Finite Group Databasebeta

← C19×#10575 #18016534

Subgroups — C19×#10575 #18016534

Order 4864.

478 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C19×#2551C211yesmaximal, characteristic
2C19×#1948C211yesmaximal, characteristic
3C19×#1947C211yesmaximal, characteristic
4C19×#1834C211yesmaximal, characteristic
5C19×#1296C211yesmaximal, characteristic
6C19×#1279C211yesmaximal, characteristic
7C19×#1279C211yesmaximal, characteristic
8C2×C19×C4⋊Q8—21no—
9C2×C19×C4⋊Q8—21no—
10C2×C19×#107—21no—
11C2×C19×#106—21no—
12C2×C19×C4⋊C8C2211yescharacteristic
13C2×C19×C4⋊C8C2211yescharacteristic
14C2×C4×C8×C19C2211yescharacteristic
15C19×#395—22no—
16C19×#389—21no—
17C19×#389—21no—
18C19×#384C2211yescharacteristic
19C19×#384C2211yescharacteristic
20C4×C4⋊C4×C19C2211yescharacteristic
21C4×C4⋊C4×C19C2211yescharacteristic
22C19×#340—21no—
23C19×#340—21no—
24C19×#340—22no—
25C22×Q8×C19—22no—
26C22×C8×C19—21no—
27C22×C8×C19—21no—
28C22×C8×C19—21no—
29C19×C4⋊Q8—42no—
30C19×C4⋊Q8—42no—
31C19×C4⋊Q8—42no—
32C19×C4⋊Q8—42no—
33C2×C4⋊C4×C19—22no—
34C2×C4⋊C4×C19—22no—
35C2×C4⋊C4×C19—21no—
36C2×C4⋊C4×C19—21no—
37C2×C4⋊C4×C19—21no—
38C2×C4⋊C4×C19—21no—
39C2×C4⋊C4×C19—21no—
40C2×C4⋊C4×C19D411yescharacteristic
41C2×C4⋊C4×C19D411yescharacteristic
42C2×C4⋊C4×C19D411yescharacteristic
43C2×C4⋊C4×C19D411yescharacteristic
44C2×C4⋊C4×C19D412yes—
45C2×C42×C19—21no—
46C2×C42×C19—21no—
47C2×C42×C19C2311yescharacteristic
48C19×#107—42no—
49C19×#106—42no—
50C19×C4⋊C8—21no—
51C19×C4⋊C8—21no—
52C19×C4⋊C8Q812yescomplemented
53C19×C4⋊C8Q812yescomplemented
54C4×C8×C19—21no—
55C4×C8×C19Q812yescomplemented
56C19×#95—22no—
57C19×#95—21no—
58C19×#95—21no—
59C2×Q8×C19—44no—
60C2×Q8×C19—44no—
61C2×Q8×C19—82no—
62C22×C4×C19—21no—
63C22×C4×C19—21no—
64C22×C4×C19—21no—
65C22×C4×C19—21no—
66C22×C4×C19—22no—
67C22×C4×C19—41no—
68C22×C4×C19C2×D411yescharacteristic
69C22×C4×C19C2×D411yescharacteristic
70C22×C4×C19C2×D411yescharacteristic
71C2×C8×C19—22no—
72C2×C8×C19—22no—
73C2×C8×C19—22no—
74C2×C8×C19—41no—
75C2×C8×C19—41no—
76C2×C8×C19—41no—
77C2×C8×C19—41no—
78C2×C8×C19—41no—
79C2×C8×C19—41no—
80C4⋊C4×C19—21no—
81C4⋊C4×C19—21no—
82C4⋊C4×C19—21no—
83C4⋊C4×C19—21no—
84C4⋊C4×C19—42no—
85C4⋊C4×C19—44no—
86C4⋊C4×C19—44no—
87C4⋊C4×C19—42no—
88C4⋊C4×C19—41no—
89C4⋊C4×C19—41no—
90C4⋊C4×C19—41no—
91C4⋊C4×C19—41no—
92C4⋊C4×C19—41no—
93C4⋊C4×C19—41no—
94C4⋊C4×C19—41no—
95C4⋊C4×C19—41no—
96C4⋊C4×C19D812yes—
97C4⋊C4×C19SD1612yes—
98C4⋊C4×C19SD1612yes—
99C4⋊C4×C19Q1612yes—
100C42×C19—41no—
101C42×C19—41no—
102C42×C19—41no—
103C42×C19—41no—
104C42×C19C2×Q811yescharacteristic
105C42×C19C2×Q811yescharacteristic
106C42×C19C2×Q811yescharacteristic
107C42×C19#4111yescharacteristic
108#10575C1911yesmaximal, characteristic, direct product factor, Sylow
109C23×C19#12011yescharacteristic
110Q8×C19—88no—
111C2×C4×C19—21no—
112C2×C4×C19—21no—
113C2×C4×C19—22no—
114C2×C4×C19—22no—
115C2×C4×C19—22no—
116C2×C4×C19—22no—
117C2×C4×C19—41no—
