteristic, complemented
5#19128095C211yesmaximal, characteristic, complemented
6#19127960C211yesmaximal, characteristic, complemented
7#19127931C211yesmaximal, characteristic, complemented
8#19127916C211yesmaximal, characteristic, complemented
9#19127906C211yesmaximal, characteristic, complemented
10#19127864C211yesmaximal, characteristic, complemented
11#19127864C211yesmaximal, characteristic, complemented
12#19127853C211yesmaximal, characteristic, complemented
13#19127847C211yesmaximal, characteristic, complemented
14#19127774C211yesmaximal, characteristic, complemented
15#442×C83C211yesmaximal, characteristic, complemented
16C2×#13050589C2211yescharacteristic
17C2×#13050589C2211yescharacteristic
18C2×#13050589C2211yescharacteristic, complemented
19C2×D4×D83C2211yescharacteristic
20#14581816—24no—
21#14581811—24no—
22C2×Dic332C2211yescharacteristic, complemented
23C2×Dic332C2211yescharacteristic, complemented
24C2×#13050579C2211yescharacteristic
25C2×#13050579C2211yescharacteristic
26C2×#13050578C2211yescharacteristic
27C2×#13050578C2211yescharacteristic
28C2×#13050578C2211yescharacteristic, complemented
29C2×#13050575C2211yescharacteristic
30C2×#13050573C2211yescharacteristic
31C2×C8×D83C2211yescharacteristic, complemented
32#14581792C2211yescharacteristic, complemented
33#14581780C2211yescharacteristic
34#14581776—21no—
35#14581776—21no—
36#14581776—21no—
37#14581772C2211yescharacteristic
38#14581772C2211yescharacteristic
39#14581772C2211yescharacteristic, complemented
40#14581767C2211yescharacteristic
41#14581766—21no—
42#14581766—21no—
43#14581762—21no—
44C4×D332C2211yescharacteristic
45C2×C4⋊Dic83—21no—
46C2×(C2×D83)⋊C4—21no—
47C4⋊(C83⋊C8)C2211yescharacteristic, complemented
48#14581715C2211yescharacteristic, complemented
49#14581715C2211yescharacteristic, complemented
50#14581715C2211yescharacteristic, complemented
51#14581712C2211yescharacteristic
52(C2×D83)⋊C8C2211yescharacteristic
53(C2×D83)⋊C8C2211yescharacteristic, complemented
54C2×D8×C83C2211yescharacteristic
55C4×D4×C83C2211yescharacteristic
56C4×D4×C83C2211yescharacteristic, complemented
57#106×C83C2211yescharacteristic, complemented
58#102×C83C2211yescharacteristic
59#102×C83C2211yescharacteristic, complemented
60#97×C83C2211yescharacteristic, complemented
61C23×D83—21no—
62#13050589—22no—
63#13050589—22no—
64#13050589—22no—
65#13050589—41no—
66#13050589—41no—
67#13050589—41no—
68C2×Dic166C2311yescharacteristic
69C2×Dic166C2311yescharacteristic
70C2×Dic166C2311yescharacteristic
71C2×D332—21no—
72C2×D332D411yescharacteristic
73C2×D332C2311yescharacteristic
74C2×C22⋊D83—21no—
75C2×C22⋊D83—21no—
76C2×C22⋊D83—21no—
77C2×C22⋊D83—21no—
78D4×D83—22no—
79D4×D83—41no—
80C22×Dic83—21no—
81C22×Dic83—21no—
82C22×Dic83—21no—
83C2×C4×D83C2311yescharacteristic
84C2×C4×D83C2311yescharacteristic
85Dic332—22no—
86Dic332—41no—
87#13050579—22no—
88#13050579—41no—
89#13050578—22no—
90#13050578—22no—
91#13050578—22no—
92#13050575—22no—
93#13050573—22no—
94C2×C83⋊C8C2311yescharacteristic
95C2×C83⋊C8C2311yescharacteristic
96C8×D83—22no—
97C4⋊Dic83—21no—
98C4⋊Dic83—21no—
99C4⋊Dic83—21no—
100C4⋊Dic83—21no—
101C4⋊Dic83—21no—
102C4⋊Dic83D411yescharacteristic
103(C2×D83)⋊C4—21no—
104(C2×D83)⋊C4—21no—
105(C2×D83)⋊C4—21no—
106(C2×D83)⋊C4—21no—
107(C2×D83)⋊C4—21no—
108(C2×D83)⋊C4—21no—
109(C2×D83)⋊C4D411yescharacteristic
110(C2×D83)⋊C4D411yescharacteristic
111C2×D4×C83C2311yescharacteristic
112C2×D4×C83C2311yescharacteristic
113C22×C4×C83—21no—
114C22×C4×C83—21no—
115D8×C83D414yescomplemented
116C2×C8×C83C2311yescharacteristic
117C2×C8×C83C2311yescharacteristic
