Finite Group Databasebeta

← #21460719

Subgroups — #21460719

Order 7808.

200 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 46 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#16840733C211yesmaximal, characteristic
2#16840704C211yesmaximal, characteristic
3#16839725C211yesmaximal, characteristic
4C2×#11758213—21no—
5C2×C4⋊#6923—21no—
6C2×C22⋊#6923C412yes—
7#14519834—21no—
8C22⋊#92420C412yescomplemented
9(C2×#6923)⋊C4—21no—
10C22×C4×D61C2211yescharacteristic
11C2×#11758194C411yescharacteristic, complemented
12#14519689—21no—
13#14519689—21no—
14C2×M16×C61C411yescharacteristic, complemented
15C23×D61C2×C411yescharacteristic
16C22×#6923—22no—
17C22×C4×C61C2×C411yescharacteristic
18C22×Dic61C2×C411yescharacteristic
19C2×C4×D61—41no—
20C2×C4×D61—41no—
21C2×C4×D61D411yescharacteristic
22C2×C4×D61D411yescharacteristic
23C2×C4×D61D411yescharacteristic
24C2×C4×D61Q811yescharacteristic
25C22⋊#6923—42no—
26C2×#92420—22no—
27C4⋊#6923—41no—
28C4⋊#6923—41no—
29#11758213—41no—
30#11758213—41no—
31M16×C61—41no—
32C2×C8×C61—21no—
33#11758194—41no—
34C2×#92418—21no—
35C23×C61C4211yescharacteristic
36C22×D61—21no—
37C22×D61—21no—
38C22×D61—41no—
39C22×D61—41no—
40C22×D61C22⋊C411yescharacteristic
41C22×D61C4⋊C411yescharacteristic
42C2×#6923—42no—
43C2×#6923—42no—
44C2×#6923—42no—
45C2×C4×C61—21no—
46C2×C4×C61—21no—
47C2×C4×C61C22⋊C411yescharacteristic
48C2×C4×C61C4⋊C411yescharacteristic
49C2×Dic61—41no—
50C2×Dic61C22⋊C411yescharacteristic
51C2×Dic61C4⋊C411yescharacteristic
52C4×D61—21no—
53C4×D61—21no—
54C4×D61—21no—
55C4×D61—21no—
56C4×D61—41no—
57C4×D61—41no—
58#92420—42no—
59C8×C61—41no—
60#92418—41no—
61C22×C61—21no—
62C22×C61—21no—
63C22×C61—21no—
64C22×C61#9511yescharacteristic
65C2×D61—21no—
66C2×D61—21no—
67C2×D61—21no—
68C2×D61—21no—
69C2×D61—21no—
70C2×D61—42no—
71C2×D61—42no—
72C2×D61#10011yescharacteristic
73C2×D61#10111yescharacteristic
74#6923—82no—
75C4×C61—21no—
76C4×C61#9911yescharacteristic
77C4×C61#9911yescharacteristic
78Dic61—21no—
79Dic61—21no—
80#1305—611nomaximal, Sylow
81C2×C61—41no—
82C2×C61#34211yescharacteristic
83C2×C61#34311yescharacteristic
84C2×C61#34411yescharacteristic
85D61—21no—
86D61—21no—
87D61—41no—
88#407—611no—
89#407—611no—
90#380—611no—
91C61#130511yescharacteristic, complemented, Sylow
92C23×C4—611no—
93C2×M16—611no—
94C2×M16—1221no—
95C2×M16#692311yescharacteristic, complemented
96C2×C4⋊C4—1221no—
97C2×C22⋊C4—612no—
98C22⋊C8—612no—
99C22⋊C8—1221no—
100C22⋊C8—1221no—
101C22⋊C8—1221no—
102#95—1221no—
103C24—611no—
104C22×C4—611no—
105C22×C4—611no—
106C22×C4—611no—
107C22×C4—611no—
108C22×C4—611no—
109C22×C4—1222no—
110C22×C4—2441no—
111C22×C4—2441no—
112C22×C4C2×#692311yescharacteristic
113M16—41no—
114M16—2441no—
115M16—2441no—
116M16—2441no—
117C2×C8—21no—
118C2×C8—1222no—
119C2×C8—1221no—
120C4⋊C4—2441no—
121C4⋊C4—2441no—
122C22⋊C4—2442no—
123C23—611no—
124C23—611no—
125C23—1221no—
126C23—1221no—
127C23—2441no—
128C23—2441no—
129C23C4×#692311yescharacteristic
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—611no—
133C2×C4—611no—
134C2×C4—1221no—
135C2×C4—1221no—
136C2×C4—1221no—
137C2×C4—1221no—
138C2×C4—2441no—
139C2×C4—2441no—
140C2×C4—2441no—
141C2×C4—2442no—
142C2×C4—2442no—
143C2×C4—2442no—
144C2×C4C4⋊#692311yescharacteristic
145C2×C4C22⋊#692311yescharacteristic
146C8—41no—
147C8—2442no—
148C8—2441no—
149C22—21no—
150C22—21no—
151C22—21no—
152C22—611no—
153C22—611no—
154C22—1221no—
155C22—1221no—
156C22—1221no—
157C22—1221no—
158C22—1221no—
159C22—2442no—
160C22—2442no—
161C22(C2×#6923)⋊C411yescharacteristic
162C4—21no—
163C4—1221no—
164C4—1221no—
165C4—4882no—
166C4#1451983511yescharacteristic
167C4#1451983611yescharacteristic
168C2—41no—
169C2—1221no—
170C2—1221no—
171C2—2441no—
172C2#1684064011yescharacteristic
173C2#1684064111yescharacteristic
174C2#1684064511yescharacteristic
subgroupG/H
centerC22(C2×#6923)⋊C4
commutatorC23×C61C42
FrattiniC22×C4C2×#6923
FittingC2×M16×C61C4
socleC22×C61#95
hypercenterC2×M16#6923
hypocenterC61#1305
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
8. C22⋊#92420C4semidirect
11. C2×#11758194C4semidirect
14. C2×M16×C61C4semidirect
91. C61#1305semidirect
95. C2×M16#6923semidirect