Finite Group Databasebeta

← C19×#10795 #18016754

Subgroups — C19×#10795 #18016754

Order 4864.

1062 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×C19C211yesmaximal, characteristic
2C2×C19×#336C212yesmaximal
3C2×C19×#336C212yesmaximal
4C2×C19×#336C212yesmaximal
5C23×C8×C19C2214yes—
6C22×C42×C19C412yes—
7C22×C42×C19C412yes—
8C22×C42×C19C2211yescharacteristic
9C22×C42×C19C2211yescharacteristic
10C22×C42×C19C2211yescharacteristic
11C43×C19—24no—
12C19×#336—24no—
13C19×#336—24no—
14C19×#336C418yescomplemented
15C23×C4×C19C2×C411yescharacteristic
16C23×C4×C19C2×C411yescharacteristic
17C23×C4×C19C2×C412yes—
18C23×C4×C19C2×C412yes—
19C23×C4×C19C2311yescharacteristic
20C22×C8×C19—24no—
21C22×C8×C19—24no—
22C22×C8×C19—24no—
23C22×C8×C19—24no—
24C22×C8×C19—24no—
25C22×C8×C19—24no—
26C22×C8×C19C2×C418yes—
27C2×C42×C19—24no—
28C2×C42×C19—24no—
29C2×C42×C19—24no—
30C2×C42×C19—24no—
31C2×C42×C19—24no—
32C2×C42×C19—22no—
33C2×C42×C19—22no—
34C2×C42×C19—22no—
35C2×C42×C19—22no—
36C2×C42×C19—22no—
37C2×C42×C19—22no—
38C2×C42×C19C818yescomplemented
39C2×C42×C19C2×C414yes—
40C2×C42×C19D414yes—
41C2×C42×C19D412yes—
42C2×C42×C19Q812yes—
43C24×C19C22×C411yescharacteristic
44C22×C4×C19—21no—
45C22×C4×C19—21no—
46C22×C4×C19—22no—
47C22×C4×C19—21no—
48C22×C4×C19—21no—
49C22×C4×C19—22no—
50C22×C4×C19—22no—
51C22×C4×C19—22no—
52C22×C4×C19—22no—
53C22×C4×C19—22no—
54C22×C4×C19—22no—
55C22×C4×C19—22no—
56C22×C4×C19—22no—
57C22×C4×C19—22no—
58C22×C4×C19C4212yes—
59C22×C4×C19C4212yes—
60C22×C4×C19C22⋊C414yes—
61C22×C4×C19C4⋊C414yes—
62C22×C4×C19C2×C814yes—
63C22×C4×C19C2×C814yes—
64C22×C4×C19C2×C814yes—
65C22×C4×C19M1614yes—
66C22×C4×C19M1614yes—
67C22×C4×C19M1614yes—
68C22×C4×C19C22×C412yes—
69C22×C4×C19C2×D411yescharacteristic
70C22×C4×C19C2×D412yes—
71C22×C4×C19C2×Q811yescharacteristic
72C22×C4×C19#4112yes—
73C22×C4×C19#4112yes—
74C22×C4×C19#4112yes—
75C22×C4×C19#4112yes—
76C2×C8×C19—28no—
77C2×C8×C19—28no—
78C2×C8×C19—28no—
79C2×C8×C19—44no—
80C2×C8×C19—44no—
81C2×C8×C19—44no—
82C2×C8×C19—44no—
83C42×C19—216no—
84C42×C19—216no—
85C42×C19—28no—
86C42×C19—24no—
87C42×C19—24no—
88C42×C19—28no—
89#10795C1911yesmaximal, characteristic, direct product factor, Sylow
90C23×C19C2×C4211yescharacteristic
91C23×C19C2×C22⋊C411yescharacteristic
92C23×C19C2×C4⋊C411yescharacteristic
93C23×C19#11711yescharacteristic
94C23×C19#11711yescharacteristic
95C23×C19#11711yescharacteristic
96C23×C19#11711yescharacteristic
97C23×C19C22×C812yes—
98C23×C19C2×M1612yes—
99C23×C19C2×M1612yes—
100C23×C19C2×M1612yes—
101C2×C4×C19—22no—
102C2×C4×C19—22no—
103C2×C4×C19—24no—
104C2×C4×C19—24no—
105C2×C4×C19—22no—
106C2×C4×C19—22no—
107C2×C4×C19—24no—
108C2×C4×C19—24no—
109C2×C4×C19—24no—
110C2×C4×C19—24no—
111C2×C4×C19—24no—
112C2×C4×C19—24no—
113C2×C4×C19—24no—
114C2×C4×C19—24no—
115C2×C4×C19—24no—
116C2×C4×C19—24no—
117C2×C4×C19—24no—
118C2×C4×C19—24no—
119C2×C4×C19—24no—
120C2×C4×C19—24no—
