Finite Group Databasebeta

← C19×#62185 #18068144

Subgroups — C19×#62185 #18068144

Order 4864.

1738 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C19×#3544C211yesmaximal, characteristic, complemented
2C19×#3517C211yesmaximal, characteristic, complemented
3C19×#3387C211yesmaximal, characteristic, complemented
4C19×#3381C211yesmaximal, characteristic, complemented
5C19×#3366C211yesmaximal, characteristic, complemented
6C19×#3362C211yesmaximal, characteristic, complemented
7C19×#3354C211yesmaximal, characteristic, complemented
8C19×#3351C212yesmaximal, complemented
9C19×#3345C212yesmaximal, complemented
10C19×#3335C211yesmaximal, characteristic, complemented
11C19×#3333C211yesmaximal, characteristic, complemented
12C19×#3332C212yesmaximal, complemented
13C19×#3317C212yesmaximal, complemented
14C19×#3305C211yesmaximal, characteristic, complemented
15C19×#3257C212yesmaximal, complemented
16C19×#3251C211yesmaximal, characteristic, complemented
17C19×#3241C212yesmaximal, complemented
18C19×#3227C211yesmaximal, characteristic, complemented
19C19×#3125C212yesmaximal, complemented
20C19×#3102C211yesmaximal, characteristic, complemented
21C19×#3084C212yesmaximal, complemented
22C19×#3079C211yesmaximal, characteristic, complemented
23C19×#2993C211yesmaximal, characteristic, complemented
24C19×#563—22no—
25Q82×C19C2211yescharacteristic
26C19×#557C2211yescharacteristic
27C19×#555C2211yescharacteristic
28C19×#554C2211yescharacteristic
29C19×#554C2211yescharacteristic
30C19×#553—22no—
31C19×#553C2212yes—
32C19×#552—21no—
33C19×#552C2212yes—
34C19×#550—21no—
35C19×#550C2211yescharacteristic
36C19×#550C2212yes—
37C19×#550C2211yescharacteristic
38C19×#547—21no—
39C19×#547—21no—
40C19×#547C2211yescharacteristic
41C19×#547C2212yes—
42C19×#544—21no—
43C19×#544C2212yes—
44C19×#542—21no—
45C19×#542C2212yes—
46C19×#540—22no—
47C19×#540C2212yes—
48C19×#536—22no—
49C19×#532—21no—
50C19×#532C2211yescharacteristic
51C2×C19×C4⋊Q8C2211yescharacteristic
52C19×#529—21no—
53C19×#529C2211yescharacteristic
54C19×#529C2211yescharacteristic
55C19×#520C2212yes—
56C4×#41×C19C2211yescharacteristic
57C19×#501C2212yes—
58C19×#499C2212yes—
59C19×#498C2211yescharacteristic
60C19×#498C2211yescharacteristic
61C19×#490C2212yes—
62C19×#486C2211yescharacteristic
63C19×#486C2211yescharacteristic
64C19×#486C2212yes—
65C19×#485C2211yescharacteristic
66C19×#483C2212yes—
67C19×#482C2212yes—
68C19×#482C2212yes—
69C19×#482C2211yescharacteristic
70C19×#481C2212yes—
71C19×#481C2212yes—
72C19×#481C2212yes—
73C19×#481C2212yes—
74C19×#480C2212yes—
75C19×#479C2212yes—
76C19×#479C2212yes—
77C19×#479C2211yescharacteristic
78C19×#478C2211yescharacteristic
79C19×#478C2212yes—
80C19×#478C2212yes—
81C19×#478C2212yes—
82C19×#477C2211yescharacteristic
83C19×#477C2211yescharacteristic
84C19×#476C2212yes—
85C19×#476C2212yes—
86C19×#476C2211yescharacteristic
87C19×#476C2211yescharacteristic
88C19×#476C2212yes—
89C19×#475C2211yescharacteristic
90C19×#475C2212yes—
91C19×#475C2212yes—
92C19×#474C2212yes—
93C19×#474C2211yescharacteristic
94C19×#469C2212yes—
95C19×#469C2212yes—
96C19×#468C2212yes—
97C19×#468C2212yes—
98C19×#466C2212yes—
99C19×#465C2212yes—
100C19×#464C2211yescharacteristic
101C19×#463C2212yes—
102C19×#463C2211yescharacteristic
103C19×#460C2211yescharacteristic
104C19×#460C2212yes—
105C19×#459C2211yescharacteristic
106C19×#459C2212yes—
107C19×#452C2211yescharacteristic
108C19×#452C2212yes—
109C19×#449C2212yes—
110C19×#449C2211yescharacteristic
