Finite Group Databasebeta

← #16846878

Subgroups — #16846878

Order 3968.

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

normal subgroups only

This group has 290 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
1#14521675C211yesmaximal, characteristic
2#14520912C212yesmaximal
3#14520816C211yesmaximal, characteristic
4#14520815C212yesmaximal
5C31×#381C211yesmaximal, characteristic
6C23×C4×C31C2211yescharacteristic
7C2×C22⋊C4×C31C2211yescharacteristic
8C2×C22⋊C4×C31C2211yescharacteristic
9C2×C22⋊Dic31C2212yes—
10C2×C22⋊Dic31C2212yes—
11#11758501—22no—
12#11758455—24no—
13C31×#95—22no—
14C31⋊#95—24no—
15C24×C31C2311yescharacteristic
16C22×C4×C31—22no—
17C22×C4×C31—21no—
18C22×C4×C31—21no—
19C22×C4×C31—22no—
20C22×C4×C31—21no—
21C22×C4×C31D412yes—
22C22×C4×C31Q812yescomplemented
23C22×Dic31—22no—
24C22×Dic31D414yes—
25C2×Dic62—22no—
26C22⋊C4×C31—22no—
27C22⋊C4×C31—22no—
28C22⋊Dic31—22no—
29C22⋊Dic31—22no—
30C22⋊Dic31—22no—
31C22⋊Dic31—22no—
32C4⋊Dic31—22no—
33Dic31⋊C4—24no—
34C23×C31—42no—
35C23×C31C2×D412yes—
36C23×C31C2×D411yescharacteristic
37C23×C31C2×Q811yescharacteristic
38C23×C31#4111yescharacteristic
39C23×C31#4112yes—
40C2×C4×C31—22no—
41C2×C4×C31—24no—
42C2×C4×C31—22no—
43C2×C4×C31—41no—
44C2×C4×C31—42no—
45C2×C4×C31—41no—
46C2×C4×C31—42no—
47C2×C4×C31—42no—
48C2×C4×C31—41no—
49C2×Dic31—24no—
50C2×Dic31—44no—
51C2×Dic31—44no—
52C2×Dic31—42no—
53Dic62—82no—
54#2030—311nomaximal, Sylow
55C22×C31—24no—
56C22×C31—22no—
57C22×C31—41no—
58C22×C31—41no—
59C22×C31—42no—
60C22×C31#12011yescharacteristic
61C22×C31C22⋊Q812yes—
62C22×C31C22⋊Q811yescharacteristic
63C22×C31#12412yes—
64C22×C31#12411yescharacteristic
65C4×C31—42no—
66C4×C31—42no—
67C4×C31—81no—
68Dic31—44no—
69Dic31—82no—
70#543—311no—
71#381—312no—
72#381D3111yescharacteristic
73#342—312no—
74#342—311no—
75C2×C31—22no—
76C2×C31—21no—
77C2×C31—22no—
78C2×C31—21no—
79C2×C31#39311yescharacteristic
80C2×C31#45812yes—
81C23×C4C2×D3111yescharacteristic
82C22⋊Q8—624no—
83C22⋊Q8—622no—
84C2×C22⋊C4—312no—
85C2×C22⋊C4—312no—
86C2×C22⋊C4C2×D3111yescharacteristic
87C2×C22⋊C4C2×D3111yescharacteristic
88#95—22no—
89#95—624no—
90C31#203011yescharacteristic, complemented, Sylow
91C24C22×D3111yescharacteristic
92C2×Q8—622no—
93C22×C4—21no—
94C22×C4—22no—
95C22×C4—22no—
96C22×C4—21no—
97C22×C4—21no—
98C22×C4—314no—
99C22×C4—622no—
100C22×C4Dic6212yescomplemented
101C22×C4C22⋊D3112yes—
102C4⋊C4—624no—
103C4⋊C4—622no—
104C22⋊C4—22no—
105C22⋊C4—22no—
106C22⋊C4—622no—
107C22⋊C4—622no—
108C22⋊C4—622no—
109C22⋊C4—622no—
110C23—42no—
111C23C2×Dic6211yescharacteristic
112C23#9249511yescharacteristic
113C23D4×D3112yes—
114C23#9249712yes—
115C23C2×C22⋊D3111yescharacteristic
116Q8—2482no—
117C2×C4—24no—
118C2×C4—22no—
119C2×C4—22no—
120C2×C4—42no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—42no—
124C2×C4—42no—
125C2×C4—41no—
126C2×C4—624no—
127C2×C4—1244no—
128C2×C4—1244no—
129C2×C4—1242no—
130C22—22no—
131C22—24no—
132C22—41no—
133C22—41no—
134C22—42no—
135C22#1175845512yes—
136C22#1175846212yes—
137C22#1175850111yescharacteristic
138C22#1175851311yescharacteristic
139C22#1175851411yescharacteristic
140C4—42no—
141C4—42no—
142C4—81no—
143C4—1244no—
144C4—2482no—
145C2—21no—
146C2—22no—
147C2—22no—
148C2—21no—
149C2#1452096111yescharacteristic
150C2#1452123812yes—
subgroupG/H
centerC22#11758514
commutator, prime radical, cosocleC24×C31C23
FrattiniC24C22×D31
FittingC31×#381C2
socleC22×C31#120
hypercenter#381D31
hypocenterC31#2030
LCSG ▷ C24×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C24 ◁ #381

Complements

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

NH ≅ G/Ntype
22. C22×C4×C31Q8semidirect
90. C31#2030semidirect
100. C22×C4Dic62semidirect

Maximal subgroups

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

subgroupindex
#145216752
#145209122
#145208162
#145208152
C31×#3812
#203031