Finite Group Databasebeta

← C2×#14521376 #16855598

Subgroups — C2×#14521376 #16855598

Order 3968.

468 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 141 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×#11758472C211yesmaximal, characteristic
2C2×#11758469C211yesmaximal, characteristic, complemented
3#14521376C218yesmaximal, direct product factor
4C2×#11758396C211yesmaximal, characteristic, complemented
5C2×#11758409C211yesmaximal, characteristic, complemented
6C2×#11758397C211yesmaximal, characteristic, complemented
7C2×(C2×D31)⋊C8C211yesmaximal, characteristic, complemented
8C2×C31×#107C211yesmaximal, characteristic, complemented
9C22×D124—21no—
10C22×D124C2211yescharacteristic
11C22×C4×D31C2211yescharacteristic
12C22×C8×C31C2211yescharacteristic
13C2×C4⋊C4×C31C2211yescharacteristic
14C2×C4⋊C4×C31C2211yescharacteristic
15C2×(C2×D31)⋊C4—21no—
16C2×(C2×D31)⋊C4—21no—
17C2×C4⋊Dic31C2211yescharacteristic
18C2×C4×Dic31—21no—
19C22×C31⋊C8C2211yescharacteristic
20#11758472—22no—
21#11758472C2214yes—
22#11758469—22no—
23#11758469C2214yescomplemented
24C31×#107C2214yescomplemented
25#11758409C2214yescomplemented
26(C2×D31)⋊C8C2214yescomplemented
27#11758397C2214yescomplemented
28#11758396C2214yescomplemented
29C23×D31—21no—
30C23×D31D411yescharacteristic
31C22×C4×C31—21no—
32C22×C4×C31—21no—
33C22×C4×C31C2311yescharacteristic
34C22×Dic31—21no—
35C22×Dic31D411yescharacteristic
36C2×D124—22no—
37C2×D124—22no—
38C2×D124—24no—
39C2×D124—21no—
40C2×D124—44no—
41C2×D124C2312yes—
42C2×C4×D31—22no—
43C2×C4×D31—22no—
44C2×C4×D31D412yes—
45C2×C4×D31C2312yes—
46C2×C8×C31—22no—
47C2×C8×C31C2312yes—
48C4⋊C4×C31—21no—
49C4⋊C4×C31—21no—
50C4⋊C4×C31C2312yes—
51C4⋊C4×C31C2312yes—
52(C2×D31)⋊C4—24no—
53(C2×D31)⋊C4—24no—
54C4⋊Dic31—21no—
55C4⋊Dic31C2312yes—
56C4×Dic31—24no—
57C2×C31⋊C8—22no—
58C2×C31⋊C8C2312yes—
59C23×C31C2×D411yescharacteristic
60C22×D31—22no—
61C22×D31—22no—
62C22×D31—22no—
63C22×D31—22no—
64C22×D31—42no—
65C22×D31—42no—
66C22×D31—42no—
67C22×D31C2×D412yes—
68C2×C4×C31—22no—
69C2×C4×C31—22no—
70C2×C4×C31—42no—
71C2×C4×C31—42no—
72C2×C4×C31C2×D411yescharacteristic
73C2×C4×C31#4112yes—
74C2×C4×C31#4112yes—
75C2×C4×C31C2411yescharacteristic
76C2×Dic31—22no—
77C2×Dic31—22no—
78C2×Dic31—42no—
79C2×Dic31C2×D412yes—
80D124—22no—
81D124—22no—
82D124—48no—
83D124—42no—
84C4×D31—24no—
85C4×D31—22no—
86C4×D31—22no—
87C8×C31—22no—
88C31⋊C8—22no—
89C2×#482—311nomaximal, Sylow
90C22×C31#12312yes—
91C22×C31#13512yes—
92C22×C31AGL(1,ℤ/8)12yes—
93C22×C31C22×D411yescharacteristic
94C2×D31—22no—
95C2×D31—22no—
96C2×D31—22no—
97C2×D31—44no—
98C2×D31—42no—
99C2×D31—42no—
100C2×D31—42no—
101C2×D31—84no—
102C4×C31—42no—
103C4×C31—42no—
104C4×C31#12312yes—
105C4×C31C2×#4111yescharacteristic
106C4×C31C2×#4111yescharacteristic
107Dic31—22no—
108Dic31—42no—
109C2×#121—311no—
110C2×#117—311no—
111#482—318no—
112C2×#107D3111yescharacteristic, complemented
113C2×#106—311no—
114C2×#102—311no—
115C2×#102—311no—
116C2×C22⋊C8—311no—
117C2×C31#48214yescomplemented
118C2×C31C2×#12311yescharacteristic