111C19×#446C2211yescharacteristic
112C8×Q8×C19C2211yescharacteristic
113C19×#442C2212yes—
114C19×#441C2212yes—
115C4×Q16×C19C2211yescharacteristic
116C4×SD16×C19C2211yescharacteristic
117C4×SD16×C19C2212yes—
118C4×SD16×C19C2211yescharacteristic
119C4×SD16×C19C2212yes—
120C4×D8×C19C2211yescharacteristic
121C19×#436C2212yes—
122C19×#436C2211yescharacteristic
123C19×#435C2212yes—
124C8×D4×C19C2211yescharacteristic
125C19×#433C2212yes—
126C19×#431C2211yescharacteristic
127C19×#428C2212yes—
128C19×#428C2212yes—
129C2×C19×#106C2212yes—
130C19×#424C2212yes—
131C19×#423C2211yescharacteristic
132C19×#417C2212yes—
133C19×#417C2212yes—
134C19×#416C2212yes—
135C2×#41×C19—21no—
136C2×#41×C19—21no—
137C2×#41×C19—22no—
138C2×#41×C19—21no—
139C2×#41×C19C2312yes—
140C2×#41×C19C2311yescharacteristic
141C22×Q8×C19—21no—
142C2×Q16×C19C2311yescharacteristic
143C2×SD16×C19C2311yescharacteristic
144C2×SD16×C19C2311yescharacteristic
145C2×SD16×C19C2312yes—
146C2×D8×C19C2311yescharacteristic
147C2×D8×C19C2312yes—
148C2×M16×C19C2312yes—
149C2×M16×C19C2312yes—
150C22×C8×C19C2312yes—
151C19×C4⋊Q8—21no—
152C19×C4⋊Q8—22no—
153C19×C4⋊Q8—22no—
154C19×C4⋊Q8—21no—
155C19×C4⋊Q8—21no—
156C19×C4⋊Q8—21no—
157C19×C4⋊Q8C2312yes—
158C19×C4⋊Q8C2311yescharacteristic
159C19×C4⋊Q8C2312yes—
160C19×C4⋊Q8C2311yescharacteristic
161C19×C4⋊Q8C2311yescharacteristic
162C19×#127—21no—
163C19×#127—22no—
164C19×#127C2311yescharacteristic
165C19×#127C2312yes—
166C19×#126—22no—
167C19×#126—22no—
168C19×#126—22no—
169C19×#126—21no—
170C19×#126D412yes—
171C19×#125—22no—
172C19×#125—21no—
173C19×#125—22no—
174C19×#125—22no—
175C19×#125D411yescharacteristic
176C19×#125C2311yescharacteristic
177C19×#125C2312yes—
178C19×#125C2312yes—
179C19×#124—22no—
180C19×#124—22no—
181C19×#124—21no—
182C19×#124D411yescharacteristic
183C19×#124C2311yescharacteristic
184C19×#123—22no—
185C19×#123—21no—
186C19×#123—22no—
187C19×#123—22no—
188C19×#123—22no—
189C19×#123—22no—
190C19×#123—22no—
191C19×#123—22no—
192C19×#123—22no—
193C19×#123D412yes—
194C19×C22⋊Q8—21no—
195C19×C22⋊Q8—21no—
196C19×C22⋊Q8—22no—
197C19×C22⋊Q8—22no—
198C19×C22⋊Q8—22no—
199C19×C22⋊Q8—22no—
200C19×C22⋊Q8—22no—
201C19×C22⋊Q8—22no—
202C19×C22⋊Q8D411yescharacteristic
203C19×C22⋊Q8C2312yes—
204C19×C22⋊Q8C2311yescharacteristic
205C19×#121—22no—
206C19×#121—21no—
207C19×#121—21no—
208C19×#121—21no—
209C19×#121—22no—
210C19×#121—22no—
211C19×#121—22no—
212C19×#121—22no—
213C19×#121—22no—
214C19×#121—22no—
215C19×#121D411yescharacteristic
216C19×#121C2312yes—
217C19×#121C2311yescharacteristic
218C19×#121C2312yes—
219C19×#121C2312yes—
220C19×#121C2312yes—
221C4×Q8×C19—21no—
222C4×Q8×C19—21no—
223C4×Q8×C19C2311yescharacteristic
224C4×Q8×C19C2311yescharacteristic
225C4×Q8×C19C2312yes—
226C4×Q8×C19C2312yes—
227C4×Q8×C19C2311yescharacteristic
228C4×Q8×C19C2311yescharacteristic
229C4×D4×C19—21no—
230C4×D4×C19—21no—
231C4×D4×C19—21no—
232C4×D4×C19—21no—
233C4×D4×C19—21no—
234C4×D4×C19—22no—
235C4×D4×C19—22no—
236C4×D4×C19—22no—
237C4×D4×C19—22no—
238C4×D4×C19—21no—
239C4×D4×C19C2311yescharacteristic
240C4×D4×C19C2311yescharacteristic
241C4×D4×C19C2312yes—
242C4×D4×C19C2312yes—
243C4×D4×C19C2311yescharacteristic
244C4×D4×C19C2312yes—
245C4×D4×C19C2311yescharacteristic
246C4×D4×C19C2312yes—
247C19×#117—22no—
248C19×#117—21no—
249C19×#117—22no—
250C19×#117—21no—
251C19×#117—21no—
252C19×#117C2312yes—
253C19×#117C2311yescharacteristic
254C19×#117C2312yes—
255C2×C4⋊C4×C19—21no—
256C2×C4⋊C4×C19—22no—
257C2×C4⋊C4×C19—21no—
