Finite Group Databasebeta

← #14569975

Subgroups — #14569975

Order 2432.

568 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 141 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×#10597340C212yesmaximal
2C2×#10597342C212yesmaximal, complemented
3#11926475C212yesmaximal, complemented
4#11926470C212yesmaximal, complemented
5#11926464C211yesmaximal, characteristic, complemented
6#11926461C211yesmaximal, characteristic
7#11926435C212yesmaximal, complemented
8#11926415C212yesmaximal, complemented
9C19×#384C211yesmaximal, characteristic, complemented
10C22×D76C2211yescharacteristic
11C22×C4×D19C2212yes—
12C22×Dic38C2211yescharacteristic
13C2×C4⋊C4×C19C2212yes—
14C2×C4⋊C4×C19C2212yes—
15C2×C4⋊C4×C19C2211yescharacteristic
16C2×C4⋊C4×C19C2211yescharacteristic
17C2×C42×C19C2211yescharacteristic
18C2×(C2×D19)⋊C4C2212yes—
19C2×(C2×D19)⋊C4C2212yes—
20C2×(C2×D19)⋊C4C2212yes—
21C2×(C2×D19)⋊C4C2212yes—
22C2×(C2×D19)⋊C4C2212yes—
23C2×Dic19⋊C4C2212yes—
24C2×Dic19⋊C4C2212yes—
25C2×Dic19⋊C4C2212yes—
26#10597342—28no—
27#10597340—28no—
28C19⋊#95C2212yes—
29C19⋊#95C2212yes—
30C19⋊#95C2212yes—
31C19⋊#95C2211yescharacteristic
32C19⋊#95C2211yescharacteristic
33C23×D19C2312yes—
34C22×C4×C19C2311yescharacteristic
35C22×C4×C19C2312yes—
36C22×C4×C19C2311yescharacteristic
37C22×C4×C19C2312yes—
38C22×C4×C19C2311yescharacteristic
39C22×Dic19C2312yes—
40C22×Dic19C2312yes—
41C22×Dic19C2312yes—
42C2×D76—24no—
43C2×D76—41no—
44C2×C4×D19—24no—
45C2×C4×D19—24no—
46C2×C4×D19—42no—
47C2×Dic38—24no—
48C2×Dic38—41no—
49C4⋊C4×C19—24no—
50C4⋊C4×C19—24no—
51C4⋊C4×C19—41no—
52C4⋊C4×C19—41no—
53C42×C19—22no—
54(C2×D19)⋊C4—24no—
55(C2×D19)⋊C4—24no—
56(C2×D19)⋊C4—24no—
57(C2×D19)⋊C4—24no—
58(C2×D19)⋊C4D418yes—
59Dic19⋊C4—24no—
60Dic19⋊C4—24no—
61Dic19⋊C4—24no—
62C23×C19C2411yescharacteristic
63C22×D19—22no—
64C22×D19—22no—
65C22×D19—22no—
66C22×D19—22no—
67C22×D19—22no—
68C22×D19—22no—
69C22×D19C2×D414yes—
70C2×C4×C19—22no—
71C2×C4×C19—21no—
72C2×C4×C19—21no—
73C2×C4×C19—22no—
74C2×C4×C19—22no—
75C2×C4×C19—22no—
76C2×C4×C19—22no—
77C2×C4×C19—22no—
78C2×C4×C19—21no—
79C2×C4×C19—22no—
80C2×C4×C19—21no—
81C2×C4×C19C2×D414yes—
82C2×C4×C19#4112yes—
83C2×Dic19—22no—
84C2×Dic19—22no—
85C2×Dic19—22no—
86C2×Dic19—22no—
87C2×Dic19—22no—
88C2×Dic19—22no—
89C2×Dic19—22no—
90C2×Dic19—22no—
91C2×Dic19C2×D414yes—
92D76—44no—
93C4×D19—48no—
94Dic38—44no—
95#2680—191nomaximal, Sylow
96C22×C19C22×D412yes—
97C22×C19C2×#4111yescharacteristic
98C22×C19H(5,𝔽2)11yescharacteristic
99C22×C192−1+411yescharacteristic
100C22×C192−1+412yes—
101C2×D19—24no—
102C2×D19—24no—
103C2×D19—24no—
104C2×D19—42no—
105C2×D19—42no—
106C2×D19—42no—
107C2×D19—42no—
108C4×C19—22no—
109C4×C19—24no—
110C4×C19—41no—
111C4×C19—42no—
112C4×C19—41no—
113Dic19—24no—
114Dic19—42no—
115Dic19—42no—
116C2×#123—192no—
117C2×C22⋊Q8—192no—
118#398—192no—
