Finite Group Databasebeta

← C19×#62837 #18068796

Subgroups — C19×#62837 #18068796

Order 4864.

6428 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C19×#3563C218yesmaximal, complemented
2C19×#3556C212yesmaximal, complemented
3C19×#3555C218yesmaximal, complemented
4C19×#3550C212yesmaximal, complemented
5C19×#3538C214yesmaximal, complemented
6C19×#3523C218yesmaximal, complemented
7C19×#3509C214yesmaximal, complemented
8C19×#3509C214yesmaximal, complemented
9C19×#3507C214yesmaximal, complemented
10C19×#3503C214yesmaximal, complemented
11C19×#3502C214yesmaximal, complemented
12C19×#3495C218yesmaximal, complemented
13C19×#3444C211yesmaximal, characteristic
14C2×C19×#533C212yesmaximal, complemented
15C19×#564C2218yescomplemented
16C19×#563C22116yes—
17C19×#563C2218yescomplemented
18C19×#559C2214yescomplemented
19Q82×C19C2214yescomplemented
20Q82×C19C2218yescomplemented
21C19×#557C2218yescomplemented
22C19×#557C2218yescomplemented
23C19×#557C22116yescomplemented
24C19×#557C22116yescomplemented
25C19×#557C2218yescomplemented
26C19×#557C2218yescomplemented
27C19×#556C22116yes—
28C19×#556C2218yescomplemented
29C19×#556C22116yescomplemented
30C19×#556C2218yescomplemented
31C19×#554C22116yes—
32C19×#554C2218yescomplemented
33C19×#552C22116yes—
34C19×#552C22116yes—
35C19×#552C22132yes—
36C19×#552C22116yes—
37C19×#552C22116yescomplemented
38C19×#551C22116yes—
39D4×Q8×C19C22116yes—
40D4×Q8×C19C2218yescomplemented
41C19×#544C2218yes—
42C19×#544C22116yes—
43C19×#544C22116yescomplemented
44C19×#542C22116yes—
45C19×#541C22116yes—
46C19×#541C2218yes—
47C19×#541C2218yescomplemented
48C19×#541C22116yescomplemented
49C19×#541C22132yescomplemented
50C19×#539C22116yes—
51C19×#536C2218yes—
52C19×#536C2218yes—
53C19×#533C2214yes—
54C19×#533C2214yes—
55C19×#533C2214yes—
56C19×#533C2214yes—
57C19×#533C2214yes—
58C19×#533C2214yes—
59C19×#533C2214yes—
60C19×#533C2214yes—
61C19×#533C2212yes—
62C19×#533C2211yescharacteristic
63C19×#533C22116yes—
64C19×#533C2218yescomplemented
65C19×#533C2214yescomplemented
66C19×#532C2212yes—
67C19×#532C2211yescharacteristic
68C2×C19×C4⋊Q8C2212yes—
69C2×C19×C4⋊Q8C2212yes—
70C2×C19×C4⋊Q8C2214yescomplemented
71C19×#529C2214yes—
72C19×#529C2214yes—
73C19×#529C2214yes—
74C19×#529C22116yes—
75C2×C19×#125C2214yes—
76C19×#525C2214yes—
77C19×#525C2212yes—
78C2×C19×C22⋊Q8C2214yes—
79C2×C19×C22⋊Q8C2214yes—
80C19×#520C2218yes—
81C19×#519C2218yes—
82C19×#519C2218yescomplemented
83C4×#41×C19C2214yes—
84C4×#41×C19C2212yes—
