Finite Group Databasebeta

← D61⋊#329 #21461265

Subgroups — D61⋊#329 #21461265

Order 7808.

284 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 64 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#16840721C212yesmaximal, complemented
2#16840618C212yesmaximal, complemented
3#16840617C212yesmaximal, complemented
4#124×D61C211yesmaximal, characteristic
5C2×D61⋊C8—22no—
6#14519832—22no—
7#14519832C2214yescomplemented
8C2×Q8×D61C411yescharacteristic
9C2×D4×D61C411yescharacteristic
10#14519766C2211yescharacteristic
11#14519765C411yescharacteristic
12#14519764C2211yescharacteristic
13#14519763—22no—
14C22⋊C4×D61—22no—
15C42×D61C2211yescharacteristic
16#124×C61C411yescharacteristic
17C23×D61—21no—
18C2×Q8×C61C2×C411yescharacteristic
19C2×D4×C61C2×C411yescharacteristic
20C2×C22⋊D61—21no—
21Q8×D61—42no—
22D4×D61—42no—
23C2×D244C2×C411yescharacteristic
24C2×C4×D61—21no—
25C2×C4×D61C2×C411yescharacteristic
26C2×C4×D61D412yes—
27C2×Dic122—21no—
28C2×Dic122C2×C411yescharacteristic
29C2×#92420—24no—
30D61⋊C8—28no—
31C22⋊C4×C61—22no—
32C42×C61C2×C411yescharacteristic
33C22⋊Dic61—22no—
34#11758198—22no—
35#11758198—22no—
36C4×Dic61D412yes—
37C4×Dic61C2311yescharacteristic
38C23×C61—21no—
39C22×D61—21no—
40C22×D61—42no—
41C22×D61—44no—
42C22×D61C22⋊C411yescharacteristic
43Q8×C61—41no—
44D4×C61—41no—
45C2×C4×C61—21no—
46C2×C4×C61C22⋊C412yes—
47C2×C4×C61C22×C411yescharacteristic
48C22⋊D61—42no—
49C2×Dic61—21no—
50C2×Dic61C22⋊C411yescharacteristic
51C2×Dic61C2×D412yes—
52D244—41no—
53C4×D61—22no—
54C4×D61—24no—
55C4×D61—42no—
56Dic122—42no—
57Dic122—41no—
58#92420—28no—
59C22×C61—41no—
60C22×C61—42no—
61C22×C61C2×C22⋊C411yescharacteristic
62C2×D61—41no—
63C2×D61—42no—
64C2×D61—84no—
65C2×D61#10012yes—
66C2×D61#10414yes—
67C4×C61—21no—
68C4×C61—22no—
69C4×C61—41no—
70Dic61—21no—
71Dic61—22no—
72Dic61—41no—
73C2×#329—611nomaximal, Sylow
74C2×C61—81no—
75C2×C61C2×#10011yescharacteristic
76C2×C61C2×#10412yes—
77D61—81no—
78D61#32914yescomplemented
79C2×#124—611no—
80C2×#97—612no—
81#329—612no—
82#329—612no—
83C61C2×#32911yescharacteristic, complemented, Sylow
84C22×Q8—611no—
85C22×D4—611no—
86C22×C8—1222no—
87#124—611no—
88#124—611no—
89#124—611no—
90#124—1222no—
91#124#692311yescharacteristic
92C2×C22⋊C4—1222no—
93C2×C42—611no—
94#97—614no—
95#97—1222no—
96C24—1221no—
97C2×Q8—611no—
98C2×Q8—1221no—
99C2×Q8—2442no—
100C2×Q8C2×#692311yescharacteristic
101C2×D4—611no—
102C2×D4—1221no—
103C2×D4—2442no—
104C2×D4C2×#692311yescharacteristic
105C22×C4—612no—
106C22×C4—611no—
107C22×C4—1221no—
108C2×C8—1224no—
109C2×C8—1228no—
110C22⋊C4—22no—
111C22⋊C4—1222no—
112C22⋊C4—1222no—
113C22⋊C4—1222no—
114C42—612no—
115C42—611no—
116C42C2×#692311yescharacteristic
117C23—21no—
118C23—611no—
119C23—1221no—
120C23—2442no—
121C23—2444no—
122Q8—41no—
123Q8—2441no—
124Q8—2442no—
125D4—41no—
126D4—2441no—
127D4—2442no—
128C2×C4—21no—
129C2×C4—611no—
130C2×C4—612no—
131C2×C4—1224no—
132C2×C4—1222no—
133C2×C4—1221no—
134C2×C4—2442no—
135C2×C4C22⋊#692312yes—
136C2×C4C22×#692311yescharacteristic
137C8—1228no—
138C22—41no—
139C22—42no—
140C22—612no—
141C22—614no—
142C22—4884no—
143C22—2441no—
144C22—2442no—
145C22C2×C22⋊#692311yescharacteristic
146C4—21no—
147C4—22no—
148C4—41no—
149C4—1221no—
150C4—1222no—
151C4—2441no—
152C2—81no—
153C2—614no—
154C2—4881no—
155C2D61⋊#10011yescharacteristic
156C2D61⋊#10412yes—
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#124×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#124#6923
hypocenterC61C2×#329
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. #16840721C2semidirect
2. #16840618C2semidirect
3. #16840617C2semidirect
7. #14519832C22semidirect
78. D61#329semidirect
83. C61C2×#329semidirect