Finite Group Databasebeta

← C19×#62838 #18068797

Subgroups — C19×#62838 #18068797

Order 4864.

6518 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C19×#3565C218yesmaximal, complemented
2C19×#3555C214yesmaximal, complemented
3C19×#3547C214yesmaximal, complemented
4C19×#3541C218yesmaximal, complemented
5C19×#3518C214yesmaximal, complemented
6C19×#3516C218yesmaximal, complemented
7C19×#3515C214yesmaximal, complemented
8C19×#3512C212yesmaximal, complemented
9C19×#3511C212yesmaximal, complemented
10C19×#3511C214yesmaximal, complemented
11C19×#3509C214yesmaximal, complemented
12C19×#3504C212yesmaximal, complemented
13C19×#3503C212yesmaximal, complemented
14C19×#3493C214yesmaximal, complemented
15C19×#3444C211yesmaximal, characteristic, complemented
16C19×#3444C211yesmaximal, characteristic, complemented
17C2×C19×#533C211yesmaximal, characteristic, complemented
18C19×#563C22116yes—
19C19×#562C22116yes—
20Q82×C19C2214yescomplemented
21C19×#557C2214yescomplemented
22C19×#557C2218yescomplemented
23C19×#557C2218yescomplemented
24C19×#556C2218yes—
25C19×#556C2218yes—
26C19×#556C2218yes—
27C19×#556C2218yescomplemented
28C19×#556C2214yescomplemented
29C19×#556C22116yescomplemented
30C19×#555C2218yes—
31C19×#555C2218yes—
32C19×#555C2214yescomplemented
33C19×#554C2218yes—
34C19×#554C22116yes—
35C19×#554C2214yescomplemented
36C19×#554C2218yescomplemented
37C19×#554C2214yescomplemented
38C19×#553C2218yes—
39C19×#553C2218yes—
40C19×#553C2218yes—
41C19×#553C22116yes—
42C19×#553C2218yescomplemented
43C19×#552C2218yes—
44C19×#552C2218yes—
45C19×#552C2218yes—
46C19×#552C2218yescomplemented
47C19×#552C2218yescomplemented
48C19×#552C22116yescomplemented
49D4×Q8×C19C2218yes—
50D4×Q8×C19C2214yescomplemented
51C19×#548C2218yes—
52C19×#548C2218yes—
53C19×#548C2218yescomplemented
54C19×#547C2218yes—
55C19×#547C2214yescomplemented
56C19×#544C2214yes—
57C19×#544C2218yescomplemented
58C19×#544C2218yescomplemented
59C19×#542C2218yes—
60C19×#542C22116yes—
61C19×#542C2218yescomplemented
62C19×#542C2218yescomplemented
63C19×#542C22116yescomplemented
64C19×#541C2218yes—
65C19×#541C2218yescomplemented
66C19×#541C2214yescomplemented
67C19×#541C22116yescomplemented
68C19×#540C2214yescomplemented
69C19×#539C22116yes—
70C19×#538C22116yes—
71C19×#537C2214yes—
72C19×#537C2218yes—
73C19×#536C2218yes—
74C19×#533C2214yes—
75C19×#533C2214yes—
76C19×#533C2214yes—
77C19×#533C2214yes—
78C19×#533C2211yescharacteristic
79C19×#533C2211yescharacteristic
80C19×#533C2212yes—
81C19×#533C2212yes—
82C19×#533C2214yescomplemented
83C19×#533C2214yescomplemented
84C19×#533C2214yescomplemented
85C19×#532C2211yescharacteristic
86C19×#532C2212yes—
87C19×#532C2211yescharacteristic
88C19×#532C2212yes—
89C19×#532C2214yescomplemented
90C2×C19×C4⋊Q8C2212yes—
91C2×C19×C4⋊Q8C2214yescomplemented
92C19×#529C2212yes—
93C19×#529C2214yes—
94C19×#529C2214yes—
95C19×#529C2212yes—
96C19×#529C2214yes—
97C19×#529C2214yes—
98C19×#529C2214yes—
99C19×#529C22116yes—
100C19×#529C2218yescomplemented
101C2×C19×#125C2212yes—
102C2×C19×#125C2214yescomplemented
103C19×#525C2212yes—
104C19×#525C2212yes—
105C19×#525C2214yes—
106C19×#525C2214yes—
107C2×C19×C22⋊Q8C2214yes—
108C19×#520C2214yes—
109C19×#520C2214yes—
110C19×#520C2218yescomplemented
111C19×#519C2218yescomplemented
112C4×#41×C19C2212yes—
113C4×#41×C19C2212yes—
114C4×#41×C19C2214yes—