258C2×C4⋊C4×C19C2312yes—
259C2×C4⋊C4×C19C2312yes—
260C2×C4⋊C4×C19C2312yes—
261C2×C42×C19—21no—
262C2×C42×C19C2311yescharacteristic
263C19×#107C2311yescharacteristic
264C19×#107C2312yes—
265C19×#107C2312yes—
266C19×#107C2312yes—
267C19×#107C2311yescharacteristic
268C19×#106C2311yescharacteristic
269C19×#106C2312yes—
270C19×#106C2312yes—
271C19×#106C2312yes—
272C19×#106C2312yes—
273C19×#106C2312yes—
274C19×#106C2312yes—
275C19×#106C2311yescharacteristic
276C19×#106C2312yes—
277C19×C4⋊C8C2312yes—
278C19×C4⋊C8C2311yescharacteristic
279C19×C4⋊C8C2311yescharacteristic
280C19×C4⋊C8C2311yescharacteristic
281C19×C4⋊C8C2312yes—
282C19×C4⋊C8C2312yes—
283C19×C4⋊C8C2311yescharacteristic
284C19×#103C2311yescharacteristic
285C19×#103C2312yes—
286C19×#103C2312yes—
287C19×#103C2311yescharacteristic
288C19×#103C2311yescharacteristic
289C19×#103C2311yescharacteristic
290C19×#103C2312yes—
291C19×#102C2312yes—
292C19×#102C2312yes—
293C19×#102C2312yes—
294C19×#102C2312yes—
295C19×#102C2312yes—
296C19×#102C2312yes—
297C19×#102C2311yescharacteristic
298C19×#102C2311yescharacteristic
299C19×#102C2312yes—
300C19×#102C2311yescharacteristic
301C19×#102C2311yescharacteristic
302C19×#102C2312yes—
303C19×#102C2312yes—
304C19×C22⋊C8C2311yescharacteristic
305C19×C22⋊C8C2311yescharacteristic
306C19×C22⋊C8C2312yes—
307C19×C22⋊C8C2312yes—
308C19×#97C2312yes—
309C4×C8×C19C2311yescharacteristic
310C4×C8×C19C2311yescharacteristic
311C4×C8×C19C2312yes—
312#41×C19—24no—
313#41×C19—22no—
314#41×C19—42no—
315#41×C19—41no—
316#41×C19—82no—
317#41×C19—82no—
318#41×C19—84no—
319#41×C19—82no—
320C2×Q8×C19—21no—
321C2×Q8×C19—21no—
322C2×Q8×C19—22no—
323C2×Q8×C19—22no—
324C2×Q8×C19—21no—
325C2×Q8×C19—82no—
326C2×Q8×C19C2×D411yescharacteristic
327C2×Q8×C19C2411yescharacteristic
328C2×Q8×C19C2411yescharacteristic
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×C19—22no—
339C2×D4×C19—22no—
340C2×D4×C19C2×D411yescharacteristic
341C2×D4×C19C2×D412yes—
342C2×D4×C19C2411yescharacteristic
343C2×D4×C19C2411yescharacteristic
344C2×D4×C19C2412yes—
345C22×C4×C19—22no—
346C22×C4×C19—22no—
347C22×C4×C19—22no—
348C22×C4×C19—21no—
349C22×C4×C19—21no—
350C22×C4×C19—21no—
351C22×C4×C19—22no—
352C22×C4×C19—21no—
353C22×C4×C19—22no—
354C22×C4×C19—22no—
355C22×C4×C19—22no—
356C22×C4×C19C2×D411yescharacteristic
357C22×C4×C19C2×D411yescharacteristic
358C22×C4×C19C2411yescharacteristic
359C22×C4×C19C2412yes—
360Q16×C19—22no—
361SD16×C19—22no—
362SD16×C19—41no—
363SD16×C19—42no—
364D8×C19—42no—
365D8×C19—41no—
366M16×C19—42no—
367M16×C19—42no—
368C2×C8×C19—42no—
369C2×C8×C19C2411yescharacteristic
370C2×C8×C19C2412yes—
371C2×C8×C19C2411yescharacteristic
372C2×C8×C19C2412yes—
373C2×C8×C19C2411yescharacteristic
374C2×C8×C19C2411yescharacteristic
375C4⋊C4×C19—21no—
376C4⋊C4×C19—21no—
377C4⋊C4×C19—22no—
378C4⋊C4×C19—21no—
379C4⋊C4×C19—22no—
380C4⋊C4×C19—22no—
381C4⋊C4×C19—22no—
382C4⋊C4×C19—22no—
383C4⋊C4×C19—22no—
384C4⋊C4×C19—21no—
385C4⋊C4×C19—22no—
386C4⋊C4×C19—22no—
387C4⋊C4×C19—21no—
388C4⋊C4×C19—21no—
389C4⋊C4×C19—21no—
390C4⋊C4×C19—22no—
391C4⋊C4×C19—21no—
392C4⋊C4×C19—22no—
393C4⋊C4×C19—22no—
394C4⋊C4×C19—21no—
395C4⋊C4×C19—22no—
396C4⋊C4×C19C2×D412yes—
397C4⋊C4×C19C2×D411yescharacteristic
398C4⋊C4×C19C2×D412yes—
399C4⋊C4×C19C2×D411yescharacteristic
400C4⋊C4×C19C2×D412yes—
401C4⋊C4×C19C2×D412yes—
402C4⋊C4×C19C2411yescharacteristic
403C4⋊C4×C19C2412yes—
404C4⋊C4×C19C2411yescharacteristic
405C4⋊C4×C19C2412yes—
406C4⋊C4×C19C2412yes—
407C4⋊C4×C19C2411yescharacteristic
