Finite Group Databasebeta

← #14569979

Subgroups — #14569979

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×#10597392C212yesmaximal, complemented
3#11926477C212yesmaximal, complemented
4#11926473C212yesmaximal, complemented
5#11926461C211yesmaximal, characteristic
6#11926436C212yesmaximal, complemented
7#11926418C212yesmaximal, complemented
8#11926413C211yesmaximal, characteristic, complemented
9C19×#395C211yesmaximal, characteristic, complemented
10C22×Q8×C19C2211yescharacteristic
11C22×D76C2211yescharacteristic
12C22×C4×D19C2212yes—
13C2×C4⋊C4×C19C2212yes—
14C2×C4⋊C4×C19C2211yescharacteristic
15#10597392—28no—
16C2×(C2×D19)⋊C4C2212yes—
17C2×(C2×D19)⋊C4C2212yes—
18C2×(C2×D19)⋊C4C2212yes—
19C2×(C2×D19)⋊C4C2212yes—
20C2×(C2×D19)⋊C4C2212yes—
21C2×C4⋊Dic19C2212yes—
22C2×C4⋊Dic19C2211yescharacteristic
23C2×Dic19⋊C4C2212yes—
24C2×Dic19⋊C4C2212yes—
25C2×Dic19⋊C4C2212yes—
26C2×C4×Dic19C2211yescharacteristic
27#10597340—28no—
28C19×#95C2212yes—
29C19×#95C2211yescharacteristic
30C19⋊#95C2212yes—
31C19⋊#95C2212yes—
32C19⋊#95C2211yescharacteristic
33C23×D19C2312yes—
34C2×Q8×C19—24no—
35C2×Q8×C19—41no—
36C22×C4×C19C2311yescharacteristic
37C22×C4×C19C2311yescharacteristic
38C22×C4×C19C2312yes—
39C22×C4×C19C2312yes—
40C22×C4×C19C2311yescharacteristic
41C22×Dic19C2312yes—
42C22×Dic19C2312yes—
43C22×Dic19C2312yes—
44C2×D76—24no—
45C2×D76—41no—
46C2×C4×D19—24no—
47C2×C4×D19—24no—
48C2×C4×D19—42no—
49C4⋊C4×C19—24no—
50C4⋊C4×C19—41no—
51(C2×D19)⋊C4—24no—
52(C2×D19)⋊C4—24no—
53(C2×D19)⋊C4—24no—
54(C2×D19)⋊C4—24no—
55(C2×D19)⋊C4D418yes—
56C4⋊Dic19—24no—
57C4⋊Dic19—41no—
58Dic19⋊C4—24no—
59Dic19⋊C4—24no—
60Dic19⋊C4—24no—
61C4×Dic19—22no—
62C23×C19C2411yescharacteristic
63C22×D19—22no—
64C22×D19—22no—
65C22×D19—22no—
66C22×D19—22no—
67C22×D19—22no—
68C22×D19—22no—
69C22×D19C2×D414yes—
70Q8×C19—44no—
71C2×C4×C19—22no—
72C2×C4×C19—21no—
73C2×C4×C19—22no—
74C2×C4×C19—21no—
75C2×C4×C19—22no—
76C2×C4×C19—22no—
77C2×C4×C19—22no—
78C2×C4×C19—21no—
79C2×C4×C19—21no—
80C2×C4×C19—22no—
81C2×C4×C19—22no—
82C2×C4×C19C2×D414yes—
83C2×C4×C19#4112yes—
84C2×Dic19—22no—
85C2×Dic19—22no—
86C2×Dic19—22no—
87C2×Dic19—22no—
88C2×Dic19—22no—
89C2×Dic19—22no—
90C2×Dic19—22no—
91C2×Dic19—22no—
92C2×Dic19C2×D414yes—
93D76—44no—
94C4×D19—48no—
95#2680—191nomaximal, Sylow
96C22×C19C22×D412yes—
97C22×C19C2×#4111yescharacteristic
98C22×C19H(5,𝔽2)11yescharacteristic
99C22×C192−1+412yes—
100C22×C192−1+411yescharacteristic
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—42no—
111C4×C19—41no—
112C4×C19—41no—
113Dic19—24no—
114Dic19—42no—
115Dic19—42no—
116C2×#123—192no—
117C2×C22⋊Q8—192no—
118#398—192no—
119#397—192no—
120#395D1911yescharacteristic, complemented
121#394—191no—
122#388—192no—
123#385—192no—
124#384—191no—
125C2×C19#53612yes—
126C2×C19#53911yescharacteristic
127C2×C19D4211yescharacteristic
128C2×C19#54712yes—
129C2×C19#56311yescharacteristic
130D19—44no—
131C22×Q8C2×D1911yescharacteristic
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⋊C4—192no—
140C2×C4⋊C4—191no—
141C2×C4⋊C4C2×D1912yes—
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×C42—191no—
149#95—192no—
150#95—192no—
151#95—191no—
152#95C2×D1912yes—
153#95C2×D1911yescharacteristic
154C19#268011yescharacteristic, complemented, Sylow
155C24—192no—
156C2×Q8—24no—
157C2×Q8—41no—
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×D1912yes—
167C22×C4C22×D1911yescharacteristic
168C22×C4C22×D1911yescharacteristic
169C22×C4C22×D1912yes—
170C22×C4C22×D1911yescharacteristic
171C4⋊C4—24no—
172C4⋊C4—41no—
173C4⋊C4—384no—
174C4⋊C4—384no—
175C4⋊C4—384no—
176C4⋊C4—384no—
177C4⋊C4—761no—
178C22⋊C4—198no—
179C22⋊C4—384no—
180C22⋊C4—384no—
181C22⋊C4—384no—
182C22⋊C4—384no—
183C42—382no—
184C23—194no—
185C23—382no—
186C23—382no—
187C23—382no—
188C23—382no—
189C23—382no—
190C23—382no—
191C23C23×D1911yescharacteristic
192Q8—44no—
193D4—764no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
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×C4D4×D1914yes—
216C2×C4#6454512yes—
217C22—384no—
218C22—384no—
219C22—384no—
220C22—762no—
221C22—762no—
222C22—762no—
223C22—762no—
224C22C2×D4×D1912yes—
225C22#1059743011yescharacteristic
226C22C2×#6454511yescharacteristic
227C22#1059743312yes—
228C22#1059743611yescharacteristic
229C4—22no—
230C4—24no—
231C4—42no—
232C4—41no—
233C4—41no—
234C4—384no—
235C4—762no—
236C4—762no—
237C2—764no—
238C2#1192711712yes—
239C2#1192714311yescharacteristic
240C2#1192717611yescharacteristic
241C2#1192719712yes—
242C2#1192729311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#395C2
prime radicalC22×D76C22
hypercenter#395D19
hypocenterC19#2680
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
2. C2×#10597392C2semidirect
3. #11926477C2semidirect
4. #11926473C2semidirect
6. #11926436C2semidirect
7. #11926418C2semidirect
8. #11926413C2semidirect
9. C19×#395C2semidirect
120. #395D19semidirect
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×#105973922
#119264772
#119264732
#119264612
#119264362
#119264182
#119264132
C19×#3952
#268019