Finite Group Databasebeta

← C19×#62761 #18068720

Subgroups — C19×#62761 #18068720

Order 4864.

6518 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C19×#3557C214yesmaximal, complemented
2C19×#3556C211yesmaximal, characteristic, complemented
3C19×#3555C214yesmaximal, complemented
4C19×#3554C214yesmaximal, complemented
5C19×#3553C214yesmaximal, complemented
6C19×#3552C214yesmaximal, complemented
7C19×#3550C212yesmaximal, complemented
8C19×#3548C211yesmaximal, characteristic, complemented
9C19×#3541C218yesmaximal, complemented
10C19×#3531C214yesmaximal, complemented
11C19×#3482C214yesmaximal, complemented
12C19×#3480C214yesmaximal, complemented
13Q8×#41×C19C214yesmaximal, complemented
14C19×#3461C218yesmaximal, complemented
15C19×#3455C214yesmaximal, complemented
16C19×#3444C212yesmaximal, complemented
17C2×C19×#533C211yesmaximal, characteristic, complemented
18C19×#564C2214yescomplemented
19C19×#563C22116yes—
20C19×#563C2218yescomplemented
21C19×#563C22116yescomplemented
22C19×#562C22116yes—
23C19×#562C2214yescomplemented
24C19×#559C2214yescomplemented
25C19×#559C2218yescomplemented
26Q82×C19C2214yescomplemented
27C19×#557C2214yescomplemented
28C19×#557C2218yescomplemented
29C19×#557C2214yescomplemented
30C19×#557C2214yescomplemented
31C19×#556C2218yes—
32C19×#556C2214yescomplemented
33C19×#556C2218yescomplemented
34C19×#556C2214yescomplemented
35C19×#554C2218yes—
36C19×#554C22116yes—
37C19×#554C2214yescomplemented
38C19×#554C2218yescomplemented
39C19×#553C2218yes—
40C19×#553C22116yes—
41C19×#552C2218yes—
42C19×#552C22116yescomplemented
43C19×#550C2214yescomplemented
44D4×Q8×C19C2218yes—
45D4×Q8×C19C2214yescomplemented
46D4×Q8×C19C2214yescomplemented
47C19×#548C2218yes—
48C19×#548C2218yes—
49C19×#547C2218yes—
50C19×#547C2214yescomplemented
51C19×#544C2218yescomplemented
52C19×#542C2218yes—
53C19×#542C2218yes—
54C19×#542C2218yes—
55C19×#542C22116yes—
56C19×#542C2218yescomplemented
57C19×#541C2214yes—
58C19×#541C2214yes—
59C19×#541C2218yes—
60C19×#541C2218yescomplemented
61C19×#541C22116yescomplemented
62C19×#540C2214yes—
63C19×#540C2214yes—
64C19×#539C22116yes—
65C19×#539C22116yes—
66C19×#539C22116yescomplemented
67C19×#538C22116yes—
68C19×#537C2218yes—
69C19×#536C2218yes—
70C19×#536C2218yescomplemented
71C19×#533C2214yes—
72C19×#533C2212yes—
73C19×#533C2212yes—
74C19×#533C2211yescharacteristic
75C19×#533C2211yescharacteristic
76C19×#533C2214yes—
77C19×#533C2212yes—
78C19×#533C2212yes—
79C19×#533C2212yes—
80C19×#533C2212yes—
81C19×#533C2214yes—
82C19×#533C2218yescomplemented
83C19×#533C22116yescomplemented
84C19×#532C2212yes—
85C19×#532C2212yes—
86C19×#532C2212yes—
87C19×#532C2214yes—
88C2×C19×C4⋊Q8C2212yes—
89C19×#529C2214yes—
90C19×#529C2214yes—
91C19×#529C2214yes—
92C19×#529C2214yes—
93C19×#529C2214yes—
94C19×#529C2214yes—
95C19×#529C22116yes—
96C19×#529C22116yes—
97C19×#529C2218yescomplemented
98C19×#529C22116yescomplemented
99C2×C19×#125C2212yes—
100C19×#525C2214yes—
101C19×#525C2214yes—
102C19×#525C2214yes—
103C2×C19×C22⋊Q8C2214yes—
104C4×#41×C19C2214yes—
105C4×#41×C19C2214yes—
106C4×#41×C19C2214yes—
107C4×#41×C19C2218yes—
108C4×#41×C19C2218yescomplemented
109C2×C4×Q8×C19C2214yes—
