Finite Group Databasebeta

← C2×#14521378 #16855587

Subgroups — C2×#14521378 #16855587

Order 3968.

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

normal subgroups only

This group has 460 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×#11758523C211yesmaximal, characteristic
2C2×C4⋊C4×D31C211yesmaximal, characteristic
3#14521378C218yesmaximal, direct product factor
4C2×#11758405C211yesmaximal, characteristic, complemented
5C2×#11758396C211yesmaximal, characteristic, complemented
6C2×#11758423C211yesmaximal, characteristic, complemented
7C2×(C2×D31)⋊C8C211yesmaximal, characteristic
8C2×C31×#103C211yesmaximal, characteristic, complemented
9C22×Q8×C31C2211yescharacteristic
10C22×C4×D31—21no—
11C22×C4×D31C2211yescharacteristic
12C22×C8×C31C2211yescharacteristic
13C2×C4⋊C4×C31C2211yescharacteristic
14#11758523—22no—
15#11758523C2214yes—
16C2×(C2×D31)⋊C4—21no—
17C2×C4⋊Dic31C2211yescharacteristic
18C2×C4⋊Dic31C2211yescharacteristic
19C2×Dic31⋊C4—21no—
20C2×Dic31⋊C4—21no—
21C22×C31⋊C8C2211yescharacteristic
22C4⋊C4×D31—22no—
23C4⋊C4×D31C2214yes—
24C31×#103C2214yescomplemented
25#11758423C2214yescomplemented
26(C2×D31)⋊C8C2214yes—
27#11758405C2214yescomplemented
28#11758396C2214yescomplemented
29C23×D31D411yescharacteristic
30C2×Q8×C31—21no—
31C2×Q8×C31—22no—
32C2×Q8×C31—22no—
33C2×Q8×C31C2312yes—
34C22×C4×C31—21no—
35C22×C4×C31—21no—
36C22×C4×C31C2311yescharacteristic
37C22×Dic31—21no—
38C22×Dic31—21no—
39C22×Dic31D411yescharacteristic
40C2×C4×D31—22no—
41C2×C4×D31—22no—
42C2×C4×D31—24no—
43C2×C4×D31—44no—
44C2×C4×D31D412yes—
45C2×C4×D31C2312yes—
46C2×C8×C31—22no—
47C2×C8×C31C2312yes—
48C4⋊C4×C31—21no—
49C4⋊C4×C31C2312yes—
50(C2×D31)⋊C4—24no—
51C4⋊Dic31—21no—
52C4⋊Dic31—21no—
53C4⋊Dic31C2312yes—
54C4⋊Dic31C2312yes—
55Dic31⋊C4—24no—
56Dic31⋊C4—24no—
57C2×C31⋊C8—22no—
58C2×C31⋊C8C2312yes—
59C23×C31C2×D411yescharacteristic
60C22×D31—22no—
61C22×D31—22no—
62C22×D31SD1614yes—
63C22×D31C2×D412yes—
64Q8×C31—22no—
65Q8×C31—22no—
66Q8×C31—42no—
67C2×C4×C31—22no—
68C2×C4×C31—22no—
69C2×C4×C31—42no—
70C2×C4×C31—42no—
71C2×C4×C31C2×D411yescharacteristic
72C2×C4×C31#4112yes—
73C2×C4×C31#4112yes—
74C2×C4×C31C2411yescharacteristic
75C2×Dic31—22no—
76C2×Dic31—22no—
77C2×Dic31—22no—
78C2×Dic31—42no—
79C2×Dic31—42no—
80C2×Dic31C2×D412yes—
81C4×D31—24no—
82C4×D31—22no—
83C4×D31—22no—
84C4×D31—48no—
85C8×C31—22no—
86C31⋊C8—22no—
87C2×#483—311nomaximal, Sylow
88C22×C31#12312yes—
89C22×C31C2×SD1612yes—
90C22×C31#13712yes—
91C22×C31C22×D411yescharacteristic
92C2×D31—22no—
93C2×D31—22no—
94C2×D31—28no—
95C2×D31C2×SD1614yes—
96C4×C31—42no—
97C4×C31—42no—
98C4×C31#12312yes—
99C4×C31C2×#4111yescharacteristic
100C4×C31C2×#4111yescharacteristic
101Dic31—22no—
102Dic31—42no—
103Dic31—42no—
104C2×C22⋊Q8—311no—
105C22×C4⋊C4—311no—
106#483—318no—
107C2×#106—311no—
108C2×#106—311no—
109C2×#103—311no—
110C2×#103D3111yescharacteristic, complemented
