Finite Group Databasebeta

← C19×#16257 #18022216

Subgroups — C19×#16257 #18022216

Order 4864.

1994 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C19×#123C211yesmaximal, characteristic
2C2×C19×#398C211yesmaximal, characteristic, complemented
3C2×C19×#396C211yesmaximal, characteristic, complemented
4C2×C19×#394C211yesmaximal, characteristic
5C2×C19×#385C211yesmaximal, characteristic, complemented
6C2×C19×#380C211yesmaximal, characteristic, complemented
7C19×#1444C211yesmaximal, characteristic, complemented
8C19×#1441C211yesmaximal, characteristic, complemented
9C19×#1441C211yesmaximal, characteristic, complemented
10C19×#1440C211yesmaximal, characteristic, complemented
11C19×#1440C211yesmaximal, characteristic, complemented
12C19×#1439C211yesmaximal, characteristic, complemented
13C19×#1439C211yesmaximal, characteristic, complemented
14C19×#1439C211yesmaximal, characteristic, complemented
15C19×#1438C211yesmaximal, characteristic
16C23×D4×C19C2211yescharacteristic
17C24×C4×C19C2211yescharacteristic
18C2×C19×#123—24no—
19C2×C19×#123—24no—
20C2×C19×#123—24no—
21C22×C4⋊C4×C19C2211yescharacteristic
22C22×C4⋊C4×C19C2211yescharacteristic
23C22×C4⋊C4×C19C2211yescharacteristic
24C22×C4⋊C4×C19C2211yescharacteristic
25C22×C4⋊C4×C19C2211yescharacteristic
26C22×C4⋊C4×C19C2211yescharacteristic
27C22×C4⋊C4×C19C2211yescharacteristic
28C22×C4⋊C4×C19C2211yescharacteristic
29C22×C22⋊C4×C19C2211yescharacteristic
30C22×C22⋊C4×C19C2211yescharacteristic
31C22×C22⋊C4×C19C2211yescharacteristic
32C22×C22⋊C4×C19C2211yescharacteristic
33C22×C22⋊C4×C19C2211yescharacteristic
34C22×C22⋊C4×C19C2211yescharacteristic
35C22×C22⋊C4×C19C2211yescharacteristic
36C22×C22⋊C4×C19C2211yescharacteristic
37C22×C22⋊C4×C19C2211yescharacteristic
38C22×C22⋊C4×C19C2211yescharacteristic
39C22×C22⋊C4×C19C2211yescharacteristic
40C19×#398—24no—
41C19×#396—24no—
42C19×#394—24no—
43C19×#385—24no—
44C19×#380—24no—
45C2×C19×#95C2211yescharacteristic
46C2×C19×#95C2211yescharacteristic
47C2×C19×#95C2211yescharacteristic
48C2×C19×#95C2211yescharacteristic
49C2×C19×#95C2211yescharacteristic
50C2×C19×#95C2211yescharacteristic
51C2×C19×#95C2211yescharacteristic
52C2×C19×#95C2211yescharacteristic
53C2×C19×#95C2211yescharacteristic
54C2×C19×#95C2211yescharacteristic
55C2×C19×#95C2211yescharacteristic
56C2×C19×#95C2211yescharacteristic
57C2×C19×#95C2211yescharacteristic
58C2×C19×#95C2211yescharacteristic
59C25×C19C2311yescharacteristic
60C25×C19C2311yescharacteristic
61C22×D4×C19—22no—
62C22×D4×C19—22no—
63C22×D4×C19—22no—
64C22×D4×C19—22no—
65C22×D4×C19—22no—
66C22×D4×C19—41no—
67C22×D4×C19—41no—
68C23×C4×C19—22no—
69C23×C4×C19—22no—
70C23×C4×C19—22no—
71C23×C4×C19—22no—
72C23×C4×C19—41no—
73C23×C4×C19—41no—
74C23×C4×C19D414yes—
75C23×C4×C19C2311yescharacteristic
76C23×C4×C19C2311yescharacteristic
