Finite Group Databasebeta

← #27169138

Subgroups — #27169138

Order 12928.

124 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 37 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#20264946C211yesmaximal, characteristic
2#20264903C211yesmaximal, characteristic
3#398×C101C211yesmaximal, characteristic
4C2×#13108058—21no—
5C22⋊#11717579—21no—
6C2×C4⋊C4×C101—21no—
7C2×C4⋊C4×C101C411yescharacteristic
8C2×C4⋊C4×C101C2211yescharacteristic
9#95×C101—21no—
10#95×C101C411yescharacteristic
11#13108058—22no—
12#13108058—41no—
13C2×#11717579—41no—
14C2×#11717579—41no—
15C22×C4×C101—21no—
16C22×C4×C101—21no—
17C22×C4×C101C2×C411yescharacteristic
18C22×C4×C101D411yescharacteristic
19C22×C4×C101D411yescharacteristic
20C4⋊C4×C101—41no—
21C4⋊C4×C101—41no—
22C4⋊C4×C101—41no—
23C4⋊C4×C101—41no—
24C23×C101C22⋊C411yescharacteristic
25C2×C4×C101—21no—
26C2×C4×C101—21no—
27C2×C4×C101—22no—
28C2×C4×C101—21no—
29C2×C4×C101—21no—
30C2×C4×C101—41no—
31C2×C4×C101—41no—
32C2×C4×C101—41no—
33C2×C4×C101—41no—
34C2×C4×C101—41no—
35C2×C4×C101—41no—
36C2×C4×C101—41no—
37C2×C4×C101D811yescharacteristic
38C2×C4×C101SD1611yescharacteristic
39#11717579—42no—
40#11717579—81no—
41C22×C101—21no—
42C22×C101—21no—
43C22×C101#9911yescharacteristic
44C22×C101#10211yescharacteristic
45C22×C101#10411yescharacteristic
46C4×C101—21no—
47C4×C101—21no—
48C4×C101—42no—
49C4×C101—41no—
50C4×C101—41no—
51C4×C101—81no—
52C2×C101—21no—
53C2×C101—21no—
54C2×C101#32711yescharacteristic
55C2×C101#35211yescharacteristic
56C2×C101#35611yescharacteristic
57#1346—1011nomaximal, Sylow
58C101#134611yescharacteristic, complemented, Sylow
59#398D10111yescharacteristic
60#343—1011no—
61#324—1011no—
62C2×M16—2021no—
63C2×C4⋊C4—21no—
64C2×C4⋊C4Dic10111yescharacteristic
65C2×C4⋊C4C2×D10111yescharacteristic
66C22⋊C8—2021no—
67#95—21no—
68#95Dic10111yescharacteristic
69C22×C4—21no—
70C22×C4—21no—
71C22×C4C2×Dic10111yescharacteristic
72C22×C4C22⋊D10111yescharacteristic
73C22×C4C22⋊D10111yescharacteristic
74M16—4041no—
75M16—2022no—
76C2×C8—4041no—
77C2×C8—4041no—
78C4⋊C4—41no—
79C4⋊C4—41no—
80C4⋊C4—41no—
81C4⋊C4—41no—
82C23C22⋊Dic10111yescharacteristic
83C2×C4—21no—
84C2×C4—21no—
85C2×C4—22no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—41no—
89C2×C4—41no—
90C2×C4—41no—
91C2×C4—41no—
92C2×C4—41no—
93C2×C4—41no—
94C2×C4—41no—
95C2×C4#1310805911yescharacteristic
96C2×C4#1310806211yescharacteristic
97C8—8081no—
98C8—4042no—
99C22—21no—
100C22—21no—
101C22#1569217011yescharacteristic
102C22#1569217611yescharacteristic
103C22#1569218211yescharacteristic
104C4—21no—
105C4—21no—
106C4—42no—
107C4—41no—
108C4—41no—
109C4—81no—
110C2—21no—
111C2—21no—
112C2#2026491111yescharacteristic
113C2#2026496711yescharacteristic
114C2#2026497611yescharacteristic
subgroupG/H
centerC22#15692170
commutatorC22×C4×C101C2×C4
FrattiniC2×C4⋊C4C2×D101
Fitting#398×C101C2
socleC22×C101#99
prime radicalC23×C101C22⋊C4
cosocleC2×C4⋊C4×C101C22
hypercenter#398D101
hypocenterC101#1346
LCSG ▷ C22×C4×C101 ▷ C23×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #398

Complements

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

NH ≅ G/Ntype
58. C101#1346semidirect

Maximal subgroups

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

subgroupindex
#202649462
#202649032
#398×C1012
#1346101