Finite Group Databasebeta

← C2×#16839503 #21444402

Subgroups — C2×#16839503 #21444402

Order 7808.

232 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 85 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
1C2×#14519769C211yesmaximal, characteristic
2C2×#14519688C211yesmaximal, characteristic
3#16839503C214yesmaximal, direct product factor
4C2×#97×C61C211yesmaximal, characteristic
5C22×#92418—21no—
6#14519769—21no—
7#14519769—21no—
8#14519769C412yes—
9#14519769C2212yes—
10C2×C4⋊Dic61C411yescharacteristic
11C2×C4⋊Dic61C411yescharacteristic
12C2×#11758196—21no—
13C2×#11758196—21no—
14#14519688—21no—
15#14519688C2212yes—
16C22×C8×C61—21no—
17C2×C42×C61C2211yescharacteristic
18#97×C61—21no—
19#97×C61C2212yes—
20C22×C4×C61C2×C411yescharacteristic
21C22×C4×C61D411yescharacteristic
22C22×C4×C61D411yescharacteristic
23C22×Dic61—21no—
24C22×Dic61—21no—
25C2×C8×C61—24no—
26C2×C8×C61—22no—
27C42×C61C2×C411yescharacteristic
28C42×C61D411yescharacteristic
29C42×C61D411yescharacteristic
30C42×C61C2311yescharacteristic
31C4⋊Dic61—21no—
32C4⋊Dic61—21no—
33C4⋊Dic61C2×C412yes—
34C4⋊Dic61C2×C412yes—
35#11758196—22no—
36#11758196—22no—
37#11758196—22no—
38#11758196—22no—
39C2×#92418—24no—
40C2×#92418—22no—
41C23×C61C22⋊C411yescharacteristic
42C2×C4×C61—22no—
43C2×C4×C61—22no—
44C2×C4×C61—22no—
45C2×C4×C61C22⋊C411yescharacteristic
46C2×C4×C61C22⋊C411yescharacteristic
47C2×C4×C61C22⋊C411yescharacteristic
48C2×C4×C61C22×C411yescharacteristic
49C2×C4×C61C2×D411yescharacteristic
50C2×C4×C61C2×D411yescharacteristic
51C2×Dic61—22no—
52C2×Dic61—22no—
53C2×Dic61—42no—
54C2×Dic61—42no—
55C8×C61—24no—
56#92418—24no—
57C22×C61#10112yes—
58C22×C61#10412yes—
59C22×C61#10412yes—
60C22×C61C2×C22⋊C411yescharacteristic
61C4×C61—21no—
62C4×C61—21no—
63C4×C61—21no—
64C4×C61—21no—
65C4×C61—21no—
66C4×C61—21no—
67Dic61—42no—
68Dic61—42no—
69C2×#330—611nomaximal, Sylow
70C2×C61#33014yescomplemented
71C2×C61C2×#10111yescharacteristic
72C2×C61C2×#10411yescharacteristic
73C2×C61C2×#10411yescharacteristic
74C2×#125—611no—
75C2×#97—611no—
76C2×#97D6111yescharacteristic
77#330—614no—
78C61C2×#33011yescharacteristic, complemented, Sylow
79C22×C8—21no—
80C22×C8—1221no—
81#125—612no—
82#125—612no—
83#125—1221no—
84#125—1221no—
85C2×C4⋊C4—611no—
86C2×C4⋊C4—611no—
87C2×C4⋊C4—1221no—
88C2×C4⋊C4—1221no—
89C2×C42C2×D6111yescharacteristic
90#97—21no—
91#97—612no—
92#97—1221no—
93#97C2×D6112yes—
94C22×C4—1221no—
95C22×C4—1221no—
96C22×C4C4×D6111yescharacteristic
97C22×C4D24411yescharacteristic
98C22×C4C22⋊D6111yescharacteristic
99C2×C8—24no—
100C2×C8—22no—
101C2×C8—1224no—
102C2×C8—1222no—
103C4⋊C4—612no—
104C4⋊C4—612no—
105C4⋊C4—1221no—
106C4⋊C4—1221no—
107C4⋊C4—1222no—
108C4⋊C4—1222no—
109C4⋊C4—1222no—
110C4⋊C4—1222no—
111C42C4×D6111yescharacteristic
112C42D24411yescharacteristic
113C42C22⋊D6111yescharacteristic
114C42C22×D6111yescharacteristic
115C23#1175819811yescharacteristic
116C2×C4—22no—
117C2×C4—22no—
118C2×C4—22no—
119C2×C4—1222no—
120C2×C4—1222no—
121C2×C4—2442no—
122C2×C4—2442no—
123C2×C4#1175819811yescharacteristic
124C2×C4#1175819811yescharacteristic
125C2×C4#1175819811yescharacteristic
126C2×C4C2×C4×D6111yescharacteristic
127C2×C4C2×D24411yescharacteristic
128C2×C4C2×C22⋊D6111yescharacteristic
129C8—24no—
130C8—1224no—
131C22#1451969512yes—
132C22#1451970312yes—
133C22#1451970512yes—
134C22C2×#1175819811yescharacteristic
135C4—21no—
136C4—21no—
137C4—21no—
138C4—21no—
139C4—21no—
140C4—21no—
141C4—2442no—
142C4—2442no—
143C2#1683950314yesdirect product factor
144C2C2×#1451969511yescharacteristic
145C2C2×#1451970311yescharacteristic
146C2C2×#1451970511yescharacteristic
subgroupG/H
centerC23#11758198
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC2×#97×C61C2
socleC23×C61C22⋊C4
hypercenterC2×#97D61
hypocenterC61C2×#330
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
3. #16839503C2direct (N × H)
70. C2×C61#330semidirect
78. C61C2×#330semidirect
143. C2#16839503direct (N × H)