Finite Group Databasebeta

← #36374418

Subgroups — #36374418

Order 22336.

100 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 100 conjugacy classes of subgroups — too many to draw. Only its 35 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#26013672C211yesmaximal, characteristic
2#26013670C211yesmaximal, characteristic
3C2×#19150223C211yesmaximal, characteristic, complemented
4#26013647C211yesmaximal, characteristic
5#26013574C211yesmaximal, characteristic, complemented
6#26013557C211yesmaximal, characteristic, complemented
7#101×C349C211yesmaximal, characteristic, complemented
8#19150233C2211yescharacteristic
9C2×Dic698C2211yescharacteristic
10Dic1396—21no—
11#19150223—21no—
12#19150223—21no—
13#19150223—21no—
14#19150222—21no—
15#19150220—21no—
16#19150217C2211yescharacteristic
17#19150216—21no—
18C2×#14584095C2211yescharacteristic
19C8×D349—21no—
20C2×Q8×C349C2211yescharacteristic
21M16×C349C2211yescharacteristic
22M16×C349C2211yescharacteristic
23Dic698—21no—
24Dic698—21no—
25Dic698D411yescharacteristic
26D1396D411yescharacteristic
27C22⋊D349—21no—
28C2×Dic349—21no—
29C4×D349—21no—
30#14584095—21no—
31#14584095D411yescharacteristic
32#14584095D411yescharacteristic
33Q8×C349—21no—
34Q8×C349—21no—
35C2×C4×C349—21no—
36C2×C4×C349C2311yescharacteristic
37C8×C349—21no—
38C8×C349—21no—
39C22×C349#4111yescharacteristic
40C2×D349—21no—
41C4×C349—41no—
42C4×C349C2×D411yescharacteristic
43C4×C349C2×D411yescharacteristic
44Dic349—21no—
45Dic349—41no—
46C2×C349—21no—
47C2×C349#12111yescharacteristic
48D349—41no—
49C349#47311yescharacteristic, complemented, Sylow
50#473—3491nomaximal, Sylow
51#137—3491no—
52#137—3491no—
53C2×Q16—3491no—
54#131—3491no—
55#108—3491no—
56#101—3491no—
57#101D34911yescharacteristic, complemented
58#41—3491no—
59C2×Q8—3491no—
60C2×Q8C2×D34911yescharacteristic
61Q16—6981no—
62Q16—6981no—
63Q16—6981no—
64Q16—6981no—
65SD16—6981no—
66SD16—6981no—
67M16—3491no—
68M16—6981no—
69M16C2×D34911yescharacteristic
70M16C2×D34911yescharacteristic
71C2×C8—3491no—
72C2×C8—6981no—
73Q8—21no—
74Q8—21no—
75Q8—3491no—
76Q8—6981no—
77Q8—6981no—
78D4—3491no—
79D4—6981no—
80C2×C4—21no—
81C2×C4—6981no—
82C2×C4—6981no—
83C2×C4C22×D34911yescharacteristic
84C8—21no—
85C8—21no—
86C8—3491no—
87C8—3491no—
88C8—6981no—
89C22—6981no—
90C22#1915023311yescharacteristic
91C4—41no—
92C4—13961no—
93C4—6981no—
94C4D4×D34911yescharacteristic
95C4D4×D34911yescharacteristic
96C2—21no—
97C2—13961no—
98C2#2601361211yescharacteristic
subgroupG/H
centerC2#26013612
commutator, cosocleC2×C4×C349C23
FrattiniC2×C4C22×D349
Fitting#101×C349C2
socleC2×C349#121
prime radical#19150233C22
hypercenter#101D349
hypocenterC349#473
LCSG ▷ C2×C4×C349 ▷ C2×C349 ▷ C349
UCSC1 ◁ C2 ◁ C2×C4 ◁ #101

Complements

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

NH ≅ G/Ntype
3. C2×#19150223C2semidirect
5. #26013574C2semidirect
6. #26013557C2semidirect
7. #101×C349C2semidirect
49. C349#473semidirect
57. #101D349semidirect

Maximal subgroups

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

subgroupindex
#260136722
#260136702
C2×#191502232
#260136472
#260135742
#260135572
#101×C3492
#473349