Finite Group Databasebeta

← C2×#14521386 #16855618

Subgroups — C2×#14521386 #16855618

Order 3968.

460 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11758474C211yesmaximal, characteristic
2C2×C4⋊C4×D31C211yesmaximal, characteristic
3#14521386C218yesmaximal, direct product factor
4C2×#11758395C211yesmaximal, characteristic, complemented
5C2×#11758404C211yesmaximal, characteristic, complemented
6C2×#11758398C211yesmaximal, characteristic, complemented
7C2×(C2×D31)⋊C8C211yesmaximal, characteristic
8C2×C31×#107C211yesmaximal, characteristic, complemented
9C22×C4×D31—21no—
10C22×C4×D31C2211yescharacteristic
11C22×Dic62C2211yescharacteristic
12C22×C8×C31C2211yescharacteristic
13C2×C4⋊C4×C31C2211yescharacteristic
14C2×C4⋊C4×C31C2211yescharacteristic
15C2×(C2×D31)⋊C4—21no—
16C2×C4⋊Dic31—21no—
17C2×C4⋊Dic31C2211yescharacteristic
18C2×Dic31⋊C4—21no—
19C22×C31⋊C8C2211yescharacteristic
20#11758474—22no—
21#11758474C2214yes—
22C4⋊C4×D31—22no—
23C4⋊C4×D31C2214yes—
24C31×#107C2214yescomplemented
25(C2×D31)⋊C8C2214yes—
26#11758404C2214yescomplemented
27#11758398C2214yescomplemented
28#11758395C2214yescomplemented
29C23×D31D411yescharacteristic
30C22×C4×C31—21no—
31C22×C4×C31—21no—
32C22×C4×C31C2311yescharacteristic
33C22×Dic31—21no—
34C22×Dic31—21no—
35C22×Dic31D411yescharacteristic
36C2×C4×D31—22no—
37C2×C4×D31—22no—
38C2×C4×D31—24no—
39C2×C4×D31—44no—
40C2×C4×D31D412yes—
41C2×C4×D31C2312yes—
42C2×Dic62—22no—
43C2×Dic62—22no—
44C2×Dic62—21no—
45C2×Dic62C2312yes—
46C2×C8×C31—22no—
47C2×C8×C31C2312yes—
48C4⋊C4×C31—21no—
49C4⋊C4×C31—21no—
50C4⋊C4×C31C2312yes—
51C4⋊C4×C31C2312yes—
52(C2×D31)⋊C4—24no—
53C4⋊Dic31—21no—
54C4⋊Dic31—24no—
55C4⋊Dic31C2312yes—
56Dic31⋊C4—24no—
57C2×C31⋊C8—22no—
58C2×C31⋊C8C2312yes—
59C23×C31C2×D411yescharacteristic
60C22×D31—22no—
61C22×D31—22no—
62C22×D31Q1614yes—
63C22×D31C2×D412yes—
64C2×C4×C31—22no—
65C2×C4×C31—22no—
66C2×C4×C31—42no—
67C2×C4×C31—42no—
68C2×C4×C31C2×D411yescharacteristic
69C2×C4×C31#4112yes—
70C2×C4×C31#4112yes—
71C2×C4×C31C2411yescharacteristic
72C2×Dic31—22no—
73C2×Dic31—22no—
74C2×Dic31—22no—
75C2×Dic31—42no—
76C2×Dic31—42no—
77C2×Dic31C2×D412yes—
78C4×D31—24no—
79C4×D31—22no—
80C4×D31—22no—
81C4×D31—48no—
82Dic62—22no—
83Dic62—22no—
84Dic62—42no—
85C8×C31—22no—
86C31⋊C8—22no—
87C2×#484—311nomaximal, Sylow
88C22×C31#12312yes—
89C22×C31C2×Q1612yes—
90C22×C31AGL(1,ℤ/8)12yes—
91C22×C31C22×D411yescharacteristic
92C2×D31—22no—
93C2×D31—22no—
94C2×D31—28no—
95C2×D31C2×Q1614yes—
96C4×C31—42no—
97C4×C31—42no—
98C4×C31#12312yes—
99C4×C31C2×#4111yescharacteristic
100C4×C31C2×#4111yescharacteristic
101Dic31—22no—
102Dic31—42no—
103Dic31—42no—
104C2×C22⋊Q8—311no—
105C22×C4⋊C4—311no—
106#484—318no—
107C2×#107—311no—
108C2×#107D3111yescharacteristic, complemented
109C2×#103—311no—
110C2×#103—311no—
111C2×C22⋊C8—311no—
112C2×C31#48414yescomplemented
113C2×C31C2×#12311yescharacteristic
