Finite Group Databasebeta

← #21461357

Subgroups — #21461357

Order 7808.

254 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 60 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#16840767C212yesmaximal, complemented
2#16840622C212yesmaximal, complemented
3#16840620C212yesmaximal, complemented
4#16840311C211yesmaximal, characteristic
5C2×#11758213—22no—
6#14519844—22no—
7#14519844C2214yes—
8C2×#11758226C411yescharacteristic
9C2×#11758224C411yescharacteristic
10#14519775C2211yescharacteristic
11#14519773C2211yescharacteristic
12#14519765C411yescharacteristic
13#14519750—22no—
14#14519737—22no—
15C42×D61C2211yescharacteristic
16#124×C61C411yescharacteristic
17C2×Q8×C61C2×C411yescharacteristic
18C2×D4×C61C2×C411yescharacteristic
19C2×C22⋊D61—21no—
20C2×C22⋊D61—22no—
21C22×Dic61—21no—
22#11758226—42no—
23#11758224—42no—
24C2×D244—21no—
25C2×D244C2×C411yescharacteristic
26C2×C4×D61—21no—
27C2×C4×D61C2×C411yescharacteristic
28C2×C4×D61D412yes—
29C2×Dic122C2×C411yescharacteristic
30C2×#92420—24no—
31#11758213—44no—
32C22⋊C4×C61—22no—
33C42×C61C2×C411yescharacteristic
34#11758198—22no—
35#11758196—22no—
36C4×Dic61D412yes—
37C4×Dic61C2311yescharacteristic
38C23×C61—21no—
39C22×D61—21no—
40C22×D61C22⋊C411yescharacteristic
41Q8×C61—41no—
42D4×C61—41no—
43C2×C4×C61—21no—
44C2×C4×C61C22⋊C412yes—
45C2×C4×C61C22×C411yescharacteristic
46C22⋊D61—42no—
47C22⋊D61—42no—
48C22⋊D61—42no—
49C2×Dic61—21no—
50C2×Dic61—42no—
51C2×Dic61C22⋊C411yescharacteristic
52C2×Dic61C2×D412yes—
53D244—41no—
54D244—42no—
55C4×D61—22no—
56C4×D61—22no—
57C4×D61—22no—
58C4×D61—42no—
59Dic122—41no—
60#92420—44no—
61C22×C61—41no—
62C22×C61—42no—
63C22×C61C2×C22⋊C411yescharacteristic
64C2×D61—21no—
65C2×D61—22no—
66C2×D61—41no—
67C2×D61—42no—
68C4×C61—21no—
69C4×C61—22no—
70C4×C61—41no—
71Dic61—41no—
72Dic61#10012yes—
73Dic61AGL(1,ℤ/8)12yes—
74Dic61#13712yes—
75#1560—611nomaximal, Sylow
76C2×C61—81no—
77C2×C61C2×#10011yescharacteristic
78C2×C61#41712yes—
79D61—41no—
80D61—81no—
81#532—611no—
82#423—612no—
83#333—612no—
84#331—612no—
85C61#156011yescharacteristic, complemented, Sylow
86C2×#41—611no—
87C2×#41—611no—
88C2×M16—1222no—
89C4⋊Q8—611no—
90#127—611no—
91#124—611no—
92#124#692311yescharacteristic
93#121—1222no—
94C4×D4—1222no—
95C2×C42—611no—
96C4⋊C8—614no—
97C4⋊C8—1222no—
98#41—2442no—
99#41—2442no—
100C2×Q8—611no—
101C2×Q8C2×#692311yescharacteristic
102C2×D4—611no—
103C2×D4—1221no—
104C2×D4—1222no—
105C2×D4—1221no—
106C2×D4C2×#692311yescharacteristic
107C22×C4—612no—
108C22×C4—611no—
109C22×C4—1221no—
110C22×C4—1221no—
111M16—2444no—
112C2×C8—1224no—
113C4⋊C4—1222no—
114C22⋊C4—22no—
115C22⋊C4—1222no—
116C42—612no—
117C42—611no—
118C42C2×#692311yescharacteristic
119C23—21no—
120C23—611no—
121C23—1221no—
122Q8—41no—
123Q8—2441no—
124D4—41no—
125D4—2441no—
126D4—2442no—
127D4—2442no—
128D4—2442no—
129D4—2442no—
130C2×C4—21no—
131C2×C4—611no—
132C2×C4—612no—
133C2×C4—1222no—
134C2×C4—1222no—
135C2×C4—1222no—
136C2×C4—1221no—
137C2×C4—2442no—
138C2×C4—2442no—
139C2×C4C22⋊#692312yes—
140C2×C4C22×#692311yescharacteristic
141C8—2444no—
142C22—41no—
143C22—42no—
144C22—1221no—
145C22—1222no—
146C22—2441no—
147C22—2442no—
148C22C2×C22⋊#692311yescharacteristic
149C4—21no—
150C4—22no—
151C4—41no—
152C4—612no—
153C4—612no—
154C4—612no—
155C4—2441no—
156C2—81no—
157C2—4881no—
158C2—2441no—
159C2D61⋊#10011yescharacteristic
160C2#1684075312yes—
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#124×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#124#6923
hypocenterC61#1560
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #16840767C2semidirect
2. #16840622C2semidirect
3. #16840620C2semidirect
85. C61#1560semidirect