Finite Group Databasebeta

← C2×#14521373 #16855595

Subgroups — C2×#14521373 #16855595

Order 3968.

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

normal subgroups only

This group has 468 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×#11758507C211yesmaximal, characteristic
2#14521373C218yesmaximal, direct product factor
3C2×#11758395C211yesmaximal, characteristic, complemented
4C2×#11758396C211yesmaximal, characteristic, complemented
5C2×#11758397C211yesmaximal, characteristic, complemented
6C2×#11758397C211yesmaximal, characteristic, complemented
7C2×C22⋊(C31⋊C8)C211yesmaximal, characteristic, complemented
8C2×C31×#117C211yesmaximal, characteristic, complemented
9C23×C4×C31C2211yescharacteristic
10C22×C22⋊D31—21no—
11C22×D124C2211yescharacteristic
12C31×#117—22no—
13C31×#117C2214yescomplemented
14C2×C4⋊C4×C31C2211yescharacteristic
15C2×C4⋊C4×C31C2211yescharacteristic
16C2×C22⋊C4×C31—21no—
17C2×C42×C31—21no—
18#11758507—22no—
19#11758507C2214yes—
20C2×(C2×D31)⋊C4—21no—
21C2×C4⋊Dic31C2211yescharacteristic
22C22×C31⋊C8C2211yescharacteristic
23C22×C31⋊C8C2211yescharacteristic
24C22⋊(C31⋊C8)C2214yescomplemented
25#11758397C2214yescomplemented
26#11758397C2214yescomplemented
27#11758396C2214yescomplemented
28#11758395C2214yescomplemented
29C24×C31D411yescharacteristic
30C23×D31—21no—
31C22×C4×C31—22no—
32C22×C4×C31—22no—
33C22×C4×C31—21no—
34C22×C4×C31—21no—
35C22×C4×C31D411yescharacteristic
36C22×C4×C31D412yes—
37C22×C4×C31C2312yes—
38C22×C4×C31C2311yescharacteristic
39C2×C22⋊D31—24no—
40C2×C22⋊D31—44no—
41C22×Dic31—21no—
42C2×D124—22no—
43C2×D124—22no—
44C2×D124—21no—
45C2×D124C2312yes—
46C4⋊C4×C31—21no—
47C4⋊C4×C31—21no—
48C4⋊C4×C31C2312yes—
49C4⋊C4×C31C2312yes—
50C22⋊C4×C31—24no—
51C42×C31—24no—
52(C2×D31)⋊C4—24no—
53C4⋊Dic31—21no—
54C4⋊Dic31C2312yes—
55C2×C31⋊C8—22no—
56C2×C31⋊C8—22no—
57C2×C31⋊C8C2312yes—
58C2×C31⋊C8C2312yes—
59C23×C31—22no—
60C23×C31—22no—
61C23×C31—22no—
62C23×C31C2×D412yes—
63C23×C31C2×D411yescharacteristic
64C22×D31—22no—
65C22×D31—42no—
66C22×D31—42no—
67C22×D31—42no—
68C2×C4×C31—22no—
69C2×C4×C31—24no—
70C2×C4×C31—22no—
71C2×C4×C31—22no—
72C2×C4×C31—22no—
73C2×C4×C31—22no—
74C2×C4×C31—42no—
75C2×C4×C31—42no—
76C2×C4×C31C2×D412yes—
77C2×C4×C31C2×D411yescharacteristic
78C2×C4×C31#4112yes—
79C2×C4×C31#4112yes—
80C2×C4×C31C2411yescharacteristic
81C22⋊D31—48no—
82C2×Dic31—22no—
83C2×Dic31—42no—
84D124—22no—
85D124—22no—
86D124—42no—
87C31⋊C8—22no—
88C31⋊C8—22no—
89C2×#482—311nomaximal, Sylow
90C22×C31—22no—
91C22×C31—22no—
92C22×C31—22no—
93C22×C31—44no—
94C22×C31#12312yes—
95C22×C31#13512yes—
96C22×C31AGL(1,ℤ/8)12yes—
97C22×C31C22×D411yescharacteristic
98C2×D31—42no—
99C2×D31—42no—
100C2×D31—42no—
101C2×D31—84no—
102C4×C31—22no—
103C4×C31—42no—
104C4×C31—42no—
105C4×C31#12312yes—
106C4×C31C2×#4111yescharacteristic
107C4×C31C2×#4111yescharacteristic
108Dic31—42no—
109C2×#121—311no—
110C2×#117D3111yescharacteristic, complemented
111#482—318no—
112C2×#107—311no—
113C2×#106—311no—
114C2×#102—311no—
115C2×#102—311no—
116C2×C22⋊C8—311no—
117C2×C31—42no—
