Finite Group Databasebeta

← #21444267

Subgroups — #21444267

Order 7808.

252 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 81 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×C4×Dic122C211yesmaximal, characteristic
2#16839819C211yesmaximal, characteristic
3#16839494C214yesmaximal, complemented
4C4×M16×C61C211yesmaximal, characteristic
5C22×Dic122C411yescharacteristic
6C4×Dic122—21no—
7C4×Dic122—21no—
8C4×Dic122C412yes—
9C4×Dic122C2212yes—
10C2×C4⋊Dic61C411yescharacteristic
11C2×#11758196—21no—
12C2×C4×Dic61—21no—
13C4⋊#92418C2212yes—
14C22⋊#92418—21no—
15#14519688—21no—
16C2×M16×C61—21no—
17C2×C42×C61C2211yescharacteristic
18#97×C61—21no—
19C4×C8×C61C2212yes—
20C22×C4×C61C2×C411yescharacteristic
21C22×C4×C61D411yescharacteristic
22C22×C4×C61D411yescharacteristic
23C22×Dic61—21no—
24C22×Dic61—21no—
25C2×Dic122—21no—
26C2×Dic122—24no—
27C2×Dic122C2×C412yes—
28M16×C61—24no—
29C2×C8×C61—22no—
30C42×C61C2×C411yescharacteristic
31C42×C61D411yescharacteristic
32C42×C61D411yescharacteristic
33C42×C61C2311yescharacteristic
34C4⋊Dic61—21no—
35C4⋊Dic61C2×C412yes—
36#11758196—22no—
37#11758196—22no—
38C4×Dic61—22no—
39C4×Dic61—22no—
40C2×#92418—22no—
41C23×C61C22⋊C411yescharacteristic
42C2×C4×C61—22no—
43C2×C4×C61—22no—
44C2×C4×C61—22no—
45C2×C4×C61C22⋊C411yescharacteristic
46C2×C4×C61C22⋊C411yescharacteristic
47C2×C4×C61C22⋊C411yescharacteristic
48C2×C4×C61C22×C411yescharacteristic
49C2×C4×C61C2×D411yescharacteristic
50C2×C4×C61C2×D411yescharacteristic
51C2×Dic61—24no—
52C2×Dic61—22no—
53C2×Dic61—22no—
54C2×Dic61—42no—
55Dic122—24no—
56Dic122—22no—
57Dic122M1614yescomplemented
58C8×C61—24no—
59#92418—42no—
60C22×C61—21no—
61C22×C61—21no—
62C22×C61#10412yes—
63C22×C61C2×C22⋊C411yescharacteristic
64C4×C61—21no—
65C4×C61—21no—
66C4×C61—21no—
67C4×C61—21no—
68C4×C61C2×M1612yes—
69C4×C61#13712yes—
70Dic61—24no—
71Dic61—42no—
72#1491—611nomaximal, Sylow
73C2×C61—22no—
74C2×C61#40711yescharacteristic
75C2×C61#41911yescharacteristic
76C2×C61C2×#10411yescharacteristic
77C2×C4×Q8—611no—
78#432—611no—
79C4×M16D6111yescharacteristic
80Q8⋊C8—614no—
81C61#149111yescharacteristic, complemented, Sylow
82C22×Q8—611no—
83C2×M16—21no—
84C4×Q8—612no—
85C4×Q8—612no—
86C4×Q8—1221no—
87C4×Q8—1221no—
88C2×C4⋊C4—611no—
89C2×C4⋊C4—1221no—
90C2×C42—1221no—
91C2×C42C2×D6111yescharacteristic
92C4⋊C8—612no—
93C22⋊C8—1221no—
94#97—21no—
95#97—1221no—
96C4×C8C2×D6112yes—
97C2×Q8—612no—
98C2×Q8—1224no—
99C2×Q8—1221no—
100C22×C4—1221no—
101C22×C4—1221no—
102C22×C4C4×D6111yescharacteristic
103C22×C4D24411yescharacteristic
104C22×C4C22⋊D6111yescharacteristic
105M16—24no—
106C2×C8—22no—
107C2×C8—1222no—
108C4⋊C4—612no—
109C4⋊C4—1221no—
110C4⋊C4—1222no—
111C4⋊C4—1222no—
112C42—1222no—
113C42—1222no—
114C42C4×D6111yescharacteristic
115C42D24411yescharacteristic
116C42C22⋊D6111yescharacteristic
117C42C22×D6111yescharacteristic
118C23#1175819811yescharacteristic
119Q8—614no—
120Q8—1224no—
121Q8—1222no—
122C2×C4—22no—
123C2×C4—22no—
124C2×C4—22no—
125C2×C4—1224no—
126C2×C4—1222no—
127C2×C4—1222no—
128C2×C4—2442no—
129C2×C4#1175819811yescharacteristic
130C2×C4#1175819811yescharacteristic
131C2×C4#1175819811yescharacteristic
132C2×C4C2×C4×D6111yescharacteristic
133C2×C4C2×D24411yescharacteristic
134C2×C4C2×C22⋊D6111yescharacteristic
135C8—24no—
136C8—2442no—
137C22—21no—
138C22—21no—
139C22#1451970512yes—
140C22C2×#1175819811yescharacteristic
141C4—21no—
142C4—21no—
143C4—21no—
144C4—21no—
145C4—1224no—
146C4—2442no—
147C4M16×D6112yes—
148C4#1451981012yes—
149C2—22no—
150C2#1683972511yescharacteristic
151C2#1683977211yescharacteristic
152C2C2×#1451970511yescharacteristic
subgroupG/H
centerC2×C4C2×D244
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC4×M16×C61C2
socleC22×C61C2×C22⋊C4
hypercenterC4×M16D61
hypocenterC61#1491
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
3. #16839494C2semidirect
57. Dic122M16semidirect
81. C61#1491semidirect