Finite Group Databasebeta

← #46826008

Subgroups — #46826008

Order 34432.

112 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 20 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#31771511C211yesmaximal, characteristic, complemented
2#31771461C211yesmaximal, characteristic, complemented
3#31770778C211yesmaximal, characteristic
4#22575512—21no—
5#22575508—21no—
6#22575478—21no—
7#22575442C2211yescharacteristic
8#22575380—21no—
9#22575372C411yescharacteristic, complemented
102−1+4×C269C411yescharacteristic, complemented
11C2×#14524137—41no—
12C22⋊#11761640—41no—
13C2×D1076D411yescharacteristic
14#16864389—41no—
15#16864387—41no—
16#16864386—21no—
17#16864379—41no—
18C4×Dic269D411yescharacteristic
19#41×C269—21no—
20#41×C269—41no—
21#41×C269—41no—
22C2×Q8×C269—41no—
23C2×Q8×C269C2×C411yescharacteristic
24C2×#11761640—81no—
25#14524137—42no—
26C22×D269—21no—
27D1076—41no—
28C2×Dic269—21no—
29#14524130—41no—
30Q8×C269—21no—
31Q8×C269—41no—
32Q8×C269—41no—
33D4×C269—21no—
34D4×C269—41no—
35D4×C269—41no—
36C2×C4×C269—21no—
37C2×C4×C269—41no—
38C2×C4×C269—42no—
39C2×C4×C269C22⋊C411yescharacteristic
40C22×C269—41no—
41C22×C269#9911yescharacteristic
42C2×D269—41no—
43C2×D269—81no—
44#11761640—161no—
45C4×C269—21no—
46C4×C269—41no—
47C4×C269—41no—
48Dic269—41no—
49C2×C269—21no—
50C2×C269—81no—
51C2×C269AΣL(1,𝔽16)11yescharacteristic
52D269—81no—
53C269#140411yescharacteristic, complemented, Sylow
54#1404—2691nomaximal, Sylow
55#454—2691no—
56#354—2691no—
57#329—2691no—
582−1+4#1176164011yescharacteristic, complemented
59AGL(1,ℤ/8)—5381no—
60#124—2691no—
61#104—5381no—
62#101—2691no—
63#99—5381no—
64#97—5381no—
65#41—21no—
66#41—41no—
67#41—41no—
68C2×Q8—41no—
69C2×Q8C2×#1176164011yescharacteristic
70C2×D4—2691no—
71SD16—10761no—
72D8—10761no—
73M16—5381no—
74C2×C8—10761no—
75C22⋊C4—10761no—
76C22⋊C4—10761no—
77C42—2691no—
78C23—5381no—
79Q8—21no—
80Q8—41no—
81Q8—41no—
82D4—21no—
83D4—41no—
84D4—41no—
85D4—10761no—
86C2×C4—21no—
87C2×C4—41no—
88C2×C4—42no—
89C2×C4—5381no—
90C2×C4—21521no—
91C2×C4C22⋊#1176164011yescharacteristic
92C8—10761no—
93C8—10762no—
94C22—41no—
95C22—10761no—
96C22—21521no—
97C22#2257551111yescharacteristic
98C4—21no—
99C4—41no—
100C4—41no—
101C4—10761no—
102C4—43041no—
103C2—21no—
104C2—81no—
105C2—21521no—
106C2#3177150511yescharacteristic
subgroupG/H
centerC2#31771505
commutatorC2×Q8×C269C2×C4
FrattiniC2×Q8C2×#11761640
Fitting2−1+4×C269C4
socleC2×C269AΣL(1,𝔽16)
prime radical#31770778C2
cosocle#22575442C22
hypercenter2−1+4#11761640
hypocenterC269#1404
LCSG ▷ C2×Q8×C269 ▷ C2×C4×C269 ▷ C22×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×Q8 ◁ 2−1+4

Complements

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

NH ≅ G/Ntype
1. #31771511C2semidirect
2. #31771461C2semidirect
9. #22575372C4semidirect
10. 2−1+4×C269C4semidirect
53. C269#1404semidirect
58. 2−1+4#11761640semidirect

Maximal subgroups

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

subgroupindex
#317715112
#317714612
#317707782
#1404269