Finite Group Databasebeta

← C19×#10203 #18016162

Subgroups — C19×#10203 #18016162

Order 4864.

490 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C19×#3249C211yesmaximal, characteristic
2C19×#3230C211yesmaximal, characteristic
3C19×#3165C211yesmaximal, characteristic
4C19×#1986C211yesmaximal, characteristic
5C19×#1981C211yesmaximal, characteristic
6C19×#1503C211yesmaximal, characteristic
7C19×#1283C211yesmaximal, characteristic
8C19×#533C2211yescharacteristic
9C19×#533C2211yescharacteristic
10C2×C19×C4⋊Q8C2211yescharacteristic
11C19×#501—22no—
12C19×#500—21no—
13C19×#500—21no—
14C19×#498—21no—
15C19×#487—21no—
16C19×#484—22no—
17C19×#477—22no—
18C19×#477—21no—
19C19×#477—21no—
20C19×#467—22no—
21C19×#462—21no—
22C19×#462—21no—
23C19×#431C2211yescharacteristic
24C19×#428—22no—
25C2×C19×C4⋊C8C2211yescharacteristic
26C2×C19×#103—22no—
27C4×M16×C19C2211yescharacteristic
28C4×C4⋊C4×C19C2211yescharacteristic
29C19×#339—22no—
30C19×#328—22no—
31C22×Q8×C19—21no—
32C2×Q16×C19—22no—
33C2×M16×C19D412yes—
34C22×C8×C19D412yes—
35C19×C4⋊Q8—21no—
36C19×C4⋊Q8—21no—
37C19×C4⋊Q8—21no—
38C19×C4⋊Q8D411yescharacteristic
39C19×C4⋊Q8D411yescharacteristic
40C19×C4⋊Q8D411yescharacteristic
41C19×C4⋊Q8D411yescharacteristic
42C19×C4⋊Q8D412yes—
43C19×#125—21no—
44C19×#125—21no—
45C19×C22⋊Q8—21no—
46C19×C22⋊Q8—21no—
47C19×C22⋊Q8—21no—
48C19×C22⋊Q8—21no—
49C4×Q8×C19—21no—
50C4×Q8×C19—21no—
51C4×Q8×C19—21no—
52C4×Q8×C19—21no—
53C19×#117—21no—
54C19×#117—21no—
55C2×C4⋊C4×C19—21no—
56C2×C4⋊C4×C19—21no—
57C2×C4⋊C4×C19—21no—
58C2×C42×C19—21no—
59C2×C42×C19C2311yescharacteristic
60C19×#107—24no—
61C19×#107—22no—
62C19×#107—24no—
63C19×#106—24no—
64C19×C4⋊C8—21no—
65C19×C4⋊C8—21no—
66C19×C4⋊C8—21no—
67C19×#103—22no—
68C19×#103—22no—
69C19×#103—24no—
70C19×#103—44no—
71C19×C22⋊C8D412yes—
72C19×#97—21no—
73C4×C8×C19—21no—
74C4×C8×C19—21no—
75C19×#95—21no—
76C2×Q8×C19—21no—
77C2×Q8×C19—21no—
78C2×Q8×C19—21no—
79C2×Q8×C19—22no—
80C2×Q8×C19—21no—
81C2×Q8×C19—42no—
82C2×Q8×C19—42no—
83C2×Q8×C19—41no—
84C22×C4×C19—41no—
85C22×C4×C19—41no—
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19C2×D411yescharacteristic
88C22×C4×C19C2×D411yescharacteristic
89Q16×C19—82no—
90M16×C19—22no—
91M16×C19Q1614yescomplemented
92C2×C8×C19—22no—
93C2×C8×C19—22no—
94C2×C8×C19—22no—
95C2×C8×C19—42no—
96C4⋊C4×C19—22no—
97C4⋊C4×C19—22no—
98C4⋊C4×C19—22no—
99C4⋊C4×C19—21no—
100C4⋊C4×C19—21no—
101C4⋊C4×C19—21no—
102C4⋊C4×C19—21no—
103C4⋊C4×C19—21no—
104C4⋊C4×C19—21no—
105C4⋊C4×C19—21no—
106C4⋊C4×C19—21no—
107C4⋊C4×C19—41no—
108C4⋊C4×C19—41no—
109C4⋊C4×C19—41no—
110C4⋊C4×C19—41no—
111C4⋊C4×C19—41no—
112C4⋊C4×C19—41no—
113C4⋊C4×C19—41no—
114C22⋊C4×C19—41no—