115C4×#41×C19C2214yes—
116C2×C4×Q8×C19C2214yes—
117C2×C19×#117C2212yes—
118C22×C42×C19C2211yescharacteristic
119C2×#41×C19C2312yes—
120C2×#41×C19C2312yes—
121C2×#41×C19C2314yes—
122C2×#41×C19C2314yes—
123C2×#41×C19C2318yes—
124C22×Q8×C19C2314yes—
125C22×Q8×C19C2318yes—
126C23×C4×C19C2311yescharacteristic
127C23×C4×C19C2312yes—
128C19×C4⋊Q8C2314yes—
129C19×C4⋊Q8C2314yes—
130C19×C4⋊Q8C2314yes—
131C19×C4⋊Q8C2314yes—
132C19×C4⋊Q8C2312yes—
133C19×C4⋊Q8C2318yes—
134C19×C4⋊Q8C2318yes—
135C19×C4⋊Q8C2318yes—
136C19×C4⋊Q8C2311yescharacteristic
137C19×C4⋊Q8C2311yescharacteristic
138C19×C4⋊Q8C2312yes—
139C19×C4⋊Q8C2318yes—
140C19×C4⋊Q8C23116yes—
141C19×C4⋊Q8C23116yes—
142C19×#127C2311yescharacteristic
143C19×#127C2311yescharacteristic
144C19×#126C2318yes—
145C19×#126C2314yes—
146C19×#126C2314yes—
147C19×#126C23116yes—
148C19×#126C23116yes—
149C19×#126C23116yes—
150C19×#126C23116yes—
151C19×#126C23116yes—
152C19×#126C23116yes—
153C19×#126C23116yes—
154C19×#125C2314yes—
155C19×#125C2314yes—
156C19×#125C2318yes—
157C19×#125C2311yescharacteristic
158C19×#125C23116yes—
159C19×#125C2318yes—
160C19×#125C2311yescharacteristic
161C19×#125C2314yes—
162C19×#125C2312yes—
163C19×#125C2314yes—
164C19×#125C23116yes—
165C19×#125C2318yes—
166C19×#125C2318yes—
167C19×#125C23116yes—
168C19×#125C23116yes—
169C19×#125C23116yes—
170C19×#124C2312yes—
171C19×#124C2312yes—
172C19×#124C2314yes—
173C19×#124C2314yes—
174C19×#124C23116yes—
175C19×#124C2318yes—
176C19×#124C23116yes—
177C19×#124C23116yes—
178C19×#124C23116yes—
179C19×#123C2314yes—
180C19×#123C2314yes—
181C19×#123C2314yes—
182C19×#123C2314yes—
183C19×#123C2318yes—
184C19×#123C23116yes—
185C19×#123C23116yes—
186C19×#123C23116yes—
187C19×#123C23116yes—
188C19×#123C23116yes—
189C19×C22⋊Q8C2318yes—
190C19×C22⋊Q8C2318yes—
191C19×C22⋊Q8C2318yes—
192C19×C22⋊Q8C2318yes—
193C19×C22⋊Q8C2314yes—
194C19×C22⋊Q8C2314yes—
195C19×C22⋊Q8C2312yes—
196C19×C22⋊Q8C2314yes—
197C19×C22⋊Q8C2314yes—
198C19×C22⋊Q8C2312yes—
199C19×C22⋊Q8C2314yes—
200C19×C22⋊Q8C23116yes—
201C19×C22⋊Q8C2318yes—
202C19×C22⋊Q8C2318yes—
203C19×C22⋊Q8C2318yes—
204C19×C22⋊Q8C2318yes—
205C19×C22⋊Q8C2318yes—
206C19×C22⋊Q8C23116yes—
207C19×C22⋊Q8C23116yes—
208C19×C22⋊Q8C23116yes—
209C19×C22⋊Q8C23116yes—
210C19×C22⋊Q8C23116yes—
211C19×C22⋊Q8C23116yes—
212C19×#121C2314yes—
213C19×#121C2314yes—
214C19×#121C2314yes—
215C19×#121C2312yes—
216C19×#121C2314yes—
217C19×#121C2312yes—
218C19×#121C2314yes—
219C19×#121C23116yes—
220C19×#121C2318yes—
221C19×#121C2318yes—
222C19×#121C2318yes—
223C19×#121C23116yes—
224C19×#121C23116yes—
225C19×#121C23116yes—
226C19×#120C2314yes—
227C19×#120C2314yes—
228C4×Q8×C19C2318yes—
229C4×Q8×C19C2318yes—
230C4×Q8×C19C2318yes—
231C4×Q8×C19C2318yes—
232C4×Q8×C19C2314yes—
233C4×Q8×C19C2314yes—
234C4×Q8×C19C2314yes—
235C4×Q8×C19C2314yes—
236C4×Q8×C19C2312yes—
237C4×Q8×C19C2314yes—
238C4×Q8×C19C2312yes—
239C4×Q8×C19C23116yes—
240C4×Q8×C19C2318yes—
241C4×Q8×C19C2318yes—
242C4×Q8×C19C23116yes—
243C4×Q8×C19C2318yes—
244C4×Q8×C19C2318yes—
245C4×Q8×C19C2318yes—
246C4×D4×C19C2314yes—
247C4×D4×C19C2318yes—
248C4×D4×C19C2314yes—
249C4×D4×C19C2314yes—
250C4×D4×C19C2314yes—
251C4×D4×C19C2314yes—
252C4×D4×C19C2314yes—
253C4×D4×C19C2318yes—
254C4×D4×C19C2318yes—
255C4×D4×C19C2314yes—
256C4×D4×C19C2312yes—
257C4×D4×C19C2314yes—
258C4×D4×C19C2314yes—
259C4×D4×C19C2312yes—
260C4×D4×C19C2314yes—
