Finite Group Databasebeta

← C19×#62401 #18068360

Subgroups — C19×#62401 #18068360

Order 4864.

1706 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C19×#3555C211yesmaximal, characteristic, complemented
2C19×#3548C211yesmaximal, characteristic, complemented
3C19×#3397C211yesmaximal, characteristic, complemented
4C19×#3397C212yesmaximal, complemented
5C19×#3392C211yesmaximal, characteristic, complemented
6C19×#3388C212yesmaximal, complemented
7C19×#3385C211yesmaximal, characteristic, complemented
8C19×#3380C211yesmaximal, characteristic, complemented
9C19×#3376C212yesmaximal, complemented
10C19×#3372C211yesmaximal, characteristic, complemented
11C19×#3368C212yesmaximal, complemented
12C19×#3366C211yesmaximal, characteristic, complemented
13C19×#3362C211yesmaximal, characteristic, complemented
14C19×#3360C211yesmaximal, characteristic, complemented
15C19×#3260C212yesmaximal, complemented
16C19×#3257C212yesmaximal, complemented
17C19×#3247C211yesmaximal, characteristic, complemented
18C19×#3246C211yesmaximal, characteristic, complemented
19C19×#3182C211yesmaximal, characteristic, complemented
20C19×#3179C212yesmaximal, complemented
21C19×#3174C212yesmaximal, complemented
22C19×#3171C211yesmaximal, characteristic, complemented
23C19×#2962C211yesmaximal, characteristic, complemented
24C19×#563—22no—
25C19×#562—22no—
26Q82×C19C2211yescharacteristic
27C19×#557C2211yescharacteristic
28C19×#557C2212yes—
29C19×#556—21no—
30C19×#556C2211yescharacteristic
31C19×#556C2212yes—
32C19×#554C2211yescharacteristic
33C19×#554C2211yescharacteristic
34C19×#554C2212yes—
35C19×#554C2211yescharacteristic
36C19×#552—21no—
37C19×#550C2211yescharacteristic
38C19×#550C2211yescharacteristic
39C19×#550C2212yes—
40C19×#547—21no—
41C19×#547—21no—
42C19×#544—21no—
43C19×#542C2212yes—
44C19×#541—21no—
45C19×#541—22no—
46C19×#541C2212yes—
47C19×#540C2212yes—
48C19×#540C2212yes—
49C19×#537—21no—
50C19×#537—21no—
51C19×#537—22no—
52C19×#533C2211yescharacteristic
53C19×#533C2211yescharacteristic
54C19×#532C2211yescharacteristic
55C19×#532C2211yescharacteristic
56C19×#529C2211yescharacteristic
57C19×#501C2211yescharacteristic
58C19×#501C2212yes—
59C19×#500C2211yescharacteristic
60C19×#499C2212yes—
61C19×#496C2211yescharacteristic
62C19×#496C2212yes—
63C19×#492C2212yes—
64C19×#492C2211yescharacteristic
65C19×#491C2212yes—
66C19×#490C2211yescharacteristic
67C19×#490C2212yes—
68C19×#489C2211yescharacteristic
69C19×#488C2212yes—
70C19×#487C2211yescharacteristic
71C19×#486C2212yes—
72C19×#486C2211yescharacteristic
73C19×#479C2212yes—
74C19×#479C2212yes—
75C19×#479C2212yes—
76C19×#478C2212yes—
77C19×#478C2212yes—
78C19×#478C2212yes—
79C19×#478C2212yes—
80C19×#477C2211yescharacteristic
81C19×#476C2211yescharacteristic
82C19×#476C2211yescharacteristic
83C19×#476C2211yescharacteristic
84C19×#476C2212yes—
85C19×#475C2212yes—
86C19×#474C2212yes—
87C19×#469C2211yescharacteristic
88C19×#469C2211yescharacteristic
89C19×#468C2211yescharacteristic
90C19×#468C2211yescharacteristic
91C19×#468C2212yes—
92C19×#468C2212yes—
93C19×#466C2212yes—
94C19×#465C2212yes—
95C19×#465C2212yes—
96C19×#465C2212yes—
97C19×#463C2212yes—
98C19×#463C2212yes—
99C19×#463C2212yes—
100C19×#461C2211yescharacteristic
101C19×#461C2211yescharacteristic
102C19×#461C2212yes—
103C19×#461C2212yes—
104C19×#460C2212yes—
105C19×#460C2211yescharacteristic
106C19×#460C2212yes—
107C19×#460C2212yes—
108C19×#460C2212yes—
109C19×#459C2211yescharacteristic
110C19×#459C2212yes—
111C19×#446C2211yescharacteristic
