Finite Group Databasebeta

← #14569831

Subgroups — #14569831

Order 2432.

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

normal subgroups only

This group has 408 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
1#11926480C212yesmaximal
2#11926478C212yesmaximal, complemented
3#11926476C212yesmaximal, complemented
4#11926467C212yesmaximal
5#11926441C212yesmaximal, complemented
6#11926431C212yesmaximal, complemented
7#11926404C211yesmaximal, characteristic
8C4×C22⋊Dic19C211yesmaximal, characteristic
9C19×#381C211yesmaximal, characteristic
10C23×C4×C19C2211yescharacteristic
11C2×C22⋊C4×C19C2212yes—
12C2×C22⋊Dic19C2212yes—
13C2×C22⋊Dic19C2211yescharacteristic
14C2×C22⋊Dic19C2211yescharacteristic
15C2×C4⋊Dic19C2212yes—
16C2×C4⋊Dic19C2212yes—
17C2×C4⋊Dic19C2212yes—
18C2×Dic19⋊C4C2212yes—
19C2×Dic19⋊C4C2212yes—
20C2×Dic19⋊C4C2212yes—
21C2×Dic19⋊C4C2212yes—
22C2×C4×Dic19C2212yes—
23C19×#95C2211yescharacteristic
24C19×#95C2211yescharacteristic
25C19×#95C2212yes—
26C19⋊#95C2211yescharacteristic
27C19⋊#95C2211yescharacteristic
28C19⋊#95C2212yes—
29C19⋊#95C2212yes—
30C19⋊#95C2212yes—
31C24×C19C2311yescharacteristic
32C22×C4×C19—42no—
33C22×C4×C19Q814yes—
34C22×C4×C19C2312yes—
35C22×C4×C19C2312yes—
36C22×C4×C19C2311yescharacteristic
37C22×C4×C19C2311yescharacteristic
38C22×Dic19C2312yes—
39C22×Dic19C2312yes—
40C22×Dic19C2312yes—
41C22×Dic19C2312yes—
42C22⋊C4×C19—42no—
43C22⋊Dic19—24no—
44C22⋊Dic19—41no—
45C22⋊Dic19—41no—
46C4⋊Dic19—42no—
47C4⋊Dic19—42no—
48C4⋊Dic19—42no—
49Dic19⋊C4—24no—
50Dic19⋊C4—24no—
51Dic19⋊C4—42no—
52Dic19⋊C4—42no—
53C4×Dic19—42no—
54C23×C19—22no—
55C23×C19—21no—
56C23×C19—22no—
57C23×C19—21no—
58C23×C19C2×Q812yes—
59C23×C19C2411yescharacteristic
60C2×C4×C19—22no—
61C2×C4×C19—22no—
62C2×C4×C19—22no—
63C2×C4×C19—22no—
64C2×C4×C19—22no—
65C2×C4×C19—22no—
66C2×C4×C19—22no—
67C2×C4×C19—22no—
68C2×C4×C19—44no—
69C2×C4×C19C2×Q812yes—
70C2×C4×C19C2×Q812yes—
71C2×Dic19—22no—
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#4114yes—
83#2667—191nomaximal, Sylow
84C22×C19—22no—
85C22×C19—22no—
86C22×C19—22no—
87C22×C19—42no—
88C22×C19—42no—
89C22×C19C22×Q811yescharacteristic
90C22×C19C2×#4112yes—
91C22×C19H(5,𝔽2)12yes—
92C22×C19H(5,𝔽2)11yescharacteristic
93C22×C192−1+411yescharacteristic
94C4×C19—22no—
95C4×C19—22no—
96C4×C19—42no—
97C4×C19—42no—
98Dic19—24no—
99Dic19—42no—
100Dic19—42no—
101Dic19—42no—
102#399—192no—
103#398—192no—
104#398—192no—
105#396—192no—
106#389—192no—
107#387—192no—
108#381D1911yescharacteristic
109#380—191no—
110C4×C22⋊C4—191no—
111C2×C19—42no—
112C2×C19#53311yescharacteristic
113C2×C19#53912yes—
114C2×C19#54012yes—
115C2×C19#54311yescharacteristic
116C2×C19#54411yescharacteristic
117C23×C4C2×D1911yescharacteristic
118C2×C4⋊C4—192no—
119C2×C4⋊C4—192no—
120C2×C4⋊C4—192no—
121C2×C4⋊C4—192no—
122C2×C4⋊C4—192no—
123C2×C4⋊C4—192no—
124C2×C4⋊C4—192no—
125C2×C22⋊C4—192no—
126C2×C22⋊C4—191no—
127C2×C22⋊C4—191no—
128C2×C22⋊C4C2×D1912yes—
129C2×C42—192no—
130#95—191no—
131#95—191no—
132#95—192no—
133#95—192no—
134#95—192no—
135#95C2×D1911yescharacteristic
136#95C2×D1911yescharacteristic
137#95C2×D1912yes—
138C19#266711yescharacteristic, complemented, Sylow
139C24C22×D1911yescharacteristic
140C22×C4—42no—
141C22×C4—192no—
142C22×C4—192no—
143C22×C4—192no—
144C22×C4—192no—
145C22×C4Dic3814yes—
146C22×C4C22×D1912yes—
147C22×C4C22×D1912yes—
148C22×C4C22×D1911yescharacteristic
149C22×C4C22×D1911yescharacteristic
150C4⋊C4—384no—
151C4⋊C4—384no—
152C4⋊C4—762no—
153C4⋊C4—762no—
154C4⋊C4—762no—
155C4⋊C4—762no—
156C4⋊C4—762no—
157C22⋊C4—42no—
158C22⋊C4—384no—
159C22⋊C4—761no—
160C22⋊C4—761no—
161C42—762no—
162C23—22no—
163C23—22no—
164C23—21no—
165C23—21no—
166C23C2×Dic3812yes—
167C23C23×D1911yescharacteristic
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—44no—
177C2×C4—194no—
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×C4—382no—
189C2×C4C2×Dic3812yes—
190C2×C4C2×Dic3812yes—
191C22—22no—
192C22—22no—
193C22—22no—
194C22—42no—
195C22—42no—
196C22C22×Dic3811yescharacteristic
197C22#1059743012yes—
198C22#41×D1912yes—
199C22#1059743511yescharacteristic
200C22#1059743611yescharacteristic
201C4—22no—
202C4—22no—
203C4—42no—
204C4—42no—
205C4—384no—
206C4—762no—
207C4—762no—
208C4—762no—
209C2—42no—
210C2#1192709711yescharacteristic
211C2#1192713712yes—
212C2#1192714612yes—
213C2#1192717011yescharacteristic
214C2#1192717211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#381C2
prime radicalC24×C19C23
hypercenter#381D19
hypocenterC19#2667
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. #11926478C2semidirect
3. #11926476C2semidirect
5. #11926441C2semidirect
6. #11926431C2semidirect
138. C19#2667semidirect

Maximal subgroups

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

subgroupindex
#119264802
#119264782
#119264762
#119264672
#119264412
#119264312
#119264042
C4×C22⋊Dic192
C19×#3812
#266719