85C2×C4×Q8×C19C2214yes—
86C2×C4×Q8×C19C2214yes—
87C2×C19×#117C2214yes—
88C22×C42×C19C2211yescharacteristic
89C2×#41×C19C2314yes—
90C2×#41×C19C2312yes—
91C22×Q8×C19C2314yes—
92C22×Q8×C19C2314yes—
93C22×Q8×C19C2318yes—
94C23×C4×C19C2312yes—
95C23×C4×C19C2311yescharacteristic
96C19×C4⋊Q8C2314yes—
97C19×C4⋊Q8C2314yes—
98C19×C4⋊Q8C2314yes—
99C19×C4⋊Q8C2314yes—
100C19×C4⋊Q8C2314yes—
101C19×C4⋊Q8C2314yes—
102C19×C4⋊Q8C2314yes—
103C19×C4⋊Q8C2314yes—
104C19×C4⋊Q8C2318yes—
105C19×C4⋊Q8C23116yes—
106C19×C4⋊Q8C2312yes—
107C19×C4⋊Q8C2311yescharacteristic
108C19×C4⋊Q8C23116yes—
109C19×C4⋊Q8C23116yes—
110C19×C4⋊Q8C23116yes—
111C19×C4⋊Q8C23132yes—
112C19×#127C2311yescharacteristic
113C19×#126C2318yes—
114C19×#126C23132yes—
115C19×#126C23132yes—
116C19×#126C23132yes—
117C19×#126C23132yes—
118C19×#125C2318yes—
119C19×#125C2318yes—
120C19×#125C2318yes—
121C19×#125C2318yes—
122C19×#125C2314yes—
123C19×#125C2312yes—
124C19×#125C23116yes—
125C19×#125C23132yes—
126C19×#125C2318yes—
127C19×#125C23116yes—
128C19×#125C23132yes—
129C19×#125C23132yes—
130C19×#125C23132yes—
131C19×#125C23132yes—
132C19×#124C2314yes—
133C19×#124C2312yes—
134C19×#124C23116yes—
135C19×#124C23116yes—
136C19×#123C2318yes—
137C19×#123C2314yes—
138C19×#123C23132yes—
139C19×#123C23116yes—
140C19×#123C23116yes—
141C19×C22⋊Q8C2318yes—
142C19×C22⋊Q8C2318yes—
143C19×C22⋊Q8C2318yes—
144C19×C22⋊Q8C2318yes—
145C19×C22⋊Q8C2318yes—
146C19×C22⋊Q8C2318yes—
147C19×C22⋊Q8C2318yes—
148C19×C22⋊Q8C2318yes—
149C19×C22⋊Q8C2314yes—
150C19×C22⋊Q8C2314yes—
151C19×C22⋊Q8C2314yes—
152C19×C22⋊Q8C23132yes—
153C19×C22⋊Q8C23116yes—
154C19×C22⋊Q8C23116yes—
155C19×C22⋊Q8C23116yes—
156C19×C22⋊Q8C23132yes—
157C19×C22⋊Q8C23132yes—
158C19×#121C2314yes—
159C19×#121C2314yes—
160C19×#121C2314yes—
161C19×#120C2314yes—
162C4×Q8×C19C2318yes—
163C4×Q8×C19C2318yes—
164C4×Q8×C19C2318yes—
165C4×Q8×C19C2318yes—
166C4×Q8×C19C2318yes—
167C4×Q8×C19C2318yes—
168C4×Q8×C19C2318yes—
169C4×Q8×C19C2318yes—
170C4×Q8×C19C2314yes—
171C4×Q8×C19C2314yes—
172C4×Q8×C19C2314yes—
173C4×Q8×C19C23116yes—
174C4×Q8×C19C23116yes—
175C4×Q8×C19C23116yes—
176C4×Q8×C19C23116yes—
177C4×Q8×C19C23132yes—
178C4×Q8×C19C23116yes—
179C4×Q8×C19C23116yes—
180C4×D4×C19C2318yes—
181C4×D4×C19C2318yes—
182C4×D4×C19C2318yes—
183C4×D4×C19C2314yes—
184C4×D4×C19C2314yes—
185C4×D4×C19C2314yes—
186C4×D4×C19C23132yes—
187C4×D4×C19C23116yes—
188C19×#117C2318yes—
189C19×#117C2318yes—
190C19×#117C2318yes—
191C19×#117C2318yes—
192C19×#117C2314yes—
