Finite Group Databasebeta

← #16846253

Subgroups — #16846253

Order 3968.

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

normal subgroups only

This group has 380 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
1#14521608C211yesmaximal, characteristic
2C2×#11758422C211yesmaximal, characteristic, complemented
3C2×#11758394C212yesmaximal, complemented
4#14520815C212yesmaximal, complemented
5C31×#518C211yesmaximal, characteristic, complemented
6C22×D4×C31C2211yescharacteristic
7C22×C22⋊D31C2211yescharacteristic
8C4×D4×C31—24no—
9C31×#117—21no—
10C2×C22⋊C4×C31—21no—
11C2×C22⋊C4×C31C2212yes—
12#11758530—21no—
13C2×C22⋊Dic31C2212yes—
14C2×C22⋊Dic31C2211yescharacteristic
15#11758516—22no—
16#11758514C412yescomplemented
17#11758512C412yescomplemented
18#11758506—21no—
19#11758422—22no—
20#11758394—24no—
21C24×C31D411yescharacteristic
22C24×C31C2311yescharacteristic
23C23×D31C2×C411yescharacteristic, complemented
24C2×D4×C31—22no—
25C2×D4×C31—22no—
26C2×D4×C31C2×C412yes—
27C2×D4×C31D412yes—
28C22×C4×C31—22no—
29C22×C4×C31—22no—
30C22×C4×C31D411yescharacteristic
31C2×C22⋊D31—22no—
32C2×C22⋊D31—21no—
33C2×C22⋊D31—21no—
34C2×C22⋊D31—22no—
35C2×C22⋊D31—22no—
36C22×Dic31—21no—
37C22×Dic31—22no—
38C22×Dic31C2×C411yescharacteristic, complemented
39C4⋊C4×C31—22no—
40C22⋊C4×C31—22no—
41C22⋊C4×C31—22no—
42C22⋊C4×C31D414yescomplemented
43C42×C31—22no—
44C22⋊Dic31—22no—
45C22⋊Dic31—21no—
46C22⋊Dic31—22no—
47C22⋊Dic31—22no—
48C22⋊Dic31C2×C412yescomplemented
49(C2×D31)⋊C4—22no—
50Dic31⋊C4—22no—
51C23×C31—21no—
52C23×C31—21no—
53C23×C31—81no—
54C23×C31—81no—
55C23×C31C22⋊C412yes—
56C23×C31C22×C411yescharacteristic
57C23×C31C2×D411yescharacteristic
58C23×C31C2×D411yescharacteristic
59C23×C31C2×D412yes—
60C23×C31#4112yes—
61C22×D31—21no—
62C22×D31—22no—
63C22×D31—81no—
64D4×C31—24no—
65D4×C31—24no—
66C2×C4×C31—21no—
67C2×C4×C31—21no—
68C2×C4×C31—24no—
69C2×C4×C31—82no—
70C2×C4×C31—82no—
71C2×C4×C31C22⋊C412yes—
72C22⋊D31—41no—
73C22⋊D31—42no—
74C22⋊D31—41no—
75C22⋊D31—82no—
76C2×Dic31—21no—
77C2×Dic31—22no—
78C2×Dic31—22no—
79C2×Dic31—42no—
80C2×Dic31—81no—
81C2×Dic31—82no—
82#1913—311nomaximal, Sylow
83C22×C31—22no—
84C22×C31—41no—
85C22×C31—42no—
86C22×C31—42no—
87C22×C31—41no—
88C22×C31—41no—
89C22×C31—42no—
90C22×C31—42no—
91C22×C31—81no—
92C22×C31C2×C22⋊C411yescharacteristic
93C22×C31C4×D412yes—
94C22×C31#12011yescharacteristic
95C22×C31#12112yes—
96C22×C31#12311yescharacteristic
97C2×D31—42no—
98C2×D31—41no—
99C2×D31—82no—
100C4×C31—22no—
101C4×C31—44no—
102Dic31—42no—
103Dic31—41no—
104Dic31—82no—
105#534—311no—
106#518D3111yescharacteristic, complemented
107C2×#99—311no—
108C2×#99—312no—
109#342—312no—
110C2×C31—21no—
111C2×C31—22no—
112C2×C31—21no—
113C2×C31—22no—
114C2×C31—21no—
115C2×C31—42no—
116C2×C31#38611yescharacteristic
117D31—81no—
