Finite Group Databasebeta

← C2×#14521258 #16855148

Subgroups — C2×#14521258 #16855148

Order 3968.

480 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 157 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×Dic124C211yesmaximal, characteristic
2C22×#92482C211yesmaximal, characteristic
3C2×#11758521C211yesmaximal, characteristic
4C2×#11758464C211yesmaximal, characteristic
5#14521258C218yesmaximal, direct product factor
6C2×Dic31⋊C8C211yesmaximal, characteristic
7C2×#11758398C211yesmaximal, characteristic
8C2×C31×#103C211yesmaximal, characteristic
9C22×Q8×C31C2211yescharacteristic
10C22×Dic62C2211yescharacteristic
11C22×Dic62C2211yescharacteristic
12C22×C8×C31C2211yescharacteristic
13C2×C4⋊C4×C31C2211yescharacteristic
14#11758521—22no—
15#11758521C2214yes—
16C2×#92482—24no—
17C2×#92482C2214yes—
18C2×Dic31⋊C4—21no—
19C2×Dic31⋊C4—21no—
20C2×Dic31⋊C4—21no—
21C2×C4×Dic31—21no—
22C2×C4×Dic31C2211yescharacteristic
23C22×C31⋊C8C2211yescharacteristic
24C2×Dic124—24no—
25C2×Dic124C2214yes—
26#11758464—22no—
27#11758464C2214yes—
28C31×#103C2214yes—
29Dic31⋊C8C2214yes—
30#11758398C2214yes—
31C2×Q8×C31—21no—
32C2×Q8×C31—22no—
33C2×Q8×C31—22no—
34C2×Q8×C31C2312yes—
35C22×C4×C31—21no—
36C22×C4×C31—21no—
37C22×C4×C31C2311yescharacteristic
38C22×Dic31—21no—
39C22×Dic31—21no—
40C22×Dic31D411yescharacteristic
41C22×Dic31D411yescharacteristic
42C2×Dic62—21no—
43C2×Dic62—22no—
44C2×Dic62—22no—
45C2×Dic62—22no—
46C2×Dic62—21no—
47C2×Dic62D414yes—
48C2×Dic62C2312yes—
49C2×Dic62C2312yes—
50C2×C8×C31—22no—
51C2×C8×C31C2312yes—
52C4⋊C4×C31—21no—
53C4⋊C4×C31C2312yes—
54#92482—28no—
55Dic31⋊C4—24no—
56Dic31⋊C4—24no—
57Dic31⋊C4—24no—
58C4×Dic31—24no—
59C4×Dic31D412yes—
60C4×Dic31C2312yes—
61C2×C31⋊C8—22no—
62C2×C31⋊C8C2312yes—
63Dic124—28no—
64C23×C31C2×D411yescharacteristic
65Q8×C31—22no—
66Q8×C31—22no—
67Q8×C31—42no—
68C2×C4×C31—22no—
69C2×C4×C31—22no—
70C2×C4×C31—42no—
71C2×C4×C31—42no—
72C2×C4×C31C2×D411yescharacteristic
73C2×C4×C31C2×D412yes—
74C2×C4×C31#4112yes—
75C2×C4×C31C2411yescharacteristic
76C2×Dic31—24no—
77C2×Dic31—22no—
78C2×Dic31—22no—
79C2×Dic31—22no—
80C2×Dic31—42no—
81C2×Dic31Q1614yescomplemented
82C2×Dic31C2×D412yes—
83C2×Dic31C2×D412yes—
84Dic62—24no—
85Dic62—22no—
86Dic62—22no—
87Dic62—22no—
88Dic62—42no—
89Dic62C2×D414yes—
90C8×C31—22no—
91C31⋊C8—22no—
92C2×#462—311nomaximal, Sylow
93C22×C31#12112yes—
94C22×C31C2×Q1612yes—
95C22×C31#13712yes—
96C22×C31C22×D411yescharacteristic
97C4×C31—42no—
98C4×C31—42no—
99C4×C31#12112yes—
100C4×C31C22×D411yescharacteristic
101C4×C31C2×#4111yescharacteristic
102Dic31—24no—
103Dic31—22no—
104Dic31—42no—
105Dic31C2×Q1614yescomplemented
106C22×Q16—311no—
107C22×Q16—311no—
108C2×C4⋊Q8—311no—
