Finite Group Databasebeta

← #14568647

Subgroups — #14568647

Order 2432.

544 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 169 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×#10597324C212yesmaximal
2#11926477C212yesmaximal, complemented
3#11926464C212yesmaximal, complemented
4#11926448C212yesmaximal, complemented
5#11926441C212yesmaximal, complemented
6#11926416C212yesmaximal
7C4×C22⋊Dic19C211yesmaximal, characteristic
8C2×C19⋊#95C211yesmaximal, characteristic
9C19×#380C211yesmaximal, characteristic
10C23×C4×C19C2211yescharacteristic
11C23×Dic19C2212yes—
12C22×Dic38C2212yes—
13C2×C4⋊C4×C19C2212yes—
14C2×C22⋊C4×C19C2212yes—
15C2×C22⋊Dic19C2211yescharacteristic
16C2×C22⋊Dic19C2211yescharacteristic
17C2×C4⋊Dic19C2212yes—
18C2×Dic19⋊C4C2212yes—
19C2×Dic19⋊C4C2212yes—
20C2×Dic19⋊C4C2212yes—
21C2×Dic19⋊C4C2212yes—
22C2×C4×Dic19C2212yes—
23#10597324—28no—
24C19×#95C2211yescharacteristic
25C19×#95C2211yescharacteristic
26C19⋊#95C2212yes—
27C19⋊#95C2211yescharacteristic
28C19⋊#95C2211yescharacteristic
29C19⋊#95C2212yes—
30C19⋊#95C2212yes—
31C19⋊#95C2212yes—
32C24×C19C2311yescharacteristic
33C22×C4×C19—42no—
34C22×C4×C19Q814yescomplemented
35C22×C4×C19C2312yes—
36C22×C4×C19C2312yes—
37C22×C4×C19C2311yescharacteristic
38C22×C4×C19C2311yescharacteristic
39C22×Dic19—24no—
40C22×Dic19—24no—
41C22×Dic19—42no—
42C22×Dic19C2312yes—
43C22×Dic19C2312yes—
44C22×Dic19C2312yes—
45C22×Dic19C2312yes—
46C2×Dic38—24no—
47C2×Dic38—24no—
48C2×Dic38—42no—
49C4⋊C4×C19—42no—
50C22⋊C4×C19—24no—
51C22⋊Dic19D414yes—
52C22⋊Dic19Q814yescomplemented
53C4⋊Dic19—24no—
54Dic19⋊C4—24no—
55Dic19⋊C4—24no—
56Dic19⋊C4—24no—
57Dic19⋊C4—42no—
58C4×Dic19—42no—
59C23×C19—22no—
60C23×C19—22no—
61C23×C19C2×D412yes—
62C23×C19C2×Q812yes—
63C23×C19C2×Q812yes—
64C23×C19C2411yescharacteristic
65C2×C4×C19—22no—
66C2×C4×C19—22no—
67C2×C4×C19—22no—
68C2×C4×C19—22no—
69C2×C4×C19—22no—
70C2×C4×C19—22no—
71C2×C4×C19—22no—
72C2×C4×C19—22no—
73C2×C4×C19—44no—
74C2×C4×C19C2×Q812yes—
75C2×C4×C19C2×Q812yes—
76C2×Dic19—22no—
77C2×Dic19—22no—
78C2×Dic19—22no—
79C2×Dic19—22no—
80C2×Dic19—22no—
81C2×Dic19—22no—
82C2×Dic19—22no—
83C2×Dic19—22no—
84C2×Dic19—22no—
85C2×Dic19—48no—
86C2×Dic19C2×D414yes—
87C2×Dic19C2×Q814yes—
88C2×Dic19#4114yes—
89Dic38—48no—
90#2549—191nomaximal, Sylow
91C22×C19—22no—
92C22×C19—22no—
93C22×C19—24no—
94C22×C19—24no—
95C22×C19C4⋊Q814yes—
96C22×C19C22×D411yescharacteristic
97C22×C19C22×Q811yescharacteristic
98C22×C19C22×Q811yescharacteristic
99C22×C19C2×#4112yes—
100C22×C19H(5,𝔽2)12yes—
101C4×C19—22no—
102C4×C19—22no—
103C4×C19—42no—
104C4×C19—42no—
105Dic19—24no—
106Dic19—24no—
107Dic19—24no—
108Dic19—42no—
109C2×C22⋊Q8—192no—
110#398—192no—
111#395—192no—
112#391—192no—
113#389—192no—
114#385—192no—
