Finite Group Databasebeta

← #14568568

Subgroups — #14568568

Order 2432.

760 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 760 conjugacy classes of subgroups — too many to draw. Only its 161 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×#10597331C211yesmaximal, characteristic, complemented
2C2×#10597324C212yesmaximal, complemented
3C2×#10597385C212yesmaximal, complemented
4C2×D4×Dic19C211yesmaximal, characteristic, complemented
5#11926481C211yesmaximal, characteristic, complemented
6#11926480C211yesmaximal, characteristic, complemented
7#11926452C211yesmaximal, characteristic, complemented
8#11926447C212yesmaximal, complemented
9#11926444C212yesmaximal, complemented
10#11926395C211yesmaximal, characteristic, complemented
11C19×#392C211yesmaximal, characteristic, complemented
12C22×D4×C19C2211yescharacteristic
13C22×D4×C19C2212yes—
14C22×C22⋊D19C2211yescharacteristic
15C22×C22⋊D19C2212yes—
16C23×Dic19C2212yes—
17C22×Dic38C2211yescharacteristic
18C2×C22⋊C4×C19C2212yes—
19C2×C22⋊C4×C19C2211yescharacteristic
20C2×C22⋊Dic19C2212yes—
21C2×C22⋊Dic19C2211yescharacteristic
22C2×C22⋊Dic19C2212yes—
23C2×C22⋊Dic19C2212yes—
24#10597385—28no—
25D4×Dic19—24no—
26C2×(C2×D19)⋊C4C2211yescharacteristic
27C2×(C2×D19)⋊C4C2211yescharacteristic
28C2×(C2×D19)⋊C4C2212yes—
29C2×C4⋊Dic19C2212yes—
30C2×C4⋊Dic19C2211yescharacteristic
31C2×Dic19⋊C4C2212yes—
32C2×Dic19⋊C4C2212yes—
33C2×C4×Dic19C2212yes—
34C2×C4×Dic19C2211yescharacteristic
35#10597331—24no—
36#10597324—28no—
37C19×#95C2211yescharacteristic
38C19⋊#95C2211yescharacteristic
39C24×C19C2311yescharacteristic
40C24×C19C2312yes—
41C23×D19C2311yescharacteristic
42C2×D4×C19—24no—
43C2×D4×C19—24no—
44C2×D4×C19—22no—
45C2×D4×C19—24no—
46C2×D4×C19—42no—
47C22×C4×C19C2311yescharacteristic
48C22×C4×C19C2311yescharacteristic
49C22×C4×C19C2312yes—
50C2×C22⋊D19—24no—
51C2×C22⋊D19—24no—
52C2×C22⋊D19—24no—
53C2×C22⋊D19—22no—
54C2×C22⋊D19—42no—
55C22×Dic19—24no—
56C22×Dic19—24no—
57C22×Dic19—24no—
58C22×Dic19C2311yescharacteristic
59C22×Dic19C2312yes—
60C22×Dic19C2311yescharacteristic
61C22×Dic19C2312yes—
62C22×Dic19C2311yescharacteristic
63C2×Dic38—24no—
64C2×Dic38—22no—
65C22⋊C4×C19—24no—
66C22⋊C4×C19—22no—
67C22⋊Dic19—24no—
68C22⋊Dic19—24no—
69C22⋊Dic19—24no—
70C22⋊Dic19—22no—
71(C2×D19)⋊C4—24no—
72(C2×D19)⋊C4—22no—
73(C2×D19)⋊C4—22no—
74C4⋊Dic19—22no—
75C4⋊Dic19—24no—
76Dic19⋊C4—24no—
77Dic19⋊C4D418yescomplemented
78C4×Dic19—42no—
79C4×Dic19D414yescomplemented
80C23×C19—22no—
81C23×C19—22no—
82C23×C19—22no—
83C23×C19—22no—
84C23×C19—22no—
85C23×C19—22no—