77C23×C4×C19C2311yescharacteristic
78C23×C4×C19C2311yescharacteristic
79C23×C4×C19C2311yescharacteristic
80C23×C4×C19C2311yescharacteristic
81C23×C4×C19C2311yescharacteristic
82C23×C4×C19C2311yescharacteristic
83C23×C4×C19C2311yescharacteristic
84C23×C4×C19C2311yescharacteristic
85C23×C4×C19C2311yescharacteristic
86C23×C4×C19C2311yescharacteristic
87C23×C4×C19C2311yescharacteristic
88C19×#123—232no—
89C2×C4⋊C4×C19—22no—
90C2×C4⋊C4×C19—22no—
91C2×C4⋊C4×C19—22no—
92C2×C4⋊C4×C19—22no—
93C2×C4⋊C4×C19—22no—
94C2×C4⋊C4×C19—22no—
95C2×C4⋊C4×C19—22no—
96C2×C4⋊C4×C19—22no—
97C2×C4⋊C4×C19—22no—
98C2×C4⋊C4×C19—22no—
99C2×C4⋊C4×C19—22no—
100C2×C4⋊C4×C19—22no—
101C2×C4⋊C4×C19—22no—
102C2×C4⋊C4×C19—22no—
103C2×C4⋊C4×C19—22no—
104C2×C4⋊C4×C19—22no—
105C2×C4⋊C4×C19—22no—
106C2×C4⋊C4×C19—41no—
107C2×C4⋊C4×C19—41no—
108C2×C4⋊C4×C19—41no—
109C2×C4⋊C4×C19—41no—
110C2×C4⋊C4×C19—41no—
111C2×C4⋊C4×C19—41no—
112C2×C4⋊C4×C19D414yes—
113C2×C22⋊C4×C19—22no—
114C2×C22⋊C4×C19—22no—
115C2×C22⋊C4×C19—22no—
116C2×C22⋊C4×C19—22no—
117C2×C22⋊C4×C19—22no—
118C2×C22⋊C4×C19—22no—
119C2×C22⋊C4×C19—22no—
120C2×C22⋊C4×C19—22no—
121C2×C22⋊C4×C19—22no—
122C2×C22⋊C4×C19—22no—
123C2×C22⋊C4×C19—22no—
124C2×C22⋊C4×C19—22no—
125C2×C22⋊C4×C19—22no—
126C2×C22⋊C4×C19—22no—
127C2×C22⋊C4×C19—22no—
128C2×C22⋊C4×C19—22no—
129C2×C22⋊C4×C19—22no—
130C2×C22⋊C4×C19—22no—
131C2×C22⋊C4×C19—22no—
132C2×C22⋊C4×C19—22no—
133C2×C22⋊C4×C19—22no—
134C2×C22⋊C4×C19—41no—
135C2×C22⋊C4×C19—41no—
136C2×C22⋊C4×C19—41no—
137C2×C22⋊C4×C19—41no—
138C2×C22⋊C4×C19—41no—
139C2×C22⋊C4×C19—41no—
140C2×C22⋊C4×C19—41no—
141C2×C22⋊C4×C19—41no—
142C2×C22⋊C4×C19—41no—
143C2×C22⋊C4×C19—41no—
144C2×C22⋊C4×C19D414yes—
145C2×C22⋊C4×C19D414yes—
146C19×#95—22no—
147C19×#95—22no—
148C19×#95—22no—
149C19×#95—22no—
150C19×#95—22no—
151C19×#95—22no—
152C19×#95—22no—
153C19×#95—22no—
154C19×#95—22no—
155C19×#95—22no—
156C19×#95—41no—
157C19×#95—41no—
158C19×#95—41no—
159C19×#95—41no—
160C24×C19—21no—
161C24×C19—21no—
162C24×C19—21no—
163C24×C19—21no—
164C24×C19—21no—
165C24×C19—21no—
166C24×C19—21no—
167C24×C19—21no—
168C24×C19—21no—
169C24×C19—21no—
170C24×C19—21no—
171C24×C19—21no—
172C24×C19—21no—
173C24×C19—21no—
174C24×C19—21no—
175C24×C19—21no—
176C24×C19—21no—
177C24×C19—21no—
178C24×C19—21no—
179C24×C19—21no—
180C24×C19—21no—
181C24×C19—21no—
182C24×C19—21no—
183C24×C19—21no—
184C24×C19—21no—
185C24×C19—21no—
186C24×C19C2×D412yes—
187C24×C19C2×D412yes—
188C24×C19C2×D412yes—
189C24×C19#4112yes—
190C24×C19C2411yescharacteristic
191C2×D4×C19—28no—
192C2×D4×C19—44no—
193C2×D4×C19—44no—
194C2×D4×C19—44no—
195C2×D4×C19—44no—
196C2×D4×C19—44no—
197C2×D4×C19—44no—
198C22×C4×C19—21no—
199C22×C4×C19—21no—
200C22×C4×C19—21no—
201C22×C4×C19—21no—
202C22×C4×C19—28no—
203C22×C4×C19—21no—
204C22×C4×C19—21no—
205C22×C4×C19—21no—
206C22×C4×C19—21no—
207C22×C4×C19—21no—
