Finite Group Databasebeta

← #49093452

Subgroups — #49093452

Order 35968.

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

normal subgroups only

This group has 112 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#31823640C211yesmaximal, characteristic
2#31823260C211yesmaximal, characteristic, complemented
3#329×C281C211yesmaximal, characteristic, complemented
4#22582924C411yescharacteristic
5#22582910—21no—
6#22582807—21no—
7#22582798—21no—
8#22582796C411yescharacteristic
9#124×C281C2211yescharacteristic
10#97×C281—21no—
11#17985138—21no—
12#17985137—41no—
13C2×C22⋊D281—41no—
14D4×D281—41no—
15#17985128—41no—
16#17985125—41no—
17#17985122—21no—
18#17985122—41no—
19C2×Q8×C281D411yescharacteristic
20C2×D4×C281C2×C411yescharacteristic
21C2×C8×C281—41no—
22C22⋊C4×C281—41no—
23C42×C281D411yescharacteristic
24C22×D281—41no—
25Dic562—21no—
26D1124—21no—
27C22⋊D281—42no—
28C22⋊D281—41no—
29C2×Dic281—41no—
30C4×D281—41no—
31#14555886—41no—
32#14555886—81no—
33C23×C281—21no—
34Q8×C281—41no—
35D4×C281—41no—
36C2×C4×C281—21no—
37C2×C4×C281—21no—
38C2×C4×C281C22⋊C411yescharacteristic
39C8×C281—42no—
40C22×C281—41no—
41C22×C281—81no—
42C22×C281#9911yescharacteristic
43C2×D281—41no—
44C2×D281—161no—
45C4×C281—21no—
46C4×C281—41no—
47C4×C281—41no—
48Dic281—41no—
49C2×C281—21no—
50C2×C281—81no—
51C2×C281AΣL(1,𝔽16)11yescharacteristic
52D281—81no—
53C281#140311yescharacteristic, complemented, Sylow
54#1403—2811nomaximal, Sylow
55#455—2811no—
56#355—2811no—
57#329D28111yescharacteristic, complemented
58H(5,𝔽2)—2811no—
59#137—5621no—
60#124C2×D28111yescharacteristic
61#104—5621no—
62#101—5621no—
63#100—2811no—
64#97—21no—
65#41—5621no—
66#41—11241no—
67C2×Q8D112411yescharacteristic
68C2×D4—11241no—
69C2×D4—11241no—
70C2×D4C4×D28111yescharacteristic
71Q16—11241no—
72SD16—11241no—
73M16—5621no—
74M16—11241no—
75C2×C8—41no—
76C22⋊C4—41no—
77C42C22⋊D28111yescharacteristic
78C23—21no—
79C23—11241no—
80Q8—41no—
81Q8—5621no—
82D4—41no—
83D4—5621no—
84D4—11242no—
85D4—11241no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—11241no—
89C2×C4—11241no—
90C2×C4#1798511511yescharacteristic
91C8—42no—
92C8—11241no—
93C8—22481no—
94C22—41no—
95C22—81no—
96C22—11241no—
97C22—44961no—
98C22#2258279311yescharacteristic
99C4—21no—
100C4—41no—
101C4—41no—
102C4—11241no—
103C2—21no—
104C2—81no—
105C2—22481no—
106C2#3182325111yescharacteristic
subgroupG/H
centerC2#31823251
commutatorC2×D4×C281C2×C4
Frattini#124C2×D281
Fitting#329×C281C2
socleC2×C281AΣL(1,𝔽16)
prime radical#22582924C4
cosocle#124×C281C22
hypercenter#329D281
hypocenterC281#1403
LCSG ▷ C2×D4×C281 ▷ C2×C4×C281 ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #31823260C2semidirect
3. #329×C281C2semidirect
53. C281#1403semidirect
57. #329D281semidirect

Maximal subgroups

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

subgroupindex
#318236402
#318232602
#329×C2812
#1403281