Finite Group Databasebeta

← #37526669

Subgroups — #37526669

Order 22976.

124 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 43 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
1C2×C8×D359C211yesmaximal, characteristic, complemented
2#26039991C211yesmaximal, characteristic, complemented
3#26039986C211yesmaximal, characteristic
4#26039947C211yesmaximal, characteristic, complemented
5#26039939C211yesmaximal, characteristic, complemented
6#26039936C211yesmaximal, characteristic, complemented
7C2×SD16×C359C211yesmaximal, characteristic, complemented
8C2×C22⋊D359—21no—
9C2×C4×D359C2211yescharacteristic
10C2×C359⋊C8C2211yescharacteristic
11C8×D359—22no—
12C4⋊Dic359C2211yescharacteristic
13C4⋊Dic359C2211yescharacteristic
14Dic359⋊C4—21no—
15C22⋊Dic359—21no—
16(C2×D359)⋊C4—21no—
17C2×Q8×C359C2211yescharacteristic
18C2×D4×C359C2211yescharacteristic
19SD16×C359—22no—
20C2×C8×C359C2211yescharacteristic
21C22×D359D411yescharacteristic
22C22⋊D359—42no—
23C2×Dic359—21no—
24C2×Dic359—21no—
25C2×Dic359D411yescharacteristic
26C4×D359—21no—
27C4×D359—21no—
28C359⋊C8—21no—
29C23×C359—21no—
30Q8×C359—21no—
31Q8×C359—21no—
32D4×C359—21no—
33D4×C359—21no—
34C2×C4×C359—21no—
35C2×C4×C359C2311yescharacteristic
36C8×C359D412yescomplemented
37C22×C359—41no—
38C22×C359—41no—
39C22×C359—41no—
40C22×C359C2×D411yescharacteristic
41C2×D359—21no—
42C2×D359—21no—
43C2×D359SD1612yescomplemented
44C4×C359—41no—
45C4×C359C2×D411yescharacteristic
46C4×C359#4111yescharacteristic
47Dic359—21no—
48Dic359—41no—
49Dic359—41no—
50C2×C359—81no—
51C2×C359#12111yescharacteristic
52C2×C359C2×SD1611yescharacteristic
53C2×C359#13511yescharacteristic
54D359—22no—
55C359#46511yescharacteristic, complemented, Sylow
56#465—3591nomaximal, Sylow
57C2×SD16D35911yescharacteristic, complemented
58C22×C8—3591no—
59C22⋊Q8—3591no—
60#121—3591no—
61#106—3591no—
62#103—3591no—
63#102—3591no—
64C2×Q8C2×D35911yescharacteristic
65C2×D4—7181no—
66C2×D4C2×D35911yescharacteristic
67C22×C4—3591no—
68SD16—22no—
69C2×C8—3591no—
70C2×C8—7182no—
71C2×C8C2×D35911yescharacteristic
72C4⋊C4—3591no—
73C4⋊C4—3591no—
74C4⋊C4—7181no—
75C22⋊C4—7181no—
76C22⋊C4—7181no—
77C23—21no—
78C23—3591no—
79Q8—21no—
80Q8—21no—
81D4—21no—
82D4—21no—
83D4—14362no—
84C2×C4—21no—
85C2×C4—3591no—
86C2×C4—7181no—
87C2×C4—7181no—
88C2×C4—7181no—
89C2×C4—7181no—
90C2×C4C22×D35911yescharacteristic
91C8—7181no—
92C8C22⋊D35912yescomplemented
93C22—41no—
94C22—41no—
95C22—41no—
96C22—3592no—
97C22—7181no—
98C22—7181no—
99C22D4×D35911yescharacteristic
100C4—41no—
101C4—14361no—
102C4—14361no—
103C4—7181no—
104C4C2×C22⋊D35911yescharacteristic
105C4#1915334011yescharacteristic
106C2—81no—
107C2—7182no—
108C2#2603998611yescharacteristic
109C2SD16×D35911yescharacteristic
110C2#2604003611yescharacteristic
subgroupG/H
centerC22D4×D359
commutator, cosocleC2×C4×C359C23
FrattiniC2×C4C22×D359
FittingC2×SD16×C359C2
socleC22×C359C2×D4
prime radical#26039986C2
hypercenterC2×SD16D359
hypocenterC359#465
LCSG ▷ C2×C4×C359 ▷ C2×C359 ▷ C359
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×C8×D359C2semidirect
2. #26039991C2semidirect
4. #26039947C2semidirect
5. #26039939C2semidirect
6. #26039936C2semidirect
7. C2×SD16×C359C2semidirect
36. C8×C359D4semidirect
43. C2×D359SD16semidirect
55. C359#465semidirect
57. C2×SD16D359semidirect
92. C8C22⋊D359semidirect

Maximal subgroups

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

subgroupindex
C2×C8×D3592
#260399912
#260399862
#260399472
#260399392
#260399362
C2×SD16×C3592
#465359