208C22×C4×C19—21no—
209C22×C4×C19—21no—
210C22×C4×C19—21no—
211C22×C4×C19—21no—
212C22×C4×C19—21no—
213C22×C4×C19—21no—
214C22×C4×C19—21no—
215C22×C4×C19—21no—
216C22×C4×C19—21no—
217C22×C4×C19—21no—
218C22×C4×C19—21no—
219C22×C4×C19—21no—
220C22×C4×C19—21no—
221C22×C4×C19—21no—
222C22×C4×C19—21no—
223C22×C4×C19—21no—
224C22×C4×C19—21no—
225C22×C4×C19—21no—
226C22×C4×C19—21no—
227C22×C4×C19—21no—
228C22×C4×C19—21no—
229C22×C4×C19—21no—
230C22×C4×C19—21no—
231C22×C4×C19—21no—
232C22×C4×C19—21no—
233C22×C4×C19—21no—
234C22×C4×C19—21no—
235C22×C4×C19—21no—
236C22×C4×C19—21no—
237C22×C4×C19—21no—
238C22×C4×C19—21no—
239C22×C4×C19—21no—
240C22×C4×C19—21no—
241C22×C4×C19—21no—
242C22×C4×C19—21no—
243C22×C4×C19—21no—
244C22×C4×C19—21no—
245C22×C4×C19—21no—
246C22×C4×C19—21no—
247C22×C4×C19—21no—
248C22×C4×C19—21no—
249C22×C4×C19—21no—
250C22×C4×C19—21no—
251C22×C4×C19—28no—
252C22×C4×C19—21no—
253C22×C4×C19—21no—
254C22×C4×C19—21no—
255C22×C4×C19—21no—
256C22×C4×C19—21no—
257C22×C4×C19—21no—
258C22×C4×C19—21no—
259C22×C4×C19—21no—
260C22×C4×C19—21no—
261C22×C4×C19—21no—
262C22×C4×C19—21no—
263C22×C4×C19—21no—
264C22×C4×C19—21no—
265C22×C4×C19—21no—
266C22×C4×C19—21no—
267C22×C4×C19—21no—
268C22×C4×C19—21no—
269C22×C4×C19—21no—
270C22×C4×C19—21no—
271C22×C4×C19—21no—
272C22×C4×C19—21no—
273C22×C4×C19—21no—
274C22×C4×C19—21no—
275C22×C4×C19—21no—
276C22×C4×C19—21no—
277C22×C4×C19—21no—
278C22×C4×C19—21no—
279C22×C4×C19—21no—
280C22×C4×C19—44no—
281C22×C4×C19—44no—
282C22×C4×C19—44no—
283C22×C4×C19—44no—
284C22×C4×C19—44no—
285C22×C4×C19C2×D412yes—
286C22×C4×C19C2×D412yes—
287C22×C4×C19C2×D412yes—
288C22×C4×C19C2×D412yes—
289C22×C4×C19C2×D412yes—
290C22×C4×C19C2×D412yes—
291C22×C4×C19C2×D412yes—
292C22×C4×C19C2×D412yes—
293C22×C4×C19C2×D412yes—
294C22×C4×C19#4112yes—
295C22×C4×C19#4112yes—
296C4⋊C4×C19—28no—
297C4⋊C4×C19—28no—
298C4⋊C4×C19—44no—
299C4⋊C4×C19—44no—
300C4⋊C4×C19—44no—
301C4⋊C4×C19—44no—
302C4⋊C4×C19—44no—
303C4⋊C4×C19—44no—
304C22⋊C4×C19—28no—
305C22⋊C4×C19—28no—
306C22⋊C4×C19—28no—
307C22⋊C4×C19—28no—
308C22⋊C4×C19—44no—
309C22⋊C4×C19—44no—
310C22⋊C4×C19—44no—
311C22⋊C4×C19—44no—
312C22⋊C4×C19—44no—
313C22⋊C4×C19—44no—
314C22⋊C4×C19—44no—
315#16257C1911yesmaximal, characteristic, direct product factor, Sylow
316C23×C19—22no—
317C23×C19—22no—
318C23×C19—22no—
319C23×C19—22no—
320C23×C19—22no—
321C23×C19—22no—
322C23×C19—22no—
323C23×C19—22no—
324C23×C19—22no—
325C23×C19—22no—
326C23×C19—22no—
327C23×C19—22no—
328C23×C19—22no—
329C23×C19—22no—
330C23×C19—22no—
331C23×C19—22no—
332C23×C19—22no—
333C23×C19—22no—
334C23×C19—22no—
335C23×C19—22no—
336C23×C19—22no—
337C23×C19—22no—
338C23×C19—22no—
339C23×C19—22no—
340C23×C19—22no—
341C23×C19—41no—
342C23×C19—41no—
343C23×C19—41no—
344C23×C19—41no—
345C23×C19—41no—
346C23×C19—41no—
347C23×C19—41no—
348C23×C19—41no—
