Finite Group Databasebeta

← #14570563

Subgroups — #14570563

Order 2432.

504 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 137 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×#10597381C211yesmaximal, characteristic
2#11926477C212yesmaximal, complemented
3#11926472C212yesmaximal, complemented
4#11926472C212yesmaximal, complemented
5#11926447C211yesmaximal, characteristic
6#11926439C212yesmaximal, complemented
7#11926417C212yesmaximal, complemented
8#11926416C212yesmaximal, complemented
9C2×C19×#123C211yesmaximal, characteristic
10C22×D4×C19C2211yescharacteristic
11C23×C4×C19C2211yescharacteristic
12C23×Dic19C2211yescharacteristic
13C19×#123—24no—
14C2×C4⋊C4×C19C2212yes—
15C2×C22⋊C4×C19C2212yes—
16C2×C22⋊C4×C19C2211yescharacteristic
17C2×C22⋊Dic19C2212yes—
18C2×C22⋊Dic19C2211yescharacteristic
19C2×C22⋊Dic19C2212yes—
20C2×C22⋊Dic19C2212yes—
21#10597381—24no—
22C2×C4⋊Dic19C2211yescharacteristic
23C2×Dic19⋊C4C2212yes—
24C2×Dic19⋊C4C2212yes—
25C2×Dic19⋊C4C2212yes—
26C2×Dic19⋊C4C2212yes—
27C2×C4×Dic19C2211yescharacteristic
28C19⋊#95C2212yes—
29C19⋊#95C2212yes—
30C19⋊#95C2212yes—
31C19⋊#95C2212yes—
32C19⋊#95C2212yes—
33C24×C19C2311yescharacteristic
34C24×C19C2311yescharacteristic
35C2×D4×C19—41no—
36C2×D4×C19—41no—
37C2×D4×C19D414yes—
38C22×C4×C19—22no—
39C22×C4×C19—41no—
40C22×C4×C19—41no—
41C22×C4×C19C2312yes—
42C22×C4×C19C2312yes—
43C22×C4×C19C2311yescharacteristic
44C22×Dic19—22no—
45C22×Dic19—41no—
46C22×Dic19—41no—
47C22×Dic19C2312yes—
48C22×Dic19C2312yes—
49C22×Dic19C2312yes—
50C22×Dic19C2312yes—
51C4⋊C4×C19—24no—
52C22⋊C4×C19—22no—
53C22⋊C4×C19—24no—
54C22⋊Dic19—22no—
55C22⋊Dic19—24no—
56C22⋊Dic19—24no—
57C22⋊Dic19—24no—
58C4⋊Dic19—41no—
59Dic19⋊C4—24no—
60Dic19⋊C4—24no—
61Dic19⋊C4—42no—
62Dic19⋊C4—42no—
63C4×Dic19—41no—
64C23×C19—22no—
65C23×C19—22no—
66C23×C19—21no—
67C23×C19—21no—
68C23×C19—21no—
69C23×C19—21no—
70C23×C19—22no—
71C23×C19—22no—
72C23×C19C2×D412yes—
73C23×C19C2×D412yes—
74C23×C19C2411yescharacteristic
75D4×C19—44no—
76C2×C4×C19—21no—
77C2×C4×C19—21no—
78C2×C4×C19—22no—
79C2×C4×C19—22no—
80C2×C4×C19—22no—
81C2×C4×C19—22no—
82C2×C4×C19—22no—
83C2×C4×C19—22no—
84C2×C4×C19—44no—
85C2×C4×C19C2×D412yes—
86C2×Dic19—22no—
87C2×Dic19—22no—
88C2×Dic19—22no—
89C2×Dic19—22no—
90C2×Dic19—22no—
91C2×Dic19—22no—
92C2×Dic19—22no—
93C2×Dic19—22no—
94C2×Dic19—22no—
95C2×Dic19—22no—
96C2×Dic19—22no—
97C2×Dic19—44no—
98C2×Dic19#4114yes—
99#2724—191nomaximal, Sylow
100C22×C19—22no—
101C22×C19—22no—
102C22×C19—24no—
103C22×C19—24no—
104C22×C19—42no—
105C22×C19—42no—
106C22×C19—41no—
107C22×C19—41no—
108C22×C19—41no—
109C22×C19—41no—
110C22×C19C22×D411yescharacteristic
111C22×C19C2×#4112yes—
112C22×C19H(5,𝔽2)11yescharacteristic
113C22×C19H(5,𝔽2)11yescharacteristic
114C22×C192−1+412yes—
115C4×C19—22no—
116C4×C19—42no—
117C4×C19—42no—
118Dic19—24no—
119Dic19—42no—
120Dic19—42no—
121Dic19—42no—
122C2×#123—191no—
123C2×#123D1911yescharacteristic
124#398—192no—
