Finite Group Databasebeta

← #14566993

Subgroups — #14566993

Order 2432.

840 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 840 conjugacy classes of subgroups — too many to draw. Only its 171 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
1C22×Q8×D19C211yesmaximal, characteristic, complemented
2C2×#10597324C212yesmaximal, complemented
3C2×(C22⋊D19)⋊C4C211yesmaximal, characteristic
4#11926465C211yesmaximal, characteristic, complemented
5#11926463C211yesmaximal, characteristic, complemented
6#11926456C211yesmaximal, characteristic, complemented
7#11926448C212yesmaximal, complemented
8#11926420C212yesmaximal
9#11926418C212yesmaximal, complemented
10#11926403C211yesmaximal, characteristic, complemented
11C19×#393C211yesmaximal, characteristic, complemented
12C22×Q8×C19C2211yescharacteristic
13C22×C22⋊D19C2211yescharacteristic
14C23×Dic19C2211yescharacteristic
15C2×Q8×D19—24no—
16C2×Q8×D19—28no—
17C22×C4×D19C2212yes—
18C22×C4×D19C2211yescharacteristic
19C22×Dic38C2211yescharacteristic
20C22×Dic38C2212yes—
21C2×C22⋊C4×C19C2212yes—
22C2×C22⋊C4×C19C2211yescharacteristic
23C2×C22⋊Dic19C2212yes—
24C2×(C2×D19)⋊C4C2212yes—
25C2×(C2×D19)⋊C4C2211yescharacteristic
26C2×C4⋊Dic19C2212yes—
27C2×Dic19⋊C4C2212yes—
28C2×Dic19⋊C4C2212yes—
29C2×Dic19⋊C4C2211yescharacteristic
30C2×C4×Dic19C2211yescharacteristic
31(C22⋊D19)⋊C4—24no—
32#10597324—28no—
33C19×#95C2211yescharacteristic
34C19×#95C2212yes—
35C19⋊#95C2211yescharacteristic
36C19⋊#95C2212yes—
37C19⋊#95C2212yes—
38C19⋊#95C2212yes—
39C24×C19C2311yescharacteristic
40C23×D19C2311yescharacteristic
41C2×Q8×C19—22no—
42C2×Q8×C19—24no—
43C22×C4×C19C2311yescharacteristic
44C22×C4×C19C2312yes—
45C22×C4×C19C2311yescharacteristic
46C22×C4×C19C2312yes—
47C2×C22⋊D19—22no—
48C2×C22⋊D19—22no—
49C2×C22⋊D19Q814yescomplemented
50C22×Dic19—24no—
51C22×Dic19—22no—
52C22×Dic19C2312yes—
53C22×Dic19C2311yescharacteristic
54C22×Dic19C2312yes—
55C22×Dic19C2311yescharacteristic
56C22×Dic19C2311yescharacteristic
57Q8×D19—232no—
58C2×C4×D19—24no—
59C2×C4×D19—24no—
60C2×C4×D19—24no—
61C2×C4×D19—24no—
62C2×C4×D19D414yes—
63C2×Dic38—22no—
64C2×Dic38—24no—
65C2×Dic38—24no—
66C2×Dic38—24no—
67C2×Dic38D418yescomplemented
68C22⋊C4×C19—24no—
69C22⋊C4×C19—22no—
70C22⋊Dic19—24no—
71(C2×D19)⋊C4—22no—
72(C2×D19)⋊C4—24no—
73C4⋊Dic19—24no—
74Dic19⋊C4—24no—
75Dic19⋊C4—22no—
76Dic19⋊C4—24no—
77C4×Dic19—22no—
78C23×C19—22no—
79C23×C19—21no—
80C23×C19—21no—
81C23×C19—22no—
82C23×C19C2×Q812yescomplemented
83C23×C19C2411yescharacteristic
84C22×D19—22no—
85C22×D19—22no—
86C22×D19C2×D412yes—
87C22×D19C2×Q812yes—
88C22×D19#4112yes—
89Q8×C19—28no—
90C2×C4×C19—22no—
91C2×C4×C19—22no—
92C2×C4×C19—22no—
93C2×C4×C19—21no—
94C2×C4×C19—22no—
95C2×C4×C19—22no—
96C2×C4×C19—22no—
97C2×C4×C19—22no—
98C2×C4×C19C2×D412yes—
99C2×C4×C19C2×D414yes—
100C22⋊D19—28no—
101C2×Dic19—21no—
102C2×Dic19—22no—
103C2×Dic19—22no—
104C2×Dic19—21no—
105C2×Dic19—22no—
106C2×Dic19—22no—
107C2×Dic19—21no—
108C2×Dic19—22no—
109C2×Dic19—22no—
110C2×Dic19—44no—
111C2×Dic19C2×D414yes—
112C2×Dic19C2×D412yes—
113C2×Dic19C2×D414yes—
114C2×Dic19C2×Q812yescomplemented
115C4×D19—216no—
116C4×D19—28no—
117Dic38—28no—
118Dic38—216no—
119#2409—191nomaximal, Sylow
120C22×C19—22no—
121C22×C19—24no—
122C22×C19—41no—
123C22×C19—41no—
124C22×C19—42no—
125C22×C19C22×D411yescharacteristic
126C22×C19C22×D412yes—
127C22×C19C22×Q811yescharacteristic
128C22×C19C2×#4111yescharacteristic
129C22×C192−1+412yes—
130C2×D19—22no—
131C2×D19—22no—
132C2×D19—24no—
133C2×D19—24no—
134C2×D19C22⋊Q814yescomplemented
135C4×C19—22no—
136C4×C19—24no—
137C4×C19—41no—
138C4×C19—42no—
139Dic19—24no—
140Dic19—22no—
141Dic19—41no—
