Finite Group Databasebeta

← C2×#14521408 #16856039

Subgroups — C2×#14521408 #16856039

Order 3968.

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

normal subgroups only

This group has 436 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×#11758446C211yesmaximal, characteristic, complemented
2#14521408C218yesmaximal, direct product factor
3C2×#11758423C212yesmaximal, complemented
4C2×#11758420C212yesmaximal
5C2×#11758391C211yesmaximal, characteristic, complemented
6C2×C31×#124C211yesmaximal, characteristic
7C22×Q8×C31C2211yescharacteristic
8C22×D4×C31C2211yescharacteristic
9C22×Dic62—21no—
10C31×#124—22no—
11C31×#124C2214yes—
12C2×C22⋊C4×C31—21no—
13C2×C22⋊C4×C31—21no—
14C2×C42×C31C2211yescharacteristic
15C2×C4⋊Dic31—21no—
16C2×C4⋊Dic31C2212yes—
17C22×C31⋊C8C2212yes—
18#11758446—22no—
19#11758446C2214yescomplemented
20#11758423C2218yescomplemented
21#11758420C2218yes—
22#11758391C2214yescomplemented
23C24×C31—21no—
24C2×Q8×C31—21no—
25C2×Q8×C31—24no—
26C2×Q8×C31C2312yes—
27C2×D4×C31—21no—
28C2×D4×C31—24no—
29C2×D4×C31C2312yes—
30C22×C4×C31—21no—
31C22×C4×C31D411yescharacteristic
32C22×C4×C31D411yescharacteristic
33C22×C4×C31C2311yescharacteristic
34C22×Dic31—22no—
35C2×Dic62—24no—
36C2×Dic62—44no—
37C22⋊C4×C31—24no—
38C22⋊C4×C31—24no—
39C42×C31D412yes—
40C42×C31C2312yes—
41C4⋊Dic31—22no—
42C4⋊Dic31—24no—
43C4⋊Dic31C2314yes—
44C2×C31⋊C8—24no—
45C2×C31⋊C8C2314yes—
46C23×C31—22no—
47C23×C31—42no—
48C23×C31—42no—
49C23×C31—42no—
50C23×C31C2×D411yescharacteristic
51Q8×C31—24no—
52Q8×C31—42no—
53D4×C31—24no—
54D4×C31—42no—
55C2×C4×C31—22no—
56C2×C4×C31—22no—
57C2×C4×C31—22no—
58C2×C4×C31—42no—
59C2×C4×C31C2×D412yes—
60C2×C4×C31C2×D412yes—
61C2×C4×C31C2×D411yescharacteristic
62C2×C4×C31#4114yes—
63C2×C4×C31C2411yescharacteristic
64C2×Dic31—24no—
65C2×Dic31—44no—
66Dic62—48no—
67C31⋊C8—24no—
68C2×#489—311nomaximal, Sylow
69C22×C31—42no—
70C22×C31—42no—
71C22×C31—42no—
72C22×C31—84no—
73C22×C31#12412yes—
74C22×C31AGL(1,ℤ/8)12yes—
75C22×C31#13712yes—
76C22×C31C22×D411yescharacteristic
77C4×C31—22no—
78C4×C31—22no—
79C4×C31—42no—
80C4×C31#12412yes—
81C4×C31C2×#4112yes—
82Dic31—44no—
83C2×C4⋊Q8—311no—
84C2×#124D3111yescharacteristic
85#489—318no—
86C2×#103—312no—
87C2×#102—312no—
88C2×#97—311no—
89C2×C31—82no—
90C2×C31#48914yescomplemented
91C2×C31C2×#12411yescharacteristic
92C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
93C2×C31C2×#13711yescharacteristic
94C22×Q8—621no—
95C22×Q8C2×D3111yescharacteristic
96C22×D4C2×D3111yescharacteristic
97C22×C8—312no—
98C4⋊Q8—314no—
99C4⋊Q8—622no—
100#124—22no—
101#124C2×D3114yes—
102C2×C4⋊C4—312no—
103C2×C4⋊C4—621no—
104C2×C22⋊C4—21no—
105C2×C22⋊C4—21no—
106C2×C42C2×D3111yescharacteristic
107#103—318no—
108#102—318no—
109#97—314no—
110C31C2×#48911yescharacteristic, complemented, Sylow
111C24—21no—
112C2×Q8—21no—
113C2×Q8—24no—
114C2×Q8—624no—
115C2×Q8—1244no—
116C2×Q8C22×D3112yes—
117C2×D4—24no—
118C2×D4—21no—
119C2×D4C22×D3112yes—
120C22×C4—21no—
121C22×C4—622no—
122C22×C4C22⋊D3111yescharacteristic
123C22×C4C22⋊D3111yescharacteristic
124C22×C4C22×D3111yescharacteristic
125C2×C8—314no—
126C2×C8—624no—
127C4⋊C4—314no—
128C4⋊C4—622no—
129C4⋊C4—624no—
130C22⋊C4—24no—
131C22⋊C4—24no—
132C42C22⋊D3112yes—
133C42C22×D3112yes—
134C23—22no—
135C23—42no—
136C23—42no—
137C23—42no—
138C23C2×C22⋊D3111yescharacteristic
139Q8—24no—
140Q8—42no—
141Q8—1248no—
142D4—24no—
143D4—42no—
144C2×C4—22no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—42no—
148C2×C4—624no—
149C2×C4—1244no—
150C2×C4#9249714yes—
151C2×C4C2×C22⋊D3112yes—
152C2×C4C2×C22⋊D3112yes—
153C2×C4C2×C22⋊D3111yescharacteristic
154C2×C4C23×D3111yescharacteristic
155C8—624no—
156C22—42no—
157C22—42no—
158C22—42no—
159C22—84no—
160C22#1175851312yes—
161C22#1175852612yes—
162C22#1175852812yes—
163C22C22×C22⋊D3111yescharacteristic
164C4—22no—
165C4—22no—
166C4—42no—
167C4—1244no—
168C4#1175851312yes—
169C4C2×#9249712yes—
170C2—82no—
171C2#1452140814yesdirect product factor
172C2C2×#1175851311yescharacteristic
173C2C2×#1175852611yescharacteristic
174C2C2×#1175852811yescharacteristic
subgroupG/H
centerC23C2×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC2×C31×#124C2
socleC23×C31C2×D4
prime radicalC22×D4×C31C22
hypercenterC2×#124D31
hypocenterC31C2×#489
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#11758446C2semidirect
2. #14521408C2direct (N × H)
3. C2×#11758423C2semidirect
5. C2×#11758391C2semidirect
19. #11758446C22semidirect
20. #11758423C22semidirect
22. #11758391C22semidirect
90. C2×C31#489semidirect
110. C31C2×#489semidirect
171. C2#14521408direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117584462
#145214082
C2×#117584232
C2×#117584202
C2×#117583912
C2×C31×#1242
C2×#48931