Finite Group Databasebeta

← #36375123

Subgroups — #36375123

Order 22336.

158 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 48 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#26013718C212yesmaximal, complemented
2#26013698C212yesmaximal, complemented
3#26013697C212yesmaximal, complemented
4C2×#19150233C211yesmaximal, characteristic
5C4⋊#13063703—22no—
6C22⋊#13063703C2214yes—
7C4×#13063703—22no—
8#19150233—22no—
9#19150233—22no—
10C2×Dic698C411yescharacteristic, complemented
11C2×D1396C2211yescharacteristic
12C2×C22⋊D349C411yescharacteristic, complemented
13C2×C22⋊D349C2211yescharacteristic
14C2×C4×D349C411yescharacteristic, complemented
15C2×C4×D349C2211yescharacteristic
16C22×C4×C349C411yescharacteristic, complemented
17C2×#13063703—24no—
18C22×D349C2×C411yescharacteristic
19C22×D349C2311yescharacteristic
20Dic698—22no—
21D1396—22no—
22C22⋊D349—22no—
23C22⋊D349—22no—
24C2×Dic349C2×C411yescharacteristic
25C2×Dic349C2×C411yescharacteristic
26C4×D349—21no—
27C4×D349—21no—
28C4×D349D412yes—
29C4×D349D412yes—
30C23×C349C2×C411yescharacteristic
31C2×C4×C349—21no—
32C2×C4×C349—21no—
33C2×C4×C349C2×C411yescharacteristic
34C2×C4×C349C2×C411yescharacteristic
35C22×C349—21no—
36C22×C349—41no—
37C22×C349C22×C411yescharacteristic
38C2×D349—21no—
39C2×D349—41no—
40C2×D349—41no—
41C2×D349C2×D412yes—
42#13063703—44no—
43C4×C349—21no—
44C4×C349C22⋊C411yescharacteristic
45C4×C349C22⋊C411yescharacteristic
46Dic349—21no—
47Dic349C22⋊C412yes—
48C2×C349—21no—
49C2×C349—41no—
50C2×C349C2×C22⋊C411yescharacteristic
51D349—22no—
52D349—41no—
53C349#41011yescharacteristic, complemented, Sylow
54#410—3491nomaximal, Sylow
55C2×#41—3491no—
56#117—3492no—
57#99—3492no—
58#99—3492no—
59#41—6982no—
60#41—6982no—
61C2×Q8—3491no—
62C2×D4—3491no—
63C2×D4—3491no—
64C2×D4—3491no—
65C22×C4—3491no—
66C22×C4—3491no—
67C22×C4#1306370311yescharacteristic, complemented
68C4⋊C4—6982no—
69C22⋊C4—3494no—
70C42—6982no—
71C23—3491no—
72C23—3491no—
73C23C2×#1306370311yescharacteristic
74Q8—6982no—
75D4—6982no—
76D4—6982no—
77D4—6982no—
78C2×C4—21no—
79C2×C4—21no—
80C2×C4—3491no—
81C2×C4—3492no—
82C2×C4—3492no—
83C2×C4—3491no—
84C2×C4—6984no—
85C2×C4—6981no—
86C2×C4—6981no—
87C2×C4C2×#1306370311yescharacteristic
88C2×C4C2×#1306370311yescharacteristic
89C22—21no—
90C22—41no—
91C22—3492no—
92C22—13961no—
93C22—13961no—
94C22—6981no—
95C22C22×#1306370311yescharacteristic
96C4—21no—
97C4—3492no—
98C4—13964no—
99C4—6981no—
100C4C22⋊#1306370311yescharacteristic
101C4C22⋊#1306370311yescharacteristic
102C2—21no—
103C2—41no—
104C2—13961no—
105C2—6982no—
106C2C2×C22⋊#1306370311yescharacteristic
subgroupG/H
centerC4C22⋊#13063703
commutatorC22×C349C22×C4
FrattiniC22C22×#13063703
FittingC22×C4×C349C4
socleC2×C349C2×C22⋊C4
prime radicalC2×#19150233C2
cosocleC22×D349C23
hypercenterC22×C4#13063703
hypocenterC349#410
LCSG ▷ C22×C349 ▷ C2×C349 ▷ C349
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. #26013718C2semidirect
2. #26013698C2semidirect
3. #26013697C2semidirect
10. C2×Dic698C4semidirect
12. C2×C22⋊D349C4semidirect
14. C2×C4×D349C4semidirect
16. C22×C4×C349C4semidirect
53. C349#410semidirect
67. C22×C4#13063703semidirect

Maximal subgroups

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

subgroupindex
#260137182
#260136982
#260136972
C2×#191502332
#410349