110C2×C4×Q8×C19C2218yescomplemented
111C2×C19×#117C2212yes—
112C22×C42×C19C2211yescharacteristic
113C2×#41×C19C2314yes—
114C2×#41×C19C2314yes—
115C2×#41×C19C2314yes—
116C2×#41×C19C2318yes—
117C22×Q8×C19C2314yes—
118C22×Q8×C19C2318yes—
119C23×C4×C19C2311yescharacteristic
120C23×C4×C19C2312yes—
121C19×C4⋊Q8C2314yes—
122C19×C4⋊Q8C2314yes—
123C19×C4⋊Q8C2312yes—
124C19×C4⋊Q8C2312yes—
125C19×C4⋊Q8C2314yes—
126C19×C4⋊Q8C2312yes—
127C19×C4⋊Q8C2312yes—
128C19×C4⋊Q8C2312yes—
129C19×C4⋊Q8C2314yes—
130C19×C4⋊Q8C2318yes—
131C19×C4⋊Q8C23116yes—
132C19×C4⋊Q8C2318yes—
133C19×C4⋊Q8C23116yes—
134C19×C4⋊Q8C2318yes—
135C19×#127C2312yes—
136C19×#127C2314yes—
137C19×#126C2318yes—
138C19×#126C2318yes—
139C19×#126C23116yes—
140C19×#126C23116yes—
141C19×#126C23116yes—
142C19×#126C23116yes—
143C19×#126C23116yes—
144C19×#126C23116yes—
145C19×#126C23116yes—
146C19×#125C2318yes—
147C19×#125C2314yes—
148C19×#125C2312yes—
149C19×#125C2312yes—
150C19×#125C2314yes—
151C19×#125C2314yes—
152C19×#125C2314yes—
153C19×#125C23116yes—
154C19×#125C23116yes—
155C19×#125C23116yes—
156C19×#125C2318yes—
157C19×#125C2314yes—
158C19×#125C2314yes—
159C19×#125C23116yes—
160C19×#125C23116yes—
161C19×#125C23116yes—
162C19×#124C2314yes—
163C19×#124C2314yes—
164C19×#124C2314yes—
165C19×#124C23116yes—
166C19×#124C23116yes—
167C19×#124C2318yes—
168C19×#124C23116yes—
169C19×#124C2318yes—
170C19×#123C2318yes—
171C19×#123C2318yes—
172C19×#123C2318yes—
173C19×#123C23116yes—
174C19×#123C23116yes—
175C19×#123C23116yes—
176C19×#123C23116yes—
177C19×#123C23116yes—
178C19×#123C23116yes—
179C19×#123C23116yes—
180C19×C22⋊Q8C2314yes—
181C19×C22⋊Q8C2314yes—
182C19×C22⋊Q8C2318yes—
183C19×C22⋊Q8C2314yes—
184C19×C22⋊Q8C2314yes—
185C19×C22⋊Q8C2318yes—
186C19×C22⋊Q8C2314yes—
187C19×C22⋊Q8C2314yes—
188C19×C22⋊Q8C2314yes—
189C19×C22⋊Q8C2314yes—
190C19×C22⋊Q8C2314yes—
191C19×C22⋊Q8C2314yes—
192C19×C22⋊Q8C23116yes—
193C19×C22⋊Q8C23116yes—
194C19×C22⋊Q8C2318yes—
195C19×C22⋊Q8C23116yes—
196C19×C22⋊Q8C23116yes—
197C19×C22⋊Q8C2318yes—
198C19×C22⋊Q8C23116yes—
199C19×C22⋊Q8C2318yes—
200C19×C22⋊Q8C23116yes—
201C19×C22⋊Q8C23116yes—
202C19×C22⋊Q8C23116yes—
203C19×C22⋊Q8C23116yes—
204C19×#121C2314yes—
205C19×#121C2314yes—
206C19×#121C2314yes—
207C19×#121C2314yes—
208C19×#121C2314yes—
209C19×#121C2314yes—
210C19×#121C23116yes—
211C19×#121C23116yes—
212C19×#121C23116yes—
213C19×#121C2318yes—
214C19×#121C23116yes—
215C19×#120C2318yes—
216C4×Q8×C19C2314yes—
217C4×Q8×C19C2314yes—
218C4×Q8×C19C2318yes—
219C4×Q8×C19C2314yes—
220C4×Q8×C19C2314yes—
221C4×Q8×C19C2318yes—
222C4×Q8×C19C2314yes—
223C4×Q8×C19C23116yes—
224C4×Q8×C19C2318yes—
225C4×Q8×C19C2318yes—
226C4×Q8×C19C23116yes—
227C4×Q8×C19C2314yes—
228C4×Q8×C19C2314yes—
229C4×Q8×C19C2314yes—
230C4×Q8×C19C2314yes—
231C4×Q8×C19C2314yes—
232C4×Q8×C19C2318yes—
233C4×Q8×C19C2318yes—
234C4×Q8×C19C2318yes—
235C4×D4×C19C2314yes—
236C4×D4×C19C2318yes—
237C4×D4×C19C2318yes—
238C4×D4×C19C2318yes—
239C4×D4×C19C2318yes—
240C4×D4×C19C2318yes—
241C4×D4×C19C2318yes—
242C4×D4×C19C2314yes—
243C4×D4×C19C2314yes—
244C4×D4×C19C2314yes—
245C4×D4×C19C2314yes—
246C4×D4×C19C2314yes—
247C4×D4×C19C23116yes—
248C4×D4×C19C23116yes—
249C4×D4×C19C2318yes—
250C4×D4×C19C2318yes—
