Finite Group Databasebeta

← #14566953

Subgroups — #14566953

Order 2432.

1056 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#64543C211yesmaximal, characteristic, complemented
2C2×#10597328C211yesmaximal, characteristic, complemented
3C2×#10597383C211yesmaximal, characteristic, complemented
4C22×(C2×D19)⋊C4C211yesmaximal, characteristic, complemented
5#11926457C212yesmaximal, complemented
6#11926453C212yesmaximal, complemented
7#11926423C211yesmaximal, characteristic, complemented
8#11926422C212yesmaximal, complemented
9#11926421C212yesmaximal, complemented
10#11926405C211yesmaximal, characteristic, complemented
11C19×#386C211yesmaximal, characteristic, complemented
12C24×D19C2211yescharacteristic
13C22×D4×C19C2211yescharacteristic
14C23×C4×C19C2211yescharacteristic
15C22×C22⋊D19C2212yes—
16C22×C22⋊D19C2211yescharacteristic
17C22×C22⋊D19C2211yescharacteristic, complemented
18C23×Dic19C2211yescharacteristic
19C23×Dic19C2211yescharacteristic, complemented
20C2×#64543—24no—
21C2×#64543—24no—
22C2×#64543—24no—
23C22×D76C2212yes—
24C22×C4×D19C2211yescharacteristic, complemented
25C22×Dic38C2211yescharacteristic, complemented
26C2×C22⋊C4×C19C2211yescharacteristic
27C2×C22⋊C4×C19C2212yescomplemented
28C2×C22⋊Dic19C2211yescharacteristic
29#10597383—24no—
30C2×(C2×D19)⋊C4—24no—
31C2×(C2×D19)⋊C4C2212yes—
32C2×(C2×D19)⋊C4C2212yes—
33C2×(C2×D19)⋊C4C2212yes—
34C2×(C2×D19)⋊C4C2212yes—
35C2×(C2×D19)⋊C4C2212yescomplemented
36#10597328—24no—
37C19×#95C2212yescomplemented
38C19⋊#95C2212yescomplemented
39C19⋊#95C2212yescomplemented
40C19⋊#95C2212yescomplemented
41C24×C19C2311yescharacteristic
42C24×C19C2311yescharacteristic
43C23×D19—22no—
44C23×D19—24no—
45C23×D19—22no—
46C23×D19—22no—
47C23×D19—42no—
48C23×D19C2311yescharacteristic
49C23×D19C2312yes—
50C2×D4×C19—22no—
51C2×D4×C19—22no—
52C2×D4×C19D414yescomplemented
53C22×C4×C19—22no—
54C22×C4×C19—42no—
55C22×C4×C19C2312yes—
56C22×C4×C19C2312yes—
57C22×C4×C19C2311yescharacteristic
58C2×C22⋊D19—22no—
59C2×C22⋊D19—22no—
60C2×C22⋊D19—22no—
61C2×C22⋊D19—22no—
62C2×C22⋊D19—24no—
63C2×C22⋊D19—24no—
64C2×C22⋊D19—22no—
65C2×C22⋊D19—42no—
66C2×C22⋊D19D414yescomplemented
67C22×Dic19—22no—
68C22×Dic19—22no—
69C22×Dic19—22no—
70C22×Dic19—22no—
71C22×Dic19—22no—
72C22×Dic19D414yescomplemented
73C22×Dic19C2312yes—
74C22×Dic19C2311yescharacteristic
75C22×Dic19C2311yescharacteristic
76C22×Dic19C2311yescharacteristic
77#64543—232no—
78C2×D76—24no—
79C2×D76—24no—
80C2×D76—42no—
81C2×C4×D19—22no—
82C2×C4×D19—22no—
83C2×C4×D19—22no—
84C2×Dic38—22no—
85C2×Dic38—22no—
86C2×Dic38—22no—
87C22⋊C4×C19—22no—
88C22⋊C4×C19—42no—
89C22⋊Dic19—22no—
90(C2×D19)⋊C4—24no—
91(C2×D19)⋊C4—24no—
92(C2×D19)⋊C4—24no—
93(C2×D19)⋊C4—24no—
94(C2×D19)⋊C4—42no—
95C23×C19—22no—
96C23×C19—22no—
97C23×C19—21no—
98C23×C19—21no—
99C23×C19—22no—
100C23×C19—22no—
101C23×C19C2×D412yes—
102C23×C19C2×D412yes—
103C23×C19C2×D412yes—
104C23×C19C2×D412yes—
105C23×C19C2411yescharacteristic
106C22×D19—28no—
107C22×D19—22no—
108C22×D19—22no—
109C22×D19—22no—
110C22×D19—21no—
111C22×D19—21no—
112C22×D19—22no—
113C22×D19—22no—
114C22×D19—22no—
