Finite Group Databasebeta

← C2×#14521359 #16855491

Subgroups — C2×#14521359 #16855491

Order 3968.

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

normal subgroups only

This group has 384 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×#11758467C211yesmaximal, characteristic
2C2×#11758464C211yesmaximal, characteristic
3#14521359C218yesmaximal, direct product factor
4C2×#11758395C211yesmaximal, characteristic
5C2×Dic31⋊C8C211yesmaximal, characteristic
6C2×#11758404C211yesmaximal, characteristic
7C2×#11758398C211yesmaximal, characteristic
8C2×C31×#106C211yesmaximal, characteristic
9C22×Dic62C2211yescharacteristic
10C22×C8×C31C2211yescharacteristic
11C2×C4⋊C4×C31C2211yescharacteristic
12C2×C4⋊C4×C31C2211yescharacteristic
13C2×C4⋊Dic31—21no—
14C2×C4⋊Dic31C2211yescharacteristic
15C2×Dic31⋊C4—21no—
16C2×Dic31⋊C4—21no—
17C2×C4×Dic31—21no—
18C2×C4×Dic31C2211yescharacteristic
19C22×C31⋊C8C2211yescharacteristic
20#11758467—22no—
21#11758467C2214yes—
22#11758464—22no—
23#11758464C2214yes—
24C31×#106C2214yes—
25#11758404C2214yes—
26Dic31⋊C8C2214yes—
27#11758398C2214yes—
28#11758395C2214yes—
29C22×C4×C31—21no—
30C22×C4×C31—21no—
31C22×C4×C31C2311yescharacteristic
32C22×Dic31—21no—
33C22×Dic31—21no—
34C22×Dic31D411yescharacteristic
35C22×Dic31D411yescharacteristic
36C2×Dic62—21no—
37C2×Dic62—22no—
38C2×Dic62Q814yes—
39C2×Dic62C2312yes—
40C2×C8×C31—22no—
41C2×C8×C31C2312yes—
42C4⋊C4×C31—21no—
43C4⋊C4×C31—21no—
44C4⋊C4×C31C2312yes—
45C4⋊C4×C31C2312yes—
46C4⋊Dic31—21no—
47C4⋊Dic31—24no—
48C4⋊Dic31C2312yes—
49Dic31⋊C4—24no—
50Dic31⋊C4—24no—
51C4×Dic31—24no—
52C4×Dic31D412yes—
53C4×Dic31C2312yes—
54C2×C31⋊C8—22no—
55C2×C31⋊C8C2312yes—
56C23×C31C2×D411yescharacteristic
57C2×C4×C31—22no—
58C2×C4×C31—22no—
59C2×C4×C31—42no—
60C2×C4×C31—42no—
61C2×C4×C31C2×D411yescharacteristic
62C2×C4×C31C2×Q812yes—
63C2×C4×C31#4112yes—
64C2×C4×C31C2411yescharacteristic
65C2×Dic31—24no—
66C2×Dic31—22no—
67C2×Dic31—22no—
68C2×Dic31—22no—
69C2×Dic31—22no—
70C2×Dic31—42no—
71C2×Dic31C2×D412yes—
72C2×Dic31C2×D412yes—
73Dic62—24no—
74Dic62—22no—
75Dic62C2×Q814yes—
76C8×C31—22no—
77C31⋊C8—22no—
78C2×#479—311nomaximal, Sylow
79C22×C31C22⋊Q812yes—
80C22×C31#13512yes—
81C22×C31#13712yes—
82C22×C31C22×D411yescharacteristic
83C4×C31—42no—
84C4×C31—42no—
85C4×C31C22⋊Q812yes—
86C4×C31C22×Q811yescharacteristic
87C4×C31C2×#4111yescharacteristic
88Dic31—24no—
89Dic31—22no—
90Dic31—22no—
91Dic31—42no—
92C2×#125—311no—
93C2×C4×Q8—311no—
94#479—318no—
95C2×#107—311no—
96C2×#106D3111yescharacteristic
97C2×C4⋊C8—311no—
98C2×#103—311no—
99C2×#103—311no—
100C2×C31#47914yescomplemented
101C2×C31C2×C22⋊Q811yescharacteristic
102C2×C31C2×#13511yescharacteristic
103C2×C31C2×#13711yescharacteristic
104C22×Q8—311no—
105C22×C8—311no—
106C22×C8C2×D3111yescharacteristic
107#125—314no—
108#125—622no—
109C4×Q8—314no—
110C4×Q8—622no—
111C2×C4⋊C4—311no—
112C2×C4⋊C4—621no—
113C2×C4⋊C4—621no—
114C2×C4⋊C4—621no—
115C2×C4⋊C4C2×D3111yescharacteristic
116C2×C4⋊C4C2×D3111yescharacteristic
117C2×C42—311no—
118C2×C42—621no—
119#107—314no—
120#106C2×D3114yes—
121C4⋊C8—314no—
122#103—314no—
123#103—314no—
124C31C2×#47911yescharacteristic, complemented, Sylow
125C2×Q8—314no—
126C2×Q8—312no—
127C2×Q8—622no—
128C2×Q8—621no—
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—311no—
132C22×C4—311no—
133C22×C4—621no—
134C22×C4—621no—
135C22×C4C22×D3111yescharacteristic
136C2×C8—22no—
137C2×C8—312no—
138C2×C8—622no—
139C2×C8C22×D3112yes—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—312no—
143C4⋊C4—624no—
144C4⋊C4—624no—
145C4⋊C4—624no—
146C4⋊C4—621no—
147C4⋊C4C22×D3112yes—
148C4⋊C4C22×D3112yes—
149C42—312no—
150C42—312no—
151C42—624no—
152C23D4×D3111yescharacteristic
153Q8—314no—
154Q8—624no—
155Q8—622no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—312no—
161C2×C4—312no—
162C2×C4—624no—
163C2×C4—622no—
164C2×C4—622no—
165C2×C4—622no—
166C2×C4—622no—
167C2×C4—1242no—
168C2×C4#9249512yes—
169C2×C4D4×D3111yescharacteristic
170C2×C4Q8×D3112yes—
171C2×C4C23×D3111yescharacteristic
172C8—22no—
173C8—622no—
174C22#1175847312yes—
175C22#1175849212yes—
176C22#1175849312yes—
177C22C2×D4×D3111yescharacteristic
178C4—42no—
179C4—42no—
180C4—624no—
181C4—622no—
182C4—622no—
183C4—1242no—
184C4#1175847312yes—
185C4C2×#9249511yescharacteristic
186C4C2×Q8×D3111yescharacteristic
187C2#1452135914yesdirect product factor
188C2C2×#1175847311yescharacteristic
189C2C2×#1175849311yescharacteristic
190C2C2×#1175849211yescharacteristic
subgroupG/H
centerC23D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC2×C31×#106C2
socle, prime radicalC23×C31C2×D4
hypercenterC2×#106D31
hypocenterC31C2×#479
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
3. #14521359C2direct (N × H)
100. C2×C31#479semidirect
124. C31C2×#479semidirect
187. C2#14521359direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117584672
C2×#117584642
#145213592
C2×#117583952
C2×Dic31⋊C82
C2×#117584042
C2×#117583982
C2×C31×#1062
C2×#47931