114C2×C31C22×Q1611yescharacteristic
115C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
116D31—24no—
117C22×Q8—311no—
118C23×C4—311no—
119C23×C4—621no—
120C22×C8—311no—
121C22×C8C2×D3111yescharacteristic
122C22⋊Q8—314no—
123C22⋊Q8—622no—
124C2×C4⋊C4—311no—
125C2×C4⋊C4—314no—
126C2×C4⋊C4—622no—
127C2×C4⋊C4—621no—
128C2×C4⋊C4—621no—
129C2×C4⋊C4C2×D3111yescharacteristic
130C2×C4⋊C4C2×D3111yescharacteristic
131C2×C22⋊C4—621no—
132#107—314no—
133#107C2×D3114yescomplemented
134#103—314no—
135#103—314no—
136C22⋊C8—314no—
137C31C2×#48411yescharacteristic, complemented, Sylow
138C24—311no—
139C2×Q8—312no—
140C2×Q8—621no—
141C2×Q8—622no—
142C2×Q8—622no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—311no—
146C22×C4—312no—
147C22×C4—312no—
148C22×C4—624no—
149C22×C4—622no—
150C22×C4—622no—
151C22×C4—621no—
152C22×C4—621no—
153C22×C4—1244no—
154C22×C4C22×D3111yescharacteristic
155C2×C8—22no—
156C2×C8—312no—
157C2×C8—622no—
158C2×C8C22×D3112yes—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—312no—
162C4⋊C4—624no—
163C4⋊C4—624no—
164C4⋊C4—621no—
165C4⋊C4C22×D3112yes—
166C4⋊C4C22×D3112yes—
167C22⋊C4—624no—
168C23—314no—
169C23—312no—
170C23—622no—
171C23—622no—
172C23D4×D3111yescharacteristic
173Q8—622no—
174Q8—622no—
175Q8—1242no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—312no—
181C2×C4—622no—
182C2×C4—624no—
183C2×C4—622no—
184C2×C4—622no—
185C2×C4—622no—
186C2×C4—622no—
187C2×C4—1248no—
188C2×C4—1242no—
189C2×C4—1242no—
190C2×C4#9249512yes—
191C2×C4D4×D3111yescharacteristic
192C2×C4#9249912yes—
193C2×C4C23×D3111yescharacteristic
194C8—22no—
195C8—622no—
196C22—314no—
197C22—628no—
198C22—622no—
199C22—622no—
200C22#1175847112yes—
201C22#1175848812yes—
202C22Q16×D3112yes—
203C22C2×D4×D3111yescharacteristic
204C4—42no—
205C4—42no—
206C4—622no—
207C4—1242no—
208C4—1242no—
209C4#1175847112yes—
210C4C2×#9249511yescharacteristic
211C4C2×#9249911yescharacteristic
212C2—624no—
213C2#1452138614yesdirect product factor
214C2C2×#1175847111yescharacteristic
215C2C2×Q16×D3111yescharacteristic
216C2C2×#1175848811yescharacteristic
subgroupG/H
centerC23D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC2×C31×#107C2
socleC23×C31C2×D4
prime radicalC23×D31D4
hypercenterC2×#107D31
hypocenterC31C2×#484
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
3. #14521386C2direct (N × H)
4. C2×#11758395C2semidirect
5. C2×#11758404C2semidirect
6. C2×#11758398C2semidirect
8. C2×C31×#107C2semidirect
24. C31×#107C22semidirect
26. #11758404C22semidirect
27. #11758398C22semidirect
28. #11758395C22semidirect
108. C2×#107D31semidirect
112. C2×C31#484semidirect
133. #107C2×D31semidirect
137. C31C2×#484semidirect
213. C2#14521386direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117584742
C2×C4⋊C4×D312
#145213862
C2×#117583952
C2×#117584042
C2×#117583982
C2×(C2×D31)⋊C82
C2×C31×#1072
C2×#48431