261C4×D4×C19C2314yes—
262C4×D4×C19C23116yes—
263C4×D4×C19C23116yes—
264C4×D4×C19C2318yes—
265C4×D4×C19C2318yes—
266C4×D4×C19C23116yes—
267C4×D4×C19C23116yes—
268C4×D4×C19C2318yes—
269C19×#117C2318yes—
270C19×#117C2318yes—
271C19×#117C2314yes—
272C19×#117C2312yes—
273C19×#117C2312yes—
274C19×#117C2314yes—
275C19×#117C2314yes—
276C19×#117C2314yes—
277C19×#117C2314yes—
278C19×#117C2314yes—
279C19×#117C2318yes—
280C19×#117C23116yes—
281C19×#117C23116yes—
282C19×#117C2318yes—
283C19×#117C2318yes—
284C19×#117C2318yes—
285C19×#117C23116yes—
286C2×C4⋊C4×C19C2314yes—
287C2×C4⋊C4×C19C2318yes—
288C2×C4⋊C4×C19C2314yes—
289C2×C4⋊C4×C19C2318yes—
290C2×C4⋊C4×C19C2318yes—
291C2×C4⋊C4×C19C23116yes—
292C2×C4⋊C4×C19C2318yes—
293C2×C22⋊C4×C19C2314yes—
294C2×C42×C19C2312yes—
295C2×C42×C19C2311yescharacteristic
296C2×C42×C19C2312yes—
297C2×C42×C19C2311yescharacteristic
298C2×C42×C19C2312yes—
299C2×C42×C19C2312yes—
300C2×C42×C19C2312yes—
301C2×C42×C19C2314yes—
302C2×C42×C19C2314yes—
303C2×C42×C19C2314yes—
304C24×C19C2411yescharacteristic
305#41×C19—28no—
306#41×C19—28no—
307#41×C19—48no—
308#41×C19—48no—
309#41×C19—416no—
310C2×Q8×C19—48no—
311C2×Q8×C19—416no—
312C2×Q8×C19C2412yes—
313C2×Q8×C19C2412yes—
314C2×Q8×C19C2418yes—
315C2×Q8×C19C2414yes—
316C2×Q8×C19C2418yes—
317C2×Q8×C19C2414yes—
318C2×Q8×C19C24116yes—
319C2×D4×C19C2414yes—
320C2×D4×C19C2414yes—
321C2×D4×C19C2412yes—
322C2×D4×C19C2412yes—
323C2×D4×C19C2414yes—
324C2×D4×C19C2414yes—
325C2×D4×C19C2418yes—
326C2×D4×C19C2414yes—
327C2×D4×C19C24116yes—
328C2×D4×C19C2414yes—
329C22×C4×C19—24no—
330C22×C4×C19—44no—
331C22×C4×C19C2411yescharacteristic
332C22×C4×C19C2412yes—
333C22×C4×C19C2412yes—
334C22×C4×C19C2412yes—
335C22×C4×C19C2412yes—
336C22×C4×C19C2412yes—
337C22×C4×C19C2414yes—
338C22×C4×C19C2414yes—
339C22×C4×C19C2414yes—
340C22×C4×C19C2414yes—
341C22×C4×C19C2412yes—
342C22×C4×C19C2412yes—
343C22×C4×C19C2412yes—
344C22×C4×C19C2418yes—
345C22×C4×C19C2418yes—
346C22×C4×C19C24116yes—
347C22×C4×C19C24116yes—
348C22×C4×C19C2411yescharacteristic
349C4⋊C4×C19C2412yes—
350C4⋊C4×C19C2414yes—
351C4⋊C4×C19C2418yes—
352C4⋊C4×C19C2418yes—
353C4⋊C4×C19C2414yes—
354C4⋊C4×C19C2418yes—
355C4⋊C4×C19C2414yes—
356C4⋊C4×C19C24116yes—
357C4⋊C4×C19C24116yes—
358C4⋊C4×C19C24116yes—
359C4⋊C4×C19C24116yes—
360C4⋊C4×C19C24116yes—
361C4⋊C4×C19C24116yes—
362C4⋊C4×C19C2418yes—
363C4⋊C4×C19C2412yes—
364C4⋊C4×C19C2414yes—
365C4⋊C4×C19C2414yes—
366C4⋊C4×C19C2418yes—
367C4⋊C4×C19C2414yes—
368C4⋊C4×C19C2414yes—
369C4⋊C4×C19C2414yes—
370C4⋊C4×C19C2414yes—
371C4⋊C4×C19C2414yes—
372C4⋊C4×C19C2418yes—
373C4⋊C4×C19C2418yes—
374C4⋊C4×C19C2414yes—
375C4⋊C4×C19C24116yes—
376C4⋊C4×C19C24116yes—
377C22⋊C4×C19C24116yes—
378C22⋊C4×C19C2414yes—
379C22⋊C4×C19C2414yes—
380C22⋊C4×C19C2418yes—
381C22⋊C4×C19C24116yes—
382C22⋊C4×C19C2414yes—
383C22⋊C4×C19C2414yes—
384C22⋊C4×C19C2414yes—
385C22⋊C4×C19C2414yes—
386C22⋊C4×C19C2414yes—
387C22⋊C4×C19C2418yes—
388C22⋊C4×C19C2414yes—
389C22⋊C4×C19C2418yes—
390C22⋊C4×C19C24116yes—
391C22⋊C4×C19C24116yes—
392C22⋊C4×C19C24116yes—
393C22⋊C4×C19C2414yes—
394C22⋊C4×C19C2414yes—
395C22⋊C4×C19C2418yes—
396C42×C19C2411yescharacteristic
397C42×C19C2411yescharacteristic
398C42×C19C2412yes—
399C42×C19C2412yes—
400C42×C19C2411yescharacteristic
401C42×C19C2411yescharacteristic
402C42×C19C2412yes—
403C42×C19C2412yes—
404C42×C19C2412yes—
