Finite Group Databasebeta

← #36375176

Subgroups — #36375176

Order 22336.

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

normal subgroups only

This group has 124 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×#19150242C211yesmaximal, characteristic, complemented
2C2×D349⋊C8C211yesmaximal, characteristic, complemented
3C4⋊#14584102C211yesmaximal, characteristic, complemented
4#26013696C211yesmaximal, characteristic, complemented
5C22⋊#14584102C211yesmaximal, characteristic, complemented
6#26013694C211yesmaximal, characteristic, complemented
7#26013599C211yesmaximal, characteristic
8#19150242—22no—
9D349⋊C8—22no—
10C2×#14584102C2211yescharacteristic
11C2×#14584102C2211yescharacteristic
12C2×#14584102C2211yescharacteristic
13C2×#14584102C2211yescharacteristic
14C2×C22⋊D349C411yescharacteristic
15C22×Dic349C2211yescharacteristic
16C2×C4×D349C2211yescharacteristic
17#19150212C411yescharacteristic
18#19150210C411yescharacteristic
19C4×Dic349C2211yescharacteristic
20C22⋊C4×C349C411yescharacteristic
21#14584102—21no—
22#14584102—21no—
23#14584102—21no—
24#14584102D412yescomplemented
25C22×D349C2×C411yescharacteristic
26C22⋊D349—22no—
27C2×Dic349—21no—
28C2×Dic349—21no—
29C2×Dic349C2×C411yescharacteristic
30C2×Dic349C2×C411yescharacteristic
31C2×Dic349C2311yescharacteristic
32C4×D349—21no—
33C4×D349—21no—
34C23×C349C2×C411yescharacteristic
35C2×C4×C349C2×C411yescharacteristic
36C2×C4×C349C2×C411yescharacteristic
37C22×C349—21no—
38C22×C349—21no—
39C22×C349—21no—
40C22×C349C22×C411yescharacteristic
41C2×D349—21no—
42C2×D349—21no—
43C2×D349M1612yescomplemented
44C4×C349—21no—
45C4×C349—21no—
46Dic349—21no—
47Dic349—21no—
48Dic349C2×D411yescharacteristic
49Dic349#4111yescharacteristic
50C2×C349—41no—
51C2×C349C4×D411yescharacteristic
52C2×C349C2×M1611yescharacteristic
53C2×C349#13111yescharacteristic
54D349—22no—
55C349#43511yescharacteristic, complemented, Sylow
56#435—3491nomaximal, Sylow
57C2×M16—3491no—
58C22×C8—3491no—
59C4×D4—3491no—
60C4⋊C8—3491no—
61C22⋊C8—3491no—
62C22⋊C8—3491no—
63#97—3491no—
64C2×D4—3491no—
65C22×C4—3491no—
66C22×C4—3491no—
67M16—6982no—
68C2×C8—3491no—
69C2×C8—3491no—
70C2×C8—3491no—
71C2×C8—3491no—
72C2×C8—6982no—
73C4⋊C4—3491no—
74C22⋊C4—3491no—
75C22⋊C4#1306370311yescharacteristic
76C42—3491no—
77C23—3491no—
78C23C2×#1306370311yescharacteristic
79D4—6982no—
80C2×C4—3491no—
81C2×C4—3491no—
82C2×C4—3491no—
83C2×C4—6981no—
84C2×C4—6981no—
85C2×C4—6981no—
86C2×C4—6981no—
87C2×C4C2×#1306370311yescharacteristic
88C2×C4C2×#1306370311yescharacteristic
89C8—3492no—
90C8—6981no—
91C8—6981no—
92C8—6981no—
93C22—21no—
94C22—21no—
95C22—21no—
96C22—3492no—
97C22—6981no—
98C22—6981no—
99C22C22×#1306370311yescharacteristic
100C4—21no—
101C4—21no—
102C4—3491no—
103C4—3491no—
104C4—6981no—
105C4—6981no—
106C2—41no—
107C2—6982no—
108C2D4×#1306370311yescharacteristic
109C2D349⋊M1611yescharacteristic
110C2#2601372611yescharacteristic
subgroupG/H
center, FrattiniC22C22×#13063703
commutator, socleC22×C349C22×C4
FittingC22⋊C4×C349C4
prime radicalC2×C22⋊D349C4
cosocleC2×Dic349C23
hypercenterC22⋊C4#13063703
hypocenterC349#435
LCSG ▷ C22×C349 ▷ C349
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#19150242C2semidirect
2. C2×D349⋊C8C2semidirect
3. C4⋊#14584102C2semidirect
4. #26013696C2semidirect
5. C22⋊#14584102C2semidirect
6. #26013694C2semidirect
24. #14584102D4semidirect
43. C2×D349M16semidirect
55. C349#435semidirect

Maximal subgroups

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

subgroupindex
C2×#191502422
C2×D349⋊C82
C4⋊#145841022
#260136962
C22⋊#145841022
#260136942
#260135992
#435349