Finite Group Databasebeta

← #46855177

Subgroups — #46855177

Order 35008.

152 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 39 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#31776048C211yesmaximal, characteristic
2#31776033C211yesmaximal, characteristic, complemented
3#31775991C211yesmaximal, characteristic, complemented
4#31775929C211yesmaximal, characteristic, complemented
5#31775928C211yesmaximal, characteristic, complemented
6#31775918C211yesmaximal, characteristic, complemented
7#137×C547C211yesmaximal, characteristic, complemented
8#22576777—21no—
9#22576776—21no—
10#22576776C2211yescharacteristic
11C2×D2188—21no—
12C2×D2188C2211yescharacteristic
13D4×D547—22no—
14D4×D547—21no—
15#22576766—21no—
16#22576763—21no—
17#22576760C2211yescharacteristic, complemented
18(C2×D547)⋊C4—22no—
19C4×Dic547C2211yescharacteristic, complemented
20#41×C547C2211yescharacteristic
21C2×Q8×C547C2211yescharacteristic, complemented
22Q16×C547—21no—
23SD16×C547—21no—
24M16×C547C2211yescharacteristic, complemented
25C22×D547—22no—
26C22×D547D412yes—
27Dic1094D411yescharacteristic
28D2188—22no—
29D2188—21no—
30D2188—21no—
31D2188D411yescharacteristic
32C22⋊D547—22no—
33C22⋊D547—21no—
34C2×Dic547—21no—
35C4×D547—22no—
36C4×D547—21no—
37C547⋊C8—21no—
38Q8×C547—21no—
39Q8×C547—21no—
40Q8×C547D411yescharacteristic
41D4×C547—21no—
42D4×C547D411yescharacteristic
43C2×C4×C547—21no—
44C2×C4×C547—21no—
45C2×C4×C547C2311yescharacteristic
46C8×C547—21no—
47C22×C547—21no—
48C22×C547C2×D411yescharacteristic
49C2×D547—22no—
50C2×D547—21no—
51C2×D547—42no—
52C2×D547—82no—
53C4×C547—21no—
54C4×C547—41no—
55C4×C547C2×D411yescharacteristic
56C4×C547C2×D411yescharacteristic
57Dic547—21no—
58Dic547—41no—
59C2×C547—21no—
60C2×C547—41no—
61C2×C547#12011yescharacteristic
62D547—42no—
63D547—41no—
64C547#45511yescharacteristic, complemented, Sylow
65#455—5471nomaximal, Sylow
66H(5,𝔽2)—5471no—
67#137—5471no—
68#137D54711yescharacteristic, complemented
69#124—5471no—
70#104—5471no—
71#104—5471no—
72#100—5471no—
73#41—5471no—
74#41—10941no—
75#41—10941no—
76#41C2×D54711yescharacteristic
77C2×Q8C2×D54711yescharacteristic, complemented
78C2×D4—5471no—
79C2×D4—10941no—
80C2×D4—10942no—
81C2×D4—10941no—
82Q16—21no—
83Q16—10941no—
84SD16—21no—
85SD16—10941no—
86M16—5471no—
87M16C2×D54711yescharacteristic, complemented
88C22⋊C4—10942no—
89C42—5471no—
90C23—5472no—
91C23—10942no—
92Q8—21no—
93Q8—21no—
94Q8—5471no—
95Q8C22⋊D54711yescharacteristic
96D4—21no—
97D4—5471no—
98D4—10942no—
99D4—10942no—
100D4—10941no—
101D4—10941no—
102D4—10941no—
103D4C22⋊D54711yescharacteristic
104C2×C4—21no—
105C2×C4—21no—
106C2×C4—10942no—
107C2×C4—10941no—
108C2×C4—10941no—
109C2×C4C22×D54711yescharacteristic
110C8—21no—
111C8—10941no—
112C22—21no—
113C22—43762no—
114C22—10941no—
115C22—10942no—
116C22—21882no—
117C22D4×D54711yescharacteristic
118C4—21no—
119C4—41no—
120C4—10941no—
121C4—21881no—
122C4D4×D54711yescharacteristic
123C4C2×C22⋊D54711yescharacteristic
124C2—21no—
125C2—41no—
126C2—21881no—
127C2—21882no—
128C2#3177597011yescharacteristic
subgroupG/H
centerC2#31775970
commutator, cosocleC2×C4×C547C23
FrattiniC2×C4C22×D547
Fitting#137×C547C2
socleC2×C547#120
prime radical#31776048C2
hypercenter#137D547
hypocenterC547#455
LCSG ▷ C2×C4×C547 ▷ C2×C547 ▷ C547
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
2. #31776033C2semidirect
3. #31775991C2semidirect
4. #31775929C2semidirect
5. #31775928C2semidirect
6. #31775918C2semidirect
7. #137×C547C2semidirect
17. #22576760C22semidirect
19. C4×Dic547C22semidirect
21. C2×Q8×C547C22semidirect
24. M16×C547C22semidirect
64. C547#455semidirect
68. #137D547semidirect
77. C2×Q8C2×D547semidirect
87. M16C2×D547semidirect

Maximal subgroups

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

subgroupindex
#317760482
#317760332
#317759912
#317759292
#317759282
#317759182
#137×C5472
#455547