Finite Group Databasebeta

← C19×#8525 #18014484

Subgroups — C19×#8525 #18014484

Order 4864.

694 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C19×#544C211yesmaximal, characteristic
2C19×#1556C212yesmaximal, complemented
3C19×#1534C212yesmaximal, complemented
4C19×#1464C211yesmaximal, characteristic
5C19×#1464C211yesmaximal, characteristic
6C19×#544—24no—
7C19×#544—24no—
8C2×C19×C4⋊Q8—21no—
9C2×C19×C4⋊Q8C411yescharacteristic
10C2×C19×C4⋊Q8C2211yescharacteristic
11C2×C19×#125—21no—
12C2×C19×#125C411yescharacteristic
13C2×C19×#125C2211yescharacteristic
14C2×C19×C22⋊Q8—21no—
15C2×C19×C22⋊Q8—21no—
16C2×C19×#117C411yescharacteristic
17C2×C19×#117C2211yescharacteristic
18C22×C4⋊C4×C19C411yescharacteristic
19C19×#432C2212yes—
20C19×#432C2212yes—
21C19×#332—24no—
22C19×#330—24no—
23C19×#324—21no—
24C19×#324—21no—
25C19×#323—21no—
26C19×#323—21no—
27C22×Q8×C19—21no—
28C22×Q8×C19—21no—
29C23×C4×C19—21no—
30C23×C4×C19C2×C411yescharacteristic
31C19×C4⋊Q8—28no—
32C19×C4⋊Q8—22no—
33C19×C4⋊Q8—22no—
34C19×C4⋊Q8—22no—
35C19×C4⋊Q8D414yes—
36C19×#125—28no—
37C19×#125—22no—
38C19×#125—22no—
39C19×#125—22no—
40C19×#125D414yes—
41C19×C22⋊Q8—28no—
42C19×C22⋊Q8—28no—
43C19×#117—22no—
44C19×#117—22no—
45C19×#117—22no—
46C19×#117—22no—
47C2×C4⋊C4×C19—21no—
48C2×C4⋊C4×C19—21no—
49C2×C4⋊C4×C19—21no—
50C2×C4⋊C4×C19—21no—
51C2×C4⋊C4×C19—21no—
52C2×C4⋊C4×C19—21no—
53C2×C4⋊C4×C19—21no—
54C2×C4⋊C4×C19—22no—
55C2×C4⋊C4×C19—22no—
56C2×C4⋊C4×C19C2×C411yescharacteristic
57C2×C4⋊C4×C19C2×C411yescharacteristic
58C2×C4⋊C4×C19C2×C411yescharacteristic
59C2×C4⋊C4×C19C2×C411yescharacteristic
60C2×C4⋊C4×C19D411yescharacteristic
61C2×C4⋊C4×C19D411yescharacteristic
62C2×C22⋊C4×C19—21no—
63C2×C22⋊C4×C19D411yescharacteristic
64C2×C22⋊C4×C19D411yescharacteristic
65C2×C42×C19—21no—
66C2×C42×C19C2×C411yescharacteristic
67C2×C42×C19C2311yescharacteristic
68C19×C4⋊C8—22no—
69C19×C4⋊C8—22no—
70C19×C22⋊C8—22no—
71C19×C22⋊C8—22no—
72C19×#97—22no—
73C19×#97—22no—
74C24×C19C22⋊C411yescharacteristic
75C2×Q8×C19—24no—
76C2×Q8×C19—24no—
77C2×Q8×C19—82no—
78C2×Q8×C19—82no—
79C22×C4×C19—22no—
80C22×C4×C19—22no—
81C22×C4×C19—21no—
82C22×C4×C19—21no—
83C22×C4×C19—21no—
84C22×C4×C19—21no—
85C22×C4×C19—21no—
86C22×C4×C19—21no—
87C22×C4×C19—24no—
88C22×C4×C19—82no—
89C22×C4×C19C22⋊C411yescharacteristic
90C22×C4×C19C22⋊C411yescharacteristic
91C22×C4×C19C22⋊C411yescharacteristic
92C22×C4×C19C22×C411yescharacteristic
93C22×C4×C19C2×D411yescharacteristic
94C22×C4×C19C2×D411yescharacteristic
95C2×C8×C19—42no—
96C2×C8×C19—42no—
97C4⋊C4×C19—24no—
98C4⋊C4×C19—24no—
99C4⋊C4×C19—24no—
100C4⋊C4×C19—24no—
101C4⋊C4×C19—21no—
102C4⋊C4×C19—21no—
103C4⋊C4×C19—21no—
104C4⋊C4×C19—21no—
105C4⋊C4×C19—24no—
106C4⋊C4×C19—24no—
107C4⋊C4×C19—24no—
108C4⋊C4×C19—22no—
109C4⋊C4×C19—22no—
110C4⋊C4×C19C22⋊C412yes—
