Finite Group Databasebeta

← C19×#60338 #18066297

Subgroups — C19×#60338 #18066297

Order 4864.

1628 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C19×#3531C211yesmaximal, characteristic
2C19×#2995C212yesmaximal, complemented
3C19×#2994C214yesmaximal, complemented
4C19×#2992C214yesmaximal, complemented
5C19×#2987C211yesmaximal, characteristic, complemented
6C19×#2985C214yesmaximal, complemented
7C19×#2969C214yesmaximal, complemented
8C19×#2967C214yesmaximal, complemented
9C19×#2966C212yesmaximal, complemented
10C19×#2962C214yesmaximal, complemented
11C19×#2960C211yesmaximal, characteristic, complemented
12C19×#564C411yescharacteristic
13C19×#563C414yes—
14C19×#563C412yes—
15C19×#563C414yes—
16C19×#562C414yes—
17C19×#562C411yescharacteristic
18C19×#533C2211yescharacteristic
19C19×#533C2214yes—
20C19×#529C2212yes—
21C19×#529C2214yes—
22C19×#529C2214yes—
23C19×#446C2214yes—
24C19×#446C2212yes—
25C19×#446C2214yes—
26C19×#446C2214yes—
27C19×#446C2214yes—
28C19×#446C2214yes—
29C19×#446C2214yes—
30C19×#446C2214yes—
31C8×Q8×C19C2214yes—
32C8×Q8×C19C2214yes—
33C8×Q8×C19C2212yes—
34C19×#436C2212yes—
35C19×#436C2214yes—
36C19×#436C2214yes—
37C19×#435C2214yes—
38C19×#435C2214yes—
39C19×#435C2214yes—
40C19×#435C2214yes—
41C19×#435C2214yes—
42C8×D4×C19C2212yes—
43C8×D4×C19C2214yes—
44C8×D4×C19C2214yes—
45C19×#433C2214yes—
46C19×#433C2214yes—
47C19×#433C2214yes—
48C19×#433C2214yes—
49C19×#433C2214yes—
50C19×#432C2212yes—
51C19×#432C2214yes—
52C19×#431C2214yes—
53C19×#424C2212yes—
54C19×#424C2214yes—
55C19×#424C2214yes—
56C19×#423C2211yescharacteristic
57C2×C19×C4⋊C8C2214yes—
58C19×#405C2212yes—
59C19×#405C2214yes—
60C19×#405C2214yes—
61C4×M16×C19C2214yes—
62C2×C4×C8×C19C2211yescharacteristic
63C2×M16×C19C2314yes—
64C2×M16×C19C2314yes—
65C2×M16×C19C2312yes—
66C22×C8×C19C2311yescharacteristic
67C22×C8×C19C2311yescharacteristic
68C22×C8×C19C2314yes—
69C22×C8×C19C2314yes—
70C19×C4⋊Q8C2×C412yes—
71C19×C4⋊Q8C2×C414yes—
72C19×C4⋊Q8C2×C414yes—
73C19×#126C2×C414yes—
74C19×#126C2×C414yes—
75C19×#126C2×C414yes—
76C19×#126C2×C414yes—
77C19×#126C2×C414yes—
78C19×#125C2×C412yes—
79C19×#125C2×C414yes—
80C19×#125C2×C414yes—
81C19×#125C2×C411yescharacteristic
82C19×#125C2×C414yes—
83C19×#125C2×C411yescharacteristic
84C19×#125C2×C414yes—
85C19×#124C2×C412yes—
86C19×#124C2×C414yes—
87C19×#124C2×C414yes—
88C19×#123C2×C414yes—
89C19×#123C2×C414yes—
90C19×#123C2×C414yes—
91C19×#123C2×C414yes—
92C19×#123C2×C414yes—
93C19×C22⋊Q8C2×C412yes—
94C19×C22⋊Q8C2×C414yes—
95C19×C22⋊Q8C2×C414yes—
96C19×C22⋊Q8C2×C414yes—
97C19×C22⋊Q8C2×C414yes—
98C19×C22⋊Q8C2×C414yes—
