Finite Group Databasebeta

← D4×D2168 #46848041

Subgroups — D4×D2168 #46848041

Order 34688.

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

normal subgroups only

This group has 620 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
1C22×D2168C212yesmaximal, complemented
2D4×D1084C212yesmaximal, complemented
3#31774274C211yesmaximal, characteristic, complemented
4#31774133C212yesmaximal, complemented
5#31774093C212yesmaximal, complemented
6#31774033C214yesmaximal, complemented
7C4×D2168C211yesmaximal, characteristic, complemented
8C8×D4×C271C211yesmaximal, characteristic, complemented
9C22×D1084C2214yescomplemented
10C2×D4×D271—22no—
11C2×D2168—28no—
12C2×D2168C2211yescharacteristic
13C2×D2168C2212yescomplemented
14C2×D2168C2214yescomplemented
15C2×D2168C2212yescomplemented
16#22576157C2212yescomplemented
17#22576135—22no—
18#22576134C2214yescomplemented
19#22576130—24no—
20C4×D1084C2212yescomplemented
21#22576094C2211yescharacteristic, complemented
22#22576082C2212yescomplemented
23#22576082C2214yescomplemented
24C22×C8×C271C2212yescomplemented
25C4×D4×C271C2211yescharacteristic
26C4⋊C8×C271C2211yescharacteristic, complemented
27C22⋊C8×C271C2212yescomplemented
28C4×C8×C271C2211yescharacteristic, complemented
29C23×D271—24no—
30C2×D1084—28no—
31C2×D1084—24no—
32C2×D1084—22no—
33C2×D1084—22no—
34C2×D1084—44no—
35C2×D1084C2314yes—
36C2×D1084C2312yes—
37C2×C22⋊D271—24no—
38D4×D271—48no—
39C2×C4×D271—22no—
40D2168—28no—
41D2168—24no—
42D2168—42no—
43D2168D414yesdirect product factor
44C4⋊Dic271C2312yes—
45(C2×D271)⋊C4—22no—
46(C2×D271)⋊C4—24no—
47C2×D4×C271D411yescharacteristic
48C22×C4×C271C2312yes—
49C2×C8×C271—24no—
50C2×C8×C271C2311yescharacteristic
51C2×C8×C271C2312yes—
52C2×C8×C271C2311yescharacteristic
53C4⋊C4×C271D411yescharacteristic
54C22⋊C4×C271D412yes—
55C42×C271C2311yescharacteristic
56C22×D271—22no—
57C22×D271—24no—
58C22×D271—48no—
59C22×D271—48no—
60C22×D271—84no—
61D1084—24no—
62D1084—22no—
63D1084—24no—
64D1084—48no—
65D1084—44no—
66D1084—82no—
67D1084C2×D414yescomplemented
68C22⋊D271—48no—
69C2×Dic271—22no—
70C4×D271—44no—
71C23×C271C2×D412yes—
72D4×C271D814yescomplemented
73C2×C4×C271—22no—
74C2×C4×C271—22no—
75C2×C4×C271C2×D411yescharacteristic
76C2×C4×C271C2×D412yes—
77C2×C4×C271C2×D411yescharacteristic
78C2×C4×C271C2411yescharacteristic
79C8×C271—22no—
80C8×C271—21no—
81C8×C271C2×D412yescomplemented
82C22×C271—22no—
83C22×C271—22no—
84C22×C271C2×D814yescomplemented
85C22×C271C22×D411yescharacteristic
86C2×D271—24no—
87C2×D271—42no—
88C2×D271—42no—
89C2×D271—44no—
90C2×D271—44no—
91C2×D271—44no—
92C2×D271—816no—
93C4×C271—22no—
94C4×C271—21no—
95C4×C271C2×D812yescomplemented
96C4×C271C22×D411yescharacteristic
97C4×C271H(5,𝔽2)11yescharacteristic
98Dic271—42no—
99C2×C271—24no—
100C2×C271D4211yescharacteristic
101C2×C271C22×D811yescharacteristic
102C2×C271#57611yescharacteristic
103D271—44no—
104D271—84no—
105C271D4×D811yescharacteristic, complemented, Sylow
106D4×D8—2711nomaximal, Sylow
107C22×D8—2712no—
108D42—2712no—
109#493—2711no—
110#466—2712no—
111#459—2712no—
112#447—2714no—
113C4×D8—2711no—
114C8×D4D27111yescharacteristic, complemented
115C22×D4—2714no—
116C22×D4—5422no—
117C2×D8—2711no—
118C2×D8—2714no—
119C2×D8—2712no—
120C2×D8—2712no—
121C2×D8—5428no—
122C22×C8C2×D27112yescomplemented
