Finite Group Databasebeta

← #24919707

Subgroups — #24919707

Order 10624.

460 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19128416C211yesmaximal, characteristic, complemented
2D4×D332C211yesmaximal, characteristic, complemented
3#19128048C211yesmaximal, characteristic, complemented
4#19128028C212yesmaximal, complemented
5#19127991C211yesmaximal, characteristic, complemented
6#19127953C212yesmaximal, complemented
7#19127896C211yesmaximal, characteristic, complemented
8#19127833C212yesmaximal, complemented
9#19127780C211yesmaximal, characteristic, complemented
10#19127704C212yesmaximal, complemented
11C4×D8×C83C211yesmaximal, characteristic, complemented
12C22×D332—21no—
13C2×D4×D83C2212yes—
14C2×#13050575C2212yescomplemented
15C2×#13050573C2212yescomplemented
16#14581792C2211yescharacteristic, complemented
17#14581789C2211yescharacteristic
18#14581778—22no—
19#14581767C2212yes—
20#14581766—21no—
21#14581766—21no—
22#14581763C2212yescomplemented
23#14581762—22no—
24C4×D332C2211yescharacteristic
25#14581751—21no—
26#14581750C2212yescomplemented
27#14581723C2212yescomplemented
28C4⋊(C83⋊C8)C2211yescharacteristic, complemented
29#14581714C2212yescomplemented
30#14581714C2212yescomplemented
31#14581713C2212yes—
32#14581712C2212yescomplemented
33(C2×D83)⋊C8C2212yescomplemented
34C2×D8×C83C2211yescharacteristic
35C4×D4×C83C2211yescharacteristic
36C4×D4×C83C2211yescharacteristic, complemented
37#107×C83C2211yescharacteristic, complemented
38#102×C83C2211yescharacteristic
39#102×C83C2211yescharacteristic, complemented
40C4×C8×C83C2211yescharacteristic, complemented
41C23×D83—22no—
42C2×Dic166—21no—
43C2×D332—22no—
44C2×D332—21no—
45C2×D332—21no—
46C2×D332—44no—
47C2×D332D411yescharacteristic
48C2×D332C2312yes—
49C2×C22⋊D83—22no—
50C2×C22⋊D83—22no—
51D4×D83—24no—
52D4×D83—42no—
53C2×C4×D83C2312yes—
54#13050575—42no—
55#13050573—42no—
56C2×C83⋊C8C2312yes—
57C4⋊Dic83—21no—
58C4⋊Dic83D411yescharacteristic
59C4⋊Dic83C2312yes—
60C22⋊Dic83—22no—
61(C2×D83)⋊C4—22no—
62(C2×D83)⋊C4—22no—
63(C2×D83)⋊C4D412yes—
64C4×Dic83—22no—
65C2×D4×C83C2311yescharacteristic
66C2×D4×C83C2311yescharacteristic
67C22×C4×C83—21no—
68C22×C4×C83—21no—
69D8×C83—22no—
70C2×C8×C83C2311yescharacteristic
71C2×C8×C83C2311yescharacteristic
72C4⋊C4×C83C2311yescharacteristic
73C4⋊C4×C83C2311yescharacteristic
74C22⋊C4×C83—21no—
75C22⋊C4×C83—21no—
76C42×C83C2311yescharacteristic
77C23×C83—21no—
78C23×C83—21no—
79C22×D83—22no—
80C22×D83—44no—
81C22×D83—44no—
82C22×D83—82no—
83C22×D83C2×D412yes—
84D4×C83—21no—
85D4×C83—21no—
86D4×C83—21no—
87D4×C83#4112yes—
88C2×C4×C83—21no—
89C2×C4×C83—21no—
90C2×C4×C83—42no—
91C2×C4×C83—42no—
92C2×C4×C83C2×D411yescharacteristic
93C2×C4×C83C2×D411yescharacteristic
94C2×C4×C83C2411yescharacteristic
95C22⋊D83—44no—
96C22⋊D83—82no—
97C2×Dic83—22no—
98C2×Dic83C2×D412yes—
99D332—22no—
100D332—22no—
101D332—22no—
102D332—44no—
103D332—42no—
104D332—81no—
105C4×D83—22no—
106C4×D83—22no—
107Dic166—81no—
108C8×C83—21no—
109C8×C83—21no—
110C83⋊C8—22no—
111C22×C83—22no—
112C22×C83—41no—
113C22×C83—41no—
114C22×C83—41no—
115C22×C83—41no—
116C22×C83—41no—
117C22×C83C22×D411yescharacteristic
118C2×D83—22no—
119C2×D83—22no—
120C2×D83—22no—
121C2×D83—42no—
122C2×D83—42no—
123C2×D83—42no—
124C2×D83—88no—
125C4×C83—21no—
126C4×C83—41no—
127C4×C83—41no—
128C4×C83AGL(1,ℤ/8)12yes—
129C4×C83C2×#4111yescharacteristic
130C4×C83H(5,𝔽2)11yescharacteristic
131Dic83—22no—
132Dic83—42no—
133C2×C83—42no—
134C2×C83—81no—
135C2×C83#54611yescharacteristic
136C2×C83C2×AGL(1,ℤ/8)11yescharacteristic
137C2×C83#57611yescharacteristic
138D83—42no—
139D83—82no—
140#3325—831nomaximal, Sylow
141C83#332511yescharacteristic, complemented, Sylow
142#555—831no—
143D42—831no—
144#486—831no—
145#482—832no—
146#476—831no—
147#469—832no—
148#459—831no—
149#447—832no—
