Finite Group Databasebeta

← #14567248

Subgroups — #14567248

Order 2432.

914 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 914 conjugacy classes of subgroups — too many to draw. Only its 157 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×#64545C211yesmaximal, characteristic, complemented
2C2×#10597329C211yesmaximal, characteristic, complemented
3C2×#10597330C212yesmaximal, complemented
4#11926463C211yesmaximal, characteristic, complemented
5#11926462C211yesmaximal, characteristic, complemented
6#11926453C211yesmaximal, characteristic, complemented
7#11926422C212yesmaximal, complemented
8#11926420C212yesmaximal, complemented
9#11926418C212yesmaximal, complemented
10#95×D19C211yesmaximal, characteristic, complemented
11C19×#393C211yesmaximal, characteristic, complemented
12C22×Q8×C19C2211yescharacteristic
13C22×C22⋊D19C2211yescharacteristic
14C22×C22⋊D19C2212yes—
15C2×#64545—28no—
16C2×#64545—24no—
17C22×D76C2211yescharacteristic
18C22×D76C2212yes—
19C22×C4×D19C2212yes—
20C22×C4×D19C2212yes—
21C22×C4×D19C2211yescharacteristic
22C2×C22⋊C4×C19C2211yescharacteristic
23C2×C22⋊C4×C19C2212yes—
24C2×C22⋊Dic19C2211yescharacteristic
25C2×(C2×D19)⋊C4C2211yescharacteristic
26C2×(C2×D19)⋊C4C2212yes—
27C2×(C2×D19)⋊C4C2212yes—
28C2×(C2×D19)⋊C4C2212yes—
29C2×C4⋊Dic19C2211yescharacteristic
30C2×Dic19⋊C4C2211yescharacteristic
31C2×Dic19⋊C4C2212yes—
32#10597330—28no—
33#10597329—24no—
34C19×#95C2211yescharacteristic
35C19×#95C2212yes—
36C19⋊#95C2212yes—
37C19⋊#95C2211yescharacteristic
38C19⋊#95C2212yes—
39C24×C19C2311yescharacteristic
40C23×D19C2312yes—
41C23×D19C2311yescharacteristic
42C2×Q8×C19—24no—
43C2×Q8×C19—22no—
44C22×C4×C19C2312yes—
45C22×C4×C19C2311yescharacteristic
46C22×C4×C19C2312yes—
47C22×C4×C19C2311yescharacteristic
48C2×C22⋊D19—22no—
49C2×C22⋊D19—24no—
50C2×C22⋊D19—24no—
51C2×C22⋊D19—24no—
52C2×C22⋊D19—42no—
53C22×Dic19C2311yescharacteristic
54C22×Dic19C2311yescharacteristic
55C22×Dic19C2311yescharacteristic
56C22×Dic19C2312yes—
57#64545—232no—
58C2×D76—24no—
59C2×D76—24no—
60C2×D76—24no—
61C2×D76—22no—
62C2×D76D418yescomplemented
63C2×C4×D19—24no—
64C2×C4×D19—24no—
65C2×C4×D19—24no—
66C2×C4×D19—24no—
67C2×C4×D19—24no—
68C2×C4×D19—24no—
69C2×C4×D19—42no—
70C2×C4×D19D414yescomplemented
71C22⋊C4×C19—22no—
72C22⋊C4×C19—24no—
73C22⋊Dic19—22no—
74(C2×D19)⋊C4—22no—
75(C2×D19)⋊C4—24no—
76(C2×D19)⋊C4—24no—
77(C2×D19)⋊C4—42no—
78C4⋊Dic19—22no—
79Dic19⋊C4—22no—
80Dic19⋊C4—24no—
81C23×C19—21no—
82C23×C19—22no—
83C23×C19—22no—
84C23×C19—21no—
85C23×C19—21no—
86C23×C19C2411yescharacteristic
