Finite Group Databasebeta

← #27170460

Subgroups — #27170460

Order 12928.

172 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 49 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#20265587C212yesmaximal
2#20265547C211yesmaximal, characteristic
3#20264919C211yesmaximal, characteristic
4#20264919C212yesmaximal
5#564×C101C211yesmaximal, characteristic
6#15692255C2211yescharacteristic
7#15692188—22no—
8#15692186—22no—
9#15692178—22no—
10#15692166C2211yescharacteristic
11#15692166C2212yes—
12#125×C101—22no—
13#125×C101—22no—
14#125×C101—22no—
15#125×C101C2211yescharacteristic
16#125×C101C2212yes—
17C2×Dic202—21no—
18C2×#11717579—22no—
19C2×#11717579—21no—
20C4⋊Dic101—22no—
21C4⋊C4×C101—22no—
22C4⋊C4×C101—22no—
23C4⋊C4×C101—22no—
24C4⋊C4×C101—22no—
25C4⋊C4×C101—22no—
26C4⋊C4×C101—22no—
27C4⋊C4×C101D412yes—
28C4⋊C4×C101D412yes—
29C4⋊C4×C101D412yes—
30C42×C101—22no—
31C42×C101C2311yescharacteristic
32C2×C4×C101—22no—
33C2×C4×C101—22no—
34C2×C4×C101—22no—
35C2×C4×C101C2×D412yes—
36C2×C4×C101C2×D411yescharacteristic
37C2×Dic101—41no—
38Dic202—42no—
39#11717579—24no—
40#11717579—41no—
41C22×C101#12011yescharacteristic
42C4×C101—21no—
43C4×C101—22no—
44C4×C101—42no—
45C4×C101—42no—
46C4×C101—42no—
47Dic101—81no—
48C2×C101#45411yescharacteristic
49C2×C101#45612yes—
50#1663—1011nomaximal, Sylow
51C101#166311yescharacteristic, complemented, Sylow
52#564D10111yescharacteristic
53#501—1012no—
54#491—1011no—
55#330—1012no—
56#330—1011no—
57C4⋊Q8—1011no—
58#125—22no—
59#125—22no—
60#125—22no—
61#125C2×D10111yescharacteristic
62#125C2×D10112yes—
63#107—2022no—
64#106—2022no—
65#103—2022no—
66#97—1011no—
67#97—1012no—
68C2×Q8—2021no—
69C2×C8—2021no—
70C2×C8—2022no—
71C4⋊C4—22no—
72C4⋊C4—22no—
73C4⋊C4—22no—
74C4⋊C4—22no—
75C4⋊C4—22no—
76C4⋊C4—22no—
77C4⋊C4—2022no—
78C4⋊C4C22⋊D10112yes—
79C4⋊C4C22⋊D10112yes—
80C4⋊C4C22⋊D10112yes—
81C42—22no—
82C42C22×D10111yescharacteristic
83Q8—4042no—
84C2×C4—22no—
85C2×C4—22no—
86C2×C4—22no—
87C2×C4—4041no—
88C2×C4C2×C22⋊D10112yes—
89C2×C4C2×C22⋊D10111yescharacteristic
90C8—4041no—
91C8—2024no—
92C22#1569222411yescharacteristic
93C4—21no—
94C4—22no—
95C4—42no—
96C4—42no—
97C4—42no—
98C4—8081no—
99C2#2026535011yescharacteristic
100C2#2026536012yes—
subgroupG/H
centerC22#15692224
commutator, cosocleC42×C101C23
FrattiniC42C22×D101
Fitting#564×C101C2
socle, prime radicalC22×C101#120
hypercenter#564D101
hypocenterC101#1663
LCSG ▷ C42×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #564

Complements

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

NH ≅ G/Ntype
51. C101#1663semidirect

Maximal subgroups

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

subgroupindex
#202655872
#202655472
#202649192
#564×C1012
#1663101