251C4×D4×C19C23116yes—
252C4×D4×C19C23116yes—
253C4×D4×C19C2318yes—
254C19×#117C2314yes—
255C19×#117C2314yes—
256C19×#117C2312yes—
257C19×#117C2314yes—
258C19×#117C2312yes—
259C19×#117C2314yes—
260C19×#117C2314yes—
261C19×#117C2314yes—
262C19×#117C2318yes—
263C19×#117C23116yes—
264C19×#117C2318yes—
265C19×#117C2318yes—
266C19×#117C2318yes—
267C19×#117C23116yes—
268C2×C4⋊C4×C19C2314yes—
269C2×C4⋊C4×C19C2318yes—
270C2×C4⋊C4×C19C2314yes—
271C2×C4⋊C4×C19C2318yes—
272C2×C4⋊C4×C19C23116yes—
273C2×C22⋊C4×C19C2314yes—
274C2×C42×C19C2312yes—
275C2×C42×C19C2311yescharacteristic
276C2×C42×C19C2312yes—
277C2×C42×C19C2311yescharacteristic
278C2×C42×C19C2311yescharacteristic
279C2×C42×C19C2311yescharacteristic
280C2×C42×C19C2311yescharacteristic
281C2×C42×C19C2312yes—
282C2×C42×C19C2311yescharacteristic
283C2×C42×C19C2314yes—
284C2×C42×C19C2318yes—
285C2×C42×C19C23116yes—
286C24×C19C2411yescharacteristic
287#41×C19—216no—
288#41×C19—48no—
289#41×C19—48no—
290#41×C19—416no—
291C2×Q8×C19—48no—
292C2×Q8×C19—416no—
293C2×Q8×C19C2414yes—
294C2×Q8×C19C2414yes—
295C2×Q8×C19C2414yes—
296C2×Q8×C19C2414yes—
297C2×Q8×C19C2418yes—
298C2×Q8×C19C24116yes—
299C2×Q8×C19C2414yes—
300C2×D4×C19C2418yes—
301C2×D4×C19C2414yes—
302C2×D4×C19C2414yes—
303C2×D4×C19C2418yes—
304C2×D4×C19C2418yes—
305C2×D4×C19C2414yes—
306C2×D4×C19C24116yes—
307C22×C4×C19—24no—
308C22×C4×C19—44no—
309C22×C4×C19C2411yescharacteristic
310C22×C4×C19C2412yes—
311C22×C4×C19C2411yescharacteristic
312C22×C4×C19C2411yescharacteristic
313C22×C4×C19C2412yes—
314C22×C4×C19C2412yes—
315C22×C4×C19C2418yes—
316C22×C4×C19C2418yes—
317C22×C4×C19C2411yescharacteristic
318C22×C4×C19C2411yescharacteristic
319C22×C4×C19C2412yes—
320C22×C4×C19C2412yes—
321C22×C4×C19C2412yes—
322C22×C4×C19C2418yes—
323C22×C4×C19C2418yes—
324C22×C4×C19C24116yes—
325C22×C4×C19C24116yes—
326C22×C4×C19C2411yescharacteristic
327C4⋊C4×C19C2414yes—
328C4⋊C4×C19C2418yes—
329C4⋊C4×C19C2414yes—
330C4⋊C4×C19C2418yes—
331C4⋊C4×C19C2418yes—
332C4⋊C4×C19C2414yes—
333C4⋊C4×C19C2414yes—
334C4⋊C4×C19C2418yes—
335C4⋊C4×C19C2414yes—
336C4⋊C4×C19C2418yes—
337C4⋊C4×C19C24116yes—
338C4⋊C4×C19C24116yes—
339C4⋊C4×C19C2418yes—
340C4⋊C4×C19C2418yes—
341C4⋊C4×C19C24116yes—
342C4⋊C4×C19C2414yes—
343C4⋊C4×C19C2414yes—
344C4⋊C4×C19C2414yes—
345C4⋊C4×C19C2414yes—
346C4⋊C4×C19C2414yes—
347C4⋊C4×C19C24116yes—
348C4⋊C4×C19C2418yes—
349C4⋊C4×C19C2418yes—
350C4⋊C4×C19C2418yes—
351C4⋊C4×C19C2418yes—
352C4⋊C4×C19C24116yes—
353C4⋊C4×C19C2418yes—
354C4⋊C4×C19C24116yes—
355C22⋊C4×C19C2414yes—
356C22⋊C4×C19C2418yes—
357C22⋊C4×C19C2414yes—
358C22⋊C4×C19C2418yes—
359C22⋊C4×C19C2418yes—
360C22⋊C4×C19C2418yes—
361C22⋊C4×C19C2418yes—
362C22⋊C4×C19C2418yes—
363C22⋊C4×C19C24116yes—
364C22⋊C4×C19C2418yes—
365C22⋊C4×C19C24116yes—
366C22⋊C4×C19C2418yes—
367C22⋊C4×C19C2418yes—
368C22⋊C4×C19C2418yes—
369C22⋊C4×C19C24116yes—
370C22⋊C4×C19C24116yes—
371C42×C19C2411yescharacteristic
372C42×C19C2412yes—
373C42×C19C2411yescharacteristic
374C42×C19C2412yes—
375C42×C19C2412yes—
376C42×C19C2412yes—
377C42×C19C2411yescharacteristic
378C42×C19C2411yescharacteristic
379C42×C19C2418yes—
380C42×C19C2418yes—
381C42×C19C2414yes—
382C42×C19C2414yes—
383C42×C19C24116yes—
