Finite Group Databasebeta

← #14569368

Subgroups — #14569368

Order 2432.

824 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 824 conjugacy classes of subgroups — too many to draw. Only its 143 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×#10597384C211yesmaximal, characteristic, complemented
2C2×#10597383C212yesmaximal, complemented
3C2×C22⋊C4×D19C211yesmaximal, characteristic, complemented
4#11926471C211yesmaximal, characteristic, complemented
5#11926469C211yesmaximal, characteristic, complemented
6#11926459C212yesmaximal, complemented
7#11926458C212yesmaximal, complemented
8#11926452C211yesmaximal, characteristic, complemented
9#11926420C212yesmaximal, complemented
10#11926403C211yesmaximal, characteristic, complemented
11C19×#392C211yesmaximal, characteristic, complemented
12C24×D19C2211yescharacteristic
13C22×D4×C19C2212yes—
14C22×D4×C19C2211yescharacteristic, complemented
15C22×C22⋊D19C2212yes—
16C22×C22⋊D19C2212yes—
17C22×C4×D19C2211yescharacteristic
18C22×C4×D19C2211yescharacteristic
19C2×C22⋊C4×C19C2211yescharacteristic
20C2×C22⋊C4×C19C2212yescomplemented
21C2×C22⋊Dic19C2211yescharacteristic
22C2×C22⋊Dic19C2212yes—
23C2×C22⋊Dic19C2212yescomplemented
24C2×C22⋊Dic19C2212yescomplemented
25#10597384—24no—
26#10597383—28no—
27C2×(C2×D19)⋊C4C2212yes—
28C2×(C2×D19)⋊C4C2211yescharacteristic
29C2×(C2×D19)⋊C4C2211yescharacteristic
30C2×(C2×D19)⋊C4C2212yes—
31C2×C4⋊Dic19C2211yescharacteristic, complemented
32C2×Dic19⋊C4C2212yescomplemented
33C22⋊C4×D19—24no—
34C19×#95C2211yescharacteristic, complemented
35C19⋊#95C2211yescharacteristic, complemented
36C19⋊#95C2212yescomplemented
37C19⋊#95C2212yescomplemented
38C24×C19C2312yes—
39C24×C19C2311yescharacteristic
40C23×D19—22no—
41C23×D19—22no—
42C23×D19—42no—
43C23×D19—42no—
44C23×D19D414yescomplemented
45C23×D19C2311yescharacteristic
46C23×D19C2311yescharacteristic
47C2×D4×C19—24no—
48C2×D4×C19—22no—
49C2×D4×C19—42no—
50C2×D4×C19—42no—
51C2×D4×C19—42no—
52C22×C4×C19C2311yescharacteristic
53C22×C4×C19C2312yes—
54C22×C4×C19C2311yescharacteristic
55C2×C22⋊D19—24no—
56C2×C22⋊D19—24no—
57C2×C22⋊D19—24no—
58C2×C22⋊D19—24no—
59C2×C22⋊D19—42no—
60C2×C22⋊D19—42no—
61C22×Dic19C2311yescharacteristic
62C22×Dic19C2312yes—
63C22×Dic19C2312yes—
64C22×Dic19C2311yescharacteristic
65C2×C4×D19—22no—
66C2×C4×D19—42no—
67C2×C4×D19—42no—
68C2×C4×D19D414yescomplemented
69C22⋊C4×C19—22no—
70C22⋊C4×C19—42no—
71C22⋊Dic19—24no—
72C22⋊Dic19—24no—
73C22⋊Dic19—22no—
74C22⋊Dic19—42no—
75(C2×D19)⋊C4—24no—
76(C2×D19)⋊C4—24no—
77(C2×D19)⋊C4—22no—
78(C2×D19)⋊C4—22no—
79C4⋊Dic19—22no—
80Dic19⋊C4—42no—
81C23×C19—21no—
82C23×C19—21no—
83C23×C19—22no—
84C23×C19—22no—
85C23×C19—22no—
86C23×C19—22no—
87C23×C19—22no—
88C23×C19—22no—
89C23×C19—22no—
90C23×C19—22no—
91C23×C19—22no—
92C23×C19C2×D412yes—
93C23×C19C2411yescharacteristic
94C22×D19—22no—
95C22×D19—22no—
