Finite Group Databasebeta

← #14565641

Subgroups — #14565641

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#11927281C211yesmaximal, characteristic, complemented
2#11926734C211yesmaximal, characteristic, complemented
3#11926731C211yesmaximal, characteristic, complemented
4#11926337C211yesmaximal, characteristic, complemented
5#11926335C211yesmaximal, characteristic, complemented
6#11926332C211yesmaximal, characteristic, complemented
7C19×#453C211yesmaximal, characteristic, complemented
8C19×H(5,𝔽2)C2211yescharacteristic
9C19×AGL(1,ℤ/8)—21no—
10C19×#127C2211yescharacteristic
11#10597385—21no—
12#10597385—21no—
13#10597385—21no—
14#10597383—21no—
15#10597383—21no—
16#10597383C2211yescharacteristic
17#10597381—21no—
18#10597381—21no—
19#10597381C2211yescharacteristic
20#10597322—21no—
21C19×#104—21no—
22C19×#100C2211yescharacteristic
23#10597291—21no—
24#10597291—21no—
25#10597291C2211yescharacteristic
26#10597291C2211yescharacteristic
27C23×D19D411yescharacteristic
28#41×C19—21no—
29#41×C19—41no—
30C2×D4×C19—21no—
31C2×D4×C19—21no—
32C2×D4×C19—21no—
33C2×D4×C19—21no—
34C2×D4×C19—41no—
35C2×D4×C19D411yescharacteristic, complemented
36C2×D4×C19C2311yescharacteristic
37C2×C22⋊D19—21no—
38C2×C22⋊D19—21no—
39C2×C22⋊D19—21no—
40C2×C22⋊D19—41no—
41C22×Dic19—21no—
42C22×Dic19D411yescharacteristic, complemented
43SD16×C19—41no—
44D8×C19—41no—
45M16×C19—21no—
46C42×C19D411yescharacteristic, complemented
47C22⋊Dic19—21no—
48C22⋊Dic19—21no—
49C22⋊Dic19—21no—
50C22⋊Dic19—21no—
51C22⋊Dic19—41no—
52C22⋊Dic19D411yescharacteristic
53C22⋊Dic19D411yescharacteristic, complemented
54(C2×D19)⋊C4—21no—
55(C2×D19)⋊C4—21no—
56(C2×D19)⋊C4—21no—
57(C2×D19)⋊C4—41no—
58Dic19⋊C4—21no—
59Dic19⋊C4—21no—
60Dic19⋊C4—21no—
61Dic19⋊C4—41no—
62C23×C19—21no—
63C23×C19—21no—
64C23×C19—21no—
65C23×C19C2×D411yescharacteristic
66C23×C19C2×D411yescharacteristic
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—
76D4×C19—41no—
77D4×C19—81no—
78D4×C19—81no—
79C2×C4×C19—21no—
80C2×C4×C19—21no—
81C2×C4×C19—21no—
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—21no—
91C2×Dic19—41no—
92C2×Dic19—41no—
93C2×Dic19—41no—
94C2×Dic19—81no—
95C8×C19—41no—
96#2200—191nomaximal, Sylow
97C22×C19—21no—
98C22×C19—21no—
99C22×C19—41no—
100C22×C19—41no—
101C22×C19—41no—
102C22×C19—41no—
103C22×C19—41no—
104C22×C19—41no—
105C22×C19—81no—
106C22×C19—81no—
107C22×C19#12011yescharacteristic
108C2×D19—41no—
109C2×D19—41no—
110C2×D19—42no—
111C2×D19—41no—
112C2×D19—81no—
113C4×C19—21no—
114C4×C19—41no—
115C4×C19—41no—
116Dic19—41no—
117Dic19—41no—
118Dic19—41no—
119Dic19—81no—
120Dic19—81no—
121#560—191no—
122#458—191no—
123B(4,𝔽2)—191no—
124#453D1911yescharacteristic, complemented
125#353—191no—
126#352—191no—
127AΣL(1,𝔽16)—191no—
128C2×C19—21no—
129C2×C19—41no—
130C2×C19—41no—
131C2×C19—81no—
132C2×C19—81no—
