Finite Group Databasebeta

← #14568082

Subgroups — #14568082

Order 2432.

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

normal subgroups only

This group has 546 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×#10597329C211yesmaximal, characteristic
2C2×#10597338C211yesmaximal, characteristic, complemented
3#11926484C211yesmaximal, characteristic, complemented
4#11926480C211yesmaximal, characteristic, complemented
5#11926475C211yesmaximal, characteristic, complemented
6#11926438C212yesmaximal, complemented
7#11926431C212yesmaximal, complemented
8#11926420C212yesmaximal
9#11926403C212yesmaximal, complemented
10#95×D19C211yesmaximal, characteristic, complemented
11C19×#397C211yesmaximal, characteristic, complemented
12C22×C22⋊D19C2211yescharacteristic
13C22×C4×D19C2212yes—
14C22×C4×D19C2211yescharacteristic
15C2×C4⋊C4×C19C2211yescharacteristic
16C2×C22⋊C4×C19C2211yescharacteristic
17C2×C22⋊C4×C19C2212yes—
18C2×C22⋊Dic19C2211yescharacteristic
19C2×C22⋊Dic19C2212yes—
20C2×(C2×D19)⋊C4C2211yescharacteristic
21C2×(C2×D19)⋊C4C2212yes—
22C2×C4⋊Dic19C2211yescharacteristic
23C2×C4⋊Dic19C2211yescharacteristic
24C2×Dic19⋊C4C2211yescharacteristic
25C2×Dic19⋊C4C2212yes—
26C2×Dic19⋊C4C2212yes—
27C2×C4×Dic19C2212yes—
28#10597338—24no—
29#10597329—24no—
30C19×#95C2211yescharacteristic
31C19×#95C2212yes—
32C19⋊#95C2212yes—
33C19⋊#95C2211yescharacteristic
34C19⋊#95C2212yes—
35C19⋊#95C2212yes—
36C19⋊#95C2212yes—
37C24×C19C2311yescharacteristic
38C23×D19C2311yescharacteristic
39C22×C4×C19C2312yes—
40C22×C4×C19C2312yes—
41C22×C4×C19C2311yescharacteristic
42C22×C4×C19C2311yescharacteristic
43C2×C22⋊D19—22no—
44C2×C22⋊D19—24no—
45C22×Dic19C2312yes—
46C22×Dic19C2311yescharacteristic
47C22×Dic19C2311yescharacteristic
48C22×Dic19C2311yescharacteristic
49C22×Dic19C2312yes—
50C2×C4×D19—24no—
51C2×C4×D19—24no—
52C2×C4×D19—24no—
53C2×C4×D19—42no—
54C2×C4×D19D414yes—
55C4⋊C4×C19—22no—
56C22⋊C4×C19—22no—
57C22⋊C4×C19—42no—
58C22⋊Dic19—22no—
59C22⋊Dic19—24no—
60(C2×D19)⋊C4—22no—
61(C2×D19)⋊C4—24no—
62C4⋊Dic19—22no—
63C4⋊Dic19—22no—
64Dic19⋊C4—22no—
65Dic19⋊C4—24no—
66Dic19⋊C4—42no—
67C4×Dic19—24no—
68C23×C19—21no—
69C23×C19—22no—
70C23×C19—22no—
71C23×C19—21no—
72C23×C19—21no—
73C23×C19C2411yescharacteristic
74C22×D19—22no—
75C22×D19—21no—
76C22×D19—21no—
77C22×D19C2×D412yes—
78C22×D19#4114yes—
79C2×C4×C19—22no—
80C2×C4×C19—22no—
81C2×C4×C19—21no—
82C2×C4×C19—22no—
83C2×C4×C19—22no—
84C2×C4×C19—22no—
85C2×C4×C19—22no—
86C2×C4×C19—22no—
87C2×C4×C19—22no—
88C2×C4×C19C2×D412yes—
89C22⋊D19—44no—
90C2×Dic19—22no—
91C2×Dic19—22no—
92C2×Dic19—22no—
93C2×Dic19—22no—
94C2×Dic19—21no—
95C2×Dic19—21no—
96C2×Dic19—22no—
97C2×Dic19—22no—
98C2×Dic19—22no—
99C2×Dic19—21no—
100C2×Dic19—21no—
101C2×Dic19C2×D412yes—
102C2×Dic19#4114yes—
103C4×D19—28no—
104C4×D19—48no—
105#2498—191nomaximal, Sylow
106C22×C19—41no—
107C22×C19—41no—
108C22×C19—41no—
109C22×C19—42no—
110C22×C19—42no—
111C22×C19C22×D411yescharacteristic
112C22×C19C2×#4112yes—
113C22×C19C2×#4112yes—
114C22×C19H(5,𝔽2)11yescharacteristic
115C22×C192−1+411yescharacteristic
116C2×D19—22no—
117C2×D19—22no—
118C2×D19—24no—
119C2×D19—24no—
120C2×D19#12314yes—
121C4×C19—22no—
122C4×C19—41no—
123C4×C19—42no—
124C4×C19—42no—
125Dic19—22no—
126Dic19—24no—
127Dic19—41no—
