Finite Group Databasebeta

← #14571540

Subgroups — #14571540

Order 2432.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C19⋊#401C211yesmaximal, characteristic, complemented
2#11926479C211yesmaximal, characteristic, complemented
3#11926466C211yesmaximal, characteristic, complemented
4#11926462C211yesmaximal, characteristic
5#11926461C211yesmaximal, characteristic
6#11926461C211yesmaximal, characteristic
7#11926440C211yesmaximal, characteristic, complemented
8#11926439C211yesmaximal, characteristic, complemented
9#11926436C211yesmaximal, characteristic, complemented
10#11926435C211yesmaximal, characteristic, complemented
11#11926435C211yesmaximal, characteristic, complemented
12#11926434C211yesmaximal, characteristic, complemented
13#11926434C211yesmaximal, characteristic, complemented
14#11926433C211yesmaximal, characteristic, complemented
15C19×#389C211yesmaximal, characteristic, complemented
16C22×D76C2211yescharacteristic
17C2×C4⋊C4×C19C2211yescharacteristic
18C2×C4⋊C4×C19C2211yescharacteristic
19C2×C4⋊C4×C19C2211yescharacteristic
20C2×C4⋊C4×C19C2211yescharacteristic
21C2×C42×C19C2211yescharacteristic
22C2×(C2×D19)⋊C4C2211yescharacteristic
23C2×(C2×D19)⋊C4C2211yescharacteristic
24C2×(C2×D19)⋊C4C2211yescharacteristic
25C2×(C2×D19)⋊C4C2211yescharacteristic
26C2×(C2×D19)⋊C4C2211yescharacteristic
27C2×(C2×D19)⋊C4C2211yescharacteristic
28C2×(C2×D19)⋊C4C2211yescharacteristic
29C2×(C2×D19)⋊C4C2211yescharacteristic
30C2×(C2×D19)⋊C4C2211yescharacteristic
31C2×(C2×D19)⋊C4C2211yescharacteristic
32C2×(C2×D19)⋊C4C2211yescharacteristic
33C2×(C2×D19)⋊C4C2211yescharacteristic
34C2×C4⋊Dic19C2211yescharacteristic
35C2×Dic19⋊C4C2211yescharacteristic
36C2×Dic19⋊C4C2211yescharacteristic
37C2×Dic19⋊C4C2211yescharacteristic
38C2×Dic19⋊C4C2211yescharacteristic
39C2×C4×Dic19C2211yescharacteristic
40C2×C4×Dic19C2211yescharacteristic
41C19×#95C2211yescharacteristic
42C19×#95C2211yescharacteristic
43C19⋊#95C2211yescharacteristic
44C19⋊#95C2211yescharacteristic
45C19⋊#95C2211yescharacteristic
46C19⋊#95C2211yescharacteristic
47C19⋊#95C2211yescharacteristic
48C19⋊#95C2211yescharacteristic
49C19⋊#95C2211yescharacteristic
50C19⋊#95C2211yescharacteristic
51C23×D19C2311yescharacteristic
52C23×D19C2311yescharacteristic
53C22×C4×C19C2311yescharacteristic
54C22×C4×C19C2311yescharacteristic
55C22×C4×C19C2311yescharacteristic
56C22×C4×C19C2311yescharacteristic
57C22×C4×C19C2311yescharacteristic
58C22×C4×C19C2311yescharacteristic
59C22×C4×C19C2311yescharacteristic
60C22×Dic19C2311yescharacteristic
61C22×Dic19C2311yescharacteristic
62C22×Dic19C2311yescharacteristic
63C22×Dic19C2311yescharacteristic
64C22×Dic19C2311yescharacteristic
65C22×Dic19C2311yescharacteristic
66C2×D76—41no—
67C2×D76—41no—
68C2×D76—41no—
69C4⋊C4×C19—22no—
70C4⋊C4×C19—41no—
71C4⋊C4×C19—41no—
72C4⋊C4×C19—41no—
73C42×C19—41no—
74(C2×D19)⋊C4—22no—
75(C2×D19)⋊C4—22no—
76(C2×D19)⋊C4—22no—
77(C2×D19)⋊C4—22no—
78(C2×D19)⋊C4—22no—
79(C2×D19)⋊C4—22no—
80(C2×D19)⋊C4—41no—
81(C2×D19)⋊C4—41no—
82(C2×D19)⋊C4—41no—
83(C2×D19)⋊C4—41no—
84(C2×D19)⋊C4—41no—
85(C2×D19)⋊C4—41no—
