Finite Group Databasebeta

← C19×#32830 #18038789

Subgroups — C19×#32830 #18038789

Order 4864.

612 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C19×#2647C211yesmaximal, characteristic, complemented
2C19×#2640C211yesmaximal, characteristic
3C19×#2096C211yesmaximal, characteristic, complemented
4C19×#2094C211yesmaximal, characteristic
5C19×#2074C211yesmaximal, characteristic, complemented
6C19×#2073C211yesmaximal, characteristic
7C19×#2066C212yesmaximal, complemented
8C19×#2065C212yesmaximal
9C19×#2058C212yesmaximal, complemented
10C19×#2042C212yesmaximal
11C19×#1832C211yesmaximal, characteristic, complemented
12C2×C19×C4⋊Q8C2211yescharacteristic
13C2×C19×#124C2211yescharacteristic
14C2×C19×#106C2212yes—
15C2×C19×#106C2212yes—
16C2×C19×C4⋊C8C2212yes—
17C2×C19×#103C2212yes—
18C2×C19×#103C2212yes—
19C2×C19×#102C2212yes—
20C2×C19×#102C2212yes—
21C19×#400—22no—
22C19×#398—22no—
23C19×#397—22no—
24C19×#393—22no—
25C19×#391C2211yescharacteristic
26C19×#391C2211yescharacteristic
27C19×#390C2211yescharacteristic
28C19×#390C2211yescharacteristic
29C19×#389C2212yes—
30C19×#389C2212yes—
31C19×#384C2211yescharacteristic
32C19×#382C2211yescharacteristic
33C19×#376C2211yescharacteristic
34C19×#340C2212yes—
35C19×#340C2212yes—
36C19×#336C2212yes—
37C19×#336C2211yescharacteristic
38C19×#336C2211yescharacteristic
39C22×Q8×C19—21no—
40C22×Q8×C19C2311yescharacteristic
41C22×D4×C19C2311yescharacteristic
42C22×C8×C19C2312yes—
43C22×C8×C19C2312yes—
44C19×C4⋊Q8—42no—
45C19×#124—42no—
46C2×C4⋊C4×C19—21no—
47C2×C4⋊C4×C19—22no—
48C2×C4⋊C4×C19—22no—
49C2×C4⋊C4×C19—22no—
50C2×C4⋊C4×C19C2312yes—
51C2×C4⋊C4×C19C2311yescharacteristic
52C2×C4⋊C4×C19C2311yescharacteristic
53C2×C4⋊C4×C19C2312yes—
54C2×C22⋊C4×C19—21no—
55C2×C22⋊C4×C19—21no—
56C2×C22⋊C4×C19—22no—
57C2×C22⋊C4×C19—22no—
58C2×C42×C19C2311yescharacteristic
59C2×C42×C19C2311yescharacteristic
60C2×C42×C19C2311yescharacteristic
61C19×#106—42no—
62C19×#106—42no—
63C19×C4⋊C8—42no—
64C19×#103—42no—
65C19×#103—42no—
66C19×#102—42no—
67C19×#102—42no—
68C19×#95—22no—
69C19×#95—22no—
70C19×#95—22no—
71C19×#95—22no—
72C19×#95—22no—
73C19×#95D412yes—
74C19×#95D412yes—
75C24×C19—21no—
76C2×Q8×C19—22no—
77C2×Q8×C19—21no—
78C2×Q8×C19—22no—
79C2×Q8×C19—21no—
80C2×Q8×C19—42no—
81C2×Q8×C19—82no—
82C2×D4×C19—22no—
83C2×D4×C19—21no—
84C2×D4×C19—22no—
85C2×D4×C19—21no—
86C22×C4×C19—21no—
87C22×C4×C19—21no—
88C22×C4×C19—21no—
89C22×C4×C19—22no—
90C22×C4×C19—22no—
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19C2×D412yes—
93C22×C4×C19C2×D412yes—
94C22×C4×C19C2×D411yescharacteristic
95C22×C4×C19C2411yescharacteristic
96C2×C8×C19—22no—
97C2×C8×C19—22no—
98C2×C8×C19—22no—
99C2×C8×C19—22no—
100C2×C8×C19—22no—
101C2×C8×C19—22no—
102C4⋊C4×C19—22no—
103C4⋊C4×C19—22no—
104C4⋊C4×C19—22no—
105C4⋊C4×C19—22no—
106C4⋊C4×C19—22no—
107C4⋊C4×C19—22no—
108C4⋊C4×C19—42no—
109C4⋊C4×C19—82no—
110C4⋊C4×C19—82no—
111C4⋊C4×C19—82no—
112C22⋊C4×C19—42no—
113C22⋊C4×C19—42no—
114C22⋊C4×C19—82no—
