Finite Group Databasebeta

← C2×#14521377 #16855586

Subgroups — C2×#14521377 #16855586

Order 3968.

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

normal subgroups only

This group has 460 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
1C22×C4⋊Dic31C211yesmaximal, characteristic
2#14521377C218yesmaximal, direct product factor
3C2×#11758396C212yesmaximal, complemented
4C2×#11758423C212yesmaximal, complemented
5C2×C22⋊(C31⋊C8)C211yesmaximal, characteristic
6C2×C31×C22⋊Q8C211yesmaximal, characteristic
7C22×Q8×C31C2211yescharacteristic
8C23×C4×C31C2211yescharacteristic
9C23×Dic31—21no—
10C31×C22⋊Q8—22no—
11C31×C22⋊Q8C2214yes—
12C2×C4⋊C4×C31—21no—
13C2×C4⋊C4×C31C2211yescharacteristic
14C2×C22⋊C4×C31—21no—
15C2×C4⋊Dic31—21no—
16C2×C4⋊Dic31—22no—
17C2×C4⋊Dic31C2214yes—
18C2×C4⋊Dic31C2212yes—
19C22×C31⋊C8C2212yes—
20#11758423C2218yescomplemented
21C22⋊(C31⋊C8)C2214yes—
22#11758396C2218yescomplemented
23C24×C31D411yescharacteristic
24C2×Q8×C31—21no—
25C2×Q8×C31—24no—
26C2×Q8×C31C2312yes—
27C22×C4×C31—24no—
28C22×C4×C31—21no—
29C22×C4×C31—21no—
30C22×C4×C31D411yescharacteristic
31C22×C4×C31D412yes—
32C22×C4×C31C2312yes—
33C22×C4×C31C2311yescharacteristic
34C22×Dic31—24no—
35C22×Dic31—22no—
36C22×Dic31—44no—
37C4⋊C4×C31—24no—
38C4⋊C4×C31—21no—
39C4⋊C4×C31C2312yes—
40C22⋊C4×C31—24no—
41C4⋊Dic31—24no—
42C4⋊Dic31—22no—
43C4⋊Dic31C2314yes—
44C2×C31⋊C8—24no—
45C2×C31⋊C8C2314yes—
46C23×C31—22no—
47C23×C31—22no—
48C23×C31SD1614yes—
49C23×C31C2×D412yes—
50C23×C31C2×D411yescharacteristic
51Q8×C31—24no—
52Q8×C31—42no—
53C2×C4×C31—22no—
54C2×C4×C31—24no—
55C2×C4×C31—24no—
56C2×C4×C31—22no—
57C2×C4×C31—22no—
58C2×C4×C31—42no—
59C2×C4×C31—42no—
60C2×C4×C31C2×D412yes—
61C2×C4×C31C2×D411yescharacteristic
62C2×C4×C31#4114yes—
63C2×C4×C31C2411yescharacteristic
64C2×Dic31—24no—
65C2×Dic31—48no—
66C2×Dic31—44no—
67C31⋊C8—24no—
68C2×#483—311nomaximal, Sylow
69C22×C31—22no—
70C22×C31—22no—
71C22×C31—28no—
72C22×C31#12312yes—
73C22×C31C2×SD1614yes—
74C22×C31C2×SD1612yes—
75C22×C31#13712yes—
76C22×C31C22×D411yescharacteristic
77C4×C31—22no—
78C4×C31—42no—
79C4×C31—42no—
80C4×C31#12312yes—
81C4×C31C2×#4112yes—
82Dic31—44no—
83C2×C22⋊Q8D3111yescharacteristic
84C22×C4⋊C4—311no—
85#483—318no—
86C2×#106—312no—
87C2×#103—312no—
88C2×C22⋊C8—311no—
89C2×C31—24no—
90C2×C31#48314yescomplemented
91C2×C31C2×#12311yescharacteristic
92C2×C31C22×SD1611yescharacteristic
93C2×C31C2×#13711yescharacteristic
94C22×Q8C2×D3111yescharacteristic
95C23×C4—621no—
96C23×C4C2×D3111yescharacteristic
97C22×C8—312no—
98C22⋊Q8—22no—
99C22⋊Q8C2×D3114yes—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—312no—
102C2×C4⋊C4—314no—
103C2×C4⋊C4—622no—
104C2×C4⋊C4—621no—
105C2×C4⋊C4C2×D3111yescharacteristic
106C2×C22⋊C4—21no—
107#106—318no—
108#103—318no—
109C22⋊C8—314no—
110C31C2×#48311yescharacteristic, complemented, Sylow
111C24C22⋊D3111yescharacteristic
112C2×Q8—21no—
113C2×Q8—24no—
114C2×Q8C22×D3112yes—
115C22×C4—24no—
116C22×C4—21no—
117C22×C4—21no—
118C22×C4—624no—
119C22×C4—622no—
120C22×C4—1244no—
121C22×C4C22⋊D3112yes—
122C22×C4C22⋊D3111yescharacteristic
123C22×C4C22×D3112yes—
124C22×C4C22×D3111yescharacteristic
125C2×C8—314no—
126C2×C8—624no—
127C4⋊C4—24no—
128C4⋊C4—21no—
129C4⋊C4—314no—
130C4⋊C4—624no—
131C4⋊C4—622no—
132C4⋊C4C22×D3112yes—
133C22⋊C4—24no—
134C23—22no—
135C23—22no—
136C23#9248114yes—
137C23C2×C22⋊D3112yes—
138C23C2×C22⋊D3111yescharacteristic
139Q8—24no—
140Q8—42no—
141C2×C4—22no—
142C2×C4—24no—
143C2×C4—24no—
144C2×C4—22no—
145C2×C4—22no—
146C2×C4—42no—
147C2×C4—42no—
148C2×C4—624no—
149C2×C4—1248no—
150C2×C4—1244no—
151C2×C4#9249714yes—
152C2×C4C2×C22⋊D3112yes—
153C2×C4C2×C22⋊D3111yescharacteristic
154C2×C4C23×D3111yescharacteristic
155C8—624no—
156C22—28no—
157C22—22no—
158C22—22no—
159C22#1175851212yes—
160C22C2×#9248114yes—
161C22C2×#9248112yes—
162C22#1175852812yes—
163C22C22×C22⋊D3111yescharacteristic
164C4—22no—
165C4—42no—
166C4—42no—
167C4—1244no—
168C4#1175851212yes—
169C4C2×#9249712yes—
170C2—24no—
171C2#1452137714yesdirect product factor
172C2C2×#1175851211yescharacteristic
173C2C22×#9248111yescharacteristic
174C2C2×#1175852811yescharacteristic
subgroupG/H
centerC23C2×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC2×C31×C22⋊Q8C2
socleC23×C31C2×D4
prime radicalC24×C31D4
hypercenterC2×C22⋊Q8D31
hypocenterC31C2×#483
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #14521377C2direct (N × H)
3. C2×#11758396C2semidirect
4. C2×#11758423C2semidirect
20. #11758423C22semidirect
22. #11758396C22semidirect
90. C2×C31#483semidirect
110. C31C2×#483semidirect
171. C2#14521377direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊Dic312
#145213772
C2×#117583962
C2×#117584232
C2×C22⋊(C31⋊C8)2
C2×C31×C22⋊Q82
C2×#48331