Finite Group Databasebeta

← #36375142

Subgroups — #36375142

Order 22336.

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

normal subgroups only

This group has 154 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
1D349⋊M16C211yesmaximal, characteristic, complemented
2#26013718C211yesmaximal, characteristic, complemented
3#26013703C214yesmaximal, complemented
4C2×#19150232C211yesmaximal, characteristic
5#19150243C2212yescomplemented
6#19150242—21no—
7D349⋊C8—21no—
8C4⋊#13063703—21no—
9C22⋊#13063703—21no—
10C4×#13063703C2212yescomplemented
11#19150232—21no—
12#19150232—21no—
13#19150232C412yescomplemented
14#19150232C2212yes—
15C2×Dic698C411yescharacteristic, complemented
16C2×C22⋊D349—21no—
17C22×Dic349—21no—
18C2×C4×D349C2211yescharacteristic
19C2×D4×C349C411yescharacteristic, complemented
20C2×#13063703—22no—
21#14584102—22no—
22C22×D349D411yescharacteristic
23Dic698—21no—
24Dic698C2×C412yes—
25C22⋊D349—22no—
26C22⋊D349—22no—
27C2×Dic349—21no—
28C2×Dic349—22no—
29C2×Dic349—22no—
30C2×Dic349D411yescharacteristic
31C4×D349C2×C411yescharacteristic
32C4×D349D411yescharacteristic
33C4×D349D411yescharacteristic
34C4×D349C2311yescharacteristic
35C23×C349—21no—
36D4×C349—21no—
37D4×C349C2×C412yes—
38C2×C4×C349C2×C411yescharacteristic
39C22×C349—22no—
40C22×C349—42no—
41C22×C349C22⋊C411yescharacteristic
42C2×D349—41no—
43C2×D349C22⋊C411yescharacteristic
44C2×D349C2×D411yescharacteristic
45#13063703—42no—
46C4×C349C22⋊C411yescharacteristic
47C4×C349C22×C411yescharacteristic
48Dic349—22no—
49Dic349C22⋊C411yescharacteristic
50Dic349C2×D411yescharacteristic
51C2×C349—21no—
52C2×C349—42no—
53C2×C349C2×C22⋊C411yescharacteristic
54D349—21no—
55D349—21no—
56C349#42111yescharacteristic, complemented, Sylow
57#421—3491nomaximal, Sylow
58C2×#41—3491no—
59C2×M16—3491no—
60#117—3491no—
61#104—3494no—
62#41—3492no—
63#41—3492no—
64#41—6981no—
65#41—6981no—
66C2×Q8—3491no—
67C2×D4—6981no—
68C2×D4#1306370311yescharacteristic, complemented
69C22×C4—3491no—
70C22×C4—6981no—
71M16—3492no—
72M16—6981no—
73C2×C8—6981no—
74C4⋊C4—6981no—
75C22⋊C4—6981no—
76C42—3492no—
77C23—21no—
78C23—3491no—
79Q8—3492no—
80Q8—6981no—
81D4—21no—
82D4—6982no—
83D4—6982no—
84D4C2×#1306370312yes—
85C2×C4—3491no—
86C2×C4—3491no—
87C2×C4—3491no—
88C2×C4—3491no—
89C2×C4—3491no—
90C2×C4—6982no—
91C2×C4—6982no—
92C2×C4—6982no—
93C2×C4—6981no—
94C2×C4C2×#1306370311yescharacteristic
95C8—6982no—
96C22—22no—
97C22—42no—
98C22—3491no—
99C22—3491no—
100C22—13961no—
101C22C22⋊#1306370311yescharacteristic
102C4—3491no—
103C4—3491no—
104C4—13962no—
105C4—6982no—
106C4C22⋊#1306370311yescharacteristic
107C4C22×#1306370311yescharacteristic
108C2—21no—
109C2—42no—
110C2—6981no—
111C2—6981no—
112C2C2×C22⋊#1306370311yescharacteristic
subgroupG/H
centerC2C2×C22⋊#13063703
commutatorC4×C349C22×C4
FrattiniC4C22×#13063703
FittingC2×D4×C349C4
socleC2×C349C2×C22⋊C4
prime radicalC2×#19150232C2
cosocleC4×D349C23
hypercenterC2×D4#13063703
hypocenterC349#421
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. #26013703C2semidirect
5. #19150243C22semidirect
10. C4×#13063703C22semidirect
13. #19150232C4semidirect
15. C2×Dic698C4semidirect
19. C2×D4×C349C4semidirect
56. C349#421semidirect
68. 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
#260137032
C2×#191502322
#421349