Finite Group Databasebeta

← D8×D788 #38754388

Subgroups — D8×D788 #38754388

Order 25216.

620 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C2×D8×D197C212yesmaximal, complemented
2D4×D788C212yesmaximal, complemented
3#27161456C211yesmaximal, characteristic, complemented
4#27161316C212yesmaximal, complemented
5#27161274C212yesmaximal, complemented
6#27161214C214yesmaximal, complemented
7C8×D788C211yesmaximal, characteristic, complemented
8C4×D8×C197C211yesmaximal, characteristic, complemented
9C22×D788—22no—
10C2×D4×D197C2214yescomplemented
11C2×D1576C2212yescomplemented
12C2×D1576C2212yescomplemented
13C2×#15691343C2214yescomplemented
14D8×D197—28no—
15C2×C8×D197C2212yescomplemented
16#20263323C2212yescomplemented
17#20263301C2214yescomplemented
18#20263300—22no—
19#20263296—24no—
20C4×D788C2211yescharacteristic
21C4⋊#13096802C2211yescharacteristic, complemented
22#20263246C2214yescomplemented
23#20263238C2212yescomplemented
24C2×D8×C197C2211yescharacteristic
25C4×D4×C197C2212yescomplemented
26#107×C197C2211yescharacteristic, complemented
27#102×C197C2212yescomplemented
28C4×C8×C197C2211yescharacteristic, complemented
29C23×D197—24no—
30C2×D788—24no—
31C2×D788—22no—
32C2×D788—22no—
33C2×D788—48no—
34C2×D788D411yescharacteristic
35C2×D788C2314yes—
36C2×C22⋊D197—24no—
37D4×D197—28no—
38D4×D197—44no—
39C2×C4×D197C2312yes—
40D1576—24no—
41D1576—42no—
42#15691343—28no—
43C2×#13096802C2312yes—
44C8×D197—24no—
45C4⋊Dic197D411yescharacteristic
46#15691335—24no—
47#15691335D412yes—
48C2×D4×C197C2312yes—
49C22×C4×C197—22no—
50D8×C197D414yescomplemented
51C2×C8×C197C2311yescharacteristic
52C2×C8×C197C2311yescharacteristic
53C4⋊C4×C197C2312yes—
54C22⋊C4×C197—22no—
55C42×C197C2311yescharacteristic
56C22×D197—24no—
57C22×D197—48no—
58C22×D197—48no—
59C22×D197—84no—
60C22×D197C2×D412yes—
61D788—24no—
62D788—24no—
63D788—48no—
64D788—44no—
65D788—82no—
66D788D814yesdirect product factor
67C22⋊D197—48no—
68C2×Dic197C2×D412yes—
69C4×D197—22no—
70C4×D197—22no—
71#13096802—22no—
72C23×C197—22no—
73D4×C197—22no—
74D4×C197C2×D414yescomplemented
75C2×C4×C197—22no—
76C2×C4×C197—44no—
77C2×C4×C197C2×D411yescharacteristic
78C2×C4×C197C2×D411yescharacteristic
79C2×C4×C197C2411yescharacteristic
80C8×C197—21no—
81C8×C197C2×D412yescomplemented
82C22×C197—24no—
83C22×C197—42no—
84C22×C197—42no—
85C22×C197C22×D411yescharacteristic
86C2×D197—22no—
87C2×D197—22no—
88C2×D197—44no—
89C2×D197—44no—
90C2×D197—44no—
91C2×D197—816no—
92C2×D197C2×D814yescomplemented
93C4×C197—21no—
94C4×C197—42no—
95C4×C197C2×D812yescomplemented
96C4×C197C22×D411yescharacteristic
97C4×C197H(5,𝔽2)11yescharacteristic
98Dic197—22no—
99C2×C197—44no—
100C2×C197D4211yescharacteristic
101C2×C197C22×D811yescharacteristic
102C2×C197#57611yescharacteristic
103D197—24no—
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×D8D19711yescharacteristic, complemented
114C8×D4—1971no—
115C22×D4—3942no—
116C22×D4—1974no—
117C2×D8—3948no—
118C2×D8—1974no—
119C2×D8—1972no—
120C2×D8—1972no—
121C2×D8C2×D19711yescharacteristic
122C22×C8—1972no—
123#127—1972no—
124#121—3942no—
125#121—1974no—
126#120—3944no—
