Finite Group Databasebeta

← C2×#14521231 #16855052

Subgroups — C2×#14521231 #16855052

Order 3968.

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

normal subgroups only

This group has 708 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×#11758564C211yesmaximal, characteristic
2C2×#11758519C212yesmaximal, complemented
3#14521231C218yesmaximal, direct product factor
4C2×#11758393C212yesmaximal, complemented
5C2×#11758424C211yesmaximal, characteristic, complemented
6C2×C31×C4⋊Q8C211yesmaximal, characteristic, complemented
7C22×Q8×C31C2211yescharacteristic
8C22×Q8×C31C2211yescharacteristic
9#11758564—22no—
10#11758564—24no—
11#11758564C2214yes—
12C2×#92499—22no—
13C2×Q8×D31—22no—
14C2×#92495—22no—
15C2×#92495C2212yes—
16C31×C4⋊Q8—22no—
17C31×C4⋊Q8C2214yescomplemented
18C2×C4⋊C4×C31—22no—
19C2×C42×C31C2211yescharacteristic
20C2×#92482—22no—
21#11758519—24no—
22#11758519C2218yescomplemented
23C2×#92481—22no—
24C2×#92474C2212yes—
25#11758424C2214yescomplemented
26#11758393C2218yescomplemented
27C2×Q8×C31—22no—
28C2×Q8×C31—22no—
29C2×Q8×C31—21no—
30C2×Q8×C31—22no—
31C2×Q8×C31—22no—
32C2×Q8×C31D412yes—
33C2×Q8×C31C2312yes—
34C2×Q8×C31C2312yes—
35C22×C4×C31—21no—
36C22×C4×C31—21no—
37C22×C4×C31D412yes—
38C22×C4×C31C2311yescharacteristic
39C2×C22⋊D31—22no—
40#92499—28no—
41#92499—28no—
42Q8×D31—28no—
43Q8×D31—28no—
44#92495—28no—
45#92495—28no—
46#92495—22no—
47#92495—22no—
48#92495D414yes—
49#92495C2314yes—
50C2×D124—22no—
51C2×D124D412yes—
52C2×C4×D31—24no—
53C2×C4×D31—22no—
54C2×Dic62—22no—
55C2×Dic62D412yes—
56C4⋊C4×C31—28no—
57C42×C31—21no—
58C42×C31C2312yes—
59#92482—28no—
60#92481—28no—
61#92474—22no—
62#92474C2314yes—
63C2×C31⋊C8—22no—
64C23×C31C2×D411yescharacteristic
65C22×D31—22no—
66Q8×C31—24no—
67Q8×C31—24no—
68Q8×C31—24no—
69Q8×C31—42no—
70C2×C4×C31—24no—
71C2×C4×C31—22no—
72C2×C4×C31—22no—
73C2×C4×C31—22no—
74C2×C4×C31—22no—
75C2×C4×C31—41no—
76C2×C4×C31—41no—
77C2×C4×C31C2×D412yes—
78C2×C4×C31C2×D412yes—
79C2×C4×C31C2×D414yes—
80C2×C4×C31C2×D411yescharacteristic
81C2×C4×C31C2411yescharacteristic
82C22⋊D31—24no—
83C22⋊D31—24no—
84C2×Dic31—22no—
85D124—28no—
86D124—22no—
87D124C2×D414yes—
88C4×D31—216no—
89C4×D31—24no—
90C4×D31—24no—
91Dic62—28no—
92Dic62—22no—
93Dic62C2×D414yes—
94C31⋊C8—24no—
95C2×#456—311nomaximal, Sylow
96C22×C31—22no—
97C22×C31#12011yescharacteristic
98C22×C31#12011yescharacteristic
99C22×C31C22×D411yescharacteristic
100C2×D31—24no—
101C2×D31—44no—
102C4×C31—24no—
103C4×C31—24no—
104C4×C31—42no—
105C4×C31#12012yes—
106C4×C31C22×D412yes—
107Dic31—24no—
108C2×2−1+4—311no—
109C2×#137—312no—
110C2×C4⋊Q8D3111yescharacteristic, complemented
111#456—318no—
112C2×#104—312no—
113C2×#101—311no—
114C2×C31—21no—
115C2×C31—21no—
116C2×C31#45612yescomplemented
