Finite Group Databasebeta

← #36374410

Subgroups — #36374410

Order 22336.

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

normal subgroups only

This group has 104 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#26013670C211yesmaximal, characteristic, complemented
2#26013667C211yesmaximal, characteristic
3C2×#19150220C211yesmaximal, characteristic, complemented
4#26013647C211yesmaximal, characteristic, complemented
5#26013574C211yesmaximal, characteristic, complemented
6#26013555C211yesmaximal, characteristic, complemented
7#101×C349C211yesmaximal, characteristic, complemented
8#19150233C2211yescharacteristic
9C2×D1396C2211yescharacteristic
10#19150223—21no—
11#19150222—21no—
12#19150220—21no—
13#19150220—21no—
14#19150220—21no—
15D2792—21no—
16#19150217C2211yescharacteristic
17#19150216—21no—
18C2×#14584095C2211yescharacteristic
19C8×D349—21no—
20C2×Q8×C349C2211yescharacteristic
21M16×C349C2211yescharacteristic
22M16×C349C2211yescharacteristic
23C22×D349—21no—
24Dic698D411yescharacteristic
25D1396—21no—
26D1396—21no—
27D1396D411yescharacteristic
28C22⋊D349—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—
41C2×D349—41no—
42C2×D349—81no—
43C4×C349—41no—
44C4×C349C2×D411yescharacteristic
45C4×C349C2×D411yescharacteristic
46Dic349—21no—
47C2×C349—21no—
48C2×C349#12111yescharacteristic
49D349—41no—
50D349—81no—
51C349#47111yescharacteristic, complemented, Sylow
52#471—3491nomaximal, Sylow
53#137—3491no—
54AGL(1,ℤ/8)—3491no—
55C2×SD16—3491no—
56#131—3491no—
57#108—3491no—
58#101D34911yescharacteristic, complemented
59#100—3491no—
60#41—3491no—
61C2×Q8C2×D34911yescharacteristic
62C2×D4—3491no—
63Q16—6981no—
64SD16—6981no—
65SD16—6981no—
66SD16—6981no—
67SD16—6981no—
68D8—6981no—
69M16—3491no—
70M16—6981no—
71M16C2×D34911yescharacteristic
72M16C2×D34911yescharacteristic
73C2×C8—3491no—
74C2×C8—6981no—
75C23—6981no—
76Q8—21no—
77Q8—21no—
78Q8—3491no—
79D4—3491no—
80D4—6981no—
81D4—6981no—
82D4—6981no—
83C2×C4—21no—
84C2×C4—6981no—
85C2×C4C22×D34911yescharacteristic
86C8—21no—
87C8—21no—
88C8—3491no—
89C8—3491no—
90C8—6981no—
91C22—13961no—
92C22—6981no—
93C22—27921no—
94C22#1915023311yescharacteristic
95C4—41no—
96C4—6981no—
97C4D4×D34911yescharacteristic
98C4D4×D34911yescharacteristic
99C2—21no—
100C2—13961no—
101C2—27921no—
102C2#2601361211yescharacteristic
subgroupG/H
centerC2#26013612
commutator, cosocleC2×C4×C349C23
FrattiniC2×C4C22×D349
Fitting#101×C349C2
socleC2×C349#121
prime radical#26013667C2
hypercenter#101D349
hypocenterC349#471
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
1. #26013670C2semidirect
3. C2×#19150220C2semidirect
4. #26013647C2semidirect
5. #26013574C2semidirect
6. #26013555C2semidirect
7. #101×C349C2semidirect
51. C349#471semidirect
58. #101D349semidirect

Maximal subgroups

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

subgroupindex
#260136702
#260136672
C2×#191502202
#260136472
#260135742
#260135552
#101×C3492
#471349