111C4⋊C4×C19C22⋊C412yes—
112C4⋊C4×C19C22⋊C412yes—
113C4⋊C4×C19C22⋊C412yes—
114C22⋊C4×C19—24no—
115C22⋊C4×C19—22no—
116C22⋊C4×C19—22no—
117C42×C19—24no—
118C42×C19—21no—
119C42×C19—21no—
120C42×C19C2×D412yes—
121C42×C19C2×D412yes—
122#8525C1911yesmaximal, characteristic, direct product factor, Sylow
123C23×C19—21no—
124C23×C19—21no—
125C23×C19—41no—
126C23×C19—41no—
127C23×C19#10112yes—
128C23×C19C2×C22⋊C411yescharacteristic
129Q8×C19—84no—
130Q8×C19—84no—
131C2×C4×C19—24no—
132C2×C4×C19—24no—
133C2×C4×C19—21no—
134C2×C4×C19—21no—
135C2×C4×C19—21no—
136C2×C4×C19—21no—
137C2×C4×C19—21no—
138C2×C4×C19—22no—
139C2×C4×C19—21no—
140C2×C4×C19—22no—
141C2×C4×C19—22no—
142C2×C4×C19—22no—
143C2×C4×C19—41no—
144C2×C4×C19—41no—
145C2×C4×C19—42no—
146C2×C4×C19—42no—
147C2×C4×C19—42no—
148C2×C4×C19—42no—
149C2×C4×C19—41no—
150C2×C4×C19—41no—
151C2×C4×C19—84no—
152C2×C4×C19#10112yes—
153C2×C4×C19C2×C22⋊C411yescharacteristic
154C2×C4×C19C2×C22⋊C411yescharacteristic
155C2×C4×C19#12012yes—
156C2×C4×C19#12012yes—
157C8×C19—82no—
158C8×C19—82no—
159C2×#544C2×C1911yescharacteristic
160#1556C2×C1912yescomplemented
161#1534C2×C1912yescomplemented
162#1464C2×C1911yescharacteristic
163#1464C2×C1911yescharacteristic
164C22×C19—21no—
165C22×C19—21no—
166C22×C19—22no—
167C22×C19—42no—
168C22×C19—42no—
169C22×C19—41no—
170C22×C19—41no—
171C22×C19#37911yescharacteristic
172C22×C19C2×#10111yescharacteristic
173C22×C19C2×#10111yescharacteristic
174C4×C19—22no—
175C4×C19—22no—
176C4×C19—22no—
177C4×C19—21no—
178C4×C19—21no—
179C4×C19—42no—
180C4×C19—42no—
181C4×C19—42no—
182C4×C19—41no—
183C4×C19—41no—
184C4×C19—42no—
185#544—24no—
186#544—24no—
187C2×C4⋊Q8—21no—
188C2×C4⋊Q8C4×C1911yescharacteristic
189C2×C4⋊Q8C22×C1911yescharacteristic
190C2×#125—21no—
191C2×#125C4×C1911yescharacteristic
192C2×#125C22×C1911yescharacteristic
193C2×C22⋊Q8—21no—
194C2×C22⋊Q8—21no—
195C2×#117C4×C1911yescharacteristic
196C2×#117C22×C1911yescharacteristic
197C22×C4⋊C4C4×C1911yescharacteristic
198#432C22×C1912yes—
199#432C22×C1912yes—
200#332—24no—
201#330—24no—
202#324—21no—
203#324—21no—
204#323—21no—
205#323—21no—
206C2×C19—21no—
207C2×C19—21no—
208C2×C19—42no—
209C2×C19#178411yescharacteristic
210C2×C19#179511yescharacteristic
211C2×C19#179611yescharacteristic
212C22×Q8—21no—
213C22×Q8—21no—
214C23×C4—21no—
215C23×C4C2×C4×C1911yescharacteristic
216C4⋊Q8—28no—
217C4⋊Q8—22no—
218C4⋊Q8—22no—
219C4⋊Q8—22no—
220C4⋊Q8D4×C1914yes—
221#125—28no—
222#125—22no—
223#125—22no—
224#125—22no—
225#125D4×C1914yes—
226C22⋊Q8—28no—
227C22⋊Q8—28no—
228#117—22no—
229#117—22no—
230#117—22no—
231#117—22no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4C2×C4×C1911yescharacteristic
242C2×C4⋊C4C2×C4×C1911yescharacteristic
243C2×C4⋊C4C2×C4×C1911yescharacteristic
244C2×C4⋊C4C2×C4×C1911yescharacteristic