118C2×C4×C19—41no—
119C2×C4×C19—41no—
120C2×C4×C19—41no—
121C2×C4×C19—41no—
122C2×C4×C19—41no—
123C2×C4×C19—41no—
124C2×C4×C19—41no—
125C2×C4×C19—42no—
126C2×C4×C19—42no—
127C2×C4×C19—42no—
128C2×C4×C19—81no—
129C2×C4×C19—81no—
130C2×C4×C19—81no—
131C2×C4×C19C22⋊Q811yescharacteristic
132C2×C4×C19C22⋊Q811yescharacteristic
133C2×C4×C19C22⋊Q811yescharacteristic
134C2×C4×C19C4⋊Q811yescharacteristic
135C2×C4×C19C4⋊Q811yescharacteristic
136C2×C4×C19C4⋊Q811yescharacteristic
137C2×C4×C19C2×D811yescharacteristic
138C2×C4×C19C2×SD1611yescharacteristic
139C2×C4×C19C2×SD1611yescharacteristic
140C2×C4×C19C2×Q1611yescharacteristic
141C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C19#13711yescharacteristic
144C2×C4×C19#13711yescharacteristic
145C8×C19—42no—
146C8×C19—42no—
147C8×C19—42no—
148#2551C2×C1911yescharacteristic
149#1948C2×C1911yescharacteristic
150#1947C2×C1911yescharacteristic
151#1834C2×C1911yescharacteristic
152#1296C2×C1911yescharacteristic
153#1279C2×C1911yescharacteristic
154#1279C2×C1911yescharacteristic
155C22×C19#39511yescharacteristic
156C22×C19#44711yescharacteristic
157C22×C19#44811yescharacteristic
158C22×C19#45011yescharacteristic
159C22×C19#45111yescharacteristic
160C22×C19#45411yescharacteristic
161C22×C19#45511yescharacteristic
162C4×C19—21no—
163C4×C19—21no—
164C4×C19—42no—
165C4×C19—42no—
166C4×C19—42no—
167C4×C19—42no—
168C4×C19—82no—
169C4×C19—161no—
170C4×C19#47411yescharacteristic
171C4×C19#47511yescharacteristic
172C4×C19#47611yescharacteristic
173C4×C19#47711yescharacteristic
174C4×C19#49811yescharacteristic
175C4×C19#50011yescharacteristic
176C4×C19#50111yescharacteristic
177C4×C19#50111yescharacteristic
178C2×C4⋊Q8—21no—
179C2×C4⋊Q8—21no—
180C2×#107—21no—
181C2×#106—21no—
182C2×C4⋊C8C22×C1911yescharacteristic
183C2×C4⋊C8C22×C1911yescharacteristic
184C2×C4×C8C22×C1911yescharacteristic
185#395—22no—
186#389—21no—
187#389—21no—
188#384C22×C1911yescharacteristic
189#384C22×C1911yescharacteristic
190C4×C4⋊C4C22×C1911yescharacteristic
191C4×C4⋊C4C22×C1911yescharacteristic
192#340—22no—
193#340—21no—
194#340—21no—
195C2×C19#162711yescharacteristic
196C2×C19#163711yescharacteristic
197C2×C19#163911yescharacteristic
198C2×C19#164511yescharacteristic
199C2×C19#205711yescharacteristic
200C2×C19#205811yescharacteristic
201C2×C19#206111yescharacteristic
202C22×Q8—22no—
203C22×C8—21no—
204C22×C8—21no—
205C22×C8—21no—
206C4⋊Q8—42no—
207C4⋊Q8—42no—
208C4⋊Q8—42no—
209C4⋊Q8—42no—
210C2×C4⋊C4—22no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4D4×C1911yescharacteristic
218C2×C4⋊C4D4×C1911yescharacteristic
219C2×C4⋊C4D4×C1911yescharacteristic
220C2×C4⋊C4D4×C1911yescharacteristic
221C2×C4⋊C4D4×C1912yes—
222C2×C42—21no—
223C2×C42—21no—
224C2×C42C23×C1911yescharacteristic
225#107—42no—
226#106—42no—
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8Q8×C1912yescomplemented
230C4⋊C8Q8×C1912yescomplemented
231C4×C8—21no—
232C4×C8Q8×C1912yescomplemented
233#95—22no—