119#397—192no—
120#395—191no—
121#394—191no—
122#388—192no—
123#385—192no—
124#384D1911yescharacteristic, complemented
125C2×C19#53612yes—
126C2×C19#53911yescharacteristic
127C2×C19D4211yescharacteristic
128C2×C19#54712yes—
129C2×C19#56311yescharacteristic
130D19—44no—
131C22×Q8—191no—
132C22×D4—191no—
133C23×C4—192no—
134#123—388no—
135C22⋊Q8—388no—
136C2×C4⋊C4—192no—
137C2×C4⋊C4—192no—
138C2×C4⋊C4—192no—
139C2×C4⋊C4C2×D1912yes—
140C2×C4⋊C4C2×D1912yes—
141C2×C4⋊C4C2×D1911yescharacteristic
142C2×C4⋊C4C2×D1911yescharacteristic
143C2×C22⋊C4—192no—
144C2×C22⋊C4—192no—
145C2×C22⋊C4—192no—
146C2×C22⋊C4—192no—
147C2×C22⋊C4—192no—
148C2×C42C2×D1911yescharacteristic
149#95—192no—
150#95—192no—
151#95—192no—
152#95—191no—
153#95—191no—
154C19#268011yescharacteristic, complemented, Sylow
155C24—192no—
156C2×Q8—384no—
157C2×Q8—761no—
158C2×D4—384no—
159C2×D4—761no—
160C22×C4—192no—
161C22×C4—192no—
162C22×C4—192no—
163C22×C4—384no—
164C22×C4—384no—
165C22×C4—762no—
166C22×C4C22×D1911yescharacteristic
167C22×C4C22×D1912yes—
168C22×C4C22×D1911yescharacteristic
169C22×C4C22×D1911yescharacteristic
170C22×C4C22×D1912yes—
171C4⋊C4—24no—
172C4⋊C4—24no—
173C4⋊C4—41no—
174C4⋊C4—41no—
175C4⋊C4—384no—
176C4⋊C4—384no—
177C4⋊C4—384no—
178C22⋊C4—198no—
179C22⋊C4—384no—
180C22⋊C4—384no—
181C22⋊C4—384no—
182C22⋊C4—384no—
183C42—22no—
184C23—194no—
185C23—382no—
186C23—382no—
187C23—382no—
188C23—382no—
189C23—382no—
190C23—382no—
191C23C23×D1911yescharacteristic
192Q8—764no—
193D4—764no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—194no—
206C2×C4—382no—
207C2×C4—382no—
208C2×C4—382no—
209C2×C4—382no—
210C2×C4—382no—
211C2×C4—382no—
212C2×C4—382no—
213C2×C4—382no—
214C2×C4—768no—
215C2×C4#6454112yes—
216C2×C4D4×D1914yes—
217C22—384no—
218C22—384no—
219C22—384no—
220C22—762no—
221C22—762no—
222C22—762no—
223C22—762no—
224C22C2×#6454111yescharacteristic
225C22C2×D4×D1912yes—
226C22#1059743011yescharacteristic
227C22#1059743311yescharacteristic
228C22#1059743312yes—
229C4—22no—
230C4—24no—
231C4—42no—
232C4—41no—
233C4—41no—
234C4—384no—
235C4—762no—
236C4—762no—
237C2—764no—
238C2#1192711912yes—
239C2#1192714111yescharacteristic
240C2#1192717911yescharacteristic
241C2#1192719512yes—
242C2#1192729311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#384C2
prime radicalC22×D76C22
hypercenter#384D19
hypocenterC19#2680
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
2. C2×#10597342C2semidirect
3. #11926475C2semidirect
4. #11926470C2semidirect
5. #11926464C2semidirect
7. #11926435C2semidirect
8. #11926415C2semidirect
9. C19×#384C2semidirect
124. #384D19semidirect
154. C19#2680semidirect

Maximal subgroups

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

subgroupindex
C2×#105973402
C2×#105973422
#119264752
#119264702
#119264642
#119264612
#119264352
#119264152
C19×#3842
#268019