112C19×#446C2212yes—
113C19×#446C2211yescharacteristic
114C19×#446C2212yes—
115C8×Q8×C19C2211yescharacteristic
116C8×Q8×C19C2211yescharacteristic
117C19×#442C2212yes—
118C19×#440C2212yes—
119C19×#440C2212yes—
120C19×#440C2212yes—
121C19×#440C2212yes—
122C19×#440C2212yes—
123C4×SD16×C19C2211yescharacteristic
124C4×SD16×C19C2211yescharacteristic
125C4×SD16×C19C2212yes—
126C4×SD16×C19C2212yes—
127C4×SD16×C19C2212yes—
128C4×D8×C19C2211yescharacteristic
129C4×D8×C19C2211yescharacteristic
130C4×D8×C19C2212yes—
131C19×#424C2212yes—
132C2×C19×C4⋊C8C2211yescharacteristic
133C19×#405C2212yes—
134C4×M16×C19C2211yescharacteristic
135C2×#41×C19—21no—
136C2×#41×C19—21no—
137C2×#41×C19—22no—
138C2×#41×C19—21no—
139C2×#41×C19—21no—
140C2×SD16×C19C2311yescharacteristic
141C2×SD16×C19C2312yes—
142C2×SD16×C19C2311yescharacteristic
143C2×SD16×C19C2312yes—
144C2×SD16×C19C2312yes—
145C2×SD16×C19C2312yes—
146C2×SD16×C19C2312yes—
147C2×D8×C19C2311yescharacteristic
148C2×D8×C19C2311yescharacteristic
149C2×D8×C19C2312yes—
150C2×M16×C19C2311yescharacteristic
151C2×M16×C19C2311yescharacteristic
152C22×C8×C19C2312yes—
153C19×C4⋊Q8—22no—
154C19×C4⋊Q8—22no—
155C19×C4⋊Q8—21no—
156C19×C4⋊Q8D411yescharacteristic
157C19×C4⋊Q8D411yescharacteristic
158C19×C4⋊Q8C2311yescharacteristic
159C19×C4⋊Q8C2312yes—
160C19×C4⋊Q8C2312yes—
161C19×C4⋊Q8C2311yescharacteristic
162C19×C4⋊Q8C2311yescharacteristic
163C19×C4⋊Q8C2311yescharacteristic
164C19×#127C2311yescharacteristic
165C19×#127C2312yes—
166C19×#127C2312yes—
167C19×#127C2311yescharacteristic
168C19×#126—22no—
169C19×#126—22no—
170C19×#126—22no—
171C19×#126—22no—
172C19×#126—22no—
173C19×#126—22no—
174C19×#126—21no—
175C19×#125—22no—
176C19×#125—22no—
177C19×#125—22no—
178C19×#125—22no—
179C19×#125—22no—
180C19×#125—21no—
181C19×#125—21no—
182C19×#125D412yes—
183C19×#125C2312yes—
184C19×#125C2311yescharacteristic
185C19×#125C2312yes—
186C19×#125C2312yes—
187C19×#124—22no—
188C19×#124—21no—
189C19×#124—21no—
190C19×#124C2312yes—
191C19×#124C2311yescharacteristic
192C19×#123—21no—
193C19×#123—22no—
194C19×#123—22no—
195C19×#123—22no—
196C19×#123—22no—
197C19×#123—22no—
198C19×C22⋊Q8—21no—
199C19×C22⋊Q8—21no—
200C19×C22⋊Q8—22no—
201C19×C22⋊Q8—21no—
202C19×C22⋊Q8—21no—
203C19×C22⋊Q8—22no—
204C19×C22⋊Q8—21no—
205C19×C22⋊Q8—22no—
206C19×C22⋊Q8—22no—
207C19×C22⋊Q8—22no—
208C19×C22⋊Q8—22no—
209C19×C22⋊Q8—22no—
210C19×C22⋊Q8—22no—
211C19×C22⋊Q8D411yescharacteristic
212C19×C22⋊Q8D411yescharacteristic
213C19×C22⋊Q8D412yes—
214C19×C22⋊Q8C2311yescharacteristic
215C19×C22⋊Q8C2312yes—
216C19×#121—21no—
217C19×#121—21no—
218C19×#121—21no—
219C19×#121—21no—
220C19×#121—22no—
221C19×#121—22no—
222C19×#121—22no—
223C19×#121—22no—
224C19×#121—22no—
225C19×#121—22no—
226C19×#121—22no—
227C19×#121—22no—
228C19×#121—22no—
229C19×#121C2311yescharacteristic
230C19×#121C2311yescharacteristic
231C19×#121C2312yes—
232C19×#121C2311yescharacteristic
233C4×Q8×C19—21no—
234C4×Q8×C19—21no—
235C4×Q8×C19—22no—
236C4×Q8×C19—21no—
237C4×Q8×C19C2311yescharacteristic
238C4×Q8×C19C2312yes—
239C4×Q8×C19C2312yes—
240C4×Q8×C19C2312yes—
241C4×Q8×C19C2312yes—
242C4×Q8×C19C2311yescharacteristic
243C4×Q8×C19C2311yescharacteristic
244C4×Q8×C19C2312yes—
245C4×D4×C19—21no—
246C4×D4×C19—21no—
247C4×D4×C19—21no—
248C4×D4×C19C2311yescharacteristic
249C4×D4×C19C2311yescharacteristic
250C4×D4×C19C2311yescharacteristic
251C4×D4×C19C2312yes—
252C4×D4×C19C2312yes—
253C4×D4×C19C2312yes—
254C4×D4×C19C2312yes—
255C4×D4×C19C2312yes—
256C4×D4×C19C2312yes—
