Finite Group Databasebeta

← #21444171

Subgroups — #21444171

Order 7808.

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

normal subgroups only

This group has 256 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
2#16839815C211yesmaximal, characteristic, complemented
3#16839486C214yesmaximal, complemented
4C2×#124×C61C211yesmaximal, characteristic
5C4⋊#92418—21no—
6C4⋊#92418—21no—
7C22⋊#92418C2212yes—
8C22⋊#92418C2212yes—
9#14519688—21no—
10C4×#92418—21no—
11C22×Q8×C61C411yescharacteristic
12C22×D4×C61C411yescharacteristic
13#124×C61—21no—
14#124×C61—21no—
15#124×C61—21no—
16#124×C61—21no—
17C2×C22⋊C4×C61C412yes—
18C2×C22⋊C4×C61C2212yes—
19C2×C42×C61C2211yescharacteristic
20C24×C61C2×C412yes—
21C2×Q8×C61—21no—
22C2×Q8×C61—21no—
23C2×Q8×C61—42no—
24C2×D4×C61—21no—
25C2×D4×C61—21no—
26C2×D4×C61—42no—
27C22×C4×C61C2×C411yescharacteristic
28C22×C4×C61C2×C411yescharacteristic
29C22×C4×C61C2×C412yes—
30C22×C4×C61C2311yescharacteristic
31C22⋊C4×C61—22no—
32C22⋊C4×C61—22no—
33C22⋊C4×C61—22no—
34C22⋊C4×C61—22no—
35C42×C61D411yescharacteristic
36C42×C61D411yescharacteristic
37C42×C61D411yescharacteristic
38C42×C61D411yescharacteristic
39C2×#92418—22no—
40C2×#92418—22no—
41C23×C61—22no—
42C23×C61—24no—
43C23×C61—42no—
44C23×C61—42no—
45C23×C61C22×C411yescharacteristic
46Q8×C61—42no—
47Q8×C61—42no—
48D4×C61—42no—
49D4×C61—42no—
50C2×C4×C61—22no—
51C2×C4×C61—22no—
52C2×C4×C61—22no—
53C2×C4×C61—41no—
54C2×C4×C61—42no—
55C2×C4×C61C22⋊C411yescharacteristic
56C2×C4×C61C22⋊C411yescharacteristic
57C2×C4×C61C22⋊C411yescharacteristic
58C2×C4×C61C22⋊C411yescharacteristic
59C2×C4×C61C2×D411yescharacteristic
60C2×C4×C61C2×D411yescharacteristic
61#92418—42no—
62#92418—42no—
63C22×C61—21no—
64C22×C61—21no—
65C22×C61—42no—
66C22×C61—42no—
67C22×C61—42no—
68C22×C61—84no—
69C22×C61C2×C22⋊C411yescharacteristic
70C22×C61#13112yes—
71C4×C61—21no—
72C4×C61—21no—
73C4×C61—21no—
74C4×C61—21no—
75C4×C61—21no—
76C4×C61—42no—
77C4×C61#10012yes—
78#1469—611nomaximal, Sylow
79C2×C61—22no—
80C2×C61—82no—
81C2×C61#40811yescharacteristic
82C2×C61#41011yescharacteristic
83C2×C61C2×#10011yescharacteristic
84C2×#124D6111yescharacteristic
85#432—611no—
86#431—611no—
87#323—614no—
88C61#146911yescharacteristic, complemented, Sylow
89C22×Q8Dic6111yescharacteristic
90C22×D4Dic6111yescharacteristic
91#124—21no—
92#124—21no—
93#124—21no—
94#124—21no—
95C2×C22⋊C4Dic6112yes—
96C2×C22⋊C4C2×D6112yes—
97C2×C42C2×D6111yescharacteristic
98C4⋊C8—1221no—
99C4⋊C8—1221no—
100C22⋊C8—612no—
101C22⋊C8—612no—
102#97—1221no—
103C4×C8—1221no—
104C24C2×Dic6112yes—
105C2×Q8—21no—
106C2×Q8—21no—
107C2×Q8—42no—
108C2×D4—21no—
109C2×D4—21no—
110C2×D4—42no—
111C22×C4C2×Dic6111yescharacteristic
112C22×C4C2×Dic6111yescharacteristic
113C22×C4C2×Dic6112yes—
114C22×C4C22×D6111yescharacteristic
115C2×C8—1222no—
116C2×C8—1222no—
117C22⋊C4—22no—
118C22⋊C4—22no—
119C22⋊C4—22no—
120C22⋊C4—22no—
121C42C22⋊D6111yescharacteristic
122C42C22⋊D6111yescharacteristic
123C42C22⋊D6111yescharacteristic
124C42C22⋊D6111yescharacteristic
125C23—22no—
126C23—24no—
127C23—42no—
128C23—42no—
129C23C22×Dic6111yescharacteristic
130Q8—42no—
131Q8—42no—
132D4—42no—
133D4—42no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—22no—
137C2×C4—41no—
138C2×C4—42no—
139C2×C4C22⋊Dic6111yescharacteristic
140C2×C4C22⋊Dic6111yescharacteristic
141C2×C4C22⋊Dic6111yescharacteristic
142C2×C4C22⋊Dic6111yescharacteristic
143C2×C4C2×C22⋊D6111yescharacteristic
144C2×C4C2×C22⋊D6111yescharacteristic
145C8—2442no—
146C8—2442no—
147C22—21no—
148C22—21no—
149C22—42no—
150C22—42no—
151C22—42no—
152C22—84no—
153C22C2×C22⋊Dic6111yescharacteristic
154C22#1451978412yes—
155C4—21no—
156C4—21no—
157C4—21no—
158C4—21no—
159C4—21no—
160C4—42no—
161C4#1451969412yes—
162C2—22no—
163C2—82no—
164C2#1683972911yescharacteristic
165C2#1683973611yescharacteristic
166C2C2×#1451969411yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic61
commutatorC23×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#124×C61C2
socleC22×C61C2×C22⋊C4
hypercenterC2×#124D61
hypocenterC61#1469
LCSG ▷ C23×C61 ▷ C2×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. #16839815C2semidirect
3. #16839486C2semidirect
88. C61#1469semidirect