408C4⋊C4×C19C2411yescharacteristic
409C22⋊C4×C19—21no—
410C22⋊C4×C19—21no—
411C22⋊C4×C19—22no—
412C22⋊C4×C19—22no—
413C22⋊C4×C19—22no—
414C22⋊C4×C19—21no—
415C22⋊C4×C19—21no—
416C22⋊C4×C19—22no—
417C22⋊C4×C19—21no—
418C22⋊C4×C19—22no—
419C22⋊C4×C19—21no—
420C22⋊C4×C19—22no—
421C22⋊C4×C19—22no—
422C22⋊C4×C19—22no—
423C22⋊C4×C19—21no—
424C22⋊C4×C19—22no—
425C22⋊C4×C19—21no—
426C22⋊C4×C19C2×D412yes—
427C22⋊C4×C19C2×D412yes—
428C22⋊C4×C19C2×D412yes—
429C22⋊C4×C19C2×D412yes—
430C22⋊C4×C19C2×D412yes—
431C42×C19—21no—
432C42×C19—21no—
433C42×C19—21no—
434C42×C19—22no—
435C42×C19—22no—
436C42×C19—21no—
437C42×C19—22no—
438C42×C19C2×D411yescharacteristic
439C42×C19C2×D411yescharacteristic
440C42×C19C2411yescharacteristic
441C42×C19C2411yescharacteristic
442C42×C19C2412yes—
443#62185C1911yesmaximal, characteristic, direct product factor, Sylow
444C23×C19—21no—
445C23×C19—21no—
446C23×C19—22no—
447C23×C19C22×D412yes—
448C23×C19C22×D411yescharacteristic
449Q8×C19—22no—
450Q8×C19—21no—
451Q8×C19—21no—
452Q8×C19—21no—
453Q8×C19—42no—
454Q8×C19—82no—
455Q8×C19—81no—
456Q8×C19—81no—
457Q8×C19—82no—
458Q8×C192−1+412yes—
459D4×C19—22no—
460D4×C19—21no—
461D4×C19—21no—
462D4×C19—22no—
463D4×C19—21no—
464D4×C19—22no—
465D4×C19—21no—
466D4×C19—42no—
467D4×C19—44no—
468D4×C19—42no—
469D4×C19—42no—
470D4×C19—42no—
471D4×C19—81no—
472D4×C19—82no—
473D4×C19—82no—
474D4×C19—82no—
475D4×C19—82no—
476D4×C19—82no—
477D4×C19—82no—
478C2×C4×C19—21no—
479C2×C4×C19—22no—
480C2×C4×C19—21no—
481C2×C4×C19—22no—
482C2×C4×C19—22no—
483C2×C4×C19—21no—
484C2×C4×C19—21no—
485C2×C4×C19—21no—
486C2×C4×C19—21no—
487C2×C4×C19—21no—
488C2×C4×C19—22no—
489C2×C4×C19—22no—
490C2×C4×C19—21no—
491C2×C4×C19—22no—
492C2×C4×C19—41no—
493C2×C4×C19—42no—
494C2×C4×C19—44no—
495C2×C4×C19—44no—
496C2×C4×C19—42no—
497C2×C4×C19—42no—
498C2×C4×C19—81no—
499C2×C4×C19—82no—
500C2×C4×C19—82no—
501C2×C4×C19—82no—
502C2×C4×C19—82no—
503C2×C4×C19—82no—
504C2×C4×C19C22×D411yescharacteristic
505C2×C4×C19C22×D411yescharacteristic
506C2×C4×C19C22×D412yes—
507C2×C4×C19C22×D412yes—
508C2×C4×C19C22×D412yes—
509C2×C4×C19C22×D411yescharacteristic
510C2×C4×C19C22×D411yescharacteristic
511C2×C4×C19C22×D411yescharacteristic
512C2×C4×C19C2511yescharacteristic
513C8×C19—21no—
514C8×C19—21no—
515C8×C19—21no—
516C8×C19—22no—
517C8×C19—21no—
518C8×C19—22no—
519#3544C2×C1911yescharacteristic, complemented
520#3517C2×C1911yescharacteristic, complemented
521#3387C2×C1911yescharacteristic, complemented
522#3381C2×C1911yescharacteristic, complemented
523#3366C2×C1911yescharacteristic, complemented
524#3362C2×C1911yescharacteristic, complemented
525#3354C2×C1911yescharacteristic, complemented
526#3351C2×C1912yescomplemented
527#3345C2×C1912yescomplemented
528#3335C2×C1911yescharacteristic, complemented
529#3333C2×C1911yescharacteristic, complemented
530#3332C2×C1912yescomplemented
531#3317C2×C1912yescomplemented
532#3305C2×C1911yescharacteristic, complemented
533#3257C2×C1912yescomplemented
534#3251C2×C1911yescharacteristic, complemented
535#3241C2×C1912yescomplemented
536#3227C2×C1911yescharacteristic, complemented
537#3125C2×C1912yescomplemented
538#3102C2×C1911yescharacteristic, complemented
539#3084C2×C1912yescomplemented
540#3079C2×C1911yescharacteristic, complemented
541#2993C2×C1911yescharacteristic, complemented
542C22×C19—21no—
543C22×C19—22no—
544C22×C19—22no—
545C22×C19—21no—
546C22×C19—21no—
547C22×C19—22no—
548C22×C19—41no—
549C22×C19—41no—
550C22×C19—42no—
