Finite Group Databasebeta

← C19×#10199 #18016158

Subgroups — C19×#10199 #18016158

Order 4864.

486 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×#3249C211yesmaximal, characteristic
2C19×#3209C211yesmaximal, characteristic
3C19×#3165C211yesmaximal, characteristic
4C19×#1987C211yesmaximal, characteristic
5C19×#1986C211yesmaximal, characteristic
6C19×#1503C211yesmaximal, characteristic
7C19×#1283C211yesmaximal, characteristic
8C19×#533C2211yescharacteristic
9C19×#533C2211yescharacteristic
10C2×C19×C4⋊Q8C2211yescharacteristic
11C19×#501—22no—
12C19×#500—21no—
13C19×#498—21no—
14C19×#494—21no—
15C19×#487—21no—
16C19×#477—21no—
17C19×#477—21no—
18C19×#467—22no—
19C19×#462—22no—
20C19×#462—21no—
21C19×#462—21no—
22C19×#451—22no—
23C19×#431C2211yescharacteristic
24C19×#428—22no—
25C2×C19×C4⋊C8C2211yescharacteristic
26C4×M16×C19C2211yescharacteristic
27C4×C4⋊C4×C19C2211yescharacteristic
28C19×#340—22no—
29C19×#339—22no—
30C19×#328—22no—
31C22×Q8×C19—21no—
32C2×Q16×C19—24no—
33C2×Q16×C19—22no—
34C2×M16×C19D412yes—
35C22×C8×C19D412yes—
36C19×C4⋊Q8—21no—
37C19×C4⋊Q8—21no—
38C19×C4⋊Q8—21no—
39C19×C4⋊Q8D411yescharacteristic
40C19×C4⋊Q8D411yescharacteristic
41C19×C4⋊Q8D412yes—
42C19×C4⋊Q8D411yescharacteristic
43C19×C4⋊Q8D411yescharacteristic
44C19×#125—21no—
45C19×#125—21no—
46C19×C22⋊Q8—21no—
47C19×C22⋊Q8—21no—
48C19×C22⋊Q8—21no—
49C19×C22⋊Q8—21no—
50C4×Q8×C19—21no—
51C4×Q8×C19—21no—
52C4×Q8×C19—21no—
53C4×Q8×C19—21no—
54C19×#117—21no—
55C19×#117—21no—
56C2×C4⋊C4×C19—21no—
57C2×C4⋊C4×C19—21no—
58C2×C4⋊C4×C19—21no—
59C2×C42×C19—21no—
60C2×C42×C19C2311yescharacteristic
61C19×#107—24no—
62C19×#107—22no—
63C19×#106—24no—
64C19×C4⋊C8—21no—
65C19×C4⋊C8—21no—
66C19×C4⋊C8—21no—
67C19×#103—24no—
68C19×#103—22no—
69C19×#103—22no—
70C19×C22⋊C8D412yes—
71C19×#97—21no—
72C4×C8×C19—21no—
73C4×C8×C19—21no—
74C19×#95—21no—
75C2×Q8×C19—21no—
76C2×Q8×C19—21no—
77C2×Q8×C19—21no—
78C2×Q8×C19—22no—
79C2×Q8×C19—21no—
80C2×Q8×C19—41no—
81C2×Q8×C19—82no—
82C22×C4×C19—41no—
83C22×C4×C19—41no—
84C22×C4×C19C2×D411yescharacteristic
85C22×C4×C19C2×D411yescharacteristic
86C22×C4×C19C2×D411yescharacteristic
87Q16×C19—84no—
88Q16×C19—82no—
89M16×C19—22no—
90M16×C19Q1614yescomplemented
91C2×C8×C19—22no—
92C2×C8×C19—22no—
93C2×C8×C19—22no—
94C2×C8×C19—42no—
95C4⋊C4×C19—22no—
96C4⋊C4×C19—22no—
97C4⋊C4×C19—21no—
98C4⋊C4×C19—21no—
99C4⋊C4×C19—21no—
100C4⋊C4×C19—21no—
101C4⋊C4×C19—21no—
102C4⋊C4×C19—22no—
103C4⋊C4×C19—21no—
104C4⋊C4×C19—21no—
105C4⋊C4×C19—21no—
106C4⋊C4×C19—41no—
107C4⋊C4×C19—41no—
108C4⋊C4×C19—41no—
109C4⋊C4×C19—41no—
110C4⋊C4×C19—41no—
111C4⋊C4×C19—41no—
112C4⋊C4×C19—41no—
113C22⋊C4×C19—41no—
114C22⋊C4×C19—41no—
115C42×C19—41no—
116C42×C19—41no—
117C42×C19—42no—
118C42×C19C2×D411yescharacteristic
119C42×C19C2×D411yescharacteristic
120C42×C19C2×D411yescharacteristic
121C42×C19#4111yescharacteristic
122#10199C1911yesmaximal, characteristic, direct product factor, Sylow
123C23×C19#12711yescharacteristic
124Q8×C19—42no—
125Q8×C19—44no—
126Q8×C19—41no—
127Q8×C19—41no—
128Q8×C19—41no—
129Q8×C19—41no—
130Q8×C19—81no—
131Q8×C19—82no—
132C2×C4×C19—21no—
133C2×C4×C19—21no—
134C2×C4×C19—41no—
135C2×C4×C19—42no—
136C2×C4×C19—41no—
137C2×C4×C19—41no—
138C2×C4×C19—41no—
139C2×C4×C19—41no—
140C2×C4×C19—42no—
141C2×C4×C19—81no—
142C2×C4×C19—82no—
143C2×C4×C19—81no—
144C2×C4×C19#12011yescharacteristic
145C2×C4×C19#12011yescharacteristic
146C2×C4×C19#12011yescharacteristic
147C2×C4×C19#12111yescharacteristic
148C2×C4×C19#12111yescharacteristic
149C2×C4×C19#12111yescharacteristic
150C2×C4×C19C2×Q1612yes—
151C2×C4×C19#13712yes—
152C8×C19—24no—
153C8×C19—42no—
154C8×C19—42no—
155#3249C2×C1911yescharacteristic
156#3209C2×C1911yescharacteristic
157#3165C2×C1911yescharacteristic
158#1987C2×C1911yescharacteristic
159#1986C2×C1911yescharacteristic
160#1503C2×C1911yescharacteristic
161#1283C2×C1911yescharacteristic
