Finite Group Databasebeta

← #46855175

Subgroups — #46855175

Order 35008.

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

normal subgroups only

This group has 146 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#31776049C211yesmaximal, characteristic, complemented
2#31776030C211yesmaximal, characteristic, complemented
3#31776027C211yesmaximal, characteristic, complemented
4#31775990C211yesmaximal, characteristic, complemented
5#31775930C211yesmaximal, characteristic, complemented
6#31775920C211yesmaximal, characteristic, complemented
7#104×C547C211yesmaximal, characteristic, complemented
8#22576776—21no—
9#22576776C2211yescharacteristic
10#22576775—22no—
11#22576775—21no—
12C2×Dic1094—21no—
13C2×Dic1094C2211yescharacteristic
14Q8×D547—21no—
15C2×D2188C2211yescharacteristic
16#22576765—21no—
17#22576763—21no—
18D4376—21no—
19#22576761—21no—
20#22576760C2211yescharacteristic
21(C2×D547)⋊C4—22no—
22#41×C547C2211yescharacteristic
23M16×C547C2211yescharacteristic
24C42×C547C2211yescharacteristic
25C22×D547—21no—
26Dic1094—22no—
27Dic1094—21no—
28Dic1094—21no—
29Dic1094D411yescharacteristic
30D2188—21no—
31D2188—21no—
32D2188D411yescharacteristic
33C22⋊D547—22no—
34C22⋊D547—21no—
35C2×Dic547—22no—
36C2×Dic547D412yes—
37C4×D547—22no—
38C4×D547—21no—
39C547⋊C8—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—21no—
50C2×D547—42no—
51C2×D547—41no—
52C4×C547—21no—
53C4×C547—41no—
54C4×C547C2×D411yescharacteristic
55C4×C547C2×D411yescharacteristic
56Dic547—21no—
57Dic547—22no—
58C2×C547—21no—
59C2×C547—41no—
60C2×C547#12011yescharacteristic
61D547—41no—
62D547—81no—
63C547#45411yescharacteristic, complemented, Sylow
64#454—5471nomaximal, Sylow
652−1+4—5471no—
66AGL(1,ℤ/8)—5471no—
67AGL(1,ℤ/8)—5471no—
68#124—5471no—
69#104—5471no—
70#104D54711yescharacteristic, complemented
71#101—5471no—
72#41—5471no—
73#41—10941no—
74#41—10942no—
75#41—10941no—
76#41C2×D54711yescharacteristic
77C2×Q8—5471no—
78C2×Q8—10941no—
79C2×Q8—10941no—
80C2×D4—5471no—
81SD16—10941no—
82SD16—10941no—
83D8—10941no—
84D8—10941no—
85M16—5471no—
86M16C2×D54711yescharacteristic
87C22⋊C4—10942no—
88C42C2×D54711yescharacteristic
89C23—10941no—
90Q8—5471no—
91Q8—10942no—
92Q8—10941no—
93Q8—10941no—
94Q8D218811yescharacteristic
95D4—21no—
96D4—5471no—
97D4—10942no—
98D4—10941no—
99D4—10941no—
100D4—10941no—
101D4D218811yescharacteristic
102C2×C4—21no—
103C2×C4—21no—
104C2×C4—5472no—
105C2×C4—10942no—
106C2×C4—10942no—
107C2×C4—10941no—
108C2×C4C22×D54711yescharacteristic
109C8—21no—
110C8—10941no—
111C22—21no—
112C22—10941no—
113C22—21882no—
114C22—21881no—
115C22D4×D54711yescharacteristic
116C4—21no—
117C4—41no—
118C4—10942no—
119C4—10941no—
120C4D4×D54711yescharacteristic
121C4C2×D218811yescharacteristic
122C2—21no—
123C2—41no—
124C2—43761no—
125C2—21881no—
126C2#3177597211yescharacteristic
subgroupG/H
centerC2#31775972
commutator, cosocleC2×C4×C547C23
FrattiniC2×C4C22×D547
Fitting#104×C547C2
socleC2×C547#120
hypercenter#104D547
hypocenterC547#454
LCSG ▷ C2×C4×C547 ▷ C2×C547 ▷ C547
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
1. #31776049C2semidirect
2. #31776030C2semidirect
3. #31776027C2semidirect
4. #31775990C2semidirect
5. #31775930C2semidirect
6. #31775920C2semidirect
7. #104×C547C2semidirect
63. C547#454semidirect
70. #104D547semidirect

Maximal subgroups

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

subgroupindex
#317760492
#317760302
#317760272
#317759902
#317759302
#317759202
#104×C5472
#454547