Finite Group Databasebeta

← #14567044

Subgroups — #14567044

Order 2432.

610 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 153 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×#10597332C211yesmaximal, characteristic
2C2×#10597375C211yesmaximal, characteristic
3C2×#10597323C211yesmaximal, characteristic, complemented
4C22×Dic19⋊C4C211yesmaximal, characteristic, complemented
5#11926478C212yesmaximal, complemented
6#11926468C212yesmaximal, complemented
7#11926441C212yesmaximal, complemented
8#11926433C212yesmaximal, complemented
9#11926421C211yesmaximal, characteristic
10#11926416C211yesmaximal, characteristic, complemented
11C19×#381C211yesmaximal, characteristic, complemented
12C23×C4×C19C2211yescharacteristic
13C22×C22⋊D19C2211yescharacteristic
14C23×Dic19C2211yescharacteristic
15C23×Dic19C2211yescharacteristic
16C2×C22⋊C4×C19C2211yescharacteristic
17C2×C22⋊C4×C19C2211yescharacteristic
18C2×C22⋊Dic19C2211yescharacteristic
19#10597375—24no—
20C2×(C2×D19)⋊C4C2212yes—
21C2×(C2×D19)⋊C4C2211yescharacteristic
22C2×(C2×D19)⋊C4C2211yescharacteristic
23C2×(C2×D19)⋊C4C2212yes—
24C2×C4⋊Dic19C2211yescharacteristic
25C2×C4⋊Dic19C2211yescharacteristic
26C2×Dic19⋊C4—24no—
27C2×Dic19⋊C4C2212yes—
28C2×Dic19⋊C4C2212yes—
29C2×Dic19⋊C4C2212yes—
30C2×Dic19⋊C4C2212yes—
31C2×Dic19⋊C4C2212yes—
32C2×C4×Dic19C2212yes—
33#10597332—24no—
34#10597323—24no—
35C19×#95C2212yes—
36C19×#95C2212yes—
37C19⋊#95C2212yes—
38C19⋊#95C2212yes—
39C24×C19C2311yescharacteristic
40C23×D19C2311yescharacteristic
41C22×C4×C19—22no—
42C22×C4×C19—22no—
43C22×C4×C19—22no—
44C22×C4×C19C2311yescharacteristic
45C22×C4×C19C2312yes—
46C22×C4×C19C2311yescharacteristic
47C22×C4×C19C2312yes—
48C2×C22⋊D19—22no—
49C2×C22⋊D19—22no—
50C2×C22⋊D19—22no—
51C22×Dic19—22no—
52C22×Dic19—22no—
53C22×Dic19—22no—
54C22×Dic19—24no—
55C22×Dic19D414yes—
56C22×Dic19C2311yescharacteristic
57C22×Dic19C2312yes—
58C22×Dic19C2311yescharacteristic
59C22×Dic19C2311yescharacteristic
60C22×Dic19C2312yes—
61C22⋊C4×C19—22no—
62C22⋊C4×C19—22no—
63C22⋊Dic19D414yes—
64(C2×D19)⋊C4—22no—
65(C2×D19)⋊C4—22no—
66(C2×D19)⋊C4—24no—
67(C2×D19)⋊C4—24no—
68C4⋊Dic19—22no—
69C4⋊Dic19—22no—
70Dic19⋊C4—24no—
71Dic19⋊C4—24no—
72Dic19⋊C4—24no—
73Dic19⋊C4—24no—
74Dic19⋊C4—24no—
75C4×Dic19—24no—
76C23×C19—22no—
77C23×C19—22no—
78C23×C19C2×D412yes—
79C23×C19C2×D412yes—
80C23×C19#4112yes—
81C23×C19C2411yescharacteristic
82C22×D19—21no—
83C22×D19—21no—
84C22×D19—22no—
85C22×D19—21no—
86C22×D19—22no—
87C2×C4×C19—22no—
88C2×C4×C19—22no—
89C2×C4×C19—22no—
90C2×C4×C19—21no—
91C2×C4×C19—21no—
92C2×C4×C19—22no—
93C2×C4×C19—22no—
94C2×C4×C19—22no—
95C2×C4×C19—22no—
96C2×C4×C19—22no—
97C2×C4×C19—44no—
98C22⋊D19—44no—
99C2×Dic19—28no—
100C2×Dic19—28no—
101C2×Dic19—21no—
102C2×Dic19—21no—
103C2×Dic19—22no—
104C2×Dic19—22no—
105C2×Dic19—21no—
106C2×Dic19—21no—
107C2×Dic19—22no—
108C2×Dic19—22no—
109C2×Dic19—21no—
110C2×Dic19—21no—
111C2×Dic19—21no—
112C2×Dic19C2×D414yes—
113C2×Dic19C2×D412yes—
114C2×Dic19C2×D412yes—
115C2×Dic19#4114yes—
116#2413—191nomaximal, Sylow
117C22×C19—22no—
118C22×C19—22no—
119C22×C19—24no—
120C22×C19—24no—
121C22×C19#12114yes—
122C22×C19C22×D411yescharacteristic
123C22×C19C22×D411yescharacteristic
124C22×C19C2×#4111yescharacteristic
125C22×C19C2×#4112yes—
126C22×C192−1+412yes—
127C2×D19—41no—
128C2×D19—41no—
129C2×D19—41no—
130C2×D19—42no—
131C2×D19—42no—
132C4×C19—42no—
133C4×C19—41no—
134C4×C19—41no—
135C4×C19—42no—
136Dic19—22no—
137Dic19—22no—
138Dic19—24no—
