Finite Group Databasebeta

← #36375017

Subgroups — #36375017

Order 22336.

114 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 114 conjugacy classes of subgroups — too many to draw. Only its 46 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×D349⋊C8C211yesmaximal, characteristic
2C2×C4⋊#13063703C211yesmaximal, characteristic
3C4⋊C4×D349C211yesmaximal, characteristic
4C22×#13063703—21no—
5D349⋊C8—21no—
6D349⋊C8C412yescomplemented
7C2×#14584102—21no—
8C4⋊#13063703—21no—
9C4⋊#13063703C412yescomplemented
10C2×C4×D349—21no—
11C2×C4×D349C2211yescharacteristic
12C4⋊Dic349C411yescharacteristic, complemented
13#19150212—21no—
14C4⋊C4×C349C411yescharacteristic, complemented
15C2×#13063703—22no—
16C2×#13063703—41no—
17C2×#13063703—41no—
18#14584102—22no—
19C22×D349D411yescharacteristic
20C2×Dic349—21no—
21C2×Dic349D411yescharacteristic
22C4×D349—41no—
23C4×D349—41no—
24C4×D349C2×C411yescharacteristic
25C4×D349C2×C411yescharacteristic
26C4×D349D411yescharacteristic
27C4×D349Q811yescharacteristic
28C2×C4×C349—21no—
29C2×C4×C349C2×C411yescharacteristic
30C22×C349C22⋊C411yescharacteristic
31C2×D349C22⋊C411yescharacteristic
32C2×D349C4⋊C411yescharacteristic
33C2×D349D811yescharacteristic
34C2×D349SD1611yescharacteristic
35C2×D349SD1611yescharacteristic
36C2×D349Q1611yescharacteristic
37#13063703—42no—
38C4×C349—41no—
39C4×C349C4211yescharacteristic
40C4×C349C4⋊C411yescharacteristic
41Dic349—41no—
42Dic349C22⋊C411yescharacteristic
43Dic349C4⋊C411yescharacteristic
44C2×C349#9511yescharacteristic
45C2×C349#10211yescharacteristic
46C2×C349#10311yescharacteristic
47D349#10211yescharacteristic
48D349#10311yescharacteristic
49D349#10611yescharacteristic
50D349#10711yescharacteristic
51C349#34011yescharacteristic, complemented, Sylow
52#340—3491nomaximal, Sylow
53C22×C8—3491no—
54C2×C4⋊C4—3491no—
55C2×C4⋊C4—3491no—
56C22×C4—3491no—
57C22×C4—6981no—
58C22×C4—6981no—
59C2×C8—3492no—
60C2×C8—6981no—
61C2×C8—6981no—
62C4⋊C4—3492no—
63C4⋊C4—3491no—
64C4⋊C4—6981no—
65C4⋊C4—6981no—
66C4⋊C4#1306370311yescharacteristic, complemented
67C23—3491no—
68C2×C4—21no—
69C2×C4—3491no—
70C2×C4—3491no—
71C2×C4—3491no—
72C2×C4—3491no—
73C2×C4—3491no—
74C2×C4—13961no—
75C2×C4—13961no—
76C2×C4—13961no—
77C2×C4—13961no—
78C2×C4—6982no—
79C2×C4—6981no—
80C2×C4C2×#1306370311yescharacteristic
81C8—6982no—
82C22—3491no—
83C22—3491no—
84C22—3491no—
85C22—3491no—
86C22—3491no—
87C22—3491no—
88C22C22⋊#1306370311yescharacteristic
89C4—41no—
90C4—3491no—
91C4—3491no—
92C4—13962no—
93C4—13961no—
94C4C4×#1306370311yescharacteristic
95C4C4⋊#1306370311yescharacteristic
96C2—3491no—
97C2—3491no—
98C2—3491no—
99C2—3491no—
100C2(C2×#13063703)⋊C411yescharacteristic
101C2#2601370111yescharacteristic
102C2#2601370211yescharacteristic
subgroupG/H
centerC22C22⋊#13063703
commutatorC4×C349C42
FrattiniC2×C4C2×#13063703
FittingC4⋊C4×C349C4
socleC22×C349C22⋊C4
prime radicalC22×D349D4
cosocleC2×C4×D349C22
hypercenterC4⋊C4#13063703
hypocenterC349#340
LCSG ▷ C4×C349 ▷ C2×C349 ▷ C349
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
6. D349⋊C8C4semidirect
9. C4⋊#13063703C4semidirect
12. C4⋊Dic349C4semidirect
14. C4⋊C4×C349C4semidirect
51. C349#340semidirect
66. C4⋊C4#13063703semidirect

Maximal subgroups

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

subgroupindex
C2×D349⋊C82
C2×C4⋊#130637032
C4⋊C4×D3492
#340349