Finite Group Databasebeta

← #27187032

Subgroups — #27187032

Order 12928.

316 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 70 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#20266149C212yesmaximal
2#20266057C214yesmaximal, complemented
3C2×C4⋊C4×D101C211yesmaximal, characteristic
4C2×#13108083C2214yes—
5#15692312—22no—
6#15692312—22no—
7C22×C4×D101C412yes—
8C22×C4×D101C2211yescharacteristic
9C2×C4⋊Dic101C411yescharacteristic
10C2×#13108053C2212yes—
11C4⋊C4×D101—22no—
12C4⋊C4×D101—22no—
13C2×C4⋊C4×C101C411yescharacteristic
14#13108083—28no—
15C2×#11717581—24no—
16C23×D101C2×C411yescharacteristic
17C22×Dic101C2×C412yes—
18C22×Dic101C2311yescharacteristic
19C2×C4×D101—24no—
20C2×C4×D101—22no—
21C2×C4×D101—22no—
22C2×C4×D101—44no—
23C2×C4×D101D412yes—
24C2×C4×D101D412yes—
25C4⋊Dic101—22no—
26#13108053—24no—
27C22×C4×C101C2×C412yes—
28C22×C4×C101C2×C411yescharacteristic
29C4⋊C4×C101—22no—
30C23×C101C22×C411yescharacteristic
31C22×D101—22no—
32C22×D101—22no—
33C22×D101—22no—
34C22×D101C22⋊C411yescharacteristic
35C22×D101C22⋊C411yescharacteristic
36C2×C4×C101—22no—
37C2×C4×C101—22no—
38C2×C4×C101—42no—
39C2×C4×C101C22⋊C412yes—
40C2×Dic101—22no—
41C2×Dic101—42no—
42C2×Dic101C2×D412yes—
43C2×Dic101#4114yes—
44C4×D101—24no—
45C4×D101—24no—
46C4×D101—44no—
47C4×D101—44no—
48#11717581—44no—
49C22×C101—21no—
50C22×C101—21no—
51C22×C101C2×C22⋊C411yescharacteristic
52C22×C101#11712yes—
53C2×D101—28no—
54C2×D101—21no—
55C2×D101—21no—
56C2×D101—21no—
57C2×D101—21no—
58C2×D101#10012yes—
59C2×D101#10112yes—
60C4×C101—22no—
61C4×C101—42no—
62Dic101—42no—
63Dic101#12314yes—
64C2×C101—22no—
65C2×C101#38111yescharacteristic
66C2×C101C2×#10011yescharacteristic
67C2×C101C2×#10111yescharacteristic
68D101—22no—
69D101—22no—
70#1821—1011nomaximal, Sylow
71C101#182111yescharacteristic, complemented, Sylow
72C22×C4⋊C4—1011no—
73#407—1012no—
74#343—1014no—
75C23×C4—1011no—
76C23×C4—1012no—
77C2×M16—1014no—
78C2×C4⋊C4—1012no—
79C2×C4⋊C4—1011no—
80C2×C4⋊C4—2022no—
81C2×C4⋊C4—2022no—
82C2×C4⋊C4#8793811yescharacteristic
83C22⋊C8—2022no—
84C22⋊C8—2022no—
85C24—1011no—
86C22×C4—1011no—
87C22×C4—1012no—
88C22×C4—1012no—
89C22×C4—1012no—
90C22×C4—4044no—
91C22×C4—2024no—
92C22×C4—2022no—
93C22×C4—2022no—
94C22×C4C2×#8793812yes—
95C22×C4C2×#8793811yescharacteristic
96M16—2028no—
97C2×C8—2024no—
98C4⋊C4—22no—
99C4⋊C4—2024no—
100C4⋊C4—2022no—
101C23—1011no—
102C23—1011no—
103C23—2022no—
104C23—2022no—
105C23—2022no—
106C23C22×#8793811yescharacteristic
107C2×C4—22no—
108C2×C4—22no—
109C2×C4—42no—
110C2×C4—1012no—
111C2×C4—1014no—
112C2×C4—4044no—
113C2×C4—4044no—
114C2×C4—4042no—
115C2×C4—2024no—
116C2×C4—2024no—
117C2×C4—2022no—
118C2×C4C22⋊#8793812yes—
119C8—4044no—
120C22—21no—
121C22—21no—
122C22—1012no—
123C22—1012no—
124C22—2028no—
125C22—2021no—
126C22—2021no—
127C22—2021no—
128C22—2021no—
129C22C2×C22⋊#8793811yescharacteristic
130C22#1569233412yes—
131C4—22no—
132C4—42no—
133C4—1014no—
134C4—4042no—
135C2—22no—
136C2—2022no—
137C2—2022no—
138C2#2026612011yescharacteristic
139C2D101⋊#10011yescharacteristic
140C2D101⋊#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC23×C101C22×C4
FrattiniC23C22×#87938
FittingC2×C4⋊C4×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC23×D101C2×C4
cosocleC22×Dic101C23
hypercenterC2×C4⋊C4#87938
hypocenterC101#1821
LCSG ▷ C23×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #20266057C2semidirect
71. C101#1821semidirect

Maximal subgroups

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

subgroupindex
#202661492
#202660572
C2×C4⋊C4×D1012
#1821101