Finite Group Databasebeta

← C2×#14521148 #16854489

Subgroups — C2×#14521148 #16854489

Order 3968.

544 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 197 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
1C22×#92470C211yesmaximal, characteristic
2C2×#11758464C211yesmaximal, characteristic, complemented
3C2×#11758470C211yesmaximal, characteristic
4#14521148C218yesmaximal, direct product factor
5C2×#11758398C211yesmaximal, characteristic, complemented
6C2×#11758397C211yesmaximal, characteristic
7C2×#11758403C211yesmaximal, characteristic, complemented
8C2×C31×#107C211yesmaximal, characteristic, complemented
9C22×D124C2211yescharacteristic
10C22×C4×D31—21no—
11C22×Dic62C2211yescharacteristic
12C22×C8×C31C2211yescharacteristic
13C2×C4⋊C4×C31C2211yescharacteristic
14C2×C4⋊C4×C31C2211yescharacteristic
15C2×(C2×D31)⋊C4—21no—
16C2×Dic31⋊C4—21no—
17C2×C4×Dic31—21no—
18C2×C4×Dic31C2211yescharacteristic
19C22×C31⋊C8C2211yescharacteristic
20C2×#92470C418yescomplemented
21C2×#92470C2214yes—
22#11758470—22no—
23#11758470C2214yes—
24#11758464—22no—
25#11758464C2214yescomplemented
26C31×#107C2214yescomplemented
27#11758403C2214yescomplemented
28#11758398C2214yescomplemented
29#11758397C2214yes—
30C23×D31—21no—
31C22×C4×C31—21no—
32C22×C4×C31—21no—
33C22×C4×C31C2311yescharacteristic
34C22×Dic31—21no—
35C22×Dic31D411yescharacteristic
36C22×Dic31D411yescharacteristic
37C2×D124—21no—
38C2×D124—22no—
39C2×D124C2×C414yes—
40C2×D124C2312yes—
41C2×C4×D31—24no—
42C2×C4×D31—44no—
43C2×Dic62—21no—
44C2×Dic62—22no—
45C2×Dic62C2×C414yescomplemented
46C2×Dic62C2312yes—
47C2×C8×C31C2×C414yescomplemented
48C2×C8×C31C2312yes—
49C4⋊C4×C31—21no—
50C4⋊C4×C31—21no—
51C4⋊C4×C31C2312yes—
52C4⋊C4×C31C2312yes—
53(C2×D31)⋊C4—24no—
54Dic31⋊C4—24no—
55C4×Dic31—24no—
56C4×Dic31D412yes—
57C4×Dic31C2312yes—
58C2×C31⋊C8—22no—
59C2×C31⋊C8C2312yes—
60#92470C2×C4116yescomplemented
61C23×C31C2×D411yescharacteristic
62C22×D31—24no—
63C22×D31—22no—
64C22×D31—42no—
65C22×D31—42no—
66C2×C4×C31—22no—
67C2×C4×C31—22no—
68C2×C4×C31—42no—
69C2×C4×C31—42no—
70C2×C4×C31C22×C412yes—
71C2×C4×C31C2×D411yescharacteristic
72C2×C4×C31#4112yes—
73C2×C4×C31C2411yescharacteristic
74C2×Dic31—24no—
75C2×Dic31—22no—
76C2×Dic31—22no—
77C2×Dic31—22no—
78C2×Dic31C2×D412yes—
79C2×Dic31C2×D412yes—
80D124—24no—
81D124—22no—
82D124C22×C414yes—
83C4×D31—48no—
84Dic62—24no—
85Dic62—22no—
86Dic62C22×C414yescomplemented
87C8×C31C22×C414yescomplemented
88C31⋊C8—22no—
89C2×#440—311nomaximal, Sylow
90C22×C31C4×D412yes—
91C22×C31AGL(1,ℤ/8)12yes—
92C22×C31#13712yes—
93C22×C31C22×D411yescharacteristic
94C2×D31—24no—
95C2×D31—42no—
96C2×D31—42no—
97C2×D31—48no—
98C4×C31—42no—
99C4×C31—42no—
100C4×C31C4×D412yes—
101C4×C31C23×C411yescharacteristic
102C4×C31C2×#4111yescharacteristic
103Dic31—24no—
104Dic31—22no—
105Dic31—22no—
106C22×SD16—311no—
107C2×C4×Q8—311no—
108C2×C4×D4—311no—
109#440—318no—
110C2×#107D3111yescharacteristic, complemented
111C2×#103—311no—
112C2×#102—311no—
113C2×#97—311no—
114C2×C31#44014yescomplemented
115C2×C31C2×C4×D411yescharacteristic
116C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
