Finite Group Databasebeta

← #21446808

Subgroups — #21446808

Order 7808.

260 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 101 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×#14519777C211yesmaximal, characteristic
2#16839786C211yesmaximal, characteristic
3#16839530C214yesmaximal
4C4×M16×C61C211yesmaximal, characteristic
5C22×Dic122C412yes—
6C2×#11758194C2212yes—
7#14519777—21no—
8#14519777—21no—
9#14519777—21no—
10#14519777—21no—
11C2×C4⋊Dic61C412yes—
12C2×C4⋊Dic61C2212yes—
13C4⋊#92418—21no—
14C4⋊#92418—21no—
15C2×M16×C61C2212yes—
16C2×C42×C61C2211yescharacteristic
17#97×C61—21no—
18C4×C8×C61—21no—
19C22×C4×C61C2×C411yescharacteristic
20C22×C4×C61C2×C411yescharacteristic
21C22×C4×C61C2311yescharacteristic
22C22×Dic61C2×C414yes—
23C2×Dic122—22no—
24C2×Dic122—22no—
25C2×Dic122—44no—
26M16×C61—22no—
27M16×C61Q814yescomplemented
28C2×C8×C61—22no—
29C42×C61D411yescharacteristic
30C42×C61D411yescharacteristic
31C42×C61D411yescharacteristic
32C42×C61D411yescharacteristic
33C4⋊Dic61—22no—
34C4⋊Dic61—22no—
35C4⋊Dic61—22no—
36C4⋊Dic61—22no—
37#11758194—24no—
38C2×#92418—22no—
39C23×C61C22×C411yescharacteristic
40C2×C4×C61—22no—
41C2×C4×C61—22no—
42C2×C4×C61C22⋊C411yescharacteristic
43C2×C4×C61C22⋊C411yescharacteristic
44C2×C4×C61C22⋊C411yescharacteristic
45C2×C4×C61C22⋊C411yescharacteristic
46C2×C4×C61C2×D411yescharacteristic
47C2×C4×C61C2×D411yescharacteristic
48C2×C4×C61C2×Q812yes—
49C2×C4×C61#4112yes—
50C2×Dic61—24no—
51C2×Dic61—44no—
52Dic122—44no—
53Dic122—44no—
54C8×C61—24no—
55#92418—42no—
56C22×C61—21no—
57C22×C61—21no—
58C22×C61C2×C22⋊C411yescharacteristic
59C22×C61C4×Q812yes—
60C4×C61—21no—
61C4×C61—21no—
62C4×C61#10012yes—
63C4×C61#10112yes—
64C4×C61C22⋊Q812yes—
65C4×C61#12411yescharacteristic
66C4×C61C4⋊Q811yescharacteristic
67Dic61—44no—
68#1997—611nomaximal, Sylow
69C2×C61—22no—
70C2×C61#39111yescharacteristic
71C2×C61C2×#10011yescharacteristic
72C2×C61C2×#10111yescharacteristic
73C2×C4⋊Q8—611no—
74#423—611no—
75C4×M16D6111yescharacteristic
76#343—614no—
77C61#199711yescharacteristic, complemented, Sylow
78C22×Q8—612no—
79C2×M16—612no—
80C2×M16C2×D6112yes—
81C4⋊Q8—1221no—
82C4⋊Q8—1221no—
83C4⋊Q8—1221no—
84C4⋊Q8—1221no—
85C2×C4⋊C4—612no—
86C2×C4⋊C4—612no—
87C2×C42C2×D6111yescharacteristic
88C4⋊C8—1221no—
89C4⋊C8—1221no—
90#97—21no—
91C4×C8—21no—
92C2×Q8—1222no—
93C2×Q8—1222no—
94C2×Q8—2444no—
95C22×C4—614no—
96C22×C4C4×D6111yescharacteristic
97C22×C4C4×D6111yescharacteristic
98C22×C4C22×D6111yescharacteristic
99M16—22no—
100M16—1224no—
101M16Dic12214yescomplemented
102C2×C8—22no—
103C2×C8—1222no—
104C4⋊C4—1222no—
105C4⋊C4—1222no—
106C4⋊C4—1222no—
107C4⋊C4—1222no—
108C42D24411yescharacteristic
109C42D24411yescharacteristic
110C42C22⋊D6111yescharacteristic
111C42C22⋊D6111yescharacteristic
112C23C2×C4×D6111yescharacteristic
113Q8—2444no—
114Q8—2444no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—1224no—
118C2×C4—2444no—
119C2×C4#1175819811yescharacteristic
120C2×C4#1175819811yescharacteristic
121C2×C4#1175819811yescharacteristic
122C2×C4#1175819811yescharacteristic
123C2×C4C2×Dic12212yes—
124C2×C4C2×D24411yescharacteristic
125C2×C4#1175822212yes—
126C2×C4C2×C22⋊D6111yescharacteristic
127C8—24no—
128C8—2442no—
129C22—21no—
130C22—21no—
131C22C2×#1175819811yescharacteristic
132C22C4×Dic12212yes—
133C4—21no—
134C4—21no—
135C4—2444no—
136C4#1451969312yes—
137C4#1451969512yes—
138C4#1451975612yes—
139C4#1451976511yescharacteristic
140C4#1451977711yescharacteristic
141C2—22no—
142C2#1683966811yescharacteristic
143C2C2×#1451969311yescharacteristic
144C2C2×#1451969511yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC23×C61C22×C4
FrattiniC22×C4C22×D61
FittingC4×M16×C61C2
socleC22×C61C2×C22⋊C4
hypercenterC4×M16D61
hypocenterC61#1997
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
27. M16×C61Q8semidirect
77. C61#1997semidirect
101. M16Dic122semidirect