Finite Group Databasebeta

← #26374425

Subgroups — #26374425

Order 12032.

472 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 127 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
1#20256525C212yesmaximal, complemented
2#20245701C212yesmaximal, complemented
3#20245699C214yesmaximal, complemented
4#20245697C211yesmaximal, characteristic, complemented
5#20245694C212yesmaximal, complemented
6D32×D47C212yesmaximal, complemented
7#20245681C211yesmaximal, characteristic, complemented
8C2×C47×D32C211yesmaximal, characteristic, complemented
9#15689924—22no—
10#15689559—22no—
11#15689557—24no—
12#15689555C2212yescomplemented
13#15689552C2214yescomplemented
14D16×D47C2214yescomplemented
15#15689539C2211yescharacteristic
16Dic752C2211yescharacteristic, complemented
17#15688962C2212yescomplemented
18#15688961C2214yescomplemented
19D1504C2211yescharacteristic, complemented
20#15688958C2214yescomplemented
21#15688957C2211yescharacteristic, complemented
22#15688956C2212yescomplemented
23C32×D47C2212yescomplemented
24C2×D16×C47C2212yescomplemented
25C47×D32C2212yescomplemented
26C47×D32C2212yescomplemented
27C2×C32×C47C2211yescharacteristic, complemented
28#13094069—42no—
29#13094050—42no—
30#13094048—44no—
31#13094046—22no—
32#13094043—24no—
33D8×D47—24no—
34#13094030D411yescharacteristic
35Dic376C2312yes—
36#13093969—22no—
37#13093968—24no—
38D752C2312yes—
39#13093965—24no—
40#13093964D411yescharacteristic
41#13093963D412yes—
42C16×D47C2312yes—
43C47⋊C32C2312yes—
44C2×D8×C47—22no—
45D16×C47—22no—
46D16×C47C2314yes—
47C2×C16×C47C2311yescharacteristic
48C32×C47C2311yescharacteristic
49C32×C47C2311yescharacteristic
50C2×D4×C47—42no—
51C2×C22⋊D47—84no—
52#10625352—44no—
53#10625352—82no—
54D4×D47—44no—
55D4×D47—82no—
56#10625350—42no—
57#10625350D811yescharacteristic
58D8×C47—24no—
59D8×C47—42no—
60C2×C8×C47C2×D411yescharacteristic
61#10625335—44no—
62#10625334—44no—
63#10625329D811yescharacteristic
64Dic188—22no—
65D376—22no—
66#10625325—42no—
67#10625324D812yes—
68C8×D47C2×D412yes—
69C16×C47C2×D411yescharacteristic
70C16×C47C2411yescharacteristic
71C47⋊C16C2×D412yes—
72C23×C47—82no—
73C22×D47—84no—
74D4×C47—44no—
75D4×C47—82no—
76C2×C4×C47C2×D811yescharacteristic
77C22⋊D47—82no—
78C22⋊D47—84no—
79C22⋊D47—84no—
80C22⋊D47D1612yes—
81C2×Dic47—84no—
82D188—42no—
83D188D1611yescharacteristic
84C4×D47—82no—
85C4×D47C2×D812yes—
86Dic94—42no—
87Dic94D1611yescharacteristic
88C8×C47C2×D811yescharacteristic
89C8×C47C22×D411yescharacteristic
90C47⋊C8C2×D812yes—
91#33982—471nomaximal, Sylow
92C22×C47—84no—
93C22×C47—322no—
94C22×C47C2×D1611yescharacteristic
95C2×D47—82no—
96C2×D47—324no—
97C2×D47C2×D1612yes—
98C4×C47C2×D1611yescharacteristic
99C4×C47C22×D811yescharacteristic
100Dic47—82no—
101Dic47C2×D1612yes—
102#3415—472no—
103#2263—472no—
104#2263—474no—
105#2262—472no—
106#2262—471no—
107C2×D32—472no—
108C2×D32D4711yescharacteristic, complemented
109#2258—471no—
110C2×C47—21no—
111C2×C47—164no—
112C2×C47C22×D1611yescharacteristic
113D47—22no—
114D47—162no—
115#576—942no—
116#509—944no—
