Finite Group Databasebeta

← #36375115

Subgroups — #36375115

Order 22336.

190 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 58 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×#19150243C212yesmaximal, complemented
2#26013696C212yesmaximal, complemented
3C22⋊#14584102C212yesmaximal, complemented
4C22×C4×D349C211yesmaximal, characteristic
5#19150243—24no—
6C2×#14584102C2214yescomplemented
7C23×D349C411yescharacteristic
8C22×Dic349C2211yescharacteristic
9C2×C4×D349—24no—
10C2×C4×D349C411yescharacteristic
11C2×C4×D349C411yescharacteristic
12C2×C4×D349C2211yescharacteristic
13C2×C4×D349C2211yescharacteristic
14C22×C4×C349C411yescharacteristic
15#14584102—24no—
16C22×D349—22no—
17C22×D349—22no—
18C22×D349—22no—
19C22×D349C2×C411yescharacteristic
20C22×D349C2×C411yescharacteristic
21C2×Dic349—22no—
22C2×Dic349C2×C411yescharacteristic
23C2×Dic349C2311yescharacteristic
24C4×D349—22no—
25C4×D349—22no—
26C4×D349—22no—
27C4×D349D414yes—
28C23×C349C2×C411yescharacteristic
29C2×C4×C349—22no—
30C2×C4×C349C2×C411yescharacteristic
31C2×C4×C349C2×C411yescharacteristic
32C22×C349—21no—
33C22×C349—21no—
34C22×C349M1612yescomplemented
35C22×C349C22×C411yescharacteristic
36C2×D349—28no—
37C2×D349—21no—
38C2×D349—21no—
39C2×D349—21no—
40C2×D349—21no—
41C2×D349C22⋊C412yes—
42C2×D349M1612yescomplemented
43C4×C349—21no—
44C4×C349C22⋊C412yes—
45Dic349—21no—
46Dic349C2×D412yes—
47C2×C349—22no—
48C2×C349C2×C22⋊C411yescharacteristic
49C2×C349C2×M1611yescharacteristic
50C2×C349C2×M1611yescharacteristic
51D349—22no—
52D349—22no—
53C349#40711yescharacteristic, complemented, Sylow
54#407—3491nomaximal, Sylow
55C23×C4—3491no—
56C2×M16—3492no—
57C22⋊C8—3492no—
58C22⋊C8—3492no—
59C24—3491no—
60C22×C4—3491no—
61C22×C4—3491no—
62C22×C4—3491no—
63C22×C4—3491no—
64C22×C4—3491no—
65C22×C4—6984no—
66C22×C4#1306370311yescharacteristic
67M16—6984no—
68C2×C8—3494no—
69C23—3491no—
70C23—3491no—
71C23—6982no—
72C23—6982no—
73C23—6982no—
74C23C2×#1306370311yescharacteristic
75C2×C4—22no—
76C2×C4—3491no—
77C2×C4—3494no—
78C2×C4—3491no—
79C2×C4—6982no—
80C2×C4—6982no—
81C2×C4—6982no—
82C2×C4—6982no—
83C2×C4C2×#1306370311yescharacteristic
84C2×C4C2×#1306370311yescharacteristic
85C8—6984no—
86C22—21no—
87C22—21no—
88C22—3492no—
89C22—3492no—
90C22—6988no—
91C22—6981no—
92C22—6981no—
93C22—6981no—
94C22—6981no—
95C22#1915024312yescomplemented
96C22C22×#1306370311yescharacteristic
97C4—21no—
98C4—3492no—
99C4—6981no—
100C4C22⋊#1306370312yes—
101C2—22no—
102C2—6982no—
103C2—6982no—
104C2C2×C22⋊#1306370311yescharacteristic
105C2D349⋊M1611yescharacteristic
106C2C2×#1915024311yescharacteristic
subgroupG/H
center, FrattiniC22C22×#13063703
commutator, socleC22×C349C22×C4
FittingC22×C4×C349C4
prime radicalC23×D349C4
cosocleC2×Dic349C23
hypercenterC22×C4#13063703
hypocenterC349#407
LCSG ▷ C22×C349 ▷ C349
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×#19150243C2semidirect
2. #26013696C2semidirect
3. C22⋊#14584102C2semidirect
6. C2×#14584102C22semidirect
34. C22×C349M16semidirect
42. C2×D349M16semidirect
53. C349#407semidirect
95. C22#19150243semidirect

Maximal subgroups

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

subgroupindex
C2×#191502432
#260136962
C22⋊#145841022
C22×C4×D3492
#407349