Finite Group Databasebeta

← #21444556

Subgroups — #21444556

Order 7808.

210 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 77 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#16840319C211yesmaximal, characteristic
2#16839786C211yesmaximal, characteristic
3#16839509C212yesmaximal, complemented
4#16839507C212yesmaximal, complemented
5C61×#423C211yesmaximal, characteristic
6C2×#11758194—21no—
7#14519777C2211yescharacteristic
8#14519777C2211yescharacteristic
9#14519769C412yes—
10#14519756—21no—
11#14519756—21no—
12C4×Dic122—21no—
13C4×Dic122—21no—
14#14519736C412yes—
15C4⋊#92418—21no—
16C4⋊#92418C2212yes—
17C2×M16×C61—21no—
18C2×C42×C61C2211yescharacteristic
19C4⋊C8×C61—21no—
20C4⋊C8×C61C2212yes—
21C22×C4×C61C2×C411yescharacteristic
22C22×C4×C61D411yescharacteristic
23C22×C4×C61D411yescharacteristic
24C2×Dic122—21no—
25C2×Dic122—21no—
26M16×C61—42no—
27C2×C8×C61—22no—
28C42×C61C2×C411yescharacteristic
29C42×C61D411yescharacteristic
30C42×C61D411yescharacteristic
31C42×C61C2311yescharacteristic
32C22⋊Dic61—22no—
33C4⋊Dic61—21no—
34C4⋊Dic61—21no—
35C4⋊Dic61C2×C412yes—
36C4⋊Dic61C2×C412yes—
37#11758196—22no—
38#11758196—22no—
39C4×Dic61—22no—
40#11758194—42no—
41C2×#92418—22no—
42C23×C61C22⋊C411yescharacteristic
43C2×C4×C61—22no—
44C2×C4×C61—21no—
45C2×C4×C61—21no—
46C2×C4×C61—21no—
47C2×C4×C61—21no—
48C2×C4×C61C22⋊C411yescharacteristic
49C2×C4×C61C22⋊C411yescharacteristic
50C2×C4×C61C22⋊C411yescharacteristic
51C2×C4×C61C22×C411yescharacteristic
52C2×C4×C61C2×D411yescharacteristic
53C2×C4×C61C2×D411yescharacteristic
54C2×Dic61—22no—
55C2×Dic61—22no—
56Dic122—41no—
57Dic122—41no—
58Dic122—41no—
59Dic122—41no—
60C8×C61—42no—
61#92418—42no—
62C22×C61—21no—
63C22×C61—21no—
64C22×C61—21no—
65C22×C61C2×C22⋊C411yescharacteristic
66C4×C61—21no—
67C4×C61—21no—
68C4×C61—21no—
69C4×C61#10112yes—
70C4×C61AGL(1,ℤ/8)11yescharacteristic
71C4×C61AGL(1,ℤ/8)11yescharacteristic
72C4×C61#13711yescharacteristic
73C4×C61#13711yescharacteristic
74Dic61—42no—
75Dic61—42no—
76#1561—611nomaximal, Sylow
77C2×C61—41no—
78C2×C61C2×#10111yescharacteristic
79C2×C61#41711yescharacteristic
80C2×C61#41711yescharacteristic
81#533—611no—
82#423—611no—
83#423D6111yescharacteristic
84#332—612no—
85#332—612no—
86C61#156111yescharacteristic, complemented, Sylow
87C2×M16—21no—
88C2×M16—1221no—
89C4⋊Q8—611no—
90C4⋊Q8—611no—
91#125—612no—
92C22⋊Q8—1221no—
93C22⋊Q8—1221no—
94C4×Q8—1221no—
95C4×Q8—1221no—
96#117—612no—
97C2×C42C2×D6111yescharacteristic
98C4⋊C8—21no—
99C4⋊C8—612no—
100C4⋊C8—1221no—
101C4⋊C8C2×D6112yes—
102C2×Q8—1221no—
103C2×Q8—1221no—
104C22×C4C4×D6111yescharacteristic
105C22×C4D24411yescharacteristic
106C22×C4C22⋊D6111yescharacteristic
107M16—42no—
108M16—2442no—
109C2×C8—22no—
110C2×C8—1222no—
111C4⋊C4—612no—
112C4⋊C4—612no—
113C4⋊C4—1222no—
114C4⋊C4—1222no—
115C4⋊C4—1221no—
116C4⋊C4—1221no—
117C22⋊C4—1222no—
118C42—1222no—
119C42C4×D6111yescharacteristic
120C42D24411yescharacteristic
121C42C22⋊D6111yescharacteristic
122C42C22×D6111yescharacteristic
123C23#1175819811yescharacteristic
124Q8—2441no—
125Q8—2441no—
126Q8—2441no—
127Q8—2441no—
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—22no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—1222no—
134C2×C4—1222no—
135C2×C4#1175819811yescharacteristic
136C2×C4#1175819811yescharacteristic
137C2×C4#1175819811yescharacteristic
138C2×C4C2×C4×D6111yescharacteristic
139C2×C4C2×D24411yescharacteristic
140C2×C4C2×C22⋊D6111yescharacteristic
141C8—42no—
142C8—2442no—
143C22—21no—
144C22—21no—
145C22—21no—
146C22C2×#1175819811yescharacteristic
147C4—21no—
148C4—21no—
149C4—21no—
150C4—2442no—
151C4—2442no—
152C4#1451969512yes—
153C4#1451980311yescharacteristic
154C4#1451980511yescharacteristic
155C4#1451980811yescharacteristic
156C4#1451981011yescharacteristic
157C2—41no—
158C2C2×#1451969511yescharacteristic
159C2#1683976111yescharacteristic
160C2#1683976411yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#423C2
socleC22×C61C2×C22⋊C4
hypercenter#423D61
hypocenterC61#1561
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
3. #16839509C2semidirect
4. #16839507C2semidirect
86. C61#1561semidirect