257C19×#117—21no—
258C19×#117—22no—
259C19×#117—21no—
260C19×#117—21no—
261C19×#117C2312yes—
262C2×C4⋊C4×C19—21no—
263C2×C4⋊C4×C19—21no—
264C2×C4⋊C4×C19—22no—
265C2×C4⋊C4×C19—21no—
266C2×C42×C19C2311yescharacteristic
267C19×#107C2311yescharacteristic
268C19×#107C2312yes—
269C19×#107C2311yescharacteristic
270C19×#107C2312yes—
271C19×#107C2312yes—
272C19×#106C2311yescharacteristic
273C19×#106C2312yes—
274C19×#106C2312yes—
275C19×#106C2311yescharacteristic
276C19×#106C2312yes—
277C19×C4⋊C8C2311yescharacteristic
278C19×C4⋊C8C2311yescharacteristic
279C19×C4⋊C8C2312yes—
280C19×C4⋊C8C2312yes—
281C19×C4⋊C8C2312yes—
282C19×C4⋊C8C2312yes—
283C19×C4⋊C8C2312yes—
284C19×#103C2311yescharacteristic
285C19×#103C2312yes—
286C19×#103C2312yes—
287C19×#103C2311yescharacteristic
288C19×#103C2312yes—
289C19×#103C2312yes—
290C19×#103C2312yes—
291C19×#102C2311yescharacteristic
292C19×#102C2311yescharacteristic
293C19×#102C2312yes—
294C19×#102C2311yescharacteristic
295C19×#102C2312yes—
296C19×#102C2311yescharacteristic
297C19×#102C2311yescharacteristic
298C19×#102C2312yes—
299C19×#102C2312yes—
300C19×#102C2311yescharacteristic
301C19×#102C2312yes—
302C19×#102C2312yes—
303C19×#102C2312yes—
304C19×#97C2311yescharacteristic
305C19×#97C2311yescharacteristic
306C19×#97C2312yes—
307C19×#97C2312yes—
308C4×C8×C19C2311yescharacteristic
309C4×C8×C19C2311yescharacteristic
310C4×C8×C19C2312yes—
311C4×C8×C19C2312yes—
312#41×C19—82no—
313#41×C19—82no—
314#41×C19—82no—
315#41×C19—82no—
316#41×C19—84no—
317C2×Q8×C19—21no—
318C2×Q8×C19—22no—
319C2×Q8×C19—21no—
320C2×Q8×C19—21no—
321C2×Q8×C19C2×D411yescharacteristic
322C2×Q8×C19C2×D411yescharacteristic
323C2×Q8×C19C2×D412yes—
324C2×Q8×C19C2411yescharacteristic
325C2×Q8×C19C2412yes—
326C2×D4×C19—21no—
327C2×D4×C19—21no—
328C2×D4×C19—21no—
329C2×D4×C19—22no—
330C2×D4×C19—21no—
331C2×D4×C19—21no—
332C2×D4×C19—22no—
333C2×D4×C19—22no—
334C2×D4×C19—22no—
335C2×D4×C19—22no—
336C2×D4×C19—21no—
337C2×D4×C19—21no—
338C2×D4×C19C2411yescharacteristic
339C2×D4×C19C2411yescharacteristic
340C2×D4×C19C2411yescharacteristic
341C2×D4×C19C2412yes—
342C22×C4×C19—21no—
343C22×C4×C19—22no—
344C22×C4×C19—21no—
345C22×C4×C19—21no—
346C22×C4×C19—22no—
347C22×C4×C19—22no—
348C22×C4×C19—22no—
349C22×C4×C19—22no—
350C22×C4×C19—22no—
351C22×C4×C19C2×D411yescharacteristic
352C22×C4×C19C2×D411yescharacteristic
353C22×C4×C19C2411yescharacteristic
354SD16×C19—22no—
355SD16×C19—24no—
356SD16×C19—42no—
357SD16×C19—42no—
358SD16×C19—42no—
359SD16×C19—41no—
360SD16×C19—42no—
361D8×C19—22no—
362D8×C19—42no—
363D8×C19—41no—
364M16×C19—22no—
365M16×C19—41no—
366C2×C8×C19—42no—
367C2×C8×C19C2412yes—
368C2×C8×C19C2412yes—
369C2×C8×C19C2411yescharacteristic
370C2×C8×C19C2411yescharacteristic
371C2×C8×C19C2411yescharacteristic
372C2×C8×C19C2411yescharacteristic
373C4⋊C4×C19—21no—
374C4⋊C4×C19—21no—
375C4⋊C4×C19—21no—
376C4⋊C4×C19—22no—
377C4⋊C4×C19—22no—
378C4⋊C4×C19—22no—
379C4⋊C4×C19—22no—
380C4⋊C4×C19—22no—
381C4⋊C4×C19—21no—
382C4⋊C4×C19—22no—
383C4⋊C4×C19—21no—
384C4⋊C4×C19—21no—
385C4⋊C4×C19—21no—
386C4⋊C4×C19—22no—
387C4⋊C4×C19—22no—
388C4⋊C4×C19—21no—
389C4⋊C4×C19—22no—
390C4⋊C4×C19—22no—
391C4⋊C4×C19—22no—
392C4⋊C4×C19—22no—
393C4⋊C4×C19—22no—
394C4⋊C4×C19—22no—
395C4⋊C4×C19—21no—
396C4⋊C4×C19C2×D411yescharacteristic
397C4⋊C4×C19C2×D411yescharacteristic
398C4⋊C4×C19C2×D412yes—
399C4⋊C4×C19C2×D412yes—
400C4⋊C4×C19C2×D412yes—
401C4⋊C4×C19C2×D412yes—
402C4⋊C4×C19C2×D412yes—
403C4⋊C4×C19C2×D412yes—
404C4⋊C4×C19C2×D412yes—
405C4⋊C4×C19C2411yescharacteristic
