Finite Group Databasebeta

← C2×#11926927 #14574055

Subgroups — C2×#11926927 #14574055

Order 2432.

592 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 165 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×Dic76C211yesmaximal, characteristic, complemented
2C22×#64526C212yesmaximal, complemented
3C2×#10597382C212yesmaximal, complemented
4#11926927C218yesmaximal, direct product factor
5C2×C8×Dic19C211yesmaximal, characteristic, complemented
6C22×D8×C19C211yesmaximal, characteristic
7C22×D4×C19C2212yes—
8C22×Dic38C2212yes—
9C2×D8×C19—24no—
10C2×D8×C19C2214yes—
11C22×C8×C19C2211yescharacteristic
12C2×C22⋊Dic19—24no—
13#10597382—24no—
14#10597382C2218yescomplemented
15C2×#64526—28no—
16C2×#64526C2218yescomplemented
17C2×C4×Dic19C2211yescharacteristic
18C22×C19⋊C8C2211yescharacteristic
19C2×Dic76—24no—
20C2×Dic76C2214yescomplemented
21C8×Dic19C2214yescomplemented
22C24×C19—22no—
23C2×D4×C19—24no—
24C2×D4×C19—24no—
25C2×D4×C19—22no—
26C2×D4×C19C2314yes—
27C22×C4×C19C2311yescharacteristic
28C22×Dic19—22no—
29C22×Dic19D412yes—
30C2×Dic38—24no—
31C2×Dic38—24no—
32C2×Dic38—22no—
33C2×Dic38C2314yes—
34D8×C19—28no—
35C2×C8×C19D414yes—
36C2×C8×C19C2312yes—
37C22⋊Dic19—216no—
38#64526—216no—
39C4×Dic19D412yes—
40C4×Dic19C2312yes—
41C2×C19⋊C8D414yes—
42C2×C19⋊C8C2312yes—
43Dic76—28no—
44C23×C19—24no—
45C23×C19—44no—
46C23×C19—48no—
47C23×C19C2×D411yescharacteristic
48D4×C19—24no—
49D4×C19—24no—
50D4×C19—44no—
51C2×C4×C19C2×D411yescharacteristic
52C2×C4×C19C2×D412yes—
53C2×C4×C19C2×D412yes—
54C2×C4×C19C2411yescharacteristic
55C2×Dic19—24no—
56C2×Dic19—24no—
57C2×Dic19—44no—
58C2×Dic19C2×D414yes—
59Dic38—24no—
60Dic38—24no—
61Dic38—44no—
62C8×C19C2×D414yes—
63C19⋊C8C2×D414yes—
64C2×#495—191nomaximal, Sylow
65C22×C19—44no—
66C22×C19—48no—
67C22×C19—88no—
68C22×C19#12712yes—
69C22×C19#13514yes—
70C22×C19C22×D411yescharacteristic
71C4×C19#12712yes—
72C4×C19C22×D411yescharacteristic
73C4×C19C22×D411yescharacteristic
74Dic19—24no—
75Dic19—44no—
76C22×Q16—191no—
77C22×SD16—192no—
78C22×D8D1911yescharacteristic
79C2×#124—192no—
80#495—198no—
81C2×C4×C8—191no—
82C2×C19—84no—
83C2×C19#49514yescomplemented
84C2×C19C2×#12711yescharacteristic
85C2×C19C2×#13512yes—
86C22×Q8—192no—
87C22×D4C2×D1912yes—
88C2×Q16—194no—
89C2×Q16—384no—
90C2×SD16—198no—
91C2×SD16—388no—
92C2×D8—24no—
93C2×D8C2×D1914yes—
94C22×C8—191no—
95C22×C8C2×D1911yescharacteristic
96#124—198no—
97#124—384no—
98C2×C22⋊C4—384no—
99C2×C42—191no—
100C4×C8—194no—
101C19C2×#49511yescharacteristic, complemented, Sylow
102C24—22no—
103C2×Q8—194no—
104C2×Q8—382no—
105C2×Q8—384no—
106C2×Q8—384no—
107C2×D4—24no—
108C2×D4—22no—
109C2×D4—24no—
110C2×D4C22×D1914yes—
111C22×C4—192no—
112C22×C4—382no—
113C22×C4C22×D1911yescharacteristic
114Q16—388no—
115SD16—3816no—
116D8—28no—
117C2×C8—194no—
118C2×C8—192no—
119C2×C8C22⋊D1914yes—
120C2×C8C22×D1912yes—
121C22⋊C4—3816no—
122C42—192no—
123C42—192no—
124C23—24no—
125C23—44no—
126C23—48no—
127C23D4×D1911yescharacteristic
128Q8—384no—
129Q8—384no—
130Q8—764no—
131D4—24no—
132D4—24no—
133D4—44no—
134C2×C4—194no—
135C2×C4—384no—
136C2×C4—384no—
137C2×C4—764no—
138C2×C4D4×D1911yescharacteristic
139C2×C4D4×D1912yes—
140C2×C4C2×C22⋊D1912yes—
141C2×C4C23×D1911yescharacteristic
142C8—194no—
143C8C2×C22⋊D1914yes—
144C22—48no—
145C22—44no—
146C22—88no—
147C22#1059735814yes—
148C22#1059738612yes—
149C22C2×D4×D1911yescharacteristic
150C4—384no—
151C4—764no—
152C4#1059738612yes—
153C4C2×D4×D1911yescharacteristic
154C4C22×C22⋊D1911yescharacteristic
155C2—84no—
156C2#1192692714yesdirect product factor
157C2C2×#1059738611yescharacteristic
158C2C2×#1059735812yes—
subgroupG/H
centerC23D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
Fitting, prime radicalC22×D8×C19C2
socleC23×C19C2×D4
hypercenterC22×D8D19
hypocenterC19C2×#495
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C22×Dic76C2semidirect
2. C22×#64526C2semidirect
3. C2×#10597382C2semidirect
4. #11926927C2direct (N × H)
5. C2×C8×Dic19C2semidirect
14. #10597382C22semidirect
16. C2×#64526C22semidirect
20. C2×Dic76C22semidirect
21. C8×Dic19C22semidirect
83. C2×C19#495semidirect
101. C19C2×#495semidirect
156. C2#11926927direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×Dic762
C22×#645262
C2×#105973822
#119269272
C2×C8×Dic192
C22×D8×C192
C2×#49519