384C42×C19C24116yes—
385C42×C19C2412yes—
386C42×C19C2412yes—
387C42×C19C2418yes—
388C42×C19C2418yes—
389#62761C1911yesmaximal, characteristic, direct product factor, Sylow
390C23×C19—22no—
391C23×C19—42no—
392C23×C19C2511yescharacteristic
393C23×C19C2511yescharacteristic
394C23×C19C2518yes—
395C23×C19C2511yescharacteristic
396Q8×C19—28no—
397Q8×C19—28no—
398Q8×C19—28no—
399Q8×C19—28no—
400Q8×C19—416no—
401Q8×C19—48no—
402Q8×C19—44no—
403D4×C19—216no—
404D4×C19—28no—
405D4×C19—28no—
406D4×C19—44no—
407D4×C19—48no—
408D4×C19—416no—
409D4×C19—48no—
410C2×C4×C19—22no—
411C2×C4×C19—22no—
412C2×C4×C19—22no—
413C2×C4×C19—22no—
414C2×C4×C19—22no—
415C2×C4×C19—216no—
416C2×C4×C19—24no—
417C2×C4×C19—24no—
418C2×C4×C19—24no—
419C2×C4×C19—216no—
420C2×C4×C19—42no—
421C2×C4×C19—42no—
422C2×C4×C19—42no—
423C2×C4×C19—48no—
424C2×C4×C19—416no—
425C2×C4×C19—48no—
426C2×C4×C19—416no—
427C2×C4×C192−1+414yes—
428C2×C4×C19C2512yes—
429C2×C4×C19C2518yes—
430C2×C4×C19C2511yescharacteristic
431C2×C4×C19C2511yescharacteristic
432C2×C4×C19C2512yes—
433C2×C4×C19C2518yes—
434C2×C4×C19C2518yes—
435C2×C4×C19C2518yes—
436C2×C4×C19C2512yes—
437C2×C4×C19C2518yes—
438C2×C4×C19C2511yescharacteristic
439C2×C4×C19C2512yes—
440C2×C4×C19C2511yescharacteristic
441#3557C2×C1914yescomplemented
442#3556C2×C1911yescharacteristic, complemented
443#3555C2×C1914yescomplemented
444#3554C2×C1914yescomplemented
445#3553C2×C1914yescomplemented
446#3552C2×C1914yescomplemented
447#3550C2×C1912yescomplemented
448#3548C2×C1911yescharacteristic, complemented
449#3541C2×C1918yescomplemented
450#3531C2×C1914yescomplemented
451#3482C2×C1914yescomplemented
452#3480C2×C1914yescomplemented
453Q8×#41C2×C1914yescomplemented
454#3461C2×C1918yescomplemented
455#3455C2×C1914yescomplemented
456#3444C2×C1912yescomplemented
457C2×#533C2×C1911yescharacteristic, complemented
458C22×C19—22no—
459C22×C19—21no—
460C22×C19—21no—
461C22×C19—28no—
462C22×C19—28no—
463C22×C19—22no—
464C22×C19—22no—
465C22×C19—28no—
466C22×C19—44no—
467C22×C19C2×2−1+412yes—
468C22×C19C2611yescharacteristic
469C4×C19—21no—
470C4×C19—21no—
471C4×C19—28no—
472C4×C19—22no—
473C4×C19—22no—
474C4×C19—28no—
475C4×C19—22no—
476C4×C19—28no—
477C4×C19—28no—
478C4×C19—28no—
479C4×C19C2×2−1+412yes—
480C4×C19C2×2−1+412yes—
481C4×C19#58514yes—
482#564C22×C1914yescomplemented
483#563C22×C19116yes—
484#563C22×C1918yescomplemented
485#563C22×C19116yescomplemented
486#562C22×C19116yes—
487#562C22×C1914yescomplemented
488#559C22×C1914yescomplemented
489#559C22×C1918yescomplemented
490Q82C22×C1914yescomplemented
491#557C22×C1914yescomplemented
492#557C22×C1918yescomplemented
493#557C22×C1914yescomplemented
494#557C22×C1914yescomplemented
495#556C22×C1918yes—
496#556C22×C1914yescomplemented
497#556C22×C1918yescomplemented
498#556C22×C1914yescomplemented
499#554C22×C1918yes—
500#554C22×C19116yes—
501#554C22×C1914yescomplemented
502#554C22×C1918yescomplemented
503#553C22×C1918yes—
504#553C22×C19116yes—
505#552C22×C1918yes—
506#552C22×C19116yescomplemented
507#550C22×C1914yescomplemented
508D4×Q8C22×C1918yes—
509D4×Q8C22×C1914yescomplemented
510D4×Q8C22×C1914yescomplemented
511#548C22×C1918yes—
512#548C22×C1918yes—