406C4⋊C4×C19C2411yescharacteristic
407C4⋊C4×C19C2412yes—
408C4⋊C4×C19C2411yescharacteristic
409C4⋊C4×C19C2412yes—
410C4⋊C4×C19C2411yescharacteristic
411C22⋊C4×C19—22no—
412C22⋊C4×C19—21no—
413C22⋊C4×C19—21no—
414C22⋊C4×C19—21no—
415C22⋊C4×C19—21no—
416C22⋊C4×C19—22no—
417C22⋊C4×C19—22no—
418C22⋊C4×C19—21no—
419C22⋊C4×C19—21no—
420C22⋊C4×C19—22no—
421C22⋊C4×C19—22no—
422C22⋊C4×C19—22no—
423C22⋊C4×C19—22no—
424C22⋊C4×C19—22no—
425C22⋊C4×C19—22no—
426C22⋊C4×C19—21no—
427C22⋊C4×C19—21no—
428C22⋊C4×C19—21no—
429C22⋊C4×C19—22no—
430C22⋊C4×C19C2×D412yes—
431C22⋊C4×C19C2×D412yes—
432C42×C19—22no—
433C42×C19—21no—
434C42×C19—22no—
435C42×C19—22no—
436C42×C19—22no—
437C42×C19C2×D411yescharacteristic
438C42×C19C2×D411yescharacteristic
439C42×C19C2411yescharacteristic
440C42×C19C2411yescharacteristic
441C42×C19C2412yes—
442C42×C19C2412yes—
443#62401C1911yesmaximal, characteristic, direct product factor, Sylow
444C23×C19—21no—
445C23×C19—22no—
446C23×C19—21no—
447C23×C19—21no—
448C23×C19C22×D411yescharacteristic
449Q8×C19—22no—
450Q8×C19—22no—
451Q8×C19—21no—
452Q8×C19—22no—
453Q8×C19—22no—
454Q8×C19—21no—
455Q8×C19—42no—
456Q8×C19—81no—
457Q8×C19—82no—
458Q8×C19—81no—
459Q8×C19—81no—
460D4×C19—21no—
461D4×C19—21no—
462D4×C19—21no—
463D4×C19—22no—
464D4×C19—21no—
465D4×C19—22no—
466D4×C19—21no—
467D4×C19—21no—
468D4×C19—42no—
469D4×C19—42no—
470D4×C19—81no—
471D4×C19—82no—
472D4×C19—82no—
473D4×C19—81no—
474D4×C19—82no—
475D4×C19—82no—
476D4×C19—81no—
477D4×C19—82no—
478D4×C19—81no—
479D4×C19—81no—
480C2×C4×C19—22no—
481C2×C4×C19—21no—
482C2×C4×C19—21no—
483C2×C4×C19—22no—
484C2×C4×C19—21no—
485C2×C4×C19—21no—
486C2×C4×C19—21no—
487C2×C4×C19—22no—
488C2×C4×C19—22no—
489C2×C4×C19—21no—
490C2×C4×C19—21no—
491C2×C4×C19—41no—
492C2×C4×C19—44no—
493C2×C4×C19—42no—
494C2×C4×C19—42no—
495C2×C4×C19—42no—
496C2×C4×C19—82no—
497C2×C4×C19—82no—
498C2×C4×C19—82no—
499C2×C4×C19—82no—
500C2×C4×C19—82no—
501C2×C4×C19C22×D411yescharacteristic
502C2×C4×C19C22×D412yes—
503C2×C4×C19C22×D412yes—
504C2×C4×C19C22×D412yes—
505C2×C4×C19C22×D411yescharacteristic
506C2×C4×C19C22×D411yescharacteristic
507C2×C4×C19C22×D411yescharacteristic
508C2×C4×C19C22×D412yes—
509C2×C4×C19C22×D411yescharacteristic
510C2×C4×C19C2511yescharacteristic
511C8×C19—21no—
512C8×C19—22no—
513C8×C19—22no—
514C8×C19—21no—
515C8×C19—21no—
516C8×C192−1+412yes—
517#3555C2×C1911yescharacteristic, complemented
518#3548C2×C1911yescharacteristic, complemented
519#3397C2×C1911yescharacteristic, complemented
520#3397C2×C1912yescomplemented
521#3392C2×C1911yescharacteristic, complemented
522#3388C2×C1912yescomplemented
523#3385C2×C1911yescharacteristic, complemented
524#3380C2×C1911yescharacteristic, complemented
525#3376C2×C1912yescomplemented
526#3372C2×C1911yescharacteristic, complemented
527#3368C2×C1912yescomplemented
528#3366C2×C1911yescharacteristic, complemented
529#3362C2×C1911yescharacteristic, complemented
530#3360C2×C1911yescharacteristic, complemented
531#3260C2×C1912yescomplemented
532#3257C2×C1912yescomplemented
533#3247C2×C1911yescharacteristic, complemented
534#3246C2×C1911yescharacteristic, complemented
535#3182C2×C1911yescharacteristic, complemented
536#3179C2×C1912yescomplemented
537#3174C2×C1912yescomplemented
538#3171C2×C1911yescharacteristic, complemented
539#2962C2×C1911yescharacteristic, complemented
540C22×C19—21no—
541C22×C19—21no—
542C22×C19—21no—
543C22×C19—42no—
544C22×C19—41no—
545C22×C19—41no—
546C22×C19—41no—
547C22×C19—41no—
548C22×C19—41no—
