Finite Group Databasebeta

← #14565639

Subgroups — #14565639

Order 2432.

260 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 41 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#11927284C211yesmaximal, characteristic, complemented
2#11926731C211yesmaximal, characteristic, complemented
3#11926712C211yesmaximal, characteristic, complemented
4#11926336C211yesmaximal, characteristic, complemented
5#11926334C211yesmaximal, characteristic, complemented
6#11926330C211yesmaximal, characteristic, complemented
7C19×#458C211yesmaximal, characteristic, complemented
8C19×H(5,𝔽2)C2211yescharacteristic
9C19×#123—21no—
10C19×#123C2211yescharacteristic
11#10597395—21no—
12#10597386C2211yescharacteristic
13#10597383—21no—
14#10597383C2211yescharacteristic
15#10597376—21no—
16#10597344—21no—
17#10597341—21no—
18#10597330—21no—
19#10597329—21no—
20#10597328—21no—
21C19×#99—21no—
22C19×#99C2211yescharacteristic
23#10597294—21no—
24#10597291—21no—
25#10597291C2211yescharacteristic
26#10597290C2211yescharacteristic
27C23×D19D411yescharacteristic
28#41×C19—21no—
29#41×C19—41no—
30C2×D4×C19—21no—
31C2×D4×C19—21no—
32C2×D4×C19—41no—
33C2×D4×C19C2311yescharacteristic
34C22×C4×C19D411yescharacteristic, complemented
35C2×C22⋊D19—21no—
36C2×C22⋊D19—21no—
37C2×C22⋊D19—21no—
38C2×C22⋊D19—41no—
39C2×D76—21no—
40C2×D76—21no—
41C2×D76D411yescharacteristic, complemented
42C2×C4×D19—21no—
43C4⋊C4×C19—21no—
44C4⋊C4×C19—41no—
45C22⋊C4×C19—21no—
46C22⋊C4×C19—21no—
47C22⋊C4×C19—41no—
48C22⋊C4×C19D411yescharacteristic, complemented
49C22⋊Dic19—21no—
50C22⋊Dic19D411yescharacteristic
51#64527—41no—
52#64525—41no—
53(C2×D19)⋊C4—21no—
54(C2×D19)⋊C4—21no—
55(C2×D19)⋊C4—21no—
56(C2×D19)⋊C4—21no—
57(C2×D19)⋊C4—41no—
58C4⋊Dic19—21no—
59Dic19⋊C4—21no—
60C4×Dic19D411yescharacteristic, complemented
61#64520—21no—
62C23×C19—21no—
63C23×C19—21no—
64C23×C19C2×D411yescharacteristic
65C23×C19C2×D411yescharacteristic
66C22×D19—21no—
67C22×D19—21no—
68C22×D19—41no—
69C22×D19—81no—
70Q8×C19—21no—
71D4×C19—21no—
72D4×C19—41no—
73D4×C19—41no—
74D4×C19—41no—
75D4×C19—41no—
76C2×C4×C19—21no—
77C2×C4×C19—21no—
78C2×C4×C19—21no—
79C2×C4×C19—21no—
80C2×C4×C19—41no—
81C2×C4×C19—41no—
82C2×C4×C19—41no—
83C2×C4×C19C2×D411yescharacteristic
84C22⋊D19—81no—
85C22⋊D19—81no—
86C22⋊D19—81no—
87C22⋊D19—82no—
88C2×Dic19—21no—
89C2×Dic19—21no—
90C2×Dic19—41no—
91D76—41no—
92D76—81no—
93D76—81no—
94C4×D19—81no—
95C19⋊C8—41no—
96#2200—191nomaximal, Sylow
97C22×C19—21no—
98C22×C19—21no—
99C22×C19—41no—
100C22×C19—41no—
101C22×C19—41no—
102C22×C19—81no—
103C22×C19—81no—
104C22×C19#12011yescharacteristic
105C2×D19—41no—
106C2×D19—41no—
107C2×D19—41no—
108C2×D19—41no—
109C2×D19—42no—
110C2×D19—41no—
111C2×D19—41no—
112C2×D19—81no—
113C4×C19—21no—
114C4×C19—41no—
115C4×C19—41no—
116C4×C19—41no—
117C4×C19—81no—
118Dic19—41no—
119Dic19—41no—
120Dic19—81no—
121#560—191no—
122#458D1911yescharacteristic, complemented
123B(4,𝔽2)—191no—
124#453—191no—
125#353—191no—
126#352—191no—
