Finite Group Databasebeta

← C19×#29533 #18035492

Subgroups — C19×#29533 #18035492

Order 4864.

840 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C19×#2293C212yesmaximal, complemented
2C19×#2087C211yesmaximal, characteristic, complemented
3C19×#2065C212yesmaximal, complemented
4C19×#2054C211yesmaximal, characteristic
5C19×#1925C212yesmaximal, complemented
6C19×#1920C212yesmaximal, complemented
7C19×#1879C212yesmaximal
8C19×#1864C212yesmaximal, complemented
9C19×#1831C211yesmaximal, characteristic, complemented
10C22×D8×C19C2211yescharacteristic
11C2×C4×D4×C19C2212yes—
12C2×C19×#117—22no—
13C2×C19×#107C2211yescharacteristic
14C2×C19×#106C2212yes—
15C2×C19×C4⋊C8C2211yescharacteristic
16C2×C19×C4⋊C8C2211yescharacteristic
17C2×C19×#102C2212yes—
18C2×C19×#102C2212yes—
19C2×C19×#102C2212yes—
20C19×#390C2212yes—
21C19×#390C2212yes—
22C19×#389C2212yes—
23C19×#389C2212yes—
24C19×#388—22no—
25C19×#388—22no—
26C4×C4⋊C4×C19C2212yes—
27C4×C22⋊C4×C19—22no—
28C43×C19C2211yescharacteristic
29C19×#340C2211yescharacteristic
30C19×#340C2212yes—
31C19×#340C2212yes—
32C19×#340C2211yescharacteristic
33C19×#336C2212yes—
34C19×#336C2212yes—
35C22×D4×C19C2312yes—
36C23×C4×C19—22no—
37C2×D8×C19—24no—
38C2×D8×C19—41no—
39C22×C8×C19C2311yescharacteristic
40C22×C8×C19C2312yes—
41C22×C8×C19C2311yescharacteristic
42C4×D4×C19—24no—
43C4×D4×C19—24no—
44C19×#117—48no—
45C2×C4⋊C4×C19—22no—
46C2×C4⋊C4×C19—22no—
47C2×C4⋊C4×C19C2312yes—
48C2×C4⋊C4×C19C2312yes—
49C2×C4⋊C4×C19C2312yes—
50C2×C22⋊C4×C19—22no—
51C2×C22⋊C4×C19—22no—
52C2×C22⋊C4×C19—22no—
53C2×C22⋊C4×C19—22no—
54C2×C22⋊C4×C19—22no—
55C2×C42×C19—22no—
56C2×C42×C19D411yescharacteristic
57C2×C42×C19D412yes—
58C2×C42×C19D411yescharacteristic
59C2×C42×C19C2312yes—
60C2×C42×C19C2311yescharacteristic
61C19×#107—41no—
62C19×#106—24no—
63C19×C4⋊C8—41no—
64C19×C4⋊C8—41no—
65C19×#102—24no—
66C19×#102—24no—
67C19×#102—42no—
68C19×#95—22no—
69C19×#95—22no—
70C19×#95—22no—
71C24×C19—22no—
72C2×D4×C19—22no—
73C2×D4×C19—22no—
74C2×D4×C19—22no—
75C2×D4×C19—22no—
76C2×D4×C19—22no—
77C2×D4×C19#4114yes—
78C22×C4×C19—28no—
79C22×C4×C19—22no—
80C22×C4×C19—22no—
81C22×C4×C19—22no—
82C22×C4×C19—44no—
83C22×C4×C19—44no—
84C22×C4×C19C2×D411yescharacteristic
85C22×C4×C19C2×D412yes—
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19C2×D412yes—
88C22×C4×C19C2411yescharacteristic
89D8×C19—44no—
90C2×C8×C19—22no—
91C2×C8×C19—22no—
92C2×C8×C19—22no—
93C2×C8×C19—22no—
94C2×C8×C19—21no—
95C2×C8×C19—22no—
96C2×C8×C19—21no—
97C4⋊C4×C19—22no—
98C4⋊C4×C19—22no—
99C4⋊C4×C19—22no—
100C4⋊C4×C19—22no—
101C4⋊C4×C19—22no—
102C4⋊C4×C19—44no—
103C4⋊C4×C19—44no—
104C4⋊C4×C19#4114yes—
105C22⋊C4×C19—28no—
106C22⋊C4×C19—44no—
107C22⋊C4×C19—44no—
108C22⋊C4×C19—44no—
109C22⋊C4×C19—44no—
110C42×C19—22no—
111C42×C19—24no—
112C42×C19—22no—
113C42×C19—22no—
114C42×C19—21no—
115C42×C19—21no—
116C42×C19—41no—
117C42×C19—44no—
118#29533C1911yesmaximal, characteristic, direct product factor, Sylow
119C23×C19—24no—
120C23×C19—42no—
