Finite Group Databasebeta

← #14564948

Subgroups — #14564948

Order 2432.

324 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 89 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×Dic19⋊C8C211yesmaximal, characteristic, complemented
2C2×#10597292C211yesmaximal, characteristic, complemented
3C2×#10597289C211yesmaximal, characteristic
4#11926451C211yesmaximal, characteristic, complemented
5#11926447C211yesmaximal, characteristic
6#11926307C211yesmaximal, characteristic, complemented
7C22×SD16×C19C211yesmaximal, characteristic
8C22×Q8×C19C2211yescharacteristic
9C22×D4×C19C2211yescharacteristic
10C2×SD16×C19—22no—
11C2×SD16×C19—22no—
12C2×SD16×C19—22no—
13C22×C8×C19C2211yescharacteristic
14C2×C22⋊Dic19—21no—
15C2×C22⋊Dic19—21no—
16C2×C4⋊Dic19C2211yescharacteristic
17C2×C4⋊Dic19C2211yescharacteristic
18C2×C4×Dic19C2211yescharacteristic
19C22×C19⋊C8C2211yescharacteristic
20#10597292—22no—
21#10597289—22no—
22C19⋊#95—21no—
23C19⋊#95—21no—
24Dic19⋊C8—22no—
25C24×C19—21no—
26C2×Q8×C19—21no—
27C2×Q8×C19—21no—
28C2×Q8×C19—21no—
29C2×Q8×C19—21no—
30C2×Q8×C19—21no—
31C2×Q8×C19D412yes—
32C2×D4×C19—21no—
33C2×D4×C19—21no—
34C2×D4×C19—21no—
35C2×D4×C19—21no—
36C2×D4×C19—21no—
37C2×D4×C19D412yes—
38C22×C4×C19—21no—
39C22×C4×C19C2311yescharacteristic
40C22×Dic19—21no—
41C22×Dic19—21no—
42C22×Dic19D411yescharacteristic
43C22×Dic19D411yescharacteristic
44SD16×C19—28no—
45C2×C8×C19—21no—
46C2×C8×C19—21no—
47C2×C8×C19D412yes—
48C22⋊Dic19—42no—
49C22⋊Dic19—42no—
50C4⋊Dic19—21no—
51C4⋊Dic19—21no—
52C4⋊Dic19—21no—
53C4⋊Dic19—21no—
54C4×Dic19—21no—
55C4×Dic19—21no—
56C2×C19⋊C8—21no—
57C2×C19⋊C8—21no—
58C2×C19⋊C8—21no—
59C23×C19—22no—
60C23×C19—41no—
61C23×C19—41no—
62C23×C19—41no—
63C23×C19—41no—
64C23×C19—41no—
65C23×C19—41no—
66C23×C19C2×D411yescharacteristic
67Q8×C19—22no—
68Q8×C19—22no—
69Q8×C19—41no—
70Q8×C19—41no—
71D4×C19—22no—
72D4×C19—22no—
73D4×C19—41no—
74D4×C19—41no—
75C2×C4×C19—22no—
76C2×C4×C19—41no—
77C2×C4×C19—41no—
78C2×C4×C19C2×D411yescharacteristic
79C2×C4×C19C2×D411yescharacteristic
80C2×C4×C19C2×D411yescharacteristic
81C2×C4×C19#4111yescharacteristic
82C2×C4×C19#4111yescharacteristic
83C2×C4×C19#4111yescharacteristic
84C2×Dic19—21no—
85C2×Dic19—21no—
86C2×Dic19—21no—
87C2×Dic19—21no—
88C2×Dic19—21no—
89C2×Dic19—41no—
90C2×Dic19—41no—
91C2×Dic19—41no—
92C2×Dic19—41no—
93C2×Dic19—41no—
94C2×Dic19—41no—
95C2×Dic19SD1612yescomplemented
96C8×C19—22no—
97C19⋊C8—41no—
98#2055—191nomaximal, Sylow
99C22×C19—42no—
100C22×C19—42no—
101C22×C19—42no—
102C22×C19—81no—
103C22×C19—81no—
104C22×C19—81no—
105C22×C19—81no—
106C22×C19#12111yescharacteristic
107C22×C19#12111yescharacteristic
108C22×C19#12111yescharacteristic
109C22×C19C2×SD1611yescharacteristic
110C22×C19#13511yescharacteristic
111C22×C19AGL(1,ℤ/8)11yescharacteristic
112C22×C19#13711yescharacteristic
113C4×C19—42no—
114C4×C19#12011yescharacteristic
115C4×C19#12311yescharacteristic
116C4×C19#12311yescharacteristic
117C4×C19#12411yescharacteristic
118Dic19—22no—
119Dic19—41no—
120Dic19—81no—
121Dic19—81no—
122C22×SD16D1911yescharacteristic
123C2×C4⋊C8—191no—
124C2×#103—191no—
125C2×#102—191no—
126#391—191no—
127#390—191no—
128#340—191no—
129C2×C19—82no—
130C2×C19#39411yescharacteristic
131C2×C19#46011yescharacteristic