513#547C22×C1918yes—
514#547C22×C1914yescomplemented
515#544C22×C1918yescomplemented
516#542C22×C1918yes—
517#542C22×C1918yes—
518#542C22×C1918yes—
519#542C22×C19116yes—
520#542C22×C1918yescomplemented
521#541C22×C1914yes—
522#541C22×C1914yes—
523#541C22×C1918yes—
524#541C22×C1918yescomplemented
525#541C22×C19116yescomplemented
526#540C22×C1914yes—
527#540C22×C1914yes—
528#539C22×C19116yes—
529#539C22×C19116yes—
530#539C22×C19116yescomplemented
531#538C22×C19116yes—
532#537C22×C1918yes—
533#536C22×C1918yes—
534#536C22×C1918yescomplemented
535#533C22×C1914yes—
536#533C22×C1912yes—
537#533C22×C1912yes—
538#533C22×C1911yescharacteristic
539#533C22×C1911yescharacteristic
540#533C22×C1914yes—
541#533C22×C1912yes—
542#533C22×C1912yes—
543#533C22×C1912yes—
544#533C22×C1912yes—
545#533C22×C1914yes—
546#533C22×C1918yescomplemented
547#533C22×C19116yescomplemented
548#532C22×C1912yes—
549#532C22×C1912yes—
550#532C22×C1912yes—
551#532C22×C1914yes—
552C2×C4⋊Q8C22×C1912yes—
553#529C22×C1914yes—
554#529C22×C1914yes—
555#529C22×C1914yes—
556#529C22×C1914yes—
557#529C22×C1914yes—
558#529C22×C1914yes—
559#529C22×C19116yes—
560#529C22×C19116yes—
561#529C22×C1918yescomplemented
562#529C22×C19116yescomplemented
563C2×#125C22×C1912yes—
564#525C22×C1914yes—
565#525C22×C1914yes—
566#525C22×C1914yes—
567C2×C22⋊Q8C22×C1914yes—
568C4×#41C22×C1914yes—
569C4×#41C22×C1914yes—
570C4×#41C22×C1914yes—
571C4×#41C22×C1918yes—
572C4×#41C22×C1918yescomplemented
573C2×C4×Q8C22×C1914yes—
574C2×C4×Q8C22×C1918yescomplemented
575C2×#117C22×C1912yes—
576C22×C42C22×C1911yescharacteristic
577C2×C19—22no—
578C2×C19—48no—
579C2×C19—41no—
580C2×C19—41no—
581C2×C19C22×2−1+411yescharacteristic
582C2×C19C2×#58512yes—
583C2×#41C23×C1914yes—
584C2×#41C23×C1914yes—
585C2×#41C23×C1914yes—
586C2×#41C23×C1918yes—
587C22×Q8C23×C1914yes—
588C22×Q8C23×C1918yes—
589C23×C4C23×C1911yescharacteristic
590C23×C4C23×C1912yes—
591C4⋊Q8C23×C1914yes—
592C4⋊Q8C23×C1914yes—
593C4⋊Q8C23×C1912yes—
594C4⋊Q8C23×C1912yes—
595C4⋊Q8C23×C1914yes—
596C4⋊Q8C23×C1912yes—
597C4⋊Q8C23×C1912yes—
598C4⋊Q8C23×C1912yes—
599C4⋊Q8C23×C1914yes—
600C4⋊Q8C23×C1918yes—
601C4⋊Q8C23×C19116yes—
602C4⋊Q8C23×C1918yes—
603C4⋊Q8C23×C19116yes—
604C4⋊Q8C23×C1918yes—
605#127C23×C1912yes—
606#127C23×C1914yes—
607#126C23×C1918yes—
608#126C23×C1918yes—
609#126C23×C19116yes—
610#126C23×C19116yes—
611#126C23×C19116yes—
612#126C23×C19116yes—
613#126C23×C19116yes—
614#126C23×C19116yes—
615#126C23×C19116yes—
616#125C23×C1918yes—
617#125C23×C1914yes—
618#125C23×C1912yes—
619#125C23×C1912yes—
620#125C23×C1914yes—
621#125C23×C1914yes—
622#125C23×C1914yes—
623#125C23×C19116yes—
624#125C23×C19116yes—
625#125C23×C19116yes—
626#125C23×C1918yes—
627#125C23×C1914yes—
628#125C23×C1914yes—
629#125C23×C19116yes—
630#125C23×C19116yes—
631#125C23×C19116yes—
632#124C23×C1914yes—
633#124C23×C1914yes—
634#124C23×C1914yes—
635#124C23×C19116yes—
636#124C23×C19116yes—
637#124C23×C1918yes—
638#124C23×C19116yes—
639#124C23×C1918yes—
640#123C23×C1918yes—
641#123C23×C1918yes—
642#123C23×C1918yes—
643#123C23×C19116yes—
644#123C23×C19116yes—
645#123C23×C19116yes—
646#123C23×C19116yes—
647#123C23×C19116yes—
648#123C23×C19116yes—
