Finite Group Databasebeta

← #14571049

Subgroups — #14571049

Order 2432.

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

normal subgroups only

This group has 424 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#11926486C212yesmaximal, complemented
2#11926464C212yesmaximal, complemented
3#11926456C211yesmaximal, characteristic
4#11926456C211yesmaximal, characteristic
5#11926448C212yesmaximal, complemented
6#11926437C212yesmaximal
7#11926417C212yesmaximal
8#11926409C212yesmaximal, complemented
9C19×#385C211yesmaximal, characteristic
10C23×C4×C19C2211yescharacteristic
11C22×Dic38C2211yescharacteristic
12C22×Dic38C2211yescharacteristic
13C2×C4⋊C4×C19C2212yes—
14C2×C22⋊C4×C19C2211yescharacteristic
15C2×C22⋊C4×C19C2211yescharacteristic
16C2×C22⋊Dic19C2212yes—
17C2×C22⋊Dic19C2212yes—
18C2×C4⋊Dic19C2212yes—
19C2×Dic19⋊C4C2212yes—
20C2×Dic19⋊C4C2212yes—
21C2×C4×Dic19C2212yes—
22C19×#95C2212yes—
23C19⋊#95C2211yescharacteristic
24C19⋊#95C2212yes—
25C19⋊#95C2212yes—
26C19⋊#95C2212yes—
27C19⋊#95C2212yes—
28C19⋊#95C2212yes—
29C19⋊#95C2212yes—
30C19⋊#95C2211yescharacteristic
31C24×C19C2311yescharacteristic
32C22×C4×C19—41no—
33C22×C4×C19—42no—
34C22×C4×C19C2311yescharacteristic
35C22×C4×C19C2311yescharacteristic
36C22×C4×C19C2312yes—
37C22×C4×C19C2312yes—
38C22×Dic19C2312yes—
39C22×Dic19C2312yes—
40C22×Dic19C2312yes—
41C22×Dic19C2312yes—
42C2×Dic38—24no—
43C2×Dic38—41no—
44C2×Dic38—41no—
45C2×Dic38—42no—
46C4⋊C4×C19—42no—
47C22⋊C4×C19—41no—
48C22⋊C4×C19Q814yescomplemented
49C22⋊Dic19—24no—
50C22⋊Dic19—42no—
51C4⋊Dic19—42no—
52Dic19⋊C4—42no—
53Dic19⋊C4—42no—
54C4×Dic19—24no—
55C23×C19—22no—
56C23×C19—22no—
57C23×C19—21no—
58C23×C19—21no—
59C23×C19C2×Q812yes—
60C23×C19C2411yescharacteristic
61C2×C4×C19—22no—
62C2×C4×C19—22no—
63C2×C4×C19—22no—
64C2×C4×C19—22no—
65C2×C4×C19—22no—
66C2×C4×C19—21no—
67C2×C4×C19—21no—
68C2×C4×C19—22no—
69C2×C4×C19—22no—
70C2×C4×C19—44no—
71C2×C4×C19C2×Q814yes—
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×Dic19#4114yes—
84Dic38—44no—
85Dic38—44no—
86#2763—191nomaximal, Sylow
87C22×C19—22no—
88C22×C19—24no—
89C22×C19—42no—
90C22×C19—41no—
91C22×C19—41no—
92C22×C19C22×Q811yescharacteristic
93C22×C19C2×#4112yes—
94C22×C19H(5,𝔽2)12yes—
95C22×C19H(5,𝔽2)11yescharacteristic
96C22×C192−1+411yescharacteristic
97C4×C19—24no—
98C4×C19—41no—
99C4×C19—41no—
100C4×C19—42no—
101Dic19—24no—
102Dic19—42no—
103Dic19—42no—
104Dic19—42no—
105#400—192no—
106#395—192no—
107#393—191no—
108#393—191no—
109#391—192no—
110#388—192no—
111#385—192no—
112#385D1911yescharacteristic
113#382—192no—
114C2×C19—42no—
115C2×C19#54212yes—
116C2×C19#54411yescharacteristic
117C2×C19#55111yescharacteristic
118C2×C19#55412yes—
119C2×C19H(3,𝔽4)11yescharacteristic
120C22×Q8—191no—
121C22×Q8—191no—
122C23×C4C2×D1911yescharacteristic
123C2×C4⋊C4—192no—
124C2×C4⋊C4—192no—
125C2×C4⋊C4—192no—
126C2×C4⋊C4C2×D1912yes—
127C2×C22⋊C4—192no—
128C2×C22⋊C4—192no—
129C2×C22⋊C4C2×D1911yescharacteristic
130C2×C22⋊C4C2×D1911yescharacteristic
131C2×C42—192no—
132#95—191no—
133#95—192no—
134#95—192no—
135#95—192no—
136#95—192no—
137#95—192no—
138#95—192no—
139#95—191no—
140#95C2×D1912yes—
141C19#276311yescharacteristic, complemented, Sylow
142C24C22×D1911yescharacteristic
143C2×Q8—384no—
144C2×Q8—761no—
145C2×Q8—761no—
146C2×Q8—762no—
147C22×C4—42no—
148C22×C4—41no—
149C22×C4—192no—
150C22×C4—192no—
151C22×C4—192no—
152C22×C4—192no—
153C22×C4C22×D1911yescharacteristic
154C22×C4C22×D1911yescharacteristic
155C22×C4C22×D1912yes—
156C22×C4C22×D1912yes—
157C4⋊C4—42no—
158C4⋊C4—762no—
159C4⋊C4—762no—
160C4⋊C4—762no—
161C22⋊C4—41no—
162C22⋊C4—384no—
163C22⋊C4—762no—
164C22⋊C4Dic3814yescomplemented
165C42—384no—
166C23—21no—
167C23—22no—
168C23—21no—
169C23—22no—
170C23C2×Dic3812yes—
171C23C23×D1911yescharacteristic
172Q8—764no—
173Q8—764no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—44no—
184C2×C4—194no—
185C2×C4—382no—
186C2×C4—382no—
187C2×C4—382no—
188C2×C4—382no—
189C2×C4—382no—
190C2×C4—382no—
191C2×C4—382no—
192C2×C4—382no—
193C2×C4—382no—
194C2×C4—382no—
195C2×C4—382no—
196C2×C4C2×Dic3814yes—
197C22—22no—
198C22—24no—
199C22—42no—
200C22—41no—
201C22—41no—
202C22C22×Dic3811yescharacteristic
203C22#1059743012yes—
204C22#1059743011yescharacteristic
205C22#1059743311yescharacteristic
206C22#41×D1912yes—
207C4—24no—
208C4—41no—
209C4—42no—
210C4—41no—
211C4—384no—
212C4—762no—
213C4—762no—
214C4—762no—
215C2—42no—
216C2#1192716412yes—
217C2#1192717511yescharacteristic
218C2#1192722211yescharacteristic
219C2#1192725312yes—
220C2#1192728711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#385C2
prime radicalC24×C19C23
hypercenter#385D19
hypocenterC19#2763
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. #11926486C2semidirect
2. #11926464C2semidirect
5. #11926448C2semidirect
8. #11926409C2semidirect
48. C22⋊C4×C19Q8semidirect
141. C19#2763semidirect
164. C22⋊C4Dic38semidirect

Maximal subgroups

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

subgroupindex
#119264862
#119264642
#119264562
#119264482
#119264372
#119264172
#119264092
C19×#3852
#276319