Finite Group Databasebeta

← #49093200

Subgroups — #49093200

Order 35968.

148 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 77 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#31823516C211yesmaximal, characteristic
2#31823487C211yesmaximal, characteristic
3C2×C4⋊C8×C281C211yesmaximal, characteristic
4C2×#17985122—21no—
5C4⋊#14555886—21no—
6C4⋊#14555886—21no—
7C4⋊#14555886C412yes—
8C22⋊#14555886C412yes—
9C4×#14555886—21no—
10C22×C8×C281—21no—
11C2×C42×C281C2211yescharacteristic
12C4⋊C8×C281—21no—
13C4⋊C8×C281C412yes—
14#17985122—41no—
15#17985122—41no—
16C2×#14555886—22no—
17C2×#14555886—22no—
18C22×C4×C281C2×C411yescharacteristic
19C22×C4×C281D411yescharacteristic
20C22×C4×C281Q811yescharacteristic
21C2×C8×C281—22no—
22C2×C8×C281—41no—
23C2×C8×C281—41no—
24C42×C281C2×C411yescharacteristic
25C42×C281C2×C411yescharacteristic
26C42×C281D411yescharacteristic
27C42×C281D411yescharacteristic
28#14555886—42no—
29#14555886—42no—
30C23×C281C4⋊C411yescharacteristic
31C2×C4×C281—22no—
32C2×C4×C281—41no—
33C2×C4×C281C4211yescharacteristic
34C2×C4×C281C22⋊C411yescharacteristic
35C2×C4×C281C22⋊C411yescharacteristic
36C2×C4×C281C22⋊C411yescharacteristic
37C2×C4×C281C4⋊C411yescharacteristic
38C2×C4×C281C4⋊C411yescharacteristic
39C2×C4×C281D811yescharacteristic
40C2×C4×C281SD1611yescharacteristic
41C2×C4×C281SD1611yescharacteristic
42C2×C4×C281Q1611yescharacteristic
43C8×C281—42no—
44C22×C281—21no—
45C22×C281—21no—
46C22×C281#9511yescharacteristic
47C22×C281#10611yescharacteristic
48C22×C281#10711yescharacteristic
49C4×C281—21no—
50C4×C281—21no—
51C4×C281—21no—
52C4×C281#10211yescharacteristic
53C4×C281#10211yescharacteristic
54C4×C281#10311yescharacteristic
55C4×C281#10311yescharacteristic
56C4×C281#10812yes—
57C2×C281—21no—
58C2×C281—21no—
59C2×C281#34011yescharacteristic
60C2×C281#34111yescharacteristic
61C2×C281#34411yescharacteristic
62C281#130111yescharacteristic, complemented, Sylow
63#1301—2811nomaximal, Sylow
64#431—2811no—
65#423—2811no—
66C2×C4⋊C8D28111yescharacteristic
67C2×M16—5621no—
68C22×C8—21no—
69C2×C42C2×D28111yescharacteristic
70C4⋊C8—21no—
71C4⋊C8—2812no—
72C4⋊C8—5621no—
73C4⋊C8—5621no—
74C4⋊C8Dic28112yes—
75C22⋊C8—2812no—
76C4×C8—5621no—
77C22×C4C4×D28111yescharacteristic
78C22×C4C22⋊D28111yescharacteristic
79C22×C4Dic56211yescharacteristic
80M16—11241no—
81M16—11241no—
82C2×C8—22no—
83C2×C8—41no—
84C2×C8—41no—
85C2×C8—5622no—
86C2×C8—5622no—
87C42C4×D28111yescharacteristic
88C42C2×Dic28111yescharacteristic
89C42C22⋊D28111yescharacteristic
90C42D112411yescharacteristic
91C23#1798511711yescharacteristic
92C2×C4—22no—
93C2×C4—41no—
94C2×C4C4×Dic28111yescharacteristic
95C2×C4#1798511511yescharacteristic
96C2×C4#1798511511yescharacteristic
97C2×C4C22⋊Dic28111yescharacteristic
98C2×C4#1798511711yescharacteristic
99C2×C4C4⋊Dic28111yescharacteristic
100C2×C4#1798512311yescharacteristic
101C2×C4#1798512511yescharacteristic
102C2×C4#1798512611yescharacteristic
103C2×C4#1798512811yescharacteristic
104C8—42no—
105C8—11242no—
106C8—11242no—
107C22—21no—
108C22—21no—
109C22#2258278611yescharacteristic
110C22#2258281011yescharacteristic
111C22#2258281211yescharacteristic
112C4—21no—
113C4—21no—
114C4—21no—
115C4#2258279911yescharacteristic
116C4#2258280011yescharacteristic
117C4#2258280211yescharacteristic
118C4#2258280311yescharacteristic
119C4#2258281512yes—
120C2—21no—
121C2—21no—
122C2#3182322511yescharacteristic
123C2#3182322811yescharacteristic
124C2#3182323511yescharacteristic
subgroupG/H
centerC2×C4#17985115
commutatorC2×C4×C281C42
FrattiniC2×C42C2×D281
FittingC2×C4⋊C8×C281C2
socleC22×C281#95
prime radicalC23×C281C4⋊C4
cosocleC2×C42×C281C22
hypercenterC2×C4⋊C8D281
hypocenterC281#1301
LCSG ▷ C2×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
62. C281#1301semidirect

Maximal subgroups

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

subgroupindex
#318235162
#318234872
C2×C4⋊C8×C2812
#1301281