649#123C23×C19116yes—
650C22⋊Q8C23×C1914yes—
651C22⋊Q8C23×C1914yes—
652C22⋊Q8C23×C1918yes—
653C22⋊Q8C23×C1914yes—
654C22⋊Q8C23×C1914yes—
655C22⋊Q8C23×C1918yes—
656C22⋊Q8C23×C1914yes—
657C22⋊Q8C23×C1914yes—
658C22⋊Q8C23×C1914yes—
659C22⋊Q8C23×C1914yes—
660C22⋊Q8C23×C1914yes—
661C22⋊Q8C23×C1914yes—
662C22⋊Q8C23×C19116yes—
663C22⋊Q8C23×C19116yes—
664C22⋊Q8C23×C1918yes—
665C22⋊Q8C23×C19116yes—
666C22⋊Q8C23×C19116yes—
667C22⋊Q8C23×C1918yes—
668C22⋊Q8C23×C19116yes—
669C22⋊Q8C23×C1918yes—
670C22⋊Q8C23×C19116yes—
671C22⋊Q8C23×C19116yes—
672C22⋊Q8C23×C19116yes—
673C22⋊Q8C23×C19116yes—
674#121C23×C1914yes—
675#121C23×C1914yes—
676#121C23×C1914yes—
677#121C23×C1914yes—
678#121C23×C1914yes—
679#121C23×C1914yes—
680#121C23×C19116yes—
681#121C23×C19116yes—
682#121C23×C19116yes—
683#121C23×C1918yes—
684#121C23×C19116yes—
685#120C23×C1918yes—
686C4×Q8C23×C1914yes—
687C4×Q8C23×C1914yes—
688C4×Q8C23×C1918yes—
689C4×Q8C23×C1914yes—
690C4×Q8C23×C1914yes—
691C4×Q8C23×C1918yes—
692C4×Q8C23×C1914yes—
693C4×Q8C23×C19116yes—
694C4×Q8C23×C1918yes—
695C4×Q8C23×C1918yes—
696C4×Q8C23×C19116yes—
697C4×Q8C23×C1914yes—
698C4×Q8C23×C1914yes—
699C4×Q8C23×C1914yes—
700C4×Q8C23×C1914yes—
701C4×Q8C23×C1914yes—
702C4×Q8C23×C1918yes—
703C4×Q8C23×C1918yes—
704C4×Q8C23×C1918yes—
705C4×D4C23×C1914yes—
706C4×D4C23×C1918yes—
707C4×D4C23×C1918yes—
708C4×D4C23×C1918yes—
709C4×D4C23×C1918yes—
710C4×D4C23×C1918yes—
711C4×D4C23×C1918yes—
712C4×D4C23×C1914yes—
713C4×D4C23×C1914yes—
714C4×D4C23×C1914yes—
715C4×D4C23×C1914yes—
716C4×D4C23×C1914yes—
717C4×D4C23×C19116yes—
718C4×D4C23×C19116yes—
719C4×D4C23×C1918yes—
720C4×D4C23×C1918yes—
721C4×D4C23×C19116yes—
722C4×D4C23×C19116yes—
723C4×D4C23×C1918yes—
724#117C23×C1914yes—
725#117C23×C1914yes—
726#117C23×C1912yes—
727#117C23×C1914yes—
728#117C23×C1912yes—
729#117C23×C1914yes—
730#117C23×C1914yes—
731#117C23×C1914yes—
732#117C23×C1918yes—
733#117C23×C19116yes—
734#117C23×C1918yes—
735#117C23×C1918yes—
736#117C23×C1918yes—
737#117C23×C19116yes—
738C2×C4⋊C4C23×C1914yes—
739C2×C4⋊C4C23×C1918yes—
740C2×C4⋊C4C23×C1914yes—
741C2×C4⋊C4C23×C1918yes—
742C2×C4⋊C4C23×C19116yes—
743C2×C22⋊C4C23×C1914yes—
744C2×C42C23×C1914yes—
745C2×C42C23×C1912yes—
746C2×C42C23×C1918yes—
747C2×C42C23×C19116yes—
748C2×C42C23×C1911yescharacteristic
749C2×C42C23×C1912yes—
750C2×C42C23×C1911yescharacteristic
751C2×C42C23×C1911yescharacteristic
752C2×C42C23×C1911yescharacteristic
753C2×C42C23×C1911yescharacteristic
754C2×C42C23×C1912yes—
755C2×C42C23×C1911yescharacteristic
756C19#6276111yescharacteristic, direct product factor, Sylow
757C24C24×C1911yescharacteristic
758#41—216no—
759#41—48no—
760#41—48no—
761#41—416no—
762C2×Q8—48no—
763C2×Q8—416no—
764C2×Q8C24×C1914yes—
765C2×Q8C24×C1914yes—
766C2×Q8C24×C1914yes—
767C2×Q8C24×C1914yes—
768C2×Q8C24×C1918yes—
769C2×Q8C24×C19116yes—
770C2×Q8C24×C1914yes—
771C2×D4C24×C1918yes—
772C2×D4C24×C1914yes—
773C2×D4C24×C1914yes—
774C2×D4C24×C1918yes—
775C2×D4C24×C1918yes—
776C2×D4C24×C1914yes—
777C2×D4C24×C19116yes—
778C22×C4—24no—
779C22×C4—44no—
780C22×C4C24×C1918yes—
781C22×C4C24×C1911yescharacteristic
782C22×C4C24×C1912yes—
783C22×C4C24×C1911yescharacteristic
784C22×C4C24×C1911yescharacteristic
