Finite Group Databasebeta

← #27186405

Subgroups — #27186405

Order 12928.

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

normal subgroups only

This group has 204 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#20266198C211yesmaximal, characteristic
2#20266194C211yesmaximal, characteristic
3#20266022C214yesmaximal
4C2×#15692246C211yesmaximal, characteristic
5#15692322—21no—
6C4⋊#11717581—21no—
7C22⋊#11717581C2212yes—
8C22⋊#11717581C2212yes—
9#15692310—21no—
10C4×#11717581—21no—
11#15692246—21no—
12#15692246—21no—
13#15692246—21no—
14#15692246—21no—
15C2×C4⋊Dic101C411yescharacteristic
16C2×C4⋊Dic101C2212yes—
17C2×#13108053C412yes—
18C2×C4×Dic101C2211yescharacteristic
19C2×C4⋊C4×C101C411yescharacteristic
20C2×#11717581—22no—
21C2×#11717581—22no—
22C22×Dic101C2×C411yescharacteristic
23C22×Dic101C2×C412yes—
24C22×Dic101C2311yescharacteristic
25C4⋊Dic101—21no—
26C4⋊Dic101—21no—
27C4⋊Dic101—22no—
28C4⋊Dic101—22no—
29#13108053—22no—
30#13108053—22no—
31C4×Dic101D411yescharacteristic
32C4×Dic101D411yescharacteristic
33C4×Dic101D411yescharacteristic
34C4×Dic101D411yescharacteristic
35C22×C4×C101C2×C412yes—
36C22×C4×C101C2×C411yescharacteristic
37C4⋊C4×C101—21no—
38C4⋊C4×C101—21no—
39C23×C101C22×C411yescharacteristic
40C2×C4×C101—22no—
41C2×C4×C101—22no—
42C2×C4×C101—24no—
43C2×C4×C101C22⋊C411yescharacteristic
44C2×C4×C101C22⋊C411yescharacteristic
45C2×Dic101—22no—
46C2×Dic101—22no—
47C2×Dic101—41no—
48C2×Dic101—42no—
49C2×Dic101C22⋊C411yescharacteristic
50C2×Dic101C22⋊C411yescharacteristic
51C2×Dic101C2×D411yescharacteristic
52C2×Dic101C2×D411yescharacteristic
53#11717581—42no—
54#11717581—42no—
55C22×C101—21no—
56C22×C101—21no—
57C22×C101C2×C22⋊C411yescharacteristic
58C22×C101#13112yes—
59C4×C101—21no—
60C4×C101—42no—
61C4×C101#10112yes—
62Dic101—21no—
63Dic101—21no—
64Dic101—21no—
65Dic101—21no—
66Dic101—42no—
67C2×C101—22no—
68C2×C101#40811yescharacteristic
69C2×C101#41011yescharacteristic
70C2×C101C2×#10111yescharacteristic
71#1470—1011nomaximal, Sylow
72C101#147011yescharacteristic, complemented, Sylow
73C2×#125—1011no—
74#432—1011no—
75#431—1011no—
76#324—1014no—
77#125—2021no—
78#125—2021no—
79#125—2021no—
80#125—2021no—
81C2×C4⋊C4—1012no—
82C2×C4⋊C4—1012no—
83C2×C4⋊C4—1011no—
84C2×C4⋊C4#8793811yescharacteristic
85C2×C42—1011no—
86C4⋊C8—2021no—
87C4⋊C8—2021no—
88C22⋊C8—1012no—
89C22⋊C8—1012no—
90#97—2021no—
91C4×C8—2021no—
92C22×C4—1011no—
93C22×C4—1011no—
94C22×C4—1012no—
95C22×C4C2×#8793812yes—
96C22×C4C2×#8793811yescharacteristic
97C2×C8—2022no—
98C2×C8—2022no—
99C4⋊C4—21no—
100C4⋊C4—21no—
101C4⋊C4—2022no—
102C4⋊C4—2022no—
103C4⋊C4—2022no—
104C4⋊C4—2022no—
105C4⋊C4—2021no—
106C4⋊C4—2021no—
107C42—1011no—
108C42—1011no—
109C42—1011no—
110C42—1011no—
111C23C22×#8793811yescharacteristic
112C2×C4—22no—
113C2×C4—22no—
114C2×C4—24no—
115C2×C4—1011no—
116C2×C4—1011no—
117C2×C4—1011no—
118C2×C4—1011no—
119C2×C4—4042no—
120C2×C4—4041no—
121C2×C4—2022no—
122C2×C4—2022no—
123C2×C4C22⋊#8793811yescharacteristic
124C2×C4C22⋊#8793811yescharacteristic
125C8—4042no—
126C8—4042no—
127C22—21no—
128C22—21no—
129C22C2×C22⋊#8793811yescharacteristic
130C22#1569234212yes—
131C4—21no—
132C4—42no—
133C4—4042no—
134C4—2021no—
135C4—2021no—
136C4—2021no—
137C4—2021no—
138C4#1569231612yes—
139C2—22no—
140C2#2026615111yescharacteristic
141C2#2026615811yescharacteristic
142C2C2×#1569231611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutator, prime radicalC23×C101C22×C4
FrattiniC23C22×#87938
FittingC2×C4⋊C4×C101C4
socleC22×C101C2×C22⋊C4
cosocleC22×Dic101C23
hypercenterC2×C4⋊C4#87938
hypocenterC101#1470
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
72. C101#1470semidirect

Maximal subgroups

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

subgroupindex
#202661982
#202661942
#202660222
C2×#156922462
#1470101