162C22×C19—21no—
163C22×C19—21no—
164C22×C19#39211yescharacteristic
165C22×C19#49411yescharacteristic
166C22×C19#49711yescharacteristic
167C4×C19—21no—
168C4×C19—21no—
169C4×C19—21no—
170C4×C19—82no—
171C4×C19—81no—
172C4×C19—81no—
173C4×C19—82no—
174C4×C19—81no—
175C4×C19—81no—
176C4×C19#45112yes—
177C4×C19#45511yescharacteristic
178C4×C19#45611yescharacteristic
179C4×C19#46212yes—
180#533C22×C1911yescharacteristic
181#533C22×C1911yescharacteristic
182C2×C4⋊Q8C22×C1911yescharacteristic
183#501—22no—
184#500—21no—
185#498—21no—
186#494—21no—
187#487—21no—
188#477—21no—
189#477—21no—
190#467—22no—
191#462—22no—
192#462—21no—
193#462—21no—
194#451—22no—
195#431C22×C1911yescharacteristic
196#428—22no—
197C2×C4⋊C8C22×C1911yescharacteristic
198C4×M16C22×C1911yescharacteristic
199C4×C4⋊C4C22×C1911yescharacteristic
200#340—22no—
201#339—22no—
202#328—22no—
203C2×C19—21no—
204C2×C19—21no—
205C2×C19#200711yescharacteristic
206C2×C19#200811yescharacteristic
207C2×C19#201611yescharacteristic
208C22×Q8—21no—
209C2×Q16—24no—
210C2×Q16—22no—
211C2×M16D4×C1912yes—
212C22×C8D4×C1912yes—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8D4×C1912yes—
217C4⋊Q8D4×C1911yescharacteristic
218C4⋊Q8D4×C1911yescharacteristic
219C4⋊Q8D4×C1911yescharacteristic
220C4⋊Q8D4×C1911yescharacteristic
221#125—21no—
222#125—21no—
223C22⋊Q8—21no—
224C22⋊Q8—21no—
225C22⋊Q8—21no—
226C22⋊Q8—21no—
227C4×Q8—21no—
228C4×Q8—21no—
229C4×Q8—21no—
230C4×Q8—21no—
231#117—21no—
232#117—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C42—21no—
237C2×C42C23×C1911yescharacteristic
238#107—24no—
239#107—22no—
240#106—24no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244#103—24no—
245#103—22no—
246#103—22no—
247C22⋊C8D4×C1912yes—
248#97—21no—
249C4×C8—21no—
250C4×C8—21no—
251#95—21no—
252C19#1019911yescharacteristic, direct product factor, Sylow
253C2×Q8—21no—
254C2×Q8—21no—
255C2×Q8—22no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8—41no—
259C2×Q8—82no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4C2×D4×C1911yescharacteristic
263C22×C4C2×D4×C1911yescharacteristic
264C22×C4C2×D4×C1911yescharacteristic
265Q16—84no—
266Q16—82no—
267M16—22no—
268M16Q16×C1914yescomplemented
269C2×C8—22no—
270C2×C8—22no—
271C2×C8—22no—
272C2×C8—42no—
273C4⋊C4—22no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—22no—
279C4⋊C4—21no—
280C4⋊C4—22no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C42—41no—
294C42—41no—
295C42—42no—
296C42C2×D4×C1911yescharacteristic
297C42C2×D4×C1911yescharacteristic
298C42C2×D4×C1911yescharacteristic
299C42#41×C1911yescharacteristic
300C23C19×#12711yescharacteristic
301Q8—42no—
302Q8—44no—
303Q8—41no—
304Q8—41no—
305Q8—41no—
306Q8—41no—
307Q8—81no—
308Q8—82no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—82no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4C19×#12011yescharacteristic
322C2×C4C19×#12011yescharacteristic
323C2×C4C19×#12011yescharacteristic
324C2×C4C19×#12111yescharacteristic
325C2×C4C19×#12111yescharacteristic
326C2×C4C19×#12111yescharacteristic
327C2×C4C2×Q16×C1912yes—
328C2×C4C19×#13712yes—
329C8—24no—
330C8—42no—
331C8—42no—
332C22—21no—
333C22—21no—
334C22C19×#39211yescharacteristic
335C22C19×#49411yescharacteristic
336C22C19×#49711yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—82no—
341C4—81no—
342C4—81no—
343C4—82no—
344C4—81no—
345C4—81no—
346C4C19×#45112yes—
347C4C19×#45511yescharacteristic
348C4C19×#45611yescharacteristic
349C4C19×#46212yes—
350C2—21no—
351C2—21no—
352C2C19×#200711yescharacteristic
353C2C19×#200811yescharacteristic
354C2C19×#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
90. M16×C19Q16semidirect
122. #10199C19direct (N × H)
252. C19#10199direct (N × H)
268. 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×#32092
C19×#31652
C19×#19872
C19×#19862
C19×#15032
C19×#12832
#1019919