193C19×#117C2314yes—
194C19×#117C2312yes—
195C19×#117C2318yes—
196C19×#117C23132yes—
197C19×#117C23132yes—
198C19×#117C2318yes—
199C19×#117C23116yes—
200C2×C4⋊C4×C19C2314yes—
201C2×C4⋊C4×C19C2314yes—
202C2×C4⋊C4×C19C2314yes—
203C2×C4⋊C4×C19C2318yes—
204C2×C4⋊C4×C19C2318yes—
205C2×C4⋊C4×C19C2314yes—
206C2×C4⋊C4×C19C23116yes—
207C2×C22⋊C4×C19C2318yes—
208C2×C42×C19C2312yes—
209C2×C42×C19C2312yes—
210C2×C42×C19C2312yes—
211C2×C42×C19C2311yescharacteristic
212C2×C42×C19C2312yes—
213C2×C42×C19C2312yes—
214C2×C42×C19C2311yescharacteristic
215C2×C42×C19C2318yes—
216C2×C42×C19C2314yes—
217C24×C19C2411yescharacteristic
218#41×C19—216no—
219#41×C19—44no—
220C2×Q8×C19—216no—
221C2×Q8×C19—48no—
222C2×Q8×C19—416no—
223C2×Q8×C19C2418yes—
224C2×Q8×C19C2418yes—
225C2×Q8×C19C2414yes—
226C2×Q8×C19C2418yes—
227C2×Q8×C19C2418yes—
228C2×Q8×C19C24116yes—
229C2×Q8×C19C2412yes—
230C2×D4×C19C2418yes—
231C2×D4×C19C2414yes—
232C2×D4×C19C2414yes—
233C2×D4×C19C2412yes—
234C22×C4×C19—28no—
235C22×C4×C19—42no—
236C22×C4×C19C2412yes—
237C22×C4×C19C2412yes—
238C22×C4×C19C2412yes—
239C22×C4×C19C2412yes—
240C22×C4×C19C2412yes—
241C22×C4×C19C2412yes—
242C22×C4×C19C2411yescharacteristic
243C22×C4×C19C2418yes—
244C22×C4×C19C2418yes—
245C22×C4×C19C2414yes—
246C22×C4×C19C2412yes—
247C22×C4×C19C2411yescharacteristic
248C22×C4×C19C2418yes—
249C22×C4×C19C24116yes—
250C22×C4×C19C2412yes—
251C4⋊C4×C19C2418yes—
252C4⋊C4×C19C2418yes—
253C4⋊C4×C19C2418yes—
254C4⋊C4×C19C2418yes—
255C4⋊C4×C19C24116yes—
256C4⋊C4×C19C2418yes—
257C4⋊C4×C19C2418yes—
258C4⋊C4×C19C2418yes—
259C4⋊C4×C19C24132yes—
260C4⋊C4×C19C24116yes—
261C4⋊C4×C19C24116yes—
262C4⋊C4×C19C24116yes—
263C4⋊C4×C19C2418yes—
264C4⋊C4×C19C2414yes—
265C4⋊C4×C19C2414yes—
266C4⋊C4×C19C2418yes—
267C4⋊C4×C19C2414yes—
268C4⋊C4×C19C2418yes—
269C4⋊C4×C19C2418yes—
270C4⋊C4×C19C24132yes—
271C4⋊C4×C19C24132yes—
272C4⋊C4×C19C24132yes—
273C22⋊C4×C19C24116yes—
274C22⋊C4×C19C24116yes—
275C22⋊C4×C19C2418yes—
276C22⋊C4×C19C2418yes—
277C22⋊C4×C19C24116yes—
278C22⋊C4×C19C2414yes—
279C22⋊C4×C19C2418yes—
280C22⋊C4×C19C2418yes—
281C22⋊C4×C19C24132yes—
282C42×C19C2411yescharacteristic
283C42×C19C2411yescharacteristic
284C42×C19C2412yes—
285C42×C19C2412yes—
286C42×C19C2412yes—
287C42×C19C2412yes—
288C42×C19C2412yes—
289C42×C19C2411yescharacteristic
290C42×C19C2412yes—
291C42×C19C2411yescharacteristic
292C42×C19C24116yes—
293C42×C19C2414yes—
294C42×C19C2418yes—
295C42×C19C24116yes—
296C42×C19C24132yes—
297C42×C19C24116yes—
