Finite Group Databasebeta

← #14564879

Subgroups — #14564879

Order 2432.

298 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 87 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×#10597390C211yesmaximal, characteristic
2C2×#10597273C211yesmaximal, characteristic
3C2×#10597292C211yesmaximal, characteristic
4C2×#10597267C211yesmaximal, characteristic
5#11926440C211yesmaximal, characteristic
6#11926298C211yesmaximal, characteristic
7C2×C19×#103C211yesmaximal, characteristic
8C22×Q8×C19C2211yescharacteristic
9C22×Dic38C2211yescharacteristic
10C22×C8×C19C2211yescharacteristic
11C2×C4⋊C4×C19C2211yescharacteristic
12#10597390—22no—
13#10597390—22no—
14C2×C4⋊Dic19C2211yescharacteristic
15C2×Dic19⋊C4—21no—
16C2×Dic19⋊C4—21no—
17C2×Dic19⋊C4—21no—
18C2×C4×Dic19C2211yescharacteristic
19C22×C19⋊C8C2211yescharacteristic
20C19×#103—22no—
21#10597292—22no—
22C19⋊#95—21no—
23#10597273—22no—
24#10597267—22no—
25C2×Q8×C19—21no—
26C2×Q8×C19—21no—
27C2×Q8×C19—21no—
28C2×Q8×C19—21no—
29C2×Q8×C19—21no—
30C2×Q8×C19D412yes—
31C22×C4×C19—21no—
32C22×C4×C19—21no—
33C22×C4×C19C2311yescharacteristic
34C22×Dic19—21no—
35C22×Dic19—21no—
36C22×Dic19D411yescharacteristic
37C22×Dic19D411yescharacteristic
38C2×Dic38—21no—
39C2×Dic38—21no—
40C2×Dic38—21no—
41C2×Dic38—21no—
42C2×Dic38—21no—
43C2×Dic38D412yes—
44C2×C8×C19—21no—
45C2×C8×C19—21no—
46C2×C8×C19—21no—
47C4⋊C4×C19—21no—
48C4⋊C4×C19—21no—
49C4⋊Dic19—21no—
50C4⋊Dic19D412yes—
51Dic19⋊C4—24no—
52Dic19⋊C4—24no—
53Dic19⋊C4—42no—
54C4×Dic19—21no—
55C4×Dic19—21no—
56C2×C19⋊C8—21no—
57C2×C19⋊C8—21no—
58C2×C19⋊C8—21no—
59C23×C19C2×D411yescharacteristic
60Q8×C19—22no—
61Q8×C19—22no—
62Q8×C19—41no—
63Q8×C19—41no—
64C2×C4×C19—22no—
65C2×C4×C19—41no—
66C2×C4×C19—41no—
67C2×C4×C19—41no—
68C2×C4×C19—41no—
69C2×C4×C19—41no—
70C2×C4×C19C2×D411yescharacteristic
71C2×C4×C19C2×D411yescharacteristic
72C2×C4×C19C2×D411yescharacteristic
73C2×C4×C19#4111yescharacteristic
74C2×C4×C19#4111yescharacteristic
75C2×C4×C19#4111yescharacteristic
76C2×Dic19—21no—
77C2×Dic19—21no—
78C2×Dic19—21no—
79C2×Dic19—21no—
80C2×Dic19—22no—
81C2×Dic19—22no—
82C2×Dic19—41no—
83C2×Dic19—41no—
84C2×Dic19—41no—
85C2×Dic19—41no—
86C2×Dic19SD1612yes—
87C2×Dic19Q1612yes—
88Dic38—22no—
89Dic38—22no—
90Dic38—41no—
91Dic38—41no—
92C8×C19—41no—
93C19⋊C8—41no—
94#2043—191nomaximal, Sylow
95C22×C19#12011yescharacteristic
96C22×C19#12111yescharacteristic
97C22×C19#12411yescharacteristic
98C22×C19C2×SD1611yescharacteristic
99C22×C19C2×Q1611yescharacteristic
100C22×C19#13711yescharacteristic
101C22×C19#13711yescharacteristic
102C4×C19—42no—
103C4×C19—81no—
104C4×C19#12111yescharacteristic
105C4×C19#12111yescharacteristic
106C4×C19#12311yescharacteristic
107C4×C19#12311yescharacteristic
108Dic19—22no—
109Dic19—22no—
110Dic19—42no—
111Dic19—42no—
112C2×C4⋊Q8—191no—
113C2×#103—191no—
114C2×#103—191no—
115C2×#103—191no—
116C2×#103D1911yescharacteristic
117#389—191no—
118#336—191no—
119C2×C19#39411yescharacteristic
