Finite Group Databasebeta

← #49093458

Subgroups — #49093458

Order 35968.

106 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 106 conjugacy classes of subgroups — too many to draw. Only its 23 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#31823645C211yesmaximal, characteristic
2#31823262C211yesmaximal, characteristic, complemented
3#333×C281C211yesmaximal, characteristic, complemented
4#22582927C411yescharacteristic
5#22582910—21no—
6#22582807—21no—
7#22582798—21no—
8#22582798C411yescharacteristic
9C4⋊Q8×C281C2211yescharacteristic
10C4⋊C8×C281—21no—
11#17985139—41no—
12#17985138—21no—
13#17985138—41no—
14Q8×D281—41no—
15#17985128—41no—
16#17985125—41no—
17#17985122—21no—
18#17985122—41no—
19C2×Q8×C281C2×C411yescharacteristic
20C2×Q8×C281D411yescharacteristic
21C2×C8×C281—41no—
22C4⋊C4×C281—41no—
23C42×C281D411yescharacteristic
24Dic562—21no—
25Dic562—41no—
26D1124—21no—
27D1124—41no—
28C22⋊D281—41no—
29C4×D281—41no—
30C4×D281—42no—
31#14555886—41no—
32#14555886—81no—
33Q8×C281—41no—
34Q8×C281—41no—
35C2×C4×C281—21no—
36C2×C4×C281—21no—
37C2×C4×C281—21no—
38C2×C4×C281C22⋊C411yescharacteristic
39C8×C281—81no—
40C22×C281#9911yescharacteristic
41C2×D281—41no—
42C4×C281—21no—
43C4×C281—21no—
44C4×C281—21no—
45C4×C281—41no—
46C4×C281—41no—
47Dic281—41no—
48C2×C281—21no—
49C2×C281AΣL(1,𝔽16)11yescharacteristic
50D281—81no—
51C281#140511yescharacteristic, complemented, Sylow
52#1405—2811nomaximal, Sylow
53#456—2811no—
54#356—2811no—
55#333D28111yescharacteristic, complemented
562−1+4—2811no—
57#137—5621no—
58C4⋊Q8C2×D28111yescharacteristic
59C4⋊C8—21no—
60#104—5621no—
61#101—2811no—
62#101—5621no—
63#41—5621no—
64#41—11241no—
65#41—11241no—
66C2×Q8—11241no—
67C2×Q8C4×D28111yescharacteristic
68C2×Q8D112411yescharacteristic
69Q16—11241no—
70SD16—11241no—
71M16—5621no—
72M16—11241no—
73C2×C8—41no—
74C4⋊C4—41no—
75C42C22⋊D28111yescharacteristic
76Q8—41no—
77Q8—41no—
78Q8—5621no—
79Q8—11241no—
80D4—5621no—
81D4—11241no—
82D4—11241no—
83C2×C4—21no—
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—11241no—
87C2×C4—11242no—
88C2×C4#1798511511yescharacteristic
89C8—81no—
90C8—11241no—
91C8—22481no—
92C22—11241no—
93C22#2258279311yescharacteristic
94C4—21no—
95C4—21no—
96C4—21no—
97C4—41no—
98C4—41no—
99C4—11241no—
100C2—21no—
101C2—22481no—
102C2#3182325111yescharacteristic
subgroupG/H
centerC2#31823251
commutatorC2×Q8×C281C2×C4
FrattiniC4⋊Q8C2×D281
Fitting#333×C281C2
socleC2×C281AΣL(1,𝔽16)
prime radical#22582927C4
cosocleC4⋊Q8×C281C22
hypercenter#333D281
hypocenterC281#1405
LCSG ▷ C2×Q8×C281 ▷ C2×C4×C281 ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #31823262C2semidirect
3. #333×C281C2semidirect
51. C281#1405semidirect
55. #333D281semidirect

Maximal subgroups

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

subgroupindex
#318236452
#318232622
#333×C2812
#1405281