99C19×C22⋊Q8C2×C414yes—
100C19×C22⋊Q8C2×C414yes—
101C19×#121C2×C412yes—
102C19×#121C2×C414yes—
103C19×#121C2×C414yes—
104C4×Q8×C19C2314yes—
105C4×Q8×C19C2314yes—
106C4×Q8×C19C2312yes—
107C4×D4×C19C2312yes—
108C4×D4×C19C2314yes—
109C4×D4×C19C2314yes—
110C19×#117C2312yes—
111C19×#117C2314yes—
112C19×#117C2314yes—
113C2×C42×C19C2311yescharacteristic
114C2×C42×C19C2314yes—
115C19×C4⋊C8C2314yes—
116C19×C4⋊C8C2314yes—
117C19×C4⋊C8C2314yes—
118C19×C4⋊C8C2314yes—
119C19×C4⋊C8C2314yes—
120C19×C4⋊C8C2314yes—
121C19×C4⋊C8C2312yes—
122C19×C4⋊C8C2314yes—
123C19×C4⋊C8C2314yes—
124C19×C4⋊C8C2314yes—
125C19×C4⋊C8C2312yes—
126C19×C22⋊C8C2314yes—
127C19×C22⋊C8C2314yes—
128C19×C22⋊C8C2314yes—
129C19×C22⋊C8C2314yes—
130C19×C22⋊C8C2314yes—
131C19×#97C2314yes—
132C19×#97C2314yes—
133C19×#97C2314yes—
134C19×#97C2314yes—
135C19×#97C2314yes—
136C4×C8×C19C2312yes—
137C4×C8×C19C2312yes—
138C4×C8×C19C2314yes—
139C4×C8×C19C2314yes—
140C4×C8×C19C2314yes—
141C4×C8×C19C2314yes—
142C2×Q8×C19C22×C414yes—
143C2×Q8×C19C22×C414yes—
144C2×Q8×C19C22×C412yes—
145C2×D4×C19C22×C412yes—
146C2×D4×C19C22×C414yes—
147C2×D4×C19C22×C414yes—
148C22×C4×C19C22×C412yes—
149C22×C4×C19C22×C414yes—
150C22×C4×C19C22×C414yes—
151C22×C4×C19C2411yescharacteristic
152C22×C4×C19C2414yes—
153M16×C19—28no—
154M16×C19—44no—
155M16×C19—42no—
156C2×C8×C19—22no—
157C2×C8×C19—41no—
158C2×C8×C19—44no—
159C2×C8×C19—44no—
160C2×C8×C19C2412yes—
161C2×C8×C19C2414yes—
162C2×C8×C19C2414yes—
163C2×C8×C19C2411yescharacteristic
164C2×C8×C19C2414yes—
165C2×C8×C19C2411yescharacteristic
166C4⋊C4×C19C22×C412yes—
167C4⋊C4×C19C22×C414yes—
168C4⋊C4×C19C22×C414yes—
169C4⋊C4×C19C22×C412yes—
170C4⋊C4×C19C22×C414yes—
171C4⋊C4×C19C22×C414yes—
172C4⋊C4×C19C22×C412yes—
173C4⋊C4×C19C22×C414yes—
174C4⋊C4×C19C22×C414yes—
175C4⋊C4×C19C22×C414yes—
176C4⋊C4×C19C22×C414yes—
177C4⋊C4×C19C22×C412yes—
178C4⋊C4×C19C22×C414yes—
179C4⋊C4×C19C22×C414yes—
180C4⋊C4×C19C22×C414yes—
181C4⋊C4×C19C22×C414yes—
182C4⋊C4×C19C22×C414yes—
183C22⋊C4×C19C22×C414yes—
184C22⋊C4×C19C22×C414yes—
185C22⋊C4×C19C22×C414yes—
186C22⋊C4×C19C22×C414yes—
187C22⋊C4×C19C22×C414yes—
188C22⋊C4×C19C22×C414yes—
189C22⋊C4×C19C22×C414yes—
190C22⋊C4×C19C22×C414yes—
191C22⋊C4×C19C22×C414yes—
192C22⋊C4×C19C22×C414yes—
193C42×C19C22×C411yescharacteristic
194C42×C19C22×C414yes—
195C42×C19C22×C411yescharacteristic
196C42×C19C22×C414yes—
197C42×C19C2412yes—
198C42×C19C2414yes—
199C42×C19C2414yes—
200#60338C1911yesmaximal, characteristic, direct product factor, Sylow
201C23×C19C23×C411yescharacteristic
202C23×C19C23×C414yes—
203Q8×C19—44no—
204Q8×C19—44no—
205Q8×C19—42no—
