Finite Group Databasebeta

← #14569513

Subgroups — #14569513

Order 2432.

416 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 129 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×#10597335C211yesmaximal, characteristic
2C2×#10597333C211yesmaximal, characteristic
3#11926485C212yesmaximal
4#11926482C211yesmaximal, characteristic
5#11926478C212yesmaximal
6#11926465C211yesmaximal, characteristic
7#11926464C211yesmaximal, characteristic
8#11926431C212yesmaximal
9#11926427C212yesmaximal
10#11926411C211yesmaximal, characteristic
11C19×#400C211yesmaximal, characteristic
12C22×Dic38C2211yescharacteristic
13C2×C4⋊C4×C19C2211yescharacteristic
14C2×C4⋊C4×C19C2211yescharacteristic
15C2×C4⋊Dic19C2211yescharacteristic
16C2×C4⋊Dic19C2212yes—
17C2×Dic19⋊C4C2211yescharacteristic
18C2×Dic19⋊C4C2211yescharacteristic
19C2×Dic19⋊C4C2211yescharacteristic
20C2×Dic19⋊C4C2211yescharacteristic
21C2×Dic19⋊C4C2212yes—
22C2×Dic19⋊C4C2212yes—
23C2×C4×Dic19C2212yes—
24C2×C4×Dic19C2211yescharacteristic
25#10597335—24no—
26#10597333—24no—
27C19×#95C2211yescharacteristic
28C19×#95C2212yes—
29C19×#95C2212yes—
30C19⋊#95C2212yes—
31C19⋊#95C2211yescharacteristic
32C19⋊#95C2212yes—
33C19⋊#95C2212yes—
34C19⋊#95C2212yes—
35C19⋊#95C2212yes—
36C19⋊#95C2212yes—
37C22×C4×C19C2312yes—
38C22×C4×C19C2311yescharacteristic
39C22×C4×C19C2311yescharacteristic
40C22×C4×C19C2312yes—
41C22×C4×C19C2311yescharacteristic
42C22×Dic19C2312yes—
43C22×Dic19C2311yescharacteristic
44C22×Dic19C2311yescharacteristic
45C22×Dic19C2311yescharacteristic
46C22×Dic19C2311yescharacteristic
47C22×Dic19C2312yes—
48C2×Dic38—22no—
49C2×Dic38—24no—
50C4⋊C4×C19—22no—
51C4⋊C4×C19—22no—
52C4⋊Dic19—22no—
53C4⋊Dic19—24no—
54Dic19⋊C4—22no—
55Dic19⋊C4—24no—
56Dic19⋊C4—22no—
57Dic19⋊C4—22no—
58Dic19⋊C4—22no—
59Dic19⋊C4—24no—
60C4×Dic19—24no—
61C4×Dic19D414yes—
62C23×C19C2411yescharacteristic
63C2×C4×C19—22no—
64C2×C4×C19—22no—
65C2×C4×C19—21no—
66C2×C4×C19—21no—
67C2×C4×C19—22no—
68C2×C4×C19—22no—
69C2×C4×C19—21no—
70C2×C4×C19—24no—
71C2×C4×C19—21no—
72C2×C4×C19—22no—
73C2×C4×C19—22no—
74C2×C4×C19C2×D412yes—
75C2×Dic19—22no—
76C2×Dic19—22no—
77C2×Dic19—21no—
78C2×Dic19—21no—
79C2×Dic19—22no—
80C2×Dic19—21no—
81C2×Dic19—21no—
82C2×Dic19—22no—
83C2×Dic19—22no—
84C2×Dic19—21no—
85C2×Dic19—22no—
86C2×Dic19—21no—
87C2×Dic19—22no—
88C2×Dic19C2×D412yes—
89C2×Dic19C2×D412yes—
90C2×Dic19#4114yes—
91Dic38—28no—
92#2634—191nomaximal, Sylow
93C22×C19C22×D411yescharacteristic
94C22×C19C2×#4112yes—
95C22×C192−1+411yescharacteristic
96C22×C192−1+412yes—
97C22×C192−1+411yescharacteristic
98C4×C19—22no—
99C4×C19—41no—
100C4×C19—42no—
101C4×C19—41no—
102C4×C19—42no—
103Dic19—24no—
104Dic19—22no—
105Dic19—22no—
