Finite Group Databasebeta

← #14571626

Subgroups — #14571626

Order 2432.

344 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 125 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#11926484C212yesmaximal
2#11926483C212yesmaximal
3#11926482C212yesmaximal
4#11926442C211yesmaximal, characteristic
5#11926442C211yesmaximal, characteristic
6#11926431C212yesmaximal
7#11926430C212yesmaximal
8#11926425C212yesmaximal
9C19×#389C211yesmaximal, characteristic
10C2×C4⋊C4×C19C2212yes—
11C2×C4⋊C4×C19C2211yescharacteristic
12C2×C4⋊C4×C19C2211yescharacteristic
13C2×C42×C19C2211yescharacteristic
14C2×C4⋊Dic19C2211yescharacteristic
15C2×C4⋊Dic19C2211yescharacteristic
16C2×C4⋊Dic19C2211yescharacteristic
17C2×C4⋊Dic19C2211yescharacteristic
18C2×Dic19⋊C4C2212yes—
19C2×Dic19⋊C4C2212yes—
20C2×C4×Dic19C2212yes—
21C19×#95C2212yes—
22C19⋊#95C2212yes—
23C19⋊#95C2212yes—
24C19⋊#95C2212yes—
25C19⋊#95C2212yes—
26C19⋊#95C2212yes—
27C19⋊#95C2212yes—
28C19⋊#95C2212yes—
29C19⋊#95C2212yes—
30C19⋊#95C2212yes—
31C22×C4×C19C2312yes—
32C22×C4×C19C2312yes—
33C22×C4×C19C2311yescharacteristic
34C22×C4×C19C2311yescharacteristic
35C22×C4×C19C2311yescharacteristic
36C22×Dic19C2312yes—
37C22×Dic19C2312yes—
38C22×Dic19C2312yes—
39C22×Dic19C2312yes—
40C4⋊C4×C19—22no—
41C4⋊C4×C19—24no—
42C4⋊C4×C19—41no—
43C42×C19—41no—
44C4⋊Dic19—22no—
45C4⋊Dic19—22no—
46C4⋊Dic19—41no—
47C4⋊Dic19—41no—
48Dic19⋊C4—24no—
49Dic19⋊C4—24no—
50C4×Dic19—42no—
51C23×C19C2411yescharacteristic
52C2×C4×C19—21no—
53C2×C4×C19—21no—
54C2×C4×C19—21no—
55C2×C4×C19—21no—
56C2×C4×C19—21no—
57C2×C4×C19—21no—
58C2×C4×C19—22no—
59C2×C4×C19—22no—
60C2×C4×C19—22no—
61C2×C4×C19—22no—
62C2×C4×C19—22no—
63C2×C4×C19—22no—
64C2×C4×C19#4112yes—
65C2×C4×C19#4112yes—
66C2×C4×C19#4112yes—
67C2×Dic19—22no—
68C2×Dic19—22no—
69C2×Dic19—22no—
70C2×Dic19—22no—
71C2×Dic19—22no—
72C2×Dic19—22no—
73C2×Dic19—22no—
74C2×Dic19—22no—
75C2×Dic19—22no—
76C2×Dic19—22no—
77C2×Dic19—22no—
78C2×Dic19—22no—
79#2810—191nomaximal, Sylow
80C22×C19C2×#4111yescharacteristic
81C22×C19C2×#4111yescharacteristic
82C22×C19C2×#4111yescharacteristic
83C22×C19H(5,𝔽2)11yescharacteristic
84C22×C192−1+411yescharacteristic
85C22×C192−1+411yescharacteristic
86C22×C192−1+411yescharacteristic
87C4×C19—22no—
88C4×C19—22no—
89C4×C19—22no—
90C4×C19—42no—
91C4×C19—42no—
92Dic19—42no—
93Dic19—42no—
94Dic19—42no—
95Dic19—42no—
96#400—192no—
97#400—192no—
98#400—192no—
99#389—191no—
100#389—191no—
101#389D1911yescharacteristic
102#387—192no—
103#387—192no—
104#387—192no—
105C2×C19#53911yescharacteristic
106C2×C19#53911yescharacteristic
107C2×C19#53911yescharacteristic
108C2×C19#55611yescharacteristic
109C2×C19#55611yescharacteristic
110C2×C19#55611yescharacteristic
111C2×C19#56411yescharacteristic
112C2×C4⋊C4—192no—
113C2×C4⋊C4—192no—
114C2×C4⋊C4—191no—
115C2×C4⋊C4—191no—
116C2×C4⋊C4—191no—
117C2×C4⋊C4—191no—
118C2×C4⋊C4C2×D1912yes—
119C2×C4⋊C4C2×D1911yescharacteristic
120C2×C4⋊C4C2×D1911yescharacteristic
121C2×C42—192no—
122C2×C42C2×D1911yescharacteristic
123#95—192no—
124#95—192no—
125#95—192no—
126#95—192no—
127#95—192no—
128#95—192no—
129#95—192no—
130#95—192no—
131#95—192no—
132#95C2×D1912yes—
133C19#281011yescharacteristic, complemented, Sylow
134C22×C4—192no—
135C22×C4—192no—
136C22×C4—192no—
137C22×C4—192no—
138C22×C4C22×D1912yes—
139C22×C4C22×D1912yes—
140C22×C4C22×D1911yescharacteristic
141C22×C4C22×D1911yescharacteristic
142C22×C4C22×D1911yescharacteristic
143C4⋊C4—22no—
144C4⋊C4—24no—
145C4⋊C4—41no—
146C4⋊C4—384no—
147C4⋊C4—382no—
148C4⋊C4—384no—
149C4⋊C4—382no—
150C4⋊C4—761no—
151C4⋊C4—761no—
152C42—41no—
153C42—762no—
154C23C23×D1911yescharacteristic
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—382no—
168C2×C4—382no—
169C2×C4—382no—
170C2×C4—382no—
171C2×C4—382no—
172C2×C4—382no—
173C2×C4—382no—
174C2×C4—382no—
175C2×C4—382no—
176C2×C4—382no—
177C2×C4—382no—
178C2×C4—382no—
179C2×C4#6454112yes—
180C2×C4#6454312yes—
181C2×C4#6454512yes—
182C22C2×#6454111yescharacteristic
183C22C2×#6454311yescharacteristic
184C22#1059743011yescharacteristic
185C22C2×#6454511yescharacteristic
186C22#1059743311yescharacteristic
187C22#1059743611yescharacteristic
188C22#1059743611yescharacteristic
189C4—22no—
190C4—22no—
191C4—22no—
192C4—42no—
193C4—42no—
194C4—762no—
195C4—762no—
196C4—762no—
197C4—762no—
198C2#1192713911yescharacteristic
199C2#1192714111yescharacteristic
200C2#1192714311yescharacteristic
201C2#1192726411yescharacteristic
202C2#1192726711yescharacteristic
203C2#1192726811yescharacteristic
204C2C19⋊#56411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, prime radical, cosocleC23×C19C24
FittingC19×#389C2
hypercenter#389D19
hypocenterC19#2810
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
133. C19#2810semidirect

Maximal subgroups

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

subgroupindex
#119264842
#119264832
#119264822
#119264422
#119264312
#119264302
#119264252
C19×#3892
#281019