Finite Group Databasebeta

← #16844278

Subgroups — #16844278

Order 3968.

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

normal subgroups only

This group has 340 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×#11758507C211yesmaximal, characteristic
2C2×C22⋊(C31⋊C8)C211yesmaximal, characteristic, complemented
3#14520782C214yesmaximal, complemented
4C31×#380C211yesmaximal, characteristic, complemented
5C23×C4×C31C2211yescharacteristic
6C22×C22⋊D31—21no—
7C22×D124C411yescharacteristic, complemented
8C2×C4⋊C4×C31—21no—
9C2×C22⋊C4×C31—21no—
10#11758507—21no—
11#11758507—21no—
12#11758507C412yescomplemented
13#11758507C2212yes—
14C2×(C2×D31)⋊C4—21no—
15C2×C4⋊Dic31C411yescharacteristic, complemented
16C22×C31⋊C8—21no—
17C31×#95C2212yescomplemented
18C22⋊(C31⋊C8)—21no—
19C22⋊(C31⋊C8)C2212yescomplemented
20C24×C31D411yescharacteristic
21C23×D31—21no—
22C22×C4×C31—22no—
23C22×C4×C31—42no—
24C22×C4×C31C2×C411yescharacteristic
25C22×C4×C31C2×C411yescharacteristic
26C22×C4×C31D411yescharacteristic
27C22×C4×C31D411yescharacteristic
28C22×C4×C31D411yescharacteristic
29C22×C4×C31C2311yescharacteristic
30C2×C22⋊D31—22no—
31C2×C22⋊D31—22no—
32C2×C22⋊D31—42no—
33C2×C22⋊D31—42no—
34C22×Dic31—21no—
35C2×D124—21no—
36C2×D124—42no—
37C2×D124C2×C412yes—
38C4⋊C4×C31—42no—
39C22⋊C4×C31—42no—
40(C2×D31)⋊C4—22no—
41(C2×D31)⋊C4—22no—
42C4⋊Dic31—21no—
43C4⋊Dic31C2×C412yes—
44C2×C31⋊C8—22no—
45C2×C31⋊C8—42no—
46C23×C31—41no—
47C23×C31—41no—
48C23×C31C22⋊C411yescharacteristic
49C23×C31C22⋊C411yescharacteristic
50C23×C31D812yes—
51C23×C31SD1612yes—
52C23×C31C2×D411yescharacteristic
53C22×D31—22no—
54C22×D31—42no—
55C22×D31—42no—
56C22×D31—42no—
57C2×C4×C31—22no—
58C2×C4×C31—22no—
59C2×C4×C31—22no—
60C2×C4×C31—41no—
61C2×C4×C31—41no—
62C2×C4×C31—41no—
63C2×C4×C31—42no—
64C2×C4×C31—42no—
65C2×C4×C31—42no—
66C2×C4×C31C22⋊C411yescharacteristic
67C2×C4×C31C22⋊C411yescharacteristic
68C2×C4×C31C22×C411yescharacteristic
69C2×C4×C31C2×D411yescharacteristic
70C22⋊D31—44no—
71C22⋊D31—42no—
72C22⋊D31—42no—
73C2×Dic31—22no—
74C2×Dic31—42no—
75D124—42no—
76D124—42no—
77C31⋊C8—42no—
78#1519—311nomaximal, Sylow
79C22×C31—21no—
80C22×C31—21no—
81C22×C31—21no—
82C22×C31—21no—
83C22×C31—21no—
84C22×C31—21no—
85C22×C31—42no—
86C22×C31—42no—
87C22×C31#10212yes—
88C22×C31#10212yes—
89C22×C31C2×C22⋊C411yescharacteristic
90C22×C31C2×D811yescharacteristic
91C22×C31C2×SD1611yescharacteristic
92C2×D31—42no—
93C2×D31—42no—
94C2×D31—42no—
95C2×D31—84no—
96C4×C31—21no—
97C4×C31—21no—
98C4×C31—21no—
99C4×C31—82no—
100C4×C31#9912yes—
101Dic31—42no—
102C2×#121—311no—
103C2×C22⋊C8—311no—
104#380D3111yescharacteristic, complemented
105#327—314no—
106C2×C31—21no—
107C2×C31—22no—
108C2×C31—22no—
109C2×C31—21no—
110C2×C31C2×#9911yescharacteristic