127C4×D4—1971no—
128C4×D4C2×D19712yescomplemented
129#107C2×D19711yescharacteristic, complemented
130C4⋊C8—1971no—
131#102—1974no—
132#102C2×D19712yescomplemented
133C22⋊C8—1972no—
134C4×C8C2×D19711yescharacteristic, complemented
135C24—3944no—
136C2×D4—7888no—
137C2×D4—7884no—
138C2×D4—3944no—
139C2×D4—3948no—
140C2×D4—3944no—
141C2×D4—3942no—
142C2×D4—3942no—
143C2×D4—1971no—
144C2×D4—1974no—
145C2×D4C22×D19712yes—
146C22×C4—22no—
147C22×C4—1972no—
148D8—7882no—
149D8—3948no—
150D8—3944no—
151D8D78814yesdirect product factor
152C2×C8—3944no—
153C2×C8—1972no—
154C2×C8C22×D19711yescharacteristic
155C2×C8C22×D19711yescharacteristic
156C4⋊C4—1971no—
157C4⋊C4C22×D19712yes—
158C22⋊C4—22no—
159C22⋊C4—3944no—
160C22⋊C4—1972no—
161C42C22×D19711yescharacteristic
162C23—22no—
163C23—7888no—
164C23—7888no—
165C23—15764no—
166C23—3944no—
167C23—1972no—
168D4—22no—
169D4—7888no—
170D4—7888no—
171D4—7884no—
172D4—15762no—
173D4—3944no—
174D4—3944no—
175D4—1974no—
176D4C2×D78814yescomplemented
177C2×C4—22no—
178C2×C4—44no—
179C2×C4—3942no—
180C2×C4—3942no—
181C2×C4—1972no—
182C2×C4D4×D19711yescharacteristic
183C2×C4D4×D19711yescharacteristic
184C2×C4C23×D19711yescharacteristic
185C8—21no—
186C8—3942no—
187C8C2×D78812yescomplemented
188C22—24no—
189C22—42no—
190C22—42no—
191C22—7884no—
192C22—7884no—
193C22—7884no—
194C22—157616no—
195C22—3942no—
196C22—3942no—
197C22—1974no—
198C22C2×D4×D19711yescharacteristic
199C4—21no—
200C4—42no—
201C4—3942no—
202C4D8×D19712yescomplemented
203C4C22×D78811yescharacteristic
204C4#2026337211yescharacteristic
205C2—44no—
206C2—15764no—
207C2—3944no—
208C2D4×D78811yescharacteristic
209C2C2×D8×D19711yescharacteristic
210C2#2716188111yescharacteristic
subgroupG/H
centerC22C2×D4×D197
commutator, cosocleC2×C4×C197C24
FrattiniC2×C4C23×D197
FittingC4×D8×C197C2
socleC22×C197C22×D4
hypercenterC4×D8D197
hypocenterC197D4×D8
LCSG ▷ C2×C4×C197 ▷ C2×C197 ▷ C197
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×D8×D197C2semidirect
2. D4×D788C2semidirect
3. #27161456C2semidirect
4. #27161316C2semidirect
5. #27161274C2semidirect
6. #27161214C2semidirect
7. C8×D788C2semidirect
8. C4×D8×C197C2semidirect
10. C2×D4×D197C22semidirect
11. C2×D1576C22semidirect
12. C2×D1576C22semidirect
13. C2×#15691343C22semidirect
15. C2×C8×D197C22semidirect
16. #20263323C22semidirect
17. #20263301C22semidirect
21. C4⋊#13096802C22semidirect
22. #20263246C22semidirect
23. #20263238C22semidirect
25. C4×D4×C197C22semidirect
26. #107×C197C22semidirect
27. #102×C197C22semidirect
28. C4×C8×C197C22semidirect
50. D8×C197D4semidirect
66. D788D8direct (N × H)
74. D4×C197C2×D4semidirect
81. C8×C197C2×D4semidirect
92. C2×D197C2×D8semidirect
95. C4×C197C2×D8semidirect
105. C197D4×D8semidirect
113. C4×D8D197semidirect
128. C4×D4C2×D197semidirect
129. #107C2×D197semidirect
132. #102C2×D197semidirect
134. C4×C8C2×D197semidirect
151. D8D788direct (N × H)
176. D4C2×D788semidirect
187. C8C2×D788semidirect
202. C4D8×D197semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1972
D4×D7882
#271614562
#271613162
#271612742
#271612142
C8×D7882
C4×D8×C1972
D4×D8197