Finite Group Databasebeta

← #16846254

Subgroups — #16846254

Order 3968.

380 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 93 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#14521524C211yesmaximal, characteristic, complemented
2C2×#11758422C211yesmaximal, characteristic, complemented
3C2×#11758422C212yesmaximal, complemented
4#14520815C212yesmaximal, complemented
5C31×#534C211yesmaximal, characteristic
6C22×D4×C31C2211yescharacteristic
7C22×D4×C31C2211yescharacteristic
8C31×#123—21no—
9C31×#123C412yescomplemented
10C31×#121—22no—
11C31×#120—21no—
12C31×#120C412yescomplemented
13C2×C22⋊C4×C31C2211yescharacteristic
14C2×C22⋊Dic31—21no—
15C2×C22⋊Dic31C2212yes—
16C2×C22⋊Dic31C2212yes—
17D4×Dic31—24no—
18#11758503—21no—
19#11758422—22no—
20#11758422—24no—
21C24×C31C2×C411yescharacteristic, complemented
22C24×C31D411yescharacteristic
23C24×C31C2311yescharacteristic
24C2×D4×C31—22no—
25C2×D4×C31—22no—
26C2×D4×C31—22no—
27C2×D4×C31—21no—
28C2×D4×C31—21no—
29C2×D4×C31—22no—
30C2×D4×C31—22no—
31C2×D4×C31C2×C412yes—
32C2×D4×C31D412yes—
33C22×C4×C31—21no—
34C22×C4×C31C2×C411yescharacteristic, complemented
35C22×C4×C31D411yescharacteristic
36C22×Dic31—22no—
37C22×Dic31—22no—
38C22×Dic31—22no—
39C4⋊C4×C31—22no—
40C22⋊C4×C31—22no—
41C22⋊C4×C31—21no—
42C22⋊C4×C31—22no—
43C22⋊C4×C31C2×C412yescomplemented
44C22⋊Dic31—22no—
45C22⋊Dic31—22no—
46C22⋊Dic31—22no—
47C22⋊Dic31—22no—
48C22⋊Dic31D414yescomplemented
49C4⋊Dic31—22no—
50C4×Dic31—22no—
51C23×C31—21no—
52C23×C31—21no—
53C23×C31—21no—
54C23×C31—22no—
55C23×C31—81no—
56C23×C31—81no—
57C23×C31—81no—
58C23×C31C22⋊C412yes—
59C23×C31C22×C411yescharacteristic
60C23×C31C2×D412yes—
61C23×C31C2×D411yescharacteristic
62C23×C31C2×D411yescharacteristic
63C23×C31#4112yes—
64D4×C31—24no—
65D4×C31—24no—
66D4×C31—41no—
67D4×C31—42no—
68D4×C31—41no—
69D4×C31—82no—
70C2×C4×C31—21no—
71C2×C4×C31—21no—
72C2×C4×C31—22no—
73C2×C4×C31—21no—
74C2×C4×C31—22no—
75C2×C4×C31—81no—
76C2×C4×C31C22⋊C412yes—
77C2×Dic31—24no—
78C2×Dic31—42no—
79C2×Dic31—82no—
80C2×Dic31—82no—
81C2×Dic31—82no—
82#1913—311nomaximal, Sylow
83C22×C31—22no—
84C22×C31—42no—
85C22×C31—42no—
86C22×C31—41no—
87C22×C31—41no—
88C22×C31—41no—
89C22×C31—42no—
90C22×C31—42no—
91C22×C31—42no—
92C22×C31—41no—
93C22×C31—81no—
94C22×C31—82no—
95C22×C31C2×C22⋊C411yescharacteristic
96C22×C31C4×D412yes—
97C22×C31#12011yescharacteristic
98C22×C31#12112yes—
99C22×C31#12311yescharacteristic
100C4×C31—22no—
101C4×C31—42no—
102C4×C31—41no—
103Dic31—44no—
104Dic31—82no—
105#534D3111yescharacteristic
106#518—311no—
107C2×#99—312no—
108C2×#99—311no—
109#342—312no—
110C2×C31—21no—
111C2×C31—22no—
112C2×C31—21no—
113C2×C31—22no—
114C2×C31—21no—
115C2×C31—42no—
116C2×C31—81no—
117C2×C31#38611yescharacteristic
118C22×D4C2×D3111yescharacteristic
119C22×D4C2×D3111yescharacteristic
120#123—21no—
