Finite Group Databasebeta

← #21456684

Subgroups — #21456684

Order 7808.

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

normal subgroups only

This group has 442 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#16840326C212yesmaximal, complemented
2#16840087C214yesmaximal, complemented
3#16840015C212yesmaximal, complemented
4#16839998C212yesmaximal, complemented
5#16839898C214yesmaximal, complemented
6C61×#408C211yesmaximal, characteristic, complemented
7C22×D244C2212yescomplemented
8C2×D488C2212yes—
9C2×D488C2212yes—
10#14519773—22no—
11#14519766—22no—
12#14519751C2214yes—
13#14519751C2214yescomplemented
14#14519745—22no—
15#14519745—22no—
16#14519736C2212yescomplemented
17#14519711C2212yescomplemented
18#14519709C2212yescomplemented
19#14519699C2214yescomplemented
20#14519699C2214yescomplemented
21C2×#41×C61C2211yescharacteristic
22C2×M16×C61C2211yescharacteristic, complemented
23C22×C8×C61C2211yescharacteristic, complemented
24C22⋊C8×C61C2214yescomplemented
25C23×D61—22no—
26#41×C61—41no—
27#41×C61—41no—
28C2×Q8×C61D411yescharacteristic
29C2×D4×C61D411yescharacteristic
30C2×D4×C61D412yes—
31C22×C4×C61C2312yes—
32C22×C4×C61C2311yescharacteristic
33C2×C22⋊D61—24no—
34C2×C22⋊D61—24no—
35C2×D244—22no—
36C2×D244—42no—
37C2×D244—42no—
38C2×D244C2314yes—
39M16×C61—41no—
40C2×C8×C61—41no—
41C2×C8×C61C2312yes—
42C2×C8×C61C2312yes—
43C22⋊Dic61—22no—
44#11758198—24no—
45#11758198—24no—
46C4⋊Dic61C2314yes—
47C4×Dic61—22no—
48D488—42no—
49D488—42no—
50C23×C61C2×D412yes—
51C23×C61C2×D411yescharacteristic
52C22×D61—24no—
53C22×D61—44no—
54C22×D61—84no—
55Q8×C61—41no—
56D4×C61—42no—
57D4×C61—41no—
58C2×C4×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61—22no—
61C2×C4×C61—22no—
62C2×C4×C61C2×D412yes—
63C2×C4×C61C2×D411yescharacteristic
64C2×C4×C61C2411yescharacteristic
65C22⋊D61—84no—
66C22⋊D61—84no—
67C2×Dic61—24no—
68D244—24no—
69D244—24no—
70D244—44no—
71C8×C61—22no—
72C8×C61—22no—
73C22×C61—22no—
74C22×C61—21no—
75C22×C61—22no—
76C22×C61—24no—
77C22×C61C22×D411yescharacteristic
78C2×D61—44no—
79C2×D61—44no—
80C2×D61—44no—
81C2×D61—88no—
82C4×C61—22no—
83C4×C61—21no—
84C4×C61H(5,𝔽2)11yescharacteristic
85C4×C61H(5,𝔽2)11yescharacteristic
86Dic61—44no—
87#3199—611nomaximal, Sylow
88C2×C61—42no—
89C2×C61—41no—
90C2×C61#53411yescharacteristic
91C2×C61#57612yes—
92D61—84no—
93#535—612no—
94#482—614no—
95#469—612no—
96#466—612no—
97#447—614no—
98#408D6111yescharacteristic, complemented
99C61#319911yescharacteristic, complemented, Sylow
100C2×#41C2×D6111yescharacteristic
101C22×D4—612no—
102C2×D8—612no—
103C2×D8—612no—
104C2×M16C2×D6111yescharacteristic, complemented
105C22×C8C2×D6111yescharacteristic, complemented
106#127—1222no—
107#124—1222no—
108#121—614no—
109#121—614no—
110#120—1222no—
111#120—1222no—
112#117—612no—
113#107—612no—
114#106—612no—
115#102—614no—
116#102—614no—
117C22⋊C8C2×D6114yescomplemented
118C24—1222no—
119#41—41no—
120#41—41no—
121C2×Q8D24411yescharacteristic
122C2×D4—614no—
123C2×D4—1224no—
124C2×D4—1224no—
125C2×D4—1222no—
126C2×D4—2442no—
127C2×D4—2442no—
128C2×D4D24411yescharacteristic
129C2×D4D24412yes—
130C22×C4C22×D6112yes—
131C22×C4C22×D6111yescharacteristic
132D8—2442no—
133D8—2442no—
134M16—41no—
135C2×C8—41no—
136C2×C8C22×D6112yes—
137C2×C8C22×D6112yes—
138C4⋊C4—614no—
139C22⋊C4—1222no—
140C22⋊C4—1224no—
141C22⋊C4—1224no—
142C42—1222no—
143C23—1224no—
144C23—4884no—
145C23—2444no—
146C23C2×D24412yes—
147C23C2×D24411yescharacteristic
148Q8—41no—
149D4—42no—
150D4—41no—
151D4—1224no—
152D4—1224no—
153D4—4884no—
154D4—4884no—
155D4—2444no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—1224no—
161C2×C4C2×D24412yes—
162C2×C4C2×D24411yescharacteristic
163C2×C4C23×D6111yescharacteristic
164C8—22no—
165C8—22no—
166C22—22no—
167C22—24no—
168C22—22no—
169C22—21no—
170C22—4888no—
171C22—2444no—
172C22—2444no—
173C22—2444no—
174C22C22×D24411yescharacteristic
175C4—22no—
176C4—21no—
177C4—2444no—
178C4#1451982211yescharacteristic
179C4#1451982211yescharacteristic
180C2—42no—
181C2—41no—
182C2—4884no—
183C2#1684032411yescharacteristic
184C2#1684056712yes—
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#408C2
socleC22×C61C22×D4
hypercenter#408D61
hypocenterC61#3199
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #16840326C2semidirect
2. #16840087C2semidirect
3. #16840015C2semidirect
4. #16839998C2semidirect
5. #16839898C2semidirect
6. C61×#408C2semidirect
7. C22×D244C22semidirect
13. #14519751C22semidirect
16. #14519736C22semidirect
17. #14519711C22semidirect
18. #14519709C22semidirect
19. #14519699C22semidirect
20. #14519699C22semidirect
22. C2×M16×C61C22semidirect
23. C22×C8×C61C22semidirect
24. C22⋊C8×C61C22semidirect
98. #408D61semidirect
99. C61#3199semidirect
104. C2×M16C2×D61semidirect
105. C22×C8C2×D61semidirect
117. C22⋊C8C2×D61semidirect