115C22⋊C4×C19—41no—
116C42×C19—41no—
117C42×C19—41no—
118C42×C19—42no—
119C42×C19C2×D411yescharacteristic
120C42×C19C2×D411yescharacteristic
121C42×C19C2×D411yescharacteristic
122C42×C19#4111yescharacteristic
123#10203C1911yesmaximal, characteristic, direct product factor, Sylow
124C23×C19#12711yescharacteristic
125Q8×C19—42no—
126Q8×C19—44no—
127Q8×C19—41no—
128Q8×C19—41no—
129Q8×C19—41no—
130Q8×C19—41no—
131Q8×C19—81no—
132Q8×C19—81no—
133Q8×C19—81no—
134C2×C4×C19—21no—
135C2×C4×C19—21no—
136C2×C4×C19—41no—
137C2×C4×C19—42no—
138C2×C4×C19—41no—
139C2×C4×C19—41no—
140C2×C4×C19—41no—
141C2×C4×C19—41no—
142C2×C4×C19—42no—
143C2×C4×C19—81no—
144C2×C4×C19—82no—
145C2×C4×C19—81no—
146C2×C4×C19#12011yescharacteristic
147C2×C4×C19#12011yescharacteristic
148C2×C4×C19#12011yescharacteristic
149C2×C4×C19#12111yescharacteristic
150C2×C4×C19#12111yescharacteristic
151C2×C4×C19#12111yescharacteristic
152C2×C4×C19C2×Q1612yes—
153C2×C4×C19#13712yes—
154C8×C19—24no—
155C8×C19—42no—
156C8×C19—42no—
157#3249C2×C1911yescharacteristic
158#3230C2×C1911yescharacteristic
159#3165C2×C1911yescharacteristic
160#1986C2×C1911yescharacteristic
161#1981C2×C1911yescharacteristic
162#1503C2×C1911yescharacteristic
163#1283C2×C1911yescharacteristic
164C22×C19—21no—
165C22×C19—21no—
166C22×C19#39211yescharacteristic
167C22×C19#49411yescharacteristic
168C22×C19#49711yescharacteristic
169C4×C19—21no—
170C4×C19—21no—
171C4×C19—21no—
172C4×C19—82no—
173C4×C19—82no—
174C4×C19—81no—
175C4×C19—81no—
176C4×C19—81no—
177C4×C19—81no—
178C4×C19#45112yes—
179C4×C19#45311yescharacteristic
180C4×C19#45411yescharacteristic
181C4×C19#46212yes—
182#533C22×C1911yescharacteristic
183#533C22×C1911yescharacteristic
184C2×C4⋊Q8C22×C1911yescharacteristic
185#501—22no—
186#500—21no—
187#500—21no—
188#498—21no—
189#487—21no—
190#484—22no—
191#477—22no—
192#477—21no—
193#477—21no—
194#467—22no—
195#462—21no—
196#462—21no—
197#431C22×C1911yescharacteristic
198#428—22no—
199C2×C4⋊C8C22×C1911yescharacteristic
200C2×#103—22no—
201C4×M16C22×C1911yescharacteristic
202C4×C4⋊C4C22×C1911yescharacteristic
203#339—22no—
204#328—22no—
205C2×C19—21no—
206C2×C19—21no—
207C2×C19#200611yescharacteristic
208C2×C19#200911yescharacteristic
209C2×C19#201611yescharacteristic
210C22×Q8—21no—
211C2×Q16—22no—
212C2×M16D4×C1912yes—
213C22×C8D4×C1912yes—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8—21no—
217C4⋊Q8D4×C1912yes—
218C4⋊Q8D4×C1911yescharacteristic
219C4⋊Q8D4×C1911yescharacteristic
220C4⋊Q8D4×C1911yescharacteristic
221C4⋊Q8D4×C1911yescharacteristic
222#125—21no—
223#125—21no—
224C22⋊Q8—21no—
225C22⋊Q8—21no—
226C22⋊Q8—21no—
227C22⋊Q8—21no—
228C4×Q8—21no—
229C4×Q8—21no—
230C4×Q8—21no—
