Finite Group Databasebeta

← #30682199

Subgroups — #30682199

Order 16832.

104 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 37 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#22554500C211yesmaximal, characteristic, complemented
2C2×#16862364C211yesmaximal, characteristic, complemented
3#22554477C211yesmaximal, characteristic, complemented
4#22554405C211yesmaximal, characteristic, complemented
5#22554388C211yesmaximal, characteristic, complemented
6#22554387C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C263C211yesmaximal, characteristic
8C2×Dic526C2211yescharacteristic
9#16862366—21no—
10#16862364—21no—
11#16862364—21no—
12#16862364—21no—
13#16862360—21no—
14#16862360C2211yescharacteristic
15#16862360C2211yescharacteristic
16C2×C263⋊C8—21no—
17C2×C263⋊C8C2211yescharacteristic
18#41×C263C2211yescharacteristic
19C2×D4×C263C2211yescharacteristic
20SD16×C263—21no—
21D8×C263—21no—
22M16×C263C2211yescharacteristic
23Dic526—21no—
24Dic526—21no—
25C2×Dic263—21no—
26C263⋊C8—21no—
27C263⋊C8—21no—
28C263⋊C8D411yescharacteristic
29C263⋊C8D411yescharacteristic
30C23×C263—21no—
31Q8×C263D411yescharacteristic
32D4×C263—21no—
33D4×C263—21no—
34D4×C263—21no—
35D4×C263D411yescharacteristic
36C2×C4×C263—21no—
37C2×C4×C263C2311yescharacteristic
38C8×C263—21no—
39C22×C263—21no—
40C22×C263—41no—
41C22×C263—81no—
42C22×C263#4111yescharacteristic
43C4×C263—21no—
44C4×C263C2×D411yescharacteristic
45C4×C263C2×D411yescharacteristic
46Dic263—41no—
47C2×C263—21no—
48C2×C263—41no—
49C2×C263—81no—
50C2×C263#12111yescharacteristic
51C263#47111yescharacteristic, complemented, Sylow
52#471—2631nomaximal, Sylow
53#137—2631no—
54AGL(1,ℤ/8)D26311yescharacteristic
55C2×SD16—2631no—
56#131—2631no—
57#108—2631no—
58#101—2631no—
59#100—2631no—
60#41C2×D26311yescharacteristic
61C2×Q8—2631no—
62C2×D4C2×D26311yescharacteristic
63Q16—5261no—
64SD16—21no—
65SD16—5261no—
66SD16—5261no—
67SD16—5261no—
68D8—21no—
69M16—2631no—
70M16—2631no—
71M16—5261no—
72M16C2×D26311yescharacteristic
73C2×C8—2631no—
74C2×C8—5261no—
75C23—21no—
76Q8—5261no—
77Q8—5261no—
78Q8C22⋊D26311yescharacteristic
79D4—21no—
80D4—21no—
81D4—21no—
82D4C22⋊D26311yescharacteristic
83C2×C4—21no—
84C2×C4—5261no—
85C2×C4C22×D26311yescharacteristic
86C8—21no—
87C8—2631no—
88C8—2631no—
89C8—5261no—
90C8—5261no—
91C22—21no—
92C22—41no—
93C22—81no—
94C22#1686237511yescharacteristic
95C4—21no—
96C4—10521no—
97C4D4×D26311yescharacteristic
98C4C2×C22⋊D26311yescharacteristic
99C2—21no—
100C2—41no—
101C2—81no—
102C2#2255444211yescharacteristic
subgroupG/H
centerC2#22554442
commutator, cosocleC2×C4×C263C23
FrattiniC2×C4C22×D263
Fitting, prime radicalAGL(1,ℤ/8)×C263C2
socleC2×C263#121
hypercenterAGL(1,ℤ/8)D263
hypocenterC263#471
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #22554500C2semidirect
2. C2×#16862364C2semidirect
3. #22554477C2semidirect
4. #22554405C2semidirect
5. #22554388C2semidirect
6. #22554387C2semidirect
51. C263#471semidirect

Maximal subgroups

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

subgroupindex
#225545002
C2×#168623642
#225544772
#225544052
#225543882
#225543872
AGL(1,ℤ/8)×C2632
#471263