117C2×C31C2×#12011yescharacteristic
118D31—44no—
1192−1+4—314no—
1202−1+4—624no—
1212−1+4—622no—
122C2×#41—312no—
123C2×#41—622no—
124C2×#41—622no—
125C22×Q8—622no—
126C22×Q8C2×D3111yescharacteristic
127C22×Q8C2×D3111yescharacteristic
128#137—318no—
129#137—624no—
130C2×Q16—622no—
131C2×SD16—622no—
132C2×M16—312no—
133C4⋊Q8—22no—
134C4⋊Q8C2×D3114yescomplemented
135C2×C4⋊C4—22no—
136C2×C42C2×D3111yescharacteristic
137#104—318no—
138#101—314no—
139C31C2×#45611yescharacteristic, complemented, Sylow
140#41—314no—
141#41—314no—
142#41—628no—
143#41—628no—
144#41—628no—
145#41—622no—
146#41—622no—
147#41—628no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—21no—
151C2×Q8—22no—
152C2×Q8—22no—
153C2×Q8—312no—
154C2×Q8—622no—
155C2×Q8—628no—
156C2×Q8—628no—
157C2×Q8C22⋊D3112yes—
158C2×Q8C22×D3112yes—
159C2×Q8C22×D3112yes—
160C2×D4—312no—
161C2×D4—622no—
162C2×D4—622no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—624no—
166C22×C4—622no—
167C22×C4C22⋊D3112yes—
168C22×C4C22×D3111yescharacteristic
169Q16—628no—
170SD16—628no—
171M16—314no—
172M16—622no—
173C2×C8—622no—
174C4⋊C4—28no—
175C42—21no—
176C42C22×D3112yes—
177C23—622no—
178C23C2×C22⋊D3111yescharacteristic
179Q8—24no—
180Q8—24no—
181Q8—24no—
182Q8—42no—
183Q8—314no—
184Q8—628no—
185Q8—622no—
186D4—314no—
187D4—628no—
188D4—624no—
189D4—624no—
190D4—622no—
191C2×C4—24no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—6216no—
199C2×C4—622no—
200C2×C4—624no—
201C2×C4—624no—
202C2×C4D4×D3112yes—
203C2×C4D4×D3112yes—
204C2×C4C2×C22⋊D3114yes—
205C2×C4C2×C22⋊D3111yescharacteristic
206C2×C4C23×D3111yescharacteristic
207C8—624no—
208C22—22no—
209C22—624no—
210C22—1244no—
211C22#1175851411yescharacteristic
212C22#1175851411yescharacteristic
213C22C22×C22⋊D3111yescharacteristic
214C4—24no—
215C4—24no—
216C4—42no—
217C4—624no—
218C4#1175851412yes—
219C4C2×D4×D3112yes—
220C2—21no—
221C2—21no—
222C2—1244no—
223C2#1452123112yesdirect product factor
224C2C2×#1175851411yescharacteristic
subgroupG/H
centerC22#11758514
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC2×C31×C4⋊Q8C2
socleC22×C31#120
prime radicalC2×#11758564C2
hypercenterC2×C4⋊Q8D31
hypocenterC31C2×#456
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#11758519C2semidirect
3. #14521231C2direct (N × H)
4. C2×#11758393C2semidirect
5. C2×#11758424C2semidirect
6. C2×C31×C4⋊Q8C2semidirect
17. C31×C4⋊Q8C22semidirect
22. #11758519C22semidirect
25. #11758424C22semidirect
26. #11758393C22semidirect
110. C2×C4⋊Q8D31semidirect
116. C2×C31#456semidirect
134. C4⋊Q8C2×D31semidirect
139. C31C2×#456semidirect
223. C2#14521231direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117585642
C2×#117585192
#145212312
C2×#117583932
C2×#117584242
C2×C31×C4⋊Q82
C2×#45631