Finite Group Databasebeta

← #16844719

Subgroups — #16844719

Order 3968.

210 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 57 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#14521377C212yesmaximal
2#14520979C211yesmaximal, characteristic
3#14520786C212yesmaximal
4#14520775C211yesmaximal, characteristic
5C31×#544C211yesmaximal, characteristic
6C31×C4⋊Q8—22no—
7C31×#125—22no—
8C31×C22⋊Q8—21no—
9C31×C22⋊Q8C2212yes—
10C31×#117—21no—
11C2×C4⋊C4×C31C2211yescharacteristic
12C2×C4⋊Dic31C2211yescharacteristic
13C2×Dic31⋊C4—21no—
14#11758423—22no—
15C31⋊#95—21no—
16C31⋊#95C2211yescharacteristic
17C22⋊(C31⋊C8)C2212yes—
18#11758396—22no—
19C2×Q8×C31—21no—
20C2×Q8×C31D412yes—
21C22×C4×C31D411yescharacteristic
22C22×C4×C31D411yescharacteristic
23C22×C4×C31C2311yescharacteristic
24C22×Dic31—21no—
25C22×Dic31—21no—
26C4⋊C4×C31—21no—
27C4⋊C4×C31—21no—
28C4⋊C4×C31—21no—
29C4⋊C4×C31—22no—
30C4⋊C4×C31—22no—
31C4⋊C4×C31—22no—
32C4⋊C4×C31D412yes—
33C22⋊C4×C31—22no—
34C42×C31—22no—
35C4⋊Dic31—22no—
36Dic31⋊C4—42no—
37C2×C31⋊C8—22no—
38C23×C31C2×D411yescharacteristic
39Q8×C31—42no—
40Q8×C31—81no—
41C2×C4×C31—21no—
42C2×C4×C31—21no—
43C2×C4×C31—22no—
44C2×C4×C31—22no—
45C2×C4×C31—21no—
46C2×C4×C31—41no—
47C2×C4×C31—41no—
48C2×C4×C31SD1612yes—
49C2×C4×C31C2×D412yes—
50C2×Dic31—22no—
51C2×Dic31—41no—
52C2×Dic31—41no—
53C2×Dic31—41no—
54C2×Dic31—41no—
55C2×Dic31—41no—
56C31⋊C8—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—42no—
66C4×C31—41no—
67C4×C31—42no—
68Dic31—42no—
69Dic31—81no—
70#544D3111yescharacteristic
71#483—312no—
72#398—311no—
73#328—312no—
74#324—311no—
75C2×C31—21no—
76C2×C31—21no—
77C2×C31#44811yescharacteristic
78C2×C31#45611yescharacteristic
79C2×C31#45811yescharacteristic
80C4⋊Q8—22no—
81#125—22no—
82C22⋊Q8—21no—
83C22⋊Q8C2×D3112yes—
84#117—21no—
85C2×C4⋊C4—311no—
86C2×C4⋊C4—621no—
87C2×C4⋊C4C2×D3111yescharacteristic
88#106—622no—
89#103—622no—
90C22⋊C8—312no—
91#95—311no—
92#95—621no—
93C31#161111yescharacteristic, complemented, Sylow
94C2×Q8—21no—
95C2×Q8C22⋊D3112yes—
96C22×C4—621no—
97C22×C4—621no—
98C22×C4C22⋊D3111yescharacteristic
99C22×C4C22⋊D3111yescharacteristic
100C22×C4C22×D3111yescharacteristic
101C2×C8—622no—
102C4⋊C4—21no—
103C4⋊C4—21no—
104C4⋊C4—21no—
105C4⋊C4—22no—
106C4⋊C4—22no—
107C4⋊C4—22no—
108C4⋊C4—622no—
109C4⋊C4—1242no—
110C4⋊C4C22⋊D3112yes—
111C22⋊C4—22no—
112C42—22no—
113C23C2×C22⋊D3111yescharacteristic
114Q8—42no—
115Q8—81no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—22no—
119C2×C4—22no—
120C2×C4—21no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—622no—
124C2×C4—1241no—
125C2×C4—1241no—
126C2×C4—1241no—
127C2×C4—1241no—
128C2×C4—1241no—
129C2×C4#9248112yes—
130C2×C4C2×C22⋊D3112yes—
131C8—1242no—
132C22—21no—
133C22—21no—
134C22C2×#9248111yescharacteristic
135C22#1175851911yescharacteristic
136C22#1175853011yescharacteristic
137C4—22no—
138C4—22no—
139C4—42no—
140C4—41no—
141C4—42no—
142C4—1242no—
143C4—2481no—
144C2—21no—
145C2—21no—
146C2#1452118811yescharacteristic
147C2#1452123211yescharacteristic
148C2#1452123911yescharacteristic
subgroupG/H
centerC22#11758530
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC31×#544C2
socleC22×C31#120
prime radicalC23×C31C2×D4
hypercenter#544D31
hypocenterC31#1611
LCSG ▷ C22×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

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
#145213772
#145209792
#145207862
#145207752
C31×#5442
#161131