119C2×C31C2×#13511yescharacteristic
120C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
121D31—42no—
122D31—82no—
123C22×D4—311no—
124C22×D4—621no—
125C23×C4—311no—
126C22×C8—311no—
127C22×C8C2×D3111yescharacteristic
128#121—314no—
129#121—622no—
130#117—314no—
131#117—622no—
132C2×C4⋊C4—311no—
133C2×C4⋊C4C2×D3111yescharacteristic
134C2×C4⋊C4C2×D3111yescharacteristic
135C2×C22⋊C4—621no—
136C2×C22⋊C4—621no—
137C2×C42—621no—
138#107C2×D3114yescomplemented
139#106—314no—
140#102—314no—
141#102—314no—
142C22⋊C8—314no—
143C31C2×#48211yescharacteristic, complemented, Sylow
144C24—311no—
145C24—621no—
146C2×D4—312no—
147C2×D4—624no—
148C2×D4—622no—
149C2×D4—621no—
150C2×D4—622no—
151C2×D4—1244no—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—311no—
155C22×C4—312no—
156C22×C4—312no—
157C22×C4—622no—
158C22×C4—622no—
159C22×C4—621no—
160C22×C4C22×D3111yescharacteristic
161C2×C8—22no—
162C2×C8—312no—
163C2×C8—622no—
164C2×C8C22×D3112yes—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—312no—
168C4⋊C4—621no—
169C4⋊C4C22×D3112yes—
170C4⋊C4C22×D3112yes—
171C22⋊C4—624no—
172C22⋊C4—624no—
173C42—624no—
174C23—312no—
175C23—622no—
176C23—622no—
177C23—622no—
178C23—622no—
179C23—1242no—
180C23—1242no—
181C23—1242no—
182C23D4×D3111yescharacteristic
183D4—622no—
184D4—622no—
185D4—1248no—
186D4—1242no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—312no—
192C2×C4—622no—
193C2×C4—624no—
194C2×C4—622no—
195C2×C4—622no—
196C2×C4—622no—
197C2×C4—1242no—
198C2×C4#9249512yes—
199C2×C4D4×D3111yescharacteristic
200C2×C4#9249912yes—
201C2×C4C23×D3111yescharacteristic
202C8—22no—
203C8—622no—
204C22—622no—
205C22—622no—
206C22—622no—
207C22—1244no—
208C22—1242no—
209C22—1242no—
210C22—1242no—
211C22—2484no—
212C22#1175847112yes—
213C22#1175848812yes—
214C22#1175849612yes—
215C22C2×D4×D3111yescharacteristic
216C4—42no—
217C4—42no—
218C4—622no—
219C4—1242no—
220C4#1175847112yes—
221C4C2×#9249511yescharacteristic
222C4C2×#9249911yescharacteristic
223C2—1242no—
224C2—2482no—
225C2#1452137614yesdirect product factor
226C2C2×#1175847111yescharacteristic
227C2C2×#1175849611yescharacteristic
228C2C2×#1175848811yescharacteristic
subgroupG/H
centerC23D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC2×C31×#107C2
socleC23×C31C2×D4
prime radicalC2×#11758472C2
hypercenterC2×#107D31
hypocenterC31C2×#482
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. C2×#11758469C2semidirect
3. #14521376C2direct (N × H)
4. C2×#11758396C2semidirect
5. C2×#11758409C2semidirect
6. C2×#11758397C2semidirect
7. C2×(C2×D31)⋊C8C2semidirect
8. C2×C31×#107C2semidirect
23. #11758469C22semidirect
24. C31×#107C22semidirect
25. #11758409C22semidirect
26. (C2×D31)⋊C8C22semidirect
27. #11758397C22semidirect
28. #11758396C22semidirect
112. C2×#107D31semidirect
117. C2×C31#482semidirect
138. #107C2×D31semidirect
143. C31C2×#482semidirect
225. C2#14521376direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117584722
C2×#117584692
#145213762
C2×#117583962
C2×#117584092
C2×#117583972
C2×(C2×D31)⋊C82
C2×C31×#1072
C2×#48231