86C4⋊Dic19—22no—
87Dic19⋊C4—22no—
88Dic19⋊C4—41no—
89Dic19⋊C4—41no—
90Dic19⋊C4—41no—
91C4×Dic19—41no—
92C4×Dic19—41no—
93C23×C19C2411yescharacteristic
94C22×D19—21no—
95C22×D19—21no—
96C22×D19—21no—
97C22×D19—21no—
98C22×D19—21no—
99C22×D19—21no—
100C22×D19—21no—
101C22×D19—21no—
102C22×D19—21no—
103C22×D19—21no—
104C22×D19—21no—
105C22×D19—21no—
106C22×D19—21no—
107C22×D19—21no—
108C2×C4×C19—21no—
109C2×C4×C19—21no—
110C2×C4×C19—21no—
111C2×C4×C19—21no—
112C2×C4×C19—21no—
113C2×C4×C19—21no—
114C2×C4×C19—21no—
115C2×C4×C19—21no—
116C2×C4×C19—21no—
117C2×C4×C19—21no—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—21no—
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—21no—
127C2×C4×C19#4112yes—
128C2×C4×C19#4112yes—
129C2×Dic19—21no—
130C2×Dic19—21no—
131C2×Dic19—21no—
132C2×Dic19—21no—
133C2×Dic19—21no—
134C2×Dic19—21no—
135C2×Dic19—21no—
136C2×Dic19—21no—
137C2×Dic19—21no—
138C2×Dic19—21no—
139C2×Dic19—21no—
140C2×Dic19—21no—
141C2×Dic19—21no—
142C2×Dic19—21no—
143C2×Dic19—21no—
144C2×Dic19—21no—
145C2×Dic19—21no—
146C2×Dic19#4112yes—
147D76—44no—
148#2801—191nomaximal, Sylow
149C22×C19C2×#4111yescharacteristic
150C22×C19C2×#4111yescharacteristic
151C22×C19C2×#4111yescharacteristic
152C22×C19H(5,𝔽2)11yescharacteristic
153C22×C19H(5,𝔽2)11yescharacteristic
154C22×C19H(5,𝔽2)11yescharacteristic
155C22×C192−1+411yescharacteristic
156C2×D19—41no—
157C2×D19—41no—
158C2×D19—41no—
159C2×D19—41no—
160C2×D19—41no—
161C2×D19—41no—
162C2×D19—41no—
163C2×D19—41no—
164C2×D19—41no—
165C2×D19—41no—
166C2×D19—41no—
167C2×D19—41no—
168C2×D19—41no—
169C2×D19—41no—
170C4×C19—22no—
171C4×C19—22no—
172C4×C19—41no—
173C4×C19—41no—
174C4×C19—41no—
175C4×C19—41no—
176C4×C19—41no—
177Dic19—22no—
178Dic19—41no—
179Dic19—41no—
180Dic19—41no—
181Dic19—41no—
182Dic19—41no—
183#401—191no—
184#399—191no—
185#396—191no—
186#394—191no—
187#394—191no—
188#394—191no—
189#389—191no—
190#389—191no—
191#389D1911yescharacteristic, complemented
192#388—191no—
193#388—191no—
194#388—191no—
195#388—191no—
196#388—191no—
197#388—191no—
198C2×C19#54211yescharacteristic
199C2×C19#54211yescharacteristic
200C2×C19#54211yescharacteristic
201C2×C19#55311yescharacteristic
202C2×C19#55311yescharacteristic
203C2×C19#55311yescharacteristic
204C2×C19#56011yescharacteristic
205D19—81no—
206D19—81no—
207C22×D4—191no—
208C2×C4⋊C4—191no—
209C2×C4⋊C4—191no—
210C2×C4⋊C4—191no—
211C2×C4⋊C4—191no—
212C2×C4⋊C4—191no—
213C2×C4⋊C4C2×D1911yescharacteristic
214C2×C4⋊C4C2×D1911yescharacteristic
215C2×C4⋊C4C2×D1911yescharacteristic
216C2×C4⋊C4C2×D1911yescharacteristic
217C2×C22⋊C4—191no—
218C2×C22⋊C4—191no—
219C2×C22⋊C4—191no—
220C2×C22⋊C4—191no—
221C2×C22⋊C4—191no—
222C2×C22⋊C4—191no—
223C2×C22⋊C4—191no—
224C2×C22⋊C4—191no—
225C2×C22⋊C4—191no—
226C2×C22⋊C4—191no—
227C2×C22⋊C4—191no—
228C2×C22⋊C4—191no—
229C2×C42—191no—
230C2×C42—191no—
231C2×C42C2×D1911yescharacteristic
232#95—191no—
233#95—191no—
234#95—191no—
235#95—191no—
236#95—191no—
237#95—191no—
238#95—191no—
239#95—191no—
240#95C2×D1911yescharacteristic
241#95C2×D1911yescharacteristic