298#62837C1911yesmaximal, characteristic, direct product factor, Sylow
299C23×C19—24no—
300C23×C19—41no—
301C23×C19C2511yescharacteristic
302C23×C19C2514yes—
303C23×C19C2512yes—
304Q8×C19—216no—
305Q8×C19—216no—
306Q8×C19—28no—
307Q8×C19—216no—
308Q8×C19—48no—
309Q8×C19—416no—
310Q8×C19—42no—
311D4×C19—216no—
312D4×C19—28no—
313D4×C19—42no—
314D4×C19—44no—
315C2×C4×C19—24no—
316C2×C4×C19—216no—
317C2×C4×C19—24no—
318C2×C4×C19—24no—
319C2×C4×C19—24no—
320C2×C4×C19—24no—
321C2×C4×C19—216no—
322C2×C4×C19—24no—
323C2×C4×C19—22no—
324C2×C4×C19—28no—
325C2×C4×C19—42no—
326C2×C4×C19—41no—
327C2×C4×C19—48no—
328C2×C4×C19—416no—
329C2×C4×C192−1+418yes—
330C2×C4×C19C2512yes—
331C2×C4×C19C25116yes—
332C2×C4×C19C2518yes—
333C2×C4×C19C2514yes—
334C2×C4×C19C2512yes—
335C2×C4×C19C2512yes—
336C2×C4×C19C25116yes—
337C2×C4×C19C2511yescharacteristic
338C2×C4×C19C2512yes—
339C2×C4×C19C2512yes—
340C2×C4×C19C2511yescharacteristic
341#3563C2×C1918yescomplemented
342#3556C2×C1912yescomplemented
343#3555C2×C1918yescomplemented
344#3550C2×C1912yescomplemented
345#3538C2×C1914yescomplemented
346#3523C2×C1918yescomplemented
347#3509C2×C1914yescomplemented
348#3509C2×C1914yescomplemented
349#3507C2×C1914yescomplemented
350#3503C2×C1914yescomplemented
351#3502C2×C1914yescomplemented
352#3495C2×C1918yescomplemented
353#3444C2×C1911yescharacteristic
354C2×#533C2×C1912yescomplemented
355C22×C19—22no—
356C22×C19—22no—
357C22×C19—22no—
358C22×C19—28no—
359C22×C19—24no—
360C22×C19—21no—
361C22×C19—44no—
362C22×C19C2×2−1+414yes—
363C22×C19C2611yescharacteristic
364C4×C19—22no—
365C4×C19—22no—
366C4×C19—28no—
367C4×C19—216no—
368C4×C19—21no—
369C4×C19—22no—
370C4×C19—24no—
371C4×C19—216no—
372C4×C19C2×2−1+414yes—
373C4×C19C2×2−1+414yes—
374C4×C19#58512yes—
375#564C22×C1918yescomplemented
376#563C22×C19116yes—
377#563C22×C1918yescomplemented
378#559C22×C1914yescomplemented
379Q82C22×C1914yescomplemented
380Q82C22×C1918yescomplemented
381#557C22×C1918yescomplemented
382#557C22×C1918yescomplemented
383#557C22×C19116yescomplemented
384#557C22×C19116yescomplemented
385#557C22×C1918yescomplemented
386#557C22×C1918yescomplemented
387#556C22×C19116yes—
388#556C22×C1918yescomplemented
389#556C22×C19116yescomplemented
390#556C22×C1918yescomplemented
391#554C22×C19116yes—
392#554C22×C1918yescomplemented
393#552C22×C19116yes—
394#552C22×C19116yes—
395#552C22×C19132yes—
396#552C22×C19116yes—
397#552C22×C19116yescomplemented
398#551C22×C19116yes—
399D4×Q8C22×C19116yes—
