Finite Group Databasebeta

← #27173205

Subgroups — #27173205

Order 12928.

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#20265613C212yesmaximal, complemented
2#20265295C211yesmaximal, characteristic, complemented
3#20264998C211yesmaximal, characteristic, complemented
4#20264990C212yesmaximal, complemented
5#493×C101C211yesmaximal, characteristic, complemented
6#15692277C2211yescharacteristic
7#15692261—21no—
8#15692199—22no—
9#15692196—22no—
10#15692195C2212yes—
11#15692191C2211yescharacteristic
12#15692183—21no—
13C2×D8×C101—21no—
14C2×D8×C101C2212yes—
15#127×C101—21no—
16C4×C8×C101C2211yescharacteristic
17#13108074—21no—
18Dic404D411yescharacteristic, complemented
19#13108063—21no—
20D808D411yescharacteristic, complemented
21#13108058—21no—
22#13108057—41no—
23C8×D101—41no—
24#13108049—22no—
25C2×D4×C101—22no—
26C2×D4×C101—42no—
27D8×C101—22no—
28D8×C101—22no—
29D8×C101—41no—
30D8×C101—41no—
31C2×C8×C101D411yescharacteristic
32C2×C8×C101C2311yescharacteristic
33C42×C101D411yescharacteristic
34C23×C101—42no—
35D4×C101—42no—
36D4×C101—42no—
37D4×C101—84no—
38C2×C4×C101—21no—
39C2×C4×C101C2×D411yescharacteristic
40C22⋊D101—41no—
41D404—21no—
42C4×D101—41no—
43Dic202—21no—
44C8×C101D811yescharacteristic
45C8×C101D811yescharacteristic
46C8×C101C2×D411yescharacteristic
47C8×C101#4111yescharacteristic
48#11717579—41no—
49C22×C101—84no—
50C22×C101—82no—
51C22×C101AGL(1,ℤ/8)11yescharacteristic
52C2×D101—41no—
53C4×C101—22no—
54C4×C101#12111yescharacteristic
55C4×C101C2×D811yescharacteristic
56Dic101—41no—
57C2×C101—21no—
58C2×C101—162no—
59C2×C101#45911yescharacteristic
60D101—81no—
61#2213—1011nomaximal, Sylow
62C101#221311yescharacteristic, complemented, Sylow
63#509—1012no—
64#493D10111yescharacteristic, complemented
65#443—1011no—
66#364—1011no—
67#361—1012no—
68#135—1011no—
69C2×D8—21no—
70C2×D8C2×D10112yes—
71#131—2021no—
72#127—21no—
73SD32—2022no—
74D16—2022no—
75M32—1012no—
76#108—1011no—
77#104—2021no—
78C4×C8C2×D10111yescharacteristic
79#41—2021no—
80C2×D4—22no—
81C2×D4—42no—
82Q16—1011no—
83SD16—2021no—
84D8—22no—
85D8—22no—
86D8—41no—
87D8—41no—
88D8—1011no—
89M16—4041no—
90M16—2021no—
91C2×C8—4041no—
92C2×C8C22⋊D10111yescharacteristic
93C2×C8C22×D10111yescharacteristic
94C42C22⋊D10111yescharacteristic
95C16—2022no—
96C23—42no—
97Q8—2021no—
98D4—42no—
99D4—42no—
100D4—84no—
101D4—4041no—
102D4—2021no—
103C2×C4—21no—
104C2×C4—4041no—
105C2×C4C2×C22⋊D10111yescharacteristic
106C8—4041no—
107C8#1310805911yescharacteristic
108C8#1310805911yescharacteristic
109C8D4×D10111yescharacteristic
110C8#1310807311yescharacteristic
111C22—84no—
112C22—82no—
113C22—4041no—
114C22#1569228111yescharacteristic
115C4—22no—
116C4—4041no—
117C4#1569222611yescharacteristic
118C4C2×#1310805911yescharacteristic
119C2—21no—
120C2—162no—
121C2—8081no—
122C2#2026536911yescharacteristic
subgroupG/H
centerC2#20265369
commutator, cosocleC2×C8×C101C23
FrattiniC2×C8C22×D101
Fitting#493×C101C2
socleC2×C101#459
hypercenter#493D101
hypocenterC101#2213
LCSG ▷ C2×C8×C101 ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #20265613C2semidirect
2. #20265295C2semidirect
3. #20264998C2semidirect
4. #20264990C2semidirect
5. #493×C101C2semidirect
18. Dic404D4semidirect
20. D808D4semidirect
62. C101#2213semidirect
64. #493D101semidirect

Maximal subgroups

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

subgroupindex
#202656132
#202652952
#202649982
#202649902
#493×C1012
#2213101