Finite Group Databasebeta

← #18074831

Subgroups — #18074831

Order 4864.

768 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564621C211yesmaximal, characteristic, complemented
2#14564104C211yesmaximal, characteristic, complemented
3#14564069C211yesmaximal, characteristic, complemented
4#14563938C211yesmaximal, characteristic
5#14562178C211yesmaximal, characteristic
6#14562155C211yesmaximal, characteristic, complemented
7C19×#3538C211yesmaximal, characteristic
8C22×#64520C2211yescharacteristic
9C2×#10597294—21no—
10C2×#10597292—21no—
11C2×#10597293—21no—
12#11926508C2211yescharacteristic
13#11926404C2211yescharacteristic
14C4×C22⋊Dic19C2211yescharacteristic
15#11926313—21no—
16#11926311—22no—
17#11926306—21no—
18#11926303—21no—
19#11926281—22no—
20#11926281—21no—
21#11926278—21no—
22C19×#563—22no—
23C19×#552—21no—
24C19×#552—21no—
25C19×#551—22no—
26D4×Q8×C19—21no—
27D4×Q8×C19—21no—
28C19×#544—21no—
29C19×#544C412yescomplemented
30C19×#541—21no—
31C19×#539—21no—
32C19×#539C412yescomplemented
33C19×#536—21no—
34C19×#525C2211yescharacteristic
35C2×C19×C22⋊Q8C2211yescharacteristic
36C2×C19×C22⋊Q8C2211yescharacteristic
37C2×#41×C19D411yescharacteristic
38C22×Q8×C19—21no—
39C22×Q8×C19D411yescharacteristic
40C22×Q8×C19D411yescharacteristic
41C23×C4×C19C2311yescharacteristic
42C19×C4⋊Q8—21no—
43C19×C4⋊Q8—22no—
44C19×C4⋊Q8—22no—
45C19×C4⋊Q8—22no—
46C19×#126—22no—
47C19×#126—22no—
48C19×#126—22no—
49C19×#126—22no—
50C19×#125—21no—
51C19×#125—22no—
52C19×#125—22no—
53C19×#125—22no—
54C19×#125—22no—
55C19×#124—22no—
56C19×#123—22no—
57C19×#123—22no—
58C19×#123—22no—
59C19×#123—22no—
60C19×#123—21no—
61C19×C22⋊Q8—21no—
62C19×C22⋊Q8—21no—
63C19×C22⋊Q8—22no—
64C19×C22⋊Q8—22no—
65C19×C22⋊Q8—22no—
66C19×C22⋊Q8—22no—
67C19×C22⋊Q8—21no—
68C19×C22⋊Q8—21no—
69C19×C22⋊Q8—21no—
70C19×C22⋊Q8—21no—
71C19×C22⋊Q8—21no—
72C19×C22⋊Q8—21no—
73C19×C22⋊Q8C2×C412yes—
74C19×C22⋊Q8C2×C411yescharacteristic
75C19×C22⋊Q8D412yes—
76C19×C22⋊Q8D411yescharacteristic
77C19×#121C2×C411yescharacteristic
78C19×#121D411yescharacteristic
79C19×#120—21no—
80C4×Q8×C19—21no—
81C4×Q8×C19—21no—
82C4×D4×C19—22no—
83C4×D4×C19—22no—
84C4×D4×C19—21no—
85C4×D4×C19—21no—
86C19×#117—21no—
87C19×#117—22no—
88C19×#117—22no—
89C19×#117D411yescharacteristic
90C2×C4⋊C4×C19—21no—
91C2×C4⋊C4×C19C2×C412yes—
92C2×C4⋊C4×C19D411yescharacteristic
93C2×C4⋊C4×C19D411yescharacteristic
94C2×C22⋊C4×C19—21no—
95C2×C22⋊C4×C19D412yes—
96C2×C22⋊Dic19—21no—
97C2×C22⋊Dic19—21no—
98C2×C4⋊Dic19—21no—
99C2×C4×Dic19—21no—
100C2×#64520—21no—
101C2×#64520—21no—
102C2×#64520—21no—
103C2×#64520—42no—
104C22×C19⋊C8—21no—
105#10597294—42no—
106#10597293—42no—
107#10597292—42no—
108C19⋊#95—21no—
109C19⋊#95—21no—
