Finite Group Databasebeta

← #14569009

Subgroups — #14569009

Order 2432.

544 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 159 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×#10597343C211yesmaximal, characteristic
2C2×C4⋊C4×D19C211yesmaximal, characteristic
3#11926475C211yesmaximal, characteristic, complemented
4#11926465C211yesmaximal, characteristic, complemented
5#11926464C211yesmaximal, characteristic, complemented
6#11926443C212yesmaximal, complemented
7#11926441C212yesmaximal, complemented
8#11926418C212yesmaximal
9#11926415C212yesmaximal
10#11926391C211yesmaximal, characteristic
11C19×#398C211yesmaximal, characteristic, complemented
12C22×C4×D19C2211yescharacteristic
13C22×C4×D19C2211yescharacteristic
14C22×C4×D19C2211yescharacteristic
15C22×Dic38C2211yescharacteristic
16C2×C4⋊C4×C19C2211yescharacteristic
17C2×C4⋊C4×C19C2212yes—
18C2×C4⋊C4×C19C2211yescharacteristic
19C2×(C2×D19)⋊C4C2212yes—
20C2×(C2×D19)⋊C4C2212yes—
21C2×C4⋊Dic19C2212yes—
22C2×C4⋊Dic19C2211yescharacteristic
23C2×C4⋊Dic19C2212yes—
24C2×Dic19⋊C4C2212yes—
25C2×Dic19⋊C4C2211yescharacteristic
26C2×Dic19⋊C4C2211yescharacteristic
27C2×Dic19⋊C4C2212yes—
28C2×C4×Dic19C2212yes—
29#10597343—24no—
30C4⋊C4×D19—24no—
31C19×#95C2211yescharacteristic
32C19×#95C2212yes—
33C19⋊#95C2211yescharacteristic
34C19⋊#95C2212yes—
35C19⋊#95C2212yes—
36C19⋊#95C2212yes—
37C23×D19C2311yescharacteristic
38C22×C4×C19C2312yes—
39C22×C4×C19C2311yescharacteristic
40C22×C4×C19C2311yescharacteristic
41C22×C4×C19C2312yes—
42C22×C4×C19C2311yescharacteristic
43C22×Dic19C2312yes—
44C22×Dic19C2311yescharacteristic
45C22×Dic19C2311yescharacteristic
46C22×Dic19C2312yes—
47C22×Dic19C2311yescharacteristic
48C2×C4×D19—22no—
49C2×C4×D19—22no—
50C2×C4×D19—22no—
51C2×C4×D19—22no—
52C2×C4×D19—42no—
53C2×C4×D19—42no—
54C2×C4×D19D414yes—
55C2×Dic38—22no—
56C2×Dic38—42no—
57C4⋊C4×C19—22no—
58C4⋊C4×C19—22no—
59C4⋊C4×C19—24no—
60(C2×D19)⋊C4—24no—
61(C2×D19)⋊C4Q818yescomplemented
62C4⋊Dic19—22no—
63C4⋊Dic19—24no—
64C4⋊Dic19—42no—
65Dic19⋊C4—22no—
66Dic19⋊C4—22no—
67Dic19⋊C4—24no—
68Dic19⋊C4—42no—
69C4×Dic19—42no—
70C23×C19C2411yescharacteristic
71C22×D19—21no—
72C22×D19—21no—
73C22×D19—22no—
74C22×D19C2×D412yes—
75C22×D19C2×Q814yes—
76C2×C4×C19—21no—
77C2×C4×C19—22no—
78C2×C4×C19—21no—
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×C19C2×D412yes—
87C2×C4×C19C2×Q814yes—
88C2×C4×C19#4112yes—
89C2×Dic19—21no—
90C2×Dic19—22no—
91C2×Dic19—21no—
92C2×Dic19—22no—
93C2×Dic19—22no—
94C2×Dic19—21no—
95C2×Dic19—22no—
96C2×Dic19—22no—
97C2×Dic19—22no—
98C2×Dic19—22no—
99C2×Dic19C2×D412yes—
100C2×Dic19C2×Q814yes—
101C2×Dic19#4112yes—
102C4×D19—28no—
103C4×D19—44no—
104C4×D19—44no—
105Dic38—44no—
106#2583—191nomaximal, Sylow
107C22×C19C22×D411yescharacteristic
108C22×C19C22×Q812yes—
109C22×C19C2×#4111yescharacteristic
110C22×C19C2×#4111yescharacteristic
111C22×C19H(5,𝔽2)12yes—
112C2×D19—22no—
113C2×D19—22no—
114C2×D19—24no—
115C2×D19—24no—
116C2×D19C4⋊Q814yes—
117C4×C19—22no—
118C4×C19—22no—
119C4×C19—24no—
120C4×C19—42no—
121C4×C19—41no—
122Dic19—22no—
123Dic19—22no—
124Dic19—24no—
125Dic19—42no—
126Dic19—41no—
127C2×C22⋊Q8—191no—
