Finite Group Databasebeta

← #21444418

Subgroups — #21444418

Order 7808.

264 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C2×#14519765C211yesmaximal, characteristic
2C4×#11758194C211yesmaximal, characteristic, complemented
3#16839501C214yesmaximal, complemented
4C61×#432C211yesmaximal, characteristic, complemented
5C22×Dic122C411yescharacteristic
6C22×D244C411yescharacteristic
7C2×#11758194—21no—
8#14519765—21no—
9#14519765—21no—
10#14519765C412yes—
11#14519765C2212yes—
12C2×#11758198—21no—
13C2×#11758198—21no—
14#14519688C2212yescomplemented
15C4×#92418—21no—
16C2×C42×C61C2211yescharacteristic
17C4⋊C8×C61—21no—
18C22⋊C8×C61—21no—
19#97×C61C2212yescomplemented
20C23×D61—21no—
21C22×C4×C61C2×C411yescharacteristic
22C22×C4×C61D411yescharacteristic
23C22×C4×C61D411yescharacteristic
24C22×Dic61—21no—
25C2×D244—21no—
26C2×D244—42no—
27C2×D244C2×C412yes—
28C2×Dic122—21no—
29C2×Dic122—42no—
30C2×Dic122C2×C412yes—
31C2×C8×C61—22no—
32C42×C61C2×C411yescharacteristic
33C42×C61D411yescharacteristic
34C42×C61D411yescharacteristic
35C42×C61C2311yescharacteristic
36#11758198—22no—
37#11758198—22no—
38#11758198—22no—
39#11758198—22no—
40#11758194—24no—
41C2×#92418—22no—
42C23×C61C22⋊C411yescharacteristic
43C22×D61—22no—
44C22×D61—42no—
45C22×D61—42no—
46C22×D61—42no—
47C2×C4×C61—22no—
48C2×C4×C61—22no—
49C2×C4×C61—41no—
50C2×C4×C61C22⋊C411yescharacteristic
51C2×C4×C61C22⋊C411yescharacteristic
52C2×C4×C61C22⋊C411yescharacteristic
53C2×C4×C61C22×C411yescharacteristic
54C2×C4×C61C2×D411yescharacteristic
55C2×C4×C61C2×D411yescharacteristic
56C2×Dic61—22no—
57C2×Dic61—42no—
58D244—42no—
59D244—42no—
60Dic122—42no—
61Dic122—42no—
62C8×C61—42no—
63#92418—24no—
64C22×C61—21no—
65C22×C61—21no—
66C22×C61#10412yes—
67C22×C61C2×C22⋊C411yescharacteristic
68C2×D61—42no—
69C2×D61—42no—
70C2×D61—42no—
71C2×D61—84no—
72C4×C61—21no—
73C4×C61—21no—
74C4×C61—21no—
75C4×C61—21no—
76C4×C61—21no—
77C4×C61#10012yes—
78Dic61—42no—
79#1527—611nomaximal, Sylow
80C2×C61—22no—
81C2×C61C2×#10011yescharacteristic
82C2×C61C2×#10411yescharacteristic
83C2×C61#42111yescharacteristic
84D61—82no—
85C2×#124—611no—
86#432D6111yescharacteristic, complemented
87C4×M16—611no—
88#329—614no—
89C61#152711yescharacteristic, complemented, Sylow
90C22×Q8—611no—
91C22×D4—611no—
92C2×M16—1221no—
93#124—612no—
94#124—612no—
95#124—1221no—
96#124—1221no—
97C2×C22⋊C4—1221no—
98C2×C22⋊C4—1221no—
99C2×C42C2×D6111yescharacteristic
100C4⋊C8—21no—
101C22⋊C8—21no—
102#97—612no—
103#97C2×D6112yescomplemented
104C4×C8—1221no—
105C24—1221no—
106C2×Q8—612no—
107C2×Q8—1221no—
108C2×Q8—2442no—
109C2×D4—612no—
110C2×D4—1221no—
111C2×D4—2442no—
112C22×C4—1221no—
113C22×C4C4×D6111yescharacteristic
114C22×C4D24411yescharacteristic
115C22×C4C22⋊D6111yescharacteristic
116M16—1224no—
117C2×C8—22no—
118C2×C8—1222no—
119C22⋊C4—1222no—
120C22⋊C4—1222no—
121C22⋊C4—1222no—
122C22⋊C4—1222no—
123C42C4×D6111yescharacteristic
124C42D24411yescharacteristic
125C42C22⋊D6111yescharacteristic
126C42C22×D6111yescharacteristic
127C23—1222no—
128C23—2442no—
129C23—2442no—
130C23—2442no—
131C23#1175819811yescharacteristic
132Q8—2442no—
133Q8—2442no—
134D4—2442no—
135D4—2442no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—41no—
139C2×C4—1222no—
140C2×C4—2442no—
141C2×C4#1175819811yescharacteristic
142C2×C4#1175819811yescharacteristic
143C2×C4#1175819811yescharacteristic
144C2×C4C2×C4×D6111yescharacteristic
145C2×C4C2×D24411yescharacteristic
146C2×C4C2×C22⋊D6111yescharacteristic
147C8—42no—
148C8—1224no—
149C22—21no—
150C22—21no—
151C22—4884no—
152C22—2442no—
153C22—2442no—
154C22—2442no—
155C22#1451970312yes—
156C22C2×#1175819811yescharacteristic
157C4—21no—
158C4—21no—
159C4—21no—
160C4—21no—
161C4—21no—
162C4—2442no—
163C4#1451969312yes—
164C2—22no—
165C2—4882no—
166C2C2×#1451969311yescharacteristic
167C2C2×#1451970311yescharacteristic
168C2#1683978011yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#432C2
socleC22×C61C2×C22⋊C4
hypercenter#432D61
hypocenterC61#1527
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C4×#11758194C2semidirect
3. #16839501C2semidirect
4. C61×#432C2semidirect
14. #14519688C22semidirect
19. #97×C61C22semidirect
86. #432D61semidirect
89. C61#1527semidirect
103. #97C2×D61semidirect