Finite Group Databasebeta

← #16844286

Subgroups — #16844286

Order 3968.

218 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 69 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#14521583C211yesmaximal, characteristic
2#14521102C211yesmaximal, characteristic, complemented
3#14520785C212yesmaximal, complemented
4#14520782C212yesmaximal
5C31×#383C211yesmaximal, characteristic, complemented
6C2×C42×C31C2211yescharacteristic
7#11758507C2211yescharacteristic
8#11758506—21no—
9C4×C22⋊D31—21no—
10#11758501C2211yescharacteristic
11#11758453—21no—
12#11758452C411yescharacteristic, complemented
13C4×D124C411yescharacteristic, complemented
14#11758449—21no—
15#11758447C411yescharacteristic, complemented
16C4×Dic62C411yescharacteristic, complemented
17C31×#95—21no—
18C31×#95—21no—
19C31×#95C2212yes—
20C22⋊(C31⋊C8)C2212yes—
21C4⋊(C31⋊C8)—21no—
22C4×C31⋊C8—21no—
23C22×C4×C31—22no—
24C22×C4×C31D411yescharacteristic
25C22×C4×C31D411yescharacteristic
26C22×C4×C31C2311yescharacteristic
27C2×C22⋊D31—21no—
28C2×D124C2×C411yescharacteristic
29C2×C4×D31—21no—
30C2×Dic62C2×C411yescharacteristic
31C42×C31C2×C411yescharacteristic
32C42×C31C2×C411yescharacteristic
33C42×C31D411yescharacteristic
34C42×C31D411yescharacteristic
35C22⋊Dic31—21no—
36(C2×D31)⋊C4—21no—
37(C2×D31)⋊C4—21no—
38(C2×D31)⋊C4—21no—
39(C2×D31)⋊C4—21no—
40C4⋊Dic31C2×C411yescharacteristic
41C4⋊Dic31C2×C411yescharacteristic
42Dic31⋊C4—21no—
43Dic31⋊C4—21no—
44Dic31⋊C4—21no—
45Dic31⋊C4—21no—
46C4×Dic31—21no—
47C2×C31⋊C8—22no—
48C23×C31C2×D411yescharacteristic
49C22×D31—21no—
50C2×C4×C31—22no—
51C2×C4×C31—41no—
52C2×C4×C31—41no—
53C2×C4×C31—42no—
54C2×C4×C31—42no—
55C2×C4×C31—42no—
56C2×C4×C31C22⋊C411yescharacteristic
57C2×C4×C31C22⋊C411yescharacteristic
58C2×C4×C31C22⋊C411yescharacteristic
59C2×C4×C31C22⋊C411yescharacteristic
60C2×C4×C31C22×C411yescharacteristic
61C2×C4×C31C2×D411yescharacteristic
62C22⋊D31—42no—
63C2×Dic31—21no—
64C2×Dic31—21no—
65C2×Dic31—21no—
66D124—41no—
67C4×D31—42no—
68Dic62—41no—
69C31⋊C8—42no—
70#1521—311nomaximal, Sylow
71C22×C31—21no—
72C22×C31—21no—
73C22×C31C2×C22⋊C411yescharacteristic
74C22×C31#13512yes—
75C2×D31—41no—
76C2×D31—41no—
77C2×D31—41no—
78C4×C31—21no—
79C4×C31—21no—
80C4×C31—21no—
81C4×C31—21no—
82C4×C31—21no—
83C4×C31—21no—
84C4×C31—82no—
85Dic31—41no—
86Dic31—41no—
87Dic31—41no—
88#529—311no—
89#431—311no—
90#383D3111yescharacteristic, complemented
91#328—312no—
92#327—312no—
93C2×C31—22no—
94C2×C31#41011yescharacteristic
95C2×C31#41611yescharacteristic
96C2×C31#42111yescharacteristic
97D31—81no—
98#126—621no—
99#125—311no—
100#124—311no—
101#123—621no—
102C22⋊Q8—311no—
103#121—311no—
104C4×Q8—311no—
105C4×D4—311no—
106C4×D4—621no—
107#117—621no—
108C2×C42C2×D3111yescharacteristic
109C4⋊C8—621no—
110C22⋊C8—312no—
111C4×C8—621no—
112#95—21no—
113#95—21no—
114#95C2×D3112yes—
115C31#152111yescharacteristic, complemented, Sylow
116C2×Q8—311no—
117C2×D4—311no—
118C2×D4—621no—
119C22×C4—22no—
120C22×C4—621no—
121C22×C4C22⋊D3111yescharacteristic
122C22×C4C22⋊D3111yescharacteristic
123C22×C4C22×D3111yescharacteristic
124C2×C8—622no—
125C4⋊C4—311no—
126C4⋊C4—311no—
127C4⋊C4—621no—
128C4⋊C4—621no—
129C4⋊C4—621no—
130C4⋊C4—621no—
131C22⋊C4—621no—
132C22⋊C4—621no—
133C22⋊C4—621no—
134C22⋊C4—621no—
135C22⋊C4—621no—
136C42—621no—
137C42C4×D3111yescharacteristic
138C42C4×D3111yescharacteristic
139C42D12411yescharacteristic
140C42D12411yescharacteristic
141C23—621no—
142C23C2×C22⋊D3111yescharacteristic
143Q8—1241no—
144D4—1241no—
145D4—1242no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—42no—
150C2×C4—42no—
151C2×C4—42no—
152C2×C4—621no—
153C2×C4—621no—
154C2×C4—621no—
155C2×C4—1242no—
156C2×C4(C2×D31)⋊C411yescharacteristic
157C2×C4(C2×D31)⋊C411yescharacteristic
158C2×C4(C2×D31)⋊C411yescharacteristic
159C2×C4(C2×D31)⋊C411yescharacteristic
160C2×C4C2×C4×D3111yescharacteristic
161C2×C4C2×D12411yescharacteristic
162C8—1242no—
163C22—21no—
164C22—21no—
165C22—1241no—
166C22—1241no—
167C22—1241no—
168C22C2×(C2×D31)⋊C411yescharacteristic
169C22#1175852712yes—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—82no—
177C4—1241no—
178C4—1241no—
179C4—1241no—
180C2—22no—
181C2—2481no—
182C2#1452102211yescharacteristic
183C2#1452104311yescharacteristic
184C2#1452106711yescharacteristic
subgroupG/H
centerC22C2×(C2×D31)⋊C4
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#383C2
socleC22×C31C2×C22⋊C4
prime radical#11758507C22
cosocleC22×C4×C31C23
hypercenter#383D31
hypocenterC31#1521
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C2×C42 ◁ #383

Complements

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

NH ≅ G/Ntype
2. #14521102C2semidirect
3. #14520785C2semidirect
5. C31×#383C2semidirect
12. #11758452C4semidirect
13. C4×D124C4semidirect
15. #11758447C4semidirect
16. C4×Dic62C4semidirect
90. #383D31semidirect
115. C31#1521semidirect

Maximal subgroups

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

subgroupindex
#145215832
#145211022
#145207852
#145207822
C31×#3832
#152131