400D4×Q8C22×C1918yescomplemented
401#544C22×C1918yes—
402#544C22×C19116yes—
403#544C22×C19116yescomplemented
404#542C22×C19116yes—
405#541C22×C19116yes—
406#541C22×C1918yes—
407#541C22×C1918yescomplemented
408#541C22×C19116yescomplemented
409#541C22×C19132yescomplemented
410#539C22×C19116yes—
411#536C22×C1918yes—
412#536C22×C1918yes—
413#533C22×C1914yes—
414#533C22×C1914yes—
415#533C22×C1914yes—
416#533C22×C1914yes—
417#533C22×C1914yes—
418#533C22×C1914yes—
419#533C22×C1914yes—
420#533C22×C1914yes—
421#533C22×C1912yes—
422#533C22×C1911yescharacteristic
423#533C22×C19116yes—
424#533C22×C1918yescomplemented
425#533C22×C1914yescomplemented
426#532C22×C1912yes—
427#532C22×C1911yescharacteristic
428C2×C4⋊Q8C22×C1912yes—
429C2×C4⋊Q8C22×C1912yes—
430C2×C4⋊Q8C22×C1914yescomplemented
431#529C22×C1914yes—
432#529C22×C1914yes—
433#529C22×C1914yes—
434#529C22×C19116yes—
435C2×#125C22×C1914yes—
436#525C22×C1914yes—
437#525C22×C1912yes—
438C2×C22⋊Q8C22×C1914yes—
439C2×C22⋊Q8C22×C1914yes—
440#520C22×C1918yes—
441#519C22×C1918yes—
442#519C22×C1918yescomplemented
443C4×#41C22×C1914yes—
444C4×#41C22×C1912yes—
445C2×C4×Q8C22×C1914yes—
446C2×C4×Q8C22×C1914yes—
447C2×#117C22×C1914yes—
448C22×C42C22×C1911yescharacteristic
449C2×C19—24no—
450C2×C19—44no—
451C2×C19—41no—
452C2×C19C22×2−1+412yes—
453C2×C19C2×#58511yescharacteristic
454C2×#41C23×C1914yes—
455C2×#41C23×C1912yes—
456C22×Q8C23×C1914yes—
457C22×Q8C23×C1914yes—
458C22×Q8C23×C1918yes—
459C23×C4C23×C1912yes—
460C23×C4C23×C1911yescharacteristic
461C4⋊Q8C23×C1914yes—
462C4⋊Q8C23×C1914yes—
463C4⋊Q8C23×C1914yes—
464C4⋊Q8C23×C1914yes—
465C4⋊Q8C23×C1914yes—
466C4⋊Q8C23×C1914yes—
467C4⋊Q8C23×C1914yes—
468C4⋊Q8C23×C1914yes—
469C4⋊Q8C23×C1918yes—
470C4⋊Q8C23×C19116yes—
471C4⋊Q8C23×C1912yes—
472C4⋊Q8C23×C1911yescharacteristic
473C4⋊Q8C23×C19116yes—
474C4⋊Q8C23×C19116yes—
475C4⋊Q8C23×C19116yes—
476C4⋊Q8C23×C19132yes—
477#127C23×C1911yescharacteristic
478#126C23×C1918yes—
479#126C23×C19132yes—
480#126C23×C19132yes—
481#126C23×C19132yes—
482#126C23×C19132yes—
483#125C23×C1918yes—
484#125C23×C1918yes—
485#125C23×C1918yes—
486#125C23×C1918yes—
487#125C23×C1914yes—
488#125C23×C1912yes—
489#125C23×C19116yes—
490#125C23×C19132yes—
491#125C23×C1918yes—
492#125C23×C19116yes—
493#125C23×C19132yes—
494#125C23×C19132yes—
495#125C23×C19132yes—
496#125C23×C19132yes—
497#124C23×C1914yes—
498#124C23×C1912yes—
499#124C23×C19116yes—
500#124C23×C19116yes—
501#123C23×C1918yes—
502#123C23×C1914yes—
503#123C23×C19132yes—