128C22×C4⋊C4—191no—
129#398—191no—
130#398D1911yescharacteristic, complemented
131#395—191no—
132#395—191no—
133#389—192no—
134#389—192no—
135#385—192no—
136#385—192no—
137C4×C22⋊C4—191no—
138C2×C19#52511yescharacteristic
139C2×C19C2×C4⋊Q811yescharacteristic
140C2×C19#53411yescharacteristic
141C2×C19#55412yes—
142C2×C19#55412yes—
143D19—24no—
144C22×Q8—191no—
145C23×C4—191no—
146C23×C4—191no—
147C23×C4—191no—
148C22⋊Q8—384no—
149C2×C4⋊C4—191no—
150C2×C4⋊C4—191no—
151C2×C4⋊C4—191no—
152C2×C4⋊C4—192no—
153C2×C4⋊C4—192no—
154C2×C4⋊C4—192no—
155C2×C4⋊C4—192no—
156C2×C4⋊C4—384no—
157C2×C4⋊C4C2×D1911yescharacteristic
158C2×C4⋊C4C2×D1911yescharacteristic
159C2×C4⋊C4C2×D1912yes—
160C2×C22⋊C4—192no—
161C2×C22⋊C4—192no—
162C2×C42—192no—
163#95—191no—
164#95—192no—
165#95—192no—
166#95—192no—
167#95C2×D1911yescharacteristic
168#95C2×D1912yes—
169C19#258311yescharacteristic, complemented, Sylow
170C24—191no—
171C2×Q8—382no—
172C2×Q8—762no—
173C22×C4—192no—
174C22×C4—191no—
175C22×C4—191no—
176C22×C4—194no—
177C22×C4—192no—
178C22×C4—191no—
179C22×C4—382no—
180C22×C4—382no—
181C22×C4—382no—
182C22×C4—382no—
183C22×C4—762no—
184C22×C4—762no—
185C22×C4C22×D1912yes—
186C22×C4C22×D1911yescharacteristic
187C22×C4C22×D1911yescharacteristic
188C22×C4C22×D1911yescharacteristic
189C22×C4C22×D1912yes—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—24no—
193C4⋊C4—384no—
194C4⋊C4—382no—
195C4⋊C4—382no—
196C4⋊C4—384no—
197C4⋊C4—382no—
198C4⋊C4—762no—
199C4⋊C4—762no—
200C22⋊C4—198no—
201C22⋊C4—384no—
202C42—762no—
203C23—192no—
204C23—194no—
205C23—381no—
206C23—381no—
207C23—382no—
208C23C23×D1911yescharacteristic
209Q8—764no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—192no—
221C2×C4—194no—
222C2×C4—192no—
223C2×C4—388no—
224C2×C4—381no—
225C2×C4—381no—
226C2×C4—382no—
227C2×C4—382no—
228C2×C4—382no—
229C2×C4—382no—
230C2×C4—381no—
231C2×C4—382no—
232C2×C4—382no—
233C2×C4—382no—
234C2×C4—764no—
235C2×C4—764no—
236C2×C4D4×D1912yes—
237C2×C4#6454312yes—
238C2×C4Q8×D1914yes—
239C22—194no—
240C22—382no—
241C22—382no—
242C22—384no—
243C22—384no—
244C22C2×D4×D1911yescharacteristic
245C22C2×#6454311yescharacteristic
246C22C2×Q8×D1912yes—
247C22#41×D1911yescharacteristic
248C22#1059743512yes—
249C4—22no—
250C4—22no—
251C4—24no—
252C4—42no—
253C4—41no—
254C4—382no—
255C4—382no—
256C4—384no—
257C4—761no—
258C4—762no—
259C2—384no—
260C2#1192705411yescharacteristic
261C2C4⋊Q8×D1911yescharacteristic
262C2#1192710511yescharacteristic
263C2#1192725012yes—
264C2#1192725212yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#398C2
prime radicalC23×D19C23
hypercenter#398D19
hypocenterC19#2583
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
3. #11926475C2semidirect
4. #11926465C2semidirect
5. #11926464C2semidirect
6. #11926443C2semidirect
7. #11926441C2semidirect
11. C19×#398C2semidirect
61. (C2×D19)⋊C4Q8semidirect
130. #398D19semidirect
169. C19#2583semidirect

Maximal subgroups

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

subgroupindex
C2×#105973432
C2×C4⋊C4×D192
#119264752
#119264652
#119264642
#119264432
#119264412
#119264182
#119264152
#119263912
C19×#3982
#258319