142Dic19—42no—
143Dic19#12014yes—
144C23×Q8—191no—
145C2×C22⋊Q8—192no—
146C2×C4×D4—191no—
147#395—191no—
148#395—191no—
149#393—191no—
150#393D1911yescharacteristic, complemented
151#391—192no—
152#386—192no—
153#385—192no—
154#380—191no—
155C2×C19—42no—
156C2×C19C2×#12011yescharacteristic
157C2×C19C2×C22⋊Q811yescharacteristic
158C2×C19#53611yescharacteristic
159C2×C19#54812yes—
160C2×C19D4×Q812yes—
161D19—24no—
162C22×Q8—192no—
163C22×Q8—191no—
164C22×Q8—384no—
165C22×Q8—388no—
166C22×Q8C2×D1911yescharacteristic
167C22×D4—191no—
168C23×C4—191no—
169C23×C4—191no—
170C23×C4—192no—
171C22⋊Q8—388no—
172C4×D4—384no—
173C2×C4⋊C4—191no—
174C2×C4⋊C4—192no—
175C2×C4⋊C4—192no—
176C2×C4⋊C4—192no—
177C2×C22⋊C4—192no—
178C2×C22⋊C4—191no—
179C2×C22⋊C4—192no—
180C2×C22⋊C4C2×D1911yescharacteristic
181C2×C22⋊C4C2×D1912yes—
182C2×C42—191no—
183#95—191no—
184#95—192no—
185#95—192no—
186#95—192no—
187#95C2×D1911yescharacteristic
188#95C2×D1912yes—
189C19#240911yescharacteristic, complemented, Sylow
190C24—191no—
191C24C22×D1911yescharacteristic
192C2×Q8—22no—
193C2×Q8—24no—
194C2×Q8—198no—
195C2×Q8—384no—
196C2×Q8—384no—
197C2×Q8—384no—
198C2×Q8—3832no—
199C2×Q8—382no—
200C2×D4—194no—
201C2×D4—382no—
202C2×D4—382no—
203C22×C4—191no—
204C22×C4—191no—
205C22×C4—192no—
206C22×C4—194no—
207C22×C4—192no—
208C22×C4—191no—
209C22×C4—384no—
210C22×C4—384no—
211C22×C4—384no—
212C22×C4—382no—
213C22×C4—384no—
214C22×C4—384no—
215C22×C4C22×D1911yescharacteristic
216C22×C4C22×D1912yes—
217C22×C4C22×D1911yescharacteristic
218C22×C4C22×D1912yes—
219C4⋊C4—384no—
220C4⋊C4—384no—
221C4⋊C4—382no—
222C4⋊C4—384no—
223C22⋊C4—22no—
224C22⋊C4—24no—
225C22⋊C4—384no—
226C22⋊C4—382no—
227C22⋊C4—384no—
228C42—382no—
229C23—22no—
230C23—21no—
231C23—21no—
232C23—22no—
233C23—192no—
234C23—192no—
235C23—192no—
236C23—382no—
237C23—382no—
238C23Q8×D1912yescomplemented
239C23C23×D1911yescharacteristic
240Q8—28no—
241Q8—3816no—
242Q8—388no—
243D4—388no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—192no—
253C2×C4—194no—
254C2×C4—194no—
255C2×C4—192no—
256C2×C4—388no—
257C2×C4—3816no—
258C2×C4—381no—
259C2×C4—382no—
260C2×C4—382no—
261C2×C4—381no—
262C2×C4—382no—
263C2×C4—381no—
264C2×C4—382no—
265C2×C4—382no—
266C2×C4—382no—
267C2×C4—764no—
268C2×C4D4×D1912yes—
269C2×C4D4×D1914yes—
270C22—24no—
271C22—22no—
272C22—41no—
273C22—42no—
274C22—41no—
275C22—194no—
276C22—382no—
277C22—384no—
278C22—384no—
279C22—382no—
280C22C2×D4×D1911yescharacteristic
281C22C2×D4×D1912yes—
282C22C2×Q8×D1911yescharacteristic
283C22#41×D1911yescharacteristic
284C22#1059743612yes—
285C4—22no—
286C4—24no—
287C4—41no—
288C4—42no—
289C4—194no—
290C4—384no—
291C4—382no—
292C4—762no—
293C4—761no—
294C2—42no—
295C2—384no—
296C2#120×D1911yescharacteristic
297C2C22⋊Q8×D1911yescharacteristic
298C2#1192711411yescharacteristic
299C2#1192720212yes—
300C2#1192720712yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#393C2
prime radicalC22×C22⋊D19C22
hypercenter#393D19
hypocenterC19#2409
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D19C2semidirect
2. C2×#10597324C2semidirect
4. #11926465C2semidirect
5. #11926463C2semidirect
6. #11926456C2semidirect
7. #11926448C2semidirect
9. #11926418C2semidirect
10. #11926403C2semidirect
11. C19×#393C2semidirect
49. C2×C22⋊D19Q8semidirect
67. C2×Dic38D4semidirect
82. C23×C19C2×Q8semidirect
114. C2×Dic19C2×Q8semidirect
134. C2×D19C22⋊Q8semidirect
150. #393D19semidirect
189. C19#2409semidirect
238. C23Q8×D19semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×D192
C2×#105973242
C2×(C22⋊D19)⋊C42
#119264652
#119264632
#119264562
#119264482
#119264202
#119264182
#119264032
C19×#3932
#240919