Finite Group Databasebeta

← #21461356

Subgroups — #21461356

Order 7808.

254 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 62 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#16840765C212yesmaximal, complemented
2#16840622C212yesmaximal, complemented
3#16840620C212yesmaximal, complemented
4#16840308C211yesmaximal, characteristic
5C2×#11758217—22no—
6#14519844C2214yes—
7C4⋊#92420—22no—
8C2×#11758222C411yescharacteristic
9#14519775C2211yescharacteristic
10#14519773C2211yescharacteristic
11#14519766C411yescharacteristic
12#14519764C411yescharacteristic
13#14519749—22no—
14C4×C22⋊D61—22no—
15C2×C4×Dic61C2211yescharacteristic
16C2×#41×C61C411yescharacteristic
17#41×C61—42no—
18C2×Q8×C61C2×C411yescharacteristic
19C2×D4×C61—21no—
20C2×D4×C61C2×C411yescharacteristic
21C22×C4×C61—21no—
22C22×C4×C61C2×C411yescharacteristic
23C2×C22⋊D61—21no—
24C2×C22⋊D61—22no—
25C22×Dic61D412yes—
26#11758222—42no—
27C2×D244C2×C411yescharacteristic
28C2×C4×D61—21no—
29C2×Dic122C2×C411yescharacteristic
30#11758217—44no—
31C2×#92420—24no—
32C22⋊Dic61—22no—
33#11758198—22no—
34#11758196—22no—
35C4×Dic61C2×C411yescharacteristic
36C4×Dic61D412yes—
37C4×Dic61C2311yescharacteristic
38C23×C61—21no—
39C23×C61C22⋊C411yescharacteristic
40C22×D61—21no—
41Q8×C61—41no—
42D4×C61—41no—
43D4×C61—42no—
44C2×C4×C61—22no—
45C2×C4×C61—21no—
46C2×C4×C61—42no—
47C2×C4×C61C22⋊C411yescharacteristic
48C2×C4×C61C22×C411yescharacteristic
49C22⋊D61—42no—
50C22⋊D61—42no—
51C22⋊D61—42no—
52C2×Dic61—22no—
53C2×Dic61—22no—
54C2×Dic61—21no—
55C2×Dic61C22⋊C412yes—
56C2×Dic61C2×D412yes—
57D244—41no—
58C4×D61—42no—
59Dic122—41no—
60#92420—44no—
61C22×C61—21no—
62C22×C61—22no—
63C22×C61—41no—
64C22×C61—42no—
65C22×C61C2×C22⋊C411yescharacteristic
66C2×D61—41no—
67C2×D61—42no—
68C4×C61—21no—
69C4×C61—41no—
70C4×C61#10012yes—
71Dic61—22no—
72Dic61—41no—
73Dic61AGL(1,ℤ/8)12yes—
74Dic61#13712yes—
75#1560—611nomaximal, Sylow
76C2×C61—41no—
77C2×C61—81no—
78C2×C61C2×#10011yescharacteristic
79C2×C61#41712yes—
80D61—81no—
81#532—611no—
82#423—612no—
83#333—612no—
84#331—612no—
85C61#156011yescharacteristic, complemented, Sylow
86C2×#41—611no—
87C2×#41#692311yescharacteristic
88C2×M16—1222no—
89C4⋊Q8—611no—
90#127—611no—
91#124—611no—
92#124—611no—
93#121—1222no—
94C4×D4—1222no—
95C2×C42—611no—
96C4⋊C8—614no—
97C4⋊C8—1222no—
98#41—42no—
99#41—2442no—
100C2×Q8—611no—
101C2×Q8C2×#692311yescharacteristic
102C2×D4—21no—
103C2×D4—611no—
104C2×D4—1222no—
105C2×D4—1221no—
106C2×D4C2×#692311yescharacteristic
107C22×C4—21no—
108C22×C4—612no—
109C22×C4—1221no—
110C22×C4C2×#692311yescharacteristic
111M16—2444no—
112C2×C8—1224no—
113C4⋊C4—1222no—
114C22⋊C4—1222no—
115C22⋊C4—1222no—
116C42—612no—
117C42—611no—
118C42—611no—
119C23—21no—
120C23—1221no—
121C23C22⋊#692311yescharacteristic
122Q8—41no—
123Q8—2441no—
124D4—41no—
125D4—42no—
126D4—2441no—
127D4—2442no—
128D4—2442no—
129D4—2442no—
130C2×C4—22no—
131C2×C4—21no—
132C2×C4—42no—
133C2×C4—612no—
134C2×C4—612no—
135C2×C4—1222no—
136C2×C4—1222no—
137C2×C4—1221no—
138C2×C4—2442no—
139C2×C4C22⋊#692311yescharacteristic
140C2×C4C22×#692311yescharacteristic
141C8—2444no—
142C22—21no—
143C22—22no—
144C22—41no—
145C22—42no—
146C22—2441no—
147C22—2442no—
148C22C2×C22⋊#692311yescharacteristic
149C4—21no—
150C4—41no—
151C4—612no—
152C4—612no—
153C4—1222no—
154C4—2441no—
155C4#1451983712yes—
156C2—41no—
157C2—81no—
158C2—4881no—
159C2C2×#1451983711yescharacteristic
160C2#1684075312yes—
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC2×#41×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC2×#41#6923
hypocenterC61#1560
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #16840765C2semidirect
2. #16840622C2semidirect
3. #16840620C2semidirect
85. C61#1560semidirect