115C22×D19—22no—
116C22×D19—22no—
117C22×D19—48no—
118C22×D19—48no—
119C22×D19—44no—
120C22×D19—44no—
121C22×D19C2×D412yes—
122C22×D19#4114yescomplemented
123D4×C19—28no—
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—22no—
127C2×C4×C19—22no—
128C2×C4×C19—22no—
129C2×C4×C19—22no—
130C2×C4×C19—22no—
131C2×C4×C19—22no—
132C2×C4×C19—44no—
133C2×C4×C19C2×D412yes—
134C22⋊D19—28no—
135C22⋊D19—28no—
136C22⋊D19—48no—
137C2×Dic19—28no—
138C2×Dic19—28no—
139C2×Dic19—21no—
140C2×Dic19—21no—
141C2×Dic19—21no—
142C2×Dic19—21no—
143C2×Dic19—21no—
144C2×Dic19—21no—
145C2×Dic19—22no—
146C2×Dic19—22no—
147C2×Dic19—22no—
148C2×Dic19C2×D412yes—
149C2×Dic19C2×D412yes—
150C2×Dic19C2×D412yes—
151D76—48no—
152C4×D19—28no—
153Dic38—28no—
154#2404—191nomaximal, Sylow
155C22×C19—22no—
156C22×C19—22no—
157C22×C19—24no—
158C22×C19—24no—
159C22×C19—22no—
160C22×C19—24no—
161C22×C19—41no—
162C22×C19—41no—
163C22×C19—42no—
164C22×C19#12014yes—
165C22×C19C22×D411yescharacteristic
166C22×C19C22×D411yescharacteristic
167C22×C19C22×D411yescharacteristic
168C22×C19C2×#4112yes—
169C22×C19H(5,𝔽2)12yes—
170C2×D19—22no—
171C2×D19—24no—
172C2×D19—24no—
173C2×D19—24no—
174C2×D19—24no—
175C2×D19—416no—
176C2×D19—42no—
177C2×D19—41no—
178C2×D19—41no—
179C2×D19—42no—
180C2×D19—42no—
181C2×D19—42no—
182C2×D19—42no—
183C4×C19—22no—
184C4×C19—42no—
185C4×C19—42no—
186Dic19—22no—
187Dic19—22no—
188Dic19—22no—
189Dic19—42no—
190C22×#41—191no—
191C2×#120—191no—
192C2×#120—191no—
193C22×C22⋊C4—191no—
194#393—192no—
195#392—192no—
196#386—191no—
197#386—192no—
198#386—192no—
199#386D1911yescharacteristic, complemented
200#381—191no—
201C2×C19—24no—
202C2×C19—42no—
203C2×C19C2×#12011yescharacteristic
204C2×C19#52511yescharacteristic
205C2×C19#53511yescharacteristic
206C2×C19#54612yes—
207C2×C19#54612yes—
208D19—42no—
209D19—44no—
210C25—191no—
211C2×#41—384no—
212C2×#41—384no—
213C2×#41—384no—
214C22×Q8—191no—
215C22×D4—191no—
216C22×D4—191no—
217C22×D4—192no—
218C22×D4—192no—
219C22×D4C2×D1911yescharacteristic
220C23×C4—191no—
221C23×C4—191no—
222C23×C4—191no—
223C23×C4C2×D1911yescharacteristic
224#120—384no—
225#120—384no—
226C2×C22⋊C4—191no—
227C2×C22⋊C4—192no—
228C2×C22⋊C4—192no—
229C2×C22⋊C4—192no—
230C2×C22⋊C4—192no—
231C2×C22⋊C4—192no—
232C2×C22⋊C4—384no—
233C2×C22⋊C4C2×D1911yescharacteristic
234C2×C22⋊C4C2×D1912yescomplemented
235#95—192no—
236#95—192no—
237#95—192no—
238#95C2×D1912yescomplemented
239C19#240411yescharacteristic, complemented, Sylow
240C24—192no—
241C24—191no—
242C24—384no—
243C24—382no—
244C24—382no—
245C24—382no—
246C24—762no—
247C24C22×D1911yescharacteristic
248C24C22×D1911yescharacteristic
249#41—3832no—
250C2×Q8—382no—
251C2×Q8—382no—
252C2×Q8—382no—
253C2×D4—22no—
254C2×D4—22no—
255C2×D4—194no—
256C2×D4—384no—
257C2×D4—384no—
258C2×D4—382no—
259C2×D4—382no—
260C2×D4—382no—
261C2×D4—382no—
262C2×D4—382no—
263C2×D4—384no—
264C2×D4—384no—
265C2×D4—762no—
266C2×D4—762no—
267C2×D4D7614yescomplemented
268C22×C4—22no—
269C22×C4—42no—
270C22×C4—194no—
271C22×C4—191no—
272C22×C4—191no—
273C22×C4—191no—
274C22×C4—192no—
275C22×C4—382no—
