Finite Group Databasebeta

← #24905985

Subgroups — #24905985

Order 10624.

242 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 63 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#19128232C211yesmaximal, characteristic
2#19127755C211yesmaximal, characteristic, complemented
3#19127552C211yesmaximal, characteristic, complemented
4#19127439C211yesmaximal, characteristic, complemented
5#19127437C211yesmaximal, characteristic, complemented
6#19127435C211yesmaximal, characteristic
7#327×C83C211yesmaximal, characteristic
8#14581785—21no—
9#14581783C411yescharacteristic, complemented
10#14581779C411yescharacteristic, complemented
11#14581773—21no—
12#14581771C2211yescharacteristic
13#14581757C411yescharacteristic, complemented
14D4×Dic83—21no—
15D4×Dic83C411yescharacteristic, complemented
16#14581748—21no—
17C2×Dic83⋊C4—21no—
18C2×C4×Dic83—21no—
19C2×C4×Dic83C2211yescharacteristic
20Dic83⋊C8—21no—
21C22⋊(C83⋊C8)C2211yescharacteristic
22#14581702—21no—
23C83⋊#95C2211yescharacteristic
24#121×C83C2211yescharacteristic
25C22⋊C8×C83C2211yescharacteristic
26#95×C83C2211yescharacteristic
27C2×Dic166C2×C411yescharacteristic
28C22×Dic83—21no—
29C22×Dic83—21no—
30C22×Dic83D411yescharacteristic
31C22×Dic83D411yescharacteristic
32C2×C83⋊C8—21no—
33C4⋊Dic83—21no—
34C4⋊Dic83C2×C411yescharacteristic
35Dic83⋊C4—24no—
36Dic83⋊C4—21no—
37Dic83⋊C4—21no—
38Dic83⋊C4—21no—
39C22⋊Dic83—21no—
40C22⋊Dic83—21no—
41C22⋊Dic83—21no—
42C22⋊Dic83—21no—
43C4×Dic83—21no—
44C4×Dic83—42no—
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
58D4×C83—41no—
59D4×C83—41no—
60D4×C83—41no—
61C2×C4×C83—22no—
62C2×C4×C83—21no—
63C2×C4×C83—41no—
64C2×C4×C83—41no—
65C2×C4×C83—41no—
66C2×C4×C83C22×C411yescharacteristic
67C2×C4×C83C2×D411yescharacteristic
68C2×Dic83—21no—
69C2×Dic83—21no—
70C2×Dic83—22no—
71C2×Dic83—22no—
72C2×Dic83—21no—
73C2×Dic83—21no—
74C2×Dic83—41no—
75C2×Dic83—41no—
76C2×Dic83—42no—
77C2×Dic83C22⋊C411yescharacteristic
78C2×Dic83C22⋊C411yescharacteristic
79C2×Dic83C22⋊C411yescharacteristic
80C2×Dic83C22⋊C411yescharacteristic
81Dic166—41no—
82C8×C83—41no—
83C83⋊C8—41no—
84C22×C83—21no—
85C22×C83—21no—
86C22×C83—41no—
87C22×C83—41no—
88C22×C83—41no—
89C22×C83C2×C22⋊C411yescharacteristic
90C22×C83AGL(1,ℤ/8)11yescharacteristic
91C22×C83#13711yescharacteristic
92C4×C83—21no—
93C4×C83—21no—
94C4×C83—42no—
95C4×C83—41no—
96Dic83—21no—
97Dic83—21no—
98Dic83—21no—
99Dic83—42no—
100Dic83—41no—
101Dic83—41no—
102Dic83#10412yes—
103C2×C83—21no—
104C2×C83—21no—
105C2×C83—81no—
106C2×C83#41011yescharacteristic
107C2×C83#41711yescharacteristic
108C2×C83C2×#10411yescharacteristic
109#1509—831nomaximal, Sylow
110C83#150911yescharacteristic, complemented, Sylow
111#529—831no—
112#432—831no—
113C4×C4⋊C4—831no—
114#328—831no—
115#328—831no—
116#327—831no—
117#327D8311yescharacteristic
118#126—1661no—
119#125—831no—
120#124—831no—
121#123—1661no—
122C22⋊Q8—831no—
123#121C2×D8311yescharacteristic
124C4×Q8—831no—
125C4×D4—831no—
126C4×D4—1661no—
127#117—1661no—
128C2×C4⋊C4—1661no—
129C2×C42—831no—
130C2×C42—1661no—
131C4⋊C8—1661no—
132C22⋊C8—831no—
133C22⋊C8C2×D8311yescharacteristic
134#97—1661no—
135#95—831no—
136#95C2×D8311yescharacteristic
137C2×Q8—831no—
138C2×D4—21no—
139C2×D4C4×D8311yescharacteristic
140C22×C4—21no—
141C22×C4—831no—
142C22×C4—831no—
143C22×C4—1661no—
144C22×C4—1661no—
145C22×C4C22×D8311yescharacteristic
146C2×C8—21no—
147C2×C8—1661no—
148C4⋊C4—831no—
149C4⋊C4—1661no—
150C4⋊C4—1661no—
151C4⋊C4—1661no—
152C4⋊C4—1664no—
153C4⋊C4—1661no—
154C4⋊C4C4×D8311yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—1661no—
157C22⋊C4—1661no—
158C22⋊C4—1661no—
159C22⋊C4—1661no—
160C42—3322no—
161C42—831no—
162C42—831no—
163C42—831no—
164C42—831no—
165C42—1661no—
166C23—21no—
167C23D4×D8311yescharacteristic
168Q8—3321no—
169D4—41no—
170D4—41no—
171D4—41no—
172C2×C4—22no—
173C2×C4—21no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—3321no—
178C2×C4—3321no—
179C2×C4—3322no—
180C2×C4—831no—
181C2×C4—831no—
182C2×C4—831no—
183C2×C4—831no—
184C2×C4—1662no—
185C2×C4—1661no—
186C2×C4—1661no—
187C2×C4—1662no—
188C2×C4—1661no—
189C2×C4—1661no—
190C2×C4C2×C4×D8311yescharacteristic
191C2×C4D4×D8311yescharacteristic
192C8—41no—
193C8—3321no—
194C22—21no—
195C22—21no—
196C22—41no—
197C22—41no—
198C22—41no—
199C22C22⋊C4×D8311yescharacteristic
200C22#1458181611yescharacteristic
201C22#1458182111yescharacteristic
202C4—21no—
203C4—21no—
204C4—42no—
205C4—41no—
206C4—3322no—
207C4—3321no—
208C4—3321no—
209C4—832no—
210C4—1661no—
211C4—1661no—
212C4—1661no—
213C2—21no—
214C2—21no—
215C2—81no—
216C2#1912767311yescharacteristic
217C2#1912769911yescharacteristic
218C2#104×D8311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D83
commutatorC2×C4×C83C22×C4
FrattiniC22×C4C22×D83
Fitting#327×C83C2
socleC22×C83C2×C22⋊C4
prime radical#121×C83C22
cosocleC22×C4×C83C23
hypercenter#327D83
hypocenterC83#1509
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. #19127552C2semidirect
4. #19127439C2semidirect
5. #19127437C2semidirect
9. #14581783C4semidirect
10. #14581779C4semidirect
13. #14581757C4semidirect
15. D4×Dic83C4semidirect
110. C83#1509semidirect