Finite Group Databasebeta

← #16844243

Subgroups — #16844243

Order 3968.

274 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 73 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×#11758501C211yesmaximal, characteristic
2#14521013C211yesmaximal, characteristic
3#14520785C214yesmaximal, complemented
4C31×#381C211yesmaximal, characteristic
5C23×C4×C31C2211yescharacteristic
6C22×Dic62C411yescharacteristic, complemented
7C2×C22⋊C4×C31—21no—
8C2×C22⋊Dic31—21no—
9C2×C4⋊Dic31C411yescharacteristic, complemented
10#11758501—21no—
11#11758501—21no—
12#11758501C412yescomplemented
13#11758501C2212yes—
14C2×Dic31⋊C4—21no—
15C2×#92474—21no—
16C31×#95—21no—
17C31×#95C2212yes—
18C22⋊(C31⋊C8)—21no—
19C22⋊(C31⋊C8)C2212yes—
20C24×C31D411yescharacteristic
21C22×C4×C31—22no—
22C22×C4×C31—42no—
23C22×C4×C31C2×C411yescharacteristic
24C22×C4×C31C2×C411yescharacteristic
25C22×C4×C31D411yescharacteristic
26C22×C4×C31D411yescharacteristic
27C22×C4×C31D411yescharacteristic
28C22×C4×C31C2311yescharacteristic
29C22×Dic31—21no—
30C22×Dic31—21no—
31C2×Dic62—21no—
32C2×Dic62—42no—
33C2×Dic62C2×C412yes—
34C22⋊C4×C31—42no—
35C22⋊Dic31—22no—
36C22⋊Dic31—22no—
37C4⋊Dic31—21no—
38C4⋊Dic31C2×C412yes—
39Dic31⋊C4—22no—
40Dic31⋊C4—22no—
41#92474—42no—
42C2×C31⋊C8—22no—
43C23×C31—22no—
44C23×C31—22no—
45C23×C31—41no—
46C23×C31C22⋊C411yescharacteristic
47C23×C31C22⋊C411yescharacteristic
48C23×C31C2×D411yescharacteristic
49C2×C4×C31—22no—
50C2×C4×C31—22no—
51C2×C4×C31—41no—
52C2×C4×C31—41no—
53C2×C4×C31—41no—
54C2×C4×C31—41no—
55C2×C4×C31—42no—
56C2×C4×C31—42no—
57C2×C4×C31—42no—
58C2×C4×C31C22⋊C411yescharacteristic
59C2×C4×C31C22⋊C411yescharacteristic
60C2×C4×C31C22×C411yescharacteristic
61C2×C4×C31C2×D411yescharacteristic
62C2×Dic31—22no—
63C2×Dic31—22no—
64C2×Dic31—42no—
65C2×Dic31—42no—
66Dic62—42no—
67Dic62—42no—
68C31⋊C8—42no—
69#1511—311nomaximal, Sylow
70C22×C31—21no—
71C22×C31—21no—
72C22×C31—21no—
73C22×C31—21no—
74C22×C31—21no—
75C22×C31—21no—
76C22×C31—21no—
77C22×C31—44no—
78C22×C31#9912yes—
79C22×C31C2×C22⋊C411yescharacteristic
80C22×C31#13712yes—
81C4×C31—21no—
82C4×C31—21no—
83C4×C31—21no—
84C4×C31—21no—
85C4×C31—82no—
86Dic31—42no—
87Dic31—42no—
88C2×C22⋊Q8—311no—
89#407—311no—
90#381D3111yescharacteristic
91#328—314no—
92C2×C31—22no—
93C2×C31—22no—
94C2×C31—41no—
95C2×C31C2×#9911yescharacteristic
96C2×C31#41911yescharacteristic
97C2×C31#42111yescharacteristic
98C22×Q8—311no—
99C23×C4C2×D3111yescharacteristic
100C2×M16—621no—
101C22⋊Q8—312no—
102C22⋊Q8—312no—
103C22⋊Q8—621no—
104C22⋊Q8—621no—
105C2×C4⋊C4—311no—
106C2×C4⋊C4—621no—
107C2×C22⋊C4—21no—
108C2×C22⋊C4—621no—
109C22⋊C8—312no—
110C22⋊C8—621no—
111#95—21no—
112#95C2×D3112yes—
113C31#151111yescharacteristic, complemented, Sylow
114C24C22⋊D3111yescharacteristic
115C2×Q8—312no—
116C2×Q8—621no—
117C2×Q8—1242no—
118C22×C4—22no—
119C22×C4—42no—
120C22×C4—621no—
121C22×C4—621no—
122C22×C4C4×D3111yescharacteristic
123C22×C4C4×D3111yescharacteristic
124C22×C4D12411yescharacteristic
125C22×C4D12411yescharacteristic
126C22×C4C22⋊D3111yescharacteristic
127C22×C4C22×D3111yescharacteristic
128M16—1242no—
129C2×C8—622no—
130C4⋊C4—312no—
131C4⋊C4—622no—
132C4⋊C4—621no—
133C4⋊C4—622no—
134C22⋊C4—42no—
135C22⋊C4—622no—
136C22⋊C4—622no—
137C23—22no—
138C23—22no—
139C23—41no—
140C23(C2×D31)⋊C411yescharacteristic
141C23(C2×D31)⋊C411yescharacteristic
142C23C2×C22⋊D3111yescharacteristic
143Q8—1242no—
144Q8—1242no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—42no—
152C2×C4—42no—
153C2×C4—42no—
154C2×C4—622no—
155C2×C4—622no—
156C2×C4—1242no—
157C2×C4—1242no—
158C2×C4(C2×D31)⋊C411yescharacteristic
159C2×C4(C2×D31)⋊C411yescharacteristic
160C2×C4C2×C4×D3111yescharacteristic
161C2×C4C2×D12411yescharacteristic
162C8—1242no—
163C22—21no—
164C22—21no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—21no—
169C22—21no—
170C22—44no—
171C22#1175839412yes—
172C22C2×(C2×D31)⋊C411yescharacteristic
173C22#1175852812yes—
174C4—21no—
175C4—21no—
176C4—21no—
177C4—21no—
178C4—82no—
179C4—1242no—
180C4—1242no—
181C2—22no—
182C2—22no—
183C2—41no—
184C2C2×#1175839411yescharacteristic
185C2#1452105711yescharacteristic
186C2#1452106711yescharacteristic
subgroupG/H
centerC22C2×(C2×D31)⋊C4
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#381C2
socleC22×C31C2×C22⋊C4
prime radicalC24×C31D4
cosocleC22×C4×C31C23
hypercenter#381D31
hypocenterC31#1511
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C23×C4 ◁ #381

Complements

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

NH ≅ G/Ntype
3. #14520785C2semidirect
6. C22×Dic62C4semidirect
9. C2×C4⋊Dic31C4semidirect
12. #11758501C4semidirect
113. C31#1511semidirect

Maximal subgroups

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

subgroupindex
C2×#117585012
#145210132
#145207852
C31×#3812
#151131