549C22×C19—42no—
550C22×C19—41no—
551C22×C19—41no—
552C22×C19—41no—
553C22×C19—41no—
554C22×C19—42no—
555C22×C19C23×D411yescharacteristic
556C4×C19—21no—
557C4×C19—21no—
558C4×C19—22no—
559C4×C19—22no—
560C4×C19—21no—
561C4×C19—21no—
562C4×C19—22no—
563C4×C19—22no—
564C4×C19—42no—
565C4×C19—42no—
566C4×C19—41no—
567C4×C19—42no—
568C4×C19—41no—
569C4×C19—41no—
570C4×C19—41no—
571C4×C19—41no—
572C4×C19#57712yes—
573C4×C19C2×2−1+411yescharacteristic
574C4×C19#58511yescharacteristic
575#563—22no—
576#562—22no—
577Q82C22×C1911yescharacteristic
578#557C22×C1911yescharacteristic
579#557C22×C1912yes—
580#556—21no—
581#556C22×C1911yescharacteristic
582#556C22×C1912yes—
583#554C22×C1911yescharacteristic
584#554C22×C1911yescharacteristic
585#554C22×C1911yescharacteristic
586#554C22×C1912yes—
587#552—21no—
588#550C22×C1911yescharacteristic
589#550C22×C1911yescharacteristic
590#550C22×C1912yes—
591#547—21no—
592#547—21no—
593#544—21no—
594#542C22×C1912yes—
595#541—21no—
596#541—22no—
597#541C22×C1912yes—
598#540C22×C1912yes—
599#540C22×C1912yes—
600#537—21no—
601#537—21no—
602#537—22no—
603#533C22×C1911yescharacteristic
604#533C22×C1911yescharacteristic
605#532C22×C1911yescharacteristic
606#532C22×C1911yescharacteristic
607#529C22×C1911yescharacteristic
608#501C22×C1912yes—
609#501C22×C1911yescharacteristic
610#500C22×C1911yescharacteristic
611#499C22×C1912yes—
612#496C22×C1911yescharacteristic
613#496C22×C1912yes—
614#492C22×C1912yes—
615#492C22×C1911yescharacteristic
616#491C22×C1912yes—
617#490C22×C1912yes—
618#490C22×C1911yescharacteristic
619#489C22×C1911yescharacteristic
620#488C22×C1912yes—
621#487C22×C1911yescharacteristic
622#486C22×C1911yescharacteristic
623#486C22×C1912yes—
624#479C22×C1912yes—
625#479C22×C1912yes—
626#479C22×C1912yes—
627#478C22×C1912yes—
628#478C22×C1912yes—
629#478C22×C1912yes—
630#478C22×C1912yes—
631#477C22×C1911yescharacteristic
632#476C22×C1911yescharacteristic
633#476C22×C1911yescharacteristic
634#476C22×C1912yes—
635#476C22×C1911yescharacteristic
636#475C22×C1912yes—
637#474C22×C1912yes—
638#469C22×C1911yescharacteristic
639#469C22×C1911yescharacteristic
640#468C22×C1911yescharacteristic
641#468C22×C1911yescharacteristic
642#468C22×C1912yes—
643#468C22×C1912yes—
644#466C22×C1912yes—
645#465C22×C1912yes—
646#465C22×C1912yes—
647#465C22×C1912yes—
648#463C22×C1912yes—
649#463C22×C1912yes—
650#463C22×C1912yes—
651#461C22×C1911yescharacteristic
652#461C22×C1911yescharacteristic
653#461C22×C1912yes—
654#461C22×C1912yes—
655#460C22×C1911yescharacteristic
656#460C22×C1912yes—
657#460C22×C1912yes—
658#460C22×C1912yes—
659#460C22×C1912yes—
660#459C22×C1911yescharacteristic
661#459C22×C1912yes—
662#446C22×C1911yescharacteristic
663#446C22×C1912yes—
664#446C22×C1911yescharacteristic
665#446C22×C1912yes—
666C8×Q8C22×C1911yescharacteristic
667C8×Q8C22×C1911yescharacteristic
668#442C22×C1912yes—
669#440C22×C1912yes—
670#440C22×C1912yes—
671#440C22×C1912yes—
672#440C22×C1912yes—
673#440C22×C1912yes—
674C4×SD16C22×C1912yes—
675C4×SD16C22×C1911yescharacteristic
676C4×SD16C22×C1912yes—
677C4×SD16C22×C1911yescharacteristic
678C4×SD16C22×C1912yes—
679C4×D8C22×C1911yescharacteristic
680C4×D8C22×C1911yescharacteristic
681C4×D8C22×C1912yes—
682#424C22×C1912yes—
683C2×C4⋊C8C22×C1911yescharacteristic
684#405C22×C1912yes—
685C4×M16C22×C1911yescharacteristic
686C2×C19—41no—
687C2×C19—82no—
688C2×C19—81no—
689C2×C19—81no—
690C2×C19—81no—
691C2×C19#349711yescharacteristic
692C2×C19C2×#57711yescharacteristic
