Finite Group Databasebeta

← #36375143

Subgroups — #36375143

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#26013704C214yesmaximal, complemented
4C2×#19150234C211yesmaximal, characteristic
5#19150243C2212yescomplemented
6#19150242—21no—
7D349⋊C8—21no—
8C4⋊#13063703—21no—
9C22⋊#13063703—21no—
10C4×#13063703C2212yescomplemented
11#19150234—21no—
12#19150234—21no—
13#19150234C412yescomplemented
14#19150234C2212yes—
15C2×D1396—21no—
16C2×D1396C411yescharacteristic, complemented
17C2×C4×D349—21no—
18C2×C4×D349C2211yescharacteristic
19C2×Q8×C349C411yescharacteristic, complemented
20C2×#13063703—22no—
21#14584102—22no—
22C22×D349—21no—
23C22×D349D411yescharacteristic
24D1396—22no—
25D1396—22no—
26D1396—21no—
27D1396C2×C412yes—
28C2×Dic349D411yescharacteristic
29C4×D349—22no—
30C4×D349—22no—
31C4×D349C2×C411yescharacteristic
32C4×D349D411yescharacteristic
33C4×D349D411yescharacteristic
34C4×D349C2311yescharacteristic
35Q8×C349—21no—
36Q8×C349C2×C412yes—
37C2×C4×C349—21no—
38C2×C4×C349C2×C411yescharacteristic
39C22×C349C22⋊C411yescharacteristic
40C2×D349—22no—
41C2×D349—41no—
42C2×D349—42no—
43C2×D349C22⋊C411yescharacteristic
44C2×D349C2×D411yescharacteristic
45#13063703—42no—
46C4×C349—22no—
47C4×C349C22⋊C411yescharacteristic
48C4×C349C22×C411yescharacteristic
49Dic349C22⋊C411yescharacteristic
50Dic349C2×D411yescharacteristic
51C2×C349—21no—
52C2×C349C2×C22⋊C411yescharacteristic
53D349—21no—
54D349—21no—
55D349—42no—
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#1306370311yescharacteristic, complemented
67C2×D4—3491no—
68C2×D4—6981no—
69C22×C4—3491no—
70C22×C4—6981no—
71M16—3492no—
72M16—6981no—
73C2×C8—6981no—
74C4⋊C4—6981no—
75C22⋊C4—6981no—
76C42—3492no—
77C23—3491no—
78C23—6981no—
79Q8—21no—
80Q8C2×#1306370312yes—
81D4—3492no—
82D4—6982no—
83D4—6982no—
84D4—6981no—
85C2×C4—21no—
86C2×C4—3491no—
87C2×C4—3491no—
88C2×C4—3491no—
89C2×C4—3491no—
90C2×C4—3491no—
91C2×C4—6982no—
92C2×C4—6982no—
93C2×C4—6982no—
94C2×C4C2×#1306370311yescharacteristic
95C8—6982no—
96C22—3491no—
97C22—3491no—
98C22—13962no—
99C22—13961no—
100C22—6982no—
101C22C22⋊#1306370311yescharacteristic
102C4—22no—
103C4—3491no—
104C4—3491no—
105C4—13962no—
106C4C22⋊#1306370311yescharacteristic
107C4C22×#1306370311yescharacteristic
108C2—21no—
109C2—13962no—
110C2—6981no—
111C2—6981no—
112C2C2×C22⋊#1306370311yescharacteristic
subgroupG/H
centerC2C2×C22⋊#13063703
commutatorC4×C349C22×C4
FrattiniC4C22×#13063703
FittingC2×Q8×C349C4
socleC2×C349C2×C22⋊C4
prime radicalC2×#19150234C2
cosocleC4×D349C23
hypercenterC2×Q8#13063703
hypocenterC349#421
LCSG ▷ C4×C349 ▷ C2×C349 ▷ C349
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. D349⋊M16C2semidirect
2. #26013718C2semidirect
3. #26013704C2semidirect
5. #19150243C22semidirect
10. C4×#13063703C22semidirect
13. #19150234C4semidirect
16. C2×D1396C4semidirect
19. C2×Q8×C349C4semidirect
56. C349#421semidirect
66. C2×Q8#13063703semidirect

Maximal subgroups

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

subgroupindex
D349⋊M162
#260137182
#260137042
C2×#191502342
#421349