349C23×C19—41no—
350C23×C19—41no—
351C23×C19—41no—
352C23×C19—41no—
353C23×C19—41no—
354C23×C19—41no—
355C23×C19—41no—
356C23×C19—41no—
357C23×C19—41no—
358C23×C19—41no—
359C23×C19—41no—
360C23×C19—41no—
361C23×C19—41no—
362C23×C19—41no—
363C23×C19—41no—
364C23×C19—41no—
365C23×C19—41no—
366C23×C19—41no—
367C23×C19—41no—
368C23×C19—41no—
369C23×C19—41no—
370C23×C19—41no—
371C23×C19—41no—
372C23×C19—41no—
373C23×C19—41no—
374C23×C19—41no—
375C23×C19—41no—
376C23×C19—41no—
377C23×C19—41no—
378C23×C19—41no—
379C23×C19—41no—
380C23×C19—41no—
381C23×C19—41no—
382C23×C19—41no—
383C23×C19—41no—
384C23×C19—41no—
385C23×C19#12114yes—
386C23×C19C22×D411yescharacteristic
387C23×C19C22×D411yescharacteristic
388C23×C19C22×D411yescharacteristic
389C23×C19C22×D411yescharacteristic
390C23×C19C2×#4111yescharacteristic
391C23×C19C2×#4111yescharacteristic
392C23×C19C2×#4111yescharacteristic
393C23×C19H(5,𝔽2)11yescharacteristic
394C23×C19H(5,𝔽2)11yescharacteristic
395C23×C19H(5,𝔽2)11yescharacteristic
396C23×C19H(5,𝔽2)11yescharacteristic
397C23×C192−1+411yescharacteristic
398C23×C192−1+411yescharacteristic
399C23×C192−1+411yescharacteristic
400C23×C192−1+411yescharacteristic
401D4×C19—416no—
402C2×C4×C19—22no—
403C2×C4×C19—22no—
404C2×C4×C19—22no—
405C2×C4×C19—22no—
406C2×C4×C19—22no—
407C2×C4×C19—22no—
408C2×C4×C19—22no—
409C2×C4×C19—22no—
410C2×C4×C19—22no—
411C2×C4×C19—22no—
412C2×C4×C19—22no—
413C2×C4×C19—22no—
414C2×C4×C19—22no—
415C2×C4×C19—22no—
416C2×C4×C19—22no—
417C2×C4×C19—22no—
418C2×C4×C19—22no—
419C2×C4×C19—22no—
420C2×C4×C19—22no—
421C2×C4×C19—22no—
422C2×C4×C19—22no—
423C2×C4×C19—22no—
424C2×C4×C19—22no—
425C2×C4×C19—22no—
426C2×C4×C19—22no—
427C2×C4×C19—22no—
428C2×C4×C19—22no—
429C2×C4×C19—22no—
430C2×C4×C19—22no—
431C2×C4×C19—22no—
432C2×C4×C19—416no—
433C2×C4×C19—41no—
434C2×C4×C19—41no—
435C2×C4×C19—41no—
436C2×C4×C19—41no—
437C2×C4×C19—41no—
438C2×C4×C19—41no—
439C2×C4×C19—41no—
440C2×C4×C19—41no—
441C2×C4×C19—41no—
442C2×C4×C19—41no—
443C2×C4×C19—41no—
444C2×C4×C19—41no—
445C2×C4×C19—41no—
446C2×C4×C19—41no—
447C2×C4×C19—41no—
448C2×C4×C19—41no—
449C2×C4×C19—41no—
450C2×C4×C19—41no—
451C2×C4×C19—41no—
452C2×C4×C19—41no—
453C2×C4×C19—41no—
454C2×C4×C19—41no—
455C2×C4×C19—41no—
456C2×C4×C19—41no—
457C2×C4×C19—41no—
458C2×C4×C19—41no—
459C2×C4×C19—41no—
460C2×C4×C19—41no—
461C2×C4×C19—41no—
462C2×C4×C19—41no—
463C2×C4×C19—41no—
464C2×C4×C19—41no—
465C2×C4×C19—41no—
466C2×C4×C19—41no—
467C2×C4×C19—41no—
468C2×C4×C19—41no—
469C2×C4×C19—41no—
470C2×C4×C19—41no—
471C2×C4×C19—41no—
472C2×C4×C19—41no—
473C2×C4×C19—41no—
474C2×C4×C19—41no—
475C2×C4×C19—41no—
476C2×C4×C19—41no—
477C2×C4×C19—41no—
478C2×C4×C19—41no—
479C2×C4×C19—41no—
480C2×C4×C19—41no—
481C2×C4×C19—41no—
482C2×C4×C19—41no—
483C2×C4×C19—41no—
484C2×C4×C19—41no—
485C2×C4×C19—41no—
486C2×C4×C19—41no—
