Finite Group Databasebeta

← D4×D1448 #37545398

Subgroups — D4×D1448 #37545398

Order 23168.

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×D1448C212yesmaximal, complemented
2D4×D724C212yesmaximal, complemented
3#26041656C211yesmaximal, characteristic, complemented
4#26041515C212yesmaximal, complemented
5#26041475C212yesmaximal, complemented
6#26041415C214yesmaximal, complemented
7C4×D1448C211yesmaximal, characteristic, complemented
8C8×D4×C181C211yesmaximal, characteristic, complemented
9C22×D724C2214yescomplemented
10C2×D4×D181—22no—
11C2×D1448—28no—
12C2×D1448C2211yescharacteristic
13C2×D1448C2212yescomplemented
14C2×D1448C2214yescomplemented
15C2×D1448C2212yescomplemented
16#19153813C2212yescomplemented
17#19153791—22no—
18#19153790C2214yescomplemented
19#19153786—24no—
20C4×D724C2212yescomplemented
21#19153750C2211yescharacteristic, complemented
22#19153738C2212yescomplemented
23#19153738C2214yescomplemented
24C22×C8×C181C2212yescomplemented
25C4×D4×C181C2211yescharacteristic
26C4⋊C8×C181C2211yescharacteristic, complemented
27C22⋊C8×C181C2212yescomplemented
28C4×C8×C181C2211yescharacteristic, complemented
29C23×D181—24no—
30C2×D724—28no—
31C2×D724—24no—
32C2×D724—22no—
33C2×D724—22no—
34C2×D724—44no—
35C2×D724C2314yes—
36C2×D724C2312yes—
37C2×C22⋊D181—24no—
38D4×D181—48no—
39C2×C4×D181—22no—
40D1448—28no—
41D1448—24no—
42D1448—42no—
43D1448D414yesdirect product factor
44C4⋊Dic181C2312yes—
45#15668426—22no—
46#15668426—24no—
47C2×D4×C181D411yescharacteristic
48C22×C4×C181C2312yes—
49C2×C8×C181—24no—
50C2×C8×C181C2311yescharacteristic
51C2×C8×C181C2312yes—
52C2×C8×C181C2311yescharacteristic
53C4⋊C4×C181D411yescharacteristic
54C22⋊C4×C181D412yes—
55C42×C181C2311yescharacteristic
56C22×D181—22no—
57C22×D181—24no—
58C22×D181—48no—
59C22×D181—48no—
60C22×D181—84no—
61D724—24no—
62D724—22no—
63D724—24no—
64D724—48no—
65D724—44no—
66D724—82no—
67D724C2×D414yescomplemented
68C22⋊D181—48no—
69C2×Dic181—22no—
70C4×D181—44no—
71C23×C181C2×D412yes—
72D4×C181D814yescomplemented
73C2×C4×C181—22no—
74C2×C4×C181—22no—
75C2×C4×C181C2×D411yescharacteristic
76C2×C4×C181C2×D412yes—
77C2×C4×C181C2×D411yescharacteristic
78C2×C4×C181C2411yescharacteristic
79C8×C181—22no—
80C8×C181—21no—
81C8×C181C2×D412yescomplemented
82C22×C181—22no—
83C22×C181—22no—
84C22×C181C2×D814yescomplemented
85C22×C181C22×D411yescharacteristic
86C2×D181—24no—
87C2×D181—42no—
88C2×D181—42no—
89C2×D181—44no—
90C2×D181—44no—
91C2×D181—44no—
92C2×D181—816no—
93C4×C181—22no—
94C4×C181—21no—
95C4×C181C2×D812yescomplemented
96C4×C181C22×D411yescharacteristic
97C4×C181H(5,𝔽2)11yescharacteristic
98Dic181—42no—
99C2×C181—24no—
100C2×C181D4211yescharacteristic
101C2×C181C22×D811yescharacteristic
102C2×C181#57611yescharacteristic
103D181—44no—
104D181—84no—
105C181D4×D811yescharacteristic, complemented, Sylow
106D4×D8—1811nomaximal, Sylow
107C22×D8—1812no—
108D42—1812no—
109#493—1811no—
110#466—1812no—
111#459—1812no—
112#447—1814no—
113C4×D8—1811no—
114C8×D4D18111yescharacteristic, complemented
115C22×D4—3622no—
116C22×D4—1814no—
117C2×D8—3628no—
118C2×D8—1814no—
119C2×D8—1812no—
120C2×D8—1811no—
121C2×D8—1812no—
122C22×C8C2×D18112yescomplemented
123#127—1812no—
124#121—3622no—
