Finite Group Databasebeta

← C2×#17989463 #22625622

Subgroups — C2×#17989463 #22625622

Order 9344.

392 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 146 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
1C22×#11924038C212yesmaximal
2#17989463C214yesmaximal, direct product factor
3C22×C8×D73C211yesmaximal, characteristic
4C2×#11924038—22no—
5C2×#11924038—24no—
6C2×#11924038C418yes—
7C2×#11924038C2214yes—
8C22×#10596833—22no—
9C22×C4×D73C2211yescharacteristic
10C22×#10596831C411yescharacteristic
11C2×C8×D73—24no—
12C2×C8×D73C412yes—
13C2×C8×D73C2212yes—
14C22×C8×C73C411yescharacteristic
15#11924038—28no—
16#11924038—24no—
17#11924038C2×C418yes—
18C2×#10596833—28no—
19C2×#10596833—24no—
20C23×D73Q811yescharacteristic
21C22×Dic73D411yescharacteristic
22C2×C4×D73C2×C411yescharacteristic
23C2×C4×D73C2×C414yes—
24C2×C4×D73D411yescharacteristic
25C2×C4×D73D414yes—
26C2×C4×D73Q811yescharacteristic
27C2×C4×D73C2311yescharacteristic
28C2×#10596831—22no—
29C2×#10596831C2×C412yes—
30C8×D73—24no—
31C8×D73—24no—
32C22×C4×C73C2×C411yescharacteristic
33C2×C8×C73—22no—
34C2×C8×C73C2×C412yes—
35C23×C73C4⋊C411yescharacteristic
36C22×D73—22no—
37C22×D73—22no—
38C22×D73C4⋊C411yescharacteristic
39C22×D73C4⋊C414yes—
40C22×D73C2×Q811yescharacteristic
41C2×C4×C73C4212yes—
42C2×C4×C73C22⋊C412yes—
43C2×C4×C73C4⋊C411yescharacteristic
44C2×C4×C73C22×C411yescharacteristic
45C2×Dic73C22⋊C414yes—
46C2×Dic73C4⋊C411yescharacteristic
47C2×Dic73C2×D411yescharacteristic
48C4×D73C4212yes—
49C4×D73C22⋊C412yes—
50C4×D73C22⋊C414yes—
51C4×D73C4⋊C414yes—
52C4×D73C22×C412yes—
53C4×D73C2×D412yes—
54#10596833—28no—
55C8×C73—22no—
56#10596831—22no—
57C22×C73#9512yes—
58C22×C73#10812yes—
59C22×C73#10812yes—
60C22×C73C2×C4⋊C411yescharacteristic
61C2×D73—28no—
62C2×D73—21no—
63C2×D73—21no—
64C2×D73—21no—
65C2×D73—21no—
66C2×D73#9512yes—
67C2×D73C2×C4⋊C412yes—
68C4×C73#9512yes—
69C4×C73C2×C4211yescharacteristic
70C4×C73C2×C22⋊C411yescharacteristic
71Dic73#9512yes—
72Dic73C2×C22⋊C412yes—
73C2×C73#34114yescomplemented
74C2×C73C2×#9511yescharacteristic
75C2×C73C2×#10811yescharacteristic
76C2×C73C2×#10811yescharacteristic
77D73—22no—
78D73—22no—
79C2×#341—731nomaximal, Sylow
80C73C2×#34111yescharacteristic, complemented, Sylow
81C22×M16—732no—
82C23×C8—731no—
83#341—734no—
84C23×C4—731no—
85C2×M16—738no—
86C2×M16—734no—
87C2×M16—1464no—
88C2×M16—1462no—
89C22×C8—731no—
90C22×C8—732no—
91C22×C8—732no—
92C22×C8—1464no—
93C22×C8—1462no—
94C22×C8#6440811yescharacteristic
95C24—731no—
96C22×C4—731no—
97C22×C4—734no—
98C22×C4—734no—
99C22×C4—731no—
100C22×C4—731no—
101C22×C4—731no—
102C22×C4—731no—
103C22×C4C2×#6440811yescharacteristic
104M16—738no—
105M16—1468no—
106M16—1464no—
107C2×C8—22no—
108C2×C8—732no—
109C2×C8—1464no—
110C2×C8—1464no—
111C2×C8—1468no—
112C2×C8—1464no—
113C2×C8—1462no—
114C2×C8C2×#6440812yes—
115C23—734no—
116C23—731no—
117C23—731no—
118C23—1462no—
119C23—1462no—
120C23C4⋊#6440811yescharacteristic
121C2×C4—734no—
122C2×C4—731no—
123C2×C4—731no—
124C2×C4—734no—
125C2×C4—734no—
126C2×C4—732no—
127C2×C4—732no—
128C2×C4—732no—
129C2×C4—732no—
130C2×C4C4×#6440812yes—
131C2×C4C22⋊#6440812yes—
132C2×C4C4⋊#6440811yescharacteristic
133C2×C4C22×#6440811yescharacteristic
134C8—22no—
135C8—1468no—
136C8—1462no—
137C22—732no—
138C22—732no—
139C22—1468no—
140C22—1461no—
141C22—1461no—
142C22—1461no—
143C22—1461no—
144C22(C2×#64408)⋊C412yes—
145C22#1455666112yes—
146C22#1455666212yes—
147C22C2×C4⋊#6440811yescharacteristic
148C4—732no—
149C4—732no—
150C4(C2×#64408)⋊C412yes—
151C4C2×C4×#6440811yescharacteristic
152C4C2×C22⋊#6440811yescharacteristic
153C2—1462no—
154C2—1462no—
155C2#1798946314yesdirect product factor
156C2C2×(C2×#64408)⋊C411yescharacteristic
157C2C2×#1455666111yescharacteristic
158C2C2×#1455666211yescharacteristic
subgroupG/H
centerC23C4⋊#64408
commutatorC4×C73C2×C42
FrattiniC2×C4C22×#64408
FittingC22×C8×C73C4
socleC23×C73C4⋊C4
hypercenterC22×C8#64408
hypocenterC73C2×#341
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #17989463C2direct (N × H)
73. C2×C73#341semidirect
80. C73C2×#341semidirect
155. C2#17989463direct (N × H)