Finite Group Databasebeta

← #14571660

Subgroups — #14571660

Order 2432.

644 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 125 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×#10597385C212yesmaximal, complemented
2#11926473C212yesmaximal, complemented
3#11926472C212yesmaximal, complemented
4#11926453C211yesmaximal, characteristic, complemented
5#11926453C212yesmaximal, complemented
6#11926452C212yesmaximal, complemented
7#11926452C212yesmaximal, complemented
8#11926405C211yesmaximal, characteristic, complemented
9C19×#392C211yesmaximal, characteristic, complemented
10C22×D4×C19C2212yes—
11C22×D4×C19C2211yescharacteristic
12C22×C22⋊D19C2212yes—
13C22×C22⋊D19C2212yes—
14C22×C22⋊D19C2212yes—
15C23×Dic19C2211yescharacteristic
16C22×D76C2211yescharacteristic
17C2×C22⋊C4×C19C2211yescharacteristic
18C2×C22⋊C4×C19C2212yes—
19C2×C22⋊Dic19C2212yes—
20C2×C22⋊Dic19C2211yescharacteristic
21C2×C22⋊Dic19C2212yes—
22#10597385—28no—
23C2×(C2×D19)⋊C4C2212yes—
24C2×(C2×D19)⋊C4C2212yes—
25C2×(C2×D19)⋊C4C2212yes—
26C2×Dic19⋊C4C2212yes—
27C19×#95C2211yescharacteristic
28C19⋊#95C2212yes—
29C19⋊#95C2212yes—
30C19⋊#95C2212yes—
31C19⋊#95C2211yescharacteristic
32C24×C19C2312yes—
33C24×C19C2311yescharacteristic
34C23×D19C2312yes—
35C2×D4×C19—24no—
36C2×D4×C19—42no—
37C2×D4×C19—42no—
38C2×D4×C19—42no—
39C2×D4×C19—41no—
40C22×C4×C19C2311yescharacteristic
41C22×C4×C19C2311yescharacteristic
42C22×C4×C19C2312yes—
43C2×C22⋊D19—24no—
44C2×C22⋊D19—24no—
45C2×C22⋊D19—42no—
46C2×C22⋊D19—42no—
47C2×C22⋊D19—42no—
48C2×C22⋊D19—42no—
49C2×C22⋊D19—42no—
50C2×C22⋊D19—42no—
51C2×C22⋊D19—42no—
52C22×Dic19—41no—
53C22×Dic19—41no—
54C22×Dic19D414yescomplemented
55C22×Dic19C2312yes—
56C22×Dic19C2312yes—
57C22×Dic19C2312yes—
58C2×D76—41no—
59C2×D76—42no—
60C22⋊C4×C19—41no—
61C22⋊C4×C19—42no—
62C22⋊Dic19—24no—
63C22⋊Dic19—41no—
64C22⋊Dic19—42no—
65(C2×D19)⋊C4—24no—
66(C2×D19)⋊C4—42no—
67(C2×D19)⋊C4—42no—
68Dic19⋊C4—24no—
69C23×C19—21no—
70C23×C19—21no—
71C23×C19—22no—
72C23×C19—22no—
73C23×C19—22no—
74C23×C19—22no—
75C23×C19—22no—
76C23×C19—22no—
77C23×C19—22no—
78C23×C19—22no—
79C23×C19—22no—
80C23×C19C2×D412yes—
81C23×C19C2411yescharacteristic
82C22×D19—22no—
83C22×D19—22no—
84C22×D19—22no—
85C22×D19—22no—
86C22×D19—22no—
87C22×D19—22no—
88C22×D19—22no—
89D4×C19—48no—
90D4×C19—44no—
91C2×C4×C19—22no—
92C2×C4×C19—22no—
93C2×C4×C19—22no—
94C2×C4×C19—21no—
95C2×C4×C19—22no—
96C2×C4×C19—22no—
97C2×C4×C19—21no—
98C22⋊D19—48no—
99C22⋊D19—48no—
100C22⋊D19—48no—
101C2×Dic19—22no—
102C2×Dic19—22no—
103C2×Dic19—22no—
104C2×Dic19—22no—
105C2×Dic19—22no—
106C2×Dic19—22no—
107C2×Dic19—22no—
108C2×Dic19—22no—
109C2×Dic19—44no—
110C2×Dic19C2×D414yes—
111D76—44no—
112#2815—191nomaximal, Sylow
113C22×C19—22no—
114C22×C19—24no—
115C22×C19—41no—
116C22×C19—42no—
117C22×C19—41no—
118C22×C19—42no—
119C22×C19—42no—
120C22×C19—42no—
121C22×C19—42no—
122C22×C19—42no—
123C22×C19—42no—
124C22×C19—42no—
125C22×C19C22×D411yescharacteristic
126C22×C19H(5,𝔽2)11yescharacteristic
127C22×C19H(5,𝔽2)12yes—
128C22×C19H(5,𝔽2)12yes—
129C22×C19H(5,𝔽2)11yescharacteristic
130C2×D19—42no—
131C2×D19—42no—
132C2×D19—42no—
133C2×D19—42no—
134C2×D19—42no—
135C2×D19—42no—
136C2×D19—42no—
137C4×C19—42no—
138C4×C19—41no—
139C4×C19—41no—
140Dic19—24no—
141Dic19—42no—
142Dic19—42no—
143C2×#121—192no—
144#397—192no—
145#397—192no—