405C42×C19C2412yes—
406C42×C19C2418yes—
407C42×C19C24116yes—
408C42×C19C2414yes—
409C42×C19C2414yes—
410C42×C19C2414yes—
411C42×C19C2414yes—
412C42×C19C24116yes—
413C42×C19C24116yes—
414#62838C1911yesmaximal, characteristic, direct product factor, Sylow
415C23×C19—22no—
416C23×C19—42no—
417C23×C19C2512yes—
418C23×C19C2514yes—
419C23×C19C2514yes—
420C23×C19C2511yescharacteristic
421Q8×C19—24no—
422Q8×C19—24no—
423Q8×C19—216no—
424Q8×C19—28no—
425Q8×C19—48no—
426Q8×C19—416no—
427Q8×C19—44no—
428D4×C19—28no—
429D4×C19—28no—
430D4×C19—24no—
431D4×C19—24no—
432D4×C19—28no—
433D4×C19—44no—
434D4×C19—44no—
435D4×C19—44no—
436D4×C19—48no—
437D4×C19—416no—
438C2×C4×C19—22no—
439C2×C4×C19—24no—
440C2×C4×C19—24no—
441C2×C4×C19—28no—
442C2×C4×C19—28no—
443C2×C4×C19—24no—
444C2×C4×C19—24no—
445C2×C4×C19—24no—
446C2×C4×C19—28no—
447C2×C4×C19—28no—
448C2×C4×C19—42no—
449C2×C4×C19—42no—
450C2×C4×C19—42no—
451C2×C4×C19—48no—
452C2×C4×C19—416no—
453C2×C4×C19—48no—
454C2×C4×C19—416no—
455C2×C4×C192−1+414yes—
456C2×C4×C19C2512yes—
457C2×C4×C19C2512yes—
458C2×C4×C19C2514yes—
459C2×C4×C19C2514yes—
460C2×C4×C19C2514yes—
461C2×C4×C19C2512yes—
462C2×C4×C19C2518yes—
463C2×C4×C19C25116yes—
464C2×C4×C19C2512yes—
465C2×C4×C19C2514yes—
466C2×C4×C19C2511yescharacteristic
467C2×C4×C19C2511yescharacteristic
468C2×C4×C19C2512yes—
469#3565C2×C1918yescomplemented
470#3555C2×C1914yescomplemented
471#3547C2×C1914yescomplemented
472#3541C2×C1918yescomplemented
473#3518C2×C1914yescomplemented
474#3516C2×C1918yescomplemented
475#3515C2×C1914yescomplemented
476#3512C2×C1912yescomplemented
477#3511C2×C1912yescomplemented
478#3511C2×C1914yescomplemented
479#3509C2×C1914yescomplemented
480#3504C2×C1912yescomplemented
481#3503C2×C1912yescomplemented
482#3493C2×C1914yescomplemented
483#3444C2×C1911yescharacteristic, complemented
484#3444C2×C1911yescharacteristic, complemented
485C2×#533C2×C1911yescharacteristic, complemented
486C22×C19—22no—
487C22×C19—22no—
488C22×C19—24no—
489C22×C19—24no—
490C22×C19—24no—
491C22×C19—22no—
492C22×C19—22no—
493C22×C19—24no—
494C22×C19—28no—
495C22×C19—44no—
496C22×C19C2×2−1+412yes—
497C22×C19C2611yescharacteristic
498C4×C19—22no—
499C4×C19—24no—
500C4×C19—24no—
501C4×C19—22no—
502C4×C19—24no—
503C4×C19—22no—
504C4×C19—22no—
505C4×C19—24no—
506C4×C19—216no—
507C4×C19—28no—
508C4×C19C2×2−1+412yes—
509C4×C19C2×2−1+412yes—
510C4×C19#58514yes—
511#563C22×C19116yes—
512#562C22×C19116yes—
513Q82C22×C1914yescomplemented
514#557C22×C1914yescomplemented
515#557C22×C1918yescomplemented
516#557C22×C1918yescomplemented
517#556C22×C1918yes—
518#556C22×C1918yes—
519#556C22×C1918yes—
520#556C22×C1918yescomplemented
521#556C22×C1914yescomplemented
522#556C22×C19116yescomplemented
523#555C22×C1918yes—
524#555C22×C1918yes—
525#555C22×C1914yescomplemented
526#554C22×C1918yes—
527#554C22×C19116yes—
528#554C22×C1914yescomplemented
529#554C22×C1918yescomplemented
530#554C22×C1914yescomplemented
531#553C22×C1918yes—
532#553C22×C1918yes—
533#553C22×C1918yes—
534#553C22×C19116yes—
535#553C22×C1918yescomplemented
536#552C22×C1918yes—
537#552C22×C1918yes—
538#552C22×C1918yes—
539#552C22×C1918yescomplemented
540#552C22×C1918yescomplemented
541#552C22×C19116yescomplemented
542D4×Q8C22×C1918yes—
543D4×Q8C22×C1914yescomplemented
544#548C22×C1918yes—
545#548C22×C1918yes—
546#548C22×C1918yescomplemented
