Finite Group Databasebeta

← #21460920

Subgroups — #21460920

Order 7808.

162 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 40 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#16840748C211yesmaximal, characteristic
2#16840741C211yesmaximal, characteristic
3#16839730C211yesmaximal, characteristic
4D61⋊M16—21no—
5#14519856—21no—
6#14519838C412yescomplemented
7#14519837—21no—
8#14519836C412yes—
9#14519835—21no—
10C2×#11758222C2211yescharacteristic
11C22×#92418C411yescharacteristic, complemented
12#14519689—21no—
13#14519689—21no—
14C2×M16×C61C411yescharacteristic, complemented
15C22×C4×C61C2×C411yescharacteristic
16C2×C22⋊D61D411yescharacteristic
17C2×C22⋊D61Q811yescharacteristic
18#11758222—41no—
19#11758222—41no—
20C2×D244C2×C411yescharacteristic
21C2×C4×D61D411yescharacteristic
22C2×C4×D61D411yescharacteristic
23C2×Dic122C2×C411yescharacteristic
24C22⋊#6923—22no—
25#11758217—22no—
26C4⋊#6923—41no—
27C4×#6923—41no—
28#11758213—41no—
29D61⋊C8—41no—
30M16×C61—41no—
31C2×C8×C61—21no—
32C2×#92418—21no—
33C2×#92418—41no—
34C23×C61C4⋊C411yescharacteristic
35C22×D61C22⋊C411yescharacteristic
36C22×D61C4⋊C411yescharacteristic
37C2×#6923—42no—
38C2×C4×C61—21no—
39C2×C4×C61—21no—
40C2×C4×C61C4211yescharacteristic
41C2×C4×C61C22⋊C411yescharacteristic
42C22⋊D61—41no—
43C22⋊D61—41no—
44C2×Dic61C22⋊C411yescharacteristic
45C2×Dic61C4⋊C411yescharacteristic
46D244—41no—
47C4×D61—21no—
48C4×D61—21no—
49C4×D61—21no—
50C4×D61—21no—
51Dic122—41no—
52#92420—42no—
53C8×C61—41no—
54#92418—41no—
55C22×C61—21no—
56C22×C61—41no—
57C22×C61#9511yescharacteristic
58C2×D61—21no—
59C2×D61—21no—
60C2×D61—41no—
61C2×D61—41no—
62#6923—82no—
63C4×C61—21no—
64C4×C61#9911yescharacteristic
65C4×C61#9911yescharacteristic
66Dic61—21no—
67Dic61—21no—
68#1395—611nomaximal, Sylow
69C2×C61—21no—
70C2×C61—41no—
71C2×C61#34211yescharacteristic
72D61—41no—
73D61—41no—
74#413—611no—
75#410—611no—
76#408—611no—
77C61#139511yescharacteristic, complemented, Sylow
78C2×#41—611no—
79C2×M16—1221no—
80C2×M16#692311yescharacteristic, complemented
81C22×C8—611no—
82#117—1221no—
83#101—612no—
84#100—1221no—
85#99—612no—
86#99—1221no—
87C22⋊C8—1221no—
88C22⋊C8—1221no—
89#41—2441no—
90#41—2441no—
91C2×Q8—611no—
92C2×D4—611no—
93C2×D4—611no—
94C2×D4—611no—
95C22×C4—611no—
96C22×C4—611no—
97C22×C4C2×#692311yescharacteristic
98M16—41no—
99M16—1222no—
100M16—2441no—
101C2×C8—21no—
102C2×C8—1221no—
103C2×C8—2441no—
104C2×C8—2441no—
105C4⋊C4—2441no—
106C22⋊C4—1222no—
107C42—2441no—
108C23—611no—
109C23—611no—
110C23C4⋊#692311yescharacteristic
111Q8—2441no—
112D4—2441no—
113D4—2441no—
114D4—2441no—
115C2×C4—21no—
116C2×C4—21no—
117C2×C4—611no—
118C2×C4—611no—
119C2×C4—1221no—
120C2×C4—1221no—
121C2×C4—1221no—
122C2×C4—1221no—
123C2×C4—2442no—
124C2×C4C4×#692311yescharacteristic
125C2×C4C22⋊#692311yescharacteristic
126C8—41no—
127C8—2442no—
128C8—2441no—
129C22—21no—
130C22—41no—
131C22—1221no—
132C22—1221no—
133C22—2441no—
134C22—2441no—
135C22(C2×#6923)⋊C411yescharacteristic
136C4—21no—
137C4—1221no—
138C4—1221no—
139C4—4882no—
140C4#1451983511yescharacteristic
141C4#1451983611yescharacteristic
142C2—21no—
143C2—41no—
144C2—2441no—
145C2—2441no—
146C2#1684064011yescharacteristic
subgroupG/H
centerC4#14519835
commutatorC2×C4×C61C42
FrattiniC22×C4C2×#6923
FittingC2×M16×C61C4
socleC2×C61#342
hypercenterC2×M16#6923
hypocenterC61#1395
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
6. #14519838C4semidirect
11. C22×#92418C4semidirect
14. C2×M16×C61C4semidirect
77. C61#1395semidirect
80. C2×M16#6923semidirect