Finite Group Databasebeta

← C2×C31×#481 #16843022

Subgroups — C2×C31×#481 #16843022

Order 3968.

512 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 216 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×C31×#121C211yesmaximal, characteristic
2C22×C4⋊C4×C31C211yesmaximal, characteristic, complemented
3C31×#481C218yesmaximal, direct product factor
4C2×C31×#106C212yesmaximal, complemented
5C2×C31×#102C212yesmaximal, complemented
6C2×C31×C22⋊C8C211yesmaximal, characteristic, complemented
7C22×D4×C31—21no—
8C22×D4×C31C2211yescharacteristic
9C23×C4×C31—21no—
10C23×C4×C31C2211yescharacteristic
11C22×C8×C31C2212yes—
12C31×#121—22no—
13C31×#121C2214yes—
14C2×C4⋊C4×C31—22no—
15C2×C4⋊C4×C31—21no—
16C2×C4⋊C4×C31C2212yes—
17C2×C4⋊C4×C31C2211yescharacteristic
18C2×C4⋊C4×C31C2214yescomplemented
19C2×C22⋊C4×C31—21no—
20C31×#106C2218yescomplemented
21C31×#102C2218yescomplemented
22C31×C22⋊C8C2214yescomplemented
23C24×C31—21no—
24C24×C31D411yescharacteristic
25C2×D4×C31—24no—
26C2×D4×C31—21no—
27C2×D4×C31—24no—
28C2×D4×C31—44no—
29C2×D4×C31C2312yes—
30C22×C4×C31—24no—
31C22×C4×C31—24no—
32C22×C4×C31—21no—
33C22×C4×C31—22no—
34C22×C4×C31—44no—
35C22×C4×C31D412yes—
36C22×C4×C31D411yescharacteristic
37C22×C4×C31C2312yes—
38C22×C4×C31C2311yescharacteristic
39C2×C8×C31—24no—
40C2×C8×C31C2314yes—
41C4⋊C4×C31—22no—
42C4⋊C4×C31—24no—
43C4⋊C4×C31—21no—
44C4⋊C4×C31C2314yes—
45C4⋊C4×C31C2312yes—
46C22⋊C4×C31—24no—
47C23×C31—22no—
48C23×C31—22no—
49C23×C31—22no—
50C23×C31—42no—
51C23×C31—42no—
52C23×C31—42no—
53C23×C31SD1614yes—
54C23×C31C2×D412yes—
55C23×C31C2×D411yescharacteristic
56D4×C31—24no—
57D4×C31—48no—
58D4×C31—42no—
59C2×C4×C31—22no—
60C2×C4×C31—24no—
61C2×C4×C31—24no—
62C2×C4×C31—22no—
63C2×C4×C31—24no—
64C2×C4×C31—48no—
65C2×C4×C31—42no—
66C2×C4×C31—44no—
67C2×C4×C31C2×D412yes—
68C2×C4×C31C2×D411yescharacteristic
69C2×C4×C31#4114yes—
70C2×C4×C31C2411yescharacteristic
71C8×C31—24no—
72C2×#481C3111yesmaximal, characteristic, direct product factor, Sylow
73C22×C31—22no—
74C22×C31—22no—
75C22×C31—28no—
76C22×C31—42no—
77C22×C31—42no—
78C22×C31—42no—
79C22×C31—84no—
80C22×C31#12312yes—
81C22×C31C2×SD1614yes—
82C22×C31C2×SD1612yes—
83C22×C31AGL(1,ℤ/8)12yes—
84C22×C31C22×D411yescharacteristic
85C4×C31—22no—
86C4×C31—42no—
87C4×C31—44no—
88C4×C31#12312yes—
89C4×C31C2×#4112yes—
90C2×#121C2×C3111yescharacteristic
91C22×C4⋊C4C2×C3111yescharacteristic, complemented
92#481C2×C3118yesdirect product factor
93C2×#106C2×C3112yescomplemented
94C2×#102C2×C3112yescomplemented
95C2×C22⋊C8C2×C3111yescharacteristic, complemented
96C2×C31—24no—
97C2×C31—82no—
98C2×C31#48114yesdirect product factor
99C2×C31C2×#12311yescharacteristic
100C2×C31C22×SD1611yescharacteristic
101C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
102C22×D4—21no—
