Finite Group Databasebeta

← #30594815

Subgroups — #30594815

Order 15616.

324 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 36 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#21460751C212yesmaximal
2#21445742C211yesmaximal, characteristic
3#16840658—22no—
4C23×Dic122C411yescharacteristic
5C2×#14519695—22no—
6#16839726C2211yescharacteristic
7C61×#407C411yescharacteristic
8#14519851—42no—
9C22×Dic122—21no—
10C22×Dic122—44no—
11C22×Dic122—41no—
12C22×Dic122—41no—
13C22×Dic122C812yes—
14C23×Dic61—21no—
15C2×#11758194D412yes—
16#14519695—44no—
17C22⋊#92418—41no—
18C23×C4×C61C2×C411yescharacteristic
19C2×M16×C61—21no—
20C22⋊C8×C61—41no—
21C24×C61M1611yescharacteristic
22C22×C4×C61—21no—
23C22×C4×C61—21no—
24C22×C4×C61—42no—
25C22×C4×C61C22⋊C411yescharacteristic
26C22×C4×C61C2×C811yescharacteristic
27C22×Dic61—22no—
28C22×Dic61—44no—
29C22×Dic61—42no—
30C2×Dic122—24no—
31C2×Dic122—42no—
32C2×Dic122—48no—
33C2×Dic122—44no—
34C2×Dic122—41no—
35C2×Dic122—41no—
36C2×Dic122—42no—
37C2×Dic122—44no—
38C2×Dic122—44no—
39M16×C61—42no—
40C2×C8×C61—41no—
41#11758194—42no—
42C2×#92418—22no—
43#11758187—82no—
44C23×C61—21no—
45C23×C61—41no—
46C23×C61—42no—
47C23×C61C22⋊C811yescharacteristic
48C2×C4×C61—22no—
49C2×C4×C61—21no—
50C2×C4×C61—42no—
51C2×C4×C61—42no—
52C2×C4×C61—41no—
53C2×C4×C61#9911yescharacteristic
54C2×C4×C61#10011yescharacteristic
55C2×Dic61—24no—
56C2×Dic61—42no—
57C2×Dic61—48no—
58C2×Dic61—42no—
59Dic122—44no—
60Dic122—44no—
61Dic122—44no—
62Dic122—44no—
63C8×C61—81no—
64#92418—42no—
65#7343—611nomaximal, Sylow
66C22×C61—22no—
67C22×C61—21no—
68C22×C61—41no—
69C22×C61—41no—
70C22×C61—42no—
71C22×C61—42no—
72C22×C61—41no—
73C22×C61#32311yescharacteristic
74C4×C61—21no—
75C4×C61—41no—
76C4×C61AΣL(1,𝔽16)12yes—
77Dic61—44no—
78#1784—611no—
79#1320—612no—
80C2×C61—21no—
81C2×C61—42no—
82C2×C61—41no—
83C2×C61#131611yescharacteristic
84C23×Q8—611no—
85C2×#101—1222no—
86#407—611no—
87#407#692311yescharacteristic
88#349—1222no—
89C61#734311yescharacteristic, complemented, Sylow
90C22×Q8—612no—
91C22×Q8—1221no—
92C22×Q8—2441no—
93C22×Q8—2441no—
94C22×Q8—2444no—
95C23×C4—1221no—
96C23×C4C2×#692311yescharacteristic
97C2×M16—21no—
98C2×M16—612no—
99M32—2442no—
100#101—2444no—
101C22⋊C8—41no—
102C22⋊C8—2441no—
103C24#1175821311yescharacteristic
104C2×Q8—1224no—
105C2×Q8—2442no—
106C2×Q8—2442no—
107C2×Q8—2444no—
108C2×Q8—2444no—
109C2×Q8—2448no—
110C2×Q8—2444no—
111C2×Q8—2441no—
112C2×Q8—2441no—
113C22×C4—21no—
114C22×C4—21no—
115C22×C4—42no—
116C22×C4—1222no—
117C22×C4—2444no—
118C22×C4—2442no—
119C22×C4D61⋊C811yescharacteristic
120C22×C4C22⋊#692311yescharacteristic
121M16—42no—
122M16—2442no—
123C2×C8—41no—
124C2×C8—1222no—
125C16—4882no—
126C23—21no—
127C23—41no—
128C23—42no—
129C23#1451983411yescharacteristic
130Q8—2444no—
131Q8—2444no—
132Q8—2444no—
133Q8—2444no—
134C2×C4—22no—
135C2×C4—21no—
136C2×C4—42no—
137C2×C4—42no—
138C2×C4—41no—
139C2×C4—1224no—
140C2×C4—2442no—
141C2×C4—2448no—
142C2×C4—2442no—
143C2×C4#1451983611yescharacteristic
144C2×C4#1451983711yescharacteristic
145C8—81no—
146C8—2442no—
147C22—22no—
148C22—21no—
149C22—41no—
150C22—41no—
151C22—42no—
152C22—42no—
153C22—41no—
154C22#1684060611yescharacteristic
155C4—21no—
156C4—41no—
157C4—2444no—
158C4#1684066312yes—
159C2—21no—
160C2—42no—
161C2—41no—
162C2#2146074411yescharacteristic
subgroupG/H
centerC2#21460744
commutatorC22×C4×C61C2×C8
FrattiniC23×C4C2×#6923
FittingC61×#407C4
socleC2×C61#1316
prime radicalC24×C61M16
cosocle#16839726C22
hypercenter#407#6923
hypocenterC61#7343
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
89. C61#7343semidirect

Maximal subgroups

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

subgroupindex
#214607512
#214457422
#734361