Finite Group Databasebeta

← #30605532

Subgroups — #30605532

Order 15616.

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

normal subgroups only

This group has 274 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#21462188C212yesmaximal
2#21460824C214yesmaximal, complemented
3#21456199C211yesmaximal, characteristic
4#16840685—22no—
5#16840658—22no—
6#16840654C2214yes—
7#16840319C411yescharacteristic
8#16840130C412yes—
9#16840130C2212yes—
10#16840112—22no—
11#16839771—22no—
12C4×#11758194C2211yescharacteristic
13C2×C4⋊Q8×C61C411yescharacteristic
14#14519851—24no—
15C2×#11758194D412yes—
16#14519777—21no—
17#14519769C2×C412yes—
18#14519756—41no—
19C4×Dic122—41no—
20#14519736—21no—
21#14519701—24no—
22#14519701—24no—
23#14519688C2×C411yescharacteristic
24#14519688C2311yescharacteristic
25C4×#92418D412yes—
26C22×Q8×C61—21no—
27C4⋊Q8×C61—21no—
28C4⋊Q8×C61—41no—
29C4⋊Q8×C61C2×C412yes—
30C2×C4⋊C4×C61—41no—
31C2×C42×C61C2×C411yescharacteristic
32C2×Q8×C61—22no—
33C2×Q8×C61—44no—
34C2×Q8×C61—41no—
35C22×C4×C61—21no—
36C22×C4×C61—41no—
37C22×C4×C61C22⋊C411yescharacteristic
38C2×Dic122—41no—
39C4⋊C4×C61—42no—
40C4⋊C4×C61—42no—
41C42×C61—21no—
42C42×C61C22⋊C411yescharacteristic
43C42×C61C22×C411yescharacteristic
44C22⋊Dic61—41no—
45C4⋊Dic61—22no—
46C4⋊Dic61—41no—
47#11758196—42no—
48C4×Dic61—41no—
49#11758194—42no—
50C2×#92418C22⋊C412yes—
51C2×#92418C2×D412yes—
52#11758187—44no—
53C23×C61#10011yescharacteristic
54Q8×C61—44no—
55Q8×C61—82no—
56C2×C4×C61—21no—
57C2×C4×C61—22no—
58C2×C4×C61—21no—
59C2×C4×C61—42no—
60C2×C4×C61—42no—
61C2×C4×C61—82no—
62C2×C4×C61#10011yescharacteristic
63C2×C4×C61C2×C22⋊C411yescharacteristic
64C2×Dic61—42no—
65Dic122—82no—
66#92418—22no—
67#92418—22no—
68#11916—611nomaximal, Sylow
69C22×C61—21no—
70C22×C61—41no—
71C22×C61C2×#10011yescharacteristic
72C4×C61—22no—
73C4×C61—21no—
74C4×C61—41no—
75C4×C61—82no—
76C4×C61#42112yes—
77Dic61—82no—
78#3139—611no—
79#2165—612no—
80#1356—614no—
81C2×C61—21no—
82C2×C61—41no—
83C2×C61#153311yescharacteristic
84#533—611no—
85C2×C4⋊Q8#692311yescharacteristic
86#491—612no—
87#491—612no—
88#487—1222no—
89#419—1222no—
90C4×M16—611no—
91#364—1222no—
92#349—1222no—
93#347—614no—
94C61#1191611yescharacteristic, complemented, Sylow
95C22×Q8—21no—
96C2×M16—612no—
97C4⋊Q8—21no—
98C4⋊Q8—41no—
99C4⋊Q8—1221no—
100C4⋊Q8C2×#692312yes—
101#125—612no—
102C22⋊Q8—2441no—
103C4×Q8—2441no—
104#117—1221no—
105C2×C4⋊C4—41no—
106C2×C42C2×#692311yescharacteristic
107M32—1224no—
108#103—1224no—
109#103—1224no—
110#97—611no—
111#97—611no—
112C4×C8—612no—
113C2×Q8—22no—
114C2×Q8—44no—
115C2×Q8—41no—
116C2×Q8—2441no—
117C22×C4—21no—
118C22×C4—41no—
119C22×C4C22⋊#692311yescharacteristic
120M16—2442no—
121C2×C8—612no—
122C2×C8—612no—
123C4⋊C4—42no—
124C4⋊C4—42no—
125C4⋊C4—1222no—
126C4⋊C4—2442no—
127C4⋊C4—2441no—
128C22⋊C4—2441no—
129C42—21no—
130C42—2441no—
131C42C22⋊#692311yescharacteristic
132C42C22×#692311yescharacteristic
133C16—2444no—
134C23#1451983711yescharacteristic
135Q8—44no—
136Q8—82no—
137Q8—4882no—
138C2×C4—21no—
139C2×C4—22no—
140C2×C4—21no—
141C2×C4—42no—
142C2×C4—42no—
143C2×C4—82no—
144C2×C4—2442no—
145C2×C4#1451983711yescharacteristic
146C2×C4C2×C22⋊#692311yescharacteristic
147C8—1222no—
148C8—1222no—
149C22—21no—
150C22—41no—
151C22C2×#1451983711yescharacteristic
152C4—22no—
153C4—21no—
154C4—41no—
155C4—82no—
156C4—4882no—
157C4#1684076012yes—
158C2—21no—
159C2—41no—
160C2#2146129811yescharacteristic
subgroupG/H
centerC2#21461298
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC2×C4⋊Q8×C61C4
socleC2×C61#1533
prime radicalC23×C61#100
cosocle#14519688C23
hypercenterC2×C4⋊Q8#6923
hypocenterC61#11916
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #21460824C2semidirect
94. C61#11916semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214621882
#214608242
#214561992
#1191661