276C22×C4—382no—
277C22×C4—382no—
278C22×C4—382no—
279C22×C4—382no—
280C22×C4—382no—
281C22×C4—382no—
282C22×C4—382no—
283C22×C4C22×D1912yes—
284C22×C4C22×D1912yes—
285C22×C4C22×D1911yescharacteristic
286C22⋊C4—22no—
287C22⋊C4—42no—
288C22⋊C4—384no—
289C22⋊C4—384no—
290C22⋊C4—384no—
291C22⋊C4—382no—
292C22⋊C4—384no—
293C22⋊C4—762no—
294C23—22no—
295C23—22no—
296C23—21no—
297C23—21no—
298C23—22no—
299C23—22no—
300C23—192no—
301C23—194no—
302C23—388no—
303C23—382no—
304C23—381no—
305C23—382no—
306C23—382no—
307C23—381no—
308C23—382no—
309C23—382no—
310C23—382no—
311C23—382no—
312C23—382no—
313C23—768no—
314C23—768no—
315C23—764no—
316C23—764no—
317C23C2×D7612yes—
318C23C2×D7612yes—
319C23D4×D1912yes—
320C23D4×D1912yes—
321C23C23×D1911yescharacteristic
322Q8—388no—
323D4—28no—
324D4—388no—
325D4—388no—
326D4—768no—
327D4—768no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—44no—
337C2×C4—192no—
338C2×C4—192no—
339C2×C4—192no—
340C2×C4—388no—
341C2×C4—388no—
342C2×C4—381no—
343C2×C4—381no—
344C2×C4—381no—
345C2×C4—381no—
346C2×C4—381no—
347C2×C4—381no—
348C2×C4—388no—
349C2×C4—382no—
350C2×C4—382no—
351C2×C4—382no—
352C2×C4C2×D7612yes—
353C22—22no—
354C22—22no—
355C22—24no—
356C22—24no—
357C22—24no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—42no—
362C22—384no—
363C22—384no—
364C22—384no—
365C22—384no—
366C22—382no—
367C22—7616no—
368C22—761no—
369C22—762no—
370C22—761no—
371C22—762no—
372C22—762no—
373C22—762no—
374C22—762no—
375C22#1059732814yes—
376C22C22×D7611yescharacteristic
377C22C2×D4×D1911yescharacteristic
378C22C2×D4×D1911yescharacteristic
379C22#1059743012yes—
380C22#41×D1912yes—
381C4—22no—
382C4—42no—
383C4—42no—
384C4—382no—
385C4—382no—
386C4—382no—
387C4—762no—
388C2—24no—
389C2—42no—
390C2—764no—
391C2—762no—
392C2C2×#1059732811yescharacteristic
393C2#1192705211yescharacteristic
394C2#1192710911yescharacteristic
395C2#1192718312yes—
396C2#1192718912yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#386C2
hypercenter#386D19
hypocenterC19#2404
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C22×#64543C2semidirect
2. C2×#10597328C2semidirect
3. C2×#10597383C2semidirect
4. C22×(C2×D19)⋊C4C2semidirect
5. #11926457C2semidirect
6. #11926453C2semidirect
7. #11926423C2semidirect
8. #11926422C2semidirect
9. #11926421C2semidirect
10. #11926405C2semidirect
11. C19×#386C2semidirect
17. C22×C22⋊D19C22semidirect
19. C23×Dic19C22semidirect
24. C22×C4×D19C22semidirect
25. C22×Dic38C22semidirect
27. C2×C22⋊C4×C19C22semidirect
35. C2×(C2×D19)⋊C4C22semidirect
37. C19×#95C22semidirect
38. C19⋊#95C22semidirect
39. C19⋊#95C22semidirect
40. C19⋊#95C22semidirect
52. C2×D4×C19D4semidirect
66. C2×C22⋊D19D4semidirect
72. C22×Dic19D4semidirect
122. C22×D19#41semidirect
199. #386D19semidirect
234. C2×C22⋊C4C2×D19semidirect
238. #95C2×D19semidirect
239. C19#2404semidirect
267. C2×D4D76semidirect

Maximal subgroups

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

subgroupindex
C22×#645432
C2×#105973282
C2×#105973832
C22×(C2×D19)⋊C42
#119264572
#119264532
#119264232
#119264222
#119264212
#119264052
C19×#3862
#240419