Finite Group Databasebeta

← #22625502

Subgroups — #22625502

Order 9344.

150 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 60 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#17989608C211yesmaximal, characteristic
2#17989603C211yesmaximal, characteristic
3#17989451C211yesmaximal, characteristic, complemented
4#17989450C211yesmaximal, characteristic, complemented
5#17989449C211yesmaximal, characteristic, complemented
6#17989448C211yesmaximal, characteristic, complemented
7#17988637C211yesmaximal, characteristic
8C4⋊#10596833C2211yescharacteristic
9C4⋊#10596833C2211yescharacteristic
10C4⋊#10596833C2211yescharacteristic
11C4⋊#10596833C2211yescharacteristic
12C22⋊#10596833—21no—
13C22⋊#10596833—21no—
14#14556646—21no—
15C4×#10596833—21no—
16C2×C4×Dic73C2211yescharacteristic
17#14556520C411yescharacteristic
18#14556520C411yescharacteristic
19C22⋊#10596831C411yescharacteristic
20C8×Dic73C2211yescharacteristic
21C8×Dic73C2211yescharacteristic
22C22⋊C8×C73C411yescharacteristic
23C2×#10596833—21no—
24C2×#10596833—21no—
25C2×#10596833—21no—
26C2×#10596833—21no—
27C22×Dic73D411yescharacteristic
28C22×Dic73Q811yescharacteristic
29C2×#10596831C2×C411yescharacteristic
30C2×#10596831C2×C411yescharacteristic
31C4×Dic73C2×C411yescharacteristic
32C4×Dic73D411yescharacteristic
33C4×Dic73Q811yescharacteristic
34C4×Dic73C2311yescharacteristic
35C22×C4×C73C2×C411yescharacteristic
36C2×C8×C73C2×C411yescharacteristic
37C2×C8×C73C2×C411yescharacteristic
38C23×C73C4⋊C411yescharacteristic
39C2×C4×C73—21no—
40C2×C4×C73—21no—
41C2×C4×C73C4⋊C411yescharacteristic
42C2×C4×C73C22×C411yescharacteristic
43C2×Dic73—21no—
44C2×Dic73—21no—
45C2×Dic73—41no—
46C2×Dic73C4⋊C411yescharacteristic
47C2×Dic73C4⋊C411yescharacteristic
48C2×Dic73C2×D411yescharacteristic
49C2×Dic73C2×Q811yescharacteristic
50#10596833—41no—
51#10596833—41no—
52#10596833—41no—
53#10596833—41no—
54C8×C73—21no—
55C8×C73—21no—
56#10596831—21no—
57#10596831—21no—
58C22×C73—21no—
59C22×C73—21no—
60C22×C73—21no—
61C22×C73C2×C4⋊C411yescharacteristic
62C4×C73—21no—
63C4×C73#13111yescharacteristic
64C4×C73#13111yescharacteristic
65Dic73—21no—
66Dic73—21no—
67Dic73—21no—
68Dic73#13511yescharacteristic
69Dic73#13511yescharacteristic
70C2×C73—41no—
71C2×C73#42411yescharacteristic
72C2×C73#42711yescharacteristic
73C2×C73#43011yescharacteristic
74#1572—731nomaximal, Sylow
75C73#157211yescharacteristic, complemented, Sylow
76#432—731no—
77#431—731no—
78#431—731no—
79#335—731no—
80#335—731no—
81#334—731no—
82#334—731no—
83C2×C42—731no—
84C4⋊C8—731no—
85C4⋊C8—731no—
86C4⋊C8—731no—
87C4⋊C8—731no—
88C4⋊C8—731no—
89C4⋊C8—731no—
90C22⋊C8—731no—
91C22⋊C8—1461no—
92C22⋊C8—1461no—
93C22⋊C8#6440811yescharacteristic
94#97—1461no—
95C4×C8—731no—
96C4×C8—731no—
97C4×C8—1461no—
98C22×C4—731no—
99C22×C4—731no—
100C22×C4C2×#6440811yescharacteristic
101C2×C8—731no—
102C2×C8—731no—
103C2×C8—1461no—
104C2×C8—1461no—
105C2×C8—1461no—
106C2×C8—1461no—
107C2×C8C2×#6440811yescharacteristic
108C2×C8C2×#6440811yescharacteristic
109C42—731no—
110C42—731no—
111C42—731no—
112C42—731no—
113C23C4⋊#6440811yescharacteristic
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—2921no—
117C2×C4—731no—
118C2×C4—731no—
119C2×C4—731no—
120C2×C4—731no—
121C2×C4—1461no—
122C2×C4—1461no—
123C2×C4C4⋊#6440811yescharacteristic
124C2×C4C22×#6440811yescharacteristic
125C8—21no—
126C8—21no—
127C8—2921no—
128C8—2921no—
129C8—2921no—
130C8—2921no—
131C8—1461no—
132C8—1461no—
133C22—21no—
134C22—21no—
135C22—21no—
136C22C2×C4⋊#6440811yescharacteristic
137C4—21no—
138C4—731no—
139C4—731no—
140C4—1461no—
141C4—1461no—
142C4—1461no—
143C4#1455667811yescharacteristic
144C4#1455667811yescharacteristic
145C2—41no—
146C2#1798959311yescharacteristic
147C2#1798959711yescharacteristic
148C2#1798960211yescharacteristic
subgroupG/H
centerC22C2×C4⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC22⋊C8×C73C4
socleC22×C73C2×C4⋊C4
hypercenterC22⋊C8#64408
hypocenterC73#1572
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
3. #17989451C2semidirect
4. #17989450C2semidirect
5. #17989449C2semidirect
6. #17989448C2semidirect
75. C73#1572semidirect