206D4×C19—42no—
207D4×C19—44no—
208D4×C19—44no—
209C2×C4×C19—21no—
210C2×C4×C19—24no—
211C2×C4×C19—24no—
212C2×C4×C19—21no—
213C2×C4×C19—42no—
214C2×C4×C19—44no—
215C2×C4×C19—44no—
216C2×C4×C19C23×C411yescharacteristic
217C2×C4×C19C23×C414yes—
218C2×C4×C19C23×C412yes—
219C2×C4×C19C23×C414yes—
220C2×C4×C19C23×C414yes—
221C2×C4×C19C23×C412yes—
222C2×C4×C19C23×C414yes—
223C2×C4×C19C23×C414yes—
224C2×C4×C19C2511yescharacteristic
225C8×C19—21no—
226C8×C19—24no—
227C8×C19—22no—
228C8×C19—24no—
229C8×C19—24no—
230C8×C192−1+412yes—
231#3531C2×C1911yescharacteristic
232#2995C2×C1912yescomplemented
233#2994C2×C1914yescomplemented
234#2992C2×C1914yescomplemented
235#2987C2×C1911yescharacteristic, complemented
236#2985C2×C1914yescomplemented
237#2969C2×C1914yescomplemented
238#2967C2×C1914yescomplemented
239#2966C2×C1912yescomplemented
240#2962C2×C1914yescomplemented
241#2960C2×C1911yescharacteristic, complemented
242C22×C19—21no—
243C22×C19—24no—
244C22×C19—22no—
245C22×C19—24no—
246C22×C19—24no—
247C22×C19C24×C411yescharacteristic
248C4×C19—21no—
249C4×C19—24no—
250C4×C19—22no—
251C4×C19—24no—
252C4×C19—24no—
253C4×C19—22no—
254C4×C19—24no—
255C4×C19—24no—
256C4×C19C2×2−1+411yescharacteristic
257C4×C19#58511yescharacteristic
258#564C4×C1911yescharacteristic
259#563C4×C1914yes—
260#563C4×C1912yes—
261#563C4×C1914yes—
262#562C4×C1914yes—
263#562C4×C1911yescharacteristic
264#533C22×C1911yescharacteristic
265#533C22×C1914yes—
266#529C22×C1912yes—
267#529C22×C1914yes—
268#529C22×C1914yes—
269#446C22×C1914yes—
270#446C22×C1912yes—
271#446C22×C1914yes—
272#446C22×C1914yes—
273#446C22×C1914yes—
274#446C22×C1914yes—
275#446C22×C1914yes—
276#446C22×C1914yes—
277C8×Q8C22×C1914yes—
278C8×Q8C22×C1914yes—
279C8×Q8C22×C1912yes—
280#436C22×C1912yes—
281#436C22×C1914yes—
282#436C22×C1914yes—
283#435C22×C1914yes—
284#435C22×C1914yes—
285#435C22×C1914yes—
286#435C22×C1914yes—
287#435C22×C1914yes—
288C8×D4C22×C1912yes—
289C8×D4C22×C1914yes—
290C8×D4C22×C1914yes—
291#433C22×C1914yes—
292#433C22×C1914yes—
293#433C22×C1914yes—
294#433C22×C1914yes—
295#433C22×C1914yes—
296#432C22×C1912yes—
297#432C22×C1914yes—
298#431C22×C1914yes—
299#424C22×C1912yes—
300#424C22×C1914yes—
301#424C22×C1914yes—
302#423C22×C1911yescharacteristic
303C2×C4⋊C8C22×C1914yes—
304#405C22×C1912yes—
305#405C22×C1914yes—
306#405C22×C1914yes—
307C4×M16C22×C1914yes—
308C2×C4×C8C22×C1911yescharacteristic
309C2×C19—41no—
310C2×C19—44no—
311C2×C19C4×2−1+411yescharacteristic
312C2×C19#357312yes—
313C2×M16C23×C1914yes—
314C2×M16C23×C1914yes—
315C2×M16C23×C1912yes—
316C22×C8C23×C1911yescharacteristic
