Finite Group Databasebeta

← C2×C4×#92479 #16854460

Subgroups — C2×C4×#92479 #16854460

Order 3968.

616 conjugacy classes of subgroups; only the 221 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 221 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
2C2×C4×D124C211yesmaximal, characteristic, complemented
3C4×#92479C218yesmaximal, direct product factor
4C2×#11758395C211yesmaximal, characteristic, complemented
5C2×#11758420C211yesmaximal, characteristic, complemented
6C2×#11758397C211yesmaximal, characteristic, complemented
7C2×C4×C31⋊C8C211yesmaximal, characteristic, complemented
8C2×C4×D4×C31C211yesmaximal, characteristic, complemented
9C22×D4×C31C2211yescharacteristic
10C23×C4×C31—21no—
11C22×D124C2211yescharacteristic
12C22×C4×D31—21no—
13C4×D4×C31—22no—
14C4×D4×C31C2214yescomplemented
15C2×C4⋊C4×C31C2211yescharacteristic
16C2×C22⋊C4×C31—21no—
17C2×C42×C31C2211yescharacteristic
18C2×#92479C418yesdirect product factor
19C2×#92479C2214yes—
20C2×(C2×D31)⋊C4—21no—
21C2×C4⋊Dic31C2211yescharacteristic
22C22×C31⋊C8C2211yescharacteristic
23C22×C31⋊C8C2211yescharacteristic
24C4×D124—22no—
25C4×D124C2214yescomplemented
26#11758420C2214yescomplemented
27#11758397C2214yescomplemented
28#11758395C2214yescomplemented
29C4×C31⋊C8C2214yescomplemented
30C24×C31—21no—
31C23×D31—21no—
32C2×D4×C31—21no—
33C2×D4×C31—22no—
34C2×D4×C31C2×C414yescomplemented
35C2×D4×C31C2312yes—
36C22×C4×C31—21no—
37C22×C4×C31—24no—
38C22×C4×C31—44no—
39C22×C4×C31D411yescharacteristic
40C22×C4×C31D411yescharacteristic
41C22×C4×C31C2311yescharacteristic
42C22×Dic31—21no—
43C2×D124—21no—
44C2×D124—22no—
45C2×D124C2×C414yescomplemented
46C2×D124C2312yes—
47C2×C4×D31—24no—
48C2×C4×D31—44no—
49C4⋊C4×C31—21no—
50C4⋊C4×C31C2312yes—
51C22⋊C4×C31—24no—
52C42×C31D412yes—
53C42×C31C2312yes—
54#92479C2×C4116yesdirect product factor
55(C2×D31)⋊C4—24no—
56C4⋊Dic31—21no—
57C4⋊Dic31C2312yes—
58C2×C31⋊C8—22no—
59C2×C31⋊C8C2×C414yescomplemented
60C2×C31⋊C8C2312yes—
61C2×C31⋊C8C2312yes—
62C23×C31—24no—
63C23×C31—22no—
64C23×C31—42no—
65C23×C31—42no—
66C23×C31C2×D411yescharacteristic
67C22×D31—24no—
68C22×D31—22no—
69C22×D31—42no—
70C22×D31—42no—
71D4×C31—24no—
72D4×C31—22no—
73D4×C31C22×C414yescomplemented
74C2×C4×C31—22no—
75C2×C4×C31—22no—
76C2×C4×C31—42no—
77C2×C4×C31—48no—
78C2×C4×C31D814yescomplemented
79C2×C4×C31C22×C412yes—
80C2×C4×C31C2×D412yes—
81C2×C4×C31C2×D411yescharacteristic
82C2×C4×C31C2×D412yes—
83C2×C4×C31#4112yes—
84C2×C4×C31C2411yescharacteristic
85C2×Dic31—22no—
86C2×Dic31—42no—
87D124—24no—
88D124—22no—
89D124C22×C414yescomplemented
90C4×D31—48no—
91C31⋊C8—22no—
92C31⋊C8C22×C414yescomplemented
93C2×C4×D8—311nomaximal, Sylow
94C22×C31—24no—
95C22×C31—42no—
96C22×C31—42no—
97C22×C31—48no—
98C22×C31C4×D412yes—
99C22×C31C2×D812yes—
100C22×C31#13512yes—
101C22×C31C22×D411yescharacteristic
102C2×D31—24no—
103C2×D31—42no—
104C2×D31—42no—
105C2×D31—48no—
106C4×C31—22no—
107C4×C31—42no—
108C4×C31C4×D412yes—
109C4×C31C2×D814yescomplemented
110C4×C31C23×C411yescharacteristic
111C4×C31C2×#4111yescharacteristic
112Dic31—42no—
113C22×D8—311no—
114C2×C4×D4—311no—
115C2×C4×D4D3111yescharacteristic, complemented
116C4×D8—318no—
117C2×#107—311no—
118C2×#102—311no—
119C2×#102—311no—
120C2×C4×C8—311no—
121C2×C31—44no—
122C2×C31C4×D814yescomplemented
123C2×C31C2×C4×D411yescharacteristic
124C2×C31C22×D811yescharacteristic
125C2×C31C2×#13511yescharacteristic
126D31—44no—
127C22×D4—311no—
128C22×D4C2×D3111yescharacteristic
129C23×C4—21no—