121C23×C19—42no—
122C23×C19—42no—
123C23×C19—42no—
124C23×C19—42no—
125C23×C19—42no—
126C23×C19C22×D411yescharacteristic
127D4×C19—24no—
128D4×C19—24no—
129D4×C19—42no—
130D4×C19—42no—
131C2×C4×C19—22no—
132C2×C4×C19—21no—
133C2×C4×C19—22no—
134C2×C4×C19—21no—
135C2×C4×C19—22no—
136C2×C4×C19—24no—
137C2×C4×C19—21no—
138C2×C4×C19—22no—
139C2×C4×C19—22no—
140C2×C4×C19—22no—
141C2×C4×C19—416no—
142C2×C4×C19—42no—
143C2×C4×C19—42no—
144C2×C4×C19—42no—
145C2×C4×C19—42no—
146C2×C4×C19—42no—
147C2×C4×C19—42no—
148C2×C4×C19—42no—
149C2×C4×C19—42no—
150C2×C4×C19#13512yes—
151C2×C4×C19AGL(1,ℤ/8)14yes—
152C2×C4×C19C2×#4112yes—
153C2×C4×C19C2×#4112yes—
154C2×C4×C19H(5,𝔽2)11yescharacteristic
155C2×C4×C192−1+411yescharacteristic
156C8×C19—41no—
157C8×C19—41no—
158C8×C19—42no—
159#2293C2×C1912yescomplemented
160#2087C2×C1911yescharacteristic, complemented
161#2065C2×C1912yescomplemented
162#2054C2×C1911yescharacteristic
163#1925C2×C1912yescomplemented
164#1920C2×C1912yescomplemented
165#1879C2×C1912yes—
166#1864C2×C1912yescomplemented
167#1831C2×C1911yescharacteristic, complemented
168C22×C19—44no—
169C22×C19—44no—
170C22×C19—44no—
171C22×C19—82no—
172C22×C19—82no—
173C22×C19—82no—
174C22×C19—82no—
175C22×C19#52512yes—
176C22×C19#53711yescharacteristic
177C22×C19C2×#13511yescharacteristic
178C22×C19C2×AGL(1,ℤ/8)12yes—
179C22×C19#57511yescharacteristic
180C4×C19—24no—
181C4×C19—22no—
182C4×C19—42no—
183C4×C19—44no—
184C4×C19—41no—
185C4×C19—82no—
186C4×C19—82no—
187C4×C19#55111yescharacteristic
188C4×C19#55212yes—
189C4×C19#55511yescharacteristic
190C22×D8C22×C1911yescharacteristic
191C2×C4×D4C22×C1912yes—
192C2×#117—22no—
193C2×#107C22×C1911yescharacteristic
194C2×#106C22×C1912yes—
195C2×C4⋊C8C22×C1911yescharacteristic
196C2×C4⋊C8C22×C1911yescharacteristic
197C2×#102C22×C1912yes—
198C2×#102C22×C1912yes—
199C2×#102C22×C1912yes—
200#390C22×C1912yes—
201#390C22×C1912yes—
202#389C22×C1912yes—
203#389C22×C1912yes—
204#388—22no—
205#388—22no—
206C4×C4⋊C4C22×C1912yes—
207C4×C22⋊C4—22no—
208C43C22×C1911yescharacteristic
209#340C22×C1911yescharacteristic
210#340C22×C1912yes—
211#340C22×C1911yescharacteristic
212#340C22×C1912yes—
213#336C22×C1912yes—
214#336C22×C1912yes—
215C2×C19—84no—
216C2×C19#260911yescharacteristic
217C2×C19#310612yes—
218C2×C19#311412yes—
219C2×C19#325011yescharacteristic
220C2×C19#325311yescharacteristic
221C22×D4C23×C1912yes—
222C23×C4—22no—
223C2×D8—24no—
224C2×D8—41no—
225C22×C8C23×C1911yescharacteristic
226C22×C8C23×C1912yes—
227C22×C8C23×C1911yescharacteristic
228C4×D4—24no—
229C4×D4—24no—
230#117—48no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4C23×C1912yes—
234C2×C4⋊C4C23×C1912yes—
235C2×C4⋊C4C23×C1912yes—
236C2×C22⋊C4—22no—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—22no—
239C2×C22⋊C4—22no—
240C2×C22⋊C4—22no—
241C2×C42—22no—
242C2×C42D4×C1912yes—
243C2×C42D4×C1911yescharacteristic
244C2×C42D4×C1911yescharacteristic
245C2×C42C23×C1912yes—
246C2×C42C23×C1911yescharacteristic
247#107—41no—