487C2×C4×C19—41no—
488C2×C4×C19—41no—
489C2×C4×C19—41no—
490C2×C4×C19—41no—
491C2×C4×C19—41no—
492C2×C4×C19—41no—
493C2×C4×C19#12014yes—
494C22×#123C2×C1911yescharacteristic
495C2×#398C2×C1911yescharacteristic, complemented
496C2×#396C2×C1911yescharacteristic, complemented
497C2×#394C2×C1911yescharacteristic
498C2×#385C2×C1911yescharacteristic, complemented
499C2×#380C2×C1911yescharacteristic, complemented
500#1444C2×C1911yescharacteristic, complemented
501#1441C2×C1911yescharacteristic, complemented
502#1441C2×C1911yescharacteristic, complemented
503#1440C2×C1911yescharacteristic, complemented
504#1440C2×C1911yescharacteristic, complemented
505#1439C2×C1911yescharacteristic, complemented
506#1439C2×C1911yescharacteristic, complemented
507#1439C2×C1911yescharacteristic, complemented
508#1438C2×C1911yescharacteristic
509C22×C19—24no—
510C22×C19—24no—
511C22×C19—24no—
512C22×C19—42no—
513C22×C19—42no—
514C22×C19—42no—
515C22×C19—42no—
516C22×C19—42no—
517C22×C19—42no—
518C22×C19—42no—
519C22×C19—42no—
520C22×C19—42no—
521C22×C19—42no—
522C22×C19—42no—
523C22×C19—42no—
524C22×C19—42no—
525C22×C19—42no—
526C22×C19—42no—
527C22×C19—42no—
528C22×C19—42no—
529C22×C19—42no—
530C22×C19—42no—
531C22×C19—81no—
532C22×C19—81no—
533C22×C19—81no—
534C22×C19—81no—
535C22×C19—81no—
536C22×C19—81no—
537C22×C19—81no—
538C22×C19—81no—
539C22×C19C2×#12011yescharacteristic
540C22×C19C2×#12111yescharacteristic
541C22×C19#52511yescharacteristic
542C22×C19#53411yescharacteristic
543C22×C19#53411yescharacteristic
544C22×C19#53611yescharacteristic
545C22×C19#53611yescharacteristic
546C22×C19#53611yescharacteristic
547C22×C19#53611yescharacteristic
548C22×C19#53711yescharacteristic
549C22×C19#53711yescharacteristic
550C22×C19#53711yescharacteristic
551C22×C19#53711yescharacteristic
552C22×C19#53811yescharacteristic
553C22×C19#53911yescharacteristic
554C22×C19#53911yescharacteristic
555C22×C19#53911yescharacteristic
556C22×C19#54011yescharacteristic
557C22×C19#54211yescharacteristic
558C22×C19D4211yescharacteristic
559C22×C19D4211yescharacteristic
560C22×C19#54611yescharacteristic
561C22×C19#54611yescharacteristic
562C22×C19#54611yescharacteristic
563C22×C19#54711yescharacteristic
564C22×C19#54711yescharacteristic
565C22×C19#54711yescharacteristic
566C22×C19#54811yescharacteristic
567C22×C19#55011yescharacteristic
568C22×C19#55211yescharacteristic
569C22×C19#55211yescharacteristic
570C22×C19#56211yescharacteristic
571C22×C19#56211yescharacteristic
572C22×C19#56311yescharacteristic
573C22×C19#56311yescharacteristic
574C4×C19—24no—
575C4×C19—42no—
576C4×C19—42no—
577C4×C19—42no—
578C4×C19—42no—
579C4×C19—42no—
580C4×C19—42no—
581C4×C19—42no—
582C4×C19—42no—
583C4×C19—81no—
584C4×C19—81no—
585C4×C19—81no—
586C4×C19—81no—
587C23×D4C22×C1911yescharacteristic
588C24×C4C22×C1911yescharacteristic