106Dic19—41no—
107Dic19—41no—
108Dic19—42no—
109C2×#125—191no—
110C2×C4×Q8—191no—
111#400—191no—
112#400—192no—
113#400D1911yescharacteristic
114#398—192no—
115#395—191no—
116#395—191no—
117#387—192no—
118#387—192no—
119#383—191no—
120C2×C19#52511yescharacteristic
121C2×C19#53611yescharacteristic
122C2×C19#53611yescharacteristic
123C2×C19#54112yes—
124C2×C19#54112yes—
125C22×Q8—191no—
126#125—384no—
127C4×Q8—384no—
128C2×C4⋊C4—192no—
129C2×C4⋊C4—191no—
130C2×C4⋊C4—191no—
131C2×C4⋊C4—191no—
132C2×C4⋊C4—191no—
133C2×C4⋊C4—191no—
134C2×C4⋊C4—192no—
135C2×C4⋊C4—192no—
136C2×C4⋊C4C2×D1911yescharacteristic
137C2×C4⋊C4C2×D1911yescharacteristic
138C2×C42—191no—
139C2×C42—192no—
140#95—192no—
141#95—191no—
142#95—192no—
143#95—192no—
144#95—192no—
145#95—192no—
146#95—192no—
147#95C2×D1911yescharacteristic
148#95C2×D1912yes—
149#95C2×D1912yes—
150C19#263411yescharacteristic, complemented, Sylow
151C2×Q8—384no—
152C2×Q8—382no—
153C22×C4—191no—
154C22×C4—191no—
155C22×C4—192no—
156C22×C4—192no—
157C22×C4—191no—
158C22×C4—191no—
159C22×C4C22×D1912yes—
160C22×C4C22×D1912yes—
161C22×C4C22×D1911yescharacteristic
162C22×C4C22×D1911yescharacteristic
163C22×C4C22×D1911yescharacteristic
164C4⋊C4—22no—
165C4⋊C4—22no—
166C4⋊C4—384no—
167C4⋊C4—384no—
168C4⋊C4—382no—
169C4⋊C4—382no—
170C4⋊C4—382no—
171C4⋊C4—384no—
172C4⋊C4—382no—
173C4⋊C4—382no—
174C42—194no—
175C42—384no—
176C23C23×D1911yescharacteristic
177Q8—388no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—24no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—192no—
190C2×C4—192no—
191C2×C4—194no—
192C2×C4—382no—
193C2×C4—381no—
194C2×C4—382no—
195C2×C4—382no—
196C2×C4—381no—
197C2×C4—381no—
198C2×C4—381no—
199C2×C4—381no—
200C2×C4—382no—
201C2×C4—382no—
202C2×C4—382no—
203C2×C4—381no—
204C2×C4—382no—
205C2×C4D4×D1912yes—
206C22C2×D4×D1911yescharacteristic
207C22#1059743311yescharacteristic
208C22#41×D1912yes—
209C22#1059743612yes—
210C22#1059743611yescharacteristic
211C4—22no—
212C4—41no—
213C4—42no—
214C4—41no—
215C4—42no—
216C4—384no—
217C4—382no—
218C4—382no—
219C4—761no—
220C4—761no—
221C4—762no—
222C2#1192705211yescharacteristic
223C2#1192711411yescharacteristic
224C2#1192711711yescharacteristic
225C2#1192715112yes—
226C2#1192715312yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, prime radical, cosocleC23×C19C24
FittingC19×#400C2
hypercenter#400D19
hypocenterC19#2634
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
150. C19#2634semidirect

Maximal subgroups

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

subgroupindex
C2×#105973352
C2×#105973332
#119264852
#119264822
#119264782
#119264652
#119264642
#119264312
#119264272
#119264112
C19×#4002
#263419