125#397—192no—
126#397—192no—
127#390—191no—
128#389—192no—
129#385—192no—
130#385—192no—
131C2×C19—42no—
132C2×C19—42no—
133C2×C19#53411yescharacteristic
134C2×C19#53912yes—
135C2×C19#54712yes—
136C2×C19#55911yescharacteristic
137C2×C19#56311yescharacteristic
138C22×D4C2×D1911yescharacteristic
139C23×C4—191no—
140C23×C4C2×D1911yescharacteristic
141#123—24no—
142#123—384no—
143C2×C4⋊C4—192no—
144C2×C4⋊C4—192no—
145C2×C4⋊C4—192no—
146C2×C4⋊C4—192no—
147C2×C4⋊C4—191no—
148C2×C4⋊C4C2×D1912yes—
149C2×C22⋊C4—192no—
150C2×C22⋊C4—191no—
151C2×C22⋊C4—192no—
152C2×C22⋊C4—192no—
153C2×C22⋊C4C2×D1912yes—
154C2×C22⋊C4C2×D1911yescharacteristic
155C2×C42—191no—
156#95—192no—
157#95—192no—
158#95—192no—
159#95—192no—
160#95—192no—
161C19#272411yescharacteristic, complemented, Sylow
162C24C22×D1911yescharacteristic
163C24C22×D1911yescharacteristic
164C2×D4—41no—
165C2×D4—41no—
166C2×D4C22⋊D1914yes—
167C22×C4—22no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4—192no—
171C22×C4—192no—
172C22×C4—192no—
173C22×C4—192no—
174C22×C4—382no—
175C22×C4—761no—
176C22×C4—761no—
177C22×C4C22×D1912yes—
178C22×C4C22×D1912yes—
179C22×C4C22×D1911yescharacteristic
180C4⋊C4—24no—
181C4⋊C4—384no—
182C4⋊C4—384no—
183C4⋊C4—762no—
184C4⋊C4—762no—
185C4⋊C4—761no—
186C22⋊C4—22no—
187C22⋊C4—24no—
188C22⋊C4—384no—
189C22⋊C4—384no—
190C22⋊C4—382no—
191C22⋊C4—384no—
192C42—761no—
193C23—21no—
194C23—21no—
195C23—21no—
196C23—21no—
197C23—22no—
198C23—22no—
199C23—22no—
200C23—22no—
201C23C2×C22⋊D1912yes—
202C23C2×C22⋊D1912yes—
203C23C23×D1911yescharacteristic
204D4—44no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—44no—
214C2×C4—194no—
215C2×C4—382no—
216C2×C4—382no—
217C2×C4—382no—
218C2×C4—382no—
219C2×C4—382no—
220C2×C4—382no—
221C2×C4—382no—
222C2×C4—382no—
223C2×C4—382no—
224C2×C4—382no—
225C2×C4—382no—
226C2×C4—764no—
227C2×C4C2×C22⋊D1912yes—
228C22—22no—
229C22—22no—
230C22—24no—
231C22—24no—
232C22—41no—
233C22—41no—
234C22—42no—
235C22—42no—
236C22—41no—
237C22—41no—
238C22#1059743011yescharacteristic
239C22#1059743011yescharacteristic
240C22#41×D1912yes—
241C22#1059743612yes—
242C22C22×C22⋊D1911yescharacteristic
243C4—22no—
244C4—42no—
245C4—42no—
246C4—384no—
247C4—762no—
248C4—762no—
249C4—762no—
250C2—42no—
251C2—42no—
252C2#1192710311yescharacteristic
253C2#1192713712yes—
254C2#1192719312yes—
255C2#1192727811yescharacteristic
256C2#1192729711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC2×C19×#123C2
prime radicalC22×D4×C19C22
hypercenterC2×#123D19
hypocenterC19#2724
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
2. #11926477C2semidirect
3. #11926472C2semidirect
4. #11926472C2semidirect
6. #11926439C2semidirect
7. #11926417C2semidirect
8. #11926416C2semidirect
161. C19#2724semidirect

Maximal subgroups

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

subgroupindex
C2×#105973812
#119264772
#119264722
#119264472
#119264392
#119264172
#119264162
C2×C19×#1232
#272419