Finite Group Databasebeta

← #36374258

Subgroups — #36374258

Order 22336.

106 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 106 conjugacy classes of subgroups — too many to draw. Only its 45 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
1#26013659C211yesmaximal, characteristic
2#26013647C211yesmaximal, characteristic, complemented
3#26013646C211yesmaximal, characteristic, complemented
4#26013574C211yesmaximal, characteristic, complemented
5#26013567C211yesmaximal, characteristic, complemented
6C4×#14584095C211yesmaximal, characteristic, complemented
7#104×C349C211yesmaximal, characteristic, complemented
8#19150233C2211yescharacteristic
9#19150223C411yescharacteristic, complemented
10#19150221C411yescharacteristic, complemented
11#19150220C411yescharacteristic, complemented
12#19150218C411yescharacteristic, complemented
13#19150217—21no—
14#19150217C2211yescharacteristic
15#19150216—21no—
16C2×#14584095—21no—
17C2×#14584095C2211yescharacteristic
18C2×#14584095C2211yescharacteristic
19C8×D349—21no—
20#41×C349C2211yescharacteristic
21M16×C349C2211yescharacteristic
22C42×C349C2211yescharacteristic
23Dic698C2×C411yescharacteristic
24D1396C2×C411yescharacteristic
25C22⋊D349—21no—
26C4×D349—21no—
27#14584095—21no—
28#14584095C2×C411yescharacteristic
29#14584095C2×C411yescharacteristic
30#14584095D411yescharacteristic
31#14584095D411yescharacteristic
32Q8×C349C2×C411yescharacteristic
33D4×C349—21no—
34D4×C349C2×C411yescharacteristic
35C2×C4×C349—21no—
36C2×C4×C349—21no—
37C2×C4×C349C2311yescharacteristic
38C8×C349—21no—
39C22×C349—21no—
40C22×C349#4111yescharacteristic
41C2×D349—21no—
42C4×C349—22no—
43C4×C349—21no—
44C4×C349C22×C411yescharacteristic
45C4×C349C2×D411yescharacteristic
46Dic349—21no—
47C2×C349—21no—
48C2×C349—41no—
49C2×C349C4×D411yescharacteristic
50D349—41no—
51C349#44311yescharacteristic, complemented, Sylow
52#443—3491nomaximal, Sylow
53#135—3491no—
54#131—3491no—
55#131—3491no—
56#108—3491no—
57#104—3491no—
58#104D34911yescharacteristic, complemented
59C4×C8—3491no—
60#41—3491no—
61#41C2×D34911yescharacteristic
62Q16—3491no—
63SD16—3491no—
64SD16—3491no—
65D8—3491no—
66M16—3491no—
67M16—6981no—
68M16—6981no—
69M16C2×D34911yescharacteristic
70C2×C8—3491no—
71C2×C8—3491no—
72C2×C8—6981no—
73C2×C8—6981no—
74C42C2×D34911yescharacteristic
75Q8—3491no—
76Q8C4×D34911yescharacteristic
77D4—21no—
78D4—3491no—
79D4—6981no—
80D4C4×D34911yescharacteristic
81C2×C4—21no—
82C2×C4—21no—
83C2×C4—6981no—
84C2×C4C22×D34911yescharacteristic
85C8—21no—
86C8—3491no—
87C8—3491no—
88C8—3491no—
89C8—3491no—
90C8—6981no—
91C22—21no—
92C22—6981no—
93C22#1915023211yescharacteristic
94C4—22no—
95C4—21no—
96C4—6981no—
97C4C2×C4×D34911yescharacteristic
98C4D4×D34911yescharacteristic
99C2—21no—
100C2—41no—
101C2—13961no—
102C2#2601359911yescharacteristic
subgroupG/H
centerC4D4×D349
commutatorC4×C349C22×C4
FrattiniC2×C4C22×D349
Fitting#104×C349C2
socleC2×C349C4×D4
prime radical#26013659C2
cosocleC2×C4×C349C23
hypercenter#104D349
hypocenterC349#443
LCSG ▷ C4×C349 ▷ C2×C349 ▷ C349
UCSC1 ◁ C4 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #26013647C2semidirect
3. #26013646C2semidirect
4. #26013574C2semidirect
5. #26013567C2semidirect
6. C4×#14584095C2semidirect
7. #104×C349C2semidirect
9. #19150223C4semidirect
10. #19150221C4semidirect
11. #19150220C4semidirect
12. #19150218C4semidirect
51. C349#443semidirect
58. #104D349semidirect

Maximal subgroups

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

subgroupindex
#260136592
#260136472
#260136462
#260135742
#260135672
C4×#145840952
#104×C3492
#443349