547#547C22×C1918yes—
548#547C22×C1914yescomplemented
549#544C22×C1914yes—
550#544C22×C1918yescomplemented
551#544C22×C1918yescomplemented
552#542C22×C1918yes—
553#542C22×C19116yes—
554#542C22×C1918yescomplemented
555#542C22×C1918yescomplemented
556#542C22×C19116yescomplemented
557#541C22×C1918yes—
558#541C22×C1918yescomplemented
559#541C22×C1914yescomplemented
560#541C22×C19116yescomplemented
561#540C22×C1914yescomplemented
562#539C22×C19116yes—
563#538C22×C19116yes—
564#537C22×C1914yes—
565#537C22×C1918yes—
566#536C22×C1918yes—
567#533C22×C1914yes—
568#533C22×C1914yes—
569#533C22×C1914yes—
570#533C22×C1914yes—
571#533C22×C1911yescharacteristic
572#533C22×C1911yescharacteristic
573#533C22×C1912yes—
574#533C22×C1912yes—
575#533C22×C1914yescomplemented
576#533C22×C1914yescomplemented
577#533C22×C1914yescomplemented
578#532C22×C1911yescharacteristic
579#532C22×C1912yes—
580#532C22×C1911yescharacteristic
581#532C22×C1912yes—
582#532C22×C1914yescomplemented
583C2×C4⋊Q8C22×C1912yes—
584C2×C4⋊Q8C22×C1914yescomplemented
585#529C22×C1912yes—
586#529C22×C1914yes—
587#529C22×C1914yes—
588#529C22×C1912yes—
589#529C22×C1914yes—
590#529C22×C1914yes—
591#529C22×C1914yes—
592#529C22×C19116yes—
593#529C22×C1918yescomplemented
594C2×#125C22×C1912yes—
595C2×#125C22×C1914yescomplemented
596#525C22×C1912yes—
597#525C22×C1912yes—
598#525C22×C1914yes—
599#525C22×C1914yes—
600C2×C22⋊Q8C22×C1914yes—
601#520C22×C1914yes—
602#520C22×C1914yes—
603#520C22×C1918yescomplemented
604#519C22×C1918yescomplemented
605C4×#41C22×C1912yes—
606C4×#41C22×C1912yes—
607C4×#41C22×C1914yes—
608C4×#41C22×C1914yes—
609C2×C4×Q8C22×C1914yes—
610C2×#117C22×C1912yes—
611C22×C42C22×C1911yescharacteristic
612C2×C19—22no—
613C2×C19—44no—
614C2×C19—44no—
615C2×C19—42no—
616C2×C19C22×2−1+411yescharacteristic
617C2×C19C2×#58512yes—
618C2×#41C23×C1912yes—
619C2×#41C23×C1912yes—
620C2×#41C23×C1914yes—
621C2×#41C23×C1914yes—
622C2×#41C23×C1918yes—
623C22×Q8C23×C1914yes—
624C22×Q8C23×C1918yes—
625C23×C4C23×C1911yescharacteristic
626C23×C4C23×C1912yes—
627C4⋊Q8C23×C1914yes—
628C4⋊Q8C23×C1914yes—
629C4⋊Q8C23×C1914yes—
630C4⋊Q8C23×C1914yes—
631C4⋊Q8C23×C1912yes—
632C4⋊Q8C23×C1918yes—
633C4⋊Q8C23×C1918yes—
634C4⋊Q8C23×C1918yes—
635C4⋊Q8C23×C1911yescharacteristic
636C4⋊Q8C23×C1911yescharacteristic
637C4⋊Q8C23×C1912yes—
638C4⋊Q8C23×C1918yes—
639C4⋊Q8C23×C19116yes—
640C4⋊Q8C23×C19116yes—
641#127C23×C1911yescharacteristic
642#127C23×C1911yescharacteristic
643#126C23×C1918yes—
644#126C23×C1914yes—
645#126C23×C1914yes—
646#126C23×C19116yes—
647#126C23×C19116yes—
648#126C23×C19116yes—
649#126C23×C19116yes—
650#126C23×C19116yes—
651#126C23×C19116yes—
652#126C23×C19116yes—
653#125C23×C1914yes—
654#125C23×C1914yes—
655#125C23×C1918yes—
656#125C23×C1911yescharacteristic
657#125C23×C19116yes—
658#125C23×C1918yes—
659#125C23×C1911yescharacteristic
660#125C23×C1914yes—
661#125C23×C1912yes—
662#125C23×C1914yes—
663#125C23×C19116yes—
664#125C23×C1918yes—
665#125C23×C1918yes—
666#125C23×C19116yes—
667#125C23×C19116yes—
668#125C23×C19116yes—
669#124C23×C1912yes—
670#124C23×C1912yes—
671#124C23×C1914yes—
672#124C23×C1914yes—
673#124C23×C19116yes—
674#124C23×C1918yes—
675#124C23×C19116yes—
676#124C23×C19116yes—
677#124C23×C19116yes—
678#123C23×C1914yes—
679#123C23×C1914yes—
680#123C23×C1914yes—
681#123C23×C1914yes—
682#123C23×C1918yes—
