Finite Group Databasebeta

← #14569788

Subgroups — #14569788

Order 2432.

498 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 133 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×#10597343C211yesmaximal, characteristic, complemented
3#11926482C211yesmaximal, characteristic, complemented
4#11926470C212yesmaximal, complemented
5#11926465C211yesmaximal, characteristic, complemented
6#11926460C212yesmaximal
7#11926456C211yesmaximal, characteristic, complemented
8#11926443C212yesmaximal, complemented
9#11926437C212yesmaximal, complemented
10#11926391C211yesmaximal, characteristic, complemented
11C19×#399C211yesmaximal, characteristic, complemented
12C22×C22⋊D19C2211yescharacteristic
13C22×C4×D19C2211yescharacteristic
14C22×Dic38C2211yescharacteristic
15C2×C4⋊C4×C19C2211yescharacteristic
16C2×C4⋊C4×C19C2212yes—
17C2×C22⋊C4×C19C2211yescharacteristic
18C2×C22⋊C4×C19C2212yes—
19C2×C22⋊Dic19C2211yescharacteristic
20C2×C22⋊Dic19C2212yes—
21C2×(C2×D19)⋊C4C2212yes—
22C2×(C2×D19)⋊C4C2211yescharacteristic
23C2×(C2×D19)⋊C4C2212yes—
24C2×C4⋊Dic19C2212yes—
25C2×C4⋊Dic19C2211yescharacteristic
26C2×C4⋊Dic19C2212yes—
27C2×Dic19⋊C4C2211yescharacteristic
28C2×C4×Dic19C2212yes—
29#10597343—24no—
30#10597329—24no—
31C19×#95C2211yescharacteristic
32C19⋊#95C2211yescharacteristic
33C19⋊#95C2212yes—
34C19⋊#95C2212yes—
35C19⋊#95C2212yes—
36C19⋊#95C2212yes—
37C24×C19C2311yescharacteristic
38C23×D19C2311yescharacteristic
39C22×C4×C19C2311yescharacteristic
40C22×C4×C19C2312yes—
41C22×C4×C19C2311yescharacteristic
42C22×C4×C19C2312yes—
43C2×C22⋊D19—22no—
44C2×C22⋊D19—42no—
45C22×Dic19C2312yes—
46C22×Dic19C2312yes—
47C22×Dic19C2311yescharacteristic
48C22×Dic19C2311yescharacteristic
49C22×Dic19C2311yescharacteristic
50C2×C4×D19—42no—
51C2×C4×D19D414yes—
52C2×Dic38—22no—
53C2×Dic38—42no—
54C4⋊C4×C19—22no—
55C4⋊C4×C19—24no—
56C22⋊C4×C19—22no—
57C22⋊C4×C19—24no—
58C22⋊Dic19—22no—
59C22⋊Dic19—42no—
60(C2×D19)⋊C4—22no—
61(C2×D19)⋊C4—24no—
62(C2×D19)⋊C4—24no—
63C4⋊Dic19—22no—
64C4⋊Dic19—24no—
65C4⋊Dic19—42no—
66Dic19⋊C4—22no—
67C4×Dic19—42no—
68C23×C19—21no—
69C23×C19—22no—
70C23×C19—22no—
71C23×C19—21no—
72C23×C19—21no—
73C23×C19C2411yescharacteristic
74C22×D19—22no—
75C22×D19—22no—
76C22×D19—21no—
77C22×D19—21no—
78C22×D19C2×D412yes—
79C2×C4×C19—22no—
80C2×C4×C19—22no—
81C2×C4×C19—22no—
82C2×C4×C19—21no—
83C2×C4×C19—22no—
84C2×C4×C19—22no—
85C2×C4×C19—22no—
86C2×C4×C19—22no—
87C2×C4×C19C2×D412yes—
88C2×C4×C19#4114yes—
89C22⋊D19—44no—
90C2×Dic19—22no—
91C2×Dic19—21no—
92C2×Dic19—21no—
93C2×Dic19—22no—
94C2×Dic19—22no—
95C2×Dic19—22no—
96C2×Dic19—22no—
97C2×Dic19—22no—
98C2×Dic19—22no—
99C2×Dic19—21no—
100C2×Dic19—22no—
101C2×Dic19—21no—
102C2×Dic19C2×D412yes—
103C4×D19—44no—
104Dic38—44no—
105#2663—191nomaximal, Sylow
106C22×C19—41no—
107C22×C19—41no—
108C22×C19—41no—
109C22×C19—42no—
110C22×C19—42no—
111C22×C19C22×D411yescharacteristic
112C22×C19C2×#4112yes—
113C22×C19H(5,𝔽2)12yes—
114C22×C192−1+411yescharacteristic
115C22×C192−1+411yescharacteristic
116C2×D19—22no—
117C2×D19—22no—
118C2×D19—22no—
119C2×D19—42no—
120C2×D19—42no—
121C4×C19—22no—
122C4×C19—24no—
123C4×C19—41no—
124C4×C19—42no—
125Dic19—22no—
126Dic19—42no—
127Dic19—41no—
128Dic19—41no—
129Dic19—42no—
130C2×#123—191no—
