Finite Group Databasebeta

← #14571702

Subgroups — #14571702

Order 2432.

380 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 133 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×#10597316C211yesmaximal, characteristic
2#11926483C212yesmaximal
3#11926482C212yesmaximal
4#11926477C214yesmaximal
5#11926475C212yesmaximal
6#11926474C212yesmaximal
7#11926410C211yesmaximal, characteristic
8C2×C19×#125C211yesmaximal, characteristic
9C19×#125—24no—
10C2×C4⋊C4×C19C2212yes—
11C2×C4⋊C4×C19C2211yescharacteristic
12C2×C4⋊C4×C19C2212yes—
13C2×C4⋊C4×C19C2211yescharacteristic
14C2×C42×C19C2211yescharacteristic
15C2×C4⋊Dic19C2211yescharacteristic
16C2×C4⋊Dic19C2211yescharacteristic
17C2×C4⋊Dic19C2212yes—
18C2×Dic19⋊C4C2212yes—
19C2×Dic19⋊C4C2212yes—
20C2×Dic19⋊C4C2214yes—
21#10597316—24no—
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—
35C4⋊C4×C19—22no—
36C4⋊C4×C19—24no—
37C4⋊C4×C19—22no—
38C4⋊C4×C19—24no—
39C42×C19D414yes—
40C4⋊Dic19—22no—
41C4⋊Dic19—22no—
42C4⋊Dic19—42no—
43Dic19⋊C4—24no—
44Dic19⋊C4—24no—
45Dic19⋊C4—44no—
46C23×C19C2411yescharacteristic
47C2×C4×C19—21no—
48C2×C4×C19—22no—
49C2×C4×C19—22no—
50C2×C4×C19—21no—
51C2×C4×C19—22no—
52C2×C4×C19—22no—
53C2×C4×C19—22no—
54C2×C4×C19—24no—
55C2×C4×C19—22no—
56C2×C4×C19C2×D412yes—
57C2×C4×C19C2×D412yes—
58C2×C4×C19C2×D412yes—
59C2×Dic19—22no—
60C2×Dic19—22no—
61C2×Dic19—22no—
62C2×Dic19—24no—
63C2×Dic19—24no—
64C2×Dic19—24no—
65C2×Dic19—22no—
66C2×Dic19—24no—
67#2822—191nomaximal, Sylow
68C22×C19C22×D411yescharacteristic
69C22×C19H(5,𝔽2)11yescharacteristic
70C22×C192−1+412yes—
71C22×C192−1+412yes—
72C22×C192−1+411yescharacteristic
73C4×C19—22no—
74C4×C19—22no—
75C4×C19—22no—
76C4×C19—42no—
77C4×C19—42no—
78Dic19—42no—
79Dic19—42no—
80Dic19—44no—
81C2×#125—191no—
82C2×#125D1911yescharacteristic
83#400—192no—
84#400—192no—
85#398—192no—
86#398—192no—
87#398—194no—
88#382—191no—
89C2×C19#53611yescharacteristic
90C2×C19#53611yescharacteristic
91C2×C19#53711yescharacteristic
92C2×C19#56312yes—
93C2×C19#56412yes—
94#125—24no—
95#125—384no—
96C2×C4⋊C4—192no—
97C2×C4⋊C4—191no—
98C2×C4⋊C4—192no—
99C2×C4⋊C4—191no—
100C2×C4⋊C4—192no—
101C2×C4⋊C4—194no—
102C2×C4⋊C4C2×D1912yes—
103C2×C4⋊C4C2×D1911yescharacteristic
104C2×C4⋊C4C2×D1912yes—
105C2×C4⋊C4C2×D1911yescharacteristic
106C2×C42C2×D1911yescharacteristic
107#95—192no—
108#95—192no—
109#95—194no—
110#95—194no—
111#95—194no—
112C19#282211yescharacteristic, complemented, Sylow
113C22×C4—194no—
114C22×C4—192no—
115C22×C4—192no—
116C22×C4C22×D1912yes—
117C22×C4C22×D1912yes—
118C22×C4C22×D1911yescharacteristic
119C22×C4C22×D1911yescharacteristic
120C22×C4C22×D1911yescharacteristic
121C4⋊C4—24no—
122C4⋊C4—22no—
123C4⋊C4—24no—
124C4⋊C4—22no—
125C4⋊C4—384no—
126C4⋊C4—384no—
127C4⋊C4—382no—
128C4⋊C4—382no—
129C4⋊C4—764no—
130C4⋊C4—762no—
131C42C22⋊D1914yes—
132C23C23×D1911yescharacteristic
133C2×C4—22no—
134C2×C4—21no—
135C2×C4—22no—
136C2×C4—21no—
137C2×C4—22no—
138C2×C4—24no—
139C2×C4—22no—
140C2×C4—22no—
141C2×C4—22no—
142C2×C4—384no—
143C2×C4—384no—
144C2×C4—384no—
145C2×C4—382no—
146C2×C4—384no—
147C2×C4—382no—
148C2×C4—382no—
149C2×C4—382no—
150C2×C4C2×C22⋊D1912yes—
151C2×C4C2×C22⋊D1912yes—
152C2×C4C2×C22⋊D1912yes—
153C22#1059743312yes—
154C22#1059743511yescharacteristic
155C22#1059743612yes—
156C22#1059743611yescharacteristic
157C22C22×C22⋊D1911yescharacteristic
158C4—22no—
159C4—22no—
160C4—22no—
161C4—42no—
162C4—42no—
163C4—764no—
164C4—762no—
165C4—762no—
166C2#1192711511yescharacteristic
167C2#1192711811yescharacteristic
168C2#1192712211yescharacteristic
169C2#1192729812yes—
170C2C19⋊#56412yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, prime radical, cosocleC23×C19C24
FittingC2×C19×#125C2
hypercenterC2×#125D19
hypocenterC19#2822
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
112. C19#2822semidirect

Maximal subgroups

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

subgroupindex
C2×#105973162
#119264832
#119264822
#119264772
#119264752
#119264742
#119264102
C2×C19×#1252
#282219