Finite Group Databasebeta

← #14562649

Subgroups — #14562649

Order 2432.

232 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 53 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#11926872C211yesmaximal, characteristic, complemented
2#11926855C211yesmaximal, characteristic, complemented
3#11926469C211yesmaximal, characteristic, complemented
4#11926281C211yesmaximal, characteristic, complemented
5#11926278C211yesmaximal, characteristic, complemented
6#11926268C211yesmaximal, characteristic, complemented
7C19×#538C211yesmaximal, characteristic
8C19×#126—21no—
9C19×#124—21no—
10C19×#123—21no—
11C19×C22⋊Q8C2211yescharacteristic
12C19×#121—21no—
13C19×#121C2211yescharacteristic
14C19×#120—21no—
15C4×D4×C19—21no—
16C2×C22⋊C4×C19C2211yescharacteristic
17C2×C22⋊Dic19—21no—
18C2×C4⋊Dic19C2211yescharacteristic
19#10597292—21no—
20#10597289—21no—
21C19⋊#95—21no—
22C19⋊#95C2211yescharacteristic
23C22⋊(C19⋊C8)C2211yescharacteristic
24C22⋊(C19⋊C8)C2211yescharacteristic
25#10597265—21no—
26#10597264—21no—
27C24×C19D411yescharacteristic
28C2×Q8×C19D411yescharacteristic
29C2×D4×C19—21no—
30C2×D4×C19—21no—
31C2×D4×C19—21no—
32C2×D4×C19D411yescharacteristic
33C22×C4×C19—21no—
34C22×C4×C19D411yescharacteristic
35C22×C4×C19C2311yescharacteristic
36C22×Dic19—21no—
37C22×Dic19—21no—
38C4⋊C4×C19—21no—
39C4⋊C4×C19—21no—
40C4⋊C4×C19D411yescharacteristic
41C4⋊C4×C19D411yescharacteristic
42C22⋊C4×C19—21no—
43C22⋊C4×C19—21no—
44C22⋊C4×C19—21no—
45C22⋊C4×C19—21no—
46C22⋊C4×C19—21no—
47C22⋊C4×C19—21no—
48C22⋊C4×C19—21no—
49C42×C19—21no—
50C22⋊Dic19—42no—
51C4⋊Dic19—21no—
52C4⋊Dic19—21no—
53C2×C19⋊C8—21no—
54C2×C19⋊C8—21no—
55C23×C19—21no—
56C23×C19—21no—
57C23×C19—21no—
58C23×C19—21no—
59C23×C19—41no—
60C23×C19—41no—
61C23×C19C2×D411yescharacteristic
62Q8×C19—41no—
63D4×C19—41no—
64D4×C19—41no—
65D4×C19—41no—
66D4×C19—81no—
67D4×C19—81no—
68C2×C4×C19—21no—
69C2×C4×C19—21no—
70C2×C4×C19—21no—
71C2×C4×C19—21no—
72C2×C4×C19—41no—
73C2×C4×C19—41no—
74C2×C4×C19—81no—
75C2×C4×C19C2×D411yescharacteristic
76C2×C4×C19C2×D411yescharacteristic
77C2×Dic19—41no—
78C2×Dic19—41no—
79C2×Dic19—41no—
80C2×Dic19—41no—
81C2×Dic19—41no—
82C2×Dic19—41no—
83C19⋊C8—41no—
84C19⋊C8—41no—
85#1612—191nomaximal, Sylow
86C22×C19—21no—
87C22×C19—21no—
88C22×C19—42no—
89C22×C19—41no—
90C22×C19—41no—
91C22×C19—41no—
92C22×C19—41no—
93C22×C19—41no—
94C22×C19—41no—
95C22×C19—81no—
96C22×C19#12011yescharacteristic
97C22×C19#13511yescharacteristic
98C22×C19AGL(1,ℤ/8)11yescharacteristic
99C4×C19—21no—
100C4×C19—21no—
101C4×C19—41no—
102C4×C19—41no—
103C4×C19—41no—
104C4×C19—41no—
105Dic19—81no—
106Dic19—81no—
107#538D1911yescharacteristic
108#483—191no—
109#480—191no—
110#397—191no—
111#328—191no—
112#327—191no—
113#323—191no—
114C2×C19—21no—
115C2×C19—21no—
116C2×C19—81no—
117C2×C19—81no—
118C2×C19#44911yescharacteristic
119C2×C19#45511yescharacteristic
120C2×C19#45811yescharacteristic
121#126—21no—
122#124—21no—
123#123—21no—
124C22⋊Q8C2×D1911yescharacteristic
125#121—21no—
126#121C2×D1911yescharacteristic
127#120—21no—
128C4×D4—21no—
129C2×C4⋊C4—191no—
130C2×C22⋊C4—381no—
131C2×C22⋊C4C2×D1911yescharacteristic
132#107—381no—
133#106—381no—
134#103—381no—
135#102—381no—
136C22⋊C8—191no—
137C22⋊C8—191no—
138#95—191no—
139#95—381no—
140C19#161211yescharacteristic, complemented, Sylow
141C24C22⋊D1911yescharacteristic
142C2×Q8C22⋊D1911yescharacteristic
143C2×D4—21no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4C22⋊D1911yescharacteristic
147C22×C4—21no—
148C22×C4—381no—
149C22×C4—381no—
150C22×C4C22⋊D1911yescharacteristic
151C22×C4C22×D1911yescharacteristic
152C2×C8—381no—
153C2×C8—381no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—381no—
157C4⋊C4—381no—
158C4⋊C4C22⋊D1911yescharacteristic
159C4⋊C4C22⋊D1911yescharacteristic
160C22⋊C4—21no—
161C22⋊C4—21no—
162C22⋊C4—21no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—21no—
166C22⋊C4—21no—
167C22⋊C4—762no—
168C42—21no—
169C23—21no—
170C23—21no—
171C23—21no—
172C23—21no—
173C23—41no—
174C23—41no—
175C23C2×C22⋊D1911yescharacteristic
176Q8—41no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—81no—
181D4—81no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—81no—
189C2×C4—761no—
190C2×C4—761no—
191C2×C4—761no—
192C2×C4—761no—
193C2×C4—761no—
194C2×C4—761no—
195C2×C4C2×C22⋊D1911yescharacteristic
196C2×C4C2×C22⋊D1911yescharacteristic
197C8—761no—
198C8—761no—
199C22—21no—
200C22—21no—
201C22—42no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—81no—
209C22#1059739511yescharacteristic
210C22#1059739611yescharacteristic
211C22#1059739911yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—41no—
216C4—41no—
217C4—41no—
218C4—1521no—
219C4—1521no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—81no—
224C2#1192668911yescharacteristic
225C2#1192672211yescharacteristic
226C2#1192673411yescharacteristic
subgroupG/H
centerC22#10597399
commutator, cosocleC22×C4×C19C23
FrattiniC22×C4C22×D19
Fitting, prime radicalC19×#538C2
socleC22×C19#120
hypercenter#538D19
hypocenterC19#1612
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #538

Complements

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

NH ≅ G/Ntype
1. #11926872C2semidirect
2. #11926855C2semidirect
3. #11926469C2semidirect
4. #11926281C2semidirect
5. #11926278C2semidirect
6. #11926268C2semidirect
140. C19#1612semidirect

Maximal subgroups

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

subgroupindex
#119268722
#119268552
#119264692
#119262812
#119262782
#119262682
C19×#5382
#161219