150C4×D8D8311yescharacteristic, complemented
151#436—831no—
152#418—832no—
153C22×D4—832no—
154C22×D4—1661no—
155C2×D8—832no—
156C2×D8C2×D8311yescharacteristic
157C2×M16—832no—
158C4⋊Q8—831no—
159#127—831no—
160#124—1662no—
161#121—832no—
162#121—832no—
163#121—1661no—
164#121—1661no—
165#120—1662no—
166C4×D4—831no—
167C4×D4C2×D8311yescharacteristic
168C4×D4C2×D8311yescharacteristic, complemented
169#117—832no—
170#117—1661no—
171#107C2×D8311yescharacteristic, complemented
172#106—832no—
173C4⋊C8—831no—
174#102—832no—
175#102—832no—
176#102—832no—
177#102—832no—
178#102C2×D8311yescharacteristic
179#102C2×D8311yescharacteristic, complemented
180C22⋊C8—832no—
181C4×C8C2×D8311yescharacteristic, complemented
182C24—1662no—
183C2×Q8—1661no—
184C2×D4—3324no—
185C2×D4—3322no—
186C2×D4—831no—
187C2×D4—832no—
188C2×D4—1662no—
189C2×D4—1662no—
190C2×D4—1664no—
191C2×D4—1662no—
192C2×D4—1661no—
193C2×D4—1661no—
194C2×D4C22×D8311yescharacteristic
195C2×D4C22×D8311yescharacteristic
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—832no—
199D8—22no—
200D8—3322no—
201M16—3322no—
202C2×C8—832no—
203C2×C8C22×D8311yescharacteristic
204C2×C8C22×D8311yescharacteristic
205C4⋊C4—831no—
206C4⋊C4—832no—
207C4⋊C4—1661no—
208C4⋊C4C22×D8311yescharacteristic
209C4⋊C4C22×D8311yescharacteristic
210C22⋊C4—21no—
211C22⋊C4—21no—
212C22⋊C4—832no—
213C22⋊C4—1662no—
214C22⋊C4—1662no—
215C22⋊C4—1662no—
216C42—1662no—
217C42C22×D8311yescharacteristic
218C23—21no—
219C23—21no—
220C23—3324no—
221C23—3324no—
222C23—832no—
223C23—6642no—
224C23—1662no—
225Q8—6641no—
226D4—21no—
227D4—21no—
228D4—21no—
229D4—3324no—
230D4—3324no—
231D4—3322no—
232D4—6641no—
233D4—6642no—
234D4—1662no—
235D4—1662no—
236D4—1662no—
237D4#1305059012yes—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—832no—
243C2×C4—1662no—
244C2×C4—1662no—
245C2×C4—1662no—
246C2×C4D4×D8311yescharacteristic
247C2×C4D4×D8311yescharacteristic
248C2×C4C23×D8311yescharacteristic
249C8—21no—
250C8—21no—
251C8—1662no—
252C22—22no—
253C22—41no—
254C22—41no—
255C22—41no—
256C22—41no—
257C22—41no—
258C22—3322no—
259C22—3322no—
260C22—3322no—
261C22—6648no—
262C22—1662no—
263C22—1662no—
264C22—1662no—
265C22C2×D4×D8311yescharacteristic
266C4—21no—
267C4—41no—
268C4—41no—
269C4—3322no—
270C4—1662no—
271C4#1458181612yes—
272C4C2×#1305059011yescharacteristic
273C4#1458183811yescharacteristic
274C2—42no—
275C2—81no—
276C2—3322no—
277C2—6642no—
278C2#1912834711yescharacteristic
279C2C2×#1458181611yescharacteristic
280C2#1912850311yescharacteristic
subgroupG/H
centerC22C2×D4×D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
FittingC4×D8×C83C2
socleC22×C83C22×D4
hypercenterC4×D8D83
hypocenterC83#3325
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #19128416C2semidirect
2. D4×D332C2semidirect
3. #19128048C2semidirect
4. #19128028C2semidirect
5. #19127991C2semidirect
6. #19127953C2semidirect
7. #19127896C2semidirect
8. #19127833C2semidirect
9. #19127780C2semidirect
10. #19127704C2semidirect
11. C4×D8×C83C2semidirect
14. C2×#13050575C22semidirect
15. C2×#13050573C22semidirect
16. #14581792C22semidirect
22. #14581763C22semidirect
26. #14581750C22semidirect
27. #14581723C22semidirect
28. C4⋊(C83⋊C8)C22semidirect
29. #14581714C22semidirect
30. #14581714C22semidirect
32. #14581712C22semidirect
33. (C2×D83)⋊C8C22semidirect
36. C4×D4×C83C22semidirect
37. #107×C83C22semidirect
39. #102×C83C22semidirect
40. C4×C8×C83C22semidirect
141. C83#3325semidirect
150. C4×D8D83semidirect
168. C4×D4C2×D83semidirect
171. #107C2×D83semidirect
179. #102C2×D83semidirect
181. C4×C8C2×D83semidirect

Maximal subgroups

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

subgroupindex
#191284162
D4×D3322
#191280482
#191280282
#191279912
#191279532
#191278962
#191278332
#191277802
#191277042
C4×D8×C832
#332583