234#95—21no—
235#95—21no—
236C19#1057511yescharacteristic, direct product factor, Sylow
237C2×Q8—44no—
238C2×Q8—44no—
239C2×Q8—82no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—22no—
245C22×C4—41no—
246C22×C4C2×D4×C1911yescharacteristic
247C22×C4C2×D4×C1911yescharacteristic
248C22×C4C2×D4×C1911yescharacteristic
249C2×C8—22no—
250C2×C8—22no—
251C2×C8—22no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—41no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—42no—
263C4⋊C4—44no—
264C4⋊C4—44no—
265C4⋊C4—42no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4D8×C1912yes—
275C4⋊C4SD16×C1912yes—
276C4⋊C4SD16×C1912yes—
277C4⋊C4Q16×C1912yes—
278C42—41no—
279C42—41no—
280C42—41no—
281C42—41no—
282C42C2×Q8×C1911yescharacteristic
283C42C2×Q8×C1911yescharacteristic
284C42C2×Q8×C1911yescharacteristic
285C42#41×C1911yescharacteristic
286C23C19×#12011yescharacteristic
287Q8—88no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4C19×C22⋊Q811yescharacteristic
309C2×C4C19×C22⋊Q811yescharacteristic
310C2×C4C19×C22⋊Q811yescharacteristic
311C2×C4C19×C4⋊Q811yescharacteristic
312C2×C4C19×C4⋊Q811yescharacteristic
313C2×C4C19×C4⋊Q811yescharacteristic
314C2×C4C2×D8×C1911yescharacteristic
315C2×C4C2×SD16×C1911yescharacteristic
316C2×C4C2×SD16×C1911yescharacteristic
317C2×C4C2×Q16×C1911yescharacteristic
318C2×C4C19×AGL(1,ℤ/8)11yescharacteristic
319C2×C4C19×AGL(1,ℤ/8)11yescharacteristic
320C2×C4C19×#13711yescharacteristic
321C2×C4C19×#13711yescharacteristic
322C8—42no—
323C8—42no—
324C8—42no—
325C22C19×#39511yescharacteristic
326C22C19×#44711yescharacteristic
327C22C19×#44811yescharacteristic
328C22C19×#45011yescharacteristic
329C22C19×#45111yescharacteristic
330C22C19×#45411yescharacteristic
331C22C19×#45511yescharacteristic
332C4—21no—
333C4—21no—
334C4—42no—
335C4—42no—
336C4—42no—
337C4—42no—
338C4—82no—
339C4—161no—
340C4C19×#47411yescharacteristic
341C4C19×#47511yescharacteristic
342C4C19×#47611yescharacteristic
343C4C19×#47711yescharacteristic
344C4C19×#49811yescharacteristic
345C4C19×#50011yescharacteristic
346C4C19×#50111yescharacteristic
347C4C19×#50111yescharacteristic
348C2C19×#162711yescharacteristic
349C2C19×#163711yescharacteristic
350C2C19×#163911yescharacteristic
351C2C19×#164511yescharacteristic
352C2C19×#205711yescharacteristic
353C2C19×#205811yescharacteristic
354C2C19×#206111yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C19#120
commutator, Frattini, cosocleC2×C42C23×C19
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C19 ◁ C2×C42×C19 ◁ G

Complements

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

NH ≅ G/Ntype
52. C19×C4⋊C8Q8semidirect
53. C19×C4⋊C8Q8semidirect
55. C4×C8×C19Q8semidirect
108. #10575C19direct (N × H)
229. C4⋊C8Q8×C19semidirect
230. C4⋊C8Q8×C19semidirect
232. C4×C8Q8×C19semidirect
236. C19#10575direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#25512
C19×#19482
C19×#19472
C19×#18342
C19×#12962
C19×#12792
#1057519