Finite Group Databasebeta

← #21444795

Subgroups — #21444795

Order 7808.

238 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 53 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#16840393C211yesmaximal, characteristic
2#16839920C212yesmaximal
3#16839682C211yesmaximal, characteristic
4#16839500C212yesmaximal
5C61×#324C211yesmaximal, characteristic
6C22×Dic122C2211yescharacteristic
7C2×Dic244—22no—
8#14519776—22no—
9#14519768—22no—
10#14519756—21no—
11#14519756C2212yes—
12#14519736—21no—
13C2×#11758196—21no—
14#14519702—22no—
15#14519684—21no—
16#14519684C2211yescharacteristic
17C2×C4⋊C4×C61C2211yescharacteristic
18C22⋊C8×C61C2212yes—
19C22×C4×C61D411yescharacteristic
20C22×C4×C61D411yescharacteristic
21C22×C4×C61C2311yescharacteristic
22C22×Dic61—21no—
23C22×Dic61—21no—
24C2×Dic122—22no—
25C2×Dic122—21no—
26C2×Dic122—42no—
27C2×Dic122D412yes—
28C2×C8×C61—22no—
29C4⋊C4×C61—22no—
30C22⋊Dic61—22no—
31C4⋊Dic61—21no—
32C4⋊Dic61—21no—
33C4⋊Dic61—21no—
34C4⋊Dic61D412yes—
35#11758196—22no—
36#11758196—22no—
37#11758196—42no—
38C4×Dic61—22no—
39Dic244—44no—
40C23×C61C2×D411yescharacteristic
41C2×C4×C61—21no—
42C2×C4×C61—21no—
43C2×C4×C61—21no—
44C2×C4×C61—41no—
45C2×C4×C61—41no—
46C2×C4×C61Q1612yescomplemented
47C2×C4×C61C2×D412yes—
48C2×Dic61—22no—
49C2×Dic61—22no—
50C2×Dic61—22no—
51C2×Dic61—22no—
52C2×Dic61—41no—
53C2×Dic61—41no—
54C2×Dic61—41no—
55C2×Dic61—41no—
56Dic122—24no—
57Dic122—42no—
58Dic122—42no—
59Dic122—81no—
60C8×C61—42no—
61C22×C61—21no—
62C22×C61—21no—
63C22×C61#12011yescharacteristic
64C22×C61C2×Q1611yescharacteristic
65C22×C61#13711yescharacteristic
66C4×C61—22no—
67C4×C61—22no—
68C4×C61—41no—
69Dic61—42no—
70Dic61—42no—
71Dic61—42no—
72Dic61—42no—
73#1605—611nomaximal, Sylow
74C2×C61—21no—
75C2×C61—21no—
76C2×C61#45111yescharacteristic
77C2×C61#45611yescharacteristic
78C2×C61B(4,𝔽2)11yescharacteristic
79#544—611no—
80#451—612no—
81#395—611no—
82#328—612no—
83#324D6111yescharacteristic
84C61#160511yescharacteristic, complemented, Sylow
85C22×Q8—611no—
86C2×Q16—1222no—
87C4⋊Q8—1222no—
88#125—1222no—
89C22⋊Q8—612no—
90C22⋊Q8—1221no—
91#117—1221no—
92C2×C4⋊C4—1221no—
93C2×C4⋊C4C2×D6111yescharacteristic
94#103—1222no—
95C22⋊C8C2×D6112yes—
96#95—611no—
97#95—1221no—
98C2×Q8—612no—
99C2×Q8—1221no—
100C2×Q8—1222no—
101C2×Q8—2442no—
102C22×C4—1221no—
103C22×C4—1221no—
104C22×C4D24411yescharacteristic
105C22×C4D24411yescharacteristic
106C22×C4C22×D6111yescharacteristic
107Q16—2444no—
108C2×C8—22no—
109C4⋊C4—22no—
110C4⋊C4—612no—
111C4⋊C4—1222no—
112C4⋊C4—1221no—
113C4⋊C4—1221no—
114C4⋊C4—1221no—
115C4⋊C4—1222no—
116C4⋊C4—2442no—
117C22⋊C4—1222no—
118C42—1222no—
119C23C2×D24411yescharacteristic
120Q8—1224no—
121Q8—4881no—
122Q8—2442no—
123Q8—2442no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—21no—
127C2×C4—41no—
128C2×C4—41no—
129C2×C4—1222no—
130C2×C4—1222no—
131C2×C4—1222no—
132C2×C4—1222no—
133C2×C4—2441no—
134C2×C4—2441no—
135C2×C4—2441no—
136C2×C4—2441no—
137C2×C4Dic24412yescomplemented
138C2×C4D4×D6112yes—
139C8—42no—
140C22—21no—
141C22—21no—
142C22#1451974711yescharacteristic
143C22C2×Dic24411yescharacteristic
144C22#1451981011yescharacteristic
145C4—22no—
146C4—22no—
147C4—41no—
148C4—2442no—
149C4—2442no—
150C4—2442no—
151C4—2442no—
152C2—21no—
153C2—21no—
154C2#1683992011yescharacteristic
155C2#1683994711yescharacteristic
156C2#1683995011yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#324C2
socleC22×C61#120
hypercenter#324D61
hypocenterC61#1605
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
46. C2×C4×C61Q16semidirect
84. C61#1605semidirect
137. C2×C4Dic244semidirect