242C19#280111yescharacteristic, complemented, Sylow
243C24—191no—
244C24—191no—
245C2×D4—761no—
246C2×D4—761no—
247C2×D4—761no—
248C22×C4—191no—
249C22×C4—191no—
250C22×C4—191no—
251C22×C4—191no—
252C22×C4—191no—
253C22×C4—191no—
254C22×C4C22×D1911yescharacteristic
255C22×C4C22×D1911yescharacteristic
256C22×C4C22×D1911yescharacteristic
257C22×C4C22×D1911yescharacteristic
258C22×C4C22×D1911yescharacteristic
259C22×C4C22×D1911yescharacteristic
260C22×C4C22×D1911yescharacteristic
261C4⋊C4—22no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—382no—
266C4⋊C4—382no—
267C4⋊C4—761no—
268C4⋊C4—761no—
269C4⋊C4—761no—
270C22⋊C4—382no—
271C22⋊C4—382no—
272C22⋊C4—382no—
273C22⋊C4—382no—
274C22⋊C4—382no—
275C22⋊C4—382no—
276C22⋊C4—761no—
277C22⋊C4—761no—
278C22⋊C4—761no—
279C22⋊C4—761no—
280C22⋊C4—761no—
281C22⋊C4—761no—
282C42—41no—
283C42—761no—
284C42—761no—
285C23—381no—
286C23—381no—
287C23—381no—
288C23—381no—
289C23—381no—
290C23—381no—
291C23—381no—
292C23—381no—
293C23—381no—
294C23—381no—
295C23—381no—
296C23—381no—
297C23—381no—
298C23—381no—
299C23C23×D1911yescharacteristic
300D4—764no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—192no—
321C2×C4—381no—
322C2×C4—381no—
323C2×C4—381no—
324C2×C4—381no—
325C2×C4—381no—
326C2×C4—381no—
327C2×C4—381no—
328C2×C4—381no—
329C2×C4—381no—
330C2×C4—381no—
331C2×C4—381no—
332C2×C4—381no—
333C2×C4—381no—
334C2×C4—381no—
335C2×C4—381no—
336C2×C4—381no—
337C2×C4—381no—
338C2×C4#6454112yes—
339C2×C4#6454512yes—
340C22—761no—
341C22—761no—
342C22—761no—
343C22—761no—
344C22—761no—
345C22—761no—
346C22—761no—
347C22—761no—
348C22—761no—
349C22—761no—
350C22—761no—
351C22—761no—
352C22—761no—
353C22—761no—
354C22C2×#6454111yescharacteristic
355C22#1059743011yescharacteristic
356C22#1059743011yescharacteristic
357C22C2×#6454511yescharacteristic
358C22#1059743311yescharacteristic
359C22#41×D1911yescharacteristic
360C22#1059743511yescharacteristic
361C4—22no—
362C4—22no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—382no—
369C4—761no—
370C4—761no—
371C4—761no—
372C4—761no—
373C4—761no—
374C2—1521no—
375C2—1521no—
376C2#1192716411yescharacteristic
377C2#1192716611yescharacteristic
378C2#1192716811yescharacteristic
379C2#1192724211yescharacteristic
380C2#1192724311yescharacteristic
381C2#1192724711yescharacteristic
382C2#1192728211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#389C2
prime radicalC22×D76C22
hypercenter#389D19
hypocenterC19#2801
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C19⋊#401C2semidirect
2. #11926479C2semidirect
3. #11926466C2semidirect
7. #11926440C2semidirect
8. #11926439C2semidirect
9. #11926436C2semidirect
10. #11926435C2semidirect
11. #11926435C2semidirect
12. #11926434C2semidirect
13. #11926434C2semidirect
14. #11926433C2semidirect
15. C19×#389C2semidirect
191. #389D19semidirect
242. C19#2801semidirect

Maximal subgroups

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

subgroupindex
C19⋊#4012
#119264792
#119264662
#119264622
#119264612
#119264402
#119264392
#119264362
#119264352
#119264342
#119264332
C19×#3892
#280119