133C2×C19B(4,𝔽2)11yescharacteristic
134D19—81no—
135H(5,𝔽2)C2×D1911yescharacteristic
136AGL(1,ℤ/8)—21no—
137#127C2×D1911yescharacteristic
138#126—381no—
139#123—191no—
140#123—381no—
141#123—381no—
142#121—381no—
143#121—381no—
144#121—381no—
145#120—191no—
146#120—381no—
147#120—381no—
148#104—21no—
149#100C2×D1911yescharacteristic
150#99—191no—
151#99—191no—
152#99—381no—
153#99—381no—
154C19#220011yescharacteristic, complemented, Sylow
155C24—191no—
156#41—21no—
157#41—41no—
158C2×D4—21no—
159C2×D4—21no—
160C2×D4—21no—
161C2×D4—21no—
162C2×D4—41no—
163C2×D4—381no—
164C2×D4—381no—
165C2×D4—381no—
166C2×D4—761no—
167C2×D4C22⋊D1911yescharacteristic, complemented
168C2×D4C22×D1911yescharacteristic
169C22×C4—191no—
170C22×C4—381no—
171SD16—41no—
172D8—41no—
173M16—21no—
174C4⋊C4—381no—
175C4⋊C4—381no—
176C4⋊C4—381no—
177C4⋊C4—761no—
178C22⋊C4—191no—
179C22⋊C4—191no—
180C22⋊C4—381no—
181C22⋊C4—381no—
182C22⋊C4—381no—
183C22⋊C4—381no—
184C22⋊C4—381no—
185C22⋊C4—381no—
186C22⋊C4—381no—
187C22⋊C4—761no—
188C22⋊C4—761no—
189C42C22⋊D1911yescharacteristic, complemented
190C23—21no—
191C23—21no—
192C23—21no—
193C23—381no—
194C23—761no—
195C23—1521no—
196C23D4×D1911yescharacteristic
197C23D4×D1911yescharacteristic
198Q8—21no—
199D4—21no—
200D4—41no—
201D4—41no—
202D4—41no—
203D4—41no—
204D4—41no—
205D4—81no—
206D4—81no—
207D4—1521no—
208D4—1521no—
209D4—1521no—
210D4—1522no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—41no—
215C2×C4—381no—
216C2×C4—381no—
217C2×C4—381no—
218C2×C4—761no—
219C2×C4—761no—
220C2×C4—761no—
221C2×C4—1521no—
222C2×C4C2×C22⋊D1911yescharacteristic
223C8—41no—
224C22—21no—
225C22—21no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—41no—
230C22—41no—
231C22—41no—
232C22—81no—
233C22—81no—
234C22—761no—
235C22—761no—
236C22—762no—
237C22—761no—
238C22—1521no—
239C22#1059738311yescharacteristic
240C4—21no—
241C4—41no—
242C4—41no—
243C4—761no—
244C4—761no—
245C4—761no—
246C4—1521no—
247C4—1521no—
248C2—21no—
249C2—41no—
250C2—41no—
251C2—81no—
252C2—81no—
253C2—1521no—
254C2#1192673011yescharacteristic
subgroupG/H
centerC2#11926730
commutator, cosocleC2×D4×C19C23
FrattiniC2×D4C22×D19
FittingC19×#453C2
socleC2×C19B(4,𝔽2)
hypercenter#453D19
hypocenterC19#2200
LCSG ▷ C2×D4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. #11927281C2semidirect
2. #11926734C2semidirect
3. #11926731C2semidirect
4. #11926337C2semidirect
5. #11926335C2semidirect
6. #11926332C2semidirect
7. C19×#453C2semidirect
35. C2×D4×C19D4semidirect
42. C22×Dic19D4semidirect
46. C42×C19D4semidirect
53. C22⋊Dic19D4semidirect
124. #453D19semidirect
154. C19#2200semidirect
167. C2×D4C22⋊D19semidirect
189. C42C22⋊D19semidirect

Maximal subgroups

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

subgroupindex
#119272812
#119267342
#119267312
#119263372
#119263352
#119263322
C19×#4532
#220019