131C2×C22⋊Q8—191no—
132#400—191no—
133#399D1911yescharacteristic, complemented
134#397—192no—
135#395—191no—
136#394—192no—
137#393—191no—
138#389—192no—
139#388—192no—
140C4×C22⋊C4—191no—
141C2×C19—81no—
142C2×C19#53211yescharacteristic
143C2×C19#53411yescharacteristic
144C2×C19#53611yescharacteristic
145C2×C19#53912yes—
146C2×C19#54212yes—
147D19—42no—
148C22×Q8—191no—
149C22×D4—191no—
150C23×C4—191no—
151#123—384no—
152C22⋊Q8—384no—
153C2×C4⋊C4—192no—
154C2×C4⋊C4—191no—
155C2×C4⋊C4—191no—
156C2×C4⋊C4—192no—
157C2×C4⋊C4C2×D1911yescharacteristic
158C2×C4⋊C4C2×D1912yes—
159C2×C22⋊C4—191no—
160C2×C22⋊C4—192no—
161C2×C22⋊C4—191no—
162C2×C22⋊C4—192no—
163C2×C22⋊C4—192no—
164C2×C22⋊C4C2×D1911yescharacteristic
165C2×C22⋊C4C2×D1912yes—
166C2×C42—192no—
167#95—191no—
168#95—192no—
169#95—192no—
170#95—192no—
171#95—192no—
172#95C2×D1911yescharacteristic
173C19#266311yescharacteristic, complemented, Sylow
174C24—191no—
175C24C22×D1911yescharacteristic
176C2×Q8—382no—
177C2×Q8—762no—
178C2×D4—382no—
179C2×D4—762no—
180C22×C4—191no—
181C22×C4—194no—
182C22×C4—192no—
183C22×C4—191no—
184C22×C4—192no—
185C22×C4—191no—
186C22×C4—762no—
187C22×C4C22×D1911yescharacteristic
188C22×C4C22×D1912yes—
189C22×C4C22×D1911yescharacteristic
190C22×C4C22×D1912yes—
191C4⋊C4—22no—
192C4⋊C4—24no—
193C4⋊C4—384no—
194C4⋊C4—382no—
195C4⋊C4—382no—
196C4⋊C4—762no—
197C22⋊C4—22no—
198C22⋊C4—24no—
199C22⋊C4—384no—
200C22⋊C4—382no—
201C22⋊C4—382no—
202C22⋊C4—384no—
203C22⋊C4—762no—
204C42—762no—
205C23—21no—
206C23—22no—
207C23—21no—
208C23—22no—
209C23—21no—
210C23—192no—
211C23—382no—
212C23—381no—
213C23—382no—
214C23—381no—
215C23C23×D1911yescharacteristic
216Q8—764no—
217D4—764no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—192no—
227C2×C4—382no—
228C2×C4—381no—
229C2×C4—382no—
230C2×C4—381no—
231C2×C4—382no—
232C2×C4—381no—
233C2×C4—382no—
234C2×C4—382no—
235C2×C4—382no—
236C2×C4—382no—
237C2×C4—382no—
238C2×C4—381no—
239C2×C4—764no—
240C2×C4D4×D1912yes—
241C2×C4#6454314yes—
242C22—41no—
243C22—41no—
244C22—41no—
245C22—42no—
246C22—42no—
247C22—382no—
248C22—382no—
249C22—382no—
250C22—762no—
251C22—762no—
252C22C2×D4×D1911yescharacteristic
253C22C2×#6454312yes—
254C22#1059743311yescharacteristic
255C22#1059743512yes—
256C22#1059743611yescharacteristic
257C4—22no—
258C4—24no—
259C4—41no—
260C4—42no—
261C4—382no—
262C4—761no—
263C4—762no—
264C4—761no—
265C4—762no—
266C2—81no—
267C2—762no—
268C2#1192709211yescharacteristic
269C2#1192710511yescharacteristic
270C2#1192711711yescharacteristic
271C2#1192713812yes—
272C2#1192716712yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#399C2
prime radicalC22×C22⋊D19C22
hypercenter#399D19
hypocenterC19#2663
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
2. C2×#10597343C2semidirect
3. #11926482C2semidirect
4. #11926470C2semidirect
5. #11926465C2semidirect
7. #11926456C2semidirect
8. #11926443C2semidirect
9. #11926437C2semidirect
10. #11926391C2semidirect
11. C19×#399C2semidirect
133. #399D19semidirect
173. C19#2663semidirect

Maximal subgroups

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

subgroupindex
C2×#105973292
C2×#105973432
#119264822
#119264702
#119264652
#119264602
#119264562
#119264432
#119264372
#119263912
C19×#3992
#266319