115#380D1911yescharacteristic
116C4×C22⋊C4—191no—
117C2×#95—191no—
118C2×C19—24no—
119C2×C19C2×C4⋊Q811yescharacteristic
120C2×C19#53311yescharacteristic
121C2×C19#54311yescharacteristic
122C2×C19#54612yes—
123C2×C19#55412yes—
124C22×Q8—192no—
125C23×C4—192no—
126C23×C4C2×D1911yescharacteristic
127C22⋊Q8—388no—
128C2×C4⋊C4—192no—
129C2×C4⋊C4—192no—
130C2×C4⋊C4—192no—
131C2×C4⋊C4—192no—
132C2×C4⋊C4—192no—
133C2×C4⋊C4C2×D1912yes—
134C2×C22⋊C4—191no—
135C2×C22⋊C4—191no—
136C2×C22⋊C4C2×D1912yes—
137C2×C42—192no—
138#95—192no—
139#95—191no—
140#95—191no—
141#95—192no—
142#95—192no—
143#95—192no—
144#95C2×D1911yescharacteristic
145#95C2×D1911yescharacteristic
146C19#254911yescharacteristic, complemented, Sylow
147C24C22×D1911yescharacteristic
148C2×Q8—384no—
149C2×Q8—384no—
150C2×Q8—762no—
151C22×C4—42no—
152C22×C4—192no—
153C22×C4—192no—
154C22×C4—192no—
155C22×C4—192no—
156C22×C4—384no—
157C22×C4—384no—
158C22×C4—762no—
159C22×C4Dic3814yescomplemented
160C22×C4C22×D1912yes—
161C22×C4C22×D1912yes—
162C22×C4C22×D1911yescharacteristic
163C22×C4C22×D1911yescharacteristic
164C4⋊C4—42no—
165C4⋊C4—384no—
166C4⋊C4—384no—
167C4⋊C4—384no—
168C4⋊C4—384no—
169C4⋊C4—762no—
170C22⋊C4—24no—
171C22⋊C4—194no—
172C22⋊C4—194no—
173C42—762no—
174C23—22no—
175C23—22no—
176C23C2×Dic3812yes—
177C23D4×D1912yes—
178C23Q8×D1912yes—
179C23C23×D1911yescharacteristic
180Q8—768no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—44no—
190C2×C4—194no—
191C2×C4—194no—
192C2×C4—194no—
193C2×C4—382no—
194C2×C4—382no—
195C2×C4—382no—
196C2×C4—382no—
197C2×C4—382no—
198C2×C4—382no—
199C2×C4—382no—
200C2×C4—382no—
201C2×C4—382no—
202C2×C4—768no—
203C2×C4C2×Dic3812yes—
204C2×C4C2×Dic3812yes—
205C22—22no—
206C22—22no—
207C22—24no—
208C22—24no—
209C22#1059733414yes—
210C22C22×Dic3811yescharacteristic
211C22C2×D4×D1911yescharacteristic
212C22#1059743012yes—
213C22C2×Q8×D1911yescharacteristic
214C22#41×D1912yes—
215C4—22no—
216C4—22no—
217C4—42no—
218C4—42no—
219C4—384no—
220C4—384no—
221C4—384no—
222C4—762no—
223C2—24no—
224C2C2×#1059733411yescharacteristic
225C2#1192709711yescharacteristic
226C2#1192717011yescharacteristic
227C2#1192718312yes—
228C2#1192724812yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#380C2
prime radicalC24×C19C23
hypercenter#380D19
hypocenterC19#2549
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. #11926477C2semidirect
3. #11926464C2semidirect
4. #11926448C2semidirect
5. #11926441C2semidirect
34. C22×C4×C19Q8semidirect
52. C22⋊Dic19Q8semidirect
146. C19#2549semidirect
159. C22×C4Dic38semidirect

Maximal subgroups

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

subgroupindex
C2×#105973242
#119264772
#119264642
#119264482
#119264412
#119264162
C4×C22⋊Dic192
C2×C19⋊#952
C19×#3802
#254919