139Dic19—24no—
140Dic19—41no—
141C2×#123—191no—
142C2×#123—191no—
143C2×#117—191no—
144C22×C4⋊C4—191no—
145#398—192no—
146#396—192no—
147#389—192no—
148#388—192no—
149#386—191no—
150#385—191no—
151#381D1911yescharacteristic, complemented
152C2×C19—24no—
153C2×C19C2×#12111yescharacteristic
154C2×C19#52511yescharacteristic
155C2×C19#53611yescharacteristic
156C2×C19#54712yes—
157C2×C19#55212yes—
158D19—81no—
159C22×D4—191no—
160C23×C4—191no—
161C23×C4—191no—
162C23×C4C2×D1911yescharacteristic
163#123—384no—
164#123—384no—
165#117—384no—
166C2×C4⋊C4—192no—
167C2×C4⋊C4—192no—
168C2×C4⋊C4—192no—
169C2×C4⋊C4—191no—
170C2×C4⋊C4—192no—
171C2×C4⋊C4—191no—
172C2×C4⋊C4—192no—
173C2×C4⋊C4—384no—
174C2×C22⋊C4—191no—
175C2×C22⋊C4—191no—
176C2×C22⋊C4—192no—
177C2×C22⋊C4—191no—
178C2×C22⋊C4—192no—
179C2×C22⋊C4C2×D1911yescharacteristic
180C2×C22⋊C4C2×D1911yescharacteristic
181C2×C42—192no—
182#95—192no—
183#95—192no—
184#95C2×D1912yes—
185#95C2×D1912yes—
186C19#241311yescharacteristic, complemented, Sylow
187C24—191no—
188C24C22×D1911yescharacteristic
189C2×D4—382no—
190C2×D4—382no—
191C2×D4—382no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—194no—
196C22×C4—192no—
197C22×C4—192no—
198C22×C4—191no—
199C22×C4—191no—
200C22×C4—191no—
201C22×C4—384no—
202C22×C4—382no—
203C22×C4—382no—
204C22×C4—382no—
205C22×C4C22×D1911yescharacteristic
206C22×C4C22×D1912yes—
207C22×C4C22×D1911yescharacteristic
208C22×C4C22×D1912yes—
209C4⋊C4—384no—
210C4⋊C4—384no—
211C4⋊C4—384no—
212C4⋊C4—384no—
213C4⋊C4—384no—
214C4⋊C4—382no—
215C4⋊C4—382no—
216C22⋊C4—22no—
217C22⋊C4—22no—
218C22⋊C4—194no—
219C22⋊C4—384no—
220C22⋊C4—382no—
221C22⋊C4—382no—
222C22⋊C4—384no—
223C42—384no—
224C23—22no—
225C23—22no—
226C23—381no—
227C23—381no—
228C23—381no—
229C23—382no—
230C23—382no—
231C23#6454112yes—
232C23D4×D1912yes—
233C23D4×D1912yes—
234C23C23×D1911yescharacteristic
235D4—764no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—44no—
247C2×C4—194no—
248C2×C4—192no—
249C2×C4—192no—
250C2×C4—194no—
251C2×C4—388no—
252C2×C4—381no—
253C2×C4—381no—
254C2×C4—381no—
255C2×C4—382no—
256C2×C4—381no—
257C2×C4—382no—
258C2×C4—382no—
259C2×C4—382no—
260C2×C4—388no—
261C2×C4—381no—
262C2×C4—381no—
263C2×C4—381no—
264C22—22no—
265C22—22no—
266C22—24no—
267C22—24no—
268C22—761no—
269C22—761no—
270C22—762no—
271C22—762no—
272C22—761no—
273C22#1059733014yes—
274C22C2×#6454111yescharacteristic
275C22C2×D4×D1911yescharacteristic
276C22C2×D4×D1911yescharacteristic
277C22#41×D1912yes—
278C22#1059743612yes—
279C4—41no—
280C4—41no—
281C4—42no—
282C4—42no—
283C4—384no—
284C4—384no—
285C4—382no—
286C4—382no—
287C4—761no—
288C2—24no—
289C2—1521no—
290C2C2×#1059733011yescharacteristic
291C2#1192705211yescharacteristic
292C2#1192711611yescharacteristic
293C2#1192719212yes—
294C2#1192722712yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#381C2
prime radicalC22×C22⋊D19C22
hypercenter#381D19
hypocenterC19#2413
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
3. C2×#10597323C2semidirect
4. C22×Dic19⋊C4C2semidirect
5. #11926478C2semidirect
6. #11926468C2semidirect
7. #11926441C2semidirect
8. #11926433C2semidirect
10. #11926416C2semidirect
11. C19×#381C2semidirect
151. #381D19semidirect
186. C19#2413semidirect

Maximal subgroups

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

subgroupindex
C2×#105973322
C2×#105973752
C2×#105973232
C22×Dic19⋊C42
#119264782
#119264682
#119264412
#119264332
#119264212
#119264162
C19×#3812
#241319