Finite Group Databasebeta

← #16845816

Subgroups — #16845816

Order 3968.

262 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 81 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#41×Dic31C211yesmaximal, characteristic
2#14521023C211yesmaximal, characteristic
3#14520810C212yesmaximal, complemented
4#14520806C212yesmaximal, complemented
5C31×#413C211yesmaximal, characteristic
6C2×#41×C31C2211yescharacteristic
7C2×M16×C31C2212yes—
8Q8×Dic31—21no—
9D4×Dic31—22no—
10D4×Dic31—21no—
11#11758503C412yescomplemented
12#11758503C2212yes—
13#11758503C2211yescharacteristic
14C2×C4×Dic31C412yescomplemented
15C2×C4×Dic31C2211yescharacteristic
16C31×#101—21no—
17C31×#100—21no—
18#11758422—22no—
19#41×C31—22no—
20#41×C31—22no—
21C2×Q8×C31D411yescharacteristic
22C2×D4×C31D412yes—
23C2×D4×C31D411yescharacteristic
24C22×C4×C31C2×C412yes—
25C22×C4×C31C2311yescharacteristic
26C22×Dic31—22no—
27C22×Dic31—21no—
28M16×C31—22no—
29M16×C31—22no—
30C2×C8×C31—22no—
31C22⋊Dic31—22no—
32C22⋊Dic31—21no—
33C22⋊Dic31—22no—
34C4⋊Dic31—22no—
35C4⋊Dic31—21no—
36C4⋊Dic31—22no—
37C4×Dic31—22no—
38C4×Dic31—21no—
39C4×Dic31—22no—
40C4×Dic31C2×C411yescharacteristic
41C4×Dic31C2×C412yes—
42C4×Dic31C2×C411yescharacteristic
43C23×C31C22⋊C412yes—
44C23×C31C2×D411yescharacteristic
45Q8×C31—22no—
46D4×C31—24no—
47D4×C31—22no—
48C2×C4×C31—22no—
49C2×C4×C31—22no—
50C2×C4×C31C22⋊C412yes—
51C2×C4×C31C22×C411yescharacteristic
52C2×C4×C31C2×D411yescharacteristic
53C2×C4×C31#4112yes—
54C2×C4×C31#4112yes—
55C2×Dic31—21no—
56C2×Dic31—22no—
57C2×Dic31—21no—
58C2×Dic31—42no—
59C2×Dic31—44no—
60C2×Dic31—42no—
61C8×C31—42no—
62#1827—311nomaximal, Sylow
63C22×C31—22no—
64C22×C31—41no—
65C22×C31—42no—
66C22×C31C2×C22⋊C411yescharacteristic
67C22×C31#12312yes—
68C4×C31—22no—
69C4×C31#11711yescharacteristic
70C4×C31#11711yescharacteristic
71C4×C31#12312yes—
72Dic31—22no—
73Dic31—42no—
74Dic31—41no—
75Dic31—82no—
76C4×#41—311no—
77#413D3111yescharacteristic
78#410—311no—
79#339—312no—
80H(3,ℤ/4)—312no—
81C2×C31—21no—
82C2×C31—22no—
83C2×C31—42no—
84C2×C31#38111yescharacteristic
85C2×#41C2×D3111yescharacteristic
86C2×M16C2×D3112yes—
87C4×Q8—621no—
88C4×D4—622no—
89C4×D4—621no—
90#117—312no—
91#117—311no—
92#117—312no—
93C2×C42—312no—
94C2×C42—311no—
95#101—21no—
96#100—21no—
97#99—622no—
98C31#182711yescharacteristic, complemented, Sylow
99#41—22no—
100#41—22no—
101C2×Q8C22⋊D3111yescharacteristic
102C2×D4D12412yes—
103C2×D4C22⋊D3111yescharacteristic
104C22×C4—622no—
105C22×C4—621no—
106C22×C4C4×D3112yes—
107C22×C4C22×D3111yescharacteristic
108M16—22no—
109M16—22no—
110C2×C8—22no—
111C4⋊C4—622no—
112C4⋊C4—621no—
113C4⋊C4—622no—
114C22⋊C4—622no—
115C22⋊C4—621no—
116C22⋊C4—622no—
117C42—311no—
118C42—312no—
119C42—311no—
120C42—622no—
121C42—621no—
122C42—622no—
123C23(C2×D31)⋊C412yes—
124C23C2×D12411yescharacteristic
125Q8—22no—
126D4—24no—
127D4—22no—
128C2×C4—22no—
129C2×C4—22no—
130C2×C4—621no—
131C2×C4—622no—
132C2×C4—621no—
133C2×C4—1242no—
134C2×C4—1244no—
135C2×C4—1242no—
136C2×C4(C2×D31)⋊C412yes—
137C2×C4C2×C4×D3111yescharacteristic
138C2×C4#9249712yes—
139C2×C4#9249712yes—
140C2×C4C2×C22⋊D3111yescharacteristic
141C8—42no—
142C22—22no—
143C22—41no—
144C22—42no—
145C22#1175846312yes—
146C22C2×(C2×D31)⋊C411yescharacteristic
147C4—22no—
148C4—622no—
149C4—1242no—
150C4—1241no—
151C4—2482no—
152C4#1175845411yescharacteristic
153C4#1175845411yescharacteristic
154C4#1175851212yes—
155C2—21no—
156C2—22no—
157C2—42no—
158C2#1452091011yescharacteristic
subgroupG/H
centerC4#11758454
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#413C2
socleC2×C31#381
prime radicalC2×#41×C31C22
cosocleC22×C4×C31C23
hypercenter#413D31
hypocenterC31#1827
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
3. #14520810C2semidirect
4. #14520806C2semidirect
11. #11758503C4semidirect
14. C2×C4×Dic31C4semidirect
98. C31#1827semidirect

Maximal subgroups

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

subgroupindex
#41×Dic312
#145210232
#145208102
#145208062
C31×#4132
#182731