121#123Dic3112yescomplemented
122#121—22no—
123#120—21no—
124#120Dic3112yescomplemented
125C4×D4—624no—
126#117—621no—
127C2×C22⋊C4—312no—
128C2×C22⋊C4—312no—
129C2×C22⋊C4—621no—
130C2×C22⋊C4C2×D3111yescharacteristic
131#99—624no—
132#99—622no—
133C31#191311yescharacteristic, complemented, Sylow
134C24C2×Dic3111yescharacteristic, complemented
135C24C22⋊D3111yescharacteristic
136C24C22×D3111yescharacteristic
137C2×D4—22no—
138C2×D4—22no—
139C2×D4—22no—
140C2×D4—22no—
141C2×D4—21no—
142C2×D4—21no—
143C2×D4—22no—
144C2×D4C2×Dic3112yes—
145C2×D4C22⋊D3112yes—
146C22×C4—21no—
147C22×C4—622no—
148C22×C4—622no—
149C22×C4—622no—
150C22×C4C2×Dic3111yescharacteristic, complemented
151C22×C4C22⋊D3111yescharacteristic
152C4⋊C4—22no—
153C4⋊C4—622no—
154C22⋊C4—22no—
155C22⋊C4—21no—
156C22⋊C4—22no—
157C22⋊C4—314no—
158C22⋊C4—622no—
159C22⋊C4—622no—
160C22⋊C4—622no—
161C22⋊C4—622no—
162C22⋊C4C2×Dic3112yescomplemented
163C42—622no—
164C23—21no—
165C23—21no—
166C23—21no—
167C23—22no—
168C23—81no—
169C23—81no—
170C23—81no—
171C23C22⋊Dic3112yes—
172C23D4×D3112yes—
173C23#9249712yes—
174C23C22×Dic3111yescharacteristic
175C23C2×C22⋊D3111yescharacteristic
176C23C2×C22⋊D3111yescharacteristic
177D4—24no—
178D4—24no—
179D4—41no—
180D4—41no—
181D4—42no—
182D4—82no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—81no—
189C2×C4—624no—
190C2×C4—1242no—
191C2×C4—2482no—
192C2×C4—2482no—
193C2×C4—2482no—
194C2×C4C22⋊Dic3112yes—
195C22—22no—
196C22—41no—
197C22—42no—
198C22—42no—
199C22—41no—
200C22—41no—
201C22—42no—
202C22—42no—
203C22—42no—
204C22—41no—
205C22—81no—
206C22—82no—
207C22D4×Dic3112yes—
208C22#1175851211yescharacteristic
209C22#1175851411yescharacteristic
210C22#1175851612yes—
211C22C2×C22⋊Dic3111yescharacteristic
212C4—22no—
213C4—42no—
214C4—41no—
215C4—1244no—
216C4—2482no—
217C2—21no—
218C2—21no—
219C2—22no—
220C2—22no—
221C2—21no—
222C2—42no—
223C2—81no—
224C2#1452092911yescharacteristic
subgroupG/H
centerC2#14520929
commutatorC23×C31C22×C4
FrattiniC24C22×D31
Fitting, prime radicalC31×#534C2
socleC2×C31#386
cosocleC24×C31C23
hypercenter#534D31
hypocenterC31#1913
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C24 ◁ #534

Complements

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

NH ≅ G/Ntype
1. #14521524C2semidirect
2. C2×#11758422C2semidirect
3. C2×#11758422C2semidirect
4. #14520815C2semidirect
9. C31×#123C4semidirect
12. C31×#120C4semidirect
21. C24×C31C2×C4semidirect
34. C22×C4×C31C2×C4semidirect
43. C22⋊C4×C31C2×C4semidirect
48. C22⋊Dic31D4semidirect
121. #123Dic31semidirect
124. #120Dic31semidirect
133. C31#1913semidirect
134. C24C2×Dic31semidirect
150. C22×C4C2×Dic31semidirect
162. C22⋊C4C2×Dic31semidirect

Maximal subgroups

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

subgroupindex
#145215242
C2×#117584222
#145208152
C31×#5342
#191331