103C22×D4C22×C3111yescharacteristic
104C23×C4—21no—
105C23×C4C22×C3111yescharacteristic
106C22×C8C22×C3112yes—
107#121—22no—
108#121C22×C3114yes—
109C2×C4⋊C4—22no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4C22×C3112yes—
112C2×C4⋊C4C22×C3111yescharacteristic
113C2×C4⋊C4C22×C3114yescomplemented
114C2×C22⋊C4—21no—
115#106C22×C3118yescomplemented
116#102C22×C3118yescomplemented
117C22⋊C8C22×C3114yescomplemented
118C31C2×#48111yescharacteristic, direct product factor, Sylow
119C24—21no—
120C24D4×C3111yescharacteristic
121C2×D4—24no—
122C2×D4—21no—
123C2×D4—24no—
124C2×D4—44no—
125C2×D4C23×C3112yes—
126C22×C4—24no—
127C22×C4—21no—
128C22×C4—22no—
129C22×C4—24no—
130C22×C4—44no—
131C22×C4D4×C3111yescharacteristic
132C22×C4D4×C3112yes—
133C22×C4C23×C3112yes—
134C22×C4C23×C3111yescharacteristic
135C2×C8—24no—
136C2×C8C23×C3114yes—
137C4⋊C4—22no—
138C4⋊C4—24no—
139C4⋊C4—21no—
140C4⋊C4C23×C3114yes—
141C4⋊C4C23×C3112yes—
142C22⋊C4—24no—
143C23—22no—
144C23—22no—
145C23—22no—
146C23—42no—
147C23—42no—
148C23—42no—
149C23SD16×C3114yes—
150C23C2×D4×C3112yes—
151C23C2×D4×C3111yescharacteristic
152D4—24no—
153D4—48no—
154D4—42no—
155C2×C4—22no—
156C2×C4—24no—
157C2×C4—24no—
158C2×C4—22no—
159C2×C4—24no—
160C2×C4—48no—
161C2×C4—42no—
162C2×C4—44no—
163C2×C4C2×D4×C3112yes—
164C2×C4C2×D4×C3111yescharacteristic
165C2×C4#41×C3114yes—
166C2×C4C24×C3111yescharacteristic
167C8—24no—
168C22—28no—
169C22—22no—
170C22—22no—
171C22—42no—
172C22—42no—
173C22—42no—
174C22—84no—
175C22C31×#12312yes—
176C22C2×SD16×C3114yes—
177C22C2×SD16×C3112yes—
178C22C31×AGL(1,ℤ/8)12yes—
179C22C22×D4×C3111yescharacteristic
180C4—22no—
181C4—42no—
182C4—44no—
183C4C31×#12312yes—
184C4C2×#41×C3112yes—
185C2—24no—
186C2—82no—
187C2C31×#48114yesdirect product factor
188C2C2×C31×#12311yescharacteristic
189C2C22×SD16×C3111yescharacteristic
190C2C2×C31×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
center, socleC23×C31C2×D4
commutator, Frattini, cosocleC2×C4C24×C31
prime radicalC2×C31×#121C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×C31C2semidirect
3. C31×#481C2direct (N × H)
4. C2×C31×#106C2semidirect
5. C2×C31×#102C2semidirect
6. C2×C31×C22⋊C8C2semidirect
18. C2×C4⋊C4×C31C22semidirect
20. C31×#106C22semidirect
21. C31×#102C22semidirect
22. C31×C22⋊C8C22semidirect
72. C2×#481C31direct (N × H)
91. C22×C4⋊C4C2×C31semidirect
92. #481C2×C31direct (N × H)
93. C2×#106C2×C31semidirect
94. C2×#102C2×C31semidirect
95. C2×C22⋊C8C2×C31semidirect
98. C2×C31#481direct (N × H)
113. C2×C4⋊C4C22×C31semidirect
115. #106C22×C31semidirect
116. #102C22×C31semidirect
117. C22⋊C8C22×C31semidirect
118. C31C2×#481direct (N × H)
187. C2C31×#481direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#1212
C22×C4⋊C4×C312
C31×#4812
C2×C31×#1062
C2×C31×#1022
C2×C31×C22⋊C82
C2×#48131