785C22×C4C24×C1911yescharacteristic
786C22×C4C24×C1911yescharacteristic
787C22×C4C24×C1912yes—
788C22×C4C24×C1912yes—
789C22×C4C24×C1918yes—
790C22×C4C24×C1912yes—
791C22×C4C24×C1912yes—
792C22×C4C24×C1912yes—
793C22×C4C24×C1918yes—
794C22×C4C24×C1918yes—
795C22×C4C24×C19116yes—
796C22×C4C24×C19116yes—
797C22×C4C24×C1911yescharacteristic
798C4⋊C4C24×C1914yes—
799C4⋊C4C24×C1918yes—
800C4⋊C4C24×C1914yes—
801C4⋊C4C24×C1918yes—
802C4⋊C4C24×C1918yes—
803C4⋊C4C24×C1914yes—
804C4⋊C4C24×C1914yes—
805C4⋊C4C24×C1918yes—
806C4⋊C4C24×C1914yes—
807C4⋊C4C24×C1918yes—
808C4⋊C4C24×C19116yes—
809C4⋊C4C24×C19116yes—
810C4⋊C4C24×C1918yes—
811C4⋊C4C24×C1918yes—
812C4⋊C4C24×C19116yes—
813C4⋊C4C24×C1914yes—
814C4⋊C4C24×C1914yes—
815C4⋊C4C24×C1914yes—
816C4⋊C4C24×C1914yes—
817C4⋊C4C24×C1914yes—
818C4⋊C4C24×C19116yes—
819C4⋊C4C24×C1918yes—
820C4⋊C4C24×C1918yes—
821C4⋊C4C24×C1918yes—
822C4⋊C4C24×C1918yes—
823C4⋊C4C24×C19116yes—
824C4⋊C4C24×C1918yes—
825C4⋊C4C24×C19116yes—
826C22⋊C4C24×C1914yes—
827C22⋊C4C24×C1918yes—
828C22⋊C4C24×C1914yes—
829C22⋊C4C24×C1918yes—
830C22⋊C4C24×C1918yes—
831C22⋊C4C24×C1918yes—
832C22⋊C4C24×C1918yes—
833C22⋊C4C24×C1918yes—
834C22⋊C4C24×C19116yes—
835C22⋊C4C24×C1918yes—
836C22⋊C4C24×C19116yes—
837C22⋊C4C24×C1918yes—
838C22⋊C4C24×C1918yes—
839C22⋊C4C24×C1918yes—
840C22⋊C4C24×C19116yes—
841C22⋊C4C24×C19116yes—
842C42C24×C1912yes—
843C42C24×C1911yescharacteristic
844C42C24×C1918yes—
845C42C24×C1912yes—
846C42C24×C1918yes—
847C42C24×C1912yes—
848C42C24×C1911yescharacteristic
849C42C24×C1912yes—
850C42C24×C1912yes—
851C42C24×C1912yes—
852C42C24×C1911yescharacteristic
853C42C24×C1911yescharacteristic
854C42C24×C1918yes—
855C42C24×C1918yes—
856C42C24×C1914yes—
857C42C24×C1914yes—
858C42C24×C19116yes—
859C42C24×C19116yes—
860C23—22no—
861C23—42no—
862C23C25×C1911yescharacteristic
863C23C25×C1911yescharacteristic
864C23C25×C1918yes—
865C23C25×C1911yescharacteristic
866Q8—28no—
867Q8—28no—
868Q8—28no—
869Q8—28no—
870Q8—416no—
871Q8—48no—
872Q8—44no—
873D4—216no—
874D4—28no—
875D4—28no—
876D4—44no—
877D4—48no—
878D4—416no—
879D4—48no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—216no—
886C2×C4—24no—
887C2×C4—24no—
888C2×C4—24no—
889C2×C4—216no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—48no—
894C2×C4—416no—
895C2×C4—48no—
896C2×C4—416no—
897C2×C4C19×2−1+414yes—
898C2×C4C25×C1912yes—
899C2×C4C25×C1918yes—
900C2×C4C25×C1911yescharacteristic
901C2×C4C25×C1911yescharacteristic
902C2×C4C25×C1912yes—
903C2×C4C25×C1918yes—
904C2×C4C25×C1918yes—
905C2×C4C25×C1918yes—
906C2×C4C25×C1912yes—
907C2×C4C25×C1918yes—
908C2×C4C25×C1911yescharacteristic
909C2×C4C25×C1911yescharacteristic
910C2×C4C25×C1912yes—
911C22—22no—
912C22—21no—
913C22—21no—
914C22—28no—
915C22—28no—
916C22—22no—
917C22—22no—
918C22—28no—
919C22—44no—
920C22C2×C19×2−1+412yes—
921C22C26×C1911yescharacteristic
922C4—21no—
923C4—21no—
924C4—28no—
925C4—22no—
926C4—22no—
927C4—28no—
928C4—22no—
929C4—28no—
930C4—28no—
931C4—28no—
932C4C2×C19×2−1+412yes—
933C4C2×C19×2−1+412yes—
934C4C19×#58514yes—
935C2—22no—
936C2—41no—
937C2—41no—
938C2—48no—
939C2C22×C19×2−1+411yescharacteristic
940C2C2×C19×#58512yes—
subgroupG/H
centerC2×C4×C19C25