118C4⋊C4×C83C2311yescharacteristic
119C4⋊C4×C83C2311yescharacteristic
120C22⋊C4×C83—21no—
121C22⋊C4×C83—21no—
122C42×C83C2311yescharacteristic
123C23×C83—21no—
124C23×C83—21no—
125C22×D83—21no—
126C22×D83—42no—
127C22×D83—42no—
128C22×D83—81no—
129C22×D83C2×D411yescharacteristic
130C22×D83C2×D411yescharacteristic
131D4×C83—21no—
132D4×C83—21no—
133D4×C83C2×D412yes—
134D4×C83C2×D412yes—
135C2×C4×C83—21no—
136C2×C4×C83—21no—
137C2×C4×C83—42no—
138C2×C4×C83—81no—
139C2×C4×C83C2×D411yescharacteristic
140C2×C4×C83C2×D411yescharacteristic
141C2×C4×C83C2411yescharacteristic
142C22⋊D83—42no—
143C22⋊D83—42no—
144C22⋊D83—42no—
145C22⋊D83—42no—
146C2×Dic83—21no—
147C2×Dic83—21no—
148C2×Dic83—21no—
149C2×Dic83—42no—
150C2×Dic83—42no—
151C2×Dic83—42no—
152C2×Dic83C2×D411yescharacteristic
153C2×Dic83C2×D411yescharacteristic
154D332—21no—
155D332—21no—
156D332—41no—
157D332—81no—
158C4×D83—21no—
159C4×D83—21no—
160C4×D83—21no—
161C4×D83—21no—
162Dic166—21no—
163Dic166—21no—
164Dic166—21no—
165Dic166—21no—
166Dic166—21no—
167Dic166—21no—
168C8×C83—21no—
169C8×C83C2×D412yes—
170C83⋊C8—21no—
171C83⋊C8—21no—
172C22×C83—22no—
173C22×C83—22no—
174C22×C83—41no—
175C22×C83—41no—
176C22×C83—41no—
177C22×C83—41no—
178C22×C83C22×D411yescharacteristic
179C2×D83—21no—
180C2×D83—21no—
181C2×D83—21no—
182C2×D83—21no—
183C2×D83—21no—
184C2×D83—21no—
185C2×D83—41no—
186C2×D83—41no—
187C2×D83—41no—
188C2×D83—84no—
189C4×C83—21no—
190C4×C83—21no—
191C4×C83—41no—
192C4×C83—41no—
193C4×C83C22×D411yescharacteristic
194C4×C83H(5,𝔽2)11yescharacteristic
195Dic83—21no—
196Dic83—21no—
197Dic83—41no—
198Dic83—41no—
199Dic83—41no—
200C2×C83—42no—
201C2×C83—42no—
202C2×C83D4211yescharacteristic
203C2×C83#57511yescharacteristic
204C2×C83#57711yescharacteristic
205D83—41no—
206D83—41no—
207D83—81no—
208#3267—831nomaximal, Sylow
209C83#326711yescharacteristic, complemented, Sylow
210C2×AGL(1,ℤ/8)—831no—
211C2×#135—831no—
212#547—831no—
213#546—831no—
214#497—831no—
215#470—831no—
216#465—831no—
217#463—831no—
218#461—831no—
219#452—831no—
220#452—831no—
221#450—831no—
222#449—831no—
223#442D8311yescharacteristic, complemented
224#435—831no—
225C2×#41—831no—
226C2×#41—831no—
227C2×#41—831no—
228C22×D4—831no—
229AGL(1,ℤ/8)—1664no—
230#135—1664no—
231C2×Q16—831no—
232C2×Q16—831no—
233C2×SD16—831no—
234C2×SD16—831no—
235C2×SD16—831no—
236C2×SD16—831no—
237C2×SD16—831no—
238C2×D8—831no—
239C2×D8C2×D8311yescharacteristic
240C2×M16—831no—
241C22×C8—831no—
242C4⋊Q8—831no—
243#124—831no—
244#123—1661no—
245#123—1661no—
246#123—1661no—
247C22⋊Q8—831no—
248C22⋊Q8—831no—
249C22⋊Q8—831no—
250#121—831no—
251#121—1661no—
252#121—1661no—
253#120—1661no—
254C4×D4—831no—
255C4×D4C2×D8311yescharacteristic
256C4×D4C2×D8311yescharacteristic, complemented
257C2×C4⋊C4—1661no—
258C2×C22⋊C4—1661no—
259#106C2×D8311yescharacteristic, complemented
260C4⋊C8—831no—
261#103—831no—
262#103—831no—
263#103—831no—
264#102—831no—
265#102C2×D8311yescharacteristic
266#102C2×D8311yescharacteristic, complemented
267C22⋊C8—831no—
268C22⋊C8—831no—
269#97C2×D8311yescharacteristic, complemented
270C24—1661no—
271#41—3321no—
272#41—3321no—
273#41—3321no—
274#41—1662no—
275#41—1662no—
276#41—1662no—
277C2×Q8—831no—
278C2×Q8—831no—
279C2×Q8—831no—
280C2×D4—3321no—
281C2×D4—831no—
282C2×D4—831no—
283C2×D4—1661no—
284C2×D4—1661no—
285C2×D4—1661no—
286C2×D4—1661no—
287C2×D4—1661no—
288C2×D4—1662no—
289C2×D4C22×D8311yescharacteristic
290C2×D4C22×D8311yescharacteristic
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—831no—
294C22×C4—831no—
295C22×C4—1661no—
296C22×C4—1661no—
297C22×C4—1661no—
