Finite Group Databasebeta

← C19×#9567 #18015526

Subgroups — C19×#9567 #18015526

Order 4864.

382 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C19×#1990C211yesmaximal, characteristic
2C19×#1987C211yesmaximal, characteristic
3C19×#1948C211yesmaximal, characteristic
4C8×C4⋊C4×C19C211yesmaximal, characteristic
5C2×C19×#333C211yesmaximal, characteristic
6C19×#1296C211yesmaximal, characteristic
7C19×#1277C211yesmaximal, characteristic
8C2×C19×C4⋊Q8C2211yescharacteristic
9C2×C19×#106—21no—
10C2×C19×C4⋊C8C2211yescharacteristic
11C2×C19×C4⋊C8C2211yescharacteristic
12C2×C19×C4⋊C8C2211yescharacteristic
13C2×C4×C8×C19—21no—
14C2×C4×C8×C19C2211yescharacteristic
15C19×#384C2211yescharacteristic
16C4×C4⋊C4×C19C2211yescharacteristic
17C19×#340—21no—
18C19×#340—21no—
19C19×#340—21no—
20C19×#340—21no—
21C19×#340—21no—
22C19×#336—21no—
23C19×#333C414yescomplemented
24C22×Q8×C19—21no—
25C22×C8×C19—21no—
26C22×C8×C19—21no—
27C22×C8×C19—21no—
28C22×C8×C19D411yescharacteristic
29C22×C8×C19D411yescharacteristic
30C19×C4⋊Q8—21no—
31C19×C4⋊Q8—21no—
32C19×C4⋊Q8—21no—
33C19×C4⋊Q8C2×C412yes—
34C2×C4⋊C4×C19—21no—
35C2×C4⋊C4×C19—21no—
36C2×C4⋊C4×C19—21no—
37C2×C4⋊C4×C19—21no—
38C2×C4⋊C4×C19—21no—
39C2×C4⋊C4×C19D411yescharacteristic
40C2×C4⋊C4×C19D411yescharacteristic
41C2×C42×C19—21no—
42C2×C42×C19C2311yescharacteristic
43C19×#106—42no—
44C19×C4⋊C8—21no—
45C19×C4⋊C8—21no—
46C19×C4⋊C8—21no—
47C19×C4⋊C8—21no—
48C19×C4⋊C8C2×C412yes—
49C19×C4⋊C8C2×C412yes—
50C4×C8×C19—21no—
51C4×C8×C19—21no—
52C4×C8×C19—42no—
53C19×#95—21no—
54C2×Q8×C19—22no—
55C2×Q8×C19—41no—
56C2×Q8×C19—81no—
57C2×Q8×C19—81no—
58C22×C4×C19—21no—
59C22×C4×C19—21no—
60C22×C4×C19—41no—
61C22×C4×C19—41no—
62C22×C4×C19C2×D411yescharacteristic
63C22×C4×C19C2×D411yescharacteristic
64C22×C4×C19#4111yescharacteristic
65C2×C8×C19—21no—
66C2×C8×C19—21no—
67C2×C8×C19—22no—
68C2×C8×C19—22no—
69C2×C8×C19—21no—
70C2×C8×C19—21no—
71C2×C8×C19—21no—
72C2×C8×C19—41no—
73C2×C8×C19—41no—
74C2×C8×C19—41no—
75C2×C8×C19—41no—
76C2×C8×C19—41no—
77C2×C8×C19—41no—
78C2×C8×C19—41no—
79C2×C8×C19SD1612yes—
80C4⋊C4×C19—21no—
81C4⋊C4×C19—21no—
82C4⋊C4×C19—22no—
83C4⋊C4×C19—22no—
84C4⋊C4×C19—41no—
85C4⋊C4×C19—41no—
86C4⋊C4×C19—41no—
87C4⋊C4×C19—41no—
88C4⋊C4×C19—41no—
89C4⋊C4×C19—41no—
90C4⋊C4×C19—81no—
91C4⋊C4×C19SD1612yes—
92C4⋊C4×C19Q1612yes—
93C42×C19—41no—
94C42×C19—41no—
95C42×C19C22×C411yescharacteristic
96C42×C19#4111yescharacteristic
97C42×C19#4111yescharacteristic
98C42×C19#4111yescharacteristic
99#9567C1911yesmaximal, characteristic, direct product factor, Sylow
100C23×C19#12111yescharacteristic
101Q8×C19—82no—
102Q8×C19—82no—
103C2×C4×C19—21no—
104C2×C4×C19—21no—
105C2×C4×C19—22no—
106C2×C4×C19—22no—
107C2×C4×C19—41no—
108C2×C4×C19—41no—
109C2×C4×C19—41no—
110C2×C4×C19—41no—
