Finite Group Databasebeta

← #21444317

Subgroups — #21444317

Order 7808.

240 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 89 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#16840319C211yesmaximal, characteristic
2#16839815C211yesmaximal, characteristic
3#16839498C214yesmaximal
4C4×C4⋊C4×C61C211yesmaximal, characteristic
5#14519777C411yescharacteristic, complemented
6#14519777C411yescharacteristic, complemented
7#14519769—21no—
8#14519756—21no—
9#14519756C2212yes—
10C4×Dic122—21no—
11C4×Dic122C412yescomplemented
12#14519736—21no—
13C4⋊#92418—21no—
14C22⋊#92418C2212yes—
15C4×#92418—21no—
16C2×C4⋊C4×C61—21no—
17C2×C42×C61—21no—
18C2×C42×C61C2211yescharacteristic
19#95×C61C2212yes—
20C22×C4×C61—22no—
21C22×C4×C61D411yescharacteristic
22C22×C4×C61D411yescharacteristic
23C22×C4×C61C2311yescharacteristic
24C2×Dic122—21no—
25C2×Dic122C2×C412yes—
26C4⋊C4×C61—24no—
27C42×C61—42no—
28C42×C61C2×C411yescharacteristic
29C42×C61C2×C411yescharacteristic
30C42×C61D411yescharacteristic
31C42×C61D411yescharacteristic
32C22⋊Dic61—22no—
33C4⋊Dic61—21no—
34C4⋊Dic61—21no—
35C4⋊Dic61—21no—
36C4⋊Dic61C2×C412yes—
37#11758196—22no—
38#11758196—22no—
39C4×Dic61—22no—
40C2×#92418—22no—
41C23×C61C2×D411yescharacteristic
42C2×C4×C61—22no—
43C2×C4×C61—24no—
44C2×C4×C61—41no—
45C2×C4×C61—42no—
46C2×C4×C61—42no—
47C2×C4×C61C22⋊C411yescharacteristic
48C2×C4×C61C22⋊C411yescharacteristic
49C2×C4×C61C22⋊C411yescharacteristic
50C2×C4×C61C22⋊C411yescharacteristic
51C2×C4×C61SD1612yes—
52C2×C4×C61Q1612yes—
53C2×C4×C61C22×C411yescharacteristic
54C2×C4×C61C2×D411yescharacteristic
55C2×Dic61—22no—
56C2×Dic61—22no—
57Dic122—42no—
58Dic122—42no—
59#92418—42no—
60C22×C61—21no—
61C22×C61—21no—
62C22×C61C2×C22⋊C411yescharacteristic
63C22×C61C2×SD1611yescharacteristic
64C22×C61C2×Q1611yescharacteristic
65C4×C61—21no—
66C4×C61—21no—
67C4×C61—21no—
68C4×C61—44no—
69C4×C61#10312yes—
70C4×C61#10312yes—
71C4×C61#10412yes—
72Dic61—42no—
73Dic61—42no—
74#1503—611nomaximal, Sylow
75C2×C61—21no—
76C2×C61—21no—
77C2×C61#41011yescharacteristic
78C2×C61C2×#10311yescharacteristic
79C2×C61C2×#10411yescharacteristic
80#533—611no—
81#431—611no—
82C4×C4⋊C4D6111yescharacteristic
83#328—614no—
84C61#150311yescharacteristic, complemented, Sylow
85C4⋊Q8—611no—
86C4⋊Q8—611no—
87#125—1221no—
88C22⋊Q8—612no—
89C22⋊Q8—1221no—
90C4×Q8—612no—
91C4×Q8—1221no—
92#117—1221no—
93C2×C4⋊C4—21no—
94C2×C42—21no—
95C2×C42C2×D6111yescharacteristic
96C4⋊C8—1221no—
97C22⋊C8—612no—
98C4×C8—1221no—
99#95C2×D6112yes—
100C2×Q8—612no—
101C2×Q8—1221no—
102C22×C4—22no—
103C22×C4C22⋊D6111yescharacteristic
104C22×C4C22⋊D6111yescharacteristic
105C22×C4C22×D6111yescharacteristic
106C2×C8—1222no—
107C4⋊C4—24no—
108C4⋊C4—612no—
109C4⋊C4—1222no—
110C4⋊C4—1221no—
111C4⋊C4—1221no—
112C4⋊C4—1221no—
113C4⋊C4—1222no—
114C22⋊C4—1222no—
115C42—42no—
116C42—1222no—
117C42C4×D6111yescharacteristic
118C42C4×D6111yescharacteristic
119C42D24411yescharacteristic
120C42D24411yescharacteristic
121C23C2×C22⋊D6111yescharacteristic
122Q8—2442no—
123Q8—2442no—
124C2×C4—22no—
125C2×C4—24no—
126C2×C4—41no—
127C2×C4—42no—
128C2×C4—42no—
129C2×C4—1222no—
130C2×C4—1222no—
131C2×C4#1175819811yescharacteristic
132C2×C4#1175819811yescharacteristic
133C2×C4#1175819811yescharacteristic
134C2×C4#1175819811yescharacteristic
135C2×C4#1175820012yes—
136C2×C4#1175820212yes—
137C2×C4C2×C4×D6111yescharacteristic
138C2×C4C2×D24411yescharacteristic
139C8—2442no—
140C22—21no—
141C22—21no—
142C22C2×#1175819811yescharacteristic
143C22C2×#1175820011yescharacteristic
144C22C2×#1175820211yescharacteristic
145C4—21no—
146C4—21no—
147C4—21no—
148C4—44no—
149C4—2442no—
150C4—2442no—
151C4#1451970012yes—
152C4#1451970012yes—
153C4#1451970512yes—
154C2—21no—
155C2—21no—
156C2#1683973511yescharacteristic
157C2C2×#1451970011yescharacteristic
158C2C2×#1451970511yescharacteristic
subgroupG/H
centerC2×C4#11758198
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC4×C4⋊C4×C61C2
socleC22×C61C2×C22⋊C4
hypercenterC4×C4⋊C4D61
hypocenterC61#1503
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
5. #14519777C4semidirect
6. #14519777C4semidirect
11. C4×Dic122C4semidirect
84. C61#1503semidirect