504#123C23×C19116yes—
505#123C23×C19116yes—
506C22⋊Q8C23×C1918yes—
507C22⋊Q8C23×C1918yes—
508C22⋊Q8C23×C1918yes—
509C22⋊Q8C23×C1918yes—
510C22⋊Q8C23×C1918yes—
511C22⋊Q8C23×C1918yes—
512C22⋊Q8C23×C1918yes—
513C22⋊Q8C23×C1918yes—
514C22⋊Q8C23×C1914yes—
515C22⋊Q8C23×C1914yes—
516C22⋊Q8C23×C1914yes—
517C22⋊Q8C23×C19132yes—
518C22⋊Q8C23×C19116yes—
519C22⋊Q8C23×C19116yes—
520C22⋊Q8C23×C19116yes—
521C22⋊Q8C23×C19132yes—
522C22⋊Q8C23×C19132yes—
523#121C23×C1914yes—
524#121C23×C1914yes—
525#121C23×C1914yes—
526#120C23×C1914yes—
527C4×Q8C23×C1918yes—
528C4×Q8C23×C1918yes—
529C4×Q8C23×C1918yes—
530C4×Q8C23×C1918yes—
531C4×Q8C23×C1918yes—
532C4×Q8C23×C1918yes—
533C4×Q8C23×C1918yes—
534C4×Q8C23×C1918yes—
535C4×Q8C23×C1914yes—
536C4×Q8C23×C1914yes—
537C4×Q8C23×C1914yes—
538C4×Q8C23×C19116yes—
539C4×Q8C23×C19116yes—
540C4×Q8C23×C19116yes—
541C4×Q8C23×C19116yes—
542C4×Q8C23×C19132yes—
543C4×Q8C23×C19116yes—
544C4×Q8C23×C19116yes—
545C4×D4C23×C1918yes—
546C4×D4C23×C1918yes—
547C4×D4C23×C1918yes—
548C4×D4C23×C1914yes—
549C4×D4C23×C1914yes—
550C4×D4C23×C1914yes—
551C4×D4C23×C19132yes—
552C4×D4C23×C19116yes—
553#117C23×C1918yes—
554#117C23×C1918yes—
555#117C23×C1918yes—
556#117C23×C1918yes—
557#117C23×C1914yes—
558#117C23×C1914yes—
559#117C23×C1912yes—
560#117C23×C1918yes—
561#117C23×C19132yes—
562#117C23×C19132yes—
563#117C23×C1918yes—
564#117C23×C19116yes—
565C2×C4⋊C4C23×C1914yes—
566C2×C4⋊C4C23×C1914yes—
567C2×C4⋊C4C23×C1914yes—
568C2×C4⋊C4C23×C1918yes—
569C2×C4⋊C4C23×C1918yes—
570C2×C4⋊C4C23×C1914yes—
571C2×C4⋊C4C23×C19116yes—
572C2×C22⋊C4C23×C1918yes—
573C2×C42C23×C1918yes—
574C2×C42C23×C1912yes—
575C2×C42C23×C1912yes—
576C2×C42C23×C1914yes—
577C2×C42C23×C1912yes—
578C2×C42C23×C1911yescharacteristic
579C2×C42C23×C1912yes—
580C2×C42C23×C1912yes—
581C2×C42C23×C1911yescharacteristic
582C19#6283711yescharacteristic, direct product factor, Sylow
583C24C24×C1911yescharacteristic
584#41—216no—
585#41—44no—
586C2×Q8—216no—
587C2×Q8—48no—
588C2×Q8—416no—
589C2×Q8C24×C1918yes—
590C2×Q8C24×C1918yes—
591C2×Q8C24×C1914yes—
592C2×Q8C24×C1918yes—
593C2×Q8C24×C1918yes—
594C2×Q8C24×C19116yes—
595C2×Q8C24×C1912yes—
596C2×D4C24×C1918yes—
597C2×D4C24×C1914yes—
598C2×D4C24×C1914yes—
599C2×D4C24×C1912yes—
600C22×C4—28no—
601C22×C4—42no—
602C22×C4C24×C1912yes—
603C22×C4C24×C1912yes—
604C22×C4C24×C1912yes—
605C22×C4C24×C1912yes—
606C22×C4C24×C1912yes—
607C22×C4C24×C1912yes—
608C22×C4C24×C1911yescharacteristic
609C22×C4C24×C1918yes—
610C22×C4C24×C1918yes—
