Finite Group Databasebeta

← #16844148

Subgroups — #16844148

Order 3968.

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

normal subgroups only

This group has 266 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
1C4×#92495C211yesmaximal, characteristic
2C4×#92474C211yesmaximal, characteristic, complemented
3#14520779C212yesmaximal, complemented
4#14520776C212yesmaximal, complemented
5C31×#423C211yesmaximal, characteristic, complemented
6C2×#92495C411yescharacteristic
7C2×M16×C31—21no—
8C2×C42×C31C2211yescharacteristic
9C4×C22⋊D31—21no—
10C4×C22⋊D31—21no—
11#11758503C411yescharacteristic
12C2×#92474—21no—
13C4×D124C411yescharacteristic
14C4×D124C2211yescharacteristic
15#11758449—21no—
16C42×D31—21no—
17C4×Dic62C411yescharacteristic
18C4×Dic62C2211yescharacteristic
19C31×C4⋊C8—21no—
20C31×C4⋊C8C2212yes—
21#11758391—21no—
22C4×C31⋊C8C2212yes—
23C22×C4×C31C2×C411yescharacteristic
24C22×C4×C31D411yescharacteristic
25C22×C4×C31D411yescharacteristic
26C2×C22⋊D31—21no—
27#92495—22no—
28#92495—22no—
29C2×D124C2×C411yescharacteristic
30C2×C4×D31—21no—
31C2×C4×D31—21no—
32C2×C4×D31—21no—
33C2×Dic62C2×C411yescharacteristic
34M16×C31—42no—
35C2×C8×C31—22no—
36C42×C31C2×C411yescharacteristic
37C42×C31D411yescharacteristic
38C42×C31D411yescharacteristic
39C42×C31C2311yescharacteristic
40C22⋊Dic31—21no—
41(C2×D31)⋊C4—21no—
42(C2×D31)⋊C4—21no—
43C4⋊Dic31C2×C411yescharacteristic
44C4⋊Dic31C2×C411yescharacteristic
45Dic31⋊C4—21no—
46Dic31⋊C4—21no—
47C4×Dic31—21no—
48C4×Dic31—21no—
49C4×Dic31—21no—
50#92474—24no—
51C2×C31⋊C8—22no—
52C23×C31C22⋊C411yescharacteristic
53C22×D31—21no—
54C2×C4×C31—22no—
55C2×C4×C31—21no—
56C2×C4×C31—21no—
57C2×C4×C31—21no—
58C2×C4×C31—21no—
59C2×C4×C31C22⋊C411yescharacteristic
60C2×C4×C31C22⋊C411yescharacteristic
61C2×C4×C31C22⋊C411yescharacteristic
62C2×C4×C31C22×C411yescharacteristic
63C2×C4×C31C2×D411yescharacteristic
64C2×C4×C31C2×D411yescharacteristic
65C22⋊D31—24no—
66C2×Dic31—21no—
67C2×Dic31—21no—
68C2×Dic31—21no—
69D124—21no—
70D124M1612yescomplemented
71C4×D31—24no—
72C4×D31—42no—
73C4×D31—41no—
74C4×D31—41no—
75Dic62—21no—
76Dic62M1612yescomplemented
77C8×C31—42no—
78C31⋊C8—24no—
79#1489—311nomaximal, Sylow
80C22×C31—21no—
81C22×C31—21no—
82C22×C31—21no—
83C22×C31C2×C22⋊C411yescharacteristic
84C2×D31—22no—
85C2×D31—41no—
86C2×D31—41no—
87C4×C31—21no—
88C4×C31—21no—
89C4×C31—21no—
90C4×C31#10412yes—
91C4×C31C2×M1611yescharacteristic
92C4×C31C2×M1611yescharacteristic
93C4×C31AGL(1,ℤ/8)11yescharacteristic
94C4×C31#13711yescharacteristic
95Dic31—22no—
96Dic31—41no—
97Dic31—41no—
98C4×#41—311no—
99#423D3111yescharacteristic, complemented
100C4×M16—311no—
101Q8⋊C8—312no—
102D4⋊C8—312no—