109C2×C4×Q8—311no—
110#462—318no—
111C2×C4⋊C8—311no—
112C2×#103—311no—
113C2×#103D3111yescharacteristic
114C2×C31#46214yescomplemented
115C2×C31C2×#12111yescharacteristic
116C2×C31C22×Q1611yescharacteristic
117C2×C31C2×#13711yescharacteristic
118C22×Q8—311no—
119C22×Q8—311no—
120C22×Q8C2×D3111yescharacteristic
121C2×Q16—314no—
122C2×Q16—314no—
123C2×Q16—624no—
124C2×Q16—624no—
125C22×C8—311no—
126C22×C8C2×D3111yescharacteristic
127C4⋊Q8—314no—
128C4⋊Q8—622no—
129C4×Q8—314no—
130C4×Q8—622no—
131C2×C4⋊C4—621no—
132C2×C4⋊C4—621no—
133C2×C4⋊C4—621no—
134C2×C4⋊C4C2×D3111yescharacteristic
135C2×C42—311no—
136C2×C42—621no—
137C4⋊C8—314no—
138#103—314no—
139#103C2×D3114yes—
140C31C2×#46211yescharacteristic, complemented, Sylow
141C2×Q8—21no—
142C2×Q8—22no—
143C2×Q8—22no—
144C2×Q8—314no—
145C2×Q8—312no—
146C2×Q8—312no—
147C2×Q8—622no—
148C2×Q8—621no—
149C2×Q8—621no—
150C2×Q8—622no—
151C2×Q8—622no—
152C2×Q8C22×D3112yes—
153C22×C4—21no—
154C22×C4—21no—
155C22×C4—311no—
156C22×C4—311no—
157C22×C4—621no—
158C22×C4—621no—
159C22×C4C22×D3111yescharacteristic
160Q16—628no—
161Q16—628no—
162C2×C8—22no—
163C2×C8—312no—
164C2×C8—622no—
165C2×C8C22×D3112yes—
166C4⋊C4—21no—
167C4⋊C4—624no—
168C4⋊C4—624no—
169C4⋊C4—624no—
170C4⋊C4C22×D3112yes—
171C42—312no—
172C42—312no—
173C42—624no—
174C23D4×D3111yescharacteristic
175Q8—22no—
176Q8—22no—
177Q8—42no—
178Q8—314no—
179Q8—624no—
180Q8—622no—
181Q8—622no—
182Q8—622no—
183Q8—1242no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—314no—
189C2×C4—312no—
190C2×C4—312no—
191C2×C4—624no—
192C2×C4—622no—
193C2×C4—622no—
194C2×C4—622no—
195C2×C4—1242no—
196C2×C4#9249512yes—
197C2×C4D4×D3111yescharacteristic
198C2×C4D4×D3112yes—
199C2×C4C23×D3111yescharacteristic
200C8—22no—
201C8—622no—
202C22#1175846112yes—
203C22#1175849212yes—
204C22Q16×D3112yes—
205C22C2×D4×D3111yescharacteristic
206C4—42no—
207C4—42no—
208C4—314no—
209C4—624no—
210C4—622no—
211C4—1242no—
212C4#1175846112yes—
213C4C2×#9249511yescharacteristic
214C4C2×D4×D3111yescharacteristic
215C2#1452125814yesdirect product factor
216C2C2×#1175846111yescharacteristic
217C2C2×Q16×D3111yescharacteristic
218C2C2×#1175849211yescharacteristic
subgroupG/H
centerC23D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC2×C31×#103C2
socle, prime radicalC23×C31C2×D4
hypercenterC2×#103D31
hypocenterC31C2×#462
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
5. #14521258C2direct (N × H)
81. C2×Dic31Q16semidirect
105. Dic31C2×Q16semidirect
114. C2×C31#462semidirect
140. C31C2×#462semidirect
215. C2#14521258direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Dic1242
C22×#924822
C2×#117585212
C2×#117584642
#145212582
C2×Dic31⋊C82
C2×#117583982
C2×C31×#1032
C2×#46231