Finite Group Databasebeta

← #36375136

Subgroups — #36375136

Order 22336.

190 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 50 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
1D349⋊M16C211yesmaximal, characteristic, complemented
2#26013718C211yesmaximal, characteristic, complemented
3#26013701C214yesmaximal, complemented
4C2×D4×D349C211yesmaximal, characteristic
5#19150243—21no—
6#19150242—21no—
7D349⋊C8C2212yescomplemented
8C4⋊#13063703C2212yescomplemented
9C22⋊#13063703—21no—
10C4×#13063703—21no—
11C23×D349—21no—
12C2×D1396C411yescharacteristic, complemented
13C2×C22⋊D349—21no—
14D4×D349—21no—
15D4×D349—21no—
16D4×D349C412yescomplemented
17D4×D349C2212yes—
18C2×C4×D349C2211yescharacteristic
19C2×D4×C349C411yescharacteristic, complemented
20C2×#13063703—22no—
21#14584102—22no—
22C22×D349—21no—
23C22×D349—22no—
24C22×D349—22no—
25C22×D349—44no—
26C22×D349D411yescharacteristic
27D1396—21no—
28D1396C2×C412yes—
29C22⋊D349—22no—
30C22⋊D349—22no—
31C2×Dic349D411yescharacteristic
32C4×D349C2×C411yescharacteristic
33C4×D349D411yescharacteristic
34C4×D349D411yescharacteristic
35C4×D349C2311yescharacteristic
36C23×C349—21no—
37D4×C349—21no—
38D4×C349C2×C412yes—
39C2×C4×C349C2×C411yescharacteristic
40C22×C349—22no—
41C22×C349—42no—
42C22×C349C22⋊C411yescharacteristic
43C2×D349—22no—
44C2×D349—22no—
45C2×D349—44no—
46C2×D349—42no—
47C2×D349—44no—
48C2×D349C22⋊C411yescharacteristic
49C2×D349C2×D411yescharacteristic
50#13063703—42no—
51C4×C349C22⋊C411yescharacteristic
52C4×C349C22×C411yescharacteristic
53Dic349C22⋊C411yescharacteristic
54Dic349C2×D411yescharacteristic
55C2×C349—21no—
56C2×C349—42no—
57C2×C349C2×C22⋊C411yescharacteristic
58D349—21no—
59D349—42no—
60D349AGL(1,ℤ/8)12yes—
61C349#41811yescharacteristic, complemented, Sylow
62#418—3491nomaximal, Sylow
63C22×D4—3491no—
64C2×M16—3491no—
65#117—3491no—
66#102—3494no—
67C24—6981no—
68C2×D4—3492no—
69C2×D4—3492no—
70C2×D4—3491no—
71C2×D4—6981no—
72C2×D4—6981no—
73C2×D4—6981no—
74C2×D4#1306370311yescharacteristic, complemented
75C22×C4—3491no—
76M16—6981no—
77M16—6981no—
78C2×C8—3492no—
79C4⋊C4—3492no—
80C22⋊C4—6981no—
81C42—6981no—
82C23—21no—
83C23—3491no—
84C23—13964no—
85C23—6982no—
86C23—6982no—
87C23—6981no—
88D4—21no—
89D4—3492no—
90D4—6982no—
91D4—6982no—
92D4—6981no—
93D4C2×#1306370312yes—
94C2×C4—3491no—
95C2×C4—3491no—
96C2×C4—3491no—
97C2×C4—3491no—
98C2×C4—3491no—
99C2×C4—6982no—
100C2×C4C2×#1306370311yescharacteristic
101C8—6982no—
102C22—22no—
103C22—42no—
104C22—3491no—
105C22—3491no—
106C22—13962no—
107C22—13964no—
108C22—13964no—
109C22—6982no—
110C22—6982no—
111C22C22⋊#1306370311yescharacteristic
112C4—3491no—
113C4—3491no—
114C4—13962no—
115C4C22⋊#1306370311yescharacteristic
116C4C22×#1306370311yescharacteristic
117C2—21no—
118C2—42no—
119C2—3492no—
120C2—13962no—
121C2—6981no—
122C2C2×C22⋊#1306370311yescharacteristic
subgroupG/H
centerC2C2×C22⋊#13063703
commutatorC4×C349C22×C4
FrattiniC4C22×#13063703
FittingC2×D4×C349C4
socleC2×C349C2×C22⋊C4
prime radicalC2×D4×D349C2
cosocleC4×D349C23
hypercenterC2×D4#13063703
hypocenterC349#418
LCSG ▷ C4×C349 ▷ C2×C349 ▷ C349
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. D349⋊M16C2semidirect
2. #26013718C2semidirect
3. #26013701C2semidirect
7. D349⋊C8C22semidirect
8. C4⋊#13063703C22semidirect
12. C2×D1396C4semidirect
16. D4×D349C4semidirect
19. C2×D4×C349C4semidirect
61. C349#418semidirect
74. C2×D4#13063703semidirect

Maximal subgroups

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

subgroupindex
D349⋊M162
#260137182
#260137012
C2×D4×D3492
#418349