Finite Group Databasebeta

← #27187431

Subgroups — #27187431

Order 12928.

262 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 54 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#20266163C212yesmaximal, complemented
2#20266085C214yesmaximal, complemented
3#20265744C211yesmaximal, characteristic
4D101⋊M16—22no—
5#15692316C2214yescomplemented
6#15692315—22no—
7C2×#13108074C2211yescharacteristic
8#15692251C412yes—
9#15692242C2212yes—
10#15692226—22no—
11#15692224—22no—
12#15692214C411yescharacteristic
13C22×D4×C101C411yescharacteristic
14#13108084—42no—
15#13108083—24no—
16D101⋊C8—42no—
17#13108074—42no—
18C2×Dic202C2311yescharacteristic
19C2×D404C2×C411yescharacteristic
20C2×C22⋊D101—24no—
21C2×C22⋊D101D412yes—
22C2×C4×D101D412yes—
23C4⋊Dic101—21no—
24C22⋊Dic101—21no—
25C22⋊Dic101—24no—
26C4×Dic101C2×C412yes—
27C24×C101—21no—
28C2×D4×C101—21no—
29C2×D4×C101—42no—
30C2×D4×C101C2×C412yes—
31C22×C4×C101C2×C411yescharacteristic
32C23×C101—22no—
33C23×C101—42no—
34C23×C101—82no—
35C23×C101C22⋊C411yescharacteristic
36C22×D101C22⋊C412yes—
37D4×C101—42no—
38D4×C101—42no—
39C2×C4×C101—22no—
40C2×C4×C101C22⋊C411yescharacteristic
41C2×C4×C101C22×C411yescharacteristic
42C22⋊D101—42no—
43C22⋊D101—84no—
44C2×Dic101—22no—
45C2×Dic101C2×D412yes—
46D404—41no—
47C4×D101—22no—
48C4×D101—22no—
49Dic202—41no—
50#11717581—44no—
51C22×C101—21no—
52C22×C101—41no—
53C22×C101—44no—
54C22×C101—42no—
55C22×C101—84no—
56C22×C101C2×C22⋊C411yescharacteristic
57C2×D101—22no—
58C2×D101—42no—
59C4×C101—21no—
60C4×C101#9912yes—
61Dic101—22no—
62Dic101—42no—
63C2×C101—21no—
64C2×C101—41no—
65C2×C101—82no—
66C2×C101C2×#9911yescharacteristic
67D101—42no—
68#2134—1011nomaximal, Sylow
69C101#213411yescharacteristic, complemented, Sylow
70#535—1011no—
71#413—1012no—
72#355—1014no—
73C2×#41—1011no—
74C22×D4#8793811yescharacteristic
75C2×M16—2022no—
76#127—1012no—
77#124—1012no—
78#121—2022no—
79#120—2022no—
80#117—1011no—
81#101—1014no—
82#100—2022no—
83C24—21no—
84#41—4042no—
85C2×Q8—1011no—
86C2×D4—21no—
87C2×D4—42no—
88C2×D4—1012no—
89C2×D4—1011no—
90C2×D4—2024no—
91C2×D4C2×#8793812yes—
92C22×C4—1012no—
93C22×C4C2×#8793811yescharacteristic
94M16—4042no—
95M16—2024no—
96C2×C8—4042no—
97C4⋊C4—2021no—
98C22⋊C4—2024no—
99C22⋊C4—2021no—
100C42—1012no—
101C23—22no—
102C23—42no—
103C23—82no—
104C23—1012no—
105C23C22⋊#8793811yescharacteristic
106Q8—4041no—
107D4—42no—
108D4—42no—
109D4—8084no—
110D4—4041no—
111D4—4042no—
112C2×C4—22no—
113C2×C4—1012no—
114C2×C4—2022no—
115C2×C4—2022no—
116C2×C4—2022no—
117C2×C4C22⋊#8793811yescharacteristic
118C2×C4C22×#8793811yescharacteristic
119C8—4044no—
120C22—21no—
121C22—41no—
122C22—44no—
123C22—42no—
124C22—84no—
125C22—4042no—
126C22—2022no—
127C22C2×C22⋊#8793811yescharacteristic
128C4—21no—
129C4—4042no—
130C4—2022no—
131C4#1569231312yes—
132C2—21no—
133C2—41no—
134C2—82no—
135C2—4042no—
136C2C2×#1569231311yescharacteristic
subgroupG/H
centerC2C2×#15692313
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
FittingC22×D4×C101C4
socleC2×C101C2×#99
prime radical#20265744C2
cosocleC2×Dic202C23
hypercenterC22×D4#87938
hypocenterC101#2134
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #20266163C2semidirect
2. #20266085C2semidirect
5. #15692316C22semidirect
69. C101#2134semidirect

Maximal subgroups

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

subgroupindex
#202661632
#202660852
#202657442
#2134101