Finite Group Databasebeta

← #22608708

Subgroups — #22608708

Order 9344.

150 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 65 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#17988643C211yesmaximal, characteristic
2#17988639C211yesmaximal, characteristic
3#17988638C211yesmaximal, characteristic
4#17988339C211yesmaximal, characteristic, complemented
5#17988339C211yesmaximal, characteristic, complemented
6#17988338C211yesmaximal, characteristic, complemented
7#334×C73C211yesmaximal, characteristic, complemented
8C42×D73C2211yescharacteristic
9C4⋊#10596831C2211yescharacteristic
10C4⋊#10596831C2211yescharacteristic
11#14556520C411yescharacteristic
12#14556520C411yescharacteristic
13#14556503—21no—
14#14556503—21no—
15#14556503C411yescharacteristic
16#14556503C411yescharacteristic
17#14556501—21no—
18C4×#10596831C2211yescharacteristic
19C8×Dic73—21no—
20C4⋊C8×C73C2211yescharacteristic
21C4⋊C8×C73C2211yescharacteristic
22C4×C8×C73C2211yescharacteristic
23C2×C4×D73C2×C411yescharacteristic
24C2×C4×D73D411yescharacteristic
25C2×C4×D73Q811yescharacteristic
26C2×#10596831—21no—
27C2×#10596831—21no—
28C2×#10596831C2×C411yescharacteristic
29C2×#10596831C2×C411yescharacteristic
30C4×Dic73C2×C411yescharacteristic
31C4×Dic73D411yescharacteristic
32C4×Dic73Q811yescharacteristic
33C2×C8×C73—21no—
34C2×C8×C73—21no—
35C2×C8×C73C2×C411yescharacteristic
36C2×C8×C73C2×C411yescharacteristic
37C42×C73C2311yescharacteristic
38C22×D73C4⋊C411yescharacteristic
39C2×C4×C73C22×C411yescharacteristic
40C2×C4×C73C2×D411yescharacteristic
41C2×C4×C73C2×Q811yescharacteristic
42C2×Dic73C4⋊C411yescharacteristic
43C2×Dic73C4⋊C411yescharacteristic
44C2×Dic73C4⋊C411yescharacteristic
45C4×D73—21no—
46C4×D73—21no—
47C4×D73—21no—
48C4×D73—21no—
49C4×D73—41no—
50C8×C73—21no—
51C8×C73—21no—
52C8×C73—41no—
53C8×C73—41no—
54#10596831—21no—
55#10596831—21no—
56#10596831—41no—
57#10596831—41no—
58C22×C73C2×C4⋊C411yescharacteristic
59C2×D73—21no—
60C2×D73—21no—
61C2×D73—21no—
62C4×C73—21no—
63C4×C73#13111yescharacteristic
64C4×C73#13111yescharacteristic
65C4×C73#13511yescharacteristic
66C4×C73#13511yescharacteristic
67Dic73—21no—
68Dic73—21no—
69Dic73—21no—
70C2×C73#42411yescharacteristic
71C2×C73#42711yescharacteristic
72C2×C73#43011yescharacteristic
73D73—41no—
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#334D7311yescharacteristic, complemented
83C2×C42—731no—
84C4⋊C8—731no—
85C4⋊C8—731no—
86C4⋊C8—731no—
87C4⋊C8—731no—
88C4⋊C8C2×D7311yescharacteristic
89C4⋊C8C2×D7311yescharacteristic
90C22⋊C8—731no—
91C22⋊C8—731no—
92C22⋊C8—1461no—
93C22⋊C8—1461no—
94#97—1461no—
95C4×C8—731no—
96C4×C8—1461no—
97C4×C8C2×D7311yescharacteristic
98C22×C4—731no—
99C22×C4—731no—
100C22×C4—731no—
101C2×C8—21no—
102C2×C8—21no—
103C2×C8—731no—
104C2×C8—731no—
105C2×C8—1461no—
106C2×C8—1461no—
107C2×C8C4×D7311yescharacteristic
108C2×C8C4×D7311yescharacteristic
109C42—731no—
110C42—731no—
111C42—731no—
112C42C22×D7311yescharacteristic
113C23—731no—
114C2×C4—2921no—
115C2×C4—731no—
116C2×C4—731no—
117C2×C4—731no—
118C2×C4—1461no—
119C2×C4—1461no—
120C2×C4—1461no—
121C2×C4—1461no—
122C2×C4C2×C4×D7311yescharacteristic
123C2×C4D4×D7311yescharacteristic
124C2×C4Q8×D7311yescharacteristic
125C8—21no—
126C8—21no—
127C8—41no—
128C8—41no—
129C8—2921no—
130C8—2921no—
131C8—1461no—
132C8—1461no—
133C22—1461no—
134C22—1461no—
135C22—1461no—
136C22C4⋊C4×D7311yescharacteristic
137C4—21no—
138C4—1461no—
139C4—1461no—
140C4—1461no—
141C4#1455659711yescharacteristic
142C4#1455659911yescharacteristic
143C4#1455661211yescharacteristic
144C4#1455661211yescharacteristic
145C2—2921no—
146C2#1798861211yescharacteristic
147C2#1798862211yescharacteristic
148C2#1798863411yescharacteristic
subgroupG/H
centerC2×C4D4×D73
commutatorC2×C4×C73C22×C4
FrattiniC42C22×D73
Fitting#334×C73C2
socleC22×C73C2×C4⋊C4
hypercenter#334D73
hypocenterC73#1572
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. #17988339C2semidirect
5. #17988339C2semidirect
6. #17988338C2semidirect
7. #334×C73C2semidirect
75. C73#1572semidirect
82. #334D73semidirect