115C22⋊C4×C19—82no—
116C42×C19—22no—
117C42×C19—21no—
118C42×C19—22no—
119C42×C19—21no—
120#32830C1911yesmaximal, characteristic, direct product factor, Sylow
121C23×C19—41no—
122C23×C19—41no—
123C23×C19—41no—
124C23×C19—42no—
125C23×C19—42no—
126C23×C19C22×D411yescharacteristic
127Q8×C19—42no—
128Q8×C19—42no—
129Q8×C19—84no—
130D4×C19—42no—
131D4×C19—42no—
132C2×C4×C19—21no—
133C2×C4×C19—21no—
134C2×C4×C19—22no—
135C2×C4×C19—22no—
136C2×C4×C19—22no—
137C2×C4×C19—22no—
138C2×C4×C19—22no—
139C2×C4×C19—22no—
140C2×C4×C19—22no—
141C2×C4×C19—22no—
142C2×C4×C19—41no—
143C2×C4×C19—41no—
144C2×C4×C19—41no—
145C2×C4×C19—42no—
146C2×C4×C19—41no—
147C2×C4×C19—42no—
148C2×C4×C19—41no—
149C2×C4×C19—42no—
150C2×C4×C19—42no—
151C2×C4×C19—42no—
152C2×C4×C19—42no—
153C2×C4×C19—42no—
154C2×C4×C19—42no—
155C2×C4×C19H(5,𝔽2)11yescharacteristic
156C2×C4×C19H(5,𝔽2)12yes—
157C2×C4×C192−1+412yes—
158C2×C4×C192−1+411yescharacteristic
159C8×C19—42no—
160C8×C19—42no—
161#2647C2×C1911yescharacteristic, complemented
162#2640C2×C1911yescharacteristic
163#2096C2×C1911yescharacteristic, complemented
164#2094C2×C1911yescharacteristic
165#2074C2×C1911yescharacteristic, complemented
166#2073C2×C1911yescharacteristic
167#2066C2×C1912yescomplemented
168#2065C2×C1912yes—
169#2058C2×C1912yescomplemented
170#2042C2×C1912yes—
171#1832C2×C1911yescharacteristic, complemented
172C22×C19—81no—
173C22×C19—81no—
174C22×C19—81no—
175C22×C19—82no—
176C22×C19—82no—
177C22×C19#53511yescharacteristic
178C22×C19#53611yescharacteristic
179C22×C19#53711yescharacteristic
180C22×C19#57712yes—
181C22×C19#57712yes—
182C4×C19—41no—
183C4×C19—41no—
184C4×C19—42no—
185C4×C19—42no—
186C4×C19—81no—
187C4×C19—82no—
188C4×C19—81no—
189C4×C19—81no—
190C4×C19—82no—
191C4×C19#56212yes—
192C4×C19#56312yes—
193C2×C4⋊Q8C22×C1911yescharacteristic
194C2×#124C22×C1911yescharacteristic
195C2×#106C22×C1912yes—
196C2×#106C22×C1912yes—
197C2×C4⋊C8C22×C1912yes—
198C2×#103C22×C1912yes—
199C2×#103C22×C1912yes—
200C2×#102C22×C1912yes—
201C2×#102C22×C1912yes—
202#400—22no—
203#398—22no—
204#397—22no—
205#393—22no—
206#391C22×C1911yescharacteristic
207#391C22×C1911yescharacteristic
208#390C22×C1911yescharacteristic
209#390C22×C1911yescharacteristic
210#389C22×C1912yes—
211#389C22×C1912yes—
212#384C22×C1911yescharacteristic
213#382C22×C1911yescharacteristic
214#376C22×C1911yescharacteristic
215#340C22×C1912yes—
216#340C22×C1912yes—
217#336C22×C1912yes—
218#336C22×C1911yescharacteristic
219#336C22×C1911yescharacteristic
220C2×C19—161no—
221C2×C19#282011yescharacteristic
222C2×C19#322111yescharacteristic
223C2×C19#322211yescharacteristic
224C2×C19#324412yes—
225C2×C19#326312yes—
226C22×Q8—21no—
227C22×Q8C23×C1911yescharacteristic
228C22×D4C23×C1911yescharacteristic
229C22×C8C23×C1912yes—
230C22×C8C23×C1912yes—
231C4⋊Q8—42no—
232#124—42no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4C23×C1911yescharacteristic
238C2×C4⋊C4C23×C1911yescharacteristic