120C2×C19#44811yescharacteristic
121C2×C19#45111yescharacteristic
122C2×C19#46111yescharacteristic
123C2×C19#46211yescharacteristic
124C2×C19#48711yescharacteristic
125C2×C19#49111yescharacteristic
126C22×Q8—191no—
127C22×Q8C2×D1911yescharacteristic
128C22×C8—191no—
129C22×C8C2×D1911yescharacteristic
130C4⋊Q8—382no—
131C4⋊Q8—382no—
132C2×C4⋊C4—191no—
133C2×C4⋊C4—381no—
134C2×C4⋊C4—381no—
135C2×C4⋊C4—381no—
136C2×C4⋊C4C2×D1911yescharacteristic
137C2×C42—191no—
138#103—22no—
139#103—382no—
140#103—382no—
141#103—382no—
142#95—381no—
143C19#204311yescharacteristic, complemented, Sylow
144C2×Q8—21no—
145C2×Q8—21no—
146C2×Q8—21no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—192no—
150C2×Q8—381no—
151C2×Q8—381no—
152C2×Q8—381no—
153C2×Q8—381no—
154C2×Q8—381no—
155C2×Q8C22⋊D1912yes—
156C22×C4—21no—
157C22×C4—21no—
158C22×C4—191no—
159C22×C4—191no—
160C22×C4—381no—
161C22×C4—381no—
162C22×C4C22×D1911yescharacteristic
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—381no—
167C2×C8—381no—
168C2×C8—381no—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—192no—
172C4⋊C4—384no—
173C4⋊C4—384no—
174C4⋊C4—381no—
175C4⋊C4—762no—
176C42—381no—
177C42—381no—
178C23D4×D1911yescharacteristic
179Q8—22no—
180Q8—22no—
181Q8—41no—
182Q8—41no—
183Q8—382no—
184Q8—382no—
185Q8—761no—
186Q8—761no—
187C2×C4—22no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—192no—
194C2×C4—192no—
195C2×C4—381no—
196C2×C4—381no—
197C2×C4—381no—
198C2×C4—381no—
199C2×C4—382no—
200C2×C4—382no—
201C2×C4—761no—
202C2×C4—761no—
203C2×C4—761no—
204C2×C4—761no—
205C2×C4#6454111yescharacteristic
206C2×C4#6454111yescharacteristic
207C2×C4D4×D1911yescharacteristic
208C2×C4D4×D1911yescharacteristic
209C2×C4#6454311yescharacteristic
210C2×C4C2×C22⋊D1911yescharacteristic
211C8—41no—
212C8—761no—
213C22#1059733011yescharacteristic
214C22#1059733111yescharacteristic
215C22SD16×D1911yescharacteristic
216C22#1059736111yescharacteristic
217C22Q16×D1911yescharacteristic
218C22#1059736411yescharacteristic
219C22#1059738311yescharacteristic
220C4—42no—
221C4—81no—
222C4—382no—
223C4—382no—
224C4—762no—
225C4—762no—
226C4#1059732911yescharacteristic
227C4#1059733011yescharacteristic
228C4#1059737511yescharacteristic
229C4#1059738511yescharacteristic
230C2#1192645911yescharacteristic
231C2#1192668111yescharacteristic
232C2#1192669811yescharacteristic
233C2#1192674811yescharacteristic
234C2#1192675311yescharacteristic
235C2#1192689311yescharacteristic
236C2#1192691111yescharacteristic
subgroupG/H
centerC23D4×D19
commutator, cosocleC22×C4×C19C23
FrattiniC22×C4C22×D19
FittingC2×C19×#103C2
socle, prime radicalC23×C19C2×D4
hypercenterC2×#103D19
hypocenterC19#2043
LCSG ▷ C22×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
143. C19#2043semidirect

Maximal subgroups

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

subgroupindex
C2×#105973902
C2×#105972732
C2×#105972922
C2×#105972672
#119264402
#119262982
C2×C19×#1032
#204319