111C2×C22⋊C8—311no—
112C2×C31#48314yescomplemented
113C2×C31C2×#12311yescharacteristic
114C2×C31C22×SD1611yescharacteristic
115C2×C31C2×#13711yescharacteristic
116D31—24no—
117C22×Q8C2×D3111yescharacteristic
118C23×C4—311no—
119C23×C4—621no—
120C22×C8—311no—
121C22×C8C2×D3111yescharacteristic
122C22⋊Q8—314no—
123C22⋊Q8—622no—
124C2×C4⋊C4—311no—
125C2×C4⋊C4—311no—
126C2×C4⋊C4—314no—
127C2×C4⋊C4—622no—
128C2×C4⋊C4—621no—
129C2×C4⋊C4—621no—
130C2×C4⋊C4C2×D3111yescharacteristic
131C2×C22⋊C4—621no—
132#106—314no—
133#106—314no—
134#103—314no—
135#103C2×D3114yescomplemented
136C22⋊C8—314no—
137C31C2×#48311yescharacteristic, complemented, Sylow
138C24—311no—
139C2×Q8—21no—
140C2×Q8—22no—
141C2×Q8—22no—
142C2×Q8C22×D3112yes—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—311no—
146C22×C4—312no—
147C22×C4—312no—
148C22×C4—624no—
149C22×C4—622no—
150C22×C4—622no—
151C22×C4—621no—
152C22×C4—621no—
153C22×C4—1244no—
154C22×C4C22×D3111yescharacteristic
155C2×C8—22no—
156C2×C8—312no—
157C2×C8—622no—
158C2×C8C22×D3112yes—
159C4⋊C4—21no—
160C4⋊C4—312no—
161C4⋊C4—312no—
162C4⋊C4—624no—
163C4⋊C4—624no—
164C4⋊C4—621no—
165C4⋊C4—621no—
166C4⋊C4C22×D3112yes—
167C22⋊C4—624no—
168C23—314no—
169C23—312no—
170C23—622no—
171C23—622no—
172C23D4×D3111yescharacteristic
173Q8—22no—
174Q8—22no—
175Q8—42no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—312no—
181C2×C4—622no—
182C2×C4—624no—
183C2×C4—622no—
184C2×C4—622no—
185C2×C4—622no—
186C2×C4—622no—
187C2×C4—1248no—
188C2×C4—1242no—
189C2×C4—1242no—
190C2×C4#9249512yes—
191C2×C4D4×D3111yescharacteristic
192C2×C4#9249712yes—
193C2×C4C23×D3111yescharacteristic
194C8—22no—
195C8—622no—
196C22—314no—
197C22—628no—
198C22—622no—
199C22—622no—
200C22#1175846012yes—
201C22SD16×D3112yes—
202C22#1175849512yes—
203C22C2×D4×D3111yescharacteristic
204C4—42no—
205C4—42no—
206C4—622no—
207C4—1242no—
208C4—1242no—
209C4#1175846012yes—
210C4C2×#9249511yescharacteristic
211C4C2×#9249711yescharacteristic
212C2—624no—
213C2#1452137814yesdirect product factor
214C2C2×#1175846011yescharacteristic
215C2C2×SD16×D3111yescharacteristic
216C2C2×#1175849511yescharacteristic
subgroupG/H
centerC23D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC2×C31×#103C2
socleC23×C31C2×D4
prime radicalC23×D31D4
hypercenterC2×#103D31
hypocenterC31C2×#483
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
3. #14521378C2direct (N × H)
4. C2×#11758405C2semidirect
5. C2×#11758396C2semidirect
6. C2×#11758423C2semidirect
8. C2×C31×#103C2semidirect
24. C31×#103C22semidirect
25. #11758423C22semidirect
27. #11758405C22semidirect
28. #11758396C22semidirect
110. C2×#103D31semidirect
112. C2×C31#483semidirect
135. #103C2×D31semidirect
137. C31C2×#483semidirect
213. C2#14521378direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117585232
C2×C4⋊C4×D312
#145213782
C2×#117584052
C2×#117583962
C2×#117584232
C2×(C2×D31)⋊C82
C2×C31×#1032
C2×#48331