Finite Group Databasebeta

← #16844053

Subgroups — #16844053

Order 3968.

236 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 69 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
1C2×#11758464C211yesmaximal, characteristic
2#14521103C212yesmaximal
3#14520775C211yesmaximal, characteristic
4#14520774C212yesmaximal
5C31×#324C211yesmaximal, characteristic
6C22×Dic62C411yescharacteristic
7C2×C4⋊C4×C31C2211yescharacteristic
8C2×Dic31⋊C4C411yescharacteristic
9C2×Dic31⋊C4C2211yescharacteristic
10C2×C4×Dic31C411yescharacteristic
11C2×C4×Dic31C411yescharacteristic
12C2×C4×Dic31C2211yescharacteristic
13#11758464—22no—
14#11758464—22no—
15C31×C22⋊C8C2212yes—
16C22⋊(C31⋊C8)C2212yes—
17#11758403—22no—
18Dic31⋊C8—22no—
19C22×C4×C31C2×C411yescharacteristic
20C22×C4×C31C2×C411yescharacteristic
21C22×C4×C31C2311yescharacteristic
22C22×Dic31C2×C411yescharacteristic
23C22×Dic31C2×C411yescharacteristic
24C22×Dic31C2×C411yescharacteristic
25C22×Dic31C2×C411yescharacteristic
26C2×Dic62—22no—
27C2×Dic62—22no—
28C2×Dic62—22no—
29C2×C8×C31—22no—
30C4⋊C4×C31—22no—
31Dic31⋊C4—22no—
32Dic31⋊C4—22no—
33C4×Dic31—21no—
34C4×Dic31—21no—
35C4×Dic31—21no—
36C4×Dic31—21no—
37C4×Dic31D412yes—
38C4×Dic31D412yes—
39C2×C31⋊C8—22no—
40C23×C31C22×C411yescharacteristic
41C2×C4×C31—21no—
42C2×C4×C31—21no—
43C2×C4×C31—21no—
44C2×C4×C31—41no—
45C2×C4×C31—41no—
46C2×C4×C31M1612yes—
47C2×C4×C31C2×D412yes—
48C2×Dic31—21no—
49C2×Dic31—21no—
50C2×Dic31—21no—
51C2×Dic31—21no—
52C2×Dic31—22no—
53C2×Dic31—21no—
54C2×Dic31—41no—
55C2×Dic31C22⋊C411yescharacteristic
56C2×Dic31C22⋊C412yes—
57C2×Dic31C22⋊C411yescharacteristic
58C2×Dic31M1612yes—
59Dic62—28no—
60C8×C31—42no—
61C31⋊C8—42no—
62#1467—311nomaximal, Sylow
63C22×C31—21no—
64C22×C31—21no—
65C22×C31C2×C22⋊C411yescharacteristic
66C22×C31C2×M1611yescharacteristic
67C22×C31C2×M1611yescharacteristic
68C4×C31—22no—
69C4×C31—22no—
70C4×C31—41no—
71Dic31—22no—
72Dic31—22no—
73Dic31—21no—
74Dic31—41no—
75Dic31#10112yes—
76C2×C4×Q8—311no—
77#432—312no—
78#324—311no—
79#324—312no—
80#324D3111yescharacteristic
81C2×C31—21no—
82C2×C31—21no—
83C2×C31#40711yescharacteristic
84C2×C31#41011yescharacteristic
85C2×C31C2×#10111yescharacteristic
86C22×Q8—311no—
87C4×Q8—622no—
88C4×Q8—622no—
89C2×C4⋊C4—311no—
90C2×C4⋊C4—311no—
91C2×C4⋊C4C2×D3111yescharacteristic
92C2×C42—311no—
93C2×C42—311no—
94C2×C42—311no—
95C4⋊C8—622no—
96C22⋊C8—312no—
97C22⋊C8C2×D3112yes—
98#97—622no—
99C31#146711yescharacteristic, complemented, Sylow
100C2×Q8—622no—
101C2×Q8—622no—
102C2×Q8—622no—
103C22×C4—311no—
104C22×C4—311no—
105C22×C4—311no—
106C22×C4—311no—
107C22×C4C4×D3111yescharacteristic
108C22×C4C4×D3111yescharacteristic
109C22×C4C22×D3111yescharacteristic
110C2×C8—22no—
111C2×C8—622no—
112C4⋊C4—22no—
113C4⋊C4—622no—
114C4⋊C4—622no—
115C42—312no—
116C42—312no—
117C42—621no—
118C42—621no—
119C42—621no—
120C42—621no—
121C23C2×C4×D3111yescharacteristic
122Q8—628no—
123C2×C4—21no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—41no—
127C2×C4—41no—
128C2×C4—311no—
129C2×C4—311no—
130C2×C4—312no—
131C2×C4—312no—
132C2×C4—622no—
133C2×C4—621no—
134C2×C4—621no—
135C2×C4—621no—
136C2×C4—621no—
137C2×C4—621no—
138C2×C4—1241no—
139C2×C4#9246912yes—
140C2×C4D4×D3112yes—
141C8—42no—
142C8—1242no—
143C22—21no—
144C22—21no—
145C22C22⋊C4×D3111yescharacteristic
146C22C2×#9246911yescharacteristic
147C22M16×D3111yescharacteristic
148C4—22no—
149C4—22no—
150C4—41no—
151C4—312no—
152C4—622no—
153C4—622no—
154C4—621no—
155C4—1241no—
156C2—21no—
157C2—21no—
158C2#1452101111yescharacteristic
159C2#1452102111yescharacteristic
160C2#101×D3111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D31
commutator, prime radicalC23×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#324C2
socleC22×C31C2×C22⋊C4
cosocleC22×C4×C31C23
hypercenter#324D31
hypocenterC31#1467
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
99. C31#1467semidirect

Maximal subgroups

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

subgroupindex
C2×#117584642
#145211032
#145207752
#145207742
C31×#3242
#146731