317C22×C8C23×C1911yescharacteristic
318C22×C8C23×C1914yes—
319C22×C8C23×C1914yes—
320C4⋊Q8C2×C4×C1912yes—
321C4⋊Q8C2×C4×C1914yes—
322C4⋊Q8C2×C4×C1914yes—
323#126C2×C4×C1914yes—
324#126C2×C4×C1914yes—
325#126C2×C4×C1914yes—
326#126C2×C4×C1914yes—
327#126C2×C4×C1914yes—
328#125C2×C4×C1912yes—
329#125C2×C4×C1914yes—
330#125C2×C4×C1914yes—
331#125C2×C4×C1911yescharacteristic
332#125C2×C4×C1914yes—
333#125C2×C4×C1911yescharacteristic
334#125C2×C4×C1914yes—
335#124C2×C4×C1912yes—
336#124C2×C4×C1914yes—
337#124C2×C4×C1914yes—
338#123C2×C4×C1914yes—
339#123C2×C4×C1914yes—
340#123C2×C4×C1914yes—
341#123C2×C4×C1914yes—
342#123C2×C4×C1914yes—
343C22⋊Q8C2×C4×C1912yes—
344C22⋊Q8C2×C4×C1914yes—
345C22⋊Q8C2×C4×C1914yes—
346C22⋊Q8C2×C4×C1914yes—
347C22⋊Q8C2×C4×C1914yes—
348C22⋊Q8C2×C4×C1914yes—
349C22⋊Q8C2×C4×C1914yes—
350C22⋊Q8C2×C4×C1914yes—
351#121C2×C4×C1912yes—
352#121C2×C4×C1914yes—
353#121C2×C4×C1914yes—
354C4×Q8C23×C1912yes—
355C4×Q8C23×C1914yes—
356C4×Q8C23×C1914yes—
357C4×D4C23×C1914yes—
358C4×D4C23×C1912yes—
359C4×D4C23×C1914yes—
360#117C23×C1914yes—
361#117C23×C1912yes—
362#117C23×C1914yes—
363C2×C42C23×C1911yescharacteristic
364C2×C42C23×C1914yes—
365C4⋊C8C23×C1914yes—
366C4⋊C8C23×C1914yes—
367C4⋊C8C23×C1914yes—
368C4⋊C8C23×C1914yes—
369C4⋊C8C23×C1914yes—
370C4⋊C8C23×C1914yes—
371C4⋊C8C23×C1912yes—
372C4⋊C8C23×C1914yes—
373C4⋊C8C23×C1914yes—
374C4⋊C8C23×C1914yes—
375C4⋊C8C23×C1912yes—
376C22⋊C8C23×C1914yes—
377C22⋊C8C23×C1914yes—
378C22⋊C8C23×C1914yes—
379C22⋊C8C23×C1914yes—
380C22⋊C8C23×C1914yes—
381#97C23×C1914yes—
382#97C23×C1914yes—
383#97C23×C1914yes—
384#97C23×C1914yes—
385#97C23×C1914yes—
386C4×C8C23×C1912yes—
387C4×C8C23×C1912yes—
388C4×C8C23×C1914yes—
389C4×C8C23×C1914yes—
390C4×C8C23×C1914yes—
391C4×C8C23×C1914yes—
392C19#6033811yescharacteristic, direct product factor, Sylow
393C2×Q8C22×C4×C1912yes—
394C2×Q8C22×C4×C1914yes—
395C2×Q8C22×C4×C1914yes—
396C2×D4C22×C4×C1914yes—
397C2×D4C22×C4×C1912yes—
398C2×D4C22×C4×C1914yes—
399C22×C4C22×C4×C1912yes—
400C22×C4C22×C4×C1914yes—
401C22×C4C22×C4×C1914yes—
402C22×C4C24×C1911yescharacteristic
403C22×C4C24×C1914yes—
404M16—28no—
405M16—44no—
406M16—42no—
407C2×C8—22no—
408C2×C8—41no—
409C2×C8—44no—
410C2×C8—44no—
411C2×C8C24×C1912yes—
412C2×C8C24×C1914yes—
413C2×C8C24×C1911yescharacteristic
414C2×C8C24×C1914yes—
415C2×C8C24×C1914yes—
416C2×C8C24×C1911yescharacteristic
417C4⋊C4C22×C4×C1914yes—
418C4⋊C4C22×C4×C1912yes—
419C4⋊C4C22×C4×C1914yes—
420C4⋊C4C22×C4×C1914yes—
421C4⋊C4C22×C4×C1912yes—
422C4⋊C4C22×C4×C1914yes—
423C4⋊C4C22×C4×C1914yes—
424C4⋊C4C22×C4×C1912yes—
425C4⋊C4C22×C4×C1914yes—