693C2×C19#358511yescharacteristic
694C2×#41—21no—
695C2×#41—21no—
696C2×#41—22no—
697C2×#41—21no—
698C2×#41—21no—
699C2×SD16C23×C1911yescharacteristic
700C2×SD16C23×C1912yes—
701C2×SD16C23×C1911yescharacteristic
702C2×SD16C23×C1912yes—
703C2×SD16C23×C1912yes—
704C2×SD16C23×C1912yes—
705C2×SD16C23×C1912yes—
706C2×D8C23×C1911yescharacteristic
707C2×D8C23×C1911yescharacteristic
708C2×D8C23×C1912yes—
709C2×M16C23×C1911yescharacteristic
710C2×M16C23×C1911yescharacteristic
711C22×C8C23×C1912yes—
712C4⋊Q8—22no—
713C4⋊Q8—22no—
714C4⋊Q8—21no—
715C4⋊Q8D4×C1911yescharacteristic
716C4⋊Q8D4×C1911yescharacteristic
717C4⋊Q8C23×C1911yescharacteristic
718C4⋊Q8C23×C1912yes—
719C4⋊Q8C23×C1911yescharacteristic
720C4⋊Q8C23×C1911yescharacteristic
721C4⋊Q8C23×C1911yescharacteristic
722C4⋊Q8C23×C1912yes—
723#127C23×C1911yescharacteristic
724#127C23×C1911yescharacteristic
725#127C23×C1912yes—
726#127C23×C1912yes—
727#126—22no—
728#126—22no—
729#126—22no—
730#126—22no—
731#126—22no—
732#126—22no—
733#126—21no—
734#125—22no—
735#125—22no—
736#125—22no—
737#125—22no—
738#125—22no—
739#125—21no—
740#125—21no—
741#125D4×C1912yes—
742#125C23×C1911yescharacteristic
743#125C23×C1912yes—
744#125C23×C1912yes—
745#125C23×C1912yes—
746#124—22no—
747#124—21no—
748#124—21no—
749#124C23×C1911yescharacteristic
750#124C23×C1912yes—
751#123—21no—
752#123—22no—
753#123—22no—
754#123—22no—
755#123—22no—
756#123—22no—
757C22⋊Q8—21no—
758C22⋊Q8—21no—
759C22⋊Q8—22no—
760C22⋊Q8—21no—
761C22⋊Q8—21no—
762C22⋊Q8—22no—
763C22⋊Q8—21no—
764C22⋊Q8—22no—
765C22⋊Q8—22no—
766C22⋊Q8—22no—
767C22⋊Q8—22no—
768C22⋊Q8—22no—
769C22⋊Q8—22no—
770C22⋊Q8D4×C1911yescharacteristic
771C22⋊Q8D4×C1911yescharacteristic
772C22⋊Q8D4×C1912yes—
773C22⋊Q8C23×C1911yescharacteristic
774C22⋊Q8C23×C1912yes—
775#121—21no—
776#121—21no—
777#121—21no—
778#121—21no—
779#121—22no—
780#121—22no—
781#121—22no—
782#121—22no—
783#121—22no—
784#121—22no—
785#121—22no—
786#121—22no—
787#121—22no—
788#121C23×C1911yescharacteristic
789#121C23×C1911yescharacteristic
790#121C23×C1911yescharacteristic
791#121C23×C1912yes—
792C4×Q8—21no—
793C4×Q8—21no—
794C4×Q8—22no—
795C4×Q8—21no—
796C4×Q8C23×C1911yescharacteristic
797C4×Q8C23×C1912yes—
798C4×Q8C23×C1912yes—
799C4×Q8C23×C1912yes—
800C4×Q8C23×C1912yes—
801C4×Q8C23×C1911yescharacteristic
802C4×Q8C23×C1912yes—
803C4×Q8C23×C1911yescharacteristic
804C4×D4—21no—
805C4×D4—21no—
806C4×D4—21no—
807C4×D4C23×C1911yescharacteristic
808C4×D4C23×C1911yescharacteristic
809C4×D4C23×C1911yescharacteristic
810C4×D4C23×C1912yes—
811C4×D4C23×C1912yes—
812C4×D4C23×C1912yes—
813C4×D4C23×C1912yes—
814C4×D4C23×C1912yes—
815C4×D4C23×C1912yes—
816#117—21no—
817#117—22no—
818#117—21no—
819#117—21no—
820#117C23×C1912yes—
821C2×C4⋊C4—21no—
822C2×C4⋊C4—21no—
823C2×C4⋊C4—22no—
824C2×C4⋊C4—21no—
825C2×C42C23×C1911yescharacteristic
826#107C23×C1911yescharacteristic
827#107C23×C1912yes—
828#107C23×C1911yescharacteristic
829#107C23×C1912yes—
830#107C23×C1912yes—
831#106C23×C1911yescharacteristic
832#106C23×C1912yes—
833#106C23×C1912yes—
834#106C23×C1911yescharacteristic
835#106C23×C1912yes—
836C4⋊C8C23×C1911yescharacteristic
837C4⋊C8C23×C1911yescharacteristic
838C4⋊C8C23×C1912yes—
839C4⋊C8C23×C1912yes—
840C4⋊C8C23×C1912yes—
841C4⋊C8C23×C1912yes—
842C4⋊C8C23×C1912yes—
843#103C23×C1911yescharacteristic
844#103C23×C1912yes—
845#103C23×C1912yes—
846#103C23×C1911yescharacteristic
847#103C23×C1912yes—
848#103C23×C1912yes—
849#103C23×C1912yes—
850#102C23×C1911yescharacteristic
851#102C23×C1911yescharacteristic