683#123C23×C19116yes—
684#123C23×C19116yes—
685#123C23×C19116yes—
686#123C23×C19116yes—
687#123C23×C19116yes—
688C22⋊Q8C23×C1918yes—
689C22⋊Q8C23×C1918yes—
690C22⋊Q8C23×C1918yes—
691C22⋊Q8C23×C1918yes—
692C22⋊Q8C23×C1914yes—
693C22⋊Q8C23×C1914yes—
694C22⋊Q8C23×C1912yes—
695C22⋊Q8C23×C1914yes—
696C22⋊Q8C23×C1914yes—
697C22⋊Q8C23×C1912yes—
698C22⋊Q8C23×C1914yes—
699C22⋊Q8C23×C19116yes—
700C22⋊Q8C23×C1918yes—
701C22⋊Q8C23×C1918yes—
702C22⋊Q8C23×C1918yes—
703C22⋊Q8C23×C1918yes—
704C22⋊Q8C23×C1918yes—
705C22⋊Q8C23×C19116yes—
706C22⋊Q8C23×C19116yes—
707C22⋊Q8C23×C19116yes—
708C22⋊Q8C23×C19116yes—
709C22⋊Q8C23×C19116yes—
710C22⋊Q8C23×C19116yes—
711#121C23×C1914yes—
712#121C23×C1914yes—
713#121C23×C1914yes—
714#121C23×C1912yes—
715#121C23×C1914yes—
716#121C23×C1912yes—
717#121C23×C1914yes—
718#121C23×C19116yes—
719#121C23×C1918yes—
720#121C23×C1918yes—
721#121C23×C1918yes—
722#121C23×C19116yes—
723#121C23×C19116yes—
724#121C23×C19116yes—
725#120C23×C1914yes—
726#120C23×C1914yes—
727C4×Q8C23×C1918yes—
728C4×Q8C23×C1918yes—
729C4×Q8C23×C1918yes—
730C4×Q8C23×C1918yes—
731C4×Q8C23×C1914yes—
732C4×Q8C23×C1914yes—
733C4×Q8C23×C1914yes—
734C4×Q8C23×C1914yes—
735C4×Q8C23×C1912yes—
736C4×Q8C23×C1914yes—
737C4×Q8C23×C1912yes—
738C4×Q8C23×C19116yes—
739C4×Q8C23×C1918yes—
740C4×Q8C23×C1918yes—
741C4×Q8C23×C19116yes—
742C4×Q8C23×C1918yes—
743C4×Q8C23×C1918yes—
744C4×Q8C23×C1918yes—
745C4×D4C23×C1914yes—
746C4×D4C23×C1918yes—
747C4×D4C23×C1914yes—
748C4×D4C23×C1914yes—
749C4×D4C23×C1914yes—
750C4×D4C23×C1914yes—
751C4×D4C23×C1914yes—
752C4×D4C23×C1918yes—
753C4×D4C23×C1918yes—
754C4×D4C23×C1914yes—
755C4×D4C23×C1912yes—
756C4×D4C23×C1914yes—
757C4×D4C23×C1914yes—
758C4×D4C23×C1912yes—
759C4×D4C23×C1914yes—
760C4×D4C23×C1914yes—
761C4×D4C23×C19116yes—
762C4×D4C23×C19116yes—
763C4×D4C23×C1918yes—
764C4×D4C23×C1918yes—
765C4×D4C23×C19116yes—
766C4×D4C23×C19116yes—
767C4×D4C23×C1918yes—
768#117C23×C1918yes—
769#117C23×C1918yes—
770#117C23×C1914yes—
771#117C23×C1912yes—
772#117C23×C1912yes—
773#117C23×C1914yes—
774#117C23×C1914yes—
775#117C23×C1914yes—
776#117C23×C1914yes—
777#117C23×C1914yes—
778#117C23×C1918yes—
779#117C23×C19116yes—
780#117C23×C19116yes—
781#117C23×C1918yes—
782#117C23×C1918yes—
783#117C23×C1918yes—
784#117C23×C19116yes—
785C2×C4⋊C4C23×C1914yes—
786C2×C4⋊C4C23×C1918yes—
787C2×C4⋊C4C23×C1914yes—
788C2×C4⋊C4C23×C1918yes—
789C2×C4⋊C4C23×C1918yes—
790C2×C4⋊C4C23×C19116yes—
791C2×C4⋊C4C23×C1918yes—
792C2×C22⋊C4C23×C1914yes—
793C2×C42C23×C1914yes—
794C2×C42C23×C1912yes—
795C2×C42C23×C1914yes—
796C2×C42C23×C1914yes—
797C2×C42C23×C1911yescharacteristic
798C2×C42C23×C1912yes—
799C2×C42C23×C1911yescharacteristic
800C2×C42C23×C1912yes—
801C2×C42C23×C1912yes—
802C2×C42C23×C1912yes—
803C19#6283811yescharacteristic, direct product factor, Sylow
804C24C24×C1911yescharacteristic
805#41—28no—
806#41—28no—
807#41—48no—
808#41—48no—
809#41—416no—
810C2×Q8—48no—
811C2×Q8—416no—
812C2×Q8C24×C1912yes—
813C2×Q8C24×C1912yes—
814C2×Q8C24×C1918yes—
815C2×Q8C24×C1914yes—
816C2×Q8C24×C1918yes—
817C2×Q8C24×C1914yes—
818C2×Q8C24×C19116yes—
819C2×D4C24×C1914yes—
820C2×D4C24×C1914yes—
821C2×D4C24×C1912yes—
822C2×D4C24×C1912yes—
823C2×D4C24×C1914yes—
824C2×D4C24×C1914yes—
825C2×D4C24×C1918yes—
826C2×D4C24×C1914yes—
827C2×D4C24×C19116yes—
828C2×D4C24×C1914yes—
829C22×C4—24no—
830C22×C4—44no—
