Finite Group Databasebeta

← #16854066

Subgroups — #16854066

Order 3968.

752 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 752 conjugacy classes of subgroups — too many to draw. Only its 181 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×#11758521C211yesmaximal, characteristic, complemented
2C2×#11758517C211yesmaximal, characteristic
3C2×#11758524C211yesmaximal, characteristic, complemented
4C2×#11758452C211yesmaximal, characteristic, complemented
5C2×#11758513C211yesmaximal, characteristic, complemented
6#14520949C218yesmaximal, complemented
7C42×Dic31C211yesmaximal, characteristic, complemented
8C2×C31×#124C211yesmaximal, characteristic, complemented
9C22×Q8×C31C2211yescharacteristic
10C22×D4×C31C2211yescharacteristic
11C22×C22⋊D31C2214yes—
12C22×D124C2211yescharacteristic
13C22×Dic62C2211yescharacteristic
14C31×#124—24no—
15C2×C22⋊C4×C31C2214yes—
16C2×C42×C31C2211yescharacteristic
17C2×C22⋊Dic31C2214yes—
18#11758524—24no—
19#11758521—24no—
20#11758517—24no—
21#11758513—24no—
22C2×(C2×D31)⋊C4C2214yes—
23C2×(C2×D31)⋊C4C2214yes—
24C2×Dic31⋊C4C2214yes—
25C2×C4×Dic31C2214yes—
26C2×C4×Dic31C2211yescharacteristic
27C2×C4×Dic31C2211yescharacteristic
28#11758452—24no—
29C24×C31C2312yes—
30C23×D31C2312yes—
31C2×Q8×C31—22no—
32C2×Q8×C31—22no—
33C2×Q8×C31—22no—
34C2×D4×C31—22no—
35C2×D4×C31—22no—
36C2×D4×C31—22no—
37C22×C4×C31C2312yes—
38C22×C4×C31C2312yes—
39C22×C4×C31C2311yescharacteristic
40C2×C22⋊D31—28no—
41C2×C22⋊D31—216no—
42C22×Dic31C2312yes—
43C22×Dic31C2312yes—
44C22×Dic31C2312yes—
45C2×D124—22no—
46C2×D124—22no—
47C2×D124—22no—
48C2×Dic62—22no—
49C2×Dic62—22no—
50C2×Dic62—22no—
51C22⋊C4×C31—28no—
52C42×C31D414yescomplemented
53C22⋊Dic31—28no—
54(C2×D31)⋊C4—28no—
55(C2×D31)⋊C4—28no—
56Dic31⋊C4—28no—
57C4×Dic31—28no—
58C4×Dic31D414yes—
59C4×Dic31D414yescomplemented
60C23×C31—22no—
61C23×C31—22no—
62C23×C31—22no—
63C23×C31—28no—
64C23×C31C2411yescharacteristic
65C22×D31—22no—
66C22×D31—22no—
67C22×D31—22no—
68C22×D31—28no—
69Q8×C31—44no—
70D4×C31—44no—
71C2×C4×C31—24no—
72C2×C4×C31—22no—
73C2×C4×C31—22no—
74C2×C4×C31—22no—
75C2×C4×C31C2×D412yes—
76C2×C4×C31C2×D412yes—
77C2×C4×C31C2×D414yes—
78C2×C4×C31C2×D412yes—
79C22⋊D31—416no—
80C2×Dic31—24no—
81C2×Dic31—22no—
82C2×Dic31—22no—
83C2×Dic31—22no—
84C2×Dic31C2×D414yes—
85C2×Dic31C2×D414yes—
86C2×Dic31#4118yes—
87D124—44no—
88Dic62—44no—
89#2858—311nomaximal, Sylow
90C22×C31—44no—
91C22×C31—42no—
92C22×C31—44no—
93C22×C31—44no—
94C22×C31C22×D411yescharacteristic
95C22×C31C22×D411yescharacteristic
96C22×C31C22×D411yescharacteristic
97C22×C31C2×#4114yes—
98C2×D31—44no—
99C2×D31—42no—
100C2×D31—44no—
101C2×D31—44no—
102C4×C31—24no—
103C4×C31—42no—
104C4×C31#12714yes—
105Dic31—24no—
106Dic31—42no—
107Dic31#12418yescomplemented
108C2×C4⋊Q8—311no—
109C2×#127—311no—
110C2×#124—311no—
111C2×#124—311no—
112C2×#124—311no—
113C2×#124D3111yescharacteristic, complemented