110C22⋊(C19⋊C8)—21no—
111C22⋊(C19⋊C8)—21no—
112C24×C19C2×D411yescharacteristic
113#41×C19—41no—
114#41×C19—41no—
115C2×Q8×C19—22no—
116C2×Q8×C19—21no—
117C2×Q8×C19—21no—
118C2×Q8×C19—21no—
119C2×Q8×C19—41no—
120C2×Q8×C19—41no—
121C2×Q8×C19—41no—
122C2×Q8×C19—41no—
123C2×Q8×C19—81no—
124C2×Q8×C19—81no—
125C2×Q8×C19C22⋊C412yes—
126C2×Q8×C19C22⋊C411yescharacteristic
127C2×D4×C19—21no—
128C2×D4×C19—21no—
129C2×D4×C19—21no—
130C2×D4×C19C22⋊C411yescharacteristic
131C22×C4×C19—21no—
132C22×C4×C19—22no—
133C22×C4×C19—21no—
134C22×C4×C19—21no—
135C22×C4×C19—41no—
136C22×C4×C19—41no—
137C22×C4×C19C22⋊C412yes—
138C22×C4×C19C22⋊C412yes—
139C22×C4×C19C22×C411yescharacteristic
140C22×C4×C19C2×D411yescharacteristic
141C22×C4×C19C2×D411yescharacteristic
142C22×C4×C19C2×D411yescharacteristic
143C22×C4×C19C2×D411yescharacteristic
144C22×C4×C19C2×D411yescharacteristic
145C22×Dic19—41no—
146C22×Dic19—41no—
147C4⋊C4×C19—22no—
148C4⋊C4×C19—22no—
149C4⋊C4×C19—22no—
150C4⋊C4×C19—22no—
151C4⋊C4×C19—22no—
152C4⋊C4×C19—22no—
153C4⋊C4×C19—22no—
154C4⋊C4×C19—22no—
155C4⋊C4×C19—22no—
156C4⋊C4×C19—22no—
157C4⋊C4×C19—22no—
158C4⋊C4×C19—21no—
159C4⋊C4×C19—22no—
160C4⋊C4×C19—21no—
161C4⋊C4×C19—21no—
162C4⋊C4×C19—21no—
163C4⋊C4×C19—21no—
164C4⋊C4×C19C22⋊C412yes—
165C4⋊C4×C19C22⋊C411yescharacteristic
166C4⋊C4×C19C22⋊C411yescharacteristic
167C22⋊C4×C19—22no—
168C22⋊C4×C19—22no—
169C22⋊C4×C19—22no—
170C22⋊C4×C19—22no—
171C22⋊C4×C19—21no—
172C22⋊C4×C19—22no—
173C22⋊C4×C19—22no—
174C22⋊C4×C19—22no—
175C22⋊C4×C19—21no—
176C22⋊C4×C19—21no—
177C22⋊C4×C19—21no—
178C22⋊C4×C19—21no—
179C42×C19—22no—
180C42×C19—22no—
181C42×C19—22no—
182C42×C19—21no—
183C22⋊Dic19—22no—
184C22⋊Dic19—41no—
185C22⋊Dic19—42no—
186C4⋊Dic19—41no—
187C4⋊Dic19—41no—
188C4×Dic19—41no—
189C4×Dic19—41no—
190#64520—22no—
191#64520—22no—
192#64520—41no—
193#64520—41no—
194#64520—41no—
195#64520—41no—
196C2×C19⋊C8—22no—
197C2×C19⋊C8—41no—
198C2×C19⋊C8—41no—
199C2×C19⋊C8—41no—
200#8482—191nomaximal, Sylow
201C23×C19—21no—
202C23×C19—21no—
203C23×C19—21no—
204C23×C19—41no—
205C23×C19—41no—
206C23×C19C2×C22⋊C411yescharacteristic
207C23×C19#12011yescharacteristic
208C23×C19#12011yescharacteristic
209Q8×C19—42no—
210Q8×C19—41no—
211Q8×C19—41no—
212Q8×C19—41no—
213Q8×C19—41no—
214Q8×C19—41no—
215Q8×C19—81no—
216Q8×C19—82no—
217D4×C19—41no—
218D4×C19—42no—
219D4×C19—41no—
220D4×C19—41no—
221D4×C19—81no—
222C2×C4×C19—21no—
223C2×C4×C19—21no—
224C2×C4×C19—21no—
225C2×C4×C19—21no—
226C2×C4×C19—21no—
227C2×C4×C19—21no—
228C2×C4×C19—21no—
229C2×C4×C19—21no—
230C2×C4×C19—22no—
231C2×C4×C19—22no—
232C2×C4×C19—21no—
233C2×C4×C19—22no—
234C2×C4×C19—22no—
235C2×C4×C19—41no—
236C2×C4×C19—41no—
237C2×C4×C19—41no—
238C2×C4×C19—41no—