commutator, Frattini, cosocleC22C26×C19
socleC22×C19C26
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C19 ◁ G

Complements

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

NH ≅ G/Ntype
1. C19×#3557C2semidirect
2. C19×#3556C2semidirect
3. C19×#3555C2semidirect
4. C19×#3554C2semidirect
5. C19×#3553C2semidirect
6. C19×#3552C2semidirect
7. C19×#3550C2semidirect
8. C19×#3548C2semidirect
9. C19×#3541C2semidirect
10. C19×#3531C2semidirect
11. C19×#3482C2semidirect
12. C19×#3480C2semidirect
13. Q8×#41×C19C2semidirect
14. C19×#3461C2semidirect
15. C19×#3455C2semidirect
16. C19×#3444C2semidirect
17. C2×C19×#533C2semidirect
18. C19×#564C22semidirect
20. C19×#563C22semidirect
21. C19×#563C22semidirect
23. C19×#562C22semidirect
24. C19×#559C22semidirect
25. C19×#559C22semidirect
26. Q82×C19C22semidirect
27. C19×#557C22semidirect
28. C19×#557C22semidirect
29. C19×#557C22semidirect
30. C19×#557C22semidirect
32. C19×#556C22semidirect
33. C19×#556C22semidirect
34. C19×#556C22semidirect
37. C19×#554C22semidirect
38. C19×#554C22semidirect
42. C19×#552C22semidirect
43. C19×#550C22semidirect
45. D4×Q8×C19C22semidirect
46. D4×Q8×C19C22semidirect
50. C19×#547C22semidirect
51. C19×#544C22semidirect
56. C19×#542C22semidirect
60. C19×#541C22semidirect
61. C19×#541C22semidirect
66. C19×#539C22semidirect
70. C19×#536C22semidirect
82. C19×#533C22semidirect
83. C19×#533C22semidirect
97. C19×#529C22semidirect
98. C19×#529C22semidirect
108. C4×#41×C19C22semidirect
110. C2×C4×Q8×C19C22semidirect
389. #62761C19direct (N × H)
441. #3557C2×C19semidirect
442. #3556C2×C19semidirect
443. #3555C2×C19semidirect
444. #3554C2×C19semidirect
445. #3553C2×C19semidirect
446. #3552C2×C19semidirect
447. #3550C2×C19semidirect
448. #3548C2×C19semidirect
449. #3541C2×C19semidirect
450. #3531C2×C19semidirect
451. #3482C2×C19semidirect
452. #3480C2×C19semidirect
453. Q8×#41C2×C19semidirect
454. #3461C2×C19semidirect
455. #3455C2×C19semidirect
456. #3444C2×C19semidirect
457. C2×#533C2×C19semidirect
482. #564C22×C19semidirect
484. #563C22×C19semidirect
485. #563C22×C19semidirect
487. #562C22×C19semidirect
488. #559C22×C19semidirect
489. #559C22×C19semidirect
490. Q82C22×C19semidirect
491. #557C22×C19semidirect
492. #557C22×C19semidirect
493. #557C22×C19semidirect
494. #557C22×C19semidirect
496. #556C22×C19semidirect
497. #556C22×C19semidirect
498. #556C22×C19semidirect
501. #554C22×C19semidirect
502. #554C22×C19semidirect
506. #552C22×C19semidirect
507. #550C22×C19semidirect
509. D4×Q8C22×C19semidirect
510. D4×Q8C22×C19semidirect
514. #547C22×C19semidirect
515. #544C22×C19semidirect
520. #542C22×C19semidirect
524. #541C22×C19semidirect
525. #541C22×C19semidirect
530. #539C22×C19semidirect
534. #536C22×C19semidirect
546. #533C22×C19semidirect
547. #533C22×C19semidirect
561. #529C22×C19semidirect
562. #529C22×C19semidirect
572. C4×#41C22×C19semidirect
574. C2×C4×Q8C22×C19semidirect
756. C19#62761direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#35572
C19×#35562
C19×#35552
C19×#35542
C19×#35532
C19×#35522
C19×#35502
C19×#35482
C19×#35412
C19×#35312
C19×#34822
C19×#34802
Q8×#41×C192
C19×#34612
C19×#34552
C19×#34442
C2×C19×#5332
#6276119