114#390—318no—
115C43—311no—
116C2×C31—82no—
117C2×C31C2×#12412yes—
118C2×C31C2×#12711yescharacteristic
119C2×C31#53212yes—
120C2×C31#53212yes—
121D31—82no—
122C22×Q8—311no—
123C22×Q8C2×D3111yescharacteristic
124C22×D4—314no—
125C22×D4—311no—
126C22×D4C2×D3111yescharacteristic
127C4⋊Q8—624no—
128#127—624no—
129#124—24no—
130#124—624no—
131#124—624no—
132#124—624no—
133C2×C4⋊C4—314no—
134C2×C22⋊C4—314no—
135C2×C22⋊C4—314no—
136C2×C22⋊C4—314no—
137C2×C22⋊C4C2×D3114yes—
138C2×C42—311no—
139C2×C42—311no—
140C2×C42—314no—
141C2×C42C2×D3111yescharacteristic
142C31#285811yescharacteristic, complemented, Sylow
143C24—312no—
144C24C22×D3112yes—
145C2×Q8—22no—
146C2×Q8—22no—
147C2×Q8—22no—
148C2×Q8—622no—
149C2×Q8—622no—
150C2×Q8—622no—
151C2×D4—22no—
152C2×D4—22no—
153C2×D4—22no—
154C2×D4—628no—
155C2×D4—6216no—
156C2×D4—622no—
157C2×D4—622no—
158C2×D4—622no—
159C22×C4—312no—
160C22×C4—312no—
161C22×C4—312no—
162C22×C4C22×D3112yes—
163C22×C4C22×D3112yes—
164C22×C4C22×D3111yescharacteristic
165C4⋊C4—628no—
166C22⋊C4—28no—
167C22⋊C4—628no—
168C22⋊C4—628no—
169C22⋊C4—628no—
170C42—314no—
171C42—314no—
172C42—628no—
173C42C22⋊D3114yescomplemented
174C23—22no—
175C23—22no—
176C23—28no—
177C23—22no—
178C23—622no—
179C23—622no—
180C23—628no—
181C23—622no—
182C23C23×D3111yescharacteristic
183Q8—44no—
184Q8—1244no—
185D4—44no—
186D4—12416no—
187D4—1244no—
188C2×C4—24no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—314no—
193C2×C4—318no—
194C2×C4—314no—
195C2×C4—624no—
196C2×C4—622no—
197C2×C4—622no—
198C2×C4—622no—
199C2×C4D4×D3112yes—
200C2×C4D4×D3112yes—
201C2×C4C2×C22⋊D3114yes—
202C2×C4C2×C22⋊D3112yes—
203C22—44no—
204C22—42no—
205C22—44no—
206C22—44no—
207C22—1244no—
208C22—1242no—
209C22—1244no—
210C22—1244no—
211C22C2×D4×D3111yescharacteristic
212C22C2×D4×D3111yescharacteristic
213C22#41×D3114yes—
214C22C22×C22⋊D3111yescharacteristic
215C4—24no—
216C4—42no—
217C4—318no—
218C4—624no—
219C4—1242no—
220C4#1175851714yes—
221C2—82no—
222C2—2482no—
223C2#124×D3112yes—
224C2C2×#1175851711yescharacteristic
225C2#1452159512yes—
226C2#1452159812yes—
subgroupG/H
center, FrattiniC23C23×D31
commutator, socle, cosocleC23×C31C24
FittingC2×C31×#124C2
prime radicalC2×#11758517C2
hypercenterC2×#124D31
hypocenterC31#2858
LCSG ▷ C23×C31 ▷ C31
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#11758521C2semidirect
3. C2×#11758524C2semidirect
4. C2×#11758452C2semidirect
5. C2×#11758513C2semidirect
6. #14520949C2semidirect
7. C42×Dic31C2semidirect
8. C2×C31×#124C2semidirect
52. C42×C31D4semidirect
59. C4×Dic31D4semidirect
107. Dic31#124semidirect
113. C2×#124D31semidirect
142. C31#2858semidirect
173. C42C22⋊D31semidirect

Maximal subgroups

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

subgroupindex
C2×#117585212
C2×#117585172
C2×#117585242
C2×#117584522
C2×#117585132
#145209492
C42×Dic312
C2×C31×#1242
#285831