87C22×D19—22no—
88C22×D19—21no—
89C22×D19—21no—
90C22×D19—22no—
91C22×D19—22no—
92C22×D19—22no—
93C22×D19—22no—
94C22×D19—22no—
95C22×D19—22no—
96C22×D19C2×D414yes—
97C22×D19C2×D412yes—
98C22×D19C2×D414yes—
99Q8×C19—28no—
100C2×C4×C19—22no—
101C2×C4×C19—22no—
102C2×C4×C19—22no—
103C2×C4×C19—21no—
104C2×C4×C19—22no—
105C2×C4×C19—22no—
106C2×C4×C19—22no—
107C2×C4×C19—22no—
108C2×C4×C19C2×D414yes—
109C2×C4×C19C2×D412yes—
110C22⋊D19—48no—
111C22⋊D19—44no—
112C2×Dic19—22no—
113C2×Dic19—22no—
114C2×Dic19—22no—
115C2×Dic19—21no—
116C2×Dic19—21no—
117C2×Dic19—22no—
118C2×Dic19—21no—
119C2×Dic19—21no—
120C2×Dic19C2×D412yes—
121C2×Dic19#4114yescomplemented
122D76—28no—
123D76—216no—
124C4×D19—216no—
125C4×D19—28no—
126C4×D19—48no—
127#2430—191nomaximal, Sylow
128C22×C19—41no—
129C22×C19—41no—
130C22×C19—41no—
131C22×C19—42no—
132C22×C19—42no—
133C22×C19C22×D411yescharacteristic
134C22×C19C22×D412yes—
135C22×C19C2×#4112yes—
136C22×C19H(5,𝔽2)11yescharacteristic
137C22×C192−1+411yescharacteristic
138C2×D19—22no—
139C2×D19—22no—
140C2×D19—24no—
141C2×D19—24no—
142C2×D19—24no—
143C2×D19—24no—
144C2×D19—24no—
145C2×D19—42no—
146C2×D19—42no—
147C2×D19—42no—
148C2×D19—42no—
149C2×D19#12014yes—
150C4×C19—24no—
151C4×C19—22no—
152C4×C19—41no—
153C4×C19—42no—
154Dic19—22no—
155Dic19—24no—
156Dic19—41no—
157Dic19—41no—
158C22×#41—191no—
159C2×#123—191no—
160C2×#121—192no—
161#395—191no—
162#394—191no—
163#393D1911yescharacteristic, complemented
164#392—191no—
165#386—192no—
166#386—192no—
167#385—192no—
168C2×#95—191no—
169C2×C19—81no—
170C2×C19C2×#12011yescharacteristic
171C2×C19#53211yescharacteristic
172C2×C19#53711yescharacteristic
173C2×C19#54612yes—
174C2×C19#54712yes—
175D19—24no—
176D19—44no—
177C2×#41—384no—
178C2×#41—388no—
179C22×Q8C2×D1911yescharacteristic
180C22×D4—191no—
181C22×D4—192no—
182C22×D4—192no—
183C22×D4—191no—
184C23×C4—191no—
185C23×C4—192no—
186C23×C4—192no—
187#123—384no—
188#121—388no—
189C2×C4⋊C4—192no—
190C2×C4⋊C4—191no—
191C2×C4⋊C4—191no—
192C2×C22⋊C4—191no—
193C2×C22⋊C4—192no—
194C2×C22⋊C4—191no—
195C2×C22⋊C4—192no—
196C2×C22⋊C4—192no—
197C2×C22⋊C4C2×D1912yes—
198C2×C22⋊C4C2×D1911yescharacteristic
199#95—192no—
200#95—191no—
201#95—192no—
202#95C2×D1911yescharacteristic
203#95C2×D1912yes—
204C19#243011yescharacteristic, complemented, Sylow
205C24—191no—
206C24—192no—
207C24C22×D1911yescharacteristic
208#41—3832no—
209C2×Q8—22no—
210C2×Q8—24no—
211C2×D4—198no—
212C2×D4—384no—
213C2×D4—384no—
214C2×D4—384no—
215C2×D4—384no—
216C2×D4—384no—
217C2×D4—384no—
218C2×D4—382no—
219C2×D4—382no—
220C2×D4—762no—
