Finite Group Databasebeta

← #36375095

Subgroups — #36375095

Order 22336.

170 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 64 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×C4⋊#13063703C212yesmaximal
2C2×C4⋊#13063703C211yesmaximal, characteristic
3C2×C4×#13063703C211yesmaximal, characteristic
4(C2×#13063703)⋊C4C212yesmaximal
5C4⋊C4×D349C211yesmaximal, characteristic
6C22×#13063703C2212yes—
7C22×#13063703C2211yescharacteristic
8C22×#13063703C2211yescharacteristic
9C4⋊#13063703—24no—
10C4⋊#13063703—22no—
11C4×#13063703—22no—
12C2×C4×D349C2212yes—
13C2×C4×D349C2211yescharacteristic
14C4⋊Dic349C411yescharacteristic, complemented
15#19150212C412yescomplemented
16C4⋊C4×C349C411yescharacteristic, complemented
17C2×#13063703—21no—
18C2×#13063703—21no—
19C2×#13063703—21no—
20C2×#13063703—21no—
21C2×#13063703—22no—
22C2×#13063703—22no—
23C2×#13063703—22no—
24C2×#13063703D412yes—
25C2×#13063703Q812yes—
26C22×D349C2311yescharacteristic
27C2×Dic349C2×C412yes—
28C2×Dic349C2×C411yescharacteristic
29C4×D349—22no—
30C4×D349—22no—
31C4×D349D412yes—
32C4×D349Q812yes—
33C2×C4×C349C2×C412yes—
34C2×C4×C349C2×C411yescharacteristic
35C22×C349C22×C411yescharacteristic
36C2×D349C2×D411yescharacteristic
37C2×D349C2×D411yescharacteristic
38C2×D349C2×Q811yescharacteristic
39C2×D349C2×Q811yescharacteristic
40C2×D349#4111yescharacteristic
41C2×D349#4111yescharacteristic
42#13063703—22no—
43#13063703—22no—
44#13063703—42no—
45C4×C349—22no—
46C4×C349C4⋊C412yescomplemented
47Dic349—22no—
48Dic349C4⋊C412yescomplemented
49C2×C349C2×C4⋊C411yescharacteristic
50C2×C349C4×D411yescharacteristic
51C2×C349C4×Q811yescharacteristic
52D349#12111yescharacteristic
53D349C22⋊Q811yescharacteristic
54D349#12511yescharacteristic
55D349C4⋊Q811yescharacteristic
56C349#38911yescharacteristic, complemented, Sylow
57#389—3491nomaximal, Sylow
58C2×C4⋊C4—3491no—
59C2×C4⋊C4—3491no—
60C2×C4⋊C4—3492no—
61C2×C42—3491no—
62#95—3492no—
63C22×C4—3491no—
64C22×C4—3491no—
65C22×C4—3491no—
66C22×C4—3492no—
67C22×C4—3492no—
68C4⋊C4—3492no—
69C4⋊C4—3491no—
70C4⋊C4—6982no—
71C4⋊C4—6984no—
72C4⋊C4#1306370311yescharacteristic, complemented
73C42—6982no—
74C23—3491no—
75C2×C4—3491no—
76C2×C4—3492no—
77C2×C4—3492no—
78C2×C4—3492no—
79C2×C4—3492no—
80C2×C4—3492no—
81C2×C4—6982no—
82C2×C4—6982no—
83C2×C4—6982no—
84C2×C4—6982no—
85C2×C4—6982no—
86C2×C4—6981no—
87C2×C4—6981no—
88C2×C4—6981no—
89C2×C4—6981no—
90C2×C4C2×#1306370312yes—
91C2×C4C2×#1306370311yescharacteristic
92C22—3491no—
93C22—3491no—
94C22—3491no—
95C22—3491no—
96C22—3491no—
97C22—3491no—
98C22C22×#1306370311yescharacteristic
99C4—22no—
100C4—3492no—
101C4—13962no—
102C4—6982no—
103C4—6982no—
104C4—6982no—
105C4C4⋊#1306370312yescomplemented
106C2—3491no—
107C2—3491no—
108C2—3491no—
109C2—3491no—
110C2C2×C4⋊#1306370311yescharacteristic
111C2D4×#1306370311yescharacteristic
112C2Q8×#1306370311yescharacteristic
subgroupG/H
center, FrattiniC22C22×#13063703
commutator, socleC22×C349C22×C4
FittingC4⋊C4×C349C4
prime radical, cosocleC22×D349C23
hypercenterC4⋊C4#13063703
hypocenterC349#389
LCSG ▷ C22×C349 ▷ C349
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
14. C4⋊Dic349C4semidirect
15. #19150212C4semidirect
16. C4⋊C4×C349C4semidirect
46. C4×C349C4⋊C4semidirect
48. Dic349C4⋊C4semidirect
56. C349#389semidirect
72. C4⋊C4#13063703semidirect
105. C4C4⋊#13063703semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊#130637032
C2×C4×#130637032
(C2×#13063703)⋊C42
C4⋊C4×D3492
#389349