Finite Group Databasebeta

← #14568873

Subgroups — #14568873

Order 2432.

380 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 141 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#11926486C212yesmaximal
2#11926483C211yesmaximal, characteristic
3#11926441C212yesmaximal
4#11926439C212yesmaximal
5#11926413C211yesmaximal, characteristic
6#11926408C212yesmaximal
7#11926408C212yesmaximal
8#11926395C212yesmaximal
9C19×#400C211yesmaximal, characteristic
10C2×C4⋊C4×C19C2211yescharacteristic
11C2×C4⋊C4×C19C2211yescharacteristic
12C2×C4⋊Dic19C2211yescharacteristic
13C2×C4⋊Dic19C2211yescharacteristic
14C2×Dic19⋊C4C2212yes—
15C2×Dic19⋊C4C2212yes—
16C2×Dic19⋊C4C2212yes—
17C2×Dic19⋊C4C2212yes—
18C2×Dic19⋊C4C2212yes—
19C2×C4×Dic19C2212yes—
20C2×C4×Dic19C2212yes—
21C2×C4×Dic19C2211yescharacteristic
22C19×#95C2212yes—
23C19×#95C2211yescharacteristic
24C19×#95C2212yes—
25C19⋊#95C2212yes—
26C19⋊#95C2211yescharacteristic
27C19⋊#95C2212yes—
28C19⋊#95C2212yes—
29C19⋊#95C2212yes—
30C19⋊#95C2212yes—
31C22×C4×C19C2311yescharacteristic
32C22×C4×C19C2312yes—
33C22×C4×C19C2311yescharacteristic
34C22×C4×C19C2312yes—
35C22×C4×C19C2311yescharacteristic
36C22×Dic19C2312yes—
37C22×Dic19C2312yes—
38C22×Dic19C2312yes—
39C22×Dic19C2312yes—
40C4⋊C4×C19—41no—
41C4⋊C4×C19—41no—
42C4⋊Dic19—41no—
43C4⋊Dic19—41no—
44Dic19⋊C4—24no—
45Dic19⋊C4—24no—
46Dic19⋊C4—24no—
47Dic19⋊C4—24no—
48Dic19⋊C4—42no—
49C4×Dic19—24no—
50C4×Dic19—24no—
51C4×Dic19Q814yes—
52C23×C19C2411yescharacteristic
53C2×C4×C19—21no—
54C2×C4×C19—21no—
55C2×C4×C19—22no—
56C2×C4×C19—22no—
57C2×C4×C19—22no—
58C2×C4×C19—22no—
59C2×C4×C19—22no—
60C2×C4×C19—22no—
61C2×C4×C19—22no—
62C2×C4×C19—21no—
63C2×C4×C19—21no—
64C2×C4×C19—22no—
65C2×C4×C19C2×Q812yes—
66C2×Dic19—22no—
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×Dic19C2×Q814yes—
76C2×Dic19#4114yes—
77C2×Dic19#4114yes—
78#2571—191nomaximal, Sylow
79C22×C19C22×Q811yescharacteristic
80C22×C19C2×#4112yes—
81C22×C19C2×#4112yes—
82C22×C19H(5,𝔽2)11yescharacteristic
83C22×C192−1+411yescharacteristic
84C4×C19—22no—
85C4×C19—42no—
86C4×C19—42no—
87C4×C19—41no—
88C4×C19—41no—
89Dic19—42no—
90Dic19—42no—
91Dic19—42no—
92Dic19#12518yes—
93#400—191no—
94#400—192no—
95#400D1911yescharacteristic
96#389—192no—
97#389—192no—
98#384—191no—
99#382—192no—
100#382—192no—
101C4×C4⋊C4—192no—
102C2×C19C2×#12512yes—
103C2×C19#54411yescharacteristic
104C2×C19#55511yescharacteristic
105C2×C19#55612yes—
106C2×C19#55911yescharacteristic
107C2×C4⋊C4—192no—
108C2×C4⋊C4—192no—
109C2×C4⋊C4—192no—
110C2×C4⋊C4—192no—
111C2×C4⋊C4—191no—
112C2×C4⋊C4—192no—
113C2×C4⋊C4—191no—
114C2×C4⋊C4C2×D1911yescharacteristic
115C2×C4⋊C4C2×D1911yescharacteristic
116C2×C42—191no—
117C2×C42—192no—
118C2×C42—192no—
119#95—192no—
120#95—191no—
121#95—192no—
122#95—192no—
123#95—192no—
124#95—192no—
125#95C2×D1912yes—
126#95C2×D1911yescharacteristic
127#95C2×D1912yes—
128C19#257111yescharacteristic, complemented, Sylow
129C22×C4—192no—
130C22×C4—192no—
131C22×C4—192no—
132C22×C4—192no—
133C22×C4C22×D1912yes—
134C22×C4C22×D1911yescharacteristic
135C22×C4C22×D1912yes—
136C22×C4C22×D1911yescharacteristic
137C22×C4C22×D1911yescharacteristic
138C4⋊C4—41no—
139C4⋊C4—41no—
140C4⋊C4—384no—
141C4⋊C4—384no—
142C4⋊C4—384no—
143C4⋊C4—384no—
144C4⋊C4—762no—
145C4⋊C4—761no—
146C4⋊C4—761no—
147C42—194no—
148C42—384no—
149C42—384no—
150C23C23×D1911yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—22no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—194no—
164C2×C4—194no—
165C2×C4—194no—
166C2×C4—382no—
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×C4Q8×D1912yes—
176C22#1059743011yescharacteristic
177C22C2×Q8×D1911yescharacteristic
178C22#41×D1912yes—
179C22#41×D1912yes—
180C22#1059743611yescharacteristic
181C4—22no—
182C4—42no—
183C4—42no—
184C4—41no—
185C4—41no—
186C4—198no—
187C4—762no—
188C4—762no—
189C4—762no—
190C2#125×D1912yes—
191C2#1192717311yescharacteristic
192C2#1192725611yescharacteristic
193C2#1192726112yes—
194C2#1192727811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, prime radical, cosocleC23×C19C24
FittingC19×#400C2
hypercenter#400D19
hypocenterC19#2571
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
128. C19#2571semidirect

Maximal subgroups

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

subgroupindex
#119264862
#119264832
#119264412
#119264392
#119264132
#119264082
#119263952
C19×#4002
#257119