130C23×C4—621no—
131C2×D8—318no—
132C2×D8—314no—
133C22×C8—311no—
134C22×C8—311no—
135C4×D4—22no—
136C4×D4—314no—
137C4×D4—622no—
138C4×D4C2×D3114yescomplemented
139C2×C4⋊C4—311no—
140C2×C4⋊C4C2×D3111yescharacteristic
141C2×C22⋊C4—21no—
142C2×C22⋊C4—621no—
143C2×C42C2×D3111yescharacteristic
144#107—314no—
145#102—314no—
146#102—314no—
147C4×C8—314no—
148C31C2×C4×D811yescharacteristic, complemented, Sylow
149C24—21no—
150C24—621no—
151C2×D4—22no—
152C2×D4—21no—
153C2×D4—314no—
154C2×D4—312no—
155C2×D4—622no—
156C2×D4—621no—
157C2×D4C4×D3114yescomplemented
158C2×D4C22×D3112yes—
159C22×C4—21no—
160C22×C4—24no—
161C22×C4—44no—
162C22×C4—621no—
163C22×C4—624no—
164C22×C4—1244no—
165C22×C4C22⋊D3111yescharacteristic
166C22×C4C22⋊D3111yescharacteristic
167C22×C4C22×D3111yescharacteristic
168D8—3116no—
169C2×C8—314no—
170C2×C8—312no—
171C2×C8—312no—
172C2×C8—622no—
173C4⋊C4—21no—
174C4⋊C4—312no—
175C4⋊C4—621no—
176C4⋊C4C22×D3112yes—
177C22⋊C4—24no—
178C22⋊C4—624no—
179C42C22⋊D3112yes—
180C42C22×D3112yes—
181C23—24no—
182C23—22no—
183C23—42no—
184C23—42no—
185C23—624no—
186C23—622no—
187C23—1242no—
188C23—1242no—
189C23C2×C22⋊D3111yescharacteristic
190D4—24no—
191D4—22no—
192D4—314no—
193D4—624no—
194D4—622no—
195D4C2×C4×D3114yescomplemented
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—42no—
199C2×C4—48no—
200C2×C4—622no—
201C2×C4—1242no—
202C2×C4—1248no—
203C2×C4#9247914yesdirect product factor
204C2×C4C2×C4×D3112yes—
205C2×C4#9249512yes—
206C2×C4C2×C22⋊D3112yes—
207C2×C4C2×C22⋊D3111yescharacteristic
208C2×C4C2×C22⋊D3112yes—
209C2×C4C23×D3111yescharacteristic
210C8—314no—
211C8—622no—
212C22—24no—
213C22—48no—
214C22—42no—
215C22—42no—
216C22—624no—
217C22—1248no—
218C22—1242no—
219C22—1242no—
220C22C4×C22⋊D3112yes—
221C22C2×#9247912yes—
222C22#1175852712yes—
223C22C22×C22⋊D3111yescharacteristic
224C4—22no—
225C4—42no—
226C4—1242no—
227C4C4×C22⋊D3112yes—
228C4C2×#9247914yesdirect product factor
229C4C22×C4×D3111yescharacteristic
230C4C2×#9249511yescharacteristic
231C2—44no—
232C2—1244no—
233C2C4×#9247914yesdirect product factor
234C2C2×C4×C22⋊D3111yescharacteristic
235C2C22×#9247911yescharacteristic
236C2C2×#1175852711yescharacteristic
subgroupG/H
centerC22×C4C22⋊D31
commutatorC4×C31C23×C4
FrattiniC2×C4C23×D31
FittingC2×C4×D4×C31C2
socleC23×C31C2×D4
prime radicalC22×#92479C2
cosocleC2×C4×C31C24
hypercenterC2×C4×D4D31
hypocenterC31C2×C4×D8
LCSG ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D124C2semidirect
3. C4×#92479C2direct (N × H)
4. C2×#11758395C2semidirect
5. C2×#11758420C2semidirect
6. C2×#11758397C2semidirect
7. C2×C4×C31⋊C8C2semidirect
8. C2×C4×D4×C31C2semidirect
14. C4×D4×C31C22semidirect
18. C2×#92479C4direct (N × H)
25. C4×D124C22semidirect
26. #11758420C22semidirect
27. #11758397C22semidirect
28. #11758395C22semidirect
29. C4×C31⋊C8C22semidirect
34. C2×D4×C31C2×C4semidirect
45. C2×D124C2×C4semidirect
54. #92479C2×C4direct (N × H)
59. C2×C31⋊C8C2×C4semidirect
73. D4×C31C22×C4semidirect
78. C2×C4×C31D8semidirect
89. D124C22×C4semidirect
92. C31⋊C8C22×C4semidirect
109. C4×C31C2×D8semidirect
115. C2×C4×D4D31semidirect
122. C2×C31C4×D8semidirect
138. C4×D4C2×D31semidirect
148. C31C2×C4×D8semidirect
157. C2×D4C4×D31semidirect
195. D4C2×C4×D31semidirect
203. C2×C4#92479direct (N × H)
228. C4C2×#92479direct (N × H)
233. C2C4×#92479direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#924792
C2×C4×D1242
C4×#924792
C2×#117583952
C2×#117584202
C2×#117583972
C2×C4×C31⋊C82
C2×C4×D4×C312
C2×C4×D831