831C22×C4C24×C1911yescharacteristic
832C22×C4C24×C1912yes—
833C22×C4C24×C1912yes—
834C22×C4C24×C1912yes—
835C22×C4C24×C1912yes—
836C22×C4C24×C1912yes—
837C22×C4C24×C1914yes—
838C22×C4C24×C1914yes—
839C22×C4C24×C1914yes—
840C22×C4C24×C1914yes—
841C22×C4C24×C1912yes—
842C22×C4C24×C1912yes—
843C22×C4C24×C1912yes—
844C22×C4C24×C1918yes—
845C22×C4C24×C1918yes—
846C22×C4C24×C19116yes—
847C22×C4C24×C19116yes—
848C22×C4C24×C1911yescharacteristic
849C4⋊C4C24×C1912yes—
850C4⋊C4C24×C1914yes—
851C4⋊C4C24×C1918yes—
852C4⋊C4C24×C1918yes—
853C4⋊C4C24×C1914yes—
854C4⋊C4C24×C1918yes—
855C4⋊C4C24×C1914yes—
856C4⋊C4C24×C19116yes—
857C4⋊C4C24×C19116yes—
858C4⋊C4C24×C19116yes—
859C4⋊C4C24×C19116yes—
860C4⋊C4C24×C19116yes—
861C4⋊C4C24×C19116yes—
862C4⋊C4C24×C1918yes—
863C4⋊C4C24×C1912yes—
864C4⋊C4C24×C1914yes—
865C4⋊C4C24×C1914yes—
866C4⋊C4C24×C1918yes—
867C4⋊C4C24×C1914yes—
868C4⋊C4C24×C1914yes—
869C4⋊C4C24×C1914yes—
870C4⋊C4C24×C1914yes—
871C4⋊C4C24×C1914yes—
872C4⋊C4C24×C1918yes—
873C4⋊C4C24×C1918yes—
874C4⋊C4C24×C1914yes—
875C4⋊C4C24×C19116yes—
876C4⋊C4C24×C19116yes—
877C22⋊C4C24×C19116yes—
878C22⋊C4C24×C1914yes—
879C22⋊C4C24×C1914yes—
880C22⋊C4C24×C1918yes—
881C22⋊C4C24×C19116yes—
882C22⋊C4C24×C1914yes—
883C22⋊C4C24×C1914yes—
884C22⋊C4C24×C1914yes—
885C22⋊C4C24×C1914yes—
886C22⋊C4C24×C1914yes—
887C22⋊C4C24×C1918yes—
888C22⋊C4C24×C1914yes—
889C22⋊C4C24×C1918yes—
890C22⋊C4C24×C19116yes—
891C22⋊C4C24×C19116yes—
892C22⋊C4C24×C19116yes—
893C22⋊C4C24×C1914yes—
894C22⋊C4C24×C1914yes—
895C22⋊C4C24×C1918yes—
896C42C24×C1911yescharacteristic
897C42C24×C1911yescharacteristic
898C42C24×C1912yes—
899C42C24×C1912yes—
900C42C24×C1911yescharacteristic
901C42C24×C1911yescharacteristic
902C42C24×C1912yes—
903C42C24×C1912yes—
904C42C24×C1912yes—
905C42C24×C1912yes—
906C42C24×C1918yes—
907C42C24×C19116yes—
908C42C24×C1914yes—
909C42C24×C1914yes—
910C42C24×C1914yes—
911C42C24×C1914yes—
912C42C24×C19116yes—
913C42C24×C19116yes—
914C23—22no—
915C23—42no—
916C23C25×C1912yes—
917C23C25×C1914yes—
918C23C25×C1914yes—
919C23C25×C1911yescharacteristic
920Q8—24no—
921Q8—24no—
922Q8—216no—
923Q8—28no—
924Q8—48no—
925Q8—416no—
926Q8—44no—
927D4—28no—
928D4—28no—
929D4—24no—
930D4—24no—
931D4—28no—
932D4—44no—
933D4—44no—
934D4—44no—
935D4—48no—
936D4—416no—
937C2×C4—22no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—28no—
941C2×C4—28no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—28no—
946C2×C4—28no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—48no—
951C2×C4—416no—
952C2×C4—48no—
953C2×C4—416no—
954C2×C4C19×2−1+414yes—
955C2×C4C25×C1912yes—
956C2×C4C25×C1912yes—
957C2×C4C25×C1914yes—
958C2×C4C25×C1914yes—
959C2×C4C25×C1914yes—
960C2×C4C25×C1912yes—
961C2×C4C25×C1918yes—
962C2×C4C25×C19116yes—
963C2×C4C25×C1912yes—
964C2×C4C25×C1914yes—
965C2×C4C25×C1911yescharacteristic
966C2×C4C25×C1911yescharacteristic
967C2×C4C25×C1912yes—
968C22—22no—
969C22—22no—
970C22—24no—
971C22—24no—
972C22—24no—
973C22—22no—
974C22—22no—
975C22—24no—
976C22—28no—
977C22—44no—
978C22C2×C19×2−1+412yes—
979C22C26×C1911yescharacteristic
980C4—22no—
981C4—24no—
982C4—24no—
983C4—22no—
984C4—24no—
985C4—22no—
986C4—22no—
987C4—24no—
988C4—216no—
989C4—28no—
990C4C2×C19×2−1+412yes—
991C4C2×C19×2−1+412yes—
992C4C19×#58514yes—
993C2—22no—
994C2—42no—
995C2—44no—
996C2—44no—
997C2C22×C19×2−1+411yescharacteristic
998C2C2×C19×#58512yes—
