Finite Group Databasebeta

← #22608718

Subgroups — #22608718

Order 9344.

158 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 67 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#17988639C211yesmaximal, characteristic
2#17988638C211yesmaximal, characteristic
3#17988609C211yesmaximal, characteristic
4#17988340C211yesmaximal, characteristic, complemented
5#17988339C211yesmaximal, characteristic, complemented
6#17988337C211yesmaximal, characteristic, complemented
7#334×C73C211yesmaximal, characteristic, complemented
8C2×#11924011—21no—
9C42×D73C2211yescharacteristic
10C4⋊#10596831C2211yescharacteristic
11C4⋊#10596831C2211yescharacteristic
12#14556520—21no—
13#14556520C411yescharacteristic
14#14556520C411yescharacteristic
15#14556503—21no—
16#14556503C411yescharacteristic
17#14556503C411yescharacteristic
18C4×#10596831C2211yescharacteristic
19C8×Dic73—21no—
20C4⋊C8×C73C2211yescharacteristic
21C4⋊C8×C73C2211yescharacteristic
22C4×C8×C73C2211yescharacteristic
23C2×C4×D73C2×C411yescharacteristic
24C2×C4×D73D411yescharacteristic
25C2×C4×D73Q811yescharacteristic
26#11924011—42no—
27C2×#10596831—21no—
28C2×#10596831—21no—
29C2×#10596831C2×C411yescharacteristic
30C2×#10596831C2×C411yescharacteristic
31C4×Dic73C2×C411yescharacteristic
32C4×Dic73D411yescharacteristic
33C4×Dic73Q811yescharacteristic
34C2×C8×C73—21no—
35C2×C8×C73—21no—
36C2×C8×C73C2×C411yescharacteristic
37C2×C8×C73C2×C411yescharacteristic
38C42×C73C2311yescharacteristic
39C22×D73C4⋊C411yescharacteristic
40C2×C4×C73C22×C411yescharacteristic
41C2×C4×C73C2×D411yescharacteristic
42C2×C4×C73C2×Q811yescharacteristic
43C2×Dic73C4⋊C411yescharacteristic
44C2×Dic73C4⋊C411yescharacteristic
45C2×Dic73C4⋊C411yescharacteristic
46C4×D73—21no—
47C4×D73—21no—
48C4×D73—21no—
49C4×D73—21no—
50C4×D73—22no—
51C8×C73—21no—
52C8×C73—21no—
53C8×C73—41no—
54C8×C73—41no—
55#10596831—21no—
56#10596831—21no—
57#10596831—41no—
58#10596831—41no—
59C22×C73C2×C4⋊C411yescharacteristic
60C2×D73—21no—
61C2×D73—21no—
62C2×D73—21no—
63C4×C73—21no—
64C4×C73#13111yescharacteristic
65C4×C73#13111yescharacteristic
66C4×C73AGL(1,ℤ/8)11yescharacteristic
67C4×C73#13711yescharacteristic
68Dic73—21no—
69Dic73—21no—
70Dic73#10812yes—
71C2×C73#42411yescharacteristic
72C2×C73#42811yescharacteristic
73C2×C73C2×#10811yescharacteristic
74D73—41no—
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#334D7311yescharacteristic, complemented
84C2×M16—1461no—
85C2×C42—731no—
86C4⋊C8—731no—
87C4⋊C8—731no—
88C4⋊C8—731no—
89C4⋊C8—731no—
90C4⋊C8—1461no—
91C4⋊C8C2×D7311yescharacteristic
92C4⋊C8C2×D7311yescharacteristic
93C22⋊C8—731no—
94C22⋊C8—731no—
95C22⋊C8—1461no—
96C4×C8—731no—
97C4×C8—1461no—
98C4×C8C2×D7311yescharacteristic
99C22×C4—731no—
100C22×C4—731no—
101C22×C4—731no—
102M16—2922no—
103C2×C8—21no—
104C2×C8—21no—
105C2×C8—731no—
106C2×C8—731no—
107C2×C8—1461no—
108C2×C8—1461no—
109C2×C8C4×D7311yescharacteristic
110C2×C8C4×D7311yescharacteristic
111C42—731no—
112C42—731no—
113C42—731no—
114C42C22×D7311yescharacteristic
115C23—731no—
116C2×C4—731no—
117C2×C4—731no—
118C2×C4—731no—
119C2×C4—1462no—
120C2×C4—1461no—
121C2×C4—1461no—
122C2×C4—1461no—
123C2×C4—1461no—
124C2×C4C2×C4×D7311yescharacteristic
125C2×C4D4×D7311yescharacteristic
126C2×C4Q8×D7311yescharacteristic
127C8—21no—
128C8—21no—
129C8—41no—
130C8—41no—
131C8—2921no—
132C8—2921no—
133C8—1461no—
134C8—1461no—
135C22—1461no—
136C22—1461no—
137C22—1461no—
138C22C4⋊C4×D7311yescharacteristic
139C4—21no—
140C4—732no—
141C4—1461no—
142C4—1461no—
143C4#1455659711yescharacteristic
144C4#1455659911yescharacteristic
145C4#1455661811yescharacteristic
146C4#1455662011yescharacteristic
147C2—2921no—
148C2#1798861211yescharacteristic
149C2#1798862611yescharacteristic
150C2#108×D7311yescharacteristic
subgroupG/H
centerC2×C4D4×D73
commutatorC2×C4×C73C22×C4
FrattiniC42C22×D73
Fitting#334×C73C2
socleC22×C73C2×C4⋊C4
hypercenter#334D73
hypocenterC73#1574
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C42 ◁ #334

Complements

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

NH ≅ G/Ntype
4. #17988340C2semidirect
5. #17988339C2semidirect
6. #17988337C2semidirect
7. #334×C73C2semidirect
76. C73#1574semidirect
83. #334D73semidirect