426C4⋊C4C22×C4×C1912yes—
427C4⋊C4C22×C4×C1914yes—
428C4⋊C4C22×C4×C1914yes—
429C4⋊C4C22×C4×C1914yes—
430C4⋊C4C22×C4×C1914yes—
431C4⋊C4C22×C4×C1914yes—
432C4⋊C4C22×C4×C1914yes—
433C4⋊C4C22×C4×C1914yes—
434C22⋊C4C22×C4×C1914yes—
435C22⋊C4C22×C4×C1914yes—
436C22⋊C4C22×C4×C1914yes—
437C22⋊C4C22×C4×C1914yes—
438C22⋊C4C22×C4×C1914yes—
439C22⋊C4C22×C4×C1914yes—
440C22⋊C4C22×C4×C1914yes—
441C22⋊C4C22×C4×C1914yes—
442C22⋊C4C22×C4×C1914yes—
443C22⋊C4C22×C4×C1914yes—
444C42C22×C4×C1911yescharacteristic
445C42C22×C4×C1914yes—
446C42C22×C4×C1911yescharacteristic
447C42C22×C4×C1914yes—
448C42C24×C1912yes—
449C42C24×C1914yes—
450C42C24×C1914yes—
451C23C23×C4×C1911yescharacteristic
452C23C23×C4×C1914yes—
453Q8—42no—
454Q8—44no—
455Q8—44no—
456D4—44no—
457D4—42no—
458D4—44no—
459C2×C4—21no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—21no—
463C2×C4—42no—
464C2×C4—44no—
465C2×C4—44no—
466C2×C4C23×C4×C1911yescharacteristic
467C2×C4C23×C4×C1914yes—
468C2×C4C23×C4×C1912yes—
469C2×C4C23×C4×C1914yes—
470C2×C4C23×C4×C1914yes—
471C2×C4C23×C4×C1912yes—
472C2×C4C23×C4×C1914yes—
473C2×C4C23×C4×C1914yes—
474C2×C4C25×C1911yescharacteristic
475C8—21no—
476C8—24no—
477C8—22no—
478C8—24no—
479C8—24no—
480C8C19×2−1+412yes—
481C22—21no—
482C22—24no—
483C22—22no—
484C22—24no—
485C22—24no—
486C22C24×C4×C1911yescharacteristic
487C4—21no—
488C4—24no—
489C4—22no—
490C4—24no—
491C4—24no—
492C4—22no—
493C4—24no—
494C4—24no—
495C4C2×C19×2−1+411yescharacteristic
496C4C19×#58511yescharacteristic
497C2—41no—
498C2—44no—
499C2C4×C19×2−1+411yescharacteristic
500C2C19×#357312yes—
subgroupG/H
centerC2×C4×C19C25
commutatorC22C24×C4×C19
Frattini, cosocleC2×C4C25×C19
socleC22×C19C24×C4
prime radicalC19×#3531C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C19 ◁ G

Complements

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

NH ≅ G/Ntype
2. C19×#2995C2semidirect
3. C19×#2994C2semidirect
4. C19×#2992C2semidirect
5. C19×#2987C2semidirect
6. C19×#2985C2semidirect
7. C19×#2969C2semidirect
8. C19×#2967C2semidirect
9. C19×#2966C2semidirect
10. C19×#2962C2semidirect
11. C19×#2960C2semidirect
200. #60338C19direct (N × H)
232. #2995C2×C19semidirect
233. #2994C2×C19semidirect
234. #2992C2×C19semidirect
235. #2987C2×C19semidirect
236. #2985C2×C19semidirect
237. #2969C2×C19semidirect
238. #2967C2×C19semidirect
239. #2966C2×C19semidirect
240. #2962C2×C19semidirect
241. #2960C2×C19semidirect
392. C19#60338direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#35312
C19×#29952
C19×#29942
C19×#29922
C19×#29872
C19×#29852
C19×#29692
C19×#29672
C19×#29662
C19×#29622
C19×#29602
#6033819