111C2×C31C2×#10211yescharacteristic
112C2×C31#42111yescharacteristic
113D31—82no—
114C22×D4—311no—
115C22×D4—621no—
116C23×C4C2×D3111yescharacteristic
117C22×C8—621no—
118#121—312no—
119#121—312no—
120#121—621no—
121#121—621no—
122C2×C4⋊C4—21no—
123C2×C4⋊C4—311no—
124C2×C22⋊C4—21no—
125C2×C22⋊C4—621no—
126C22⋊C8—312no—
127C22⋊C8—621no—
128#95C2×D3112yescomplemented
129C31#151911yescharacteristic, complemented, Sylow
130C24—621no—
131C24C22⋊D3111yescharacteristic
132C2×D4—312no—
133C2×D4—622no—
134C2×D4—622no—
135C2×D4—621no—
136C2×D4—1242no—
137C2×D4—1242no—
138C2×D4—1242no—
139C22×C4—22no—
140C22×C4—42no—
141C22×C4—621no—
142C22×C4C4×D3111yescharacteristic
143C22×C4C4×D3111yescharacteristic
144C22×C4D12411yescharacteristic
145C22×C4D12411yescharacteristic
146C22×C4C22⋊D3111yescharacteristic
147C22×C4C22×D3111yescharacteristic
148C2×C8—622no—
149C2×C8—1242no—
150C4⋊C4—42no—
151C4⋊C4—312no—
152C4⋊C4—621no—
153C22⋊C4—42no—
154C22⋊C4—622no—
155C22⋊C4—622no—
156C23—41no—
157C23—41no—
158C23—622no—
159C23—1242no—
160C23—1242no—
161C23—1242no—
162C23(C2×D31)⋊C411yescharacteristic
163C23(C2×D31)⋊C411yescharacteristic
164C23#9247912yes—
165C23#9248112yes—
166C23C2×C22⋊D3111yescharacteristic
167D4—1242no—
168D4—1244no—
169D4—1242no—
170D4—1242no—
171D4—1242no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—622no—
182C2×C4—1242no—
183C2×C4(C2×D31)⋊C411yescharacteristic
184C2×C4(C2×D31)⋊C411yescharacteristic
185C2×C4C2×C4×D3111yescharacteristic
186C2×C4C2×D12411yescharacteristic
187C8—1242no—
188C22—21no—
189C22—21no—
190C22—21no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—42no—
195C22—42no—
196C22—1242no—
197C22—1242no—
198C22—1242no—
199C22—2484no—
200C22#1175839712yes—
201C22#1175839712yes—
202C22C2×(C2×D31)⋊C411yescharacteristic
203C22C2×#9247911yescharacteristic
204C22C2×#9248111yescharacteristic
205C4—21no—
206C4—21no—
207C4—21no—
208C4—82no—
209C4—1242no—
210C4#1175839412yes—
211C2—21no—
212C2—22no—
213C2—22no—
214C2—21no—
215C2—2482no—
216C2C2×#1175839411yescharacteristic
217C2C2×#1175839711yescharacteristic
218C2#1452106711yescharacteristic
subgroupG/H
centerC22C2×(C2×D31)⋊C4
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#380C2
socleC22×C31C2×C22⋊C4
prime radicalC2×#11758507C2
cosocleC22×C4×C31C23
hypercenter#380D31
hypocenterC31#1519
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊(C31⋊C8)C2semidirect
3. #14520782C2semidirect
4. C31×#380C2semidirect
7. C22×D124C4semidirect
12. #11758507C4semidirect
15. C2×C4⋊Dic31C4semidirect
17. C31×#95C22semidirect
19. C22⋊(C31⋊C8)C22semidirect
104. #380D31semidirect
128. #95C2×D31semidirect
129. C31#1519semidirect

Maximal subgroups

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

subgroupindex
C2×#117585072
C2×C22⋊(C31⋊C8)2
#145207822
C31×#3802
#151931