Finite Group Databasebeta

← D19×#541 #14576997

Subgroups — D19×#541 #14576997

Order 2432.

1004 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927157C211yesmaximal, characteristic, complemented
2#11927156C211yesmaximal, characteristic, complemented
3#11927155C211yesmaximal, characteristic, complemented
4#11927154C212yesmaximal, complemented
5#11927153C214yesmaximal, complemented
6#11927152C212yesmaximal, complemented
7#11927151C214yesmaximal, complemented
8C4⋊Q8×D19C211yesmaximal, characteristic, complemented
9#126×D19C214yesmaximal
10#125×D19C214yesmaximal, complemented
11#125×D19C211yesmaximal, characteristic, complemented
12C22⋊Q8×D19C212yesmaximal
13C4×Q8×D19C212yesmaximal, complemented
14#117×D19C211yesmaximal, characteristic
15C19×#541C211yesmaximal, characteristic, complemented
16C2×Q8×D19C2212yes—
17C22×C4×D19C2211yescharacteristic
18C19×C4⋊Q8C2211yescharacteristic, complemented
19C19×#126C2214yes—
20C19×#125C2214yescomplemented
21C19×#125C2211yescharacteristic, complemented
22C19×C22⋊Q8C2212yes—
23C4×Q8×C19C2212yescomplemented
24C19×#117C2211yescharacteristic
25#10597392C2212yes—
26Q8×Dic19C2212yescomplemented
27#10597390C2212yescomplemented
28#10597372C2211yescharacteristic
29#10597370C2212yes—
30#10597344C2214yes—
31#10597344C2214yes—
32#10597344C2214yes—
33#10597343C2212yes—
34#10597342C2214yes—
35#10597338C2212yes—
36C4⋊C4×D19C2214yes—
37C4⋊C4×D19C2212yes—
38C4⋊C4×D19C2214yes—
39C4⋊C4×D19C2214yes—
40C4⋊C4×D19C2214yes—
41C4⋊C4×D19C2212yes—
42#10597336C2214yescomplemented
43#10597336C2212yescomplemented
44#10597336C2214yescomplemented
45#10597335C2214yescomplemented
46#10597335C2214yescomplemented
47#10597335C2214yescomplemented
48#10597335C2214yescomplemented
49#10597335C2214yescomplemented
50#10597334C2214yescomplemented
51#10597333C2214yescomplemented
52#10597333C2212yescomplemented
53C22⋊C4×D19C2212yes—
54C22⋊C4×D19C2214yes—
55#10597325C2214yes—
56#10597325C2214yes—
57#10597325C2214yes—
58#10597324C2214yes—
59#10597323C2212yes—
60#10597322C2214yes—
61#10597318C2211yescharacteristic
62#10597318C2211yescharacteristic
63C42×D19C2214yes—
64C42×D19C2211yescharacteristic
65C42×D19C2211yescharacteristic
66#10597316C2214yescomplemented
67#10597316C2211yescharacteristic, complemented
68#10597315C2211yescharacteristic, complemented
69C4×Dic38C2214yescomplemented
70C4×Dic38C2212yescomplemented
71C23×D19C2311yescharacteristic
72C2×Q8×C19C2312yes—
73C22×C4×C19C2311yescharacteristic
74C22×Dic19C2311yescharacteristic
75Q8×D19—28no—
76C2×C4×D19—24no—
77C2×C4×D19C2311yescharacteristic
78C2×C4×D19C2311yescharacteristic
79C2×C4×D19C2311yescharacteristic
80C2×C4×D19C2314yes—
81C2×C4×D19C2312yes—
82C2×C4×D19C2314yes—
83C2×C4×D19C2312yes—
84C2×C4×D19C2311yescharacteristic
85C2×Dic38C2312yes—
86C2×Dic38C2314yes—
87C4⋊C4×C19C2312yes—
88C4⋊C4×C19C2312yes—
89C4⋊C4×C19C2314yes—
90C4⋊C4×C19C2314yes—
91C4⋊C4×C19C2314yes—
92C4⋊C4×C19C2314yes—
93C22⋊C4×C19C2312yes—
94C22⋊C4×C19C2314yes—
95C42×C19C2311yescharacteristic
96C42×C19C2311yescharacteristic
97C42×C19C2314yes—
98C22⋊Dic19C2312yes—
99C22⋊Dic19C2314yes—
100(C2×D19)⋊C4C2314yes—
101(C2×D19)⋊C4C2312yes—
102(C2×D19)⋊C4C2312yes—
103(C2×D19)⋊C4C2314yes—
104C4⋊Dic19C2312yes—
105C4⋊Dic19C2314yes—
106C4⋊Dic19C2314yes—
107C4⋊Dic19C2314yes—
108C4⋊Dic19C2314yes—
109C4⋊Dic19C2312yes—
110Dic19⋊C4C2314yes—
111Dic19⋊C4C2314yes—
112Dic19⋊C4C2314yes—
113Dic19⋊C4C2314yes—
114Dic19⋊C4C2314yes—
115Dic19⋊C4C2314yes—
116Dic19⋊C4C2312yes—
117Dic19⋊C4C2314yes—
118Dic19⋊C4C2312yes—
119Dic19⋊C4C2314yes—
120Dic19⋊C4C2314yes—
121C4×Dic19C2311yescharacteristic
122C4×Dic19C2311yescharacteristic
123C4×Dic19C2314yes—
124C4×Dic19C2312yes—
125C4×Dic19C2314yes—
126C4×Dic19C2312yes—
127C4×Dic19C2314yes—
128C23×C19C2411yescharacteristic
129C22×D19—22no—
130C22×D19—24no—
131C22×D19C2411yescharacteristic
132C22×D19C2411yescharacteristic
133Q8×C19—24no—
134C2×C4×C19—22no—
135C2×C4×C19C2412yes—
136C2×C4×C19C2412yes—
137C2×C4×C19C2414yes—
138C2×C4×C19C2414yes—
139C2×C4×C19C2411yescharacteristic
140C2×C4×C19C2411yescharacteristic
141C2×Dic19—22no—
142C2×Dic19C2412yes—
143C2×Dic19C2412yes—
144C2×Dic19C2414yes—
145C2×Dic19C2414yes—
146C2×Dic19C2411yescharacteristic
147C2×Dic19C2411yescharacteristic
