Finite Group Databasebeta

← #22625507

Subgroups — #22625507

Order 9344.

158 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 62 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#17989603C211yesmaximal, characteristic
2#17989590C211yesmaximal, characteristic
3#17989451C211yesmaximal, characteristic, complemented
4#17989450C211yesmaximal, characteristic, complemented
5#17989449C211yesmaximal, characteristic, complemented
6#17989448C211yesmaximal, characteristic, complemented
7#17988637C211yesmaximal, characteristic
8C2×#11924037—21no—
9#14556658—21no—
10C4⋊#10596833C2211yescharacteristic
11C4⋊#10596833C2211yescharacteristic
12C4⋊#10596833C2211yescharacteristic
13C4⋊#10596833C2211yescharacteristic
14C22⋊#10596833—21no—
15C4×#10596833—21no—
16C2×C4×Dic73C2211yescharacteristic
17#14556520C411yescharacteristic
18#14556520C411yescharacteristic
19C22⋊#10596831C411yescharacteristic
20C8×Dic73C2211yescharacteristic
21C8×Dic73C2211yescharacteristic
22C22⋊C8×C73C411yescharacteristic
23#11924037—42no—
24C2×#10596833—21no—
25C2×#10596833—21no—
26C2×#10596833—21no—
27C2×#10596833—21no—
28C22×Dic73D411yescharacteristic
29C22×Dic73Q811yescharacteristic
30C2×#10596831C2×C411yescharacteristic
31C2×#10596831C2×C411yescharacteristic
32C4×Dic73C2×C411yescharacteristic
33C4×Dic73D411yescharacteristic
34C4×Dic73Q811yescharacteristic
35C4×Dic73C2311yescharacteristic
36C22×C4×C73C2×C411yescharacteristic
37C2×C8×C73C2×C411yescharacteristic
38C2×C8×C73C2×C411yescharacteristic
39C23×C73C4⋊C411yescharacteristic
40C2×C4×C73—21no—
41C2×C4×C73—21no—
42C2×C4×C73C4⋊C411yescharacteristic
43C2×C4×C73C22×C411yescharacteristic
44C2×Dic73—22no—
45C2×Dic73—21no—
46C2×Dic73—21no—
47C2×Dic73C4⋊C411yescharacteristic
48C2×Dic73C4⋊C411yescharacteristic
49C2×Dic73C2×D411yescharacteristic
50C2×Dic73C2×Q811yescharacteristic
51#10596833—41no—
52#10596833—41no—
53#10596833—41no—
54#10596833—41no—
55C8×C73—21no—
56C8×C73—21no—
57#10596831—21no—
58#10596831—21no—
59C22×C73—21no—
60C22×C73—21no—
61C22×C73—21no—
62C22×C73C2×C4⋊C411yescharacteristic
63C4×C73—21no—
64C4×C73#13111yescharacteristic
65C4×C73#13111yescharacteristic
66Dic73—21no—
67Dic73—21no—
68Dic73#10812yes—
69Dic73AGL(1,ℤ/8)11yescharacteristic
70Dic73#13711yescharacteristic
71C2×C73—41no—
72C2×C73#42411yescharacteristic
73C2×C73#42811yescharacteristic
74C2×C73C2×#10811yescharacteristic
75#1574—731nomaximal, Sylow
76C73#157411yescharacteristic, complemented, Sylow
77#431—731no—
78#431—731no—
79#423—731no—
80#335—731no—
81#335—731no—
82#334—731no—
83#334—731no—
84C2×M16—1461no—
85C2×C42—731no—
86C4⋊C8—731no—
87C4⋊C8—731no—
88C4⋊C8—731no—
89C4⋊C8—731no—
90C4⋊C8—731no—
91C4⋊C8—731no—
92C4⋊C8—1461no—
93C22⋊C8—731no—
94C22⋊C8—1461no—
95C22⋊C8#6440811yescharacteristic
96C4×C8—731no—
97C4×C8—731no—
98C4×C8—1461no—
99C22×C4—731no—
100C22×C4—731no—
101C22×C4C2×#6440811yescharacteristic
102M16—2922no—
103C2×C8—731no—
104C2×C8—731no—
105C2×C8—1461no—
106C2×C8—1461no—
107C2×C8—1461no—
108C2×C8—1461no—
109C2×C8C2×#6440811yescharacteristic
110C2×C8C2×#6440811yescharacteristic
111C42—731no—
112C42—731no—
113C42—731no—
114C42—731no—
115C23C4⋊#6440811yescharacteristic
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—731no—
119C2×C4—731no—
120C2×C4—731no—
121C2×C4—731no—
122C2×C4—1461no—
123C2×C4—1461no—
124C2×C4—1462no—
125C2×C4C4⋊#6440811yescharacteristic
126C2×C4C22×#6440811yescharacteristic
127C8—21no—
128C8—21no—
129C8—2921no—
130C8—2921no—
131C8—2921no—
132C8—2921no—
133C8—1461no—
134C8—1461no—
135C22—21no—
136C22—21no—
137C22—21no—
138C22C2×C4⋊#6440811yescharacteristic
139C4—21no—
140C4—731no—
141C4—731no—
142C4—732no—
143C4—1461no—
144C4—1461no—
145C4#1455667811yescharacteristic
146C4#1455667811yescharacteristic
147C2—41no—
148C2#1798959311yescharacteristic
149C2#1798959811yescharacteristic
150C2D73⋊#10811yescharacteristic
subgroupG/H
centerC22C2×C4⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC22⋊C8×C73C4
socleC22×C73C2×C4⋊C4
hypercenterC22⋊C8#64408
hypocenterC73#1574
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
76. C73#1574semidirect