127AΣL(1,𝔽16)—191no—
128C2×C19—21no—
129C2×C19—41no—
130C2×C19—41no—
131C2×C19—81no—
132C2×C19B(4,𝔽2)11yescharacteristic
133D19—81no—
134D19—81no—
135H(5,𝔽2)C2×D1911yescharacteristic
136AGL(1,ℤ/8)—381no—
137#127—191no—
138#126—381no—
139#123—21no—
140#123—381no—
141#123C2×D1911yescharacteristic
142#121—381no—
143#121—381no—
144#121—381no—
145#120—191no—
146#120—381no—
147#120—381no—
148#104—381no—
149#100—191no—
150#99—21no—
151#99—191no—
152#99—381no—
153#99C2×D1911yescharacteristic
154C19#220011yescharacteristic, complemented, Sylow
155C24—191no—
156#41—21no—
157#41—41no—
158C2×D4—21no—
159C2×D4—21no—
160C2×D4—41no—
161C2×D4—191no—
162C2×D4—381no—
163C2×D4—381no—
164C2×D4—381no—
165C2×D4—381no—
166C2×D4—381no—
167C2×D4—761no—
168C2×D4C22×D1911yescharacteristic
169C22×C4—381no—
170C22×C4C22⋊D1911yescharacteristic, complemented
171SD16—761no—
172D8—761no—
173M16—381no—
174C4⋊C4—21no—
175C4⋊C4—41no—
176C4⋊C4—381no—
177C4⋊C4—381no—
178C22⋊C4—21no—
179C22⋊C4—21no—
180C22⋊C4—41no—
181C22⋊C4—191no—
182C22⋊C4—381no—
183C22⋊C4—381no—
184C22⋊C4—381no—
185C22⋊C4—381no—
186C22⋊C4—381no—
187C22⋊C4—761no—
188C22⋊C4C22⋊D1911yescharacteristic, complemented
189C42—191no—
190C23—21no—
191C23—21no—
192C23—381no—
193C23—381no—
194C23—761no—
195C23—1521no—
196C23D4×D1911yescharacteristic
197C23C2×C22⋊D1911yescharacteristic
198Q8—21no—
199D4—21no—
200D4—41no—
201D4—41no—
202D4—41no—
203D4—41no—
204D4—761no—
205D4—1521no—
206D4—1521no—
207D4—1521no—
208D4—1521no—
209D4—1521no—
210D4—1522no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—381no—
219C2×C4—381no—
220C2×C4—761no—
221C2×C4—1521no—
222C2×C4D4×D1911yescharacteristic
223C8—761no—
224C22—21no—
225C22—21no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—81no—
230C22—81no—
231C22—761no—
232C22—761no—
233C22—761no—
234C22—761no—
235C22—762no—
236C22—761no—
237C22—761no—
238C22—1521no—
239C22#1059738311yescharacteristic
240C4—21no—
241C4—41no—
242C4—41no—
243C4—41no—
244C4—81no—
245C4—761no—
246C4—761no—
247C4—1521no—
248C2—21no—
249C2—41no—
250C2—41no—
251C2—81no—
252C2—1521no—
253C2—1521no—
254C2#1192673011yescharacteristic
subgroupG/H
centerC2#11926730
commutator, cosocleC2×D4×C19C23
FrattiniC2×D4C22×D19
FittingC19×#458C2
socleC2×C19B(4,𝔽2)
hypercenter#458D19
hypocenterC19#2200
LCSG ▷ C2×D4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #458

Complements

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

NH ≅ G/Ntype
1. #11927284C2semidirect
2. #11926731C2semidirect
3. #11926712C2semidirect
4. #11926336C2semidirect
5. #11926334C2semidirect
6. #11926330C2semidirect
7. C19×#458C2semidirect
34. C22×C4×C19D4semidirect
41. C2×D76D4semidirect
48. C22⋊C4×C19D4semidirect
60. C4×Dic19D4semidirect
122. #458D19semidirect
154. C19#2200semidirect
170. C22×C4C22⋊D19semidirect
188. C22⋊C4C22⋊D19semidirect

Maximal subgroups

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

subgroupindex
#119272842
#119267312
#119267122
#119263362
#119263342
#119263302
C19×#4582
#220019