96C22×D19—21no—
97C22×D19—21no—
98C22×D19—22no—
99C22×D19—22no—
100C22×D19—28no—
101C22×D19—48no—
102C22×D19—44no—
103C22×D19—44no—
104C22×D19—48no—
105C22×D19C2×D412yes—
106C22×D19C2×D412yes—
107C22×D19C2×D412yes—
108C22×D19#4112yes—
109D4×C19—44no—
110D4×C19—48no—
111C2×C4×C19—22no—
112C2×C4×C19—22no—
113C2×C4×C19—21no—
114C2×C4×C19—22no—
115C2×C4×C19—22no—
116C2×C4×C19—22no—
117C2×C4×C19C2×D412yes—
118C22⋊D19—48no—
119C22⋊D19—48no—
120C2×Dic19—22no—
121C2×Dic19—22no—
122C2×Dic19—21no—
123C2×Dic19—22no—
124C2×Dic19—22no—
125C2×Dic19—22no—
126C2×Dic19—22no—
127C2×Dic19—22no—
128C2×Dic19—22no—
129C2×Dic19C2×D412yes—
130C4×D19—44no—
131C4×D19—44no—
132#2617—191nomaximal, Sylow
133C22×C19—22no—
134C22×C19—24no—
135C22×C19—41no—
136C22×C19—41no—
137C22×C19—42no—
138C22×C19—42no—
139C22×C19—42no—
140C22×C19—42no—
141C22×C19—42no—
142C22×C19—42no—
143C22×C19—42no—
144C22×C19—42no—
145C22×C19C22×D411yescharacteristic
146C22×C19C22×D411yescharacteristic
147C22×C19C2×#4111yescharacteristic
148C22×C19H(5,𝔽2)12yes—
149C22×C19H(5,𝔽2)12yes—
150C2×D19—22no—
151C2×D19—24no—
152C2×D19—22no—
153C2×D19—24no—
154C2×D19—22no—
155C2×D19—24no—
156C2×D19—416no—
157C2×D19—41no—
158C2×D19—41no—
159C2×D19—42no—
160C2×D19#12114yes—
161C4×C19—22no—
162C4×C19—42no—
163C4×C19—41no—
164Dic19—22no—
165Dic19—42no—
166Dic19—42no—
167Dic19—41no—
168C2×#121—191no—
169C2×#120—192no—
170C22×C22⋊C4—191no—
171#397—191no—
172#397—191no—
173#394—192no—
174#394—192no—
175#392—191no—
176#392D1911yescharacteristic, complemented
177#386—192no—
178#380—191no—
179C2×C19—42no—
180C2×C19—82no—
181C2×C19C2×#12111yescharacteristic
182C2×C19#53411yescharacteristic
183C2×C19#53412yes—
184C2×C19#53511yescharacteristic
185C2×C19#53812yes—
186D19—24no—
187D19—42no—
188C25—191no—
189C22×D4—192no—
190C22×D4—192no—
191C22×D4C2×D1912yes—
192C22×D4C2×D1911yescharacteristic, complemented
193C23×C4—191no—
194C23×C4—191no—
195#121—384no—
196#120—388no—
197C2×C4⋊C4—191no—
198C2×C4⋊C4—192no—
199C2×C22⋊C4—191no—
200C2×C22⋊C4—192no—
201C2×C22⋊C4—192no—
202C2×C22⋊C4—191no—
203C2×C22⋊C4—191no—
204C2×C22⋊C4—192no—
205C2×C22⋊C4—192no—
206C2×C22⋊C4—192no—
207C2×C22⋊C4—384no—
208C2×C22⋊C4C2×D1911yescharacteristic
209C2×C22⋊C4C2×D1912yescomplemented
210#95—191no—
211#95—192no—
212#95—192no—
213#95C2×D1911yescharacteristic, complemented
214C19#261711yescharacteristic, complemented, Sylow
215C24—191no—
216C24—191no—
217C24—194no—
218C24—382no—
219C24—382no—
220C24—762no—
221C24—762no—
222C24C22×D1912yes—
223C24C22×D1911yescharacteristic
224C2×D4—24no—
225C2×D4—22no—
226C2×D4—42no—
227C2×D4—42no—
228C2×D4—42no—
229C2×D4—384no—
230C2×D4—384no—
231C2×D4—384no—
232C2×D4—384no—
233C2×D4—762no—
234C2×D4—762no—
235C22×C4—191no—
236C22×C4—194no—
237C22×C4—191no—
238C22×C4—192no—
239C22×C4—192no—
240C22×C4—382no—
241C22×C4—762no—
242C22×C4—762no—
243C22×C4C22×D1911yescharacteristic
