Finite Group Databasebeta

← #27186115

Subgroups — #27186115

Order 12928.

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

normal subgroups only

This group has 168 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#20266057C211yesmaximal, characteristic, complemented
2#20266023C211yesmaximal, characteristic, complemented
3#20265095C211yesmaximal, characteristic
4C2×#13108083—21no—
5C22⋊#11717581—21no—
6C22×D404C411yescharacteristic
7C2×#13108053C2211yescharacteristic
8C2×#13108051—21no—
9C2×#13108051—21no—
10#95×C101C411yescharacteristic
11#13108083—22no—
12#13108083—41no—
13C2×#11717581—41no—
14C2×#11717581—41no—
15C23×D101—21no—
16C2×D404—41no—
17C2×D404—42no—
18C22×Dic101D411yescharacteristic
19C22×Dic101D411yescharacteristic
20#13108053—41no—
21#13108051—42no—
22#13108051—41no—
23#13108051—41no—
24C22×C4×C101—21no—
25C22×C4×C101C2×C411yescharacteristic
26C23×C101C22⋊C411yescharacteristic
27C22×D101—22no—
28C22×D101—41no—
29C22×D101—41no—
30C22×D101—41no—
31C22×D101—41no—
32C22×D101—41no—
33C22×D101—41no—
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—21no—
41C2×Dic101—21no—
42C2×Dic101—41no—
43C2×Dic101D811yescharacteristic
44C2×Dic101SD1611yescharacteristic
45D404—42no—
46D404—42no—
47#11717581—42no—
48#11717581—81no—
49C22×C101—21no—
50C22×C101—21no—
51C22×C101#9911yescharacteristic
52C22×C101#10211yescharacteristic
53C22×C101#10411yescharacteristic
54C2×D101—42no—
55C2×D101—42no—
56C2×D101—42no—
57C2×D101—81no—
58C2×D101—81no—
59C2×D101—81no—
60C2×D101—81no—
61C4×C101—41no—
62C4×C101—81no—
63Dic101—21no—
64Dic101—21no—
65Dic101—41no—
66C2×C101—21no—
67C2×C101—21no—
68C2×C101#32711yescharacteristic
69C2×C101AΣL(1,𝔽16)11yescharacteristic
70C2×C101#35511yescharacteristic
71D101—82no—
72#1345—1011nomaximal, Sylow
73C101#134511yescharacteristic, complemented, Sylow
74#394—1011no—
75#343—1011no—
76#324—1011no—
77C22×D4—1011no—
78C2×M16—2021no—
79C2×C4⋊C4—1011no—
80C2×C22⋊C4—2021no—
81C2×C22⋊C4—2021no—
82C22⋊C8—2021no—
83#95#8793811yescharacteristic
84C24—2021no—
85C2×D4—4041no—
86C2×D4—4042no—
87C22×C4—21no—
88C22×C4—1011no—
89C22×C4—1011no—
90C22×C4C2×#8793811yescharacteristic
91M16—4041no—
92M16—2022no—
93C2×C8—4041no—
94C2×C8—4041no—
95C4⋊C4—4041no—
96C22⋊C4—4041no—
97C22⋊C4—4041no—
98C22⋊C4—4042no—
99C23—4041no—
100C23—4041no—
101C23—4041no—
102C23—4041no—
103C23—4041no—
104C23—4041no—
105C23—2022no—
106C23C22⋊#8793811yescharacteristic
107D4—4042no—
108D4—4042no—
109C2×C4—21no—
110C2×C4—41no—
111C2×C4—41no—
112C2×C4—41no—
113C2×C4—41no—
114C2×C4—1011no—
115C2×C4—1011no—
116C2×C4—4041no—
117C2×C4—2021no—
118C2×C4—2021no—
119C2×C4—2021no—
120C8—8081no—
121C8—4042no—
122C22—21no—
123C22—21no—
124C22—8081no—
125C22—8081no—
126C22—8081no—
127C22—8081no—
128C22—4042no—
129C22—4042no—
130C22—4042no—
131C22#1569231411yescharacteristic
132C22#1569231711yescharacteristic
133C22#1569232011yescharacteristic
134C4—41no—
135C4—81no—
136C4—4041no—
137C4—2021no—
138C4—2021no—
139C2—21no—
140C2—21no—
141C2—8082no—
142C2#2026602911yescharacteristic
143C2#2026607811yescharacteristic
144C2#2026608611yescharacteristic
subgroupG/H
centerC22#15692314
commutatorC22×C4×C101C2×C4
FrattiniC22×C4C2×#87938
Fitting#95×C101C4
socleC22×C101#99
prime radicalC22×D404C4
cosocleC2×#13108053C22
hypercenter#95#87938
hypocenterC101#1345
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
1. #20266057C2semidirect
2. #20266023C2semidirect
73. C101#1345semidirect

Maximal subgroups

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

subgroupindex
#202660572
#202660232
#202650952
#1345101