Finite Group Databasebeta

← #16846167

Subgroups — #16846167

Order 3968.

378 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 89 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×#11758506C211yesmaximal, characteristic
2C2×#11758503C211yesmaximal, characteristic, complemented
3C2×#11758394C212yesmaximal
4#14520815C212yesmaximal, complemented
5C31×#381C211yesmaximal, characteristic, complemented
6C23×C4×C31C2211yescharacteristic
7C22×C22⋊D31C2211yescharacteristic
8C2×C22⋊C4×C31C2212yes—
9C2×C22⋊Dic31C2211yescharacteristic
10C2×C22⋊Dic31C2212yes—
11#11758506—21no—
12#11758506—21no—
13#11758506—22no—
14C2×(C2×D31)⋊C4C412yescomplemented
15#11758503—24no—
16C2×C4⋊Dic31—21no—
17C2×Dic31⋊C4C412yescomplemented
18C2×C4×Dic31—21no—
19C31×#95—22no—
20#11758394—24no—
21C24×C31C2311yescharacteristic
22C23×D31C2×C411yescharacteristic
23C22×C4×C31—22no—
24C22×C4×C31—22no—
25C22×C4×C31—22no—
26C22×C4×C31C2×C412yes—
27C22×C4×C31D411yescharacteristic
28C22×C4×C31D411yescharacteristic
29C22×C4×C31D412yes—
30C2×C22⋊D31—22no—
31C2×C22⋊D31—21no—
32C2×C22⋊D31—21no—
33C2×C22⋊D31—22no—
34C22×Dic31—22no—
35C22×Dic31C2×C411yescharacteristic
36C22×Dic31C2×C412yes—
37C22⋊C4×C31—22no—
38C22⋊C4×C31—22no—
39C22⋊Dic31—22no—
40C22⋊Dic31—21no—
41C22⋊Dic31—21no—
42C22⋊Dic31D414yes—
43(C2×D31)⋊C4—22no—
44(C2×D31)⋊C4—22no—
45C4⋊Dic31—24no—
46Dic31⋊C4—22no—
47Dic31⋊C4—22no—
48C4×Dic31—24no—
49C23×C31—42no—
50C23×C31C22×C411yescharacteristic
51C23×C31C2×D411yescharacteristic
52C23×C31C2×D412yes—
53C23×C31C2×D411yescharacteristic
54C23×C31#4112yes—
55C22×D31—21no—
56C22×D31—22no—
57C22×D31—42no—
58C2×C4×C31—24no—
59C2×C4×C31—21no—
60C2×C4×C31—21no—
61C2×C4×C31—24no—
62C2×C4×C31—21no—
63C2×C4×C31—21no—
64C2×C4×C31—44no—
65C2×C4×C31—42no—
66C2×C4×C31C22⋊C412yes—
67C2×C4×C31C22⋊C412yes—
68C22⋊D31—41no—
69C22⋊D31—42no—
70C22⋊D31—41no—
71C2×Dic31—21no—
72C2×Dic31—22no—
73C2×Dic31—22no—
74C2×Dic31—24no—
75C2×Dic31—44no—
76C2×Dic31—42no—
77#1899—311nomaximal, Sylow
78C22×C31—22no—
79C22×C31—22no—
80C22×C31—22no—
81C22×C31—42no—
82C22×C31—42no—
83C22×C31C2×C22⋊C411yescharacteristic
84C22×C31C4×D412yes—
85C22×C31#12011yescharacteristic
86C22×C31#12112yes—
87C22×C31#12311yescharacteristic
88C2×D31—41no—
89C2×D31—42no—
90C2×D31—82no—
91C4×C31—22no—
92C4×C31—22no—
93C4×C31—82no—
94Dic31—44no—
95Dic31—41no—
96Dic31—42no—
97C2×#123—311no—
98C2×#117—311no—
99C2×#99—312no—
100#381D3111yescharacteristic, complemented
101#342—312no—
102C2×C31—21no—
103C2×C31—22no—
104C2×C31—22no—
105C2×C31—21no—
106C2×C31#38611yescharacteristic
107C2×C31#41012yes—
108D31—81no—
109C22×D4—311no—
110C23×C4C2×D3111yescharacteristic
111#123—621no—
112#123—621no—
113#123—622no—
114#117—624no—
115C2×C4⋊C4—312no—
116C2×C4⋊C4—621no—
117C2×C22⋊C4—312no—
118C2×C22⋊C4—311no—
119C2×C22⋊C4—312no—
120C2×C22⋊C4C2×D3112yes—
121C2×C42—621no—
122#99—624no—
123#95—22no—
124C31#189911yescharacteristic, complemented, Sylow
125C24—311no—
126C24C22×D3111yescharacteristic
127C2×D4—621no—
128C2×D4—622no—
129C2×D4—622no—
130C2×D4—621no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—311no—
135C22×C4—312no—
136C22×C4—622no—
137C22×C4C4×D3112yes—
138C22×C4D12411yescharacteristic
139C22×C4D12411yescharacteristic
140C22×C4C22⋊D3112yes—
141C4⋊C4—624no—
142C4⋊C4—622no—
143C4⋊C4—622no—
144C22⋊C4—22no—
145C22⋊C4—22no—
146C22⋊C4—314no—
147C22⋊C4—621no—
148C22⋊C4—622no—
149C22⋊C4—621no—
150C22⋊C4—622no—
151C22⋊C4—622no—
152C42—624no—
153C23—42no—
154C23—621no—
155C23—622no—
156C23—1242no—
157C23C2×C4×D3111yescharacteristic
158C23C2×D12411yescharacteristic
159C23D4×D3112yes—
160C23#9249712yes—
161C23C2×C22⋊D3111yescharacteristic
162D4—1241no—
163D4—1241no—
164D4—1242no—
165C2×C4—24no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—24no—
171C2×C4—44no—
172C2×C4—42no—
173C2×C4—622no—
174C2×C4—624no—
175C2×C4—622no—
176C2×C4—621no—
177C2×C4—1244no—
178C2×C4—1242no—
179C2×C4(C2×D31)⋊C412yes—
180C2×C4(C2×D31)⋊C412yes—
181C22—22no—
182C22—22no—
183C22—22no—
184C22—42no—
185C22—42no—
186C22—1241no—
187C22—1242no—
188C22—2482no—
189C22(C22⋊D31)⋊C412yes—
190C22#1175845911yescharacteristic
191C22#1175846311yescharacteristic
192C22C2×(C2×D31)⋊C411yescharacteristic
193C22#1175851612yes—
194C4—22no—
195C4—22no—
196C4—82no—
197C4—1244no—
198C4—1241no—
199C4—1242no—
200C2—22no—
201C2—21no—
202C2—22no—
203C2—21no—
204C2—2481no—
205C2#1452092611yescharacteristic
206C2#1452102212yes—
subgroupG/H
centerC22C2×(C2×D31)⋊C4
commutatorC23×C31C22×C4
FrattiniC24C22×D31
FittingC31×#381C2
socleC22×C31C2×C22⋊C4
prime radicalC22×C22⋊D31C22
cosocleC24×C31C23
hypercenter#381D31
hypocenterC31#1899
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C23×C4 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#11758503C2semidirect
4. #14520815C2semidirect
5. C31×#381C2semidirect
14. C2×(C2×D31)⋊C4C4semidirect
17. C2×Dic31⋊C4C4semidirect
100. #381D31semidirect
124. C31#1899semidirect

Maximal subgroups

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

subgroupindex
C2×#117585062
C2×#117585032
C2×#117583942
#145208152
C31×#3812
#189931