117C2×C31C2×#13711yescharacteristic
118D31—44no—
119C22×Q8—311no—
120C22×D4—311no—
121C23×C4—621no—
122C2×SD16—318no—
123C2×SD16—314no—
124C22×C8—311no—
125C22×C8C2×D3111yescharacteristic
126C4×Q8—314no—
127C4×Q8—622no—
128C4×D4—314no—
129C4×D4—622no—
130C2×C4⋊C4—621no—
131C2×C4⋊C4C2×D3111yescharacteristic
132C2×C4⋊C4C2×D3111yescharacteristic
133C2×C22⋊C4—621no—
134C2×C42—311no—
135C2×C42—621no—
136#107C2×D3114yescomplemented
137#103—314no—
138#102—314no—
139#97—314no—
140C31C2×#44011yescharacteristic, complemented, Sylow
141C24—621no—
142C2×Q8—314no—
143C2×Q8—312no—
144C2×Q8—621no—
145C2×Q8—622no—
146C2×D4—314no—
147C2×D4—312no—
148C2×D4—621no—
149C2×D4—622no—
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—311no—
153C22×C4—311no—
154C22×C4—624no—
155C22×C4—621no—
156C22×C4—1244no—
157C22×C4C22×D3111yescharacteristic
158SD16—3116no—
159C2×C8—312no—
160C2×C8—622no—
161C2×C8C4×D3114yescomplemented
162C2×C8C22×D3112yes—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—624no—
166C4⋊C4C22×D3112yes—
167C4⋊C4C22×D3112yes—
168C22⋊C4—624no—
169C42—312no—
170C42—312no—
171C42—624no—
172C23—624no—
173C23—622no—
174C23—1242no—
175C23—1242no—
176C23D4×D3111yescharacteristic
177Q8—314no—
178Q8—624no—
179Q8—622no—
180D4—314no—
181D4—624no—
182D4—622no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—312no—
188C2×C4—312no—
189C2×C4—624no—
190C2×C4—622no—
191C2×C4—622no—
192C2×C4—622no—
193C2×C4—1248no—
194C2×C4C2×C4×D3112yes—
195C2×C4D4×D3111yescharacteristic
196C2×C4#9249912yes—
197C2×C4C23×D3111yescharacteristic
198C8—622no—
199C8C2×C4×D3114yescomplemented
200C22—624no—
201C22—1248no—
202C22—1242no—
203C22—1242no—
204C22#1175847012yes—
205C22#1175848812yes—
206C22#1175849512yes—
207C22C2×D4×D3111yescharacteristic
208C4—42no—
209C4—42no—
210C4—624no—
211C4—622no—
212C4—622no—
213C4#1175847012yes—
214C4C22×C4×D3111yescharacteristic
215C4C2×#9249911yescharacteristic
216C2—1244no—
217C2#1452114814yesdirect product factor
218C2C2×#1175847011yescharacteristic
219C2C2×#1175848811yescharacteristic
220C2C2×#1175849511yescharacteristic
subgroupG/H
centerC23D4×D31
commutatorC4×C31C23×C4
FrattiniC2×C4C23×D31
FittingC2×C31×#107C2
socleC23×C31C2×D4
prime radicalC22×D124C22
cosocleC2×C4×C31C24
hypercenterC2×#107D31
hypocenterC31C2×#440
LCSG ▷ 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
2. C2×#11758464C2semidirect
4. #14521148C2direct (N × H)
5. C2×#11758398C2semidirect
7. C2×#11758403C2semidirect
8. C2×C31×#107C2semidirect
20. C2×#92470C4semidirect
25. #11758464C22semidirect
26. C31×#107C22semidirect
27. #11758403C22semidirect
28. #11758398C22semidirect
45. C2×Dic62C2×C4semidirect
47. C2×C8×C31C2×C4semidirect
60. #92470C2×C4semidirect
86. Dic62C22×C4semidirect
87. C8×C31C22×C4semidirect
110. C2×#107D31semidirect
114. C2×C31#440semidirect
136. #107C2×D31semidirect
140. C31C2×#440semidirect
161. C2×C8C4×D31semidirect
199. C8C2×C4×D31semidirect
217. C2#14521148direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#924702
C2×#117584642
C2×#117584702
#145211482
C2×#117583982
C2×#117583972
C2×#117584032
C2×C31×#1072
C2×#44031