Finite Group Databasebeta

← C2×#14521662 #16859080

Subgroups — C2×#14521662 #16859080

Order 3968.

1004 conjugacy classes of subgroups; only the 485 normal subgroups are shown.

normal subgroups only

This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 485 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#14521662C2116yesmaximal, direct product factor
2C2×#11758446C211yesmaximal, characteristic, complemented
3C2×#11758475C214yesmaximal
4C2×#11758467C214yesmaximal, complemented
5C2×#11758474C212yesmaximal
6C2×#11758464C212yesmaximal, complemented
7C2×#11758449C211yesmaximal, characteristic
8C2×C31×#125C211yesmaximal, characteristic, complemented
9C22×C4×D31C2211yescharacteristic
10C22×Dic62C2212yes—
11C31×#125C2218yescomplemented
12C2×C4⋊C4×C31C2212yes—
13C2×C4⋊C4×C31C2214yes—
14C2×C42×C31C2211yescharacteristic
15C2×(C2×D31)⋊C4C2212yes—
16C2×(C2×D31)⋊C4C2214yes—
17C2×C4⋊Dic31C2214yes—
18C2×C4⋊Dic31C2214yes—
19C2×Dic31⋊C4C2212yes—
20C2×Dic31⋊C4C2214yes—
21C2×C4×Dic31C2211yescharacteristic
22C2×C4×Dic31C2214yes—
23#11758475C22132yes—
24#11758474C22116yes—
25#11758467C22132yescomplemented
26#11758464C22116yescomplemented
27#11758449C2218yes—
28#11758446C2218yescomplemented
29C23×D31C2311yescharacteristic
30C22×C4×C31C2314yes—
31C22×C4×C31C2312yes—
32C22×C4×C31C2311yescharacteristic
33C22×Dic31C2312yes—
34C22×Dic31C2314yes—
35C22×Dic31C2311yescharacteristic
36C2×C4×D31—24no—
37C2×C4×D31C2314yes—
38C2×Dic62—28no—
39C2×Dic62C2318yes—
40C4⋊C4×C31C2318yes—
41C4⋊C4×C31C23116yes—
42C42×C31C2314yes—
43(C2×D31)⋊C4C2318yes—
44(C2×D31)⋊C4C23116yes—
45C4⋊Dic31C23116yes—
46C4⋊Dic31C23116yes—
47Dic31⋊C4C2318yes—
48Dic31⋊C4C23116yes—
49C4×Dic31C2314yes—
50C4×Dic31C23116yes—
51C23×C31C2411yescharacteristic
52C22×D31—22no—
53C22×D31—24no—
54C22×D31C2412yes—
55C2×C4×C31—28no—
56C2×C4×C31—24no—
57C2×C4×C31#4114yes—
58C2×C4×C31C2418yes—
59C2×C4×C31C2414yes—
60C2×C4×C31C2412yes—
61C2×Dic31—28no—
62C2×Dic31—22no—
63C2×Dic31—24no—
64C2×Dic31C2414yes—
65C2×Dic31C2418yes—
66C2×Dic31C2412yes—
67C4×D31—28no—
68Dic62—216no—
69C2×#541—311nomaximal, Sylow
70C22×C31C2×#4112yes—
71C22×C312−1+414yes—
72C22×C31C2511yescharacteristic
73C2×D31—22no—
74C2×D31—24no—
75C2×D31—44no—
76C4×C31—28no—
77C4×C31—24no—
78C4×C31C2×#4114yes—
79Dic31—28no—
80Dic31—22no—
81Dic31—24no—
82#541—3116no—
83C2×C4⋊Q8—311no—
84C2×#126—314no—
85C2×#125—314no—
86C2×#125D3111yescharacteristic, complemented
87C2×C22⋊Q8—312no—
88C2×C4×Q8—312no—
89C2×#117—311no—
90C2×C31#54114yescomplemented
91C2×C31C22×#4111yescharacteristic
92C2×C31C2×2−1+412yes—
93D31—42no—
94C22×Q8—312no—
95C23×C4—311no—
96C4⋊Q8—318no—
97#126—3132no—
98#125—3132no—
99#125C2×D3118yescomplemented
100C22⋊Q8—3116no—
101C4×Q8—3116no—
102#117—318no—
103C2×C4⋊C4—312no—
104C2×C4⋊C4—314no—
105C2×C4⋊C4—314no—
106C2×C4⋊C4—314no—
107C2×C4⋊C4C2×D3112yes—
108C2×C4⋊C4C2×D3114yes—
109C2×C22⋊C4—312no—
110C2×C22⋊C4—314no—
111C2×C42—311no—
112C2×C42—314no—
113C2×C42C2×D3111yescharacteristic
114C31C2×#54111yescharacteristic, complemented, Sylow
115C24—311no—
116C2×Q8—318no—
117C2×Q8—628no—
118C22×C4—312no—
119C22×C4—314no—
120C22×C4—311no—
121C22×C4—314no—
122C22×C4—624no—
123C22×C4C22×D3114yes—
124C22×C4C22×D3112yes—
125C22×C4C22×D3111yescharacteristic
126C4⋊C4—318no—
127C4⋊C4—3116no—
128C4⋊C4—3116no—
129C4⋊C4—3116no—
130C4⋊C4C22×D3118yes—
131C4⋊C4C22×D31116yes—
132C22⋊C4—318no—
133C22⋊C4—3116no—
134C42—314no—
135C42—3116no—
136C42C22×D3114yes—
137C23—312no—
138C23—622no—
139C23—624no—
140C23C23×D3111yescharacteristic
141Q8—6216no—
142C2×C4—28no—
143C2×C4—24no—
144C2×C4—314no—
145C2×C4—318no—
146C2×C4—312no—
147C2×C4—622no—
148C2×C4—628no—
149C2×C4—624no—
150C2×C4—628no—
151C2×C4#9249914yes—
152C2×C4C23×D3118yes—
153C2×C4C23×D3114yes—
154C2×C4C23×D3112yes—
155C22—622no—
156C22—624no—
157C22—1244no—
158C22C2×#9249912yes—
159C22#1175856714yes—
160C22C24×D3111yescharacteristic
161C4—28no—
162C4—24no—
163C4—622no—
164C4—628no—
165C4—624no—
166C4C2×#9249914yes—
167C2—1242no—
168C2#1452166214yesdirect product factor
169C2C22×#9249911yescharacteristic
170C2C2×#1175856712yes—
subgroupG/H
centerC23C23×D31
commutator, cosocleC22×C31C25
FrattiniC22C24×D31
FittingC2×C31×#125C2
socleC23×C31C24
prime radicalC23×D31C23
hypercenterC2×#125D31
hypocenterC31C2×#541
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. #14521662C2direct (N × H)
2. C2×#11758446C2semidirect
4. C2×#11758467C2semidirect
6. C2×#11758464C2semidirect
8. C2×C31×#125C2semidirect
11. C31×#125C22semidirect
25. #11758467C22semidirect
26. #11758464C22semidirect
28. #11758446C22semidirect
86. C2×#125D31semidirect
90. C2×C31#541semidirect
99. #125C2×D31semidirect
114. C31C2×#541semidirect
168. C2#14521662direct (N × H)

Maximal subgroups

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

subgroupindex
#145216622
C2×#117584462
C2×#117584752
C2×#117584672
C2×#117584742
C2×#117584642
C2×#117584492
C2×C31×#1252
C2×#54131