231C4×Q8—21no—
232#117—21no—
233#117—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C42—21no—
238C2×C42C23×C1911yescharacteristic
239#107—24no—
240#107—22no—
241#107—24no—
242#106—24no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246#103—22no—
247#103—22no—
248#103—24no—
249#103—44no—
250C22⋊C8D4×C1912yes—
251#97—21no—
252C4×C8—21no—
253C4×C8—21no—
254#95—21no—
255C19#1020311yescharacteristic, direct product factor, Sylow
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8—21no—
259C2×Q8—22no—
260C2×Q8—21no—
261C2×Q8—42no—
262C2×Q8—42no—
263C2×Q8—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4C2×D4×C1911yescharacteristic
267C22×C4C2×D4×C1911yescharacteristic
268C22×C4C2×D4×C1911yescharacteristic
269Q16—82no—
270M16—22no—
271M16Q16×C1914yescomplemented
272C2×C8—22no—
273C2×C8—22no—
274C2×C8—22no—
275C2×C8—42no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—22no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C42—41no—
297C42—41no—
298C42—42no—
299C42C2×D4×C1911yescharacteristic
300C42C2×D4×C1911yescharacteristic
301C42C2×D4×C1911yescharacteristic
302C42#41×C1911yescharacteristic
303C23C19×#12711yescharacteristic
304Q8—44no—
305Q8—42no—
306Q8—41no—
307Q8—41no—
308Q8—41no—
309Q8—41no—
310Q8—81no—
311Q8—81no—
312Q8—81no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—82no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4C19×#12011yescharacteristic
326C2×C4C19×#12011yescharacteristic
327C2×C4C19×#12011yescharacteristic
328C2×C4C19×#12111yescharacteristic
329C2×C4C19×#12111yescharacteristic
330C2×C4C19×#12111yescharacteristic
331C2×C4C2×Q16×C1912yes—
332C2×C4C19×#13712yes—
333C8—24no—
334C8—42no—
335C8—42no—
336C22—21no—
337C22—21no—
338C22C19×#39211yescharacteristic
339C22C19×#49411yescharacteristic
340C22C19×#49711yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—82no—
345C4—82no—
346C4—81no—
347C4—81no—
348C4—81no—
349C4—81no—
350C4C19×#45112yes—
351C4C19×#45311yescharacteristic
352C4C19×#45411yescharacteristic
353C4C19×#46212yes—
354C2—21no—
355C2—21no—
356C2C19×#200611yescharacteristic
357C2C19×#200911yescharacteristic
358C2C19×#201611yescharacteristic
subgroupG/H
center, socleC22×C19#392
commutator, Frattini, cosocleC2×C42C23×C19
prime radicalC23×C19#127
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G

Complements

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

NH ≅ G/Ntype
91. M16×C19Q16semidirect
123. #10203C19direct (N × H)
255. C19#10203direct (N × H)
271. M16Q16×C19semidirect

Maximal subgroups

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

subgroupindex
C19×#32492
C19×#32302
C19×#31652
C19×#19862
C19×#19812
C19×#15032
C19×#12832
#1020319