Finite Group Databasebeta

← #16846837

Subgroups — #16846837

Order 3968.

638 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 638 conjugacy classes of subgroups — too many to draw. Only its 73 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#14521611C211yesmaximal, characteristic, complemented
2C2×#11758530C212yesmaximal, complemented
3C2×#11758394C212yesmaximal, complemented
4#14520816C211yesmaximal, characteristic, complemented
5C31×#379C211yesmaximal, characteristic, complemented
6C25×C31C2211yescharacteristic
7C22×C22⋊D31—22no—
8C22×C22⋊D31C2212yes—
9C2×C22⋊C4×C31—22no—
10C2×C22⋊C4×C31C2211yescharacteristic
11C2×C22⋊C4×C31C2211yescharacteristic
12#11758530—24no—
13#11758530—24no—
14C2×C22⋊Dic31—22no—
15C2×C22⋊Dic31C2212yes—
16#11758507—22no—
17#11758463—22no—
18#11758459—22no—
19#11758394—24no—
20C24×C31—22no—
21C24×C31—21no—
22C24×C31—22no—
23C24×C31—21no—
24C24×C31—44no—
25C24×C31D412yescomplemented
26C24×C31C2311yescharacteristic
27C23×D31D412yescomplemented
28C22×C4×C31—21no—
29C22×C4×C31D412yescomplemented
30C2×C22⋊D31—28no—
31C2×C22⋊D31—22no—
32C2×C22⋊D31—22no—
33C2×C22⋊D31—22no—
34C2×C22⋊D31—22no—
35C2×C22⋊D31—22no—
36C2×C22⋊D31—22no—
37C2×C22⋊D31—48no—
38C22×Dic31—22no—
39C22×Dic31D412yescomplemented
40C2×D124—22no—
41C22⋊C4×C31—22no—
42C22⋊C4×C31—22no—
43C22⋊C4×C31—44no—
44C22⋊Dic31—28no—
45C22⋊Dic31—22no—
46C22⋊Dic31D414yescomplemented
47(C2×D31)⋊C4—24no—
48C4⋊Dic31—22no—
49C23×C31—24no—
50C23×C31—28no—
51C23×C31—24no—
52C23×C31—22no—
53C23×C31—44no—
54C23×C31—42no—
55C23×C31—44no—
56C23×C31—42no—
57C23×C31—48no—
58C23×C31—44no—
59C23×C31—41no—
60C23×C31—42no—
61C23×C31—41no—
62C23×C31C2×D411yescharacteristic
63C23×C31C2×D412yes—
64C23×C31C2×D412yes—
65C23×C31C2×D411yescharacteristic
66C23×C31#4111yescharacteristic
67C22×D31—22no—
68C22×D31—22no—
69C22×D31—22no—
70C22×D31—44no—
71C2×C4×C31—22no—
72C2×C4×C31—42no—
73C2×C4×C31—42no—
74C2×C4×C31—41no—
75C22⋊D31—416no—
76C22⋊D31—42no—
77C22⋊D31—42no—
78C22⋊D31—42no—
79C22⋊D31—42no—
80C2×Dic31—22no—
81C2×Dic31—22no—
82C2×Dic31—24no—
83C2×Dic31—22no—
84C2×Dic31—44no—
85D124—82no—
86#2021—311nomaximal, Sylow
87C22×C31—24no—
88C22×C31—22no—
89C22×C31—28no—
90C22×C31—24no—
91C22×C31—41no—
92C22×C31—42no—
93C22×C31—41no—
94C22×C31—44no—
95C22×C31—44no—
96C22×C31—48no—
97C22×C31—42no—
98C22×C31—42no—
99C22×C31—44no—
100C22×C31#12012yes—
101C22×C31#12011yescharacteristic
102C22×C31#12112yes—
103C22×C31#12111yescharacteristic
104C22×C31#12711yescharacteristic
105C2×D31—44no—
106C2×D31—42no—
107C2×D31—44no—
108C2×D31—82no—
109C4×C31—42no—
110C4×C31—81no—
111Dic31—44no—
112Dic31—42no—
113#534—311no—
114C2×#120—312no—
115C2×#99—312no—
116#379D3111yescharacteristic, complemented
117#342—311no—
118C2×C31—22no—
119C2×C31—21no—
120C2×C31—22no—
121C2×C31—21no—
122C2×C31—44no—
123C2×C31#39211yescharacteristic
124C2×C31B(4,𝔽2)12yes—