118C22×D4—311no—
119C22×D4C2×D3111yescharacteristic
120#123—312no—
121#123—621no—
122#121—622no—
123#120—312no—
124#120—621no—
125C4×D4—24no—
126#117—21no—
127C2×C22⋊C4—21no—
128C2×C22⋊C4—311no—
129C2×C22⋊C4—312no—
130C2×C22⋊C4C2×D3112yes—
131#99—622no—
132#99—624no—
133C31#191311yescharacteristic, complemented, Sylow
134C24—311no—
135C24C22⋊D3111yescharacteristic
136C24C22×D3111yescharacteristic
137C2×D4—22no—
138C2×D4—22no—
139C2×D4—621no—
140C2×D4—622no—
141C2×D4—622no—
142C2×D4—621no—
143C2×D4—622no—
144C2×D4C4×D3112yes—
145C2×D4D12412yes—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—311no—
149C22×C4—621no—
150C22×C4—622no—
151C22×C4C22⋊D3111yescharacteristic
152C4⋊C4—22no—
153C4⋊C4—622no—
154C22⋊C4—22no—
155C22⋊C4—22no—
156C22⋊C4—312no—
157C22⋊C4—622no—
158C22⋊C4—621no—
159C22⋊C4—622no—
160C22⋊C4—622no—
161C22⋊C4—622no—
162C22⋊C4C22⋊D3114yescomplemented
163C42—22no—
164C23—21no—
165C23—21no—
166C23—81no—
167C23—81no—
168C23—621no—
169C23—622no—
170C23—2481no—
171C23(C2×D31)⋊C412yes—
172C23C2×C4×D3111yescharacteristic
173C23C2×D12411yescharacteristic
174C23#9249512yes—
175C23C2×C22⋊D3111yescharacteristic
176C23C2×C22⋊D3112yes—
177D4—24no—
178D4—24no—
179D4—1241no—
180D4—1242no—
181D4—1241no—
182D4—2482no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—24no—
186C2×C4—82no—
187C2×C4—82no—
188C2×C4—622no—
189C2×C4—621no—
190C2×C4—622no—
191C2×C4—1242no—
192C2×C4—2481no—
193C2×C4—2482no—
194C2×C4(C2×D31)⋊C412yes—
195C22—22no—
196C22—42no—
197C22—41no—
198C22—42no—
199C22—41no—
200C22—41no—
201C22—42no—
202C22—42no—
203C22—81no—
204C22—1242no—
205C22—1241no—
206C22—2482no—
207C22C2×(C2×D31)⋊C411yescharacteristic
208C22C4×C22⋊D3112yes—
209C22#1175850611yescharacteristic
210C22#1175850712yes—
211C22#1175853011yescharacteristic
212C4—22no—
213C4—44no—
214C4—1242no—
215C4—1241no—
216C4—2482no—
217C2—21no—
218C2—21no—
219C2—22no—
220C2—21no—
221C2—22no—
222C2—42no—
223C2—2481no—
224C2#1452092811yescharacteristic
subgroupG/H
centerC2#14520928
commutatorC23×C31C22×C4
FrattiniC24C22×D31
FittingC31×#518C2
socleC2×C31#386
prime radical#14521608C2
cosocleC24×C31C23
hypercenter#518D31
hypocenterC31#1913
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C24 ◁ #518

Complements

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

NH ≅ G/Ntype
2. C2×#11758422C2semidirect
3. C2×#11758394C2semidirect
4. #14520815C2semidirect
5. C31×#518C2semidirect
16. #11758514C4semidirect
17. #11758512C4semidirect
23. C23×D31C2×C4semidirect
38. C22×Dic31C2×C4semidirect
42. C22⋊C4×C31D4semidirect
48. C22⋊Dic31C2×C4semidirect
106. #518D31semidirect
133. C31#1913semidirect
162. C22⋊C4C22⋊D31semidirect

Maximal subgroups

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

subgroupindex
#145216082
C2×#117584222
C2×#117583942
#145208152
C31×#5182
#191331