Finite Group Databasebeta

← #49177261

Subgroups — #49177261

Order 37568.

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

normal subgroups only

This group has 142 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#34037668C211yesmaximal, characteristic
2#34037652C211yesmaximal, characteristic, complemented
3#34037619C211yesmaximal, characteristic, complemented
4#34037548C211yesmaximal, characteristic, complemented
5#34037547C211yesmaximal, characteristic, complemented
6#34037539C211yesmaximal, characteristic, complemented
7#137×C587C211yesmaximal, characteristic, complemented
8#22627829—21no—
9#22627829C2211yescharacteristic
10#22627828—22no—
11#22627828—21no—
12C2×Dic1174—21no—
13C2×Dic1174C2211yescharacteristic
14Q8×D587—21no—
15#22627819—21no—
16#22627816—21no—
17#22627813C2211yescharacteristic
18Dic587⋊C4—22no—
19C4×Dic587C2211yescharacteristic
20#41×C587C2211yescharacteristic
21C2×Q8×C587C2211yescharacteristic
22Q16×C587—21no—
23SD16×C587—21no—
24M16×C587C2211yescharacteristic
25Dic1174—22no—
26Dic1174—21no—
27Dic1174—21no—
28Dic1174D411yescharacteristic
29D2348D411yescharacteristic
30C22⋊D587—22no—
31C22⋊D587—21no—
32C2×Dic587—22no—
33C2×Dic587—21no—
34C2×Dic587D412yes—
35C4×D587—22no—
36C4×D587—21no—
37C587⋊C8—21no—
38Q8×C587—21no—
39Q8×C587—21no—
40Q8×C587D411yescharacteristic
41D4×C587—21no—
42D4×C587D411yescharacteristic
43C2×C4×C587—21no—
44C2×C4×C587—21no—
45C2×C4×C587C2311yescharacteristic
46C8×C587—21no—
47C22×C587—21no—
48C22×C587C2×D411yescharacteristic
49C2×D587—21no—
50C4×C587—21no—
51C4×C587—41no—
52C4×C587C2×D411yescharacteristic
53C4×C587C2×D411yescharacteristic
54Dic587—22no—
55Dic587—21no—
56Dic587—22no—
57C2×C587—21no—
58C2×C587—41no—
59C2×C587#12011yescharacteristic
60D587—41no—
61C587#45611yescharacteristic, complemented, Sylow
62#456—5871nomaximal, Sylow
632−1+4—5871no—
64#137—5871no—
65#137D58711yescharacteristic, complemented
66C4⋊Q8—5871no—
67#104—5871no—
68#104—5871no—
69#101—5871no—
70#41—5871no—
71#41—11741no—
72#41—11742no—
73#41—11741no—
74#41C2×D58711yescharacteristic
75C2×Q8—5871no—
76C2×Q8—11741no—
77C2×Q8—11741no—
78C2×Q8C2×D58711yescharacteristic
79Q16—21no—
80Q16—11741no—
81SD16—21no—
82SD16—11741no—
83M16—5871no—
84M16C2×D58711yescharacteristic
85C4⋊C4—11742no—
86C42—5871no—
87Q8—21no—
88Q8—21no—
89Q8—5871no—
90Q8—11742no—
91Q8—11741no—
92Q8—11741no—
93Q8C22⋊D58711yescharacteristic
94D4—21no—
95D4—5871no—
96D4—11742no—
97D4—11741no—
98D4C22⋊D58711yescharacteristic
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—5872no—
102C2×C4—11742no—
103C2×C4—11742no—
104C2×C4—11741no—
105C2×C4—11741no—
106C2×C4C22×D58711yescharacteristic
107C8—21no—
108C8—11741no—
109C22—21no—
110C22—11741no—
111C22D4×D58711yescharacteristic
112C4—21no—
113C4—41no—
114C4—11742no—
115C4—11742no—
116C4—11741no—
117C4D4×D58711yescharacteristic
118C4C2×C22⋊D58711yescharacteristic
119C2—21no—
120C2—41no—
121C2—23481no—
122C2#3403758911yescharacteristic
subgroupG/H
centerC2#34037589
commutator, cosocleC2×C4×C587C23
FrattiniC2×C4C22×D587
Fitting#137×C587C2
socleC2×C587#120
prime radical#34037668C2
hypercenter#137D587
hypocenterC587#456
LCSG ▷ C2×C4×C587 ▷ C2×C587 ▷ C587
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
2. #34037652C2semidirect
3. #34037619C2semidirect
4. #34037548C2semidirect
5. #34037547C2semidirect
6. #34037539C2semidirect
7. #137×C587C2semidirect
61. C587#456semidirect
65. #137D587semidirect

Maximal subgroups

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

subgroupindex
#340376682
#340376522
#340376192
#340375482
#340375472
#340375392
#137×C5872
#456587