Finite Group Databasebeta

← #22625556

Subgroups — #22625556

Order 9344.

152 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 56 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#17989638C211yesmaximal, characteristic
2Q8×#10596833C211yesmaximal, characteristic
3#17989449C211yesmaximal, characteristic
4Q8⋊#10596833C211yesmaximal, characteristic
5Q8⋊#10596833C211yesmaximal, characteristic
6#17989429C211yesmaximal, characteristic
7Q16×Dic73C211yesmaximal, characteristic
8#14556658—21no—
9C4⋊#10596833—21no—
10C4⋊#10596833C2211yescharacteristic
11C4⋊#10596833C2211yescharacteristic
12#14556646—21no—
13C4×#10596833—21no—
14C4×#10596833C2211yescharacteristic
15C4×#10596833C2211yescharacteristic
16Q8×Dic73C2211yescharacteristic
17Q8×Dic73C2211yescharacteristic
18#14556525C411yescharacteristic
19#14556515C411yescharacteristic
20#14556515C411yescharacteristic
21C8×Dic73C2211yescharacteristic
22C2×Q16×C73C411yescharacteristic
23C2×#10596833—21no—
24C2×#10596833—21no—
25C2×#10596833—21no—
26C2×#10596833D411yescharacteristic
27C2×#10596833D411yescharacteristic
28C2×#10596831C2×C411yescharacteristic
29C4⋊Dic73—21no—
30C4⋊Dic73—21no—
31C4⋊Dic73C2×C411yescharacteristic
32C4⋊Dic73C2×C411yescharacteristic
33C4×Dic73—21no—
34C4×Dic73—21no—
35C4×Dic73C2311yescharacteristic
36C2×Q8×C73C2×C411yescharacteristic
37C2×Q8×C73C2×C411yescharacteristic
38Q16×C73—22no—
39C2×C8×C73C2×C411yescharacteristic
40Q8×C73—21no—
41Q8×C73—21no—
42Q8×C73—21no—
43Q8×C73M1612yes—
44C2×C4×C73—21no—
45C2×C4×C73—21no—
46C2×C4×C73C22×C411yescharacteristic
47C2×Dic73—21no—
48C2×Dic73—21no—
49C2×Dic73C2×D411yescharacteristic
50C2×Dic73#4111yescharacteristic
51#10596833—22no—
52#10596833—21no—
53#10596833—21no—
54#10596833—41no—
55#10596833—41no—
56C8×C73—21no—
57#10596831—21no—
58C22×C73C4×D411yescharacteristic
59C4×C73—22no—
60C4×C73—41no—
61C4×C73C2×M1611yescharacteristic
62C4×C73#13111yescharacteristic
63Dic73—21no—
64Dic73—41no—
65Dic73—41no—
66Dic73#13711yescharacteristic
67Dic73#13711yescharacteristic
68C2×C73#43511yescharacteristic
69C2×C73#44111yescharacteristic
70C2×C73#44311yescharacteristic
71#1587—731nomaximal, Sylow
72C73#158711yescharacteristic, complemented, Sylow
73#446—731no—
74C8×Q8—731no—
75C4×Q16—731no—
76#334—731no—
77Q8⋊C8—731no—
78Q8⋊C8—731no—
79#322—731no—
80C2×Q16#6440811yescharacteristic
81C4×Q8—731no—
82C4×Q8—731no—
83#107—731no—
84C4⋊C8—731no—
85C4⋊C8—731no—
86C4⋊C8—1461no—
87C4⋊C8—1461no—
88#103—731no—
89#103—731no—
90#97—1461no—
91C4×C8—731no—
92C4×C8—731no—
93C4×C8—731no—
94C4×C8—1461no—
95C2×Q8C2×#6440811yescharacteristic
96C2×Q8C2×#6440811yescharacteristic
97Q16—22no—
98C2×C8—731no—
99C2×C8—731no—
100C2×C8—731no—
101C2×C8—1461no—
102C2×C8—1461no—
103C2×C8—1461no—
104C2×C8C2×#6440811yescharacteristic
105C4⋊C4—731no—
106C4⋊C4—731no—
107C4⋊C4—1461no—
108C4⋊C4—1461no—
109C42—731no—
110C42—1461no—
111C42—1461no—
112Q8—21no—
113Q8—21no—
114Q8—21no—
115Q8#1192403712yes—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—731no—
119C2×C4—731no—
120C2×C4—1461no—
121C2×C4—1461no—
122C2×C4C22×#6440811yescharacteristic
123C8—21no—
124C8—2921no—
125C8—2921no—
126C8—1461no—
127C8—1461no—
128C8—1462no—
129C8—1461no—
130C22D4×#6440811yescharacteristic
131C4—22no—
132C4—41no—
133C4—2921no—
134C4—2921no—
135C4—731no—
136C4—731no—
137C4—1461no—
138C4C2×#1192403711yescharacteristic
139C4#1455667811yescharacteristic
140C2#1798961811yescharacteristic
141C2#1798962711yescharacteristic
142C2#1798963111yescharacteristic
subgroupG/H
centerC22D4×#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC2×Q16×C73C4
socleC22×C73C4×D4
hypercenterC2×Q16#64408
hypocenterC73#1587
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
72. C73#1587semidirect