Finite Group Databasebeta

← #36377968

Subgroups — #36377968

Order 22592.

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#26015039C211yesmaximal, characteristic
2#26015023C211yesmaximal, characteristic, complemented
3#26014990C211yesmaximal, characteristic, complemented
4#26014919C211yesmaximal, characteristic, complemented
5#26014918C211yesmaximal, characteristic, complemented
6#26014910C211yesmaximal, characteristic, complemented
7#137×C353C211yesmaximal, characteristic, complemented
8#19150737—21no—
9#19150737C2211yescharacteristic
10#19150736—22no—
11#19150736—21no—
12C2×Dic706—21no—
13C2×Dic706C2211yescharacteristic
14Q8×D353—21no—
15#19150727—21no—
16#19150724—21no—
17#19150721C2211yescharacteristic
18#19150716—22no—
19C4×Dic353C2211yescharacteristic
20#41×C353C2211yescharacteristic
21C2×Q8×C353C2211yescharacteristic
22Q16×C353—21no—
23SD16×C353—21no—
24M16×C353C2211yescharacteristic
25Dic706—22no—
26Dic706—21no—
27Dic706—21no—
28Dic706D411yescharacteristic
29D1412D411yescharacteristic
30C22⋊D353—22no—
31C22⋊D353—21no—
32C2×Dic353—22no—
33C2×Dic353—21no—
34C2×Dic353D412yes—
35C4×D353—22no—
36C4×D353—21no—
37#15667725—21no—
38Q8×C353—21no—
39Q8×C353—21no—
40Q8×C353D411yescharacteristic
41D4×C353—21no—
42D4×C353D411yescharacteristic
43C2×C4×C353—21no—
44C2×C4×C353—21no—
45C2×C4×C353C2311yescharacteristic
46C8×C353—21no—
47C22×C353—21no—
48C22×C353C2×D411yescharacteristic
49C2×D353—21no—
50C4×C353—21no—
51C4×C353—41no—
52C4×C353C2×D411yescharacteristic
53C4×C353C2×D411yescharacteristic
54Dic353—22no—
55Dic353—21no—
56Dic353—22no—
57C2×C353—21no—
58C2×C353—41no—
59C2×C353#12011yescharacteristic
60D353—41no—
61C353#45611yescharacteristic, complemented, Sylow
62#456—3531nomaximal, Sylow
632−1+4—3531no—
64#137—3531no—
65#137D35311yescharacteristic, complemented
66C4⋊Q8—3531no—
67#104—3531no—
68#104—3531no—
69#101—3531no—
70#41—3531no—
71#41—7061no—
72#41—7062no—
73#41—7061no—
74#41C2×D35311yescharacteristic
75C2×Q8—3531no—
76C2×Q8—7061no—
77C2×Q8—7061no—
78C2×Q8C2×D35311yescharacteristic
79Q16—21no—
80Q16—7061no—
81SD16—21no—
82SD16—7061no—
83M16—3531no—
84M16C2×D35311yescharacteristic
85C4⋊C4—7062no—
86C42—3531no—
87Q8—21no—
88Q8—21no—
89Q8—3531no—
90Q8—7062no—
91Q8—7061no—
92Q8—7061no—
93Q8C22⋊D35311yescharacteristic
94D4—21no—
95D4—3531no—
96D4—7062no—
97D4—7061no—
98D4C22⋊D35311yescharacteristic
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—3532no—
102C2×C4—7062no—
103C2×C4—7062no—
104C2×C4—7061no—
105C2×C4—7061no—
106C2×C4C22×D35311yescharacteristic
107C8—21no—
108C8—7061no—
109C22—21no—
110C22—7061no—
111C22D4×D35311yescharacteristic
112C4—21no—
113C4—41no—
114C4—7062no—
115C4—7062no—
116C4—7061no—
117C4D4×D35311yescharacteristic
118C4C2×C22⋊D35311yescharacteristic
119C2—21no—
120C2—41no—
121C2—14121no—
122C2#2601496011yescharacteristic
subgroupG/H
centerC2#26014960
commutator, cosocleC2×C4×C353C23
FrattiniC2×C4C22×D353
Fitting#137×C353C2
socleC2×C353#120
prime radical#26015039C2
hypercenter#137D353
hypocenterC353#456
LCSG ▷ C2×C4×C353 ▷ C2×C353 ▷ C353
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
2. #26015023C2semidirect
3. #26014990C2semidirect
4. #26014919C2semidirect
5. #26014918C2semidirect
6. #26014910C2semidirect
7. #137×C353C2semidirect
61. C353#456semidirect
65. #137D353semidirect

Maximal subgroups

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

subgroupindex
#260150392
#260150232
#260149902
#260149192
#260149182
#260149102
#137×C3532
#456353