148C4×D19—22no—
149C4×D19—28no—
150C4×D19—24no—
151C4×D19—28no—
152C4×D19—24no—
153C4×D19—22no—
154C4×D19—22no—
155C4×D19#4114yes—
156Dic38—24no—
157Dic38—28no—
158C2×#541—191nomaximal, Sylow
159C22×C19—21no—
160C22×C19—22no—
161C22×C19C2511yescharacteristic
162C2×D19—21no—
163C2×D19—22no—
164C2×D19—44no—
165C2×D19C2×#4112yes—
166C2×D192−1+414yes—
167C4×C19—24no—
168C4×C19—21no—
169C4×C19—22no—
170C4×C19—22no—
171C4×C19—24no—
172C4×C19C2×#4112yes—
173Dic19—24no—
174Dic19—21no—
175Dic19—22no—
176Dic19—22no—
177Dic19—24no—
178Dic19C2×#4112yes—
179#541—191no—
180#541—194no—
181#541—194no—
182#541—191no—
183#541—192no—
184#541—192no—
185#541—191no—
186#541D1911yescharacteristic, direct product factor
187C2×C4⋊Q8—191no—
188C2×#126—194no—
189C2×#125—191no—
190C2×#125—194no—
191C2×C22⋊Q8—192no—
192C2×C4×Q8—192no—
193C2×#117—191no—
194C2×C19—41no—
195C2×C19C22×#4111yescharacteristic
196C2×C19C2×2−1+412yes—
197D19—41no—
198D19#54114yesdirect product factor
199C22×Q8—192no—
200C23×C4—191no—
201C4⋊Q8—192no—
202C4⋊Q8—194no—
203C4⋊Q8—191no—
204C4⋊Q8C2×D1911yescharacteristic, complemented
205#126—194no—
206#126—194no—
207#126—194no—
208#126—194no—
209#126—194no—
210#126—194no—
211#126—194no—
212#126C2×D1914yes—
213#125—194no—
214#125—194no—
215#125—194no—
216#125—194no—
217#125—194no—
218#125—192no—
219#125—194no—
220#125—194no—
221#125—191no—
222#125—194no—
223#125C2×D1911yescharacteristic, complemented
224#125C2×D1914yescomplemented
225C22⋊Q8—192no—
226C22⋊Q8—192no—
227C22⋊Q8—194no—
228C22⋊Q8—192no—
229C22⋊Q8—194no—
230C22⋊Q8C2×D1912yes—
231C4×Q8—192no—
232C4×Q8—194no—
233C4×Q8—192no—
234C4×Q8—194no—
235C4×Q8—192no—
236C4×Q8C2×D1912yescomplemented
237#117—191no—
238#117—192no—
239#117—192no—
240#117—191no—
241#117—191no—
242#117C2×D1911yescharacteristic
243C2×C4⋊C4—192no—
244C2×C4⋊C4—192no—
245C2×C4⋊C4—194no—
246C2×C4⋊C4—194no—
247C2×C4⋊C4—194no—
248C2×C4⋊C4—194no—
249C2×C22⋊C4—192no—
250C2×C22⋊C4—194no—
251C2×C42—191no—
252C2×C42—191no—
253C2×C42—194no—
254C19C2×#54111yescharacteristic, complemented, Sylow
255C24—191no—
256C2×Q8—194no—
257C2×Q8—192no—
258C2×Q8—388no—
259C2×Q8C22×D1912yes—
260C22×C4—191no—
261C22×C4—191no—
262C22×C4—192no—
263C22×C4—192no—
264C22×C4—194no—
265C22×C4—194no—
266C22×C4—191no—
267C22×C4—191no—
268C22×C4—191no—
269C22×C4—384no—
270C22×C4C22×D1911yescharacteristic
271C4⋊C4—192no—
272C4⋊C4—192no—
273C4⋊C4—194no—
274C4⋊C4—194no—
275C4⋊C4—194no—
276C4⋊C4—194no—
277C4⋊C4—194no—
278C4⋊C4—194no—
279C4⋊C4—194no—
280C4⋊C4—194no—
281C4⋊C4—194no—
282C4⋊C4—192no—
283C4⋊C4—192no—
284C4⋊C4—194no—
285C4⋊C4—194no—
286C4⋊C4—194no—
287C4⋊C4—194no—
288C4⋊C4C22×D1912yes—
289C4⋊C4C22×D1912yes—
290C4⋊C4C22×D1914yes—
291C4⋊C4C22×D1914yes—
292C4⋊C4C22×D1914yes—
293C4⋊C4C22×D1914yes—
294C22⋊C4—192no—
295C22⋊C4—194no—
296C22⋊C4—192no—
297C22⋊C4—192no—
298C22⋊C4—194no—
299C22⋊C4—194no—
300C22⋊C4C22×D1912yes—
301C22⋊C4C22×D1914yes—
302C42—192no—
303C42—191no—
304C42—192no—
305C42—191no—
306C42—194no—
307C42—194no—
308C42—194no—
309C42C22×D1911yescharacteristic
310C42C22×D1911yescharacteristic
311C42C22×D1914yes—
312C23—191no—
313C23—191no—
314C23—382no—
315C23—384no—
316C23C23×D1911yescharacteristic
317Q8—24no—
318Q8—388no—
319Q8—384no—
320C2×C4—22no—
321C2×C4—191no—
322C2×C4—194no—
323C2×C4—192no—
324C2×C4—192no—
325C2×C4—194no—
326C2×C4—194no—
327C2×C4—191no—
328C2×C4—382no—
329C2×C4—382no—
330C2×C4—388no—
331C2×C4—384no—
332C2×C4—384no—
333C2×C4—388no—
334C2×C4—382no—
335C2×C4—382no—
336C2×C4C23×D1912yes—
337C2×C4C23×D1912yes—
338C2×C4C23×D1914yes—
339C2×C4C23×D1914yes—
340C2×C4C23×D1911yescharacteristic
341C2×C4C23×D1911yescharacteristic
342C22—21no—
343C22—22no—
344C22—192no—
345C22—194no—
346C22—381no—
347C22—382no—
348C22—764no—
349C22C24×D1911yescharacteristic
350C4—21no—
351C4—24no—
352C4—22no—
353C4—22no—
354C4—24no—
355C4—192no—
356C4—381no—
357C4—384no—
358C4—382no—
359C4—382no—
360C4—384no—
361C4#41×D1912yes—
362C2—41no—
363C2—194no—
364C2—761no—
365C2C2×#41×D1911yescharacteristic
366C22−1+4×D1912yes—
subgroupG/H
center, FrattiniC22C24×D19
commutator, socle, cosocleC22×C19C25
FittingC19×#541C2
prime radicalC23×D19C23
hypercenter#541D19
hypocenterC19C2×#541
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ #541