103C2×C31—41no—
104C2×C31#40711yescharacteristic
105C2×C31#41711yescharacteristic
106C2×C31C2×#10411yescharacteristic
107D31—42no—
108C2×#41—311no—
109C2×M16—21no—
110C2×M16—621no—
111C4×Q8—311no—
112C4×Q8—311no—
113C4×D4—311no—
114C4×D4—311no—
115C4×D4—621no—
116C4×D4—621no—
117#117—311no—
118#117—621no—
119C2×C42—621no—
120C2×C42C2×D3111yescharacteristic
121C4⋊C8—21no—
122C4⋊C8C2×D3112yes—
123#97—621no—
124C4×C8—312no—
125C31#148911yescharacteristic, complemented, Sylow
126#41—622no—
127#41—622no—
128C2×Q8—311no—
129C2×D4—311no—
130C2×D4—621no—
131C22×C4—621no—
132C22×C4—621no—
133C22×C4—621no—
134C22×C4C4×D3111yescharacteristic
135C22×C4D12411yescharacteristic
136C22×C4C22⋊D3111yescharacteristic
137M16—42no—
138M16—624no—
139C2×C8—22no—
140C2×C8—622no—
141C4⋊C4—311no—
142C4⋊C4—311no—
143C4⋊C4—621no—
144C4⋊C4—621no—
145C22⋊C4—621no—
146C22⋊C4—621no—
147C22⋊C4—621no—
148C42—621no—
149C42—621no—
150C42—621no—
151C42C4×D3111yescharacteristic
152C42D12411yescharacteristic
153C42C22⋊D3111yescharacteristic
154C42C22×D3111yescharacteristic
155C23—621no—
156C23(C2×D31)⋊C411yescharacteristic
157Q8—312no—
158Q8—621no—
159D4—312no—
160D4—624no—
161D4—621no—
162C2×C4—22no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—624no—
168C2×C4—621no—
169C2×C4—621no—
170C2×C4—621no—
171C2×C4—1242no—
172C2×C4—1241no—
173C2×C4—1241no—
174C2×C4(C2×D31)⋊C411yescharacteristic
175C2×C4(C2×D31)⋊C411yescharacteristic
176C2×C4(C2×D31)⋊C411yescharacteristic
177C2×C4C2×C4×D3111yescharacteristic
178C2×C4C2×D12411yescharacteristic
179C2×C4C2×C22⋊D3111yescharacteristic
180C8—42no—
181C8—624no—
182C22—21no—
183C22—21no—
184C22—21no—
185C22—622no—
186C22—1241no—
187C22—1241no—
188C22C2×(C2×D31)⋊C411yescharacteristic
189C4—21no—
190C4—21no—
191C4—21no—
192C4—622no—
193C4—1241no—
194C4—1241no—
195C4#1175841312yes—
196C4M16×D3111yescharacteristic
197C4M16×D3111yescharacteristic
198C4#1175850911yescharacteristic
199C4#1175851911yescharacteristic
200C2—41no—
201C2—1242no—
202C2#1452101211yescharacteristic
203C2#1452104811yescharacteristic
204C2C2×#1175841311yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D31
commutatorC2×C4×C31C22×C4
FrattiniC42C22×D31
FittingC31×#423C2
socleC22×C31C2×C22⋊C4
prime radicalC2×#92495C4
cosocleC42×C31C23
hypercenter#423D31
hypocenterC31#1489
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
2. C4×#92474C2semidirect
3. #14520779C2semidirect
4. #14520776C2semidirect
5. C31×#423C2semidirect
70. D124M16semidirect
76. Dic62M16semidirect
99. #423D31semidirect
125. C31#1489semidirect

Maximal subgroups

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

subgroupindex
C4×#924952
C4×#924742
#145207792
#145207762
C31×#4232
#148931