86C23×C19—21no—
87C23×C19—22no—
88C23×C19—22no—
89C23×C19—21no—
90C23×C19—21no—
91C23×C19#4114yes—
92C23×C19C2411yescharacteristic
93C22×D19—21no—
94C22×D19—22no—
95C22×D19—22no—
96C22×D19—21no—
97C22×D19—21no—
98D4×C19—28no—
99D4×C19—48no—
100C2×C4×C19—22no—
101C2×C4×C19—22no—
102C2×C4×C19—22no—
103C2×C4×C19—22no—
104C2×C4×C19—21no—
105C2×C4×C19C2×D412yes—
106C2×C4×C19C2×D414yes—
107C22⋊D19—48no—
108C22⋊D19—44no—
109C2×Dic19—22no—
110C2×Dic19—21no—
111C2×Dic19—22no—
112C2×Dic19—21no—
113C2×Dic19—22no—
114C2×Dic19—22no—
115C2×Dic19—22no—
116C2×Dic19—21no—
117C2×Dic19—22no—
118C2×Dic19—48no—
119C2×Dic19C2×D412yes—
120C2×Dic19C2×D414yes—
121C2×Dic19C2×D412yes—
122C2×Dic19C2×D414yes—
123Dic38—44no—
124#2540—191nomaximal, Sylow
125C22×C19—24no—
126C22×C19—24no—
127C22×C19—24no—
128C22×C19—42no—
129C22×C19—42no—
130C22×C19—42no—
131C22×C19—42no—
132C22×C19—41no—
133C22×C19—41no—
134C22×C19—41no—
135C22×C19—42no—
136C22×C19—42no—
137C22×C19C22×D411yescharacteristic
138C22×C19C22×D412yes—
139C22×C19C2×#4112yes—
140C22×C19H(5,𝔽2)11yescharacteristic
141C22×C192−1+411yescharacteristic
142C2×D19—41no—
143C2×D19—41no—
144C2×D19—41no—
145C2×D19—42no—
146C2×D19—42no—
147C4×C19—22no—
148C4×C19—24no—
149C4×C19—41no—
150Dic19—22no—
151Dic19—24no—
152Dic19—41no—
153Dic19—42no—
154Dic19#12714yes—
155C2×#124—191no—
156C2×C22⋊Q8—192no—
157C2×#121—192no—
158C2×C4×D4—191no—
159#399—191no—
160#399—191no—
161#392—191no—
162#392D1911yescharacteristic, complemented
163#390—192no—
164#390—192no—
165C4×C4⋊C4—191no—
166C2×C19—44no—
167C2×C19—81no—
168C2×C19#52511yescharacteristic
169C2×C19C2×#12711yescharacteristic
170C2×C19#53711yescharacteristic
171C2×C19#54612yes—
172C2×C19#54812yes—
173D19—81no—
174C22×Q8—191no—
175C22×D4—191no—
176C22×D4—192no—
177C22×D4C2×D1911yescharacteristic
178C22×D4C2×D1912yes—
179C23×C4—192no—
180#124—384no—
181C22⋊Q8—388no—
182#121—388no—
183C4×D4—384no—
184C2×C4⋊C4—192no—
185C2×C4⋊C4—191no—
186C2×C4⋊C4—192no—
187C2×C4⋊C4—192no—
188C2×C22⋊C4—192no—
189C2×C22⋊C4—192no—
190C2×C22⋊C4—192no—
191C2×C22⋊C4—191no—
192C2×C22⋊C4—192no—
193C2×C22⋊C4—191no—
194C2×C22⋊C4—191no—
195C2×C22⋊C4C2×D1912yes—
196C2×C22⋊C4C2×D1911yescharacteristic
197C2×C42—191no—
198C2×C42—192no—
199#95—191no—
200#95C2×D1911yescharacteristic
201C19#254011yescharacteristic, complemented, Sylow
202C24—191no—
203C24C22×D1911yescharacteristic
204C24C22×D1912yes—
205C2×Q8—384no—
206C2×Q8—382no—
207C2×D4—24no—
208C2×D4—24no—
209C2×D4—22no—
210C2×D4—24no—
211C2×D4—42no—
212C2×D4—384no—
213C2×D4—384no—
214C2×D4—382no—
215C2×D4—384no—