589C2×#123—24no—
590C2×#123—24no—
591C2×#123—24no—
592C22×C4⋊C4C22×C1911yescharacteristic
593C22×C4⋊C4C22×C1911yescharacteristic
594C22×C4⋊C4C22×C1911yescharacteristic
595C22×C4⋊C4C22×C1911yescharacteristic
596C22×C4⋊C4C22×C1911yescharacteristic
597C22×C4⋊C4C22×C1911yescharacteristic
598C22×C4⋊C4C22×C1911yescharacteristic
599C22×C4⋊C4C22×C1911yescharacteristic
600C22×C22⋊C4C22×C1911yescharacteristic
601C22×C22⋊C4C22×C1911yescharacteristic
602C22×C22⋊C4C22×C1911yescharacteristic
603C22×C22⋊C4C22×C1911yescharacteristic
604C22×C22⋊C4C22×C1911yescharacteristic
605C22×C22⋊C4C22×C1911yescharacteristic
606C22×C22⋊C4C22×C1911yescharacteristic
607C22×C22⋊C4C22×C1911yescharacteristic
608C22×C22⋊C4C22×C1911yescharacteristic
609C22×C22⋊C4C22×C1911yescharacteristic
610C22×C22⋊C4C22×C1911yescharacteristic
611#398—24no—
612#396—24no—
613#394—24no—
614#385—24no—
615#380—24no—
616C2×#95C22×C1911yescharacteristic
617C2×#95C22×C1911yescharacteristic
618C2×#95C22×C1911yescharacteristic
619C2×#95C22×C1911yescharacteristic
620C2×#95C22×C1911yescharacteristic
621C2×#95C22×C1911yescharacteristic
622C2×#95C22×C1911yescharacteristic
623C2×#95C22×C1911yescharacteristic
624C2×#95C22×C1911yescharacteristic
625C2×#95C22×C1911yescharacteristic
626C2×#95C22×C1911yescharacteristic
627C2×#95C22×C1911yescharacteristic
628C2×#95C22×C1911yescharacteristic
629C2×#95C22×C1911yescharacteristic
630C2×C19—44no—
631C2×C19—82no—
632C2×C19#240711yescharacteristic
633C2×C19#241011yescharacteristic
634C2×C19#241311yescharacteristic
635C2×C19#261611yescharacteristic
636C2×C19#261811yescharacteristic
637C2×C19#263011yescharacteristic
638C2×C19#267111yescharacteristic
639C2×C19#267411yescharacteristic
640C2×C19#268011yescharacteristic
641C2×C19#268211yescharacteristic
642C2×C19#268711yescharacteristic
643C2×C19#269411yescharacteristic
644C2×C19#269511yescharacteristic
645C2×C19#270711yescharacteristic
646C2×C19#281411yescharacteristic
647C25C23×C1911yescharacteristic
648C25C23×C1911yescharacteristic
649C22×D4—22no—
650C22×D4—22no—
651C22×D4—22no—
652C22×D4—22no—
653C22×D4—22no—
654C22×D4—41no—
655C22×D4—41no—
656C23×C4—22no—
657C23×C4—22no—
658C23×C4—22no—
659C23×C4—22no—
660C23×C4—41no—
661C23×C4—41no—
662C23×C4D4×C1914yes—
663C23×C4C23×C1911yescharacteristic
664C23×C4C23×C1911yescharacteristic
665C23×C4C23×C1911yescharacteristic
666C23×C4C23×C1911yescharacteristic
667C23×C4C23×C1911yescharacteristic
668C23×C4C23×C1911yescharacteristic
669C23×C4C23×C1911yescharacteristic
670C23×C4C23×C1911yescharacteristic
671C23×C4C23×C1911yescharacteristic
672C23×C4C23×C1911yescharacteristic
673C23×C4C23×C1911yescharacteristic
674C23×C4C23×C1911yescharacteristic
675C23×C4C23×C1911yescharacteristic
676#123—232no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4—22no—
684C2×C4⋊C4—22no—
685C2×C4⋊C4—22no—
