Finite Group Databasebeta

← #16846873

Subgroups — #16846873

Order 3968.

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

normal subgroups only

This group has 246 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#14521680C211yesmaximal, characteristic
2#14521059C212yesmaximal
3#14520954C211yesmaximal, characteristic
4#14520810C212yesmaximal
5C31×#343C211yesmaximal, characteristic
6C22×Dic62C2211yescharacteristic
7C2×M16×C31C2212yes—
8C2×C4⋊C4×C31C2211yescharacteristic
9#11758503C2212yes—
10#11758501—22no—
11C2×C4×Dic31C2211yescharacteristic
12#11758467—22no—
13#11758465—22no—
14C31⋊#95—22no—
15#11758404—22no—
16#11758404—22no—
17C22×C4×C31D412yes—
18C22×C4×C31C2311yescharacteristic
19C22×Dic31—21no—
20C22×Dic31—21no—
21C2×Dic62—22no—
22C2×Dic62—22no—
23C2×Dic62—21no—
24C2×Dic62—22no—
25C2×Dic62Q812yescomplemented
26M16×C31—22no—
27M16×C31—22no—
28C2×C8×C31—22no—
29C4⋊C4×C31—22no—
30C22⋊Dic31—22no—
31C4⋊Dic31—22no—
32C4⋊Dic31D412yes—
33C4⋊Dic31D412yes—
34Dic31⋊C4—24no—
35C4×Dic31—22no—
36C4×Dic31—22no—
37C23×C31C2×D411yescharacteristic
38C2×C4×C31—22no—
39C2×C4×C31—42no—
40C2×C4×C31C2×D412yes—
41C2×C4×C31C2×Q811yescharacteristic
42C2×C4×C31#4112yes—
43C2×C4×C31#4111yescharacteristic
44C2×Dic31—22no—
45C2×Dic31—22no—
46C2×Dic31—22no—
47C2×Dic31—22no—
48C2×Dic31—41no—
49C2×Dic31—41no—
50C2×Dic31—41no—
51C2×Dic31—41no—
52Dic62—24no—
53Dic62—42no—
54Dic62—82no—
55C8×C31—42no—
56#2028—311nomaximal, Sylow
57C22×C31—21no—
58C22×C31—21no—
59C22×C31#12011yescharacteristic
60C22×C31C22⋊Q811yescharacteristic
61C22×C31#12411yescharacteristic
62C4×C31—42no—
63C4×C31C22⋊Q812yes—
64C4×C31#12412yes—
65Dic31—42no—
66Dic31—42no—
67Dic31—42no—
68Dic31—42no—
69#544—311no—
70#419—312no—
71#391—311no—
72#343D3111yescharacteristic
73#339—312no—
74C2×C31—21no—
75C2×C31—21no—
76C2×C31#39311yescharacteristic
77C2×C31#45511yescharacteristic
78C2×C31#45611yescharacteristic
79C22×Q8—311no—
80C2×M16C2×D3112yes—
81C4⋊Q8—622no—
82#125—622no—
83C22⋊Q8—622no—
84#117—312no—
85C2×C4⋊C4C2×D3111yescharacteristic
86C2×C42—311no—
87#103—622no—
88#103—622no—
89#95—622no—
90C31#202811yescharacteristic, complemented, Sylow
91C2×Q8—312no—
92C2×Q8—622no—
93C2×Q8—621no—
94C2×Q8—622no—
95C2×Q8—622no—
96C22×C4—621no—
97C22×C4—621no—
98C22×C4D12412yes—
99C22×C4C22×D3111yescharacteristic
100M16—22no—
101M16—22no—
102C2×C8—22no—
103C4⋊C4—22no—
104C4⋊C4—312no—
105C4⋊C4—312no—
106C4⋊C4—624no—
107C4⋊C4—622no—
108C22⋊C4—622no—
109C42—622no—
110C42—622no—
111C23C2×D12411yescharacteristic
112Q8—624no—
113Q8—1242no—
114Q8—2482no—
115C2×C4—22no—
116C2×C4—42no—
117C2×C4—622no—
118C2×C4—622no—
119C2×C4—622no—
120C2×C4—622no—
121C2×C4—1241no—
122C2×C4—1241no—
123C2×C4—1241no—
124C2×C4—1241no—
125C2×C4#9249512yes—
126C2×C4D4×D3112yes—
127C2×C4#9249711yescharacteristic
128C2×C4Q8×D3111yescharacteristic
129C8—42no—
130C22—21no—
131C22—21no—
132C22#1175845211yescharacteristic
133C22#1175845911yescharacteristic
134C22#1175847411yescharacteristic
135C4—42no—
136C4—1242no—
137C4—1242no—
138C4—1242no—
139C4—1242no—
140C4#1175846212yes—
141C4#1175847312yes—
142C2—21no—
143C2—21no—
144C2#1452096211yescharacteristic
145C2#1452122911yescharacteristic
146C2#1452123411yescharacteristic
subgroupG/H
centerC22#11758459
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC31×#343C2
socleC22×C31#120
prime radicalC23×C31C2×D4
hypercenter#343D31
hypocenterC31#2028
LCSG ▷ C22×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
25. C2×Dic62Q8semidirect
90. C31#2028semidirect

Maximal subgroups

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

subgroupindex
#145216802
#145210592
#145209542
#145208102
C31×#3432
#202831