Finite Group Databasebeta

← #16846879

Subgroups — #16846879

Order 3968.

290 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 67 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#14521675C211yesmaximal, characteristic
2#14520910C211yesmaximal, characteristic
3#14520910C212yesmaximal
4#14520815C212yesmaximal
5C31×#342C211yesmaximal, characteristic
6C23×Dic31C2211yescharacteristic
7C2×C22⋊C4×C31C2212yes—
8C2×C22⋊C4×C31C2211yescharacteristic
9C2×C22⋊Dic31C2211yescharacteristic
10C2×C22⋊Dic31C2212yes—
11#11758501—22no—
12#11758455—24no—
13C31⋊#95—22no—
14C31⋊#95—24no—
15C24×C31C2311yescharacteristic
16C22×C4×C31—22no—
17C22×C4×C31D412yes—
18C22×Dic31—21no—
19C22×Dic31—22no—
20C22×Dic31—22no—
21C22×Dic31—21no—
22C22×Dic31—21no—
23C22×Dic31D414yes—
24C22×Dic31Q812yescomplemented
25C2×Dic62—22no—
26C22⋊C4×C31—22no—
27C22⋊C4×C31—22no—
28C22⋊C4×C31—22no—
29C22⋊Dic31—22no—
30C22⋊Dic31—22no—
31C22⋊Dic31—22no—
32C4⋊Dic31—22no—
33Dic31⋊C4—24no—
34C23×C31—42no—
35C23×C31C2×D411yescharacteristic
36C23×C31C2×D412yes—
37C23×C31C2×Q811yescharacteristic
38C23×C31#4112yes—
39C23×C31#4111yescharacteristic
40C2×C4×C31—22no—
41C2×C4×C31—42no—
42C2×C4×C31—44no—
43C2×C4×C31—42no—
44C2×Dic31—24no—
45C2×Dic31—24no—
46C2×Dic31—22no—
47C2×Dic31—41no—
48C2×Dic31—41no—
49C2×Dic31—42no—
50C2×Dic31—44no—
51C2×Dic31—42no—
52C2×Dic31—41no—
53Dic62—82no—
54#2030—311nomaximal, Sylow
55C22×C31—22no—
56C22×C31—24no—
57C22×C31—41no—
58C22×C31—42no—
59C22×C31—41no—
60C22×C31#12011yescharacteristic
61C22×C31C22⋊Q812yes—
62C22×C31C22⋊Q811yescharacteristic
63C22×C31#12411yescharacteristic
64C22×C31#12412yes—
65C4×C31—42no—
66C4×C31—82no—
67Dic31—42no—
68Dic31—44no—
69Dic31—81no—
70#543—311no—
71#381—312no—
72#381—311no—
73#342—312no—
74#342D3111yescharacteristic
75C2×C31—21no—
76C2×C31—22no—
77C2×C31—22no—
78C2×C31—21no—
79C2×C31#39311yescharacteristic
80C2×C31#45812yes—
81C23×C4—311no—
82C22⋊Q8—624no—
83C22⋊Q8—622no—
84C2×C22⋊C4—312no—
85C2×C22⋊C4—311no—
86C2×C22⋊C4C2×D3112yes—
87C2×C22⋊C4C2×D3111yescharacteristic
88#95—624no—
89#95—622no—
90C31#203011yescharacteristic, complemented, Sylow
91C24C22×D3111yescharacteristic
92C2×Q8—622no—
93C22×C4—22no—
94C22×C4—312no—
95C22×C4—314no—
96C22×C4—621no—
97C22×C4—622no—
98C22×C4—622no—
99C22×C4—621no—
100C22×C4—621no—
101C22×C4D12412yes—
102C4⋊C4—624no—
103C4⋊C4—622no—
104C22⋊C4—22no—
105C22⋊C4—22no—
106C22⋊C4—22no—
107C22⋊C4—622no—
108C22⋊C4—622no—
109C22⋊C4—622no—
110C23—42no—
111C23C2×D12411yescharacteristic
112C23#9249512yes—
113C23D4×D3112yes—
114C23#9249711yescharacteristic
115C23Q8×D3111yescharacteristic
116Q8—2482no—
117C2×C4—22no—
118C2×C4—42no—
119C2×C4—44no—
120C2×C4—42no—
121C2×C4—624no—
122C2×C4—624no—
123C2×C4—622no—
124C2×C4—1241no—
125C2×C4—1241no—
126C2×C4—1242no—
127C2×C4—1244no—
128C2×C4—1242no—
129C2×C4—1241no—
130C22—22no—
131C22—24no—
132C22—42no—
133C22—41no—
134C22—41no—
135C22#1175845211yescharacteristic
136C22#1175845911yescharacteristic
137C22#1175846212yes—
138C22#1175847312yes—
139C22#1175847411yescharacteristic
140C4—42no—
141C4—82no—
142C4—1242no—
143C4—1244no—
144C4—2481no—
145C2—22no—
146C2—21no—
147C2—22no—
148C2—21no—
149C2#1452096211yescharacteristic
150C2#1452124012yes—
subgroupG/H
centerC22#11758459
commutator, prime radical, cosocleC24×C31C23
FrattiniC24C22×D31
FittingC31×#342C2
socleC22×C31#120
hypercenter#342D31
hypocenterC31#2030
LCSG ▷ C24×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
24. C22×Dic31Q8semidirect
90. C31#2030semidirect

Maximal subgroups

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

subgroupindex
#145216752
#145209102
#145208152
C31×#3422
#203031