686C2×C4⋊C4—22no—
687C2×C4⋊C4—22no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—22no—
692C2×C4⋊C4—22no—
693C2×C4⋊C4—22no—
694C2×C4⋊C4—41no—
695C2×C4⋊C4—41no—
696C2×C4⋊C4—41no—
697C2×C4⋊C4—41no—
698C2×C4⋊C4—41no—
699C2×C4⋊C4—41no—
700C2×C4⋊C4D4×C1914yes—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—22no—
718C2×C22⋊C4—22no—
719C2×C22⋊C4—22no—
720C2×C22⋊C4—22no—
721C2×C22⋊C4—22no—
722C2×C22⋊C4—41no—
723C2×C22⋊C4—41no—
724C2×C22⋊C4—41no—
725C2×C22⋊C4—41no—
726C2×C22⋊C4—41no—
727C2×C22⋊C4—41no—
728C2×C22⋊C4—41no—
729C2×C22⋊C4—41no—
730C2×C22⋊C4—41no—
731C2×C22⋊C4—41no—
732C2×C22⋊C4D4×C1914yes—
733C2×C22⋊C4D4×C1914yes—
734#95—22no—
735#95—22no—
736#95—22no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—22no—
744#95—41no—
745#95—41no—
746#95—41no—
747#95—41no—
748C19#1625711yescharacteristic, direct product factor, Sylow
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24C2×D4×C1912yes—
776C24C2×D4×C1912yes—
777C24C2×D4×C1912yes—
778C24#41×C1912yes—
779C24C24×C1911yescharacteristic
780C2×D4—28no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—44no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—28no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—28no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4C2×D4×C1912yes—
875C22×C4C2×D4×C1912yes—
876C22×C4C2×D4×C1912yes—
877C22×C4C2×D4×C1912yes—
878C22×C4C2×D4×C1912yes—
879C22×C4C2×D4×C1912yes—
880C22×C4C2×D4×C1912yes—
881C22×C4C2×D4×C1912yes—
882C22×C4C2×D4×C1912yes—
883C22×C4#41×C1912yes—
884C22×C4#41×C1912yes—
885C4⋊C4—28no—
886C4⋊C4—28no—
887C4⋊C4—44no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C22⋊C4—28no—
894C22⋊C4—28no—
895C22⋊C4—28no—
896C22⋊C4—28no—
897C22⋊C4—44no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C22⋊C4—44no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23C19×#12114yes—
974C23C22×D4×C1911yescharacteristic
975C23C22×D4×C1911yescharacteristic
976C23C22×D4×C1911yescharacteristic
977C23C22×D4×C1911yescharacteristic
978C23C2×#41×C1911yescharacteristic
979C23C2×#41×C1911yescharacteristic
980C23C2×#41×C1911yescharacteristic
981C23C19×H(5,𝔽2)11yescharacteristic
982C23C19×H(5,𝔽2)11yescharacteristic
983C23C19×H(5,𝔽2)11yescharacteristic
984C23C19×H(5,𝔽2)11yescharacteristic
985C23C19×2−1+411yescharacteristic
986C23C19×2−1+411yescharacteristic
987C23C19×2−1+411yescharacteristic
988C23C19×2−1+411yescharacteristic
989D4—416no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—416no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4C19×#12014yes—
1082C22—24no—
1083C22—24no—
1084C22—24no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22—81no—
1111C22—81no—
1112C22C2×C19×#12011yescharacteristic
1113C22C2×C19×#12111yescharacteristic
1114C22C19×#52511yescharacteristic
1115C22C19×#53411yescharacteristic
1116C22C19×#53411yescharacteristic