146#392—192no—
147#392—192no—
148#392—192no—
149#392—191no—
150#392D1911yescharacteristic, complemented
151#381—191no—
152C2×C19—42no—
153C2×C19—82no—
154C2×C19#53411yescharacteristic
155C2×C19#53512yes—
156C2×C19#56011yescharacteristic
157C2×C19#56012yes—
158C2×C19#56011yescharacteristic
159D19—82no—
160C22×D4—192no—
161C22×D4—192no—
162C22×D4—192no—
163C22×D4—191no—
164C22×D4C2×D1912yes—
165C22×D4C2×D1911yescharacteristic
166C23×C4—191no—
167#121—388no—
168C2×C4⋊C4—192no—
169C2×C22⋊C4—192no—
170C2×C22⋊C4—192no—
171C2×C22⋊C4—191no—
172C2×C22⋊C4—192no—
173C2×C22⋊C4—192no—
174C2×C22⋊C4—192no—
175C2×C22⋊C4C2×D1911yescharacteristic
176C2×C22⋊C4C2×D1912yes—
177#95—192no—
178#95—192no—
179#95—192no—
180#95—191no—
181#95C2×D1911yescharacteristic
182C19#281511yescharacteristic, complemented, Sylow
183C24—192no—
184C24C22×D1912yes—
185C24C22×D1911yescharacteristic
186C2×D4—24no—
187C2×D4—42no—
188C2×D4—41no—
189C2×D4—42no—
190C2×D4—42no—
191C2×D4—384no—
192C2×D4—384no—
193C2×D4—761no—
194C2×D4—762no—
195C2×D4—762no—
196C2×D4—762no—
197C2×D4—762no—
198C2×D4—762no—
199C2×D4—762no—
200C2×D4—762no—
201C2×D4—762no—
202C22×C4—192no—
203C22×C4—194no—
204C22×C4—192no—
205C22×C4—192no—
206C22×C4—761no—
207C22×C4—761no—
208C22×C4C22×D1911yescharacteristic
209C22×C4C22×D1911yescharacteristic
210C22×C4C22×D1912yes—
211C4⋊C4—384no—
212C22⋊C4—41no—
213C22⋊C4—42no—
214C22⋊C4—384no—
215C22⋊C4—384no—
216C22⋊C4—762no—
217C22⋊C4—762no—
218C22⋊C4—762no—
219C22⋊C4—761no—
220C23—21no—
221C23—22no—
222C23—22no—
223C23—21no—
224C23—22no—
225C23—22no—
226C23—22no—
227C23—22no—
228C23—22no—
229C23—22no—
230C23—22no—
231C23—382no—
232C23—382no—
233C23—382no—
234C23—382no—
235C23—382no—
236C23—382no—
237C23—382no—
238C23D4×D1912yes—
239C23C23×D1911yescharacteristic
240D4—48no—
241D4—44no—
242D4—764no—
243D4—768no—
244D4—768no—
245D4—768no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—194no—
254C2×C4—382no—
255C2×C4—382no—
256C2×C4—382no—
257C2×C4—382no—
258C2×C4—382no—
259C2×C4—382no—
260C2×C4—382no—
261C2×C4—382no—
262C2×C4—764no—
263C22—22no—
264C22—24no—
265C22—41no—
266C22—42no—
267C22—41no—
268C22—42no—
269C22—42no—
270C22—42no—
271C22—42no—
272C22—42no—
273C22—42no—
274C22—42no—
275C22—762no—
276C22—762no—
277C22—762no—
278C22—762no—
279C22—762no—
280C22—762no—
281C22—762no—
282C22C2×D4×D1911yescharacteristic
283C22#1059743011yescharacteristic
284C22#1059743012yes—
285C22#1059743012yes—
286C22#1059743511yescharacteristic
287C4—42no—
288C4—41no—
289C4—41no—
290C4—384no—
291C4—762no—
292C4—762no—
293C2—42no—
294C2—82no—
295C2—1522no—
296C2#1192710211yescharacteristic
297C2#1192710912yes—
298C2#1192728111yescharacteristic
299C2#1192728212yes—
300C2#1192728311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#392C2
hypercenter#392D19
hypocenterC19#2815
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#10597385C2semidirect
2. #11926473C2semidirect
3. #11926472C2semidirect
4. #11926453C2semidirect
5. #11926453C2semidirect
6. #11926452C2semidirect
7. #11926452C2semidirect
8. #11926405C2semidirect
9. C19×#392C2semidirect
54. C22×Dic19D4semidirect
150. #392D19semidirect
182. C19#2815semidirect

Maximal subgroups

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

subgroupindex
C2×#105973852
#119264732
#119264722
#119264532
#119264522
#119264052
C19×#3922
#281519