Finite Group Databasebeta

← #24906008

Subgroups — #24906008

Order 10624.

252 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 61 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#19128246C211yesmaximal, characteristic
2#19127755C211yesmaximal, characteristic, complemented
3#19127568C211yesmaximal, characteristic, complemented
4#19127436C211yesmaximal, characteristic, complemented
5#19127435C211yesmaximal, characteristic, complemented
6#19127434C211yesmaximal, characteristic, complemented
7#327×C83C211yesmaximal, characteristic, complemented
8C2×#13050589—21no—
9#14581791C411yescharacteristic, complemented
10#14581788C411yescharacteristic, complemented
11#14581778—21no—
12#14581766C2211yescharacteristic
13#14581764—21no—
14D4×Dic83C411yescharacteristic, complemented
15#14581754C411yescharacteristic, complemented
16(C22⋊D83)⋊C4—21no—
17C2×C4×Dic83C2211yescharacteristic
18Dic83⋊C8—21no—
19C22⋊(C83⋊C8)C2211yescharacteristic
20#14581702—21no—
21C83⋊#95—21no—
22C83⋊#95—21no—
23C83⋊#95C2211yescharacteristic
24#121×C83C2211yescharacteristic
25C22⋊C8×C83C2211yescharacteristic
26#95×C83C2211yescharacteristic
27#13050589—42no—
28#13050589—42no—
29C2×Dic166—21no—
30C2×D332C2×C411yescharacteristic
31C2×C22⋊D83—21no—
32C2×C22⋊D83—21no—
33C2×C22⋊D83—21no—
34C22×Dic83—21no—
35C22×Dic83—21no—
36C22×Dic83D411yescharacteristic
37C22×Dic83D411yescharacteristic
38C2×C4×D83—21no—
39C2×C83⋊C8—21no—
40C4⋊Dic83C2×C411yescharacteristic
41Dic83⋊C4—21no—
42C22⋊Dic83—21no—
43(C2×D83)⋊C4—21no—
44(C2×D83)⋊C4—21no—
45C4×Dic83C2×C411yescharacteristic
46C4×Dic83C2×C411yescharacteristic
47C4×Dic83D411yescharacteristic
48C4×Dic83D411yescharacteristic
49C2×D4×C83—21no—
50C2×D4×C83C2×C411yescharacteristic
51C22×C4×C83—21no—
52C22×C4×C83C2311yescharacteristic
53C2×C8×C83—21no—
54C4⋊C4×C83C2×C411yescharacteristic
55C22⋊C4×C83—21no—
56C23×C83—21no—
57C23×C83C2×D411yescharacteristic
58C22×D83—21no—
59D4×C83—41no—
60D4×C83—41no—
61D4×C83—41no—
62C2×C4×C83—21no—
63C2×C4×C83—41no—
64C2×C4×C83—41no—
65C2×C4×C83—41no—
66C2×C4×C83—41no—
67C2×C4×C83C22×C411yescharacteristic
68C2×C4×C83C2×D411yescharacteristic
69C22⋊D83—42no—
70C22⋊D83—42no—
71C22⋊D83—41no—
72C22⋊D83—41no—
73C2×Dic83—21no—
74C2×Dic83—21no—
75C2×Dic83—21no—
76C2×Dic83—41no—
77C2×Dic83—42no—
78C2×Dic83—41no—
79C2×Dic83—41no—
80C2×Dic83—41no—
81C2×Dic83C22⋊C411yescharacteristic
82C2×Dic83C22⋊C411yescharacteristic
83C2×Dic83C22⋊C411yescharacteristic
84C2×Dic83C22⋊C411yescharacteristic
85D332—41no—
86C4×D83—42no—
87Dic166—42no—
88C8×C83—41no—
89C83⋊C8—41no—
90C22×C83—21no—
91C22×C83—21no—
92C22×C83—41no—
93C22×C83—41no—
94C22×C83—41no—
95C22×C83C2×C22⋊C411yescharacteristic
96C22×C83AGL(1,ℤ/8)11yescharacteristic
97C22×C83AGL(1,ℤ/8)11yescharacteristic
98C2×D83—41no—
99C2×D83—41no—
100C2×D83—41no—
101C4×C83—21no—
102C4×C83—21no—
103C4×C83—41no—
104C4×C83—81no—
105Dic83—21no—
106Dic83—21no—
107Dic83—21no—
108Dic83—21no—