551C22×C19—41no—
552C22×C19—42no—
553C22×C19—41no—
554C22×C19—41no—
555C22×C19—41no—
556C22×C19—42no—
557C22×C19C23×D411yescharacteristic
558C4×C19—21no—
559C4×C19—21no—
560C4×C19—22no—
561C4×C19—22no—
562C4×C19—21no—
563C4×C19—22no—
564C4×C19—21no—
565C4×C19—22no—
566C4×C19—42no—
567C4×C19—42no—
568C4×C19—41no—
569C4×C19—41no—
570C4×C19—41no—
571C4×C19—41no—
572C4×C19—41no—
573C4×C19—42no—
574C4×C19#57712yes—
575C4×C19C2×2−1+411yescharacteristic
576C4×C19#58511yescharacteristic
577#563—22no—
578Q82C22×C1911yescharacteristic
579#557C22×C1911yescharacteristic
580#555C22×C1911yescharacteristic
581#554C22×C1911yescharacteristic
582#554C22×C1911yescharacteristic
583#553—22no—
584#553C22×C1912yes—
585#552—21no—
586#552C22×C1912yes—
587#550—21no—
588#550C22×C1912yes—
589#550C22×C1911yescharacteristic
590#550C22×C1911yescharacteristic
591#547—21no—
592#547—21no—
593#547C22×C1912yes—
594#547C22×C1911yescharacteristic
595#544—21no—
596#544C22×C1912yes—
597#542—21no—
598#542C22×C1912yes—
599#540—22no—
600#540C22×C1912yes—
601#536—22no—
602#532—21no—
603#532C22×C1911yescharacteristic
604C2×C4⋊Q8C22×C1911yescharacteristic
605#529—21no—
606#529C22×C1911yescharacteristic
607#529C22×C1911yescharacteristic
608#520C22×C1912yes—
609C4×#41C22×C1911yescharacteristic
610#501C22×C1912yes—
611#499C22×C1912yes—
612#498C22×C1911yescharacteristic
613#498C22×C1911yescharacteristic
614#490C22×C1912yes—
615#486C22×C1912yes—
616#486C22×C1911yescharacteristic
617#486C22×C1911yescharacteristic
618#485C22×C1911yescharacteristic
619#483C22×C1912yes—
620#482C22×C1911yescharacteristic
621#482C22×C1912yes—
622#482C22×C1912yes—
623#481C22×C1912yes—
624#481C22×C1912yes—
625#481C22×C1912yes—
626#481C22×C1912yes—
627#480C22×C1912yes—
628#479C22×C1911yescharacteristic
629#479C22×C1912yes—
630#479C22×C1912yes—
631#478C22×C1912yes—
632#478C22×C1912yes—
633#478C22×C1912yes—
634#478C22×C1911yescharacteristic
635#477C22×C1911yescharacteristic
636#477C22×C1911yescharacteristic
637#476C22×C1911yescharacteristic
638#476C22×C1911yescharacteristic
639#476C22×C1912yes—
640#476C22×C1912yes—
641#476C22×C1912yes—
642#475C22×C1912yes—
643#475C22×C1912yes—
644#475C22×C1911yescharacteristic
645#474C22×C1912yes—
646#474C22×C1911yescharacteristic
647#469C22×C1912yes—
648#469C22×C1912yes—
649#468C22×C1912yes—
650#468C22×C1912yes—
651#466C22×C1912yes—
652#465C22×C1912yes—
653#464C22×C1911yescharacteristic
654#463C22×C1911yescharacteristic
655#463C22×C1912yes—
656#460C22×C1911yescharacteristic
657#460C22×C1912yes—
658#459C22×C1912yes—
659#459C22×C1911yescharacteristic
660#452C22×C1912yes—
661#452C22×C1911yescharacteristic
662#449C22×C1911yescharacteristic
663#449C22×C1912yes—
664#446C22×C1911yescharacteristic
665C8×Q8C22×C1911yescharacteristic
666#442C22×C1912yes—
667#441C22×C1912yes—
668C4×Q16C22×C1911yescharacteristic
669C4×SD16C22×C1912yes—
670C4×SD16C22×C1911yescharacteristic
671C4×SD16C22×C1912yes—
672C4×SD16C22×C1911yescharacteristic
673C4×D8C22×C1911yescharacteristic
674#436C22×C1912yes—
675#436C22×C1911yescharacteristic
676#435C22×C1912yes—
677C8×D4C22×C1911yescharacteristic
678#433C22×C1912yes—
679#431C22×C1911yescharacteristic
680#428C22×C1912yes—
681#428C22×C1912yes—
682C2×#106C22×C1912yes—
683#424C22×C1912yes—
684#423C22×C1911yescharacteristic
685#417C22×C1912yes—
686#417C22×C1912yes—
687#416C22×C1912yes—
688C2×C19—41no—
689C2×C19—42no—
690C2×C19—81no—
691C2×C19—81no—
692C2×C19—82no—
693C2×C19#348911yescharacteristic
694C2×C19C2×#57711yescharacteristic