subgroupG/H
center, socleC22×C19C26
commutator, Frattini, cosocleC22C26×C19
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C19 ◁ G

Complements

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

NH ≅ G/Ntype
1. C19×#3565C2semidirect
2. C19×#3555C2semidirect
3. C19×#3547C2semidirect
4. C19×#3541C2semidirect
5. C19×#3518C2semidirect
6. C19×#3516C2semidirect
7. C19×#3515C2semidirect
8. C19×#3512C2semidirect
9. C19×#3511C2semidirect
10. C19×#3511C2semidirect
11. C19×#3509C2semidirect
12. C19×#3504C2semidirect
13. C19×#3503C2semidirect
14. C19×#3493C2semidirect
15. C19×#3444C2semidirect
16. C19×#3444C2semidirect
17. C2×C19×#533C2semidirect
20. Q82×C19C22semidirect
21. C19×#557C22semidirect
22. C19×#557C22semidirect
23. C19×#557C22semidirect
27. C19×#556C22semidirect
28. C19×#556C22semidirect
29. C19×#556C22semidirect
32. C19×#555C22semidirect
35. C19×#554C22semidirect
36. C19×#554C22semidirect
37. C19×#554C22semidirect
42. C19×#553C22semidirect
46. C19×#552C22semidirect
47. C19×#552C22semidirect
48. C19×#552C22semidirect
50. D4×Q8×C19C22semidirect
53. C19×#548C22semidirect
55. C19×#547C22semidirect
57. C19×#544C22semidirect
58. C19×#544C22semidirect
61. C19×#542C22semidirect
62. C19×#542C22semidirect
63. C19×#542C22semidirect
65. C19×#541C22semidirect
66. C19×#541C22semidirect
67. C19×#541C22semidirect
68. C19×#540C22semidirect
82. C19×#533C22semidirect
83. C19×#533C22semidirect
84. C19×#533C22semidirect
89. C19×#532C22semidirect
91. C2×C19×C4⋊Q8C22semidirect
100. C19×#529C22semidirect
102. C2×C19×#125C22semidirect
110. C19×#520C22semidirect
111. C19×#519C22semidirect
414. #62838C19direct (N × H)
469. #3565C2×C19semidirect
470. #3555C2×C19semidirect
471. #3547C2×C19semidirect
472. #3541C2×C19semidirect
473. #3518C2×C19semidirect
474. #3516C2×C19semidirect
475. #3515C2×C19semidirect
476. #3512C2×C19semidirect
477. #3511C2×C19semidirect
478. #3511C2×C19semidirect
479. #3509C2×C19semidirect
480. #3504C2×C19semidirect
481. #3503C2×C19semidirect
482. #3493C2×C19semidirect
483. #3444C2×C19semidirect
484. #3444C2×C19semidirect
485. C2×#533C2×C19semidirect
513. Q82C22×C19semidirect
514. #557C22×C19semidirect
515. #557C22×C19semidirect
516. #557C22×C19semidirect
520. #556C22×C19semidirect
521. #556C22×C19semidirect
522. #556C22×C19semidirect
525. #555C22×C19semidirect
528. #554C22×C19semidirect
529. #554C22×C19semidirect
530. #554C22×C19semidirect
535. #553C22×C19semidirect
539. #552C22×C19semidirect
540. #552C22×C19semidirect
541. #552C22×C19semidirect
543. D4×Q8C22×C19semidirect
546. #548C22×C19semidirect
548. #547C22×C19semidirect
550. #544C22×C19semidirect
551. #544C22×C19semidirect
554. #542C22×C19semidirect
555. #542C22×C19semidirect
556. #542C22×C19semidirect
558. #541C22×C19semidirect
559. #541C22×C19semidirect
560. #541C22×C19semidirect
561. #540C22×C19semidirect
575. #533C22×C19semidirect
576. #533C22×C19semidirect
577. #533C22×C19semidirect
582. #532C22×C19semidirect
584. C2×C4⋊Q8C22×C19semidirect
593. #529C22×C19semidirect
595. C2×#125C22×C19semidirect
603. #520C22×C19semidirect
604. #519C22×C19semidirect
803. C19#62838direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#35652
C19×#35552
C19×#35472
C19×#35412
C19×#35182
C19×#35162
C19×#35152
C19×#35122
C19×#35112
C19×#35092
C19×#35042
C19×#35032
C19×#34932
C19×#34442
C2×C19×#5332
#6283819