118C2×C31#48214yescomplemented
119C2×C31C2×#12311yescharacteristic
120C2×C31C2×#13511yescharacteristic
121C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
122D31—82no—
123C22×D4—311no—
124C22×D4—621no—
125C23×C4C2×D3111yescharacteristic
126C22×C8—311no—
127C22×C8—311no—
128#121—314no—
129#121—622no—
130#117—22no—
131#117C2×D3114yescomplemented
132C2×C4⋊C4—311no—
133C2×C4⋊C4C2×D3111yescharacteristic
134C2×C4⋊C4C2×D3111yescharacteristic
135C2×C22⋊C4—21no—
136C2×C22⋊C4—621no—
137C2×C42—21no—
138#107—314no—
139#106—314no—
140#102—314no—
141#102—314no—
142C22⋊C8—314no—
143C31C2×#48211yescharacteristic, complemented, Sylow
144C24—621no—
145C24C22⋊D3111yescharacteristic
146C2×D4—312no—
147C2×D4—624no—
148C2×D4—622no—
149C2×D4—622no—
150C2×D4—621no—
151C2×D4—1244no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—621no—
157C22×C4C22⋊D3112yes—
158C22×C4C22⋊D3111yescharacteristic
159C22×C4C22×D3112yes—
160C22×C4C22×D3111yescharacteristic
161C2×C8—312no—
162C2×C8—312no—
163C2×C8—622no—
164C2×C8—622no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—312no—
168C4⋊C4—621no—
169C4⋊C4C22×D3112yes—
170C4⋊C4C22×D3112yes—
171C22⋊C4—24no—
172C22⋊C4—624no—
173C42—24no—
174C23—22no—
175C23—22no—
176C23—22no—
177C23—622no—
178C23—1242no—
179C23—1242no—
180C23—1242no—
181C23C2×C22⋊D3112yes—
182C23C2×C22⋊D3111yescharacteristic
183D4—622no—
184D4—622no—
185D4—1248no—
186D4—1242no—
187C2×C4—22no—
188C2×C4—24no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—622no—
196C2×C4—1242no—
197C2×C4#9249512yes—
198C2×C4#9249512yes—
199C2×C4C2×C22⋊D3112yes—
200C2×C4C2×C22⋊D3111yescharacteristic
201C2×C4C23×D3111yescharacteristic
202C8—622no—
203C8—622no—
204C22—22no—
205C22—22no—
206C22—22no—
207C22—44no—
208C22—1242no—
209C22—1242no—
210C22—1242no—
211C22—2484no—
212C22#1175850612yes—
213C22#1175852612yes—
214C22#1175852712yes—
215C22C22×C22⋊D3111yescharacteristic
216C4—22no—
217C4—42no—
218C4—42no—
219C4—1242no—
220C4#1175850612yes—
221C4C2×#9249511yescharacteristic
222C4C2×#9249511yescharacteristic
223C2—42no—
224C2—2482no—
225C2#1452137314yesdirect product factor
226C2C2×#1175850611yescharacteristic
227C2C2×#1175852711yescharacteristic
228C2C2×#1175852611yescharacteristic
subgroupG/H
centerC23C2×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC2×C31×#117C2
socleC23×C31C2×D4
prime radicalC2×#11758507C2
hypercenterC2×#117D31
hypocenterC31C2×#482
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #14521373C2direct (N × H)
3. C2×#11758395C2semidirect
4. C2×#11758396C2semidirect
5. C2×#11758397C2semidirect
6. C2×#11758397C2semidirect
7. C2×C22⋊(C31⋊C8)C2semidirect
8. C2×C31×#117C2semidirect
13. C31×#117C22semidirect
24. C22⋊(C31⋊C8)C22semidirect
25. #11758397C22semidirect
26. #11758397C22semidirect
27. #11758396C22semidirect
28. #11758395C22semidirect
110. C2×#117D31semidirect
118. C2×C31#482semidirect
131. #117C2×D31semidirect
143. C31C2×#482semidirect
225. C2#14521373direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117585072
#145213732
C2×#117583952
C2×#117583962
C2×#117583972
C2×C22⋊(C31⋊C8)2
C2×C31×#1172
C2×#48231