611C22×C4C24×C1914yes—
612C22×C4C24×C1912yes—
613C22×C4C24×C1911yescharacteristic
614C22×C4C24×C1918yes—
615C22×C4C24×C19116yes—
616C22×C4C24×C1912yes—
617C4⋊C4C24×C1918yes—
618C4⋊C4C24×C1918yes—
619C4⋊C4C24×C1918yes—
620C4⋊C4C24×C1918yes—
621C4⋊C4C24×C19116yes—
622C4⋊C4C24×C1918yes—
623C4⋊C4C24×C1918yes—
624C4⋊C4C24×C1918yes—
625C4⋊C4C24×C19132yes—
626C4⋊C4C24×C19116yes—
627C4⋊C4C24×C19116yes—
628C4⋊C4C24×C19116yes—
629C4⋊C4C24×C1918yes—
630C4⋊C4C24×C1914yes—
631C4⋊C4C24×C1914yes—
632C4⋊C4C24×C1918yes—
633C4⋊C4C24×C1914yes—
634C4⋊C4C24×C1918yes—
635C4⋊C4C24×C1918yes—
636C4⋊C4C24×C19132yes—
637C4⋊C4C24×C19132yes—
638C4⋊C4C24×C19132yes—
639C22⋊C4C24×C19116yes—
640C22⋊C4C24×C19116yes—
641C22⋊C4C24×C1918yes—
642C22⋊C4C24×C1918yes—
643C22⋊C4C24×C19116yes—
644C22⋊C4C24×C1914yes—
645C22⋊C4C24×C1918yes—
646C22⋊C4C24×C1918yes—
647C22⋊C4C24×C19132yes—
648C42C24×C1911yescharacteristic
649C42C24×C1911yescharacteristic
650C42C24×C1912yes—
651C42C24×C1912yes—
652C42C24×C1912yes—
653C42C24×C1912yes—
654C42C24×C1912yes—
655C42C24×C1911yescharacteristic
656C42C24×C1912yes—
657C42C24×C1911yescharacteristic
658C42C24×C19116yes—
659C42C24×C1914yes—
660C42C24×C1918yes—
661C42C24×C19116yes—
662C42C24×C19132yes—
663C42C24×C19116yes—
664C23—24no—
665C23—41no—
666C23C25×C1911yescharacteristic
667C23C25×C1914yes—
668C23C25×C1912yes—
669Q8—216no—
670Q8—216no—
671Q8—28no—
672Q8—216no—
673Q8—48no—
674Q8—416no—
675Q8—42no—
676D4—216no—
677D4—28no—
678D4—42no—
679D4—44no—
680C2×C4—24no—
681C2×C4—216no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—216no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—28no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—48no—
693C2×C4—416no—
694C2×C4C19×2−1+418yes—
695C2×C4C25×C1912yes—
696C2×C4C25×C19116yes—
697C2×C4C25×C1918yes—
698C2×C4C25×C1914yes—
699C2×C4C25×C1912yes—
700C2×C4C25×C1912yes—
701C2×C4C25×C19116yes—
702C2×C4C25×C1911yescharacteristic
703C2×C4C25×C1912yes—
704C2×C4C25×C1912yes—
705C2×C4C25×C1911yescharacteristic
706C22—22no—
707C22—22no—
708C22—22no—
709C22—28no—
710C22—24no—
711C22—21no—
712C22—44no—
713C22C2×C19×2−1+414yes—
714C22C26×C1911yescharacteristic
715C4—22no—
716C4—22no—
717C4—28no—
718C4—216no—
719C4—21no—
720C4—22no—
721C4—24no—
722C4—216no—
723C4C2×C19×2−1+414yes—
724C4C2×C19×2−1+414yes—
725C4C19×#58512yes—
726C2—24no—
727C2—41no—
728C2—44no—
729C2C22×C19×2−1+412yes—
730C2C2×C19×#58511yescharacteristic
subgroupG/H
center, socleC22×C19C26
