Finite Group Databasebeta

← C2×#14521300 #16855305

Subgroups — C2×#14521300 #16855305

Order 3968.

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

normal subgroups only

This group has 596 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×#92479C211yesmaximal, characteristic, complemented
2C22×#92474C211yesmaximal, characteristic, complemented
3C2×#11758507C211yesmaximal, characteristic, complemented
4#14521300C218yesmaximal, direct product factor
5C2×#11758396C211yesmaximal, characteristic, complemented
6C2×#11758420C211yesmaximal, characteristic, complemented
7C2×#11758397C211yesmaximal, characteristic, complemented
8C2×C31×#121C211yesmaximal, characteristic, complemented
9C22×D4×C31—21no—
10C22×D4×C31C2211yescharacteristic
11C23×C4×C31C2211yescharacteristic
12C22×C22⋊D31—21no—
13C22×D124C2211yescharacteristic
14C31×#121—22no—
15C31×#121C2214yescomplemented
16C2×C4⋊C4×C31C2211yescharacteristic
17C2×C22⋊C4×C31—21no—
18C2×#92479—24no—
19C2×#92479C2214yescomplemented
20#11758507—22no—
21#11758507C2214yescomplemented
22C2×(C2×D31)⋊C4—21no—
23C2×C4⋊Dic31C2211yescharacteristic
24C2×#92474—24no—
25C2×#92474C2214yescomplemented
26C22×C31⋊C8C2211yescharacteristic
27C22×C31⋊C8C2211yescharacteristic
28#11758420C2214yescomplemented
29#11758397C2214yescomplemented
30#11758396C2214yescomplemented
31C24×C31—21no—
32C24×C31D411yescharacteristic
33C23×D31—21no—
34C2×D4×C31—24no—
35C2×D4×C31—22no—
36C2×D4×C31—21no—
37C2×D4×C31—22no—
38C2×D4×C31—44no—
39C2×D4×C31C2312yes—
40C22×C4×C31—22no—
41C22×C4×C31—22no—
42C22×C4×C31—21no—
43C22×C4×C31D411yescharacteristic
44C22×C4×C31D412yes—
45C22×C4×C31C2312yes—
46C22×C4×C31C2311yescharacteristic
47C2×C22⋊D31—24no—
48C2×C22⋊D31—44no—
49C22×Dic31—21no—
50C2×D124—22no—
51C2×D124—22no—
52C2×D124—21no—
53C2×D124C2312yes—
54C4⋊C4×C31—21no—
55C4⋊C4×C31C2312yes—
56C22⋊C4×C31—24no—
57#92479—28no—
58(C2×D31)⋊C4—24no—
59C4⋊Dic31—21no—
60C4⋊Dic31C2312yes—
61#92474—28no—
62C2×C31⋊C8—22no—
63C2×C31⋊C8D414yescomplemented
64C2×C31⋊C8C2312yes—
65C2×C31⋊C8C2312yes—
66C23×C31—22no—
67C23×C31—22no—
68C23×C31—22no—
69C23×C31—22no—
70C23×C31—42no—
71C23×C31—42no—
72C23×C31—42no—
73C23×C31C2×D412yes—
74C23×C31C2×D411yescharacteristic
75C22×D31—22no—
76C22×D31—42no—
77C22×D31—42no—
78C22×D31—42no—
79D4×C31—22no—
80D4×C31—22no—
81D4×C31—48no—
82D4×C31—42no—
83C2×C4×C31—22no—
84C2×C4×C31—24no—
85C2×C4×C31—22no—
86C2×C4×C31—22no—
87C2×C4×C31—22no—
88C2×C4×C31—42no—
89C2×C4×C31C2×D412yes—
90C2×C4×C31C2×D412yes—
91C2×C4×C31C2×D411yescharacteristic
92C2×C4×C31#4112yes—
93C2×C4×C31C2411yescharacteristic
94C22⋊D31—48no—
95C2×Dic31—22no—
96C2×Dic31—42no—
97D124—22no—
98D124—22no—
99D124—42no—
100C31⋊C8—22no—
101C31⋊C8C2×D414yescomplemented
102C2×#469—311nomaximal, Sylow
103C22×C31—22no—
104C22×C31—22no—
105C22×C31—22no—
106C22×C31—44no—
107C22×C31—42no—
108C22×C31—42no—
109C22×C31—42no—
110C22×C31—84no—
111C22×C31#12112yes—
112C22×C31AGL(1,ℤ/8)12yes—
113C22×C31AGL(1,ℤ/8)12yes—
114C22×C31C22×D411yescharacteristic
115C2×D31—42no—
116C2×D31—42no—
117C2×D31—42no—
118C2×D31—84no—
119C4×C31—22no—
120C4×C31—42no—
121C4×C31#12112yes—
122C4×C31C22×D411yescharacteristic
123C4×C31C2×#4111yescharacteristic
124Dic31—42no—
125C22×D8—311no—
126C22×M16—311no—
127C2×#121—311no—
128C2×#121D3111yescharacteristic, complemented
129#469—318no—
130C2×#106—311no—
131C2×#102—311no—
132C2×#102—311no—
133C2×C31—42no—
134C2×C31—82no—
