Finite Group Databasebeta

← C2×#14521367 #16855610

Subgroups — C2×#14521367 #16855610

Order 3968.

512 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 165 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
2#14521367C218yesmaximal, direct product factor
3C2×#11758396C212yesmaximal, complemented
4C2×#11758397C212yesmaximal, complemented
5C2×C22⋊(C31⋊C8)C211yesmaximal, characteristic, complemented
6C22×C4⋊C4×C31C211yesmaximal, characteristic, complemented
7C23×C4×C31—21no—
8C23×C4×C31C2211yescharacteristic
9C22×C22⋊D31—21no—
10C22×D124C2211yescharacteristic
11C2×C4⋊C4×C31—22no—
12C2×C4⋊C4×C31—21no—
13C2×C4⋊C4×C31C2212yes—
14C2×C4⋊C4×C31C2214yescomplemented
15#11758507—22no—
16#11758507C2214yes—
17C2×(C2×D31)⋊C4—21no—
18C2×C4⋊Dic31C2211yescharacteristic
19C22×C31⋊C8C2212yes—
20C22⋊(C31⋊C8)C2214yescomplemented
21#11758397C2218yescomplemented
22#11758396C2218yescomplemented
23C24×C31D411yescharacteristic
24C23×D31—21no—
25C22×C4×C31—24no—
26C22×C4×C31—22no—
27C22×C4×C31—24no—
28C22×C4×C31—44no—
29C22×C4×C31D411yescharacteristic
30C22×C4×C31D412yes—
31C22×C4×C31C2312yes—
32C22×C4×C31C2311yescharacteristic
33C2×C22⋊D31—24no—
34C2×C22⋊D31—44no—
35C22×Dic31—21no—
36C2×D124—24no—
37C2×D124—21no—
38C2×D124C2312yes—
39C4⋊C4×C31—22no—
40C4⋊C4×C31—24no—
41C4⋊C4×C31C2314yes—
42(C2×D31)⋊C4—24no—
43C4⋊Dic31—21no—
44C4⋊Dic31C2312yes—
45C2×C31⋊C8—24no—
46C2×C31⋊C8C2314yes—
47C23×C31—22no—
48C23×C31—22no—
49C23×C31SD1614yes—
50C23×C31C2×D412yes—
51C23×C31C2×D411yescharacteristic
52C22×D31—22no—
53C22×D31—42no—
54C22×D31—42no—
55C22×D31—42no—
56C2×C4×C31—22no—
57C2×C4×C31—24no—
58C2×C4×C31—24no—
59C2×C4×C31—24no—
60C2×C4×C31—48no—
61C2×C4×C31—44no—
62C2×C4×C31C2×D412yes—
63C2×C4×C31C2×D411yescharacteristic
64C2×C4×C31#4114yes—
65C2×C4×C31C2411yescharacteristic
66C22⋊D31—48no—
67C2×Dic31—22no—
68C2×Dic31—42no—
69D124—24no—
70D124—42no—
71C31⋊C8—24no—
72C2×#481—311nomaximal, Sylow
73C22×C31—22no—
74C22×C31—22no—
75C22×C31—28no—
76C22×C31#12312yes—
77C22×C31C2×SD1614yes—
78C22×C31C2×SD1612yes—
79C22×C31AGL(1,ℤ/8)12yes—
80C22×C31C22×D411yescharacteristic
81C2×D31—42no—
82C2×D31—42no—
83C2×D31—42no—
84C2×D31—84no—
85C4×C31—22no—
86C4×C31—44no—
87C4×C31#12312yes—
88C4×C31C2×#4112yes—
89Dic31—42no—
90C2×#121—311no—
91C22×C4⋊C4D3111yescharacteristic, complemented
92#481—318no—
93C2×#106—312no—
94C2×#102—312no—
95C2×C22⋊C8—311no—
96C2×C31—24no—
97C2×C31#48114yescomplemented
98C2×C31C2×#12311yescharacteristic
99C2×C31C22×SD1611yescharacteristic
100C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
101D31—82no—
102C22×D4—311no—
