Finite Group Databasebeta

← #24917818

Subgroups — #24917818

Order 10624.

404 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19128331C211yesmaximal, characteristic, complemented
2#19128264C211yesmaximal, characteristic
3#19128064C211yesmaximal, characteristic, complemented
4#19128061C211yesmaximal, characteristic, complemented
5#19128059C211yesmaximal, characteristic, complemented
6#19128058C211yesmaximal, characteristic, complemented
7#19128054C211yesmaximal, characteristic, complemented
8#19128047C211yesmaximal, characteristic, complemented
9#19128046C211yesmaximal, characteristic, complemented
10#19127704C211yesmaximal, characteristic, complemented
11#19127699C211yesmaximal, characteristic, complemented
12#19127694C211yesmaximal, characteristic, complemented
13#102×D83C211yesmaximal, characteristic, complemented
14#19127658C211yesmaximal, characteristic, complemented
15#490×C83C211yesmaximal, characteristic, complemented
16C2×#13050589C2211yescharacteristic
17C2×D4×D83C2211yescharacteristic
18C2×#13050573C2211yescharacteristic
19C2×C8×D83C2211yescharacteristic
20#14581792C2211yescharacteristic, complemented
21#14581791—21no—
22#14581791C2211yescharacteristic, complemented
23#14581788C2211yescharacteristic
24#14581783C2211yescharacteristic, complemented
25#14581782—21no—
26#14581780C2211yescharacteristic
27#14581779C2211yescharacteristic
28#14581772—21no—
29#14581770—21no—
30#14581764—21no—
31#14581764—21no—
32#14581760—21no—
33#14581760—21no—
34#14581750C2211yescharacteristic
35#14581749C2211yescharacteristic
36C4⋊C4×D83C2211yescharacteristic
37#14581717C2211yescharacteristic, complemented
38#14581717C2211yescharacteristic, complemented
39#14581715C2211yescharacteristic, complemented
40#14581715C2211yescharacteristic, complemented
41#14581714C2211yescharacteristic
42#14581714C2211yescharacteristic
43#14581713C2211yescharacteristic
44#14581713C2211yescharacteristic
45#14581713C2211yescharacteristic, complemented
46#14581713C2211yescharacteristic, complemented
47#14581712C2211yescharacteristic
48#14581712C2211yescharacteristic
49#14581702C2211yescharacteristic, complemented
50C4×C83⋊C8C2211yescharacteristic, complemented
51C8×Dic83C2211yescharacteristic, complemented
52#127×C83C2211yescharacteristic
53#125×C83C2211yescharacteristic, complemented
54#102×C83C2211yescharacteristic
55#102×C83C2211yescharacteristic
56#102×C83C2211yescharacteristic, complemented
57#102×C83C2211yescharacteristic, complemented
58#97×C83C2211yescharacteristic, complemented
59C23×D83—21no—
60#13050589—22no—
61#13050589—22no—
62C2×Dic166—21no—
63C2×Dic166—21no—
64C2×Dic166C2311yescharacteristic
65C2×D332C2311yescharacteristic
66C2×C22⋊D83—21no—
67C2×C22⋊D83—21no—
68C2×C22⋊D83—21no—
69C2×C22⋊D83—21no—
70D4×D83—22no—
71D4×D83—22no—
72C22×Dic83—21no—
73C2×C4×D83—21no—
74C2×C4×D83C2311yescharacteristic
75#13050573—22no—
76C2×C83⋊C8C2311yescharacteristic
77C2×C83⋊C8C2311yescharacteristic
78C8×D83—22no—
79C4⋊Dic83—21no—
80C4⋊Dic83—21no—
81C4⋊Dic83C2311yescharacteristic
82C4⋊Dic83C2311yescharacteristic
83Dic83⋊C4—21no—
84Dic83⋊C4—21no—
85Dic83⋊C4—21no—
86Dic83⋊C4D411yescharacteristic
87Dic83⋊C4D411yescharacteristic
88C22⋊Dic83—21no—
89C22⋊Dic83—21no—
90(C2×D83)⋊C4—21no—
91(C2×D83)⋊C4—21no—
92(C2×D83)⋊C4—21no—
93(C2×D83)⋊C4D411yescharacteristic
94(C2×D83)⋊C4D411yescharacteristic