298Q16—3321no—
299Q16—1662no—
300SD16—3321no—
301SD16—1662no—
302SD16—1662no—
303SD16—1662no—
304SD16—1662no—
305D8—1662no—
306D8D33214yescomplemented
307M16—1662no—
308C2×C8—831no—
309C2×C8—831no—
310C2×C8—1662no—
311C2×C8C22×D8311yescharacteristic
312C2×C8C22×D8311yescharacteristic
313C4⋊C4—831no—
314C4⋊C4—1661no—
315C4⋊C4—1661no—
316C4⋊C4—1661no—
317C4⋊C4—1661no—
318C4⋊C4—1661no—
319C4⋊C4C22×D8311yescharacteristic
320C4⋊C4C22×D8311yescharacteristic
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—831no—
324C22⋊C4—831no—
325C22⋊C4—1661no—
326C22⋊C4—1661no—
327C22⋊C4—1661no—
328C22⋊C4—1661no—
329C22⋊C4—1661no—
330C22⋊C4—1661no—
331C42C22×D8311yescharacteristic
332C23—21no—
333C23—21no—
334C23—3322no—
335C23—3322no—
336C23—831no—
337C23—831no—
338C23—6641no—
339C23—1661no—
340Q8—1661no—
341Q8—1661no—
342Q8—1661no—
343Q8—1661no—
344Q8—1661no—
345Q8—1661no—
346D4—21no—
347D4—21no—
348D4—3321no—
349D4—3322no—
350D4—3322no—
351D4—3322no—
352D4—3322no—
353D4—6641no—
354D4—1661no—
355D4—1661no—
356D4C2×D33212yes—
357D4C2×D33212yes—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—42no—
361C2×C4—81no—
362C2×C4—3322no—
363C2×C4—3322no—
364C2×C4—3322no—
365C2×C4—831no—
366C2×C4—831no—
367C2×C4—1661no—
368C2×C4—1661no—
369C2×C4—1661no—
370C2×C4—1661no—
371C2×C4—1661no—
372C2×C4—1661no—
373C2×C4—1661no—
374C2×C4D4×D8311yescharacteristic
375C2×C4D4×D8311yescharacteristic
376C2×C4C23×D8311yescharacteristic
377C8—21no—
378C8—1661no—
379C8—1661no—
380C8C2×D33212yes—
381C22—22no—
382C22—22no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—3321no—
388C22—3321no—
389C22—3321no—
390C22—6644no—
391C22—1661no—
392C22—1661no—
393C22—1661no—
394C22—1661no—
395C22—1661no—
396C22—1661no—
397C22C2×D4×D8311yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—3321no—
403C4—3321no—
404C4—3321no—
405C4—1661no—
406C4—1661no—
407C4C22×D33211yescharacteristic
408C4#1458183811yescharacteristic
409C2—42no—
410C2—42no—
411C2—3321no—
412C2—3321no—
413C2—6641no—
414C2D4×D33211yescharacteristic
415C2#1912849711yescharacteristic
416C2#1912851111yescharacteristic
subgroupG/H
centerC22C2×D4×D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting#442×C83C2
socleC22×C83C22×D4
hypercenter#442D83
hypocenterC83#3267
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. C2×#14581816C2semidirect
2. C2×#14581811C2semidirect
3. #19128355C2semidirect
4. #19128346C2semidirect
5. #19128095C2semidirect
6. #19127960C2semidirect
7. #19127931C2semidirect
8. #19127916C2semidirect
9. #19127906C2semidirect
10. #19127864C2semidirect
11. #19127864C2semidirect
12. #19127853C2semidirect
13. #19127847C2semidirect
14. #19127774C2semidirect
15. #442×C83C2semidirect
18. C2×#13050589C22semidirect
22. C2×Dic332C22semidirect
23. C2×Dic332C22semidirect
28. C2×#13050578C22semidirect
31. C2×C8×D83C22semidirect
32. #14581792C22semidirect
39. #14581772C22semidirect
47. C4⋊(C83⋊C8)C22semidirect
48. #14581715C22semidirect
49. #14581715C22semidirect
50. #14581715C22semidirect
53. (C2×D83)⋊C8C22semidirect
56. C4×D4×C83C22semidirect
57. #106×C83C22semidirect
59. #102×C83C22semidirect
60. #97×C83C22semidirect
115. D8×C83D4semidirect
209. C83#3267semidirect
223. #442D83semidirect
256. C4×D4C2×D83semidirect
259. #106C2×D83semidirect
266. #102C2×D83semidirect
269. #97C2×D83semidirect
306. D8D332semidirect

Maximal subgroups

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

subgroupindex
C2×#145818162
C2×#145818112
#191283552
#191283462
#191280952
#191279602
#191279312
#191279162
#191279062
#191278642
#191278532
#191278472
#191277742
#442×C832
#326783