Finite Group Databasebeta

← #14570586

Subgroups — #14570586

Order 2432.

416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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×#10597336C212yesmaximal
2#11926477C212yesmaximal
3#11926477C212yesmaximal
4#11926476C212yesmaximal
5#11926442C211yesmaximal, characteristic
6#11926442C211yesmaximal, characteristic
7#11926441C212yesmaximal
8#11926430C212yesmaximal
9C19×#389C211yesmaximal, characteristic
10C2×C4⋊C4×C19C2212yes—
11C2×C4⋊C4×C19C2211yescharacteristic
12C2×C4⋊C4×C19C2211yescharacteristic
13C2×C42×C19C2211yescharacteristic
14C2×C4⋊Dic19C2212yes—
15C2×C4⋊Dic19C2212yes—
16C2×C4⋊Dic19C2211yescharacteristic
17C2×C4⋊Dic19C2211yescharacteristic
18C2×C4⋊Dic19C2211yescharacteristic
19C2×C4⋊Dic19C2211yescharacteristic
20C2×Dic19⋊C4C2212yes—
21C2×Dic19⋊C4C2212yes—
22C2×Dic19⋊C4C2212yes—
23C2×Dic19⋊C4C2212yes—
24C2×C4×Dic19C2212yes—
25#10597336—28no—
26C19×#95C2212yes—
27C19⋊#95C2212yes—
28C19⋊#95C2212yes—
29C19⋊#95C2212yes—
30C19⋊#95C2212yes—
31C19⋊#95C2212yes—
32C22×C4×C19C2312yes—
33C22×C4×C19C2311yescharacteristic
34C22×C4×C19C2311yescharacteristic
35C22×C4×C19C2312yes—
36C22×C4×C19C2311yescharacteristic
37C22×Dic19C2312yes—
38C22×Dic19C2312yes—
39C22×Dic19C2312yes—
40C22×Dic19C2312yes—
41C4⋊C4×C19—24no—
42C4⋊C4×C19—41no—
43C4⋊C4×C19Q814yes—
44C42×C19—41no—
45C4⋊Dic19—22no—
46C4⋊Dic19—24no—
47C4⋊Dic19—24no—
48C4⋊Dic19—41no—
49C4⋊Dic19—41no—
50C4⋊Dic19D414yes—
51Dic19⋊C4—24no—
52Dic19⋊C4—24no—
53Dic19⋊C4—24no—
54Dic19⋊C4—42no—
55C4×Dic19—24no—
56C23×C19C2411yescharacteristic
57C2×C4×C19—22no—
58C2×C4×C19—21no—
59C2×C4×C19—21no—
60C2×C4×C19—21no—
61C2×C4×C19—21no—
62C2×C4×C19—21no—
63C2×C4×C19—21no—
64C2×C4×C19—22no—
65C2×C4×C19—22no—
66C2×C4×C19—22no—
67C2×C4×C19—22no—
68C2×C4×C19C2×D412yes—
69C2×C4×C19C2×Q812yes—
70C2×C4×C19C2×Q814yes—
71C2×C4×C19#4112yes—
72C2×Dic19—22no—
73C2×Dic19—22no—
74C2×Dic19—22no—
75C2×Dic19—22no—
76C2×Dic19—22no—
77C2×Dic19—22no—
78C2×Dic19—22no—
79C2×Dic19—22no—
80C2×Dic19—22no—
81C2×Dic19—22no—
82C2×Dic19—22no—
83C2×Dic19C2×D414yes—
84#2726—191nomaximal, Sylow
85C22×C19C22×D411yescharacteristic
86C22×C19C22×Q811yescharacteristic
87C22×C19C2×#4111yescharacteristic
88C22×C19H(5,𝔽2)11yescharacteristic
89C22×C192−1+411yescharacteristic
90C22×C192−1+411yescharacteristic
91C22×C192−1+411yescharacteristic
92C4×C19—22no—
93C4×C19—22no—
94C4×C19—22no—
95C4×C19—24no—
96C4×C19—42no—
97Dic19—24no—
98Dic19—42no—
99Dic19—42no—
100Dic19—42no—
101C2×#125—192no—
102#398—192no—
103#398—192no—
104#398—192no—
105#389—191no—
106#389—191no—
107#389—192no—