95C4×Dic83—21no—
96C4×Dic83C2311yescharacteristic
97C2×D4×C83—21no—
98C2×D4×C83—21no—
99C2×D4×C83C2311yescharacteristic
100C2×D4×C83C2311yescharacteristic
101C2×C8×C83C2311yescharacteristic
102C2×C8×C83C2311yescharacteristic
103C4⋊C4×C83—21no—
104C4⋊C4×C83—21no—
105C4⋊C4×C83C2311yescharacteristic
106C4⋊C4×C83C2311yescharacteristic
107C42×C83C2311yescharacteristic
108C23×C83—21no—
109C23×C83—21no—
110C22×D83—21no—
111C22×D83—42no—
112C22×D83—81no—
113C22×D83—81no—
114C22×D83C2×D411yescharacteristic
115D4×C83—21no—
116D4×C83—21no—
117D4×C83—21no—
118D4×C83—21no—
119D4×C83—81no—
120D4×C83—81no—
121C2×C4×C83—21no—
122C2×C4×C83—21no—
123C2×C4×C83C2×D411yescharacteristic
124C2×C4×C83C2×D411yescharacteristic
125C2×C4×C83C2411yescharacteristic
126C22⋊D83—42no—
127C22⋊D83—42no—
128C22⋊D83—81no—
129C22⋊D83—81no—
130C2×Dic83—21no—
131C2×Dic83—21no—
132C2×Dic83—21no—
133C2×Dic83—42no—
134C2×Dic83C2×D411yescharacteristic
135C2×Dic83C2×D411yescharacteristic
136C2×Dic83C2×D411yescharacteristic
137D332—21no—
138D332—21no—
139C4×D83—81no—
140C4×D83#4112yes—
141C4×D83#4112yes—
142Dic166—21no—
143Dic166—21no—
144Dic166—81no—
145Dic166—81no—
146C8×C83—21no—
147C8×C83—21no—
148C83⋊C8—21no—
149C83⋊C8—21no—
150C22×C83—41no—
151C22×C83—41no—
152C22×C83—41no—
153C22×C83—41no—
154C22×C83—41no—
155C22×C83—41no—
156C22×C83C22×D411yescharacteristic
157C2×D83—21no—
158C2×D83—21no—
159C2×D83—41no—
160C2×D83—41no—
161C2×D83—41no—
162C2×D83—84no—
163C2×D83#12412yes—
164C4×C83—21no—
165C4×C83—21no—
166C4×C83—41no—
167C4×C83—41no—
168C4×C83C2×#4111yescharacteristic
169C4×C83C2×#4111yescharacteristic
170Dic83—21no—
171Dic83—21no—
172Dic83—41no—
173Dic83—41no—
174Dic83—41no—
175Dic83#12412yes—
176C2×C83—81no—
177C2×C83—81no—
178C2×C83C2×#12411yescharacteristic
179C2×C83#57611yescharacteristic
180C2×C83#57711yescharacteristic
181D83—22no—
182D83—81no—
183#3136—831nomaximal, Sylow
184C83#313611yescharacteristic, complemented, Sylow
185#544—831no—
186#535—831no—
187#490—831no—
188#490D8311yescharacteristic, complemented
189#489—831no—
190#489—831no—
191#488—831no—
192#488—831no—
193#486—831no—
194#486—831no—
195#418—831no—
196#417—831no—
197#416—831no—
198C2×#102—831no—
199#405—831no—
200C2×#41—831no—
201C22×D4—831no—
202C2×M16—831no—
203C22×C8—831no—
204C4⋊Q8—831no—
205C4⋊Q8—831no—
206C4⋊Q8—1661no—
207#127—831no—
208#127C2×D8311yescharacteristic
209#125—831no—
210#125—1661no—
211#125C2×D8311yescharacteristic, complemented
212#124—831no—
213#124—831no—
214C22⋊Q8—1661no—
215C22⋊Q8—1661no—
216#121—1661no—
217#121—1661no—
218#120—1661no—
219#120—1661no—
220#117—831no—
221#117—831no—
222C2×C4⋊C4—831no—
223#103—831no—
224#103—831no—
225#103—831no—
226#103—831no—
227#102—831no—
228#102—831no—
229#102—831no—
230#102—831no—
231#102—831no—
232#102—831no—
233#102—831no—
234#102—831no—
235#102C2×D8311yescharacteristic
236#102C2×D8311yescharacteristic
237#102C2×D8311yescharacteristic, complemented
238#102C2×D8311yescharacteristic, complemented
239#97—831no—
240#97C2×D8311yescharacteristic, complemented
241C4×C8—831no—
242C4×C8—831no—
243C24—1661no—
244#41—1662no—
245#41—1662no—
246C2×Q8—831no—
247C2×Q8—1661no—
248C2×Q8—1661no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—831no—
252C2×D4—1662no—
253C2×D4—1662no—
254C2×D4—1661no—
255C2×D4—1661no—
256C2×D4—1661no—
257C2×D4—1661no—
