Finite Group Databasebeta

← #21444417

Subgroups — #21444417

Order 7808.

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

normal subgroups only

This group has 264 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
1#16839819C211yesmaximal, characteristic, complemented
2C4×#11758194C211yesmaximal, characteristic, complemented
3#16839502C214yesmaximal, complemented
4C2×#124×C61C211yesmaximal, characteristic
5C2×#11758194—21no—
6C4⋊#92418—21no—
7C22⋊#92418—21no—
8#14519688C2212yescomplemented
9#14519688C2212yescomplemented
10C4×#92418—21no—
11C22×Q8×C61C411yescharacteristic
12C22×D4×C61C411yescharacteristic
13#124×C61—21no—
14#124×C61—21no—
15#124×C61C412yes—
16#124×C61C2212yes—
17C2×C22⋊C4×C61—21no—
18C2×C22⋊C4×C61—21no—
19C2×C42×C61C2211yescharacteristic
20C24×C61—21no—
21C2×Q8×C61—21no—
22C2×Q8×C61—42no—
23C2×Q8×C61C2×C412yes—
24C2×D4×C61—21no—
25C2×D4×C61—42no—
26C2×D4×C61C2×C412yes—
27C22×C4×C61—21no—
28C22×C4×C61C2×C411yescharacteristic
29C22×C4×C61D411yescharacteristic
30C22×C4×C61D411yescharacteristic
31C22⋊C4×C61—22no—
32C22⋊C4×C61—22no—
33C22⋊C4×C61—22no—
34C22⋊C4×C61—22no—
35C42×C61C2×C411yescharacteristic
36C42×C61D411yescharacteristic
37C42×C61D411yescharacteristic
38C42×C61C2311yescharacteristic
39#11758194—24no—
40C2×#92418—22no—
41C2×#92418—22no—
42C23×C61—22no—
43C23×C61—42no—
44C23×C61—42no—
45C23×C61—42no—
46C23×C61C22⋊C411yescharacteristic
47Q8×C61—42no—
48Q8×C61—42no—
49D4×C61—42no—
50D4×C61—42no—
51C2×C4×C61—22no—
52C2×C4×C61—22no—
53C2×C4×C61—22no—
54C2×C4×C61—41no—
55C2×C4×C61—42no—
56C2×C4×C61C22⋊C411yescharacteristic
57C2×C4×C61C22⋊C411yescharacteristic
58C2×C4×C61C22⋊C411yescharacteristic
59C2×C4×C61C22×C411yescharacteristic
60C2×C4×C61C2×D411yescharacteristic
61C2×C4×C61C2×D411yescharacteristic
62#92418—24no—
63#92418—42no—
64C22×C61—21no—
65C22×C61—21no—
66C22×C61—42no—
67C22×C61—42no—
68C22×C61—42no—
69C22×C61—84no—
70C22×C61#10412yes—
71C22×C61C2×C22⋊C411yescharacteristic
72C4×C61—21no—
73C4×C61—21no—
74C4×C61—21no—
75C4×C61—21no—
76C4×C61—21no—
77C4×C61—42no—
78C4×C61#10012yes—
79#1527—611nomaximal, Sylow
80C2×C61—22no—
81C2×C61—82no—
82C2×C61C2×#10011yescharacteristic
83C2×C61C2×#10411yescharacteristic
84C2×C61#42111yescharacteristic
85C2×#124D6111yescharacteristic
86#432—611no—
87C4×M16—611no—
88#329—614no—
89C61#152711yescharacteristic, complemented, Sylow
90C22×Q8Dic6111yescharacteristic
91C22×D4Dic6111yescharacteristic
92C2×M16—1221no—
93#124—21no—
94#124—21no—
95#124Dic6112yes—
96#124C2×D6112yes—
97C2×C22⋊C4—21no—
98C2×C22⋊C4—21no—
99C2×C42C2×D6111yescharacteristic
100C4⋊C8—1221no—
101C22⋊C8—1221no—
102#97—612no—
103#97—612no—
104C4×C8—1221no—
105C24—21no—
106C2×Q8—21no—
107C2×Q8—42no—
108C2×Q8C2×Dic6112yes—
109C2×D4—21no—
110C2×D4—42no—
111C2×D4C2×Dic6112yes—
112C22×C4—21no—
113C22×C4C2×Dic6111yescharacteristic
114C22×C4C22⋊D6111yescharacteristic
115C22×C4C22⋊D6111yescharacteristic
116M16—1224no—
117C2×C8—1222no—
118C2×C8—1222no—
119C22⋊C4—22no—
120C22⋊C4—22no—
121C22⋊C4—22no—
122C22⋊C4—22no—
123C42C2×Dic6111yescharacteristic
124C42C22⋊D6111yescharacteristic
125C42C22⋊D6111yescharacteristic
126C42C22×D6111yescharacteristic
127C23—22no—
128C23—42no—
129C23—42no—
130C23—42no—
131C23C22⋊Dic6111yescharacteristic
132Q8—42no—
133Q8—42no—
134D4—42no—
135D4—42no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—41no—
140C2×C4—42no—
141C2×C4C22⋊Dic6111yescharacteristic
142C2×C4C22⋊Dic6111yescharacteristic
143C2×C4C22⋊Dic6111yescharacteristic
144C2×C4C22×Dic6111yescharacteristic
145C2×C4C2×C22⋊D6111yescharacteristic
146C2×C4C2×C22⋊D6111yescharacteristic
147C8—1224no—
148C8—2442no—
149C22—21no—
150C22—21no—
151C22—42no—
152C22—42no—
153C22—42no—
154C22—84no—
155C22#1451970412yes—
156C22C2×C22⋊Dic6111yescharacteristic
157C4—21no—
158C4—21no—
159C4—21no—
160C4—21no—
161C4—21no—
162C4—42no—
163C4#1451969412yes—
164C2—22no—
165C2—82no—
166C2C2×#1451969411yescharacteristic
167C2C2×#1451970411yescharacteristic
168C2#1683977911yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC2×#124×C61C2
socleC22×C61C2×C22⋊C4
hypercenterC2×#124D61
hypocenterC61#1527
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #16839819C2semidirect
2. C4×#11758194C2semidirect
3. #16839502C2semidirect
8. #14519688C22semidirect
9. #14519688C22semidirect
89. C61#1527semidirect