111C2×C4×C19—42no—
112C2×C4×C19—81no—
113C2×C4×C19—81no—
114C2×C4×C19—81no—
115C2×C4×C19—81no—
116C2×C4×C19—81no—
117C2×C4×C19#11711yescharacteristic
118C2×C4×C19C4×D411yescharacteristic
119C2×C4×C19C4×D411yescharacteristic
120C2×C4×C19#12311yescharacteristic
121C2×C4×C19#12411yescharacteristic
122C2×C4×C19#12611yescharacteristic
123C2×C4×C19C2×SD1611yescharacteristic
124C2×C4×C19C2×SD1611yescharacteristic
125C2×C4×C19C2×Q1611yescharacteristic
126C2×C4×C19#13511yescharacteristic
127C2×C4×C19#13511yescharacteristic
128C2×C4×C19#13511yescharacteristic
129C2×C4×C19#13711yescharacteristic
130C2×C4×C19#13711yescharacteristic
131C8×C19—22no—
132C8×C19—42no—
133C8×C19—42no—
134C8×C19—41no—
135C8×C19—81no—
136#1990C2×C1911yescharacteristic
137#1987C2×C1911yescharacteristic
138#1948C2×C1911yescharacteristic
139C8×C4⋊C4C2×C1911yescharacteristic
140C2×#333C2×C1911yescharacteristic
141#1296C2×C1911yescharacteristic
142#1277C2×C1911yescharacteristic
143C22×C19#38811yescharacteristic
144C22×C19#46111yescharacteristic
145C22×C19#46411yescharacteristic
146C22×C19#46511yescharacteristic
147C22×C19#46711yescharacteristic
148C22×C19#47111yescharacteristic
149C22×C19#47211yescharacteristic
150C4×C19—21no—
151C4×C19—21no—
152C4×C19—42no—
153C4×C19—42no—
154C4×C19—82no—
155C4×C19—161no—
156C4×C19C4×SD1611yescharacteristic
157C4×C19C4×SD1611yescharacteristic
158C4×C19C4×Q1611yescharacteristic
159C4×C19#44111yescharacteristic
160C4×C19#48311yescharacteristic
161C4×C19#48511yescharacteristic
162C4×C19#48711yescharacteristic
163C4×C19#48811yescharacteristic
164C2×C4⋊Q8C22×C1911yescharacteristic
165C2×#106—21no—
166C2×C4⋊C8C22×C1911yescharacteristic
167C2×C4⋊C8C22×C1911yescharacteristic
168C2×C4⋊C8C22×C1911yescharacteristic
169C2×C4×C8—21no—
170C2×C4×C8C22×C1911yescharacteristic
171#384C22×C1911yescharacteristic
172C4×C4⋊C4C22×C1911yescharacteristic
173#340—21no—
174#340—21no—
175#340—21no—
176#340—21no—
177#340—21no—
178#336—21no—
179#333C4×C1914yescomplemented
180C2×C19#167111yescharacteristic
181C2×C19#167511yescharacteristic
182C2×C19#167811yescharacteristic
183C2×C19#168411yescharacteristic
184C2×C19#192711yescharacteristic
185C2×C19#193111yescharacteristic
186C2×C19#193311yescharacteristic
187C22×Q8—21no—
188C22×C8—21no—
189C22×C8—21no—
190C22×C8—21no—
191C22×C8D4×C1911yescharacteristic
192C22×C8D4×C1911yescharacteristic
193C4⋊Q8—21no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8C2×C4×C1912yes—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4D4×C1911yescharacteristic
203C2×C4⋊C4D4×C1911yescharacteristic
204C2×C42—21no—
205C2×C42C23×C1911yescharacteristic
206#106—42no—
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8C2×C4×C1912yes—
212C4⋊C8C2×C4×C1912yes—
213C4×C8—21no—
214C4×C8—21no—
215C4×C8—42no—
