Finite Group Databasebeta

← #16845790

Subgroups — #16845790

Order 3968.

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

normal subgroups only

This group has 316 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
1C2×C4⋊C4×D31C211yesmaximal, characteristic
2#14521012C212yesmaximal
3#14520818C211yesmaximal, characteristic, complemented
4#14520817C212yesmaximal, complemented
5C31×#343C211yesmaximal, characteristic, complemented
6C22×C4×D31C412yes—
7C22×C4×D31C2211yescharacteristic
8C2×M16×C31C2212yes—
9C2×C4⋊C4×C31C2211yescharacteristic
10C2×C4⋊Dic31C2211yescharacteristic
11C2×Dic31⋊C4C412yes—
12C2×#92474C2212yes—
13C4⋊C4×D31—22no—
14C4⋊C4×D31—22no—
15(C2×D31)⋊C8—22no—
16(C2×D31)⋊C8—22no—
17C23×D31C2×C411yescharacteristic
18C22×C4×C31C2×C412yes—
19C22×C4×C31C2311yescharacteristic
20C22×Dic31C2×C411yescharacteristic
21C22×Dic31C2×C412yes—
22C2×C4×D31—22no—
23C2×C4×D31—21no—
24C2×C4×D31—21no—
25C2×C4×D31—22no—
26C2×C4×D31—22no—
27C2×C4×D31—44no—
28C2×C4×D31D412yes—
29C2×C4×D31D412yes—
30M16×C31—22no—
31M16×C31—22no—
32C2×C8×C31—22no—
33C4⋊C4×C31—22no—
34C4⋊Dic31—22no—
35Dic31⋊C4—24no—
36#92474—22no—
37#92474—22no—
38C2×C31⋊C8—22no—
39C23×C31C22×C411yescharacteristic
40C22×D31—21no—
41C22×D31—21no—
42C22×D31—22no—
43C22×D31—22no—
44C22×D31C22⋊C411yescharacteristic
45C22×D31C22⋊C411yescharacteristic
46C2×C4×C31—22no—
47C2×C4×C31—42no—
48C2×C4×C31C2×D412yes—
49C2×C4×C31#4112yes—
50C2×C4×C31#4111yescharacteristic
51C2×C4×C31#4111yescharacteristic
52C2×Dic31—21no—
53C2×Dic31—21no—
54C2×Dic31—22no—
55C2×Dic31—42no—
56C2×Dic31C22⋊C412yes—
57C4×D31—22no—
58C4×D31—22no—
59C4×D31—22no—
60C4×D31—22no—
61C4×D31—44no—
62C4×D31—44no—
63C8×C31—42no—
64C31⋊C8—42no—
65#1821—311nomaximal, Sylow
66C22×C31—21no—
67C22×C31—21no—
68C22×C31C2×C22⋊C411yescharacteristic
69C22×C31#11711yescharacteristic
70C22×C31#11711yescharacteristic
71C2×D31—24no—
72C2×D31—24no—
73C2×D31—21no—
74C2×D31—21no—
75C2×D31—21no—
76C2×D31—21no—
77C2×D31#10012yes—
78C2×D31#10112yes—
79C4×C31—42no—
80C4×C31#12312yes—
81C4×C31#12312yes—
82Dic31—22no—
83Dic31—42no—
84C22×C4⋊C4—311no—
85#407—312no—
86#343—312no—
87#343—311no—
88#343D3111yescharacteristic, complemented
89C2×C31—21no—
90C2×C31—21no—
91C2×C31#38111yescharacteristic
92C2×C31C2×#10011yescharacteristic
93C2×C31C2×#10111yescharacteristic
94D31—22no—
95D31—22no—
96C23×C4—311no—
97C23×C4—312no—
98C2×M16—312no—
99C2×M16C2×D3112yes—
100C2×C4⋊C4—312no—
101C2×C4⋊C4—311no—
102C2×C4⋊C4—622no—
103C2×C4⋊C4—622no—
104C2×C4⋊C4C2×D3111yescharacteristic
105C22⋊C8—622no—
106C22⋊C8—622no—
107C31#182111yescharacteristic, complemented, Sylow
108C24—311no—
109C22×C4—311no—
110C22×C4—312no—
111C22×C4—312no—
112C22×C4—312no—
113C22×C4—622no—
114C22×C4—622no—
115C22×C4—622no—
116C22×C4—621no—
117C22×C4—621no—
118C22×C4—1244no—
119C22×C4C4×D3112yes—
120C22×C4C22×D3111yescharacteristic
121M16—22no—
122M16—22no—
123M16—622no—
124M16—622no—
125C2×C8—22no—
126C2×C8—622no—
127C4⋊C4—22no—
128C4⋊C4—624no—
129C4⋊C4—622no—
130C23—311no—
131C23—311no—
132C23—622no—
133C23—622no—
134C23—621no—
135C23—621no—
136C23C2×C4×D3111yescharacteristic
137C2×C4—22no—
138C2×C4—42no—
139C2×C4—312no—
140C2×C4—621no—
141C2×C4—621no—
142C2×C4—622no—
143C2×C4—622no—
144C2×C4—622no—
145C2×C4—622no—
146C2×C4—622no—
147C2×C4—1244no—
148C2×C4—1244no—
149C2×C4—1242no—
150C2×C4#9249512yes—
151C2×C4D4×D3112yes—
152C2×C4#9249711yescharacteristic
153C2×C4#9249911yescharacteristic
154C8—42no—
155C8—1242no—
156C22—21no—
157C22—21no—
158C22—312no—
159C22—312no—
160C22—624no—
161C22—624no—
162C22—621no—
163C22—621no—
164C22—621no—
165C22—621no—
166C22#1175844911yescharacteristic
167C22C22⋊C4×D3111yescharacteristic
168C22#1175846911yescharacteristic
169C4—42no—
170C4—622no—
171C4—1242no—
172C4#1175846012yes—
173C4#1175847112yes—
174C2—21no—
175C2—21no—
176C2—622no—
177C2—622no—
178C2#1452091111yescharacteristic
179C2#100×D3111yescharacteristic
180C2#101×D3111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D31
commutatorC23×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#343C2
socleC22×C31C2×C22⋊C4
prime radicalC23×D31C2×C4
cosocleC22×C4×C31C23
hypercenter#343D31
hypocenterC31#1821
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
3. #14520818C2semidirect
4. #14520817C2semidirect
5. C31×#343C2semidirect
88. #343D31semidirect
107. C31#1821semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D312
#145210122
#145208182
#145208172
C31×#3432
#182131