Finite Group Databasebeta

← #46855799

Subgroups — #46855799

Order 35008.

262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 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×#22576776C211yesmaximal, characteristic, complemented
2#31776033C212yesmaximal, complemented
3#31776032C212yesmaximal, complemented
4#31776028C212yesmaximal, complemented
5#31776027C212yesmaximal, complemented
6#31776022C214yesmaximal, complemented
7C2×#22576760C211yesmaximal, characteristic, complemented
8C2×#41×C547C211yesmaximal, characteristic, complemented
9#22576776—21no—
10#22576776—21no—
11#22576776C2212yes—
12#22576776C2212yescomplemented
13C2×Dic1094C2211yescharacteristic, complemented
14C2×D2188C2211yescharacteristic, complemented
15C2×C22⋊D547—21no—
16C2×C4×D547—21no—
17#22576766C2214yescomplemented
18#22576764C2214yescomplemented
19#22576763C2214yescomplemented
20#22576761C2214yescomplemented
21#22576760C2212yescomplemented
22#22576760C2212yescomplemented
23C2×C547⋊C8C2212yescomplemented
24#41×C547—21no—
25#41×C547—21no—
26#41×C547C2212yes—
27#41×C547C2212yescomplemented
28C2×Q8×C547C2211yescharacteristic, complemented
29C2×D4×C547—21no—
30C2×D4×C547C2211yescharacteristic, complemented
31C22×C4×C547—21no—
32C22×C4×C547C2211yescharacteristic
33C22×D547—21no—
34Dic1094—21no—
35Dic1094C2312yes—
36D2188—21no—
37D2188C2312yes—
38C22⋊D547—22no—
39C22⋊D547—22no—
40C2×Dic547—21no—
41C4×D547—22no—
42C4×D547—22no—
43C547⋊C8C2314yes—
44C23×C547—21no—
45C23×C547D411yescharacteristic
46Q8×C547—21no—
47Q8×C547C2312yes—
48D4×C547—22no—
49D4×C547—22no—
50D4×C547—21no—
51D4×C547C2312yes—
52C2×C4×C547—21no—
53C2×C4×C547—22no—
54C2×C4×C547—22no—
55C2×C4×C547D411yescharacteristic
56C2×C4×C547D411yescharacteristic
57C2×C4×C547D411yescharacteristic
58C2×C4×C547C2311yescharacteristic
59C2×C4×C547C2311yescharacteristic
60C2×C4×C547C2311yescharacteristic
61C22×C547—22no—
62C22×C547—41no—
63C22×C547—42no—
64C22×C547C2×D411yescharacteristic
65C22×C547C2×D411yescharacteristic
66C22×C547C2×D411yescharacteristic
67C2×D547—22no—
68C2×D547—42no—
69C4×C547—22no—
70C4×C547C2×D411yescharacteristic
71C4×C547C2×D411yescharacteristic
72C4×C547C2×D411yescharacteristic
73C4×C547C2411yescharacteristic
74Dic547—22no—
75C2×C547—21no—
76C2×C547—21no—
77C2×C547—21no—
78C2×C547—42no—
79C2×C547C22×D411yescharacteristic
80D547—42no—
81C547#57511yescharacteristic, complemented, Sylow
82#575—5471nomaximal, Sylow
83C2×#41—5471no—
84C2×#41D54711yescharacteristic, complemented
85#137—5472no—
86#137—5472no—
87AGL(1,ℤ/8)—5472no—
88AGL(1,ℤ/8)—5472no—
89#135—5474no—
90C2×M16—5471no—
91#41—21no—
92#41—21no—
93#41—5472no—
94#41—5472no—
95#41—10941no—
96#41—10941no—
97#41C2×D54712yes—
98#41C2×D54712yescomplemented
99C2×Q8—5471no—
100C2×Q8C2×D54711yescharacteristic, complemented
101C2×D4—21no—
102C2×D4—5471no—
103C2×D4—10941no—
104C2×D4C2×D54711yescharacteristic, complemented
105C22×C4—21no—
106C22×C4—10941no—
107C22×C4C2×D54711yescharacteristic
108Q16—5474no—
109SD16—5474no—
110SD16—5474no—
111D8—5474no—
112M16—5472no—
113M16—5472no—
114C2×C8—5472no—
115C23—21no—
116C23—10941no—
117C23C22⋊D54711yescharacteristic
118Q8—21no—
119Q8—5472no—
120Q8—10941no—
121Q8C22×D54712yes—
122D4—22no—
123D4—22no—
124D4—21no—
125D4—5472no—
126D4—10942no—
127D4—10942no—
128D4—10941no—
129D4C22×D54712yes—
130C2×C4—21no—
131C2×C4—22no—
132C2×C4—22no—
133C2×C4—10941no—
134C2×C4—10942no—
135C2×C4—10942no—
136C2×C4C22⋊D54711yescharacteristic
137C2×C4C22⋊D54711yescharacteristic
138C2×C4C22⋊D54711yescharacteristic
139C2×C4C22×D54711yescharacteristic
140C2×C4C22×D54711yescharacteristic
141C2×C4C22×D54711yescharacteristic
142C8—5474no—
143C22—22no—
144C22—41no—
145C22—42no—
146C22—10942no—
147C22—21882no—
148C22C2×C22⋊D54711yescharacteristic
149C22C2×C22⋊D54711yescharacteristic
150C22C2×C22⋊D54711yescharacteristic
151C4—22no—
152C4—10942no—
153C4C2×C22⋊D54711yescharacteristic
154C4C2×C22⋊D54711yescharacteristic
155C4C2×C22⋊D54711yescharacteristic
156C4C23×D54711yescharacteristic
157C2—21no—
158C2—21no—
159C2—21no—
160C2—42no—
161C2—21882no—
162C2C22×C22⋊D54711yescharacteristic
subgroupG/H
centerC4C2×C22⋊D547
commutator, cosocleC4×C547C24
FrattiniC4C23×D547
FittingC2×#41×C547C2
socleC2×C547C22×D4
hypercenterC2×#41D547
hypocenterC547#575
LCSG ▷ C4×C547 ▷ C2×C547 ▷ C547
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#22576776C2semidirect
2. #31776033C2semidirect
3. #31776032C2semidirect
4. #31776028C2semidirect
5. #31776027C2semidirect
6. #31776022C2semidirect
7. C2×#22576760C2semidirect
8. C2×#41×C547C2semidirect
12. #22576776C22semidirect
13. C2×Dic1094C22semidirect
14. C2×D2188C22semidirect
17. #22576766C22semidirect
18. #22576764C22semidirect
19. #22576763C22semidirect
20. #22576761C22semidirect
21. #22576760C22semidirect
22. #22576760C22semidirect
23. C2×C547⋊C8C22semidirect
27. #41×C547C22semidirect
28. C2×Q8×C547C22semidirect
30. C2×D4×C547C22semidirect
81. C547#575semidirect
84. C2×#41D547semidirect
98. #41C2×D547semidirect
100. C2×Q8C2×D547semidirect
104. C2×D4C2×D547semidirect

Maximal subgroups

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

subgroupindex
C2×#225767762
#317760332
#317760322
#317760282
#317760272
#317760222
C2×#225767602
C2×#41×C5472
#575547