125D31—82no—
126C25C2×D3111yescharacteristic
127C22×D4—312no—
128C22×D4—622no—
129#123—622no—
130#121—622no—
131#120—622no—
132#120—624no—
133#120—624no—
134C2×C22⋊C4—22no—
135C2×C22⋊C4—312no—
136C2×C22⋊C4—622no—
137C2×C22⋊C4C2×D3111yescharacteristic
138C2×C22⋊C4C2×D3111yescharacteristic
139#99—624no—
140C31#202111yescharacteristic, complemented, Sylow
141C24—22no—
142C24—21no—
143C24—21no—
144C24—22no—
145C24—44no—
146C24—312no—
147C24D12412yescomplemented
148C24C22×D3111yescharacteristic
149C2×D4—622no—
150C2×D4—628no—
151C2×D4—622no—
152C2×D4—622no—
153C2×D4—622no—
154C2×D4—622no—
155C2×D4—622no—
156C2×D4—622no—
157C2×D4—1248no—
158C22×C4—21no—
159C22×C4—312no—
160C22×C4—622no—
161C22×C4C22⋊D3112yescomplemented
162C4⋊C4—622no—
163C22⋊C4—22no—
164C22⋊C4—22no—
165C22⋊C4—44no—
166C22⋊C4—314no—
167C22⋊C4—624no—
168C22⋊C4—628no—
169C22⋊C4—622no—
170C23—24no—
171C23—28no—
172C23—24no—
173C23—22no—
174C23—44no—
175C23—42no—
176C23—42no—
177C23—44no—
178C23—48no—
179C23—44no—
180C23—42no—
181C23—41no—
182C23—41no—
183C23—622no—
184C23—622no—
185C23—622no—
186C23—1244no—
187C23C2×D12411yescharacteristic
188C23#9249511yescharacteristic
189C23D4×D3112yes—
190C23D4×D3112yes—
191C23C2×C22⋊D3111yescharacteristic
192D4—12416no—
193D4—1242no—
194D4—1242no—
195D4—1242no—
196D4—1242no—
197D4—2482no—
198C2×C4—22no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—41no—
202C2×C4—624no—
203C2×C4—622no—
204C2×C4—622no—
205C2×C4—622no—
206C2×C4—1244no—
207C22—22no—
208C22—24no—
209C22—28no—
210C22—24no—
211C22—41no—
212C22—41no—
213C22—42no—
214C22—44no—
215C22—44no—
216C22—42no—
217C22—48no—
218C22—42no—
219C22—44no—
220C22—1244no—
221C22—1242no—
222C22—1244no—
223C22—2482no—
224C22#1175845912yes—
225C22#1175846112yes—
226C22#1175850711yescharacteristic
227C22#1175851411yescharacteristic
228C22#1175851711yescharacteristic
229C4—42no—
230C4—81no—
231C4—1244no—
232C4—1242no—
233C2—21no—
234C2—22no—
235C2—21no—
236C2—22no—
237C2—44no—
238C2—2482no—
239C2#1452095811yescharacteristic
240C2#1452123512yes—
subgroupG/H
centerC22#11758514
commutator, cosocleC24×C31C23
FrattiniC24C22×D31
FittingC31×#379C2
socleC22×C31#120
hypercenter#379D31
hypocenterC31#2021
LCSG ▷ C24×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C24 ◁ #379

Complements

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

NH ≅ G/Ntype
1. #14521611C2semidirect
2. C2×#11758530C2semidirect
3. C2×#11758394C2semidirect
4. #14520816C2semidirect
5. C31×#379C2semidirect
25. C24×C31D4semidirect
27. C23×D31D4semidirect
29. C22×C4×C31D4semidirect
39. C22×Dic31D4semidirect
46. C22⋊Dic31D4semidirect
116. #379D31semidirect
140. C31#2021semidirect
147. C24D124semidirect
161. C22×C4C22⋊D31semidirect

Maximal subgroups

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

subgroupindex
#145216112
C2×#117585302
C2×#117583942
#145208162
C31×#3792
#202131