Finite Group Databasebeta

← #27186113

Subgroups — #27186113

Order 12928.

146 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 30 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#20266055C211yesmaximal, characteristic
2#20266021C211yesmaximal, characteristic
3#20265104C211yesmaximal, characteristic
4C2×C22⋊#87938—21no—
5C22⋊#11717581—21no—
6C2×C4⋊Dic101C411yescharacteristic, complemented
7C2×#13108051—21no—
8C2×#13108051C2211yescharacteristic
9#15692162—21no—
10#95×C101C411yescharacteristic, complemented
11C22×#87938—41no—
12C2×#11717581—41no—
13C22⋊#87938—22no—
14C22⋊#87938—41no—
15C23×D101D411yescharacteristic
16C22×Dic101—21no—
17C22×Dic101D411yescharacteristic
18C4⋊Dic101—41no—
19#13108051—41no—
20#13108051—41no—
21#13108051—41no—
22C22×C4×C101—21no—
23C22×C4×C101C2×C411yescharacteristic
24C23×C101C22⋊C411yescharacteristic
25C22×D101—21no—
26C22×D101—21no—
27C22×D101—41no—
28C22×D101—41no—
29C22×D101D811yescharacteristic
30C22×D101SD1611yescharacteristic
31C2×#87938—42no—
32C2×#87938—81no—
33C2×#87938—81no—
34C2×C4×C101—21no—
35C2×C4×C101—41no—
36C2×C4×C101—41no—
37C2×C4×C101—41no—
38C2×C4×C101—41no—
39C2×Dic101—21no—
40C2×Dic101—41no—
41C2×Dic101—41no—
42C2×Dic101—41no—
43C2×Dic101—41no—
44#11717581—81no—
45C22×C101—21no—
46C22×C101—21no—
47C22×C101#9911yescharacteristic
48C22×C101#10211yescharacteristic
49C22×C101#10411yescharacteristic
50C2×D101—21no—
51C2×D101—21no—
52C2×D101—41no—
53C2×D101—41no—
54C2×D101—41no—
55C2×D101—41no—
56C2×D101—81no—
57#87938—82no—
58C4×C101—41no—
59C4×C101—81no—
60Dic101—41no—
61Dic101—81no—
62C2×C101—21no—
63C2×C101—21no—
64C2×C101#32711yescharacteristic
65C2×C101#35211yescharacteristic
66C2×C101#35411yescharacteristic
67D101—41no—
68D101—41no—
69#1344—1011nomaximal, Sylow
70C101#134411yescharacteristic, complemented, Sylow
71#397—1011no—
72#342—1011no—
73#323—1011no—
74C2×C4⋊C4—1011no—
75C2×C22⋊C4—1011no—
76C2×C22⋊C4—2021no—
77C2×C22⋊C4—2021no—
78C22⋊C8—2021no—
79#95—2021no—
80#95#8793811yescharacteristic, complemented
81C24—1011no—
82C22×C4—21no—
83C22×C4—1011no—
84C22×C4—4041no—
85C22×C4—2021no—
86C22×C4C2×#8793811yescharacteristic
87C2×C8—4041no—
88C4⋊C4—4041no—
89C22⋊C4—4041no—
90C22⋊C4—4041no—
91C22⋊C4—4041no—
92C22⋊C4—4041no—
93C22⋊C4—2022no—
94C23—1011no—
95C23—1011no—
96C23—4041no—
97C23—4041no—
98C23—2021no—
99C23—2021no—
100C23C22⋊#8793811yescharacteristic
101C2×C4—21no—
102C2×C4—41no—
103C2×C4—41no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—8081no—
107C2×C4—8081no—
108C2×C4—4042no—
109C2×C4—4041no—
110C2×C4—4041no—
111C2×C4—4041no—
112C2×C4—4041no—
113C2×C4—2021no—
114C8—8081no—
115C22—21no—
116C22—21no—
117C22—8081no—
118C22—4041no—
119C22—4041no—
120C22—4041no—
121C22—4041no—
122C22—2021no—
123C22—2021no—
124C22#1569231411yescharacteristic
125C22#1569231711yescharacteristic
126C22#1569232011yescharacteristic
127C4—41no—
128C4—81no—
129C4—8082no—
130C4—8081no—
131C4—4041no—
132C2—21no—
133C2—21no—
134C2—4041no—
135C2—4041no—
136C2#2026602911yescharacteristic
137C2#2026608011yescharacteristic
138C2#2026608411yescharacteristic
subgroupG/H
centerC22#15692314
commutatorC22×C4×C101C2×C4
FrattiniC22×C4C2×#87938
Fitting#95×C101C4
socleC22×C101#99
prime radicalC23×D101D4
cosocleC2×#13108051C22
hypercenter#95#87938
hypocenterC101#1344
LCSG ▷ C22×C4×C101 ▷ C23×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
6. C2×C4⋊Dic101C4semidirect
10. #95×C101C4semidirect
70. C101#1344semidirect
80. #95#87938semidirect

Maximal subgroups

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

subgroupindex
#202660552
#202660212
#202651042
#1344101