244C22×C4C22×D1912yes—
245C22×C4C22×D1911yescharacteristic
246C4⋊C4—382no—
247C4⋊C4—762no—
248C22⋊C4—22no—
249C22⋊C4—42no—
250C22⋊C4—382no—
251C22⋊C4—384no—
252C22⋊C4—384no—
253C22⋊C4—382no—
254C22⋊C4—384no—
255C22⋊C4—384no—
256C22⋊C4—382no—
257C22⋊C4—762no—
258C23—21no—
259C23—22no—
260C23—22no—
261C23—21no—
262C23—22no—
263C23—22no—
264C23—22no—
265C23—22no—
266C23—22no—
267C23—22no—
268C23—22no—
269C23—192no—
270C23—192no—
271C23—192no—
272C23—192no—
273C23—388no—
274C23—382no—
275C23—382no—
276C23—381no—
277C23—382no—
278C23—382no—
279C23—381no—
280C23—768no—
281C23—764no—
282C23—764no—
283C23—768no—
284C23D4×D1912yes—
285C23C23×D1911yescharacteristic
286D4—44no—
287D4—48no—
288D4—768no—
289D4—768no—
290C2×C4—22no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—192no—
297C2×C4—382no—
298C2×C4—381no—
299C2×C4—382no—
300C2×C4—382no—
301C2×C4—382no—
302C2×C4—382no—
303C2×C4—382no—
304C2×C4—382no—
305C2×C4—382no—
306C2×C4—764no—
307C2×C4—764no—
308C2×C4D4×D1912yes—
309C22—24no—
310C22—22no—
311C22—41no—
312C22—41no—
313C22—42no—
314C22—42no—
315C22—42no—
316C22—42no—
317C22—42no—
318C22—42no—
319C22—42no—
320C22—42no—
321C22—194no—
322C22—382no—
323C22—384no—
324C22—382no—
325C22—384no—
326C22—384no—
327C22—382no—
328C22—7616no—
329C22—761no—
330C22—761no—
331C22—762no—
332C22C2×D4×D1911yescharacteristic
333C22C2×D4×D1911yescharacteristic
334C22#1059743012yes—
335C22#1059743012yes—
336C22#41×D1911yescharacteristic
337C4—22no—
338C4—42no—
339C4—41no—
340C4—382no—
341C4—762no—
342C4—761no—
343C4—762no—
344C2—42no—
345C2—82no—
346C2—384no—
347C2—762no—
348C2#121×D1911yescharacteristic
349C2#1192710411yescharacteristic
350C2#1192710412yes—
351C2#1192710711yescharacteristic
352C2#1192712612yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#392C2
hypercenter#392D19
hypocenterC19#2617
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#10597384C2semidirect
2. C2×#10597383C2semidirect
3. C2×C22⋊C4×D19C2semidirect
4. #11926471C2semidirect
5. #11926469C2semidirect
6. #11926459C2semidirect
7. #11926458C2semidirect
8. #11926452C2semidirect
9. #11926420C2semidirect
10. #11926403C2semidirect
11. C19×#392C2semidirect
14. C22×D4×C19C22semidirect
20. C2×C22⋊C4×C19C22semidirect
23. C2×C22⋊Dic19C22semidirect
24. C2×C22⋊Dic19C22semidirect
31. C2×C4⋊Dic19C22semidirect
32. C2×Dic19⋊C4C22semidirect
34. C19×#95C22semidirect
35. C19⋊#95C22semidirect
36. C19⋊#95C22semidirect
37. C19⋊#95C22semidirect
44. C23×D19D4semidirect
68. C2×C4×D19D4semidirect
176. #392D19semidirect
192. C22×D4C2×D19semidirect
209. C2×C22⋊C4C2×D19semidirect
213. #95C2×D19semidirect
214. C19#2617semidirect

Maximal subgroups

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

subgroupindex
C2×#105973842
C2×#105973832
C2×C22⋊C4×D192
#119264712
#119264692
#119264592
#119264582
#119264522
#119264202
#119264032
C19×#3922
#261719