Complements

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

NH ≅ G/Ntype
1. #11927157C2semidirect
2. #11927156C2semidirect
3. #11927155C2semidirect
4. #11927154C2semidirect
5. #11927153C2semidirect
6. #11927152C2semidirect
7. #11927151C2semidirect
8. C4⋊Q8×D19C2semidirect
10. #125×D19C2semidirect
11. #125×D19C2semidirect
13. C4×Q8×D19C2semidirect
15. C19×#541C2semidirect
18. C19×C4⋊Q8C22semidirect
20. C19×#125C22semidirect
21. C19×#125C22semidirect
23. C4×Q8×C19C22semidirect
26. Q8×Dic19C22semidirect
27. #10597390C22semidirect
42. #10597336C22semidirect
43. #10597336C22semidirect
44. #10597336C22semidirect
45. #10597335C22semidirect
46. #10597335C22semidirect
47. #10597335C22semidirect
48. #10597335C22semidirect
49. #10597335C22semidirect
50. #10597334C22semidirect
51. #10597333C22semidirect
52. #10597333C22semidirect
66. #10597316C22semidirect
67. #10597316C22semidirect
68. #10597315C22semidirect
69. C4×Dic38C22semidirect
70. C4×Dic38C22semidirect
186. #541D19direct (N × H)
198. D19#541direct (N × H)
204. C4⋊Q8C2×D19semidirect
223. #125C2×D19semidirect
224. #125C2×D19semidirect
236. C4×Q8C2×D19semidirect
254. C19C2×#541semidirect

Maximal subgroups

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

subgroupindex
#119271572
#119271562
#119271552
#119271542
#119271532
#119271522
#119271512
C4⋊Q8×D192
#126×D192
#125×D192
C22⋊Q8×D192
C4×Q8×D192
#117×D192
C19×#5412
C2×#54119