852#102C23×C1912yes—
853#102C23×C1911yescharacteristic
854#102C23×C1912yes—
855#102C23×C1911yescharacteristic
856#102C23×C1911yescharacteristic
857#102C23×C1912yes—
858#102C23×C1912yes—
859#102C23×C1911yescharacteristic
860#102C23×C1912yes—
861#102C23×C1912yes—
862#102C23×C1912yes—
863#97C23×C1911yescharacteristic
864#97C23×C1911yescharacteristic
865#97C23×C1912yes—
866#97C23×C1912yes—
867C4×C8C23×C1911yescharacteristic
868C4×C8C23×C1911yescharacteristic
869C4×C8C23×C1912yes—
870C4×C8C23×C1912yes—
871C19#6240111yescharacteristic, direct product factor, Sylow
872#41—82no—
873#41—82no—
874#41—82no—
875#41—82no—
876#41—84no—
877C2×Q8—21no—
878C2×Q8—22no—
879C2×Q8—21no—
880C2×Q8—21no—
881C2×Q8C2×D4×C1911yescharacteristic
882C2×Q8C2×D4×C1911yescharacteristic
883C2×Q8C2×D4×C1912yes—
884C2×Q8C24×C1911yescharacteristic
885C2×Q8C24×C1912yes—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—22no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—22no—
893C2×D4—22no—
894C2×D4—22no—
895C2×D4—22no—
896C2×D4—21no—
897C2×D4—21no—
898C2×D4C24×C1911yescharacteristic
899C2×D4C24×C1911yescharacteristic
900C2×D4C24×C1911yescharacteristic
901C2×D4C24×C1912yes—
902C22×C4—21no—
903C22×C4—22no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—22no—
907C22×C4—22no—
908C22×C4—22no—
909C22×C4—22no—
910C22×C4—22no—
911C22×C4C2×D4×C1911yescharacteristic
912C22×C4C2×D4×C1911yescharacteristic
913C22×C4C24×C1911yescharacteristic
914SD16—22no—
915SD16—24no—
916SD16—42no—
917SD16—42no—
918SD16—42no—
919SD16—41no—
920SD16—42no—
921D8—22no—
922D8—42no—
923D8—41no—
924M16—22no—
925M16—41no—
926C2×C8—42no—
927C2×C8C24×C1911yescharacteristic
928C2×C8C24×C1912yes—
929C2×C8C24×C1911yescharacteristic
930C2×C8C24×C1911yescharacteristic
931C2×C8C24×C1912yes—
932C2×C8C24×C1911yescharacteristic
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—22no—
937C4⋊C4—22no—
938C4⋊C4—22no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—21no—
942C4⋊C4—22no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—22no—
947C4⋊C4—22no—
948C4⋊C4—21no—
949C4⋊C4—22no—
950C4⋊C4—22no—
951C4⋊C4—22no—
952C4⋊C4—22no—
953C4⋊C4—22no—
954C4⋊C4—22no—
955C4⋊C4—21no—
956C4⋊C4C2×D4×C1911yescharacteristic
957C4⋊C4C2×D4×C1911yescharacteristic
958C4⋊C4C2×D4×C1912yes—
959C4⋊C4C2×D4×C1912yes—
960C4⋊C4C2×D4×C1912yes—
961C4⋊C4C2×D4×C1912yes—
962C4⋊C4C2×D4×C1912yes—
963C4⋊C4C2×D4×C1912yes—
964C4⋊C4C2×D4×C1912yes—
965C4⋊C4C24×C1911yescharacteristic
966C4⋊C4C24×C1912yes—
967C4⋊C4C24×C1911yescharacteristic
968C4⋊C4C24×C1911yescharacteristic
969C4⋊C4C24×C1911yescharacteristic
970C4⋊C4C24×C1912yes—
971C22⋊C4—22no—
972C22⋊C4—21no—
973C22⋊C4—21no—
974C22⋊C4—21no—
975C22⋊C4—21no—
976C22⋊C4—22no—
977C22⋊C4—22no—
978C22⋊C4—21no—
979C22⋊C4—21no—
980C22⋊C4—22no—
981C22⋊C4—22no—
982C22⋊C4—22no—
983C22⋊C4—22no—
984C22⋊C4—22no—
985C22⋊C4—22no—
986C22⋊C4—21no—
987C22⋊C4—21no—
988C22⋊C4—21no—
989C22⋊C4—22no—
990C22⋊C4C2×D4×C1912yes—
991C22⋊C4C2×D4×C1912yes—
992C42—22no—
993C42—21no—
994C42—22no—
995C42—22no—
996C42—22no—
997C42C2×D4×C1911yescharacteristic
998C42C2×D4×C1911yescharacteristic
999C42C24×C1911yescharacteristic
1000C42C24×C1912yes—
1001C42C24×C1912yes—
1002C42C24×C1911yescharacteristic
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—22no—
1007C23C22×D4×C1911yescharacteristic
1008Q8—22no—
1009Q8—22no—
1010Q8—21no—
1011Q8—22no—
1012Q8—22no—
1013Q8—21no—
1014Q8—42no—
1015Q8—81no—
1016Q8—81no—
1017Q8—81no—
1018Q8—82no—
1019D4—21no—
1020D4—21no—
1021D4—21no—
1022D4—22no—
1023D4—21no—