108#389D1911yescharacteristic
109#387—192no—
110C2×C19#53711yescharacteristic
111C2×C19#53911yescharacteristic
112C2×C19#54411yescharacteristic
113C2×C19#54711yescharacteristic
114C2×C19D4×Q811yescharacteristic
115C2×C19#55711yescharacteristic
116C2×C19#56411yescharacteristic
117#125—388no—
118C2×C4⋊C4—191no—
119C2×C4⋊C4—192no—
120C2×C4⋊C4—192no—
121C2×C4⋊C4—192no—
122C2×C4⋊C4—192no—
123C2×C4⋊C4—192no—
124C2×C4⋊C4—191no—
125C2×C4⋊C4—191no—
126C2×C4⋊C4—192no—
127C2×C4⋊C4—191no—
128C2×C4⋊C4C2×D1912yes—
129C2×C4⋊C4C2×D1911yescharacteristic
130C2×C4⋊C4C2×D1911yescharacteristic
131C2×C42—192no—
132C2×C42C2×D1911yescharacteristic
133#95—192no—
134#95—192no—
135#95—192no—
136#95—192no—
137#95—192no—
138#95C2×D1912yes—
139C19#272611yescharacteristic, complemented, Sylow
140C22×C4—192no—
141C22×C4—192no—
142C22×C4—192no—
143C22×C4—192no—
144C22×C4C22×D1912yes—
145C22×C4C22×D1911yescharacteristic
146C22×C4C22×D1912yes—
147C22×C4C22×D1911yescharacteristic
148C22×C4C22×D1911yescharacteristic
149C4⋊C4—24no—
150C4⋊C4—41no—
151C4⋊C4—194no—
152C4⋊C4—384no—
153C4⋊C4—384no—
154C4⋊C4—384no—
155C4⋊C4—384no—
156C4⋊C4—384no—
157C4⋊C4—382no—
158C4⋊C4—762no—
159C4⋊C4—761no—
160C4⋊C4—761no—
161C4⋊C4Dic3814yes—
162C42—41no—
163C42—384no—
164C23C23×D1911yescharacteristic
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—194no—
177C2×C4—382no—
178C2×C4—382no—
179C2×C4—382no—
180C2×C4—382no—
181C2×C4—382no—
182C2×C4—382no—
183C2×C4—382no—
184C2×C4—382no—
185C2×C4—382no—
186C2×C4—382no—
187C2×C4—382no—
188C2×C4C2×Dic3812yes—
189C2×C4C2×Dic3814yes—
190C2×C4D4×D1912yes—
191C2×C4#6454512yes—
192C22C22×Dic3811yescharacteristic
193C22C2×D4×D1911yescharacteristic
194C22#1059743011yescharacteristic
195C22C2×#6454511yescharacteristic
196C22#1059743311yescharacteristic
197C22#1059743611yescharacteristic
198C22#1059743611yescharacteristic
199C4—22no—
200C4—22no—
201C4—22no—
202C4—24no—
203C4—42no—
204C4—384no—
205C4—762no—
206C4—762no—
207C4—762no—
208C2#1192712111yescharacteristic
209C2#1192714311yescharacteristic
210C2#1192717511yescharacteristic
211C2#1192719711yescharacteristic
212C2D4×Dic3811yescharacteristic
213C2#1192727311yescharacteristic
214C2C19⋊#56411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, prime radical, cosocleC23×C19C24
FittingC19×#389C2
hypercenter#389D19
hypocenterC19#2726
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
139. C19#2726semidirect

Maximal subgroups

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

subgroupindex
C2×#105973362
#119264772
#119264762
#119264422
#119264412
#119264302
C19×#3892
#272619