695C2×C19#358511yescharacteristic
696C2×#41—21no—
697C2×#41—21no—
698C2×#41—22no—
699C2×#41—21no—
700C2×#41C23×C1911yescharacteristic
701C2×#41C23×C1912yes—
702C22×Q8—21no—
703C2×Q16C23×C1911yescharacteristic
704C2×SD16C23×C1911yescharacteristic
705C2×SD16C23×C1911yescharacteristic
706C2×SD16C23×C1912yes—
707C2×D8C23×C1911yescharacteristic
708C2×D8C23×C1912yes—
709C2×M16C23×C1912yes—
710C2×M16C23×C1912yes—
711C22×C8C23×C1912yes—
712C4⋊Q8—21no—
713C4⋊Q8—22no—
714C4⋊Q8—22no—
715C4⋊Q8—21no—
716C4⋊Q8—21no—
717C4⋊Q8—21no—
718C4⋊Q8C23×C1912yes—
719C4⋊Q8C23×C1911yescharacteristic
720C4⋊Q8C23×C1911yescharacteristic
721C4⋊Q8C23×C1911yescharacteristic
722C4⋊Q8C23×C1912yes—
723#127—21no—
724#127—22no—
725#127C23×C1911yescharacteristic
726#127C23×C1912yes—
727#126—22no—
728#126—22no—
729#126—22no—
730#126—21no—
731#126D4×C1912yes—
732#125—22no—
733#125—21no—
734#125—22no—
735#125—22no—
736#125D4×C1911yescharacteristic
737#125C23×C1911yescharacteristic
738#125C23×C1912yes—
739#125C23×C1912yes—
740#124—22no—
741#124—22no—
742#124—21no—
743#124D4×C1911yescharacteristic
744#124C23×C1911yescharacteristic
745#123—22no—
746#123—21no—
747#123—22no—
748#123—22no—
749#123—22no—
750#123—22no—
751#123—22no—
752#123—22no—
753#123—22no—
754#123D4×C1912yes—
755C22⋊Q8—21no—
756C22⋊Q8—21no—
757C22⋊Q8—22no—
758C22⋊Q8—22no—
759C22⋊Q8—22no—
760C22⋊Q8—22no—
761C22⋊Q8—22no—
762C22⋊Q8—22no—
763C22⋊Q8D4×C1911yescharacteristic
764C22⋊Q8C23×C1911yescharacteristic
765C22⋊Q8C23×C1912yes—
766#121—22no—
767#121—21no—
768#121—21no—
769#121—21no—
770#121—22no—
771#121—22no—
772#121—22no—
773#121—22no—
774#121—22no—
775#121—22no—
776#121D4×C1911yescharacteristic
777#121C23×C1911yescharacteristic
778#121C23×C1912yes—
779#121C23×C1912yes—
780#121C23×C1912yes—
781#121C23×C1912yes—
782C4×Q8—21no—
783C4×Q8—21no—
784C4×Q8C23×C1911yescharacteristic
785C4×Q8C23×C1911yescharacteristic
786C4×Q8C23×C1912yes—
787C4×Q8C23×C1911yescharacteristic
788C4×Q8C23×C1912yes—
789C4×Q8C23×C1911yescharacteristic
790C4×D4—21no—
791C4×D4—21no—
792C4×D4—21no—
793C4×D4—21no—
794C4×D4—21no—
795C4×D4—22no—
796C4×D4—22no—
797C4×D4—22no—
798C4×D4—22no—
799C4×D4—21no—
800C4×D4C23×C1911yescharacteristic
801C4×D4C23×C1911yescharacteristic
802C4×D4C23×C1912yes—
803C4×D4C23×C1912yes—
804C4×D4C23×C1911yescharacteristic
805C4×D4C23×C1912yes—
806C4×D4C23×C1912yes—
807C4×D4C23×C1911yescharacteristic
808#117—22no—
809#117—21no—
810#117—22no—
811#117—21no—
812#117—21no—
813#117C23×C1911yescharacteristic
814#117C23×C1912yes—
815#117C23×C1912yes—
816C2×C4⋊C4—21no—
817C2×C4⋊C4—22no—
818C2×C4⋊C4—21no—
819C2×C4⋊C4C23×C1912yes—
820C2×C4⋊C4C23×C1912yes—
821C2×C4⋊C4C23×C1912yes—
822C2×C42—21no—
823C2×C42C23×C1911yescharacteristic
824#107C23×C1911yescharacteristic
825#107C23×C1912yes—
826#107C23×C1912yes—
827#107C23×C1912yes—
828#107C23×C1911yescharacteristic
829#106C23×C1911yescharacteristic
830#106C23×C1912yes—
831#106C23×C1912yes—
832#106C23×C1912yes—
833#106C23×C1912yes—
834#106C23×C1912yes—
835#106C23×C1912yes—
836#106C23×C1911yescharacteristic
837#106C23×C1912yes—
838C4⋊C8C23×C1912yes—
839C4⋊C8C23×C1911yescharacteristic
840C4⋊C8C23×C1911yescharacteristic
841C4⋊C8C23×C1911yescharacteristic
842C4⋊C8C23×C1912yes—
843C4⋊C8C23×C1912yes—
844C4⋊C8C23×C1911yescharacteristic
845#103C23×C1911yescharacteristic
846#103C23×C1912yes—
847#103C23×C1912yes—
848#103C23×C1911yescharacteristic
849#103C23×C1911yescharacteristic
850#103C23×C1911yescharacteristic
851#103C23×C1912yes—
852#102C23×C1912yes—
