Finite Group Databasebeta

← #16844721

Subgroups — #16844721

Order 3968.

210 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 53 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#14521380C212yesmaximal
3#14520979C211yesmaximal, characteristic
4#14520787C212yesmaximal
5C31×#324C211yesmaximal, characteristic
6C2×C4⋊C4×C31C2211yescharacteristic
7#11758503—21no—
8C2×C4⋊Dic31C2211yescharacteristic
9#11758501—21no—
10#11758501C2212yes—
11C2×Dic31⋊C4—21no—
12#11758467—22no—
13#11758465—22no—
14C31×C22⋊C8C2212yes—
15C31⋊#95—21no—
16C31⋊#95C2211yescharacteristic
17#11758405—22no—
18#11758404—22no—
19C22×C4×C31D411yescharacteristic
20C22×C4×C31D411yescharacteristic
21C22×C4×C31C2311yescharacteristic
22C22×Dic31—21no—
23C22×Dic31—21no—
24C2×Dic62—21no—
25C2×Dic62D412yes—
26C2×C8×C31—22no—
27C4⋊C4×C31—22no—
28C22⋊Dic31—22no—
29C4⋊Dic31—21no—
30C4⋊Dic31—21no—
31C4⋊Dic31—21no—
32C4⋊Dic31—22no—
33C4⋊Dic31D412yes—
34Dic31⋊C4—22no—
35Dic31⋊C4—22no—
36Dic31⋊C4—42no—
37C4×Dic31—22no—
38C23×C31C2×D411yescharacteristic
39C2×C4×C31—21no—
40C2×C4×C31—21no—
41C2×C4×C31—21no—
42C2×C4×C31—41no—
43C2×C4×C31—41no—
44C2×C4×C31SD1612yes—
45C2×C4×C31C2×D412yes—
46C2×Dic31—22no—
47C2×Dic31—22no—
48C2×Dic31—22no—
49C2×Dic31—41no—
50C2×Dic31—41no—
51C2×Dic31—41no—
52C2×Dic31—41no—
53C2×Dic31—41no—
54Dic62—42no—
55Dic62—81no—
56C8×C31—42no—
57#1611—311nomaximal, Sylow
58C22×C31—21no—
59C22×C31—21no—
60C22×C31#12011yescharacteristic
61C22×C31C2×SD1611yescharacteristic
62C22×C31#13711yescharacteristic
63C4×C31—22no—
64C4×C31—22no—
65C4×C31—41no—
66Dic31—42no—
67Dic31—42no—
68Dic31—42no—
69Dic31—81no—
70#544—311no—
71#483—312no—
72#398—311no—
73#328—312no—
74#324D3111yescharacteristic
75C2×C31—21no—
76C2×C31—21no—
77C2×C31#44811yescharacteristic
78C2×C31#45611yescharacteristic
79C2×C31#45811yescharacteristic
80C4⋊Q8—622no—
81#125—622no—
82C22⋊Q8—312no—
83C22⋊Q8—621no—
84#117—621no—
85C2×C4⋊C4—311no—
86C2×C4⋊C4—621no—
87C2×C4⋊C4C2×D3111yescharacteristic
88#106—622no—
89#103—622no—
90C22⋊C8C2×D3112yes—
91#95—311no—
92#95—621no—
93C31#161111yescharacteristic, complemented, Sylow
94C2×Q8—312no—
95C2×Q8—621no—
96C22×C4—621no—
97C22×C4—621no—
98C22×C4D12411yescharacteristic
99C22×C4D12411yescharacteristic
100C22×C4C22×D3111yescharacteristic
101C2×C8—22no—
102C4⋊C4—22no—
103C4⋊C4—312no—
104C4⋊C4—622no—
105C4⋊C4—621no—
106C4⋊C4—621no—
107C4⋊C4—621no—
108C4⋊C4—622no—
109C4⋊C4—622no—
110C4⋊C4—1242no—
111C22⋊C4—622no—
112C42—622no—
113C23C2×D12411yescharacteristic
114Q8—1242no—
115Q8—2481no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—21no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—622no—
122C2×C4—622no—
123C2×C4—622no—
124C2×C4—1241no—
125C2×C4—1241no—
126C2×C4—1241no—
127C2×C4—1241no—
128C2×C4—1241no—
129C2×C4#9247012yes—
130C2×C4D4×D3112yes—
131C8—42no—
132C22—21no—
133C22—21no—
134C22#1175845911yescharacteristic
135C22C2×#9247011yescharacteristic
136C22#1175848611yescharacteristic
137C4—22no—
138C4—22no—
139C4—41no—
140C4—1242no—
141C4—1242no—
142C4—1242no—
143C4—2481no—
144C2—21no—
145C2—21no—
146C2#1452119011yescharacteristic
147C2#1452123411yescharacteristic
148C2#1452124011yescharacteristic
subgroupG/H
centerC22#11758459
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC31×#324C2
socleC22×C31#120
prime radicalC23×C31C2×D4
hypercenter#324D31
hypocenterC31#1611
LCSG ▷ C22×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
93. C31#1611semidirect

Maximal subgroups

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

subgroupindex
#145216802
#145213802
#145209792
#145207872
C31×#3242
#161131