Finite Group Databasebeta

← D4×D1576 #38754389

Subgroups — D4×D1576 #38754389

Order 25216.

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×D1576C212yesmaximal, complemented
2D4×D788C212yesmaximal, complemented
3#27161456C211yesmaximal, characteristic, complemented
4#27161315C212yesmaximal, complemented
5#27161275C212yesmaximal, complemented
6#27161215C214yesmaximal, complemented
7C4×D1576C211yesmaximal, characteristic, complemented
8C8×D4×C197C211yesmaximal, characteristic, complemented
9C22×D788C2214yescomplemented
10C2×D4×D197—22no—
11C2×D1576—28no—
12C2×D1576C2211yescharacteristic
13C2×D1576C2212yescomplemented
14C2×D1576C2214yescomplemented
15C2×D1576C2212yescomplemented
16#20263323C2212yescomplemented
17#20263301—22no—
18#20263300C2214yescomplemented
19#20263296—24no—
20C4×D788C2212yescomplemented
21#20263260C2211yescharacteristic, complemented
22#20263248C2212yescomplemented
23#20263248C2214yescomplemented
24C22×C8×C197C2212yescomplemented
25C4×D4×C197C2211yescharacteristic
26C4⋊C8×C197C2211yescharacteristic, complemented
27C22⋊C8×C197C2212yescomplemented
28C4×C8×C197C2211yescharacteristic, complemented
29C23×D197—24no—
30C2×D788—28no—
31C2×D788—24no—
32C2×D788—22no—
33C2×D788—22no—
34C2×D788—44no—
35C2×D788C2314yes—
36C2×D788C2312yes—
37C2×C22⋊D197—24no—
38D4×D197—48no—
39C2×C4×D197—22no—
40D1576—28no—
41D1576—24no—
42D1576—42no—
43D1576D414yesdirect product factor
44C4⋊Dic197C2312yes—
45#15691335—22no—
46#15691335—24no—
47C2×D4×C197D411yescharacteristic
48C22×C4×C197C2312yes—
49C2×C8×C197—24no—
50C2×C8×C197C2311yescharacteristic
51C2×C8×C197C2312yes—
52C2×C8×C197C2311yescharacteristic
53C4⋊C4×C197D411yescharacteristic
54C22⋊C4×C197D412yes—
55C42×C197C2311yescharacteristic
56C22×D197—22no—
57C22×D197—24no—
58C22×D197—48no—
59C22×D197—48no—
60C22×D197—84no—
61D788—24no—
62D788—22no—
63D788—24no—
64D788—48no—
65D788—44no—
66D788—82no—
67D788C2×D414yescomplemented
68C22⋊D197—48no—
69C2×Dic197—22no—
70C4×D197—44no—
71C23×C197C2×D412yes—
72D4×C197D814yescomplemented
73C2×C4×C197—22no—
74C2×C4×C197—22no—
75C2×C4×C197C2×D411yescharacteristic
76C2×C4×C197C2×D412yes—
77C2×C4×C197C2×D411yescharacteristic
78C2×C4×C197C2411yescharacteristic
79C8×C197—22no—
80C8×C197—21no—
81C8×C197C2×D412yescomplemented
82C22×C197—22no—
83C22×C197—22no—
84C22×C197C2×D814yescomplemented
85C22×C197C22×D411yescharacteristic
86C2×D197—24no—
87C2×D197—42no—
88C2×D197—42no—
89C2×D197—44no—
90C2×D197—44no—
91C2×D197—44no—
92C2×D197—816no—
93C4×C197—22no—
94C4×C197—21no—
95C4×C197C2×D812yescomplemented
96C4×C197C22×D411yescharacteristic
97C4×C197H(5,𝔽2)11yescharacteristic
98Dic197—42no—
99C2×C197—24no—
100C2×C197D4211yescharacteristic
101C2×C197C22×D811yescharacteristic
102C2×C197#57611yescharacteristic
103D197—44no—
104D197—84no—
105C197D4×D811yescharacteristic, complemented, Sylow
106D4×D8—1971nomaximal, Sylow
107C22×D8—1972no—
108D42—1972no—
109#493—1971no—
110#466—1972no—
111#459—1972no—
112#447—1974no—
113C4×D8—1971no—
114C8×D4D19711yescharacteristic, complemented
115C22×D4—3942no—
116C22×D4—1974no—
117C2×D8—3948no—
118C2×D8—1972no—
119C2×D8—1974no—
120C2×D8—1972no—
121C2×D8—1971no—
122C22×C8C2×D19712yescomplemented
123#127—1972no—
124#121—3942no—
125#121—1974no—