103C22×D4—621no—
104C23×C4—21no—
105C23×C4C2×D3111yescharacteristic
106C22×C8—312no—
107#121—314no—
108#121—622no—
109C2×C4⋊C4—22no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—311no—
112C2×C4⋊C4C2×D3112yes—
113C2×C4⋊C4C2×D3114yescomplemented
114C2×C22⋊C4—621no—
115#106—318no—
116#102—318no—
117C22⋊C8—314no—
118C31C2×#48111yescharacteristic, complemented, Sylow
119C24—621no—
120C24C22⋊D3111yescharacteristic
121C2×D4—312no—
122C2×D4—624no—
123C2×D4—624no—
124C2×D4—621no—
125C2×D4—1244no—
126C22×C4—24no—
127C22×C4—24no—
128C22×C4—22no—
129C22×C4—44no—
130C22×C4—621no—
131C22×C4C22⋊D3112yes—
132C22×C4C22⋊D3111yescharacteristic
133C22×C4C22×D3112yes—
134C22×C4C22×D3111yescharacteristic
135C2×C8—314no—
136C2×C8—624no—
137C4⋊C4—22no—
138C4⋊C4—24no—
139C4⋊C4—312no—
140C4⋊C4—621no—
141C4⋊C4C22×D3114yes—
142C22⋊C4—624no—
143C23—22no—
144C23—22no—
145C23—622no—
146C23—1242no—
147C23—1242no—
148C23—1242no—
149C23#9248114yes—
150C23C2×C22⋊D3112yes—
151C23C2×C22⋊D3111yescharacteristic
152D4—624no—
153D4—1248no—
154D4—1242no—
155C2×C4—22no—
156C2×C4—24no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—48no—
160C2×C4—44no—
161C2×C4—622no—
162C2×C4—1242no—
163C2×C4#9249514yes—
164C2×C4C2×C22⋊D3112yes—
165C2×C4C2×C22⋊D3111yescharacteristic
166C2×C4C23×D3111yescharacteristic
167C8—624no—
168C22—28no—
169C22—22no—
170C22—22no—
171C22—1242no—
172C22—1242no—
173C22—1242no—
174C22—2484no—
175C22#1175850612yes—
176C22#1175850912yes—
177C22C2×#9248114yes—
178C22C2×#9248112yes—
179C22C22×C22⋊D3111yescharacteristic
180C4—22no—
181C4—44no—
182C4—1242no—
183C4#1175850612yes—
184C4C2×#9249512yes—
185C2—24no—
186C2—2482no—
187C2#1452136714yesdirect product factor
188C2C2×#1175850611yescharacteristic
189C2C22×#9248111yescharacteristic
190C2C2×#1175850911yescharacteristic
subgroupG/H
centerC23C2×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC22×C4⋊C4×C31C2
socleC23×C31C2×D4
prime radicalC2×#11758507C2
hypercenterC22×C4⋊C4D31
hypocenterC31C2×#481
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #14521367C2direct (N × H)
3. C2×#11758396C2semidirect
4. C2×#11758397C2semidirect
5. C2×C22⋊(C31⋊C8)C2semidirect
6. C22×C4⋊C4×C31C2semidirect
14. C2×C4⋊C4×C31C22semidirect
20. C22⋊(C31⋊C8)C22semidirect
21. #11758397C22semidirect
22. #11758396C22semidirect
91. C22×C4⋊C4D31semidirect
97. C2×C31#481semidirect
113. C2×C4⋊C4C2×D31semidirect
118. C31C2×#481semidirect
187. C2#14521367direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117585072
#145213672
C2×#117583962
C2×#117583972
C2×C22⋊(C31⋊C8)2
C22×C4⋊C4×C312
C2×#48131