Finite Group Databasebeta

← #27170433

Subgroups — #27170433

Order 12928.

182 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C101⋊#564C211yesmaximal, characteristic, complemented
2#20265541C212yesmaximal
3#20264919C211yesmaximal, characteristic, complemented
4#20264918C212yesmaximal, complemented
5#490×C101C211yesmaximal, characteristic
6#15692247C2212yes—
7#15692246—22no—
8#15692245—22no—
9#15692245—22no—
10#15692176—22no—
11#15692176—22no—
12#15692166C2212yes—
13#127×C101C2211yescharacteristic
14#125×C101C2211yescharacteristic
15#102×C101—22no—
16#97×C101C2211yescharacteristic
17C2×#11717579—22no—
18C4⋊Dic101—22no—
19C4⋊Dic101D412yes—
20C4⋊Dic101D412yes—
21#13108053—22no—
22#13108053—22no—
23#13108053—22no—
24#13108053—22no—
25C4×Dic101—22no—
26C2×D4×C101—21no—
27C2×D4×C101—22no—
28C2×C8×C101—21no—
29C4⋊C4×C101—22no—
30C4⋊C4×C101D412yes—
31C42×C101C2311yescharacteristic
32C23×C101—41no—
33D4×C101—44no—
34D4×C101—42no—
35C2×C4×C101—22no—
36C2×C4×C101C2×D412yes—
37C2×C4×C101C2×D411yescharacteristic
38C2×Dic101—22no—
39C2×Dic101—22no—
40C8×C101—41no—
41#11717579—42no—
42C22×C101—82no—
43C22×C101—81no—
44C22×C101#12011yescharacteristic
45C4×C101—22no—
46C4×C101—21no—
47C4×C101—42no—
48Dic101—42no—
49Dic101—42no—
50C2×C101—161no—
51C2×C101#45412yes—
52C2×C101#45411yescharacteristic
53#1658—1011nomaximal, Sylow
54C101#165811yescharacteristic, complemented, Sylow
55#564—1011no—
56#490—1012no—
57#490D10111yescharacteristic
58#330—1011no—
59#330—1012no—
60#127C2×D10111yescharacteristic
61#125—1012no—
62#125—2022no—
63#125—2022no—
64#125—2022no—
65#125C2×D10111yescharacteristic
66#102—22no—
67#102—2022no—
68#102—2022no—
69#97—1012no—
70#97C2×D10111yescharacteristic
71C2×D4—22no—
72C2×D4—21no—
73C2×C8—21no—
74C2×C8—2022no—
75C4⋊C4—22no—
76C4⋊C4—1012no—
77C4⋊C4—1012no—
78C4⋊C4—2022no—
79C4⋊C4—2022no—
80C4⋊C4—2022no—
81C4⋊C4—2022no—
82C4⋊C4—2022no—
83C4⋊C4C22⋊D10112yes—
84C42—2022no—
85C42C22×D10111yescharacteristic
86C23—41no—
87D4—44no—
88D4—42no—
89C2×C4—22no—
90C2×C4—2022no—
91C2×C4—2022no—
92C2×C4D4×D10112yes—
93C2×C4C2×C22⋊D10111yescharacteristic
94C8—41no—
95C8—4042no—
96C22—82no—
97C22—81no—
98C22#1569222311yescharacteristic
99C4—22no—
100C4—21no—
101C4—42no—
102C4—4042no—
103C4—4042no—
104C2—161no—
105C2#2026534812yes—
106C2#2026534911yescharacteristic
subgroupG/H
centerC22#15692223
commutator, cosocleC42×C101C23
FrattiniC42C22×D101
Fitting#490×C101C2
socleC22×C101#120
prime radical#127×C101C22
hypercenter#490D101
hypocenterC101#1658
LCSG ▷ C42×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. C101⋊#564C2semidirect
3. #20264919C2semidirect
4. #20264918C2semidirect
54. C101#1658semidirect

Maximal subgroups

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

subgroupindex
C101⋊#5642
#202655412
#202649192
#202649182
#490×C1012
#1658101