258C2×D4C22×D8311yescharacteristic
259C2×D4C22×D8311yescharacteristic
260C22×C4—831no—
261C22×C4—1661no—
262C22×C4—1661no—
263M16—1662no—
264C2×C8—831no—
265C2×C8—831no—
266C2×C8—1662no—
267C2×C8C22×D8311yescharacteristic
268C2×C8C22×D8311yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—831no—
272C4⋊C4—831no—
273C4⋊C4—831no—
274C4⋊C4—831no—
275C4⋊C4—1661no—
276C4⋊C4—1661no—
277C4⋊C4—1661no—
278C4⋊C4—1661no—
279C4⋊C4—1661no—
280C4⋊C4C22×D8311yescharacteristic
281C4⋊C4C22×D8311yescharacteristic
282C22⋊C4—831no—
283C22⋊C4—831no—
284C22⋊C4—1661no—
285C22⋊C4—1661no—
286C22⋊C4—1661no—
287C22⋊C4—1661no—
288C22⋊C4—1661no—
289C42—831no—
290C42—1661no—
291C42C22×D8311yescharacteristic
292C23—21no—
293C23—21no—
294C23—3322no—
295C23—831no—
296C23—6641no—
297C23—6641no—
298C23—1661no—
299Q8—6641no—
300Q8—6641no—
301Q8—1661no—
302Q8—1661no—
303D4—21no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—81no—
308D4—81no—
309D4—3322no—
310D4—3322no—
311D4—6641no—
312D4—6641no—
313D4—1661no—
314D4—1661no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—3322no—
318C2×C4—831no—
319C2×C4—832no—
320C2×C4—832no—
321C2×C4—831no—
322C2×C4—831no—
323C2×C4—6641no—
324C2×C4—1661no—
325C2×C4—1661no—
326C2×C4—1661no—
327C2×C4D4×D8311yescharacteristic
328C2×C4D4×D8311yescharacteristic
329C2×C4C23×D8311yescharacteristic
330C8—21no—
331C8—21no—
332C8—1661no—
333C8—1661no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—3321no—
341C22—3321no—
342C22—3321no—
343C22—832no—
344C22—6644no—
345C22—1661no—
346C22—1661no—
347C22C2×D4×D8311yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—3321no—
353C4—3321no—
354C4—3321no—
355C4—832no—
356C4—1661no—
357C4—1661no—
358C4#41×D8311yescharacteristic
359C4#41×D8311yescharacteristic
360C2—81no—
361C2—81no—
362C2—6641no—
363C2—1662no—
364C2#124×D8311yescharacteristic
365C2#1912850511yescharacteristic
366C2#1912851111yescharacteristic
subgroupG/H
centerC22C2×D4×D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting#490×C83C2
socleC22×C83C22×D4
prime radical#19128264C2
hypercenter#490D83
hypocenterC83#3136
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #19128331C2semidirect
3. #19128064C2semidirect
4. #19128061C2semidirect
5. #19128059C2semidirect
6. #19128058C2semidirect
7. #19128054C2semidirect
8. #19128047C2semidirect
9. #19128046C2semidirect
10. #19127704C2semidirect
11. #19127699C2semidirect
12. #19127694C2semidirect
13. #102×D83C2semidirect
14. #19127658C2semidirect
15. #490×C83C2semidirect
20. #14581792C22semidirect
22. #14581791C22semidirect
24. #14581783C22semidirect
37. #14581717C22semidirect
38. #14581717C22semidirect
39. #14581715C22semidirect
40. #14581715C22semidirect
45. #14581713C22semidirect
46. #14581713C22semidirect
49. #14581702C22semidirect
50. C4×C83⋊C8C22semidirect
51. C8×Dic83C22semidirect
53. #125×C83C22semidirect
56. #102×C83C22semidirect
57. #102×C83C22semidirect
58. #97×C83C22semidirect
184. C83#3136semidirect
188. #490D83semidirect
211. #125C2×D83semidirect
237. #102C2×D83semidirect
238. #102C2×D83semidirect
240. #97C2×D83semidirect

Maximal subgroups

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

subgroupindex
#191283312
#191282642
#191280642
#191280612
#191280592
#191280582
#191280542
#191280472
#191280462
#191277042
#191276992
#191276942
#102×D832
#191276582
#490×C832
#313683