Finite Group Databasebeta

← #36377958

Subgroups — #36377958

Order 22592.

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#26015039C211yesmaximal, characteristic, complemented
2#26015018C211yesmaximal, characteristic, complemented
3#26014979C211yesmaximal, characteristic, complemented
4#26014919C211yesmaximal, characteristic, complemented
5#26014918C211yesmaximal, characteristic, complemented
6#26014910C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C353C211yesmaximal, characteristic, complemented
8#19150737—21no—
9#19150737C2211yescharacteristic
10#19150736—22no—
11#19150736—21no—
12C2×Dic706—21no—
13C2×Dic706C2211yescharacteristic
14Q8×D353—21no—
15#19150725—21no—
16#19150722—21no—
17#19150721C2211yescharacteristic
18C22⋊Dic353—22no—
19C4×Dic353C2211yescharacteristic
20#41×C353C2211yescharacteristic
21C2×D4×C353C2211yescharacteristic
22SD16×C353—21no—
23D8×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—
38C23×C353—21no—
39Q8×C353D411yescharacteristic
40D4×C353—21no—
41D4×C353—21no—
42D4×C353—21no—
43D4×C353D411yescharacteristic
44C2×C4×C353—21no—
45C2×C4×C353C2311yescharacteristic
46C8×C353—21no—
47C22×C353—21no—
48C22×C353—42no—
49C22×C353—41no—
50C22×C353C2×D411yescharacteristic
51C2×D353—21no—
52C4×C353—21no—
53C4×C353C2×D411yescharacteristic
54C4×C353C2×D411yescharacteristic
55Dic353—21no—
56Dic353—22no—
57Dic353—41no—
58C2×C353—21no—
59C2×C353—41no—
60C2×C353—81no—
61C2×C353#12011yescharacteristic
62D353—41no—
63C353#45411yescharacteristic, complemented, Sylow
64#454—3531nomaximal, Sylow
652−1+4—3531no—
66AGL(1,ℤ/8)—3531no—
67AGL(1,ℤ/8)D35311yescharacteristic, complemented
68#124—3531no—
69#104—3531no—
70#104—3531no—
71#101—3531no—
72#41—3531no—
73#41—7061no—
74#41—7062no—
75#41—7061no—
76#41C2×D35311yescharacteristic
77C2×Q8—3531no—
78C2×Q8—7061no—
79C2×Q8—7061no—
80C2×D4C2×D35311yescharacteristic
81SD16—21no—
82SD16—7061no—
83D8—21no—
84D8—7061no—
85M16—3531no—
86M16C2×D35311yescharacteristic
87C22⋊C4—7062no—
88C42—3531no—
89C23—21no—
90Q8—3531no—
91Q8—7062no—
92Q8—7061no—
93Q8—7061no—
94Q8C22⋊D35311yescharacteristic
95D4—21no—
96D4—21no—
97D4—21no—
98D4—3531no—
99D4—7062no—
100D4—7061no—
101D4C22⋊D35311yescharacteristic
102C2×C4—21no—
103C2×C4—3532no—
104C2×C4—7062no—
105C2×C4—7061no—
106C2×C4—7062no—
107C2×C4—7061no—
108C2×C4C22×D35311yescharacteristic
109C8—21no—
110C8—7061no—
111C22—21no—
112C22—42no—
113C22—41no—
114C22—7061no—
115C22D4×D35311yescharacteristic
116C4—21no—
117C4—14121no—
118C4—7062no—
119C4—7061no—
120C4D4×D35311yescharacteristic
121C4C2×C22⋊D35311yescharacteristic
122C2—21no—
123C2—41no—
124C2—81no—
125C2—14121no—
126C2#2601496011yescharacteristic
subgroupG/H
centerC2#26014960
commutator, cosocleC2×C4×C353C23
FrattiniC2×C4C22×D353
FittingAGL(1,ℤ/8)×C353C2
socleC2×C353#120
hypercenterAGL(1,ℤ/8)D353
hypocenterC353#454
LCSG ▷ C2×C4×C353 ▷ C2×C353 ▷ C353
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #26015039C2semidirect
2. #26015018C2semidirect
3. #26014979C2semidirect
4. #26014919C2semidirect
5. #26014918C2semidirect
6. #26014910C2semidirect
7. AGL(1,ℤ/8)×C353C2semidirect
63. C353#454semidirect
67. AGL(1,ℤ/8)D353semidirect

Maximal subgroups

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

subgroupindex
#260150392
#260150182
#260149792
#260149192
#260149182
#260149102
AGL(1,ℤ/8)×C3532
#454353