1117C22C19×#53611yescharacteristic
1118C22C19×#53611yescharacteristic
1119C22C19×#53611yescharacteristic
1120C22C19×#53611yescharacteristic
1121C22C19×#53711yescharacteristic
1122C22C19×#53711yescharacteristic
1123C22C19×#53711yescharacteristic
1124C22C19×#53711yescharacteristic
1125C22C19×#53811yescharacteristic
1126C22C19×#53911yescharacteristic
1127C22C19×#53911yescharacteristic
1128C22C19×#53911yescharacteristic
1129C22C19×#54011yescharacteristic
1130C22C19×#54211yescharacteristic
1131C22D42×C1911yescharacteristic
1132C22D42×C1911yescharacteristic
1133C22C19×#54611yescharacteristic
1134C22C19×#54611yescharacteristic
1135C22C19×#54611yescharacteristic
1136C22C19×#54711yescharacteristic
1137C22C19×#54711yescharacteristic
1138C22C19×#54711yescharacteristic
1139C22C19×#54811yescharacteristic
1140C22C19×#55011yescharacteristic
1141C22C19×#55211yescharacteristic
1142C22C19×#55211yescharacteristic
1143C22C19×#56211yescharacteristic
1144C22C19×#56211yescharacteristic
1145C22C19×#56311yescharacteristic
1146C22C19×#56311yescharacteristic
1147C4—24no—
1148C4—42no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—42no—
1156C4—81no—
1157C4—81no—
1158C4—81no—
1159C4—81no—
1160C2—44no—
1161C2—82no—
1162C2C19×#240711yescharacteristic
1163C2C19×#241011yescharacteristic
1164C2C19×#241311yescharacteristic
1165C2C19×#261611yescharacteristic
1166C2C19×#261811yescharacteristic
1167C2C19×#263011yescharacteristic
1168C2C19×#267111yescharacteristic
1169C2C19×#267411yescharacteristic
1170C2C19×#268011yescharacteristic
1171C2C19×#268211yescharacteristic
1172C2C19×#268711yescharacteristic
1173C2C19×#269411yescharacteristic
1174C2C19×#269511yescharacteristic
1175C2C19×#270711yescharacteristic
1176C2C19×#281411yescharacteristic
subgroupG/H
center, socleC24×C19C24
commutator, Frattini, cosocleC24C24×C19
prime radicalC23×D4×C19C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C19 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C19×#398C2semidirect
3. C2×C19×#396C2semidirect
5. C2×C19×#385C2semidirect
6. C2×C19×#380C2semidirect
7. C19×#1444C2semidirect
8. C19×#1441C2semidirect
9. C19×#1441C2semidirect
10. C19×#1440C2semidirect
11. C19×#1440C2semidirect
12. C19×#1439C2semidirect
13. C19×#1439C2semidirect
14. C19×#1439C2semidirect
315. #16257C19direct (N × H)
495. C2×#398C2×C19semidirect
496. C2×#396C2×C19semidirect
498. C2×#385C2×C19semidirect
499. C2×#380C2×C19semidirect
500. #1444C2×C19semidirect
501. #1441C2×C19semidirect
502. #1441C2×C19semidirect
503. #1440C2×C19semidirect
504. #1440C2×C19semidirect
505. #1439C2×C19semidirect
506. #1439C2×C19semidirect
507. #1439C2×C19semidirect
748. C19#16257direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C19×#1232
C2×C19×#3982
C2×C19×#3962
C2×C19×#3942
C2×C19×#3852
C2×C19×#3802
C19×#14442
C19×#14412
C19×#14402
C19×#14392
C19×#14382
#1625719