221C22×C4—192no—
222C22×C4—191no—
223C22×C4—194no—
224C22×C4—191no—
225C22×C4—191no—
226C22×C4—384no—
227C22×C4—384no—
228C22×C4—384no—
229C22×C4—384no—
230C22×C4—384no—
231C22×C4—384no—
232C22×C4—762no—
233C22×C4C22×D1912yes—
234C22×C4C22×D1911yescharacteristic
235C22×C4C22×D1911yescharacteristic
236C22×C4C22×D1912yes—
237C4⋊C4—382no—
238C4⋊C4—384no—
239C4⋊C4—382no—
240C22⋊C4—24no—
241C22⋊C4—22no—
242C22⋊C4—384no—
243C22⋊C4—384no—
244C22⋊C4—382no—
245C22⋊C4—382no—
246C22⋊C4—762no—
247C23—21no—
248C23—22no—
249C23—21no—
250C23—22no—
251C23—21no—
252C23—192no—
253C23—194no—
254C23—194no—
255C23—381no—
256C23—382no—
257C23—381no—
258C23—382no—
259C23—382no—
260C23—382no—
261C23—382no—
262C23—382no—
263C23—382no—
264C23C23×D1911yescharacteristic
265Q8—28no—
266D4—3816no—
267D4—388no—
268D4—768no—
269D4—764no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—192no—
279C2×C4—194no—
280C2×C4—388no—
281C2×C4—3816no—
282C2×C4—382no—
283C2×C4—382no—
284C2×C4—382no—
285C2×C4—381no—
286C2×C4—382no—
287C2×C4—381no—
288C2×C4—381no—
289C2×C4—381no—
290C2×C4—768no—
291C2×C4D4×D1912yes—
292C2×C4D4×D1914yes—
293C22—41no—
294C22—41no—
295C22—42no—
296C22—42no—
297C22—41no—
298C22—194no—
299C22—382no—
300C22—382no—
301C22—384no—
302C22—384no—
303C22—384no—
304C22—384no—
305C22—384no—
306C22—762no—
307C22—762no—
308C22—762no—
309C22—762no—
310C22C2×D4×D1911yescharacteristic
311C22C2×D4×D1912yes—
312C22#1059743311yescharacteristic
313C22#41×D1912yes—
314C22#1059743511yescharacteristic
315C4—22no—
316C4—24no—
317C4—41no—
318C4—42no—
319C4—384no—
320C4—382no—
321C4—761no—
322C4—761no—
323C2—81no—
324C2—384no—
325C2—764no—
326C2#120×D1911yescharacteristic
327C2#1192709311yescharacteristic
328C2#1192712411yescharacteristic
329C2#1192718712yes—
330C2#1192719612yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#393C2
hypercenter#393D19
hypocenterC19#2430
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C22×#64545C2semidirect
2. C2×#10597329C2semidirect
3. C2×#10597330C2semidirect
4. #11926463C2semidirect
5. #11926462C2semidirect
6. #11926453C2semidirect
7. #11926422C2semidirect
8. #11926420C2semidirect
9. #11926418C2semidirect
10. #95×D19C2semidirect
11. C19×#393C2semidirect
62. C2×D76D4semidirect
70. C2×C4×D19D4semidirect
121. C2×Dic19#41semidirect
163. #393D19semidirect
204. C19#2430semidirect

Maximal subgroups

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

subgroupindex
C22×#645452
C2×#105973292
C2×#105973302
#119264632
#119264622
#119264532
#119264222
#119264202
#119264182
#95×D192
C19×#3932
#243019