Finite Group Databasebeta

← #49094213

Subgroups — #49094213

Order 35968.

148 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 65 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#31823593C212yesmaximal
2C4×Dic1124C211yesmaximal, characteristic
3#31823214C211yesmaximal, characteristic
4#31823195C212yesmaximal
5#322×C281C211yesmaximal, characteristic
6C2×Dic1124C411yescharacteristic
7C4×Dic562C2212yes—
8#22582813C411yescharacteristic
9C4⋊#14555886C2212yes—
10#22582808—22no—
11#22582804C412yes—
12#22582789—22no—
13C4×C8×C281C2211yescharacteristic
14C4×C8×C281C2211yescharacteristic
15C4×C8×C281C2211yescharacteristic
16C2×Dic562C2×C412yes—
17Dic1124—22no—
18C2×#14555886—22no—
19C4⋊Dic281C2×C412yes—
20#17985117—22no—
21C4×Dic281—22no—
22C2×C8×C281—21no—
23C2×C8×C281C2×C411yescharacteristic
24C2×C8×C281C2×C411yescharacteristic
25C2×C8×C281D412yes—
26C42×C281C2311yescharacteristic
27Dic562—22no—
28Dic562—22no—
29C2×Dic281—22no—
30C2×Dic281—22no—
31#14555886—42no—
32C2×C4×C281C22×C411yescharacteristic
33C2×C4×C281C2×D411yescharacteristic
34C2×C4×C281#4111yescharacteristic
35C8×C281—21no—
36C8×C281—22no—
37C8×C281—41no—
38C8×C281M1612yes—
39C22×C281C4×D411yescharacteristic
40C4×C281—21no—
41C4×C281C2×M1611yescharacteristic
42C4×C281#13111yescharacteristic
43C4×C281#13712yes—
44Dic281—42no—
45Dic281—42no—
46C2×C281#43611yescharacteristic
47C2×C281#44111yescharacteristic
48C2×C281#44411yescharacteristic
49C281#159311yescharacteristic, complemented, Sylow
50#1593—2811nomaximal, Sylow
51#446—2812no—
52C4×Q16—2811no—
53#334—2811no—
54Q8⋊C8—2812no—
55#322D28111yescharacteristic
56C2×Q16—2811no—
57C4×Q8—2812no—
58#107—2811no—
59C4⋊C8—2812no—
60C4⋊C8—5622no—
61#103—2812no—
62#97—5622no—
63C4×C8C2×D28111yescharacteristic
64C4×C8C2×D28111yescharacteristic
65C4×C8C2×D28111yescharacteristic
66C2×Q8—2812no—
67Q16—5622no—
68C2×C8—21no—
69C2×C8—5622no—
70C2×C8C4×D28111yescharacteristic
71C2×C8C4×D28111yescharacteristic
72C2×C8D112412yes—
73C4⋊C4—2812no—
74C4⋊C4—5622no—
75C42—5622no—
76C42C22×D28111yescharacteristic
77Q8—5622no—
78Q8—5622no—
79C2×C4—5622no—
80C2×C4—5622no—
81C2×C4C2×C4×D28111yescharacteristic
82C2×C4C2×D112411yescharacteristic
83C2×C4#1798513811yescharacteristic
84C8—21no—
85C8—22no—
86C8—41no—
87C8—11242no—
88C8#1798512112yes—
89C22C4×D112411yescharacteristic
90C4—21no—
91C4—11242no—
92C4—11242no—
93C4C2×#1798512111yescharacteristic
94C4#2258288511yescharacteristic
95C4#2258291212yes—
96C2#3182354211yescharacteristic
97C2#3182357111yescharacteristic
98C2#3182358611yescharacteristic
subgroupG/H
centerC2×C4C2×D1124
commutatorC2×C4×C281C22×C4
FrattiniC42C22×D281
Fitting#322×C281C2
socle, prime radicalC22×C281C4×D4
cosocleC42×C281C23
hypercenter#322D281
hypocenterC281#1593
LCSG ▷ C2×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #322

Complements

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

NH ≅ G/Ntype
49. C281#1593semidirect

Maximal subgroups

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

subgroupindex
#318235932
C4×Dic11242
#318232142
#318231952
#322×C2812
#1593281