853#102C23×C1912yes—
854#102C23×C1912yes—
855#102C23×C1912yes—
856#102C23×C1912yes—
857#102C23×C1912yes—
858#102C23×C1911yescharacteristic
859#102C23×C1911yescharacteristic
860#102C23×C1912yes—
861#102C23×C1911yescharacteristic
862#102C23×C1911yescharacteristic
863#102C23×C1912yes—
864#102C23×C1912yes—
865C22⋊C8C23×C1911yescharacteristic
866C22⋊C8C23×C1911yescharacteristic
867C22⋊C8C23×C1912yes—
868C22⋊C8C23×C1912yes—
869#97C23×C1912yes—
870C4×C8C23×C1911yescharacteristic
871C4×C8C23×C1911yescharacteristic
872C4×C8C23×C1912yes—
873C19#6218511yescharacteristic, direct product factor, Sylow
874#41—22no—
875#41—24no—
876#41—42no—
877#41—41no—
878#41—82no—
879#41—82no—
880#41—84no—
881#41—82no—
882C2×Q8—21no—
883C2×Q8—21no—
884C2×Q8—22no—
885C2×Q8—22no—
886C2×Q8—21no—
887C2×Q8—82no—
888C2×Q8C2×D4×C1911yescharacteristic
889C2×Q8C24×C1911yescharacteristic
890C2×Q8C24×C1911yescharacteristic
891C2×D4—22no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—22no—
895C2×D4—22no—
896C2×D4—22no—
897C2×D4—22no—
898C2×D4—21no—
899C2×D4—21no—
900C2×D4—22no—
901C2×D4—22no—
902C2×D4C2×D4×C1911yescharacteristic
903C2×D4C2×D4×C1912yes—
904C2×D4C24×C1912yes—
905C2×D4C24×C1911yescharacteristic
906C2×D4C24×C1911yescharacteristic
907C22×C4—22no—
908C22×C4—22no—
909C22×C4—22no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—22no—
914C22×C4—21no—
915C22×C4—22no—
916C22×C4—22no—
917C22×C4—22no—
918C22×C4C2×D4×C1911yescharacteristic
919C22×C4C2×D4×C1911yescharacteristic
920C22×C4C24×C1911yescharacteristic
921C22×C4C24×C1912yes—
922Q16—22no—
923SD16—22no—
924SD16—41no—
925SD16—42no—
926D8—42no—
927D8—41no—
928M16—42no—
929M16—42no—
930C2×C8—42no—
931C2×C8C24×C1911yescharacteristic
932C2×C8C24×C1911yescharacteristic
933C2×C8C24×C1911yescharacteristic
934C2×C8C24×C1912yes—
935C2×C8C24×C1911yescharacteristic
936C2×C8C24×C1912yes—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—22no—
940C4⋊C4—21no—
941C4⋊C4—22no—
942C4⋊C4—22no—
943C4⋊C4—22no—
944C4⋊C4—22no—
945C4⋊C4—22no—
946C4⋊C4—21no—
947C4⋊C4—22no—
948C4⋊C4—22no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—22no—
953C4⋊C4—21no—
954C4⋊C4—22no—
955C4⋊C4—22no—
956C4⋊C4—21no—
957C4⋊C4—22no—
958C4⋊C4C2×D4×C1912yes—
959C4⋊C4C2×D4×C1911yescharacteristic
960C4⋊C4C2×D4×C1912yes—
961C4⋊C4C2×D4×C1911yescharacteristic
962C4⋊C4C2×D4×C1912yes—
963C4⋊C4C2×D4×C1912yes—
964C4⋊C4C24×C1912yes—
965C4⋊C4C24×C1911yescharacteristic
966C4⋊C4C24×C1912yes—
967C4⋊C4C24×C1911yescharacteristic
968C4⋊C4C24×C1911yescharacteristic
969C4⋊C4C24×C1912yes—
970C4⋊C4C24×C1911yescharacteristic
971C22⋊C4—21no—
972C22⋊C4—21no—
973C22⋊C4—22no—
974C22⋊C4—22no—
975C22⋊C4—22no—
976C22⋊C4—21no—
977C22⋊C4—21no—
978C22⋊C4—22no—
979C22⋊C4—21no—
980C22⋊C4—22no—
981C22⋊C4—21no—
982C22⋊C4—22no—
983C22⋊C4—22no—
984C22⋊C4—22no—
985C22⋊C4—21no—
986C22⋊C4—22no—
987C22⋊C4—21no—
988C22⋊C4C2×D4×C1912yes—
989C22⋊C4C2×D4×C1912yes—
990C22⋊C4C2×D4×C1912yes—
991C22⋊C4C2×D4×C1912yes—
992C22⋊C4C2×D4×C1912yes—
993C42—21no—
994C42—21no—
995C42—21no—
996C42—22no—
997C42—22no—
998C42—21no—
999C42—22no—
1000C42C2×D4×C1911yescharacteristic
1001C42C2×D4×C1911yescharacteristic
1002C42C24×C1911yescharacteristic
1003C42C24×C1912yes—
1004C42C24×C1911yescharacteristic
1005C23—21no—
1006C23—21no—
1007C23—22no—
1008C23C22×D4×C1912yes—
1009C23C22×D4×C1911yescharacteristic
1010Q8—22no—
1011Q8—21no—
1012Q8—21no—
1013Q8—21no—
1014Q8—42no—
1015Q8—82no—
1016Q8—81no—
1017Q8—81no—
1018Q8—82no—
1019Q8C19×2−1+412yes—
1020D4—22no—