109Dic83—41no—
110Dic83—81no—
111C2×C83—21no—
112C2×C83—21no—
113C2×C83—81no—
114C2×C83#41011yescharacteristic
115C2×C83#41811yescharacteristic
116C2×C83#42111yescharacteristic
117D83—81no—
118#1514—831nomaximal, Sylow
119C83#151411yescharacteristic, complemented, Sylow
120#532—831no—
121#432—831no—
122#383—831no—
123#327—831no—
124#327—831no—
125#327—831no—
126#327D8311yescharacteristic, complemented
127C2×#41—1661no—
128C4⋊Q8—831no—
129#127—831no—
130#124—1661no—
131#121—831no—
132#121—1661no—
133#121C2×D8311yescharacteristic
134C4×D4—831no—
135C4×D4—831no—
136C4×D4—1661no—
137C2×C42—831no—
138C4⋊C8—1661no—
139C22⋊C8—831no—
140C22⋊C8C2×D8311yescharacteristic
141#97—1661no—
142#95—831no—
143#95—1661no—
144#95—1661no—
145#95C2×D8311yescharacteristic
146#41—3322no—
147#41—3322no—
148C2×Q8—1661no—
149C2×D4—21no—
150C2×D4—831no—
151C2×D4—1661no—
152C2×D4—1661no—
153C2×D4—1661no—
154C2×D4C4×D8311yescharacteristic
155C22×C4—21no—
156C22×C4—831no—
157C22×C4—831no—
158C22×C4—1661no—
159C22×C4—1661no—
160C22×C4—1661no—
161C22×C4C22×D8311yescharacteristic
162C2×C8—21no—
163C2×C8—1661no—
164C4⋊C4—831no—
165C4⋊C4—1661no—
166C4⋊C4C4×D8311yescharacteristic
167C22⋊C4—21no—
168C22⋊C4—1661no—
169C22⋊C4—1661no—
170C22⋊C4—1661no—
171C42—831no—
172C42—831no—
173C42—831no—
174C42—831no—
175C23—21no—
176C23—1661no—
177C23D4×D8311yescharacteristic
178Q8—3322no—
179D4—41no—
180D4—41no—
181D4—41no—
182D4—3321no—
183D4—3321no—
184D4—3321no—
185D4—3322no—
186D4—3322no—
187C2×C4—21no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—3322no—
193C2×C4—3322no—
194C2×C4—3321no—
195C2×C4—3321no—
196C2×C4—3321no—
197C2×C4—3321no—
198C2×C4—831no—
199C2×C4—831no—
200C2×C4—831no—
201C2×C4—831no—
202C2×C4—1661no—
203C2×C4—1661no—
204C2×C4—1661no—
205C2×C4C2×C4×D8311yescharacteristic
206C2×C4D4×D8311yescharacteristic
207C8—41no—
208C8—3321no—
209C22—21no—
210C22—21no—
211C22—41no—
212C22—41no—
213C22—41no—
214C22—3321no—
215C22—3321no—
216C22—3321no—
217C22C22⋊C4×D8311yescharacteristic
218C22#1458181611yescharacteristic
219C22#1458181911yescharacteristic
220C4—21no—
221C4—21no—
222C4—41no—
223C4—81no—
224C4—3321no—
225C4—6641no—
226C4—1661no—
227C4—1661no—
228C4—1661no—
229C4—1661no—
230C2—21no—
231C2—21no—
232C2—81no—
233C2—6641no—
234C2#1912767311yescharacteristic
235C2#1912770411yescharacteristic
236C2#1912771611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D83
commutatorC2×C4×C83C22×C4
FrattiniC22×C4C22×D83
Fitting#327×C83C2
socleC22×C83C2×C22⋊C4
prime radical#19128246C2
cosocleC22×C4×C83C23
hypercenter#327D83
hypocenterC83#1514
LCSG ▷ C2×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #19127755C2semidirect
3. #19127568C2semidirect
4. #19127436C2semidirect
5. #19127435C2semidirect
6. #19127434C2semidirect
7. #327×C83C2semidirect
9. #14581791C4semidirect
10. #14581788C4semidirect
14. D4×Dic83C4semidirect
15. #14581754C4semidirect
119. C83#1514semidirect
126. #327D83semidirect