117#509—942no—
118#508—474no—
119#508—472no—
120C2×D16—474no—
121C2×D16C2×D4712yescomplemented
122#504—471no—
123Q64—471no—
124SD64—474no—
125SD64—472no—
126D32—474no—
127D32—471no—
128D32C2×D4712yescomplemented
129D32C2×D4712yescomplemented
130M64—471no—
131M64—472no—
132C2×C32—472no—
133C2×C32C2×D4711yescharacteristic, complemented
134C47#3398211yescharacteristic, complemented, Sylow
135H(5,𝔽2)—1882no—
136AGL(1,ℤ/8)—1884no—
137AGL(1,ℤ/8)—1882no—
138#135—944no—
139#135—942no—
140C2×D8—22no—
141C2×D8—944no—
142#131—471no—
143Q32—472no—
144SD32—944no—
145SD32—942no—
146D16—22no—
147D16—472no—
148D16—944no—
149D16C22×D4714yes—
150M32—471no—
151M32—472no—
152C2×C16—472no—
153C2×C16C22×D4711yescharacteristic
154C32—472no—
155C32C22×D4711yescharacteristic
156C32C22×D4711yescharacteristic
157#41—471no—
158#41—3762no—
159#41—1884no—
160#41—1882no—
161C2×D4—42no—
162C2×D4—3762no—
163C2×D4—3764no—
164C2×D4—1884no—
165Q16—942no—
166SD16—1884no—
167SD16—1882no—
168D8—24no—
169D8—42no—
170D8—942no—
171D8—1884no—
172M16—471no—
173M16—472no—
174C2×C8—472no—
175C2×C8D4×D4711yescharacteristic
176C16—472no—
177C16D4×D4711yescharacteristic
178C16C23×D4711yescharacteristic
179C23—82no—
180C23—3764no—
181Q8—471no—
182Q8—1882no—
183D4—44no—
184D4—82no—
185D4—472no—
186D4—471no—
187D4—3764no—
188D4—3764no—
189D4—3762no—
190D4—1882no—
191C2×C4—472no—
192C2×C4—3764no—
193C2×C4—3762no—
194C2×C4D8×D4711yescharacteristic
195C8—472no—
196C8D8×D4711yescharacteristic
197C8C2×D4×D4711yescharacteristic
198C22—84no—
199C22—322no—
200C22—472no—
201C22—3762no—
202C22—15044no—
203C22D16×D4711yescharacteristic
204C4—472no—
205C4—3762no—
206C4D16×D4711yescharacteristic
207C4C2×D8×D4711yescharacteristic
208C2—21no—
209C2—164no—
210C2—942no—
211C2—7522no—
212C2C2×D16×D4711yescharacteristic
subgroupG/H
centerC2C2×D16×D47
commutator, cosocleC16×C47C24
FrattiniC16C23×D47
FittingC2×C47×D32C2
socleC2×C47C22×D16
hypercenterC2×D32D47
hypocenterC47#33982
LCSG ▷ C16×C47 ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×D32

Complements

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

NH ≅ G/Ntype
1. #20256525C2semidirect
2. #20245701C2semidirect
3. #20245699C2semidirect
4. #20245697C2semidirect
5. #20245694C2semidirect
6. D32×D47C2semidirect
7. #20245681C2semidirect
8. C2×C47×D32C2semidirect
12. #15689555C22semidirect
13. #15689552C22semidirect
14. D16×D47C22semidirect
16. Dic752C22semidirect
17. #15688962C22semidirect
18. #15688961C22semidirect
19. D1504C22semidirect
20. #15688958C22semidirect
21. #15688957C22semidirect
22. #15688956C22semidirect
23. C32×D47C22semidirect
24. C2×D16×C47C22semidirect
25. C47×D32C22semidirect
26. C47×D32C22semidirect
27. C2×C32×C47C22semidirect
108. C2×D32D47semidirect
121. C2×D16C2×D47semidirect
128. D32C2×D47semidirect
129. D32C2×D47semidirect
133. C2×C32C2×D47semidirect
134. C47#33982semidirect

Maximal subgroups

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

subgroupindex
#202565252
#202457012
#202456992
#202456972
#202456942
D32×D472
#202456812
C2×C47×D322
#3398247