248#106—24no—
249C4⋊C8—41no—
250C4⋊C8—41no—
251#102—24no—
252#102—24no—
253#102—42no—
254#95—22no—
255#95—22no—
256#95—22no—
257C19#2953311yescharacteristic, direct product factor, Sylow
258C24—22no—
259C2×D4—22no—
260C2×D4—22no—
261C2×D4—22no—
262C2×D4—22no—
263C2×D4—22no—
264C2×D4#41×C1914yes—
265C22×C4—28no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—44no—
270C22×C4—44no—
271C22×C4C2×D4×C1912yes—
272C22×C4C2×D4×C1911yescharacteristic
273C22×C4C2×D4×C1911yescharacteristic
274C22×C4C2×D4×C1912yes—
275C22×C4C24×C1911yescharacteristic
276D8—44no—
277C2×C8—22no—
278C2×C8—22no—
279C2×C8—22no—
280C2×C8—22no—
281C2×C8—22no—
282C2×C8—21no—
283C2×C8—21no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4—22no—
289C4⋊C4—44no—
290C4⋊C4—44no—
291C4⋊C4#41×C1914yes—
292C22⋊C4—28no—
293C22⋊C4—44no—
294C22⋊C4—44no—
295C22⋊C4—44no—
296C22⋊C4—44no—
297C42—22no—
298C42—24no—
299C42—22no—
300C42—22no—
301C42—21no—
302C42—21no—
303C42—41no—
304C42—44no—
305C23—24no—
306C23—42no—
307C23—42no—
308C23—42no—
309C23—42no—
310C23—42no—
311C23—42no—
312C23C22×D4×C1911yescharacteristic
313D4—24no—
314D4—24no—
315D4—42no—
316D4—42no—
317C2×C4—22no—
318C2×C4—21no—
319C2×C4—22no—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—24no—
323C2×C4—21no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—416no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4C19×#13512yes—
337C2×C4C19×AGL(1,ℤ/8)14yes—
338C2×C4C2×#41×C1912yes—
339C2×C4C2×#41×C1912yes—
340C2×C4C19×H(5,𝔽2)11yescharacteristic
341C2×C4C19×2−1+411yescharacteristic
342C8—41no—
343C8—41no—
344C8—42no—
345C22—44no—
346C22—44no—
347C22—44no—
348C22—82no—
349C22—82no—
350C22—82no—
351C22—82no—
352C22C19×#52512yes—
353C22C19×#53711yescharacteristic
354C22C2×C19×#13511yescharacteristic
355C22C2×C19×AGL(1,ℤ/8)12yes—
356C22C19×#57511yescharacteristic
357C4—22no—
358C4—24no—
359C4—41no—
360C4—42no—
361C4—44no—
362C4—82no—
363C4—82no—
364C4C19×#55111yescharacteristic
365C4C19×#55212yes—
366C4C19×#55511yescharacteristic
367C2—84no—
368C2C19×#260911yescharacteristic
369C2C19×#310612yes—
370C2C19×#311412yes—
371C2C19×#325011yescharacteristic
372C2C19×#325311yescharacteristic
subgroupG/H
center, socleC23×C19C22×D4
commutator, Frattini, cosocleC22×C4C24×C19
prime radicalC22×D8×C19C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C19 ◁ C43×C19 ◁ G

Complements

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

NH ≅ G/Ntype
1. C19×#2293C2semidirect
2. C19×#2087C2semidirect
3. C19×#2065C2semidirect
5. C19×#1925C2semidirect
6. C19×#1920C2semidirect
8. C19×#1864C2semidirect
9. C19×#1831C2semidirect
118. #29533C19direct (N × H)
159. #2293C2×C19semidirect
160. #2087C2×C19semidirect
161. #2065C2×C19semidirect
163. #1925C2×C19semidirect
164. #1920C2×C19semidirect
166. #1864C2×C19semidirect
167. #1831C2×C19semidirect
257. C19#29533direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#22932
C19×#20872
C19×#20652
C19×#20542
C19×#19252
C19×#19202
C19×#18792
C19×#18642
C19×#18312
#2953319