Finite Group Databasebeta

← #27187045

Subgroups — #27187045

Order 12928.

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

normal subgroups only

This group has 272 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
1C2×#15692315C212yesmaximal
2#20266058C214yesmaximal, complemented
3#20265650C211yesmaximal, characteristic
4C2×#13108083C2214yes—
5#15692315—22no—
6#15692315—22no—
7C22×C22⋊D101C2211yescharacteristic
8C4×C22⋊D101—22no—
9#15692215—22no—
10#15692211C2212yes—
11C2×C22⋊Dic101C411yescharacteristic
12C22⋊C4×D101C412yes—
13C2×C22⋊C4×C101C411yescharacteristic
14#13108083—24no—
15#13108083—24no—
16C2×#11717581—24no—
17C23×D101C2×C411yescharacteristic
18C2×C22⋊D101—24no—
19C2×C22⋊D101D412yes—
20C2×C22⋊D101D412yes—
21C22×Dic101—21no—
22C22×Dic101C2311yescharacteristic
23C2×C4×D101—22no—
24#13108053—22no—
25C22⋊Dic101—21no—
26C22⋊Dic101C2×C412yes—
27#13108051—22no—
28C4×Dic101—22no—
29C24×C101C2×C411yescharacteristic
30C22×C4×C101—21no—
31C22⋊C4×C101—21no—
32C22⋊C4×C101C2×C412yes—
33C23×C101—22no—
34C23×C101—81no—
35C23×C101C22⋊C411yescharacteristic
36C23×C101C22⋊C411yescharacteristic
37C23×C101C22×C411yescharacteristic
38C22×D101—22no—
39C22×D101—81no—
40C22×D101C22⋊C412yes—
41C2×C4×C101—22no—
42C2×C4×C101—81no—
43C22⋊D101—24no—
44C22⋊D101—24no—
45C2×Dic101—22no—
46C2×Dic101—81no—
47C2×Dic101C2×D412yes—
48C2×Dic101#4114yes—
49C4×D101—82no—
50#11717581—44no—
51C22×C101—21no—
52C22×C101—21no—
53C22×C101—41no—
54C22×C101—41no—
55C22×C101—41no—
56C22×C101—82no—
57C22×C101C2×C22⋊C411yescharacteristic
58C22×C101#11712yes—
59C2×D101—22no—
60C2×D101—42no—
61C2×D101—82no—
62C4×C101—42no—
63Dic101—42no—
64Dic101#12314yes—
65C2×C101—21no—
66C2×C101—22no—
67C2×C101—41no—
68C2×C101—41no—
69C2×C101#38111yescharacteristic
70D101—42no—
71#1829—1011nomaximal, Sylow
72C101#182911yescharacteristic, complemented, Sylow
73#518—1011no—
74C2×#100—1012no—
75#344—1014no—
76C22×D4—1011no—
77C2×M16—1014no—
78C4×D4—2022no—
79C4×D4—2022no—
80#117—1012no—
81C2×C22⋊C4—1011no—
82C2×C22⋊C4—1012no—
83C2×C22⋊C4#8793811yescharacteristic
84#100—2022no—
85#100—2022no—
86C24—1011no—
87C24C2×#8793811yescharacteristic
88C2×D4—1012no—
89C2×D4—1012no—
90C2×D4—2024no—
91C22×C4—21no—
92C22×C4—1011no—
93C22×C4—2022no—
94C22×C4—2021no—
95M16—2024no—
96M16—2024no—
97C2×C8—2024no—
98C4⋊C4—2022no—
99C22⋊C4—21no—
100C22⋊C4—1012no—
101C22⋊C4—2022no—
102C22⋊C4—2021no—
103C22⋊C4C2×#8793812yes—
104C42—2022no—
105C23—22no—
106C23—81no—
107C23—8081no—
108C23—1012no—
109C23—2022no—
110C23C22⋊#8793811yescharacteristic
111C23C22⋊#8793811yescharacteristic
112C23C22×#8793811yescharacteristic
113D4—2024no—
114D4—2024no—
115C2×C4—22no—
116C2×C4—81no—
117C2×C4—8082no—
118C2×C4—8081no—
119C2×C4—1012no—
120C2×C4—1014no—
121C2×C4—2022no—
122C8—4044no—
123C22—21no—
124C22—21no—
125C22—41no—
126C22—41no—
127C22—41no—
128C22—82no—
129C22—8082no—
130C22—4042no—
131C22—2022no—
132C22C2×C22⋊#8793811yescharacteristic
133C22#1569233412yes—
134C4—42no—
135C4—1014no—
136C4—4042no—
137C2—21no—
138C2—22no—
139C2—41no—
140C2—41no—
141C2—4042no—
142C2#2026612011yescharacteristic
subgroupG/H
centerC2#20266120
commutatorC23×C101C22×C4
FrattiniC23C22×#87938
FittingC2×C22⋊C4×C101C4
socleC2×C101#381
prime radicalC22×C22⋊D101C22
cosocleC22×Dic101C23
hypercenterC2×C22⋊C4#87938
hypocenterC101#1829
LCSG ▷ C23×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #20266058C2semidirect
72. C101#1829semidirect

Maximal subgroups

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

subgroupindex
C2×#156923152
#202660582
#202656502
#1829101