216C2×D4—762no—
217C22×C4—191no—
218C22×C4—192no—
219C22×C4—191no—
220C22×C4—191no—
221C22×C4—192no—
222C22×C4—384no—
223C22×C4—384no—
224C22×C4—384no—
225C22×C4C22×D1911yescharacteristic
226C22×C4C22×D1911yescharacteristic
227C22×C4C22×D1912yes—
228C4⋊C4—198no—
229C4⋊C4—384no—
230C4⋊C4—382no—
231C4⋊C4—384no—
232C22⋊C4—24no—
233C22⋊C4—22no—
234C22⋊C4—382no—
235C22⋊C4—384no—
236C22⋊C4—384no—
237C22⋊C4—384no—
238C22⋊C4—382no—
239C22⋊C4—384no—
240C22⋊C4—382no—
241C42—194no—
242C42—762no—
243C23—22no—
244C23—22no—
245C23—22no—
246C23—22no—
247C23—22no—
248C23—22no—
249C23—21no—
250C23—22no—
251C23—22no—
252C23—21no—
253C23—21no—
254C23—381no—
255C23—382no—
256C23—382no—
257C23—381no—
258C23—381no—
259C23#6454314yes—
260C23C23×D1911yescharacteristic
261Q8—764no—
262D4—28no—
263D4—48no—
264D4—764no—
265D4—768no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—192no—
272C2×C4—194no—
273C2×C4—192no—
274C2×C4—194no—
275C2×C4—382no—
276C2×C4—381no—
277C2×C4—382no—
278C2×C4—381no—
279C2×C4—382no—
280C2×C4—381no—
281C2×C4—382no—
282C2×C4—382no—
283C2×C4—382no—
284C2×C4—768no—
285C2×C4D4×D1912yes—
286C2×C4D4×D1914yes—
287C22—24no—
288C22—24no—
289C22—24no—
290C22—42no—
291C22—42no—
292C22—42no—
293C22—42no—
294C22—41no—
295C22—41no—
296C22—41no—
297C22—42no—
298C22—42no—
299C22—761no—
300C22—761no—
301C22—761no—
302C22—762no—
303C22—762no—
304C22C2×D4×D1911yescharacteristic
305C22C2×D4×D1912yes—
306C22C2×#6454312yes—
307C22#1059743011yescharacteristic
308C22#1059743611yescharacteristic
309C4—22no—
310C4—24no—
311C4—41no—
312C4—194no—
313C4—382no—
314C4—384no—
315C4—762no—
316C4—761no—
317C2—44no—
318C2—81no—
319C2—1521no—
320C2#1192705011yescharacteristic
321C2#127×D1911yescharacteristic
322C2#1192712311yescharacteristic
323C2#1192718112yes—
324C2#1192720012yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#392C2
hypercenter#392D19
hypocenterC19#2540
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#10597331C2semidirect
2. C2×#10597324C2semidirect
3. C2×#10597385C2semidirect
4. C2×D4×Dic19C2semidirect
5. #11926481C2semidirect
6. #11926480C2semidirect
7. #11926452C2semidirect
8. #11926447C2semidirect
9. #11926444C2semidirect
10. #11926395C2semidirect
11. C19×#392C2semidirect
77. Dic19⋊C4D4semidirect
79. C4×Dic19D4semidirect
162. #392D19semidirect
201. C19#2540semidirect

Maximal subgroups

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

subgroupindex
C2×#105973312
C2×#105973242
C2×#105973852
C2×D4×Dic192
#119264812
#119264802
#119264522
#119264472
#119264442
#119263952
C19×#3922
#254019