245C2×C4⋊C4D4×C1911yescharacteristic
246C2×C4⋊C4D4×C1911yescharacteristic
247C2×C22⋊C4—21no—
248C2×C22⋊C4D4×C1911yescharacteristic
249C2×C22⋊C4D4×C1911yescharacteristic
250C2×C42—21no—
251C2×C42C2×C4×C1911yescharacteristic
252C2×C42C23×C1911yescharacteristic
253C4⋊C8—22no—
254C4⋊C8—22no—
255C22⋊C8—22no—
256C22⋊C8—22no—
257#97—22no—
258#97—22no—
259C19#852511yescharacteristic, direct product factor, Sylow
260C24C22⋊C4×C1911yescharacteristic
261C2×Q8—24no—
262C2×Q8—24no—
263C2×Q8—82no—
264C2×Q8—82no—
265C22×C4—22no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—22no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—24no—
274C22×C4—82no—
275C22×C4C22⋊C4×C1911yescharacteristic
276C22×C4C22⋊C4×C1911yescharacteristic
277C22×C4C22⋊C4×C1911yescharacteristic
278C22×C4C22×C4×C1911yescharacteristic
279C22×C4C2×D4×C1911yescharacteristic
280C22×C4C2×D4×C1911yescharacteristic
281C2×C8—42no—
282C2×C8—42no—
283C4⋊C4—24no—
284C4⋊C4—24no—
285C4⋊C4—24no—
286C4⋊C4—24no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—24no—
292C4⋊C4—24no—
293C4⋊C4—24no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4C22⋊C4×C1912yes—
297C4⋊C4C22⋊C4×C1912yes—
298C4⋊C4C22⋊C4×C1912yes—
299C4⋊C4C22⋊C4×C1912yes—
300C22⋊C4—24no—
301C22⋊C4—22no—
302C22⋊C4—22no—
303C42—24no—
304C42—21no—
305C42—21no—
306C42C2×D4×C1912yes—
307C42C2×D4×C1912yes—
308C23—21no—
309C23—21no—
310C23—41no—
311C23—41no—
312C23C19×#10112yes—
313C23C2×C22⋊C4×C1911yescharacteristic
314Q8—84no—
315Q8—84no—
316C2×C4—24no—
317C2×C4—24no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—22no—
324C2×C4—21no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—84no—
337C2×C4C19×#10112yes—
338C2×C4C2×C22⋊C4×C1911yescharacteristic
339C2×C4C2×C22⋊C4×C1911yescharacteristic
340C2×C4C19×#12012yes—
341C2×C4C19×#12012yes—
342C8—82no—
343C8—82no—
344C22—21no—
345C22—21no—
346C22—22no—
347C22—42no—
348C22—42no—
349C22—41no—
350C22—41no—
351C22C19×#37911yescharacteristic
352C22C2×C19×#10111yescharacteristic
353C22C2×C19×#10111yescharacteristic
354C4—21no—
355C4—21no—
356C4—22no—
357C4—22no—
358C4—22no—
359C4—42no—
360C4—42no—
361C4—42no—
362C4—41no—
363C4—42no—
364C4—41no—
365C2—21no—
366C2—21no—
367C2—42no—
368C2C19×#178411yescharacteristic
369C2C19×#179511yescharacteristic
370C2C19×#179611yescharacteristic
subgroupG/H
center, socleC22×C19#379
commutatorC22×C4C22×C4×C19
Frattini, cosocleC2×C42C23×C19
prime radicalC24×C19C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G

Complements

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

NH ≅ G/Ntype
2. C19×#1556C2semidirect
3. C19×#1534C2semidirect
122. #8525C19direct (N × H)
160. #1556C2×C19semidirect
161. #1534C2×C19semidirect
259. C19#8525direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C19×#5442
C19×#15562
C19×#15342
C19×#14642
#852519