Finite Group Databasebeta

← #21443939

Subgroups — #21443939

Order 7808.

166 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 53 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#16839736C211yesmaximal, characteristic
2#16839729C211yesmaximal, characteristic
3C61×#410C211yesmaximal, characteristic
4C2×#11758194C411yescharacteristic, complemented
5C22×#92418C411yescharacteristic, complemented
6#14519736—21no—
7#14519692—21no—
8#14519692C412yescomplemented
9C22⋊#92418—21no—
10C22⋊#92418—21no—
11C2×#41×C61C2211yescharacteristic
12#117×C61—21no—
13#99×C61—21no—
14#99×C61C412yescomplemented
15#41×C61—41no—
16#41×C61—41no—
17C2×Q8×C61Q811yescharacteristic
18C2×D4×C61C2×C411yescharacteristic
19C2×D4×C61C2×C411yescharacteristic
20C2×D4×C61D411yescharacteristic
21C22×C4×C61C2×C411yescharacteristic
22C22×C4×C61D411yescharacteristic
23C22×C4×C61D411yescharacteristic
24C4⋊C4×C61—41no—
25C22⋊C4×C61—22no—
26C42×C61—41no—
27C22⋊Dic61—22no—
28C4⋊Dic61—41no—
29C4×Dic61—41no—
30#11758194—41no—
31C2×#92418—21no—
32C2×#92418—21no—
33C2×#92418—41no—
34C23×C61C4211yescharacteristic
35C23×C61C22⋊C411yescharacteristic
36C23×C61C22⋊C411yescharacteristic
37Q8×C61—41no—
38D4×C61—41no—
39D4×C61—41no—
40D4×C61—41no—
41C2×C4×C61—21no—
42C2×C4×C61—21no—
43C2×C4×C61—21no—
44C2×C4×C61—21no—
45C2×C4×C61—21no—
46C2×C4×C61—21no—
47C2×C4×C61—42no—
48C2×C4×C61C22⋊C411yescharacteristic
49C2×C4×C61C4⋊C411yescharacteristic
50C2×C4×C61C4⋊C411yescharacteristic
51C2×C4×C61C4⋊C411yescharacteristic
52C2×Dic61—42no—
53#92418—41no—
54#92418—41no—
55C22×C61—21no—
56C22×C61—21no—
57C22×C61—21no—
58C22×C61—41no—
59C22×C61—41no—
60C22×C61—41no—
61C22×C61#9511yescharacteristic
62C4×C61—21no—
63C4×C61—21no—
64C4×C61—21no—
65C4×C61—82no—
66C4×C61#9911yescharacteristic
67C4×C61#9911yescharacteristic
68Dic61—82no—
69#1391—611nomaximal, Sylow
70C2×C61—21no—
71C2×C61—41no—
72C2×C61—41no—
73C2×C61—41no—
74C2×C61#34211yescharacteristic
75#410—611no—
76#410D6111yescharacteristic
77#408—611no—
78C61#139111yescharacteristic, complemented, Sylow
79C2×#41C2×D6111yescharacteristic
80C2×M16—611no—
81C22×C8—611no—
82#117—21no—
83#117—1221no—
84#99—21no—
85#99—612no—
86#99—1221no—
87#99Dic6112yescomplemented
88C22⋊C8—1221no—
89C22⋊C8—1221no—
90#41—41no—
91#41—41no—
92C2×Q8Dic12211yescharacteristic
93C2×D4C4×D6111yescharacteristic
94C2×D4C2×Dic6111yescharacteristic
95C2×D4C22⋊D6111yescharacteristic
96C22×C4C4×D6111yescharacteristic
97C22×C4D24411yescharacteristic
98C22×C4C22⋊D6111yescharacteristic
99M16—2441no—
100C2×C8—1221no—
101C2×C8—1221no—
102C2×C8—2441no—
103C4⋊C4—41no—
104C4⋊C4—2441no—
105C22⋊C4—22no—
106C22⋊C4—1222no—
107C42—41no—
108C42—2441no—
109C23C4×Dic6111yescharacteristic
110C23#1175819811yescharacteristic
111C23C22⋊Dic6111yescharacteristic
112Q8—41no—
113D4—41no—
114D4—41no—
115D4—41no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—21no—
119C2×C4—21no—
120C2×C4—21no—
121C2×C4—21no—
122C2×C4—42no—
123C2×C4—2442no—
124C2×C4#1175819611yescharacteristic
125C2×C4#1175819611yescharacteristic
126C2×C4C4⋊Dic6111yescharacteristic
127C2×C4#1175819811yescharacteristic
128C8—2441no—
129C8—2441no—
130C22—21no—
131C22—21no—
132C22—21no—
133C22—41no—
134C22—41no—
135C22—41no—
136C22#1451968411yescharacteristic
137C4—21no—
138C4—21no—
139C4—21no—
140C4—82no—
141C4—4882no—
142C4#1451969111yescharacteristic
143C4#1451969111yescharacteristic
144C2—21no—
145C2—41no—
146C2—41no—
147C2—41no—
148C2#1683952811yescharacteristic
subgroupG/H
centerC4#14519691
commutatorC23×C61C42
FrattiniC2×#41C2×D61
FittingC61×#410C2
socleC2×C61#342
hypercenter#410D61
hypocenterC61#1391
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
4. C2×#11758194C4semidirect
5. C22×#92418C4semidirect
8. #14519692C4semidirect
14. #99×C61C4semidirect
78. C61#1391semidirect
87. #99Dic61semidirect