Finite Group Databasebeta

← #21444275

Subgroups — #21444275

Order 7808.

232 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 93 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#16839494C214yesmaximal, complemented
4C2×C4×C8×C61C211yesmaximal, characteristic
5C2×#11758194—21no—
6#14519777C411yescharacteristic
7#14519777C411yescharacteristic
8#14519769—21no—
9#14519756—21no—
10#14519756C412yes—
11C4×Dic122—21no—
12C4×Dic122C2212yes—
13#14519736—21no—
14C4⋊#92418—21no—
15C4⋊#92418C2212yes—
16C22×C8×C61—21no—
17C2×C42×C61C2211yescharacteristic
18C4×C8×C61—21no—
19C4×C8×C61C2212yes—
20C22×C4×C61C2×C411yescharacteristic
21C22×C4×C61D411yescharacteristic
22C22×C4×C61D411yescharacteristic
23C2×Dic122—21no—
24C2×Dic122C2×C412yes—
25C2×C8×C61—24no—
26C2×C8×C61—22no—
27C42×C61C2×C411yescharacteristic
28C42×C61D411yescharacteristic
29C42×C61D411yescharacteristic
30C42×C61C2311yescharacteristic
31C22⋊Dic61—22no—
32C4⋊Dic61—21no—
33C4⋊Dic61—21no—
34C4⋊Dic61—21no—
35C4⋊Dic61C2×C412yes—
36#11758196—22no—
37#11758196—22no—
38C4×Dic61—22no—
39#11758194—42no—
40C2×#92418—22no—
41C23×C61C22⋊C411yescharacteristic
42C2×C4×C61—22no—
43C2×C4×C61—22no—
44C2×C4×C61C22⋊C411yescharacteristic
45C2×C4×C61C22⋊C411yescharacteristic
46C2×C4×C61C22⋊C411yescharacteristic
47C2×C4×C61SD1612yes—
48C2×C4×C61Q1612yes—
49C2×C4×C61C22×C411yescharacteristic
50C2×C4×C61C2×D411yescharacteristic
51C2×C4×C61C2×D411yescharacteristic
52C2×Dic61—22no—
53C2×Dic61—22no—
54Dic122—24no—
55Dic122—42no—
56C8×C61—24no—
57#92418—42no—
58C22×C61—21no—
59C22×C61—21no—
60C22×C61#10312yes—
61C22×C61C2×C22⋊C411yescharacteristic
62C4×C61—21no—
63C4×C61—21no—
64C4×C61#10312yes—
65C4×C61#10412yes—
66C4×C61#13112yes—
67C4×C61C2×SD1611yescharacteristic
68C4×C61C2×Q1611yescharacteristic
69Dic61—42no—
70Dic61—42no—
71#1493—611nomaximal, Sylow
72C2×C61—22no—
73C2×C61#40811yescharacteristic
74C2×C61C2×#10311yescharacteristic
75C2×C61C2×#10411yescharacteristic
76#533—611no—
77#423—611no—
78C2×C4×C8D6111yescharacteristic
79Q8⋊C8—614no—
80C61#149311yescharacteristic, complemented, Sylow
81C2×M16—1221no—
82C22×C8—21no—
83C4⋊Q8—611no—
84C4⋊Q8—611no—
85#125—1221no—
86C22⋊Q8—612no—
87C22⋊Q8—1221no—
88C4×Q8—612no—
89C4×Q8—1221no—
90#117—1221no—
91C2×C42C2×D6111yescharacteristic
92C4⋊C8—612no—
93C4⋊C8—1221no—
94C4×C8—21no—
95C4×C8C2×D6112yes—
96C2×Q8—612no—
97C2×Q8—1221no—
98C22×C4C4×D6111yescharacteristic
99C22×C4D24411yescharacteristic
100C22×C4C22⋊D6111yescharacteristic
101M16—2442no—
102C2×C8—24no—
103C2×C8—22no—
104C2×C8—1222no—
105C4⋊C4—612no—
106C4⋊C4—1222no—
107C4⋊C4—1221no—
108C4⋊C4—1221no—
109C4⋊C4—1221no—
110C4⋊C4—1222no—
111C22⋊C4—1222no—
112C42—1222no—
113C42C4×D6111yescharacteristic
114C42D24411yescharacteristic
115C42C22⋊D6111yescharacteristic
116C42C22×D6111yescharacteristic
117C23#1175819811yescharacteristic
118Q8—1224no—
119Q8—2442no—
120C2×C4—22no—
121C2×C4—22no—
122C2×C4—1222no—
123C2×C4—1222no—
124C2×C4#1175819012yes—
125C2×C4Dic24412yes—
126C2×C4#1175819811yescharacteristic
127C2×C4#1175819811yescharacteristic
128C2×C4#1175819811yescharacteristic
129C2×C4C2×C4×D6111yescharacteristic
130C2×C4C2×D24411yescharacteristic
131C2×C4C2×C22⋊D6111yescharacteristic
132C8—24no—
133C8—2442no—
134C22—21no—
135C22—21no—
136C22#1451970212yes—
137C22C2×#1175819811yescharacteristic
138C4—21no—
139C4—21no—
140C4—2442no—
141C4—2442no—
142C4#1451970212yes—
143C4#1451970512yes—
144C4#1451978312yes—
145C4C2×#1175819011yescharacteristic
146C4C2×Dic24411yescharacteristic
147C2—22no—
148C2#1683972811yescharacteristic
149C2C2×#1451970211yescharacteristic
150C2C2×#1451970511yescharacteristic
subgroupG/H
centerC2×C4C2×D244
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC2×C4×C8×C61C2
socleC22×C61C2×C22⋊C4
hypercenterC2×C4×C8D61
hypocenterC61#1493
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
3. #16839494C2semidirect
80. C61#1493semidirect