Finite Group Databasebeta

← #27186671

Subgroups — #27186671

Order 12928.

210 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 62 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#20266180C212yesmaximal
2#20266036C214yesmaximal, complemented
3#20265730C211yesmaximal, characteristic
4C2×#13108083—22no—
5#15692322C2214yes—
6C4⋊#11717581—22no—
7#15692254C2212yes—
8#15692246C412yes—
9#15692232—22no—
10C4×Dic202—22no—
11#15692214C411yescharacteristic
12C2×C4×Dic101C2211yescharacteristic
13#117×C101C411yescharacteristic
14#13108083—44no—
15C2×#11717581—24no—
16C2×Dic202—22no—
17C22×Dic101D412yes—
18C4⋊Dic101—22no—
19C4⋊Dic101C2×C412yes—
20#13108053—22no—
21#13108053—22no—
22C22⋊Dic101—21no—
23C4×Dic101—21no—
24C4×Dic101C2×C411yescharacteristic
25C4×Dic101D412yes—
26C4×Dic101C2311yescharacteristic
27C22×C4×C101C2×C411yescharacteristic
28C4⋊C4×C101C2×C412yes—
29C22⋊C4×C101—21no—
30C42×C101—21no—
31C23×C101C22⋊C411yescharacteristic
32C2×C4×C101—22no—
33C2×C4×C101—22no—
34C2×C4×C101C22⋊C411yescharacteristic
35C2×C4×C101C22×C411yescharacteristic
36C2×Dic101—22no—
37C2×Dic101—22no—
38C2×Dic101—22no—
39C2×Dic101C22⋊C412yes—
40C2×Dic101C2×D412yes—
41Dic202—42no—
42Dic202—42no—
43#11717581—44no—
44C22×C101—21no—
45C22×C101—22no—
46C22×C101C2×C22⋊C411yescharacteristic
47C4×C101—21no—
48C4×C101—42no—
49C4×C101#10112yes—
50Dic101—22no—
51Dic101—42no—
52Dic101AGL(1,ℤ/8)12yes—
53Dic101#13712yes—
54C2×C101—41no—
55C2×C101C2×#10111yescharacteristic
56C2×C101#41712yes—
57#1561—1011nomaximal, Sylow
58C101#156111yescharacteristic, complemented, Sylow
59#533—1011no—
60#423—1012no—
61#332—1014no—
62C2×M16—2022no—
63C4⋊Q8—1012no—
64#125—1012no—
65C22⋊Q8—2022no—
66C4×Q8—2022no—
67#117—1011no—
68#117#8793811yescharacteristic
69C2×C42—1011no—
70C4⋊C8—1014no—
71C4⋊C8—2022no—
72C2×Q8—2022no—
73C22×C4—1012no—
74C22×C4C2×#8793811yescharacteristic
75M16—4044no—
76C2×C8—2024no—
77C4⋊C4—1012no—
78C4⋊C4—2022no—
79C4⋊C4—2022no—
80C4⋊C4—2022no—
81C4⋊C4C2×#8793812yes—
82C22⋊C4—21no—
83C22⋊C4—2021no—
84C42—21no—
85C42—1012no—
86C42—1011no—
87C42—1011no—
88C42—2021no—
89C23C22⋊#8793811yescharacteristic
90Q8—4042no—
91Q8—4042no—
92C2×C4—22no—
93C2×C4—22no—
94C2×C4—1012no—
95C2×C4—1012no—
96C2×C4—2022no—
97C2×C4—2022no—
98C2×C4—2022no—
99C2×C4C22⋊#8793811yescharacteristic
100C2×C4C22×#8793811yescharacteristic
101C8—4044no—
102C22—21no—
103C22—22no—
104C22C2×C22⋊#8793811yescharacteristic
105C4—21no—
106C4—42no—
107C4—1012no—
108C4—1012no—
109C4—4042no—
110C4—2022no—
111C4#1569231612yes—
112C2—41no—
113C2C2×#1569231611yescharacteristic
114C2#2026616812yes—
subgroupG/H
centerC22C2×C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
Fitting#117×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC23×C101C22⋊C4
cosocleC4×Dic101C23
hypercenter#117#87938
hypocenterC101#1561
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #20266036C2semidirect
58. C101#1561semidirect

Maximal subgroups

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

subgroupindex
#202661802
#202660362
#202657302
#1561101