121C2×C4×C19C4×C814yes—
122C2×C4×C19#9714yes—
123C2×C4×C19C22⋊C818yes—
124C2×C4×C19C4⋊C818yes—
125C2×C4×C19#11714yes—
126C2×C4×C19C4×D414yes—
127C2×C4×C19C4×D412yes—
128C2×C4×C19C4×Q812yes—
129C2×C4×C19#12112yes—
130C2×C4×C19C22⋊Q812yes—
131C2×C4×C19#12314yes—
132C2×C4×C19#12412yes—
133C2×C4×C19#12512yes—
134C2×C4×C19#12614yes—
135C8×C19—48no—
136C2×C43C2×C1911yescharacteristic
137C2×#336C2×C1912yes—
138C2×#336C2×C1912yes—
139C2×#336C2×C1912yes—
140C22×C19#37611yescharacteristic
141C22×C19C4×C22⋊C411yescharacteristic
142C22×C19C4×C4⋊C411yescharacteristic
143C22×C19#38011yescharacteristic
144C22×C19#38111yescharacteristic
145C22×C19#38211yescharacteristic
146C22×C19#38311yescharacteristic
147C22×C19C2×C4×C811yescharacteristic
148C22×C19C2×#9711yescharacteristic
149C22×C19C4×M1611yescharacteristic
150C22×C19C4×M1611yescharacteristic
151C22×C19C2×C22⋊C812yes—
152C22×C19#40712yes—
153C22×C19C2×C4⋊C812yes—
154C22×C19#42312yes—
155C22×C19#43112yes—
156C22×C19#43112yes—
157C22×C19#43112yes—
158C22×C19#43112yes—
159C22×C19#43212yes—
160C22×C19#43212yes—
161C22×C19#43212yes—
162C22×C19#43212yes—
163C4×C19—28no—
164C4×C19—28no—
165C4×C19—24no—
166C4×C19—24no—
167C4×C19#38714yes—
168C4×C19#38814yes—
169C23×C8C22×C1914yes—
170C22×C42C4×C1912yes—
171C22×C42C4×C1912yes—
172C22×C42C22×C1911yescharacteristic
173C22×C42C22×C1911yescharacteristic
174C22×C42C22×C1911yescharacteristic
175C43—24no—
176#336—24no—
177#336—24no—
178#336C4×C1918yescomplemented
179C2×C19#143411yescharacteristic
180C2×C19#174411yescharacteristic
181C2×C19#174511yescharacteristic
182C2×C19C4×C22⋊C811yescharacteristic
183C2×C19#174911yescharacteristic
184C2×C19C4×C4⋊C811yescharacteristic
185C2×C19#176711yescharacteristic
186C2×C19#179712yes—
187C2×C19#181712yes—
188C2×C19#183112yes—
189C2×C19#183912yes—
190C23×C4C2×C4×C1911yescharacteristic
191C23×C4C2×C4×C1911yescharacteristic
192C23×C4C2×C4×C1912yes—
193C23×C4C2×C4×C1912yes—
194C23×C4C23×C1911yescharacteristic
195C22×C8—24no—
196C22×C8—24no—
197C22×C8—24no—
198C22×C8—24no—
199C22×C8—24no—
200C22×C8—24no—
201C22×C8C2×C4×C1918yes—
202C2×C42—24no—
203C2×C42—24no—
204C2×C42—24no—
205C2×C42—24no—
206C2×C42—24no—
207C2×C42—22no—
208C2×C42—22no—
209C2×C42—22no—
210C2×C42—22no—
211C2×C42—22no—
212C2×C42—22no—
213C2×C42C8×C1918yescomplemented
214C2×C42C2×C4×C1914yes—
215C2×C42D4×C1914yes—
216C2×C42D4×C1912yes—
217C2×C42Q8×C1912yes—
218C19#1079511yescharacteristic, direct product factor, Sylow
219C24C22×C4×C1911yescharacteristic
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—22no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4C42×C1912yes—
235C22×C4C42×C1912yes—
236C22×C4C22⋊C4×C1914yes—
237C22×C4C4⋊C4×C1914yes—
238C22×C4C2×C8×C1914yes—
239C22×C4C2×C8×C1914yes—
240C22×C4C2×C8×C1914yes—
241C22×C4M16×C1914yes—
242C22×C4M16×C1914yes—
243C22×C4M16×C1914yes—
244C22×C4C22×C4×C1912yes—
245C22×C4C2×D4×C1911yescharacteristic
246C22×C4C2×D4×C1912yes—
