Finite Group Databasebeta

← #22625050

Subgroups — #22625050

Order 9344.

122 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 122 conjugacy classes of subgroups — too many to draw. Only its 20 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#17989491C211yesmaximal, characteristic, complemented
2#17989445C211yesmaximal, characteristic, complemented
3#17988755C211yesmaximal, characteristic
4#14556658—21no—
5#14556650—21no—
6#14556616—21no—
7#14556587C2211yescharacteristic
8#14556518—21no—
9#14556508C411yescharacteristic, complemented
10H(5,𝔽2)×C73C411yescharacteristic, complemented
11C2×#10596833—41no—
12C22⋊#64408—41no—
13C2×D292D411yescharacteristic
14C2×C22⋊D73—41no—
15#11924015—41no—
16#11924013—41no—
17#11924012—21no—
18C4×Dic73D411yescharacteristic
19#41×C73—21no—
20#41×C73—41no—
21C2×D4×C73—41no—
22C2×D4×C73—41no—
23C2×D4×C73C2×C411yescharacteristic
24C23×C73—21no—
25C23×C73—41no—
26C22×D73—21no—
27C2×#64408—81no—
28Q8×C73—21no—
29D4×C73—21no—
30D4×C73—41no—
31D4×C73—42no—
32D4×C73—41no—
33C2×C4×C73—41no—
34C2×C4×C73—41no—
35C2×C4×C73C22⋊C411yescharacteristic
36C22⋊D73—81no—
37C22⋊D73—81no—
38C2×Dic73—21no—
39D292—41no—
40#10596833—81no—
41#10596831—41no—
42C22×C73—41no—
43C22×C73—41no—
44C22×C73—81no—
45C22×C73—161no—
46C22×C73#9911yescharacteristic
47C2×D73—41no—
48C2×D73—81no—
49#64408—161no—
50C4×C73—21no—
51C4×C73—41no—
52Dic73—21no—
53Dic73—21no—
54C2×C73—21no—
55C2×C73—81no—
56C2×C73—81no—
57C2×C73AΣL(1,𝔽16)11yescharacteristic
58D73—81no—
59#1402—731nomaximal, Sylow
60C73#140211yescharacteristic, complemented, Sylow
61#453—731no—
62#353—731no—
63#331—731no—
64H(5,𝔽2)#6440811yescharacteristic, complemented
65AGL(1,ℤ/8)—1461no—
66#127—731no—
67C4⋊C8—1461no—
68#104—1461no—
69#100—731no—
70#99—1461no—
71#41—21no—
72#41—41no—
73C2×D4—41no—
74C2×D4—41no—
75C2×D4—2921no—
76C2×D4—731no—
77C2×D4C2×#6440811yescharacteristic
78SD16—2921no—
79D8—2921no—
80M16—1461no—
81C2×C8—2921no—
82C22⋊C4—2921no—
83C42—731no—
84C23—21no—
85C23—41no—
86C23—1461no—
87Q8—21no—
88D4—21no—
89D4—41no—
90D4—42no—
91D4—41no—
92D4—2921no—
93D4—5841no—
94D4—5841no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—5841no—
98C2×C4—1461no—
99C2×C4C22⋊#6440811yescharacteristic
100C8—2921no—
101C8—5841no—
102C22—41no—
103C22—41no—
104C22—81no—
105C22—161no—
106C22—2921no—
107C22—5841no—
108C22#1455664911yescharacteristic
109C4—21no—
110C4—41no—
111C4—11681no—
112C4—1461no—
113C4—1461no—
114C2—21no—
115C2—81no—
116C2—81no—
117C2—5841no—
118C2#1798948711yescharacteristic
subgroupG/H
centerC2#17989487
commutatorC2×D4×C73C2×C4
FrattiniC2×D4C2×#64408
FittingH(5,𝔽2)×C73C4
socleC2×C73AΣL(1,𝔽16)
hypercenterH(5,𝔽2)#64408
hypocenterC73#1402
LCSG ▷ C2×D4×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×D4 ◁ H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #17989491C2semidirect
2. #17989445C2semidirect
9. #14556508C4semidirect
10. H(5,𝔽2)×C73C4semidirect
60. C73#1402semidirect
64. H(5,𝔽2)#64408semidirect