125#121—1814no—
126#120—3624no—
127C4×D4—1812no—
128C4×D4C2×D18111yescharacteristic
129#107—1811no—
130C4⋊C8C2×D18111yescharacteristic, complemented
131#102—1812no—
132#102—1814no—
133C22⋊C8C2×D18112yescomplemented
134C4×C8C2×D18111yescharacteristic, complemented
135C24—3624no—
136C2×D4—3628no—
137C2×D4—3624no—
138C2×D4—3622no—
139C2×D4—3624no—
140C2×D4—3622no—
141C2×D4—1814no—
142C2×D4—1812no—
143C2×D4—7244no—
144C2×D4—7248no—
145C2×D4D72411yescharacteristic
146C22×C4—3622no—
147C22×C4C22×D18112yes—
148D8—3628no—
149D8—3624no—
150D8—1814no—
151D8—7242no—
152C2×C8—24no—
153C2×C8C22×D18111yescharacteristic
154C2×C8C22×D18112yes—
155C2×C8C22×D18111yescharacteristic
156C4⋊C4—1812no—
157C4⋊C4D72411yescharacteristic
158C22⋊C4—3622no—
159C22⋊C4—3624no—
160C22⋊C4D72412yes—
161C42C22×D18111yescharacteristic
162C23—3622no—
163C23—3624no—
164C23—14484no—
165C23—7248no—
166C23—7248no—
167C23C2×D72412yes—
168D4—3624no—
169D4—3622no—
170D4—3624no—
171D4—14482no—
172D4—1814no—
173D4—7248no—
174D4—7248no—
175D4—7244no—
176D4D144814yesdirect product factor
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—3622no—
180C2×C4—7244no—
181C2×C4C2×D72411yescharacteristic
182C2×C4C2×D72412yes—
183C2×C4C2×D72411yescharacteristic
184C2×C4C23×D18111yescharacteristic
185C8—22no—
186C8—21no—
187C8D4×D18112yescomplemented
188C22—22no—
189C22—22no—
190C22—3624no—
191C22—144816no—
192C22—7244no—
193C22—7244no—
194C22—7244no—
195C22—7242no—
196C22—7242no—
197C22C2×D144814yescomplemented
198C22C22×D72411yescharacteristic
199C4—22no—
200C4—21no—
201C4—7242no—
202C4C2×D144812yescomplemented
203C4C2×D4×D18111yescharacteristic
204C4#1915386211yescharacteristic
205C2—24no—
206C2—14484no—
207C2—7244no—
208C2D4×D72411yescharacteristic
209C2C22×D144811yescharacteristic
210C2#2604208411yescharacteristic
subgroupG/H
centerC22C22×D724
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
FittingC8×D4×C181C2
socleC22×C181C22×D4
hypercenterC8×D4D181
hypocenterC181D4×D8
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. C22×D1448C2semidirect
2. D4×D724C2semidirect
3. #26041656C2semidirect
4. #26041515C2semidirect
5. #26041475C2semidirect
6. #26041415C2semidirect
7. C4×D1448C2semidirect
8. C8×D4×C181C2semidirect
9. C22×D724C22semidirect
13. C2×D1448C22semidirect
14. C2×D1448C22semidirect
15. C2×D1448C22semidirect
16. #19153813C22semidirect
18. #19153790C22semidirect
20. C4×D724C22semidirect
21. #19153750C22semidirect
22. #19153738C22semidirect
23. #19153738C22semidirect
24. C22×C8×C181C22semidirect
26. C4⋊C8×C181C22semidirect
27. C22⋊C8×C181C22semidirect
28. C4×C8×C181C22semidirect
43. D1448D4direct (N × H)
67. D724C2×D4semidirect
72. D4×C181D8semidirect
81. C8×C181C2×D4semidirect
84. C22×C181C2×D8semidirect
95. C4×C181C2×D8semidirect
105. C181D4×D8semidirect
114. C8×D4D181semidirect
122. C22×C8C2×D181semidirect
130. C4⋊C8C2×D181semidirect
133. C22⋊C8C2×D181semidirect
134. C4×C8C2×D181semidirect
176. D4D1448direct (N × H)
187. C8D4×D181semidirect
197. C22C2×D1448semidirect
202. C4C2×D1448semidirect

Maximal subgroups

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

subgroupindex
C22×D14482
D4×D7242
#260416562
#260415152
#260414752
#260414152
C4×D14482
C8×D4×C1812
D4×D8181