132C2×C19#46111yescharacteristic
133C2×C19#46311yescharacteristic
134C2×C19#46411yescharacteristic
135C2×C19#46511yescharacteristic
136C2×C19#46811yescharacteristic
137C22×Q8C2×D1911yescharacteristic
138C22×D4C2×D1911yescharacteristic
139C2×SD16—22no—
140C2×SD16—22no—
141C2×SD16—22no—
142C22×C8—191no—
143C22×C8C2×D1911yescharacteristic
144C2×C4⋊C4—191no—
145C2×C4⋊C4—191no—
146C2×C22⋊C4—381no—
147C2×C22⋊C4—381no—
148C2×C42—191no—
149C4⋊C8—382no—
150#103—382no—
151#102—382no—
152#95—381no—
153#95—381no—
154C19#205511yescharacteristic, complemented, Sylow
155C24—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8C22⋊D1912yes—
162C2×D4—21no—
163C2×D4—21no—
164C2×D4—21no—
165C2×D4—21no—
166C2×D4—21no—
167C2×D4C22⋊D1912yes—
168C22×C4—21no—
169C22×C4—191no—
170C22×C4—191no—
171C22×C4—381no—
172C22×C4—381no—
173C22×C4C22×D1911yescharacteristic
174SD16—28no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—381no—
178C2×C8—381no—
179C2×C8—381no—
180C2×C8C22⋊D1912yes—
181C4⋊C4—381no—
182C4⋊C4—381no—
183C4⋊C4—381no—
184C4⋊C4—381no—
185C22⋊C4—762no—
186C22⋊C4—762no—
187C42—381no—
188C42—381no—
189C23—22no—
190C23—41no—
191C23—41no—
192C23—41no—
193C23—41no—
194C23—41no—
195C23—41no—
196C23D4×D1911yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—41no—
200Q8—41no—
201D4—22no—
202D4—22no—
203D4—41no—
204D4—41no—
205C2×C4—22no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—192no—
209C2×C4—381no—
210C2×C4—381no—
211C2×C4—381no—
212C2×C4—381no—
213C2×C4—381no—
214C2×C4—761no—
215C2×C4—761no—
216C2×C4—761no—
217C2×C4—761no—
218C2×C4—761no—
219C2×C4—761no—
220C2×C4#6454311yescharacteristic
221C2×C4#6454311yescharacteristic
222C2×C4#6454311yescharacteristic
223C2×C4C2×C22⋊D1911yescharacteristic
224C2×C4C2×C22⋊D1911yescharacteristic
225C2×C4C2×C22⋊D1911yescharacteristic
226C8—22no—
227C8—761no—
228C22—42no—
229C22—42no—
230C22—42no—
231C22—81no—
232C22—81no—
233C22—81no—
234C22—81no—
235C22SD16×D1911yescharacteristic
236C22#1059736011yescharacteristic
237C22#1059736111yescharacteristic
238C22#1059736211yescharacteristic
239C22#1059738411yescharacteristic
240C22#1059738511yescharacteristic
241C22#1059738511yescharacteristic
242C4—42no—
243C4—382no—
244C4—761no—
245C4—1521no—
246C4—1521no—
247C4#1059738111yescharacteristic
248C4#1059738111yescharacteristic
249C4#1059738211yescharacteristic
250C4#1059739911yescharacteristic
251C2—82no—
252C2#1192645811yescharacteristic
253C2#1192674211yescharacteristic
254C2#1192674711yescharacteristic
255C2#1192676111yescharacteristic
256C2#1192676411yescharacteristic
257C2#1192677011yescharacteristic
258C2#1192678711yescharacteristic
subgroupG/H
centerC23D4×D19
commutator, cosocleC22×C4×C19C23
FrattiniC22×C4C22×D19
FittingC22×SD16×C19C2
socleC23×C19C2×D4
prime radicalC22×D4×C19C22
hypercenterC22×SD16D19
hypocenterC19#2055
LCSG ▷ C22×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×Dic19⋊C8C2semidirect
2. C2×#10597292C2semidirect
4. #11926451C2semidirect
6. #11926307C2semidirect
95. C2×Dic19SD16semidirect
154. C19#2055semidirect

Maximal subgroups

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

subgroupindex
C2×Dic19⋊C82
C2×#105972922
C2×#105972892
#119264512
#119264472
#119263072
C22×SD16×C192
#205519