216#95—21no—
217C19#956711yescharacteristic, direct product factor, Sylow
218C2×Q8—22no—
219C2×Q8—41no—
220C2×Q8—81no—
221C2×Q8—81no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4C2×D4×C1911yescharacteristic
227C22×C4C2×D4×C1911yescharacteristic
228C22×C4#41×C1911yescharacteristic
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—22no—
232C2×C8—22no—
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8SD16×C1912yes—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—22no—
247C4⋊C4—22no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—81no—
255C4⋊C4SD16×C1912yes—
256C4⋊C4Q16×C1912yes—
257C42—41no—
258C42—41no—
259C42C22×C4×C1911yescharacteristic
260C42#41×C1911yescharacteristic
261C42#41×C1911yescharacteristic
262C42#41×C1911yescharacteristic
263C23C19×#12111yescharacteristic
264Q8—82no—
265Q8—82no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4C19×#11711yescharacteristic
281C2×C4C4×D4×C1911yescharacteristic
282C2×C4C4×D4×C1911yescharacteristic
283C2×C4C19×#12311yescharacteristic
284C2×C4C19×#12411yescharacteristic
285C2×C4C19×#12611yescharacteristic
286C2×C4C2×SD16×C1911yescharacteristic
287C2×C4C2×SD16×C1911yescharacteristic
288C2×C4C2×Q16×C1911yescharacteristic
289C2×C4C19×#13511yescharacteristic
290C2×C4C19×#13511yescharacteristic
291C2×C4C19×#13511yescharacteristic
292C2×C4C19×#13711yescharacteristic
293C2×C4C19×#13711yescharacteristic
294C8—22no—
295C8—42no—
296C8—42no—
297C8—41no—
298C8—81no—
299C22C19×#38811yescharacteristic
300C22C19×#46111yescharacteristic
301C22C19×#46411yescharacteristic
302C22C19×#46511yescharacteristic
303C22C19×#46711yescharacteristic
304C22C19×#47111yescharacteristic
305C22C19×#47211yescharacteristic
306C4—21no—
307C4—21no—
308C4—42no—
309C4—42no—
310C4—82no—
311C4—161no—
312C4C4×SD16×C1911yescharacteristic
313C4C4×SD16×C1911yescharacteristic
314C4C4×Q16×C1911yescharacteristic
315C4C19×#44111yescharacteristic
316C4C19×#48311yescharacteristic
317C4C19×#48511yescharacteristic
318C4C19×#48711yescharacteristic
319C4C19×#48811yescharacteristic
320C2C19×#167111yescharacteristic
321C2C19×#167511yescharacteristic
322C2C19×#167811yescharacteristic
323C2C19×#168411yescharacteristic
324C2C19×#192711yescharacteristic
325C2C19×#193111yescharacteristic
326C2C19×#193311yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C19#121
commutatorC42C22×C4×C19
Frattini, cosocleC2×C42C23×C19
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C19 ◁ C2×C42×C19 ◁ G

Complements

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

NH ≅ G/Ntype
23. C19×#333C4semidirect
99. #9567C19direct (N × H)
179. #333C4×C19semidirect
217. C19#9567direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#19902
C19×#19872
C19×#19482
C8×C4⋊C4×C192
C2×C19×#3332
C19×#12962
C19×#12772
#956719