commutator, Frattini, cosocleC22C26×C19
prime radicalC19×#3444C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C19 ◁ G

Complements

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

NH ≅ G/Ntype
1. C19×#3563C2semidirect
2. C19×#3556C2semidirect
3. C19×#3555C2semidirect
4. C19×#3550C2semidirect
5. C19×#3538C2semidirect
6. C19×#3523C2semidirect
7. C19×#3509C2semidirect
8. C19×#3509C2semidirect
9. C19×#3507C2semidirect
10. C19×#3503C2semidirect
11. C19×#3502C2semidirect
12. C19×#3495C2semidirect
14. C2×C19×#533C2semidirect
15. C19×#564C22semidirect
17. C19×#563C22semidirect
18. C19×#559C22semidirect
19. Q82×C19C22semidirect
20. Q82×C19C22semidirect
21. C19×#557C22semidirect
22. C19×#557C22semidirect
23. C19×#557C22semidirect
24. C19×#557C22semidirect
25. C19×#557C22semidirect
26. C19×#557C22semidirect
28. C19×#556C22semidirect
29. C19×#556C22semidirect
30. C19×#556C22semidirect
32. C19×#554C22semidirect
37. C19×#552C22semidirect
40. D4×Q8×C19C22semidirect
43. C19×#544C22semidirect
47. C19×#541C22semidirect
48. C19×#541C22semidirect
49. C19×#541C22semidirect
64. C19×#533C22semidirect
65. C19×#533C22semidirect
70. C2×C19×C4⋊Q8C22semidirect
82. C19×#519C22semidirect
298. #62837C19direct (N × H)
341. #3563C2×C19semidirect
342. #3556C2×C19semidirect
343. #3555C2×C19semidirect
344. #3550C2×C19semidirect
345. #3538C2×C19semidirect
346. #3523C2×C19semidirect
347. #3509C2×C19semidirect
348. #3509C2×C19semidirect
349. #3507C2×C19semidirect
350. #3503C2×C19semidirect
351. #3502C2×C19semidirect
352. #3495C2×C19semidirect
354. C2×#533C2×C19semidirect
375. #564C22×C19semidirect
377. #563C22×C19semidirect
378. #559C22×C19semidirect
379. Q82C22×C19semidirect
380. Q82C22×C19semidirect
381. #557C22×C19semidirect
382. #557C22×C19semidirect
383. #557C22×C19semidirect
384. #557C22×C19semidirect
385. #557C22×C19semidirect
386. #557C22×C19semidirect
388. #556C22×C19semidirect
389. #556C22×C19semidirect
390. #556C22×C19semidirect
392. #554C22×C19semidirect
397. #552C22×C19semidirect
400. D4×Q8C22×C19semidirect
403. #544C22×C19semidirect
407. #541C22×C19semidirect
408. #541C22×C19semidirect
409. #541C22×C19semidirect
424. #533C22×C19semidirect
425. #533C22×C19semidirect
430. C2×C4⋊Q8C22×C19semidirect
442. #519C22×C19semidirect
582. C19#62837direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#35632
C19×#35562
C19×#35552
C19×#35502
C19×#35382
C19×#35232
C19×#35092
C19×#35072
C19×#35032
C19×#35022
C19×#34952
C19×#34442
C2×C19×#5332
#6283719