Finite Group Databasebeta

← #49093345

Subgroups — #49093345

Order 35968.

102 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 102 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#31823847C211yesmaximal, characteristic
2C4⋊#17985113C211yesmaximal, characteristic, complemented
3#334×C281C211yesmaximal, characteristic, complemented
4C2×Dic1124C411yescharacteristic
5C2×#17985127—21no—
6C2×D2248C411yescharacteristic
7#22582867—21no—
8C2×#17985113—21no—
9C4⋊C8×C281—21no—
10C4×C8×C281C2211yescharacteristic
11C2×Dic562—21no—
12C2×D1124—21no—
13Dic1124—41no—
14#17985127—41no—
15#17985127—41no—
16D2248—41no—
17#17985115—41no—
18#17985115—41no—
19#17985113—41no—
20C2×C8×C281—41no—
21C2×C8×C281C2×C411yescharacteristic
22C2×C8×C281D411yescharacteristic
23C42×C281D411yescharacteristic
24C22×D281—41no—
25Dic562—41no—
26Dic562—41no—
27D1124—41no—
28D1124—41no—
29C2×Dic281—41no—
30C2×C4×C281C22⋊C411yescharacteristic
31C2×C4×C281D811yescharacteristic
32C2×C4×C281SD1611yescharacteristic
33C8×C281—21no—
34C8×C281—81no—
35C8×C281D811yescharacteristic
36C8×C281SD1611yescharacteristic
37C22×C281#10211yescharacteristic
38C2×D281—81no—
39C2×D281—81no—
40C2×D281—81no—
41C4×C281—21no—
42C4×C281—21no—
43C4×C281#10011yescharacteristic
44C4×C281#10211yescharacteristic
45Dic281—81no—
46C2×C281#33111yescharacteristic
47C2×C281#35911yescharacteristic
48C2×C281#36011yescharacteristic
49D281—161no—
50C281#136011yescharacteristic, complemented, Sylow
51#1360—2811nomaximal, Sylow
52#495—2811no—
53C4⋊C16—2811no—
54#334D28111yescharacteristic, complemented
55C2×Q16—2811no—
56C2×SD16—5621no—
57C2×D8—2811no—
58#124—5621no—
59C2×C16—5621no—
60C4⋊C8—21no—
61C4×C8C2×D28111yescharacteristic
62C2×Q8—5621no—
63C2×D4—5621no—
64Q16—11241no—
65SD16—11241no—
66SD16—11241no—
67D8—11241no—
68C2×C8—41no—
69C2×C8C4×D28111yescharacteristic
70C2×C8D112411yescharacteristic
71C22⋊C4—11241no—
72C22⋊C4—11241no—
73C42C22⋊D28111yescharacteristic
74C16—11241no—
75C23—11241no—
76Q8—11241no—
77Q8—11241no—
78D4—11241no—
79D4—11241no—
80C2×C4—11241no—
81C2×C4#1798511511yescharacteristic
82C2×C4#1798512311yescharacteristic
83C2×C4#1798512511yescharacteristic
84C8—21no—
85C8—81no—
86C8D224811yescharacteristic
87C8#1798512711yescharacteristic
88C22—22481no—
89C22—22481no—
90C22—22481no—
91C22#2258279911yescharacteristic
92C4—21no—
93C4—21no—
94C4—22481no—
95C4#2258279511yescharacteristic
96C4#2258280111yescharacteristic
97C2—44961no—
98C2#3182320611yescharacteristic
99C2#3182326911yescharacteristic
100C2#3182327211yescharacteristic
subgroupG/H
centerC22#22582799
commutatorC2×C8×C281C2×C4
FrattiniC4×C8C2×D281
Fitting#334×C281C2
socleC22×C281#102
prime radicalC2×D2248C4
cosocleC4×C8×C281C22
hypercenter#334D281
hypocenterC281#1360
LCSG ▷ C2×C8×C281 ▷ C2×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #334

Complements

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

NH ≅ G/Ntype
2. C4⋊#17985113C2semidirect
3. #334×C281C2semidirect
50. C281#1360semidirect
54. #334D281semidirect

Maximal subgroups

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

subgroupindex
#318238472
C4⋊#179851132
#334×C2812
#1360281