1024D4—22no—
1025D4—21no—
1026D4—21no—
1027D4—42no—
1028D4—42no—
1029D4—81no—
1030D4—82no—
1031D4—82no—
1032D4—81no—
1033D4—82no—
1034D4—82no—
1035D4—81no—
1036D4—81no—
1037D4—82no—
1038D4—81no—
1039C2×C4—22no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—22no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—22no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—22no—
1050C2×C4—41no—
1051C2×C4—44no—
1052C2×C4—42no—
1053C2×C4—42no—
1054C2×C4—42no—
1055C2×C4—82no—
1056C2×C4—82no—
1057C2×C4—82no—
1058C2×C4—82no—
1059C2×C4—82no—
1060C2×C4C22×D4×C1911yescharacteristic
1061C2×C4C22×D4×C1912yes—
1062C2×C4C22×D4×C1912yes—
1063C2×C4C22×D4×C1912yes—
1064C2×C4C22×D4×C1911yescharacteristic
1065C2×C4C22×D4×C1911yescharacteristic
1066C2×C4C22×D4×C1911yescharacteristic
1067C2×C4C22×D4×C1912yes—
1068C2×C4C22×D4×C1911yescharacteristic
1069C2×C4C25×C1911yescharacteristic
1070C8—21no—
1071C8—22no—
1072C8—22no—
1073C8—21no—
1074C8—21no—
1075C8C19×2−1+412yes—
1076C22—21no—
1077C22—21no—
1078C22—21no—
1079C22—41no—
1080C22—41no—
1081C22—41no—
1082C22—42no—
1083C22—41no—
1084C22—41no—
1085C22—41no—
1086C22—42no—
1087C22—42no—
1088C22—41no—
1089C22—41no—
1090C22—41no—
1091C22C23×D4×C1911yescharacteristic
1092C4—21no—
1093C4—21no—
1094C4—22no—
1095C4—22no—
1096C4—21no—
1097C4—21no—
1098C4—22no—
1099C4—22no—
1100C4—42no—
1101C4—41no—
1102C4—41no—
1103C4—41no—
1104C4—41no—
1105C4—42no—
1106C4—42no—
1107C4—41no—
1108C4C19×#57712yes—
1109C4C2×C19×2−1+411yescharacteristic
1110C4C19×#58511yescharacteristic
1111C2—41no—
1112C2—81no—
1113C2—81no—
1114C2—81no—
1115C2—82no—
1116C2C19×#349711yescharacteristic
1117C2C2×C19×#57711yescharacteristic
1118C2C19×#358511yescharacteristic
subgroupG/H
center, socleC22×C19C23×D4
commutator, Frattini, cosocleC2×C4C25×C19
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C19 ◁ C19×#533 ◁ G

Complements

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

NH ≅ G/Ntype
1. C19×#3555C2semidirect
2. C19×#3548C2semidirect
3. C19×#3397C2semidirect
4. C19×#3397C2semidirect
5. C19×#3392C2semidirect
6. C19×#3388C2semidirect
7. C19×#3385C2semidirect
8. C19×#3380C2semidirect
9. C19×#3376C2semidirect
10. C19×#3372C2semidirect
11. C19×#3368C2semidirect
12. C19×#3366C2semidirect
13. C19×#3362C2semidirect
14. C19×#3360C2semidirect
15. C19×#3260C2semidirect
16. C19×#3257C2semidirect
17. C19×#3247C2semidirect
18. C19×#3246C2semidirect
19. C19×#3182C2semidirect
20. C19×#3179C2semidirect
21. C19×#3174C2semidirect
22. C19×#3171C2semidirect
23. C19×#2962C2semidirect
443. #62401C19direct (N × H)
517. #3555C2×C19semidirect
518. #3548C2×C19semidirect
519. #3397C2×C19semidirect
520. #3397C2×C19semidirect
521. #3392C2×C19semidirect
522. #3388C2×C19semidirect
523. #3385C2×C19semidirect
524. #3380C2×C19semidirect
525. #3376C2×C19semidirect
526. #3372C2×C19semidirect
527. #3368C2×C19semidirect
528. #3366C2×C19semidirect
529. #3362C2×C19semidirect
530. #3360C2×C19semidirect
531. #3260C2×C19semidirect
532. #3257C2×C19semidirect
533. #3247C2×C19semidirect
534. #3246C2×C19semidirect
535. #3182C2×C19semidirect
536. #3179C2×C19semidirect
537. #3174C2×C19semidirect
538. #3171C2×C19semidirect
539. #2962C2×C19semidirect
871. C19#62401direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#35552
C19×#35482
C19×#33972
C19×#33922
C19×#33882
C19×#33852
C19×#33802
C19×#33762
C19×#33722
C19×#33682
C19×#33662
C19×#33622
C19×#33602
C19×#32602
C19×#32572
C19×#32472
C19×#32462
C19×#31822
C19×#31792
C19×#31742
C19×#31712
C19×#29622
#6240119