Finite Group Databasebeta

← #14569512

Subgroups — #14569512

Order 2432.

416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 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
1C2×C4×Dic38C211yesmaximal, characteristic
2#11926483C212yesmaximal
3#11926482C212yesmaximal
4#11926475C212yesmaximal
5#11926464C212yesmaximal
6#11926425C214yesmaximal
7#11926412C211yesmaximal, characteristic
8C2×C19×#125C211yesmaximal, characteristic
9C22×Dic38C2211yescharacteristic
10C19×#125—24no—
11C2×C4⋊C4×C19C2212yes—
12C2×C4⋊C4×C19C2212yes—
13C2×C4⋊C4×C19C2211yescharacteristic
14C2×C4⋊C4×C19C2211yescharacteristic
15C2×C42×C19C2211yescharacteristic
16C2×C4⋊Dic19C2211yescharacteristic
17C2×Dic19⋊C4C2214yes—
18C2×Dic19⋊C4C2212yes—
19C2×C4×Dic19C2212yes—
20C4×Dic38—24no—
21C19⋊#95C2212yes—
22C19⋊#95C2212yes—
23C19⋊#95C2212yes—
24C19⋊#95C2214yes—
25C19⋊#95C2214yes—
26C19⋊#95C2214yes—
27C22×C4×C19C2312yes—
28C22×C4×C19C2312yes—
29C22×C4×C19C2311yescharacteristic
30C22×C4×C19C2311yescharacteristic
31C22×C4×C19C2311yescharacteristic
32C22×Dic19C2314yes—
33C22×Dic19C2312yes—
34C22×Dic19C2312yes—
35C2×Dic38—22no—
36C2×Dic38—24no—
37C4⋊C4×C19—24no—
38C4⋊C4×C19—22no—
39C4⋊C4×C19—22no—
40C4⋊C4×C19—24no—
41C42×C19D414yes—
42C4⋊Dic19—22no—
43Dic19⋊C4—24no—
44Dic19⋊C4—28no—
45C4×Dic19—24no—
46C23×C19C2411yescharacteristic
47C2×C4×C19—22no—
48C2×C4×C19—22no—
49C2×C4×C19—22no—
50C2×C4×C19—22no—
51C2×C4×C19—22no—
52C2×C4×C19—24no—
53C2×C4×C19—24no—
54C2×C4×C19C2×D412yes—
55C2×C4×C19C2×D412yes—
56C2×C4×C19C2×D412yes—
57C2×Dic19—22no—
58C2×Dic19—22no—
59C2×Dic19—22no—
60C2×Dic19—24no—
61C2×Dic19—24no—
62C2×Dic19—24no—
63C2×Dic19—24no—
64C2×Dic19#4114yes—
65Dic38—28no—
66#2634—191nomaximal, Sylow
67C22×C19C22×D411yescharacteristic
68C22×C19C2×#4112yes—
69C22×C192−1+412yes—
70C22×C192−1+412yes—
71C4×C19—22no—
72C4×C19—22no—
73C4×C19—22no—
74C4×C19—42no—
75C4×C19—42no—
76Dic19—24no—
77Dic19—42no—
78Dic19—44no—
79C2×#125D1911yescharacteristic
80C2×C4×Q8—191no—
81#400—192no—
82#400—192no—
83#398—192no—
84#395—192no—
85#387—194no—
86#383—191no—
87C2×C19#52511yescharacteristic
88C2×C19#53611yescharacteristic
89C2×C19#53611yescharacteristic
90C2×C19#54114yes—
91C22×Q8—191no—
92#125—24no—
93C4×Q8—384no—
94C2×C4⋊C4—192no—
95C2×C4⋊C4—191no—
96C2×C4⋊C4—194no—
97C2×C4⋊C4C2×D1912yes—
98C2×C4⋊C4C2×D1912yes—
99C2×C4⋊C4C2×D1911yescharacteristic
100C2×C4⋊C4C2×D1911yescharacteristic
101C2×C42—192no—
102C2×C42C2×D1911yescharacteristic
103#95—192no—
104#95—192no—
105#95—192no—
106#95—194no—
107#95—194no—
108#95—194no—
109C19#263411yescharacteristic, complemented, Sylow
110C2×Q8—384no—
111C2×Q8—382no—
112C22×C4—192no—
113C22×C4—194no—
114C22×C4—192no—
115C22×C4C22×D1912yes—
116C22×C4C22×D1912yes—
117C22×C4C22×D1911yescharacteristic
118C22×C4C22×D1911yescharacteristic
119C22×C4C22×D1911yescharacteristic
120C4⋊C4—24no—
121C4⋊C4—22no—
122C4⋊C4—22no—
123C4⋊C4—24no—
124C4⋊C4—388no—
125C4⋊C4—384no—
126C4⋊C4—382no—
127C42—384no—
128C42C22⋊D1914yes—
129C23C23×D1911yescharacteristic
130Q8—388no—
131C2×C4—22no—
132C2×C4—22no—
133C2×C4—22no—
134C2×C4—24no—
135C2×C4—24no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—194no—
139C2×C4—382no—
140C2×C4—382no—
141C2×C4—384no—
142C2×C4—384no—
143C2×C4—384no—
144C2×C4—384no—
145C2×C4—382no—
146C2×C4C2×C22⋊D1912yes—
147C2×C4C2×C22⋊D1912yes—
148C2×C4C2×C22⋊D1912yes—
149C22#1059743312yes—
150C22#41×D1912yes—
151C22#1059743612yes—
152C22C22×C22⋊D1911yescharacteristic
153C4—22no—
154C4—22no—
155C4—22no—
156C4—42no—
157C4—42no—
158C4—384no—
159C4—762no—
160C4—764no—
161C2#1192705111yescharacteristic
162C2#1192711511yescharacteristic
163C2#1192711811yescharacteristic
164C2#1192715314yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, prime radical, cosocleC23×C19C24
FittingC2×C19×#125C2
hypercenterC2×#125D19
hypocenterC19#2634
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
109. C19#2634semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Dic382
#119264832
#119264822
#119264752
#119264642
#119264252
#119264122
C2×C19×#1252
#263419