1021D4—21no—
1022D4—22no—
1023D4—21no—
1024D4—21no—
1025D4—22no—
1026D4—21no—
1027D4—42no—
1028D4—44no—
1029D4—42no—
1030D4—42no—
1031D4—42no—
1032D4—82no—
1033D4—81no—
1034D4—82no—
1035D4—82no—
1036D4—82no—
1037D4—82no—
1038D4—82no—
1039C2×C4—21no—
1040C2×C4—22no—
1041C2×C4—21no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—21no—
1052C2×C4—22no—
1053C2×C4—41no—
1054C2×C4—42no—
1055C2×C4—44no—
1056C2×C4—44no—
1057C2×C4—42no—
1058C2×C4—42no—
1059C2×C4—82no—
1060C2×C4—82no—
1061C2×C4—82no—
1062C2×C4—81no—
1063C2×C4—82no—
1064C2×C4—82no—
1065C2×C4C22×D4×C1911yescharacteristic
1066C2×C4C22×D4×C1911yescharacteristic
1067C2×C4C22×D4×C1912yes—
1068C2×C4C22×D4×C1912yes—
1069C2×C4C22×D4×C1912yes—
1070C2×C4C22×D4×C1911yescharacteristic
1071C2×C4C22×D4×C1911yescharacteristic
1072C2×C4C22×D4×C1911yescharacteristic
1073C2×C4C25×C1911yescharacteristic
1074C8—21no—
1075C8—21no—
1076C8—21no—
1077C8—22no—
1078C8—21no—
1079C8—22no—
1080C22—22no—
1081C22—21no—
1082C22—21no—
1083C22—22no—
1084C22—21no—
1085C22—22no—
1086C22—41no—
1087C22—42no—
1088C22—41no—
1089C22—41no—
1090C22—41no—
1091C22—42no—
1092C22—41no—
1093C22—41no—
1094C22—42no—
1095C22C23×D4×C1911yescharacteristic
1096C4—22no—
1097C4—21no—
1098C4—22no—
1099C4—21no—
1100C4—22no—
1101C4—21no—
1102C4—21no—
1103C4—22no—
1104C4—41no—
1105C4—41no—
1106C4—41no—
1107C4—42no—
1108C4—42no—
1109C4—42no—
1110C4—41no—
1111C4—41no—
1112C4C19×#57712yes—
1113C4C2×C19×2−1+411yescharacteristic
1114C4C19×#58511yescharacteristic
1115C2—41no—
1116C2—42no—
1117C2—81no—
1118C2—82no—
1119C2—81no—
1120C2C19×#348911yescharacteristic
1121C2C2×C19×#57711yescharacteristic
1122C2C19×#358511yescharacteristic
subgroupG/H
center, socleC22×C19C23×D4
commutator, Frattini, cosocleC2×C4C25×C19
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C19 ◁ C19×#529 ◁ G

Complements

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

NH ≅ G/Ntype
1. C19×#3544C2semidirect
2. C19×#3517C2semidirect
3. C19×#3387C2semidirect
4. C19×#3381C2semidirect
5. C19×#3366C2semidirect
6. C19×#3362C2semidirect
7. C19×#3354C2semidirect
8. C19×#3351C2semidirect
9. C19×#3345C2semidirect
10. C19×#3335C2semidirect
11. C19×#3333C2semidirect
12. C19×#3332C2semidirect
13. C19×#3317C2semidirect
14. C19×#3305C2semidirect
15. C19×#3257C2semidirect
16. C19×#3251C2semidirect
17. C19×#3241C2semidirect
18. C19×#3227C2semidirect
19. C19×#3125C2semidirect
20. C19×#3102C2semidirect
21. C19×#3084C2semidirect
22. C19×#3079C2semidirect
23. C19×#2993C2semidirect
443. #62185C19direct (N × H)
519. #3544C2×C19semidirect
520. #3517C2×C19semidirect
521. #3387C2×C19semidirect
522. #3381C2×C19semidirect
523. #3366C2×C19semidirect
524. #3362C2×C19semidirect
525. #3354C2×C19semidirect
526. #3351C2×C19semidirect
527. #3345C2×C19semidirect
528. #3335C2×C19semidirect
529. #3333C2×C19semidirect
530. #3332C2×C19semidirect
531. #3317C2×C19semidirect
532. #3305C2×C19semidirect
533. #3257C2×C19semidirect
534. #3251C2×C19semidirect
535. #3241C2×C19semidirect
536. #3227C2×C19semidirect
537. #3125C2×C19semidirect
538. #3102C2×C19semidirect
539. #3084C2×C19semidirect
540. #3079C2×C19semidirect
541. #2993C2×C19semidirect
873. C19#62185direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#35442
C19×#35172
C19×#33872
C19×#33812
C19×#33662
C19×#33622
C19×#33542
C19×#33512
C19×#33452
C19×#33352
C19×#33332
C19×#33322
C19×#33172
C19×#33052
C19×#32572
C19×#32512
C19×#32412
C19×#32272
C19×#31252
C19×#31022
C19×#30842
C19×#30792
C19×#29932
#6218519