Finite Group Databasebeta

← #44509518

Subgroups — #44509518

Order 30848.

170 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 47 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#29508153C212yesmaximal, complemented
2#29507835C211yesmaximal, characteristic, complemented
3#29507538C211yesmaximal, characteristic, complemented
4#29507530C212yesmaximal, complemented
5#493×C241C211yesmaximal, characteristic, complemented
6#21440664C2211yescharacteristic
7#21440648—21no—
8#21440586—22no—
9#21440583—22no—
10#21440582C2212yes—
11#21440578C2211yescharacteristic
12#21440570—21no—
13C2×D8×C241—21no—
14C2×D8×C241C2212yes—
15#127×C241—21no—
16C4×C8×C241C2211yescharacteristic
17#16838770—21no—
18Dic964D411yescharacteristic, complemented
19#16838759—21no—
20D1928D411yescharacteristic, complemented
21#16838754—21no—
22#16838753—41no—
23C8×D241—41no—
24#16838745—22no—
25C2×D4×C241—22no—
26C2×D4×C241—42no—
27D8×C241—22no—
28D8×C241—22no—
29D8×C241—41no—
30D8×C241—41no—
31C2×C8×C241D411yescharacteristic
32C2×C8×C241C2311yescharacteristic
33C42×C241D411yescharacteristic
34Dic482—21no—
35D964—21no—
36C22⋊D241—41no—
37C4×D241—41no—
38#14515349—41no—
39C23×C241—42no—
40D4×C241—42no—
41D4×C241—42no—
42D4×C241—84no—
43C2×C4×C241—21no—
44C2×C4×C241C2×D411yescharacteristic
45C8×C241D811yescharacteristic
46C8×C241D811yescharacteristic
47C8×C241C2×D411yescharacteristic
48C8×C241#4111yescharacteristic
49C22×C241—84no—
50C22×C241—82no—
51C22×C241AGL(1,ℤ/8)11yescharacteristic
52C2×D241—41no—
53C4×C241—22no—
54C4×C241#12111yescharacteristic
55C4×C241C2×D811yescharacteristic
56Dic241—41no—
57C2×C241—21no—
58C2×C241—162no—
59C2×C241#45911yescharacteristic
60D241—81no—
61C241#221311yescharacteristic, complemented, Sylow
62#2213—2411nomaximal, Sylow
63#509—2412no—
64#493D24111yescharacteristic, complemented
65#443—2411no—
66#364—2411no—
67#361—2412no—
68#135—2411no—
69C2×D8—21no—
70C2×D8C2×D24112yes—
71#131—4821no—
72#127—21no—
73SD32—4822no—
74D16—4822no—
75M32—2412no—
76#108—2411no—
77#104—4821no—
78C4×C8C2×D24111yescharacteristic
79#41—4821no—
80C2×D4—22no—
81C2×D4—42no—
82Q16—2411no—
83SD16—4821no—
84D8—22no—
85D8—22no—
86D8—41no—
87D8—41no—
88D8—2411no—
89M16—9641no—
90M16—4821no—
91C2×C8—9641no—
92C2×C8C22⋊D24111yescharacteristic
93C2×C8C22×D24111yescharacteristic
94C42C22⋊D24111yescharacteristic
95C16—4822no—
96C23—42no—
97Q8—4821no—
98D4—42no—
99D4—42no—
100D4—84no—
101D4—9641no—
102D4—4821no—
103C2×C4—21no—
104C2×C4—9641no—
105C2×C4C2×C22⋊D24111yescharacteristic
106C8—9641no—
107C8#1683875511yescharacteristic
108C8#1683875511yescharacteristic
109C8D4×D24111yescharacteristic
110C8#1683876911yescharacteristic
111C22—84no—
112C22—82no—
113C22—9641no—
114C22#2144066811yescharacteristic
115C4—22no—
116C4—9641no—
117C4#2144061311yescharacteristic
118C4C2×#1683875511yescharacteristic
119C2—21no—
120C2—162no—
121C2—19281no—
122C2#2950790911yescharacteristic
subgroupG/H
centerC2#29507909
commutator, cosocleC2×C8×C241C23
FrattiniC2×C8C22×D241
Fitting#493×C241C2
socleC2×C241#459
hypercenter#493D241
hypocenterC241#2213
LCSG ▷ C2×C8×C241 ▷ C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #29508153C2semidirect
2. #29507835C2semidirect
3. #29507538C2semidirect
4. #29507530C2semidirect
5. #493×C241C2semidirect
18. Dic964D4semidirect
20. D1928D4semidirect
61. C241#2213semidirect
64. #493D241semidirect

Maximal subgroups

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

subgroupindex
#295081532
#295078352
#295075382
#295075302
#493×C2412
#2213241