123#127—2712no—
124#121—2714no—
125#121—5422no—
126#120—5424no—
127C4×D4—2712no—
128C4×D4C2×D27111yescharacteristic
129#107—2711no—
130C4⋊C8C2×D27111yescharacteristic, complemented
131#102—2712no—
132#102—2714no—
133C22⋊C8C2×D27112yescomplemented
134C4×C8C2×D27111yescharacteristic, complemented
135C24—5424no—
136C2×D4—2712no—
137C2×D4—2714no—
138C2×D4—5428no—
139C2×D4—5424no—
140C2×D4—5424no—
141C2×D4—5422no—
142C2×D4—5422no—
143C2×D4—10844no—
144C2×D4—10848no—
145C2×D4D108411yescharacteristic
146C22×C4—5422no—
147C22×C4C22×D27112yes—
148D8—2714no—
149D8—5428no—
150D8—5424no—
151D8—10842no—
152C2×C8—24no—
153C2×C8C22×D27111yescharacteristic
154C2×C8C22×D27112yes—
155C2×C8C22×D27111yescharacteristic
156C4⋊C4—2712no—
157C4⋊C4D108411yescharacteristic
158C22⋊C4—5422no—
159C22⋊C4—5424no—
160C22⋊C4D108412yes—
161C42C22×D27111yescharacteristic
162C23—5422no—
163C23—5424no—
164C23—10848no—
165C23—10848no—
166C23—21684no—
167C23C2×D108412yes—
168D4—2714no—
169D4—5424no—
170D4—5422no—
171D4—5424no—
172D4—10848no—
173D4—10848no—
174D4—10844no—
175D4—21682no—
176D4D216814yesdirect product factor
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—5422no—
180C2×C4—10844no—
181C2×C4C2×D108411yescharacteristic
182C2×C4C2×D108412yes—
183C2×C4C2×D108411yescharacteristic
184C2×C4C23×D27111yescharacteristic
185C8—22no—
186C8—21no—
187C8D4×D27112yescomplemented
188C22—22no—
189C22—22no—
190C22—5424no—
191C22—10842no—
192C22—10842no—
193C22—10844no—
194C22—10844no—
195C22—10844no—
196C22—216816no—
197C22C2×D216814yescomplemented
198C22C22×D108411yescharacteristic
199C4—22no—
200C4—21no—
201C4—10842no—
202C4C2×D216812yescomplemented
203C4C2×D4×D27111yescharacteristic
204C4#2257620611yescharacteristic
205C2—24no—
206C2—10844no—
207C2—21684no—
208C2D4×D108411yescharacteristic
209C2C22×D216811yescharacteristic
210C2#3177470211yescharacteristic
subgroupG/H
centerC22C22×D1084
commutator, cosocleC2×C4×C271C24
FrattiniC2×C4C23×D271
FittingC8×D4×C271C2
socleC22×C271C22×D4
hypercenterC8×D4D271
hypocenterC271D4×D8
LCSG ▷ C2×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. C22×D2168C2semidirect
2. D4×D1084C2semidirect
3. #31774274C2semidirect
4. #31774133C2semidirect
5. #31774093C2semidirect
6. #31774033C2semidirect
7. C4×D2168C2semidirect
8. C8×D4×C271C2semidirect
9. C22×D1084C22semidirect
13. C2×D2168C22semidirect
14. C2×D2168C22semidirect
15. C2×D2168C22semidirect
16. #22576157C22semidirect
18. #22576134C22semidirect
20. C4×D1084C22semidirect
21. #22576094C22semidirect
22. #22576082C22semidirect
23. #22576082C22semidirect
24. C22×C8×C271C22semidirect
26. C4⋊C8×C271C22semidirect
27. C22⋊C8×C271C22semidirect
28. C4×C8×C271C22semidirect
43. D2168D4direct (N × H)
67. D1084C2×D4semidirect
72. D4×C271D8semidirect
81. C8×C271C2×D4semidirect
84. C22×C271C2×D8semidirect
95. C4×C271C2×D8semidirect
105. C271D4×D8semidirect
114. C8×D4D271semidirect
122. C22×C8C2×D271semidirect
130. C4⋊C8C2×D271semidirect
133. C22⋊C8C2×D271semidirect
134. C4×C8C2×D271semidirect
176. D4D2168direct (N × H)
187. C8D4×D271semidirect
197. C22C2×D2168semidirect
202. C4C2×D2168semidirect

Maximal subgroups

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

subgroupindex
C22×D21682
D4×D10842
#317742742
#317741332
#317740932
#317740332
C4×D21682
C8×D4×C2712
D4×D8271