128Dic19—42no—
129Dic19—41no—
130C2×#123—191no—
131C2×#117—191no—
132#400—191no—
133#399—191no—
134#398—191no—
135#397D1911yescharacteristic, complemented
136#388—192no—
137#387—192no—
138#386—192no—
139#380—192no—
140C2×#95—191no—
141C2×C19—81no—
142C2×C19C2×#12311yescharacteristic
143C2×C19#53211yescharacteristic
144C2×C19#53711yescharacteristic
145C2×C19#55112yes—
146C2×C19#55212yes—
147D19—24no—
148C22×D4—191no—
149C23×C4—191no—
150C23×C4—192no—
151#123—384no—
152#117—384no—
153C2×C4⋊C4—191no—
154C2×C4⋊C4—191no—
155C2×C4⋊C4—191no—
156C2×C4⋊C4—192no—
157C2×C4⋊C4—192no—
158C2×C4⋊C4C2×D1911yescharacteristic
159C2×C22⋊C4—191no—
160C2×C22⋊C4—192no—
161C2×C22⋊C4—192no—
162C2×C22⋊C4—191no—
163C2×C22⋊C4C2×D1911yescharacteristic
164C2×C22⋊C4C2×D1912yes—
165C2×C42—192no—
166#95—192no—
167#95—191no—
168#95—192no—
169#95—192no—
170#95—192no—
171#95C2×D1911yescharacteristic
172#95C2×D1912yes—
173C19#249811yescharacteristic, complemented, Sylow
174C24—191no—
175C24C22×D1911yescharacteristic
176C2×D4—382no—
177C2×D4—384no—
178C22×C4—192no—
179C22×C4—191no—
180C22×C4—194no—
181C22×C4—191no—
182C22×C4—192no—
183C22×C4—191no—
184C22×C4—384no—
185C22×C4—384no—
186C22×C4—384no—
187C22×C4—762no—
188C22×C4C22×D1912yes—
189C22×C4C22×D1912yes—
190C22×C4C22×D1911yescharacteristic
191C22×C4C22×D1911yescharacteristic
192C4⋊C4—22no—
193C4⋊C4—384no—
194C4⋊C4—382no—
195C4⋊C4—382no—
196C4⋊C4—382no—
197C4⋊C4—762no—
198C22⋊C4—22no—
199C22⋊C4—42no—
200C22⋊C4—384no—
201C22⋊C4—382no—
202C22⋊C4—384no—
203C22⋊C4—382no—
204C42—384no—
205C23—21no—
206C23—21no—
207C23—22no—
208C23—22no—
209C23—21no—
210C23—192no—
211C23—194no—
212C23—381no—
213C23—382no—
214C23—381no—
215C23C23×D1911yescharacteristic
216D4—764no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—192no—
227C2×C4—194no—
228C2×C4—388no—
229C2×C4—382no—
230C2×C4—382no—
231C2×C4—382no—
232C2×C4—382no—
233C2×C4—381no—
234C2×C4—381no—
235C2×C4—381no—
236C2×C4—382no—
237C2×C4—382no—
238C2×C4—382no—
239C2×C4—381no—
240C2×C4—768no—
241C2×C4D4×D1912yes—
242C22—41no—
243C22—41no—
244C22—41no—
245C22—42no—
246C22—42no—
247C22—194no—
248C22—382no—
249C22—382no—
250C22—384no—
251C22—384no—
252C22C2×D4×D1911yescharacteristic
253C22#1059743011yescharacteristic
254C22#41×D1912yes—
255C22#41×D1912yes—
256C22#1059743611yescharacteristic
257C4—22no—
258C4—41no—
259C4—42no—
260C4—42no—
261C4—382no—
262C4—384no—
263C4—761no—
264C4—762no—
265C4—761no—
266C2—81no—
267C2—384no—
268C2#123×D1911yescharacteristic
269C2#1192709311yescharacteristic
270C2#1192712311yescharacteristic
271C2#1192722212yes—
272C2#1192723012yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#397C2
prime radicalC22×C22⋊D19C22
hypercenter#397D19
hypocenterC19#2498
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. C2×#10597338C2semidirect
3. #11926484C2semidirect
4. #11926480C2semidirect
5. #11926475C2semidirect
6. #11926438C2semidirect
7. #11926431C2semidirect
9. #11926403C2semidirect
10. #95×D19C2semidirect
11. C19×#397C2semidirect
135. #397D19semidirect
173. C19#2498semidirect

Maximal subgroups

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

subgroupindex
C2×#105973292
C2×#105973382
#119264842
#119264802
#119264752
#119264382
#119264312
#119264202
#119264032
#95×D192
C19×#3972
#249819