126#120—3944no—
127C4×D4—1972no—
128C4×D4C2×D19711yescharacteristic
129#107—1971no—
130C4⋊C8C2×D19711yescharacteristic, complemented
131#102—1972no—
132#102—1974no—
133C22⋊C8C2×D19712yescomplemented
134C4×C8C2×D19711yescharacteristic, complemented
135C24—3944no—
136C2×D4—7884no—
137C2×D4—7888no—
138C2×D4—3948no—
139C2×D4—3944no—
140C2×D4—3944no—
141C2×D4—3942no—
142C2×D4—3942no—
143C2×D4—1974no—
144C2×D4—1972no—
145C2×D4D78811yescharacteristic
146C22×C4—3942no—
147C22×C4C22×D19712yes—
148D8—7882no—
149D8—3948no—
150D8—3944no—
151D8—1974no—
152C2×C8—24no—
153C2×C8C22×D19711yescharacteristic
154C2×C8C22×D19712yes—
155C2×C8C22×D19711yescharacteristic
156C4⋊C4—1972no—
157C4⋊C4D78811yescharacteristic
158C22⋊C4—3942no—
159C22⋊C4—3944no—
160C22⋊C4D78812yes—
161C42C22×D19711yescharacteristic
162C23—7888no—
163C23—7888no—
164C23—15764no—
165C23—3944no—
166C23—3942no—
167C23C2×D78812yes—
168D4—7888no—
169D4—7888no—
170D4—7884no—
171D4—15762no—
172D4—3944no—
173D4—3944no—
174D4—3942no—
175D4—1974no—
176D4D157614yesdirect product factor
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—7884no—
180C2×C4—3942no—
181C2×C4C2×D78811yescharacteristic
182C2×C4C2×D78812yes—
183C2×C4C2×D78811yescharacteristic
184C2×C4C23×D19711yescharacteristic
185C8—22no—
186C8—21no—
187C8D4×D19712yescomplemented
188C22—22no—
189C22—22no—
190C22—7882no—
191C22—7882no—
192C22—7884no—
193C22—7884no—
194C22—7884no—
195C22—157616no—
196C22—3944no—
197C22C2×D157614yescomplemented
198C22C22×D78811yescharacteristic
199C4—21no—
200C4—22no—
201C4—7882no—
202C4C2×D157612yescomplemented
203C4C2×D4×D19711yescharacteristic
204C4#2026337211yescharacteristic
205C2—24no—
206C2—7884no—
207C2—15764no—
208C2D4×D78811yescharacteristic
209C2C22×D157611yescharacteristic
210C2#2716188411yescharacteristic
subgroupG/H
centerC22C22×D788
commutator, cosocleC2×C4×C197C24
FrattiniC2×C4C23×D197
FittingC8×D4×C197C2
socleC22×C197C22×D4
hypercenterC8×D4D197
hypocenterC197D4×D8
LCSG ▷ C2×C4×C197 ▷ C2×C197 ▷ C197
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. C22×D1576C2semidirect
2. D4×D788C2semidirect
3. #27161456C2semidirect
4. #27161315C2semidirect
5. #27161275C2semidirect
6. #27161215C2semidirect
7. C4×D1576C2semidirect
8. C8×D4×C197C2semidirect
9. C22×D788C22semidirect
13. C2×D1576C22semidirect
14. C2×D1576C22semidirect
15. C2×D1576C22semidirect
16. #20263323C22semidirect
18. #20263300C22semidirect
20. C4×D788C22semidirect
21. #20263260C22semidirect
22. #20263248C22semidirect
23. #20263248C22semidirect
24. C22×C8×C197C22semidirect
26. C4⋊C8×C197C22semidirect
27. C22⋊C8×C197C22semidirect
28. C4×C8×C197C22semidirect
43. D1576D4direct (N × H)
67. D788C2×D4semidirect
72. D4×C197D8semidirect
81. C8×C197C2×D4semidirect
84. C22×C197C2×D8semidirect
95. C4×C197C2×D8semidirect
105. C197D4×D8semidirect
114. C8×D4D197semidirect
122. C22×C8C2×D197semidirect
130. C4⋊C8C2×D197semidirect
133. C22⋊C8C2×D197semidirect
134. C4×C8C2×D197semidirect
176. D4D1576direct (N × H)
187. C8D4×D197semidirect
197. C22C2×D1576semidirect
202. C4C2×D1576semidirect

Maximal subgroups

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

subgroupindex
C22×D15762
D4×D7882
#271614562
#271613152
#271612752
#271612152
C4×D15762
C8×D4×C1972
D4×D8197