239C2×C4⋊C4C23×C1912yes—
240C2×C4⋊C4C23×C1912yes—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—22no—
244C2×C22⋊C4—22no—
245C2×C42C23×C1911yescharacteristic
246C2×C42C23×C1911yescharacteristic
247C2×C42C23×C1911yescharacteristic
248#106—42no—
249#106—42no—
250C4⋊C8—42no—
251#103—42no—
252#103—42no—
253#102—42no—
254#102—42no—
255#95—22no—
256#95—22no—
257#95—22no—
258#95—22no—
259#95—22no—
260#95D4×C1912yes—
261#95D4×C1912yes—
262C19#3283011yescharacteristic, direct product factor, Sylow
263C24—21no—
264C2×Q8—21no—
265C2×Q8—22no—
266C2×Q8—22no—
267C2×Q8—21no—
268C2×Q8—42no—
269C2×Q8—82no—
270C2×D4—21no—
271C2×D4—22no—
272C2×D4—22no—
273C2×D4—21no—
274C22×C4—21no—
275C22×C4—22no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—22no—
279C22×C4C2×D4×C1912yes—
280C22×C4C2×D4×C1912yes—
281C22×C4C2×D4×C1911yescharacteristic
282C22×C4C2×D4×C1911yescharacteristic
283C22×C4C24×C1911yescharacteristic
284C2×C8—22no—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—22no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4—22no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—42no—
297C4⋊C4—82no—
298C4⋊C4—82no—
299C4⋊C4—82no—
300C22⋊C4—42no—
301C22⋊C4—42no—
302C22⋊C4—82no—
303C22⋊C4—82no—
304C42—21no—
305C42—22no—
306C42—22no—
307C42—21no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—42no—
312C23—42no—
313C23C22×D4×C1911yescharacteristic
314Q8—42no—
315Q8—42no—
316Q8—84no—
317D4—42no—
318D4—42no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4C19×H(5,𝔽2)11yescharacteristic
343C2×C4C19×H(5,𝔽2)12yes—
344C2×C4C19×2−1+412yes—
345C2×C4C19×2−1+411yescharacteristic
346C8—42no—
347C8—42no—
348C22—81no—
349C22—81no—
350C22—82no—
351C22—82no—
352C22—81no—
353C22C19×#53511yescharacteristic
354C22C19×#53611yescharacteristic
355C22C19×#53711yescharacteristic
356C22C19×#57712yes—
357C22C19×#57712yes—
358C4—41no—
359C4—41no—
360C4—42no—
361C4—42no—
362C4—82no—
363C4—81no—
364C4—81no—
365C4—82no—
366C4—81no—
367C4C19×#56212yes—
368C4C19×#56312yes—
369C2—161no—
370C2C19×#282011yescharacteristic
371C2C19×#322111yescharacteristic
372C2C19×#322211yescharacteristic
373C2C19×#324412yes—
374C2C19×#326312yes—
subgroupG/H
center, socleC23×C19C22×D4
commutator, Frattini, cosocleC22×C4C24×C19
prime radicalC22×D4×C19C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C19 ◁ C19×#376 ◁ G

Complements

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

NH ≅ G/Ntype
1. C19×#2647C2semidirect
3. C19×#2096C2semidirect
5. C19×#2074C2semidirect
7. C19×#2066C2semidirect
9. C19×#2058C2semidirect
11. C19×#1832C2semidirect
120. #32830C19direct (N × H)
161. #2647C2×C19semidirect
163. #2096C2×C19semidirect
165. #2074C2×C19semidirect
167. #2066C2×C19semidirect
169. #2058C2×C19semidirect
171. #1832C2×C19semidirect
262. C19#32830direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#26472
C19×#26402
C19×#20962
C19×#20942
C19×#20742
C19×#20732
C19×#20662
C19×#20652
C19×#20582
C19×#20422
C19×#18322
#3283019