247C22×C4C2×Q8×C1911yescharacteristic
248C22×C4#41×C1912yes—
249C22×C4#41×C1912yes—
250C22×C4#41×C1912yes—
251C22×C4#41×C1912yes—
252C2×C8—28no—
253C2×C8—28no—
254C2×C8—28no—
255C2×C8—44no—
256C2×C8—44no—
257C2×C8—44no—
258C2×C8—44no—
259C42—216no—
260C42—28no—
261C42—24no—
262C42—24no—
263C42—28no—
264C42—216no—
265C23C2×C42×C1911yescharacteristic
266C23C2×C22⋊C4×C1911yescharacteristic
267C23C2×C4⋊C4×C1911yescharacteristic
268C23C19×#11711yescharacteristic
269C23C19×#11711yescharacteristic
270C23C19×#11711yescharacteristic
271C23C19×#11711yescharacteristic
272C23C22×C8×C1912yes—
273C23C2×M16×C1912yes—
274C23C2×M16×C1912yes—
275C23C2×M16×C1912yes—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—24no—
279C2×C4—24no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—24no—
283C2×C4—24no—
284C2×C4—24no—
285C2×C4—24no—
286C2×C4—24no—
287C2×C4—24no—
288C2×C4—24no—
289C2×C4—24no—
290C2×C4—24no—
291C2×C4—24no—
292C2×C4—24no—
293C2×C4—24no—
294C2×C4—24no—
295C2×C4—24no—
296C2×C4C4×C8×C1914yes—
297C2×C4C19×#9714yes—
298C2×C4C19×C22⋊C818yes—
299C2×C4C19×C4⋊C818yes—
300C2×C4C19×#11714yes—
301C2×C4C4×D4×C1914yes—
302C2×C4C4×D4×C1912yes—
303C2×C4C4×Q8×C1912yes—
304C2×C4C19×#12112yes—
305C2×C4C19×C22⋊Q812yes—
306C2×C4C19×#12314yes—
307C2×C4C19×#12412yes—
308C2×C4C19×#12512yes—
309C2×C4C19×#12614yes—
310C8—48no—
311C22C19×#37611yescharacteristic
312C22C4×C22⋊C4×C1911yescharacteristic
313C22C4×C4⋊C4×C1911yescharacteristic
314C22C19×#38011yescharacteristic
315C22C19×#38111yescharacteristic
316C22C19×#38211yescharacteristic
317C22C19×#38311yescharacteristic
318C22C2×C4×C8×C1911yescharacteristic
319C22C2×C19×#9711yescharacteristic
320C22C4×M16×C1911yescharacteristic
321C22C4×M16×C1911yescharacteristic
322C22C2×C19×C22⋊C812yes—
323C22C19×#40712yes—
324C22C2×C19×C4⋊C812yes—
325C22C19×#42312yes—
326C22C19×#43112yes—
327C22C19×#43112yes—
328C22C19×#43112yes—
329C22C19×#43112yes—
330C22C19×#43212yes—
331C22C19×#43212yes—
332C22C19×#43212yes—
333C22C19×#43212yes—
334C4—24no—
335C4—24no—
336C4—28no—
337C4—28no—
338C4C19×#38714yes—
339C4C19×#38814yes—
340C2C19×#143411yescharacteristic
341C2C19×#174411yescharacteristic
342C2C19×#174511yescharacteristic
343C2C4×C19×C22⋊C811yescharacteristic
344C2C19×#174911yescharacteristic
345C2C4×C19×C4⋊C811yescharacteristic
346C2C19×#176711yescharacteristic
347C2C19×#179712yes—
348C2C19×#181712yes—
349C2C19×#183112yes—
350C2C19×#183912yes—
subgroupG/H
centerC23×C4×C19C23
commutatorC22C2×C4×C8×C19
Frattini, cosocleC23×C4C23×C19
socle, prime radicalC24×C19C22×C4
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C4×C19 ◁ G

Complements

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

NH ≅ G/Ntype
14. C19×#336C4semidirect
38. C2×C42×C19C8semidirect
89. #10795C19direct (N × H)
178. #336C4×C19semidirect
213. C2×C42C8×C19semidirect
218. C19#10795direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×C192
C2×C19×#3362
#1079519