135C2×C31#46914yescomplemented
136C2×C31C2×#12111yescharacteristic
137C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
139D31—82no—
140C22×D4—21no—
141C22×D4—311no—
142C22×D4—621no—
143C22×D4C2×D3111yescharacteristic
144C23×C4C2×D3111yescharacteristic
145C2×D8—314no—
146C2×D8—624no—
147C2×M16—314no—
148C2×M16—624no—
149C22×C8—311no—
150C22×C8—311no—
151#121—22no—
152#121—314no—
153#121—622no—
154#121C2×D3114yescomplemented
155C2×C4⋊C4—311no—
156C2×C4⋊C4C2×D3111yescharacteristic
157C2×C22⋊C4—21no—
158C2×C22⋊C4—621no—
159#106—314no—
160#102—314no—
161#102—314no—
162C31C2×#46911yescharacteristic, complemented, Sylow
163C24—21no—
164C24—621no—
165C24C22⋊D3111yescharacteristic
166C2×D4—24no—
167C2×D4—22no—
168C2×D4—22no—
169C2×D4—21no—
170C2×D4—44no—
171C2×D4—312no—
172C2×D4—624no—
173C2×D4—622no—
174C2×D4—622no—
175C2×D4—621no—
176C2×D4—1244no—
177C2×D4C22×D3112yes—
178C22×C4—22no—
179C22×C4—22no—
180C22×C4—21no—
181C22×C4—621no—
182C22×C4C22⋊D3112yes—
183C22×C4C22⋊D3111yescharacteristic
184C22×C4C22×D3112yes—
185C22×C4C22×D3111yescharacteristic
186D8—628no—
187M16—628no—
188C2×C8—314no—
189C2×C8—312no—
190C2×C8—312no—
191C2×C8—622no—
192C4⋊C4—21no—
193C4⋊C4—312no—
194C4⋊C4—621no—
195C4⋊C4C22×D3112yes—
196C22⋊C4—24no—
197C22⋊C4—624no—
198C23—22no—
199C23—22no—
200C23—22no—
201C23—22no—
202C23—42no—
203C23—42no—
204C23—42no—
205C23—622no—
206C23—1242no—
207C23—1242no—
208C23—1242no—
209C23C2×C22⋊D3112yes—
210C23C2×C22⋊D3111yescharacteristic
211D4—22no—
212D4—22no—
213D4—48no—
214D4—42no—
215D4—622no—
216D4—622no—
217D4—1248no—
218D4—1242no—
219C2×C4—22no—
220C2×C4—24no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—42no—
225C2×C4—622no—
226C2×C4—1242no—
227C2×C4D4×D3112yes—
228C2×C4#9249712yes—
229C2×C4C2×C22⋊D3112yes—
230C2×C4C2×C22⋊D3111yescharacteristic
231C2×C4C23×D3111yescharacteristic
232C8—314no—
233C8—622no—
234C22—22no—
235C22—22no—
236C22—22no—
237C22—44no—
238C22—42no—
239C22—42no—
240C22—42no—
241C22—84no—
242C22—1242no—
243C22—1242no—
244C22—1242no—
245C22—2484no—
246C22#1175850912yes—
247C22#1175851612yes—
248C22#1175852612yes—
249C22C22×C22⋊D3111yescharacteristic
250C4—22no—
251C4—42no—
252C4—1242no—
253C4#1175851612yes—
254C4C2×D4×D3111yescharacteristic
255C4C2×#9249711yescharacteristic
256C2—42no—
257C2—82no—
258C2—2482no—
259C2#1452130014yesdirect product factor
260C2C2×#1175851611yescharacteristic
261C2C2×#1175852611yescharacteristic
262C2C2×#1175850911yescharacteristic
subgroupG/H
centerC23C2×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC2×C31×#121C2
socleC23×C31C2×D4
hypercenterC2×#121D31
hypocenterC31C2×#469
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C22×#92479C2semidirect
2. C22×#92474C2semidirect
3. C2×#11758507C2semidirect
4. #14521300C2direct (N × H)
5. C2×#11758396C2semidirect
6. C2×#11758420C2semidirect
7. C2×#11758397C2semidirect
8. C2×C31×#121C2semidirect
15. C31×#121C22semidirect
19. C2×#92479C22semidirect
21. #11758507C22semidirect
25. C2×#92474C22semidirect
28. #11758420C22semidirect
29. #11758397C22semidirect
30. #11758396C22semidirect
63. C2×C31⋊C8D4semidirect
101. C31⋊C8C2×D4semidirect
128. C2×#121D31semidirect
135. C2×C31#469semidirect
154. #121C2×D31semidirect
162. C31C2×#469semidirect
259. C2#14521300direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#924792
C22×#924742
C2×#117585072
#145213002
C2×#117583962
C2×#117584202
C2×#117583972
C2×C31×#1212
C2×#46931