239C2×C4×C19—41no—
240C2×C4×C19—41no—
241C2×C4×C19—41no—
242C2×C4×C19—42no—
243C2×C4×C19—42no—
244C2×C4×C19—81no—
245C2×C4×C19—82no—
246C2×C4×C19C2×C22⋊C411yescharacteristic
247C2×C4×C19C2×C22⋊C411yescharacteristic
248C2×C4×C19#12011yescharacteristic
249C2×C4×C19#12011yescharacteristic
250C2×Dic19—42no—
251C2×Dic19—81no—
252C2×Dic19—81no—
253C2×Dic19—81no—
254C2×Dic19—81no—
255C2×Dic19—81no—
256C19⋊C8—42no—
257C19⋊C8—81no—
258#3538D1911yescharacteristic
259#1996—191no—
260#1901—191no—
261#1894—191no—
262#1871—191no—
263#1513—191no—
264#1508—191no—
265C22×C19—21no—
266C22×C19—21no—
267C22×C19—21no—
268C22×C19—21no—
269C22×C19—21no—
270C22×C19—21no—
271C22×C19—21no—
272C22×C19—21no—
273C22×C19—41no—
274C22×C19—41no—
275C22×C19—41no—
276C22×C19—81no—
277C22×C19—81no—
278C22×C19#37911yescharacteristic
279C22×C19#45411yescharacteristic
280C22×C19#45611yescharacteristic
281C4×C19—21no—
282C4×C19—21no—
283C4×C19—21no—
284C4×C19—42no—
285C4×C19—41no—
286C4×C19—42no—
287C4×C19—41no—
288C4×C19—41no—
289C4×C19—42no—
290C4×C19—42no—
291C4×C19B(4,𝔽2)11yescharacteristic
292C4×C19#45811yescharacteristic
293Dic19—82no—
294Dic19—161no—
295C22×M16—191no—
296#563—22no—
297#552—21no—
298#552—21no—
299#551—22no—
300D4×Q8—21no—
301D4×Q8—21no—
302#544—21no—
303#544Dic1912yescomplemented
304#541—21no—
305#539—21no—
306#539Dic1912yescomplemented
307#536—21no—
308#525C2×D1911yescharacteristic
309C2×C22⋊Q8C2×D1911yescharacteristic
310C2×C22⋊Q8C2×D1911yescharacteristic
311C2×#104—381no—
312C2×#103—381no—
313C2×#101—381no—
314#407—191no—
315#380—191no—
316C4×C22⋊C4—191no—
317#343—381no—
318#342—382no—
319#340—381no—
320#339—381no—
321#328—382no—
322#328—381no—
323#327—381no—
324C2×C19—21no—
325C2×C19—21no—
326C2×C19—41no—
327C2×C19—41no—
328C2×C19—81no—
329C2×C19#179011yescharacteristic
330C2×C19#179311yescharacteristic
331C2×C19#179611yescharacteristic
332C2×#41C22⋊D1911yescharacteristic
333C22×Q8—21no—
334C22×Q8C22⋊D1911yescharacteristic
335C22×Q8C22⋊D1911yescharacteristic
336C23×C4C22×D1911yescharacteristic
337C2×M16—381no—
338C2×M16—381no—
339C2×M16—381no—
340C2×M16—762no—
341C22×C8—381no—
342C4⋊Q8—21no—
343C4⋊Q8—22no—
344C4⋊Q8—22no—
345C4⋊Q8—22no—
346#126—22no—
347#126—22no—
348#126—22no—
349#126—22no—
350#125—21no—
351#125—22no—
352#125—22no—
353#125—22no—
354#125—22no—
355#124—22no—
356#123—22no—
357#123—22no—
358#123—22no—
359#123—22no—
360#123—21no—
361C22⋊Q8—21no—
362C22⋊Q8—21no—
363C22⋊Q8—22no—
364C22⋊Q8—22no—
365C22⋊Q8—22no—
366C22⋊Q8—22no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369C22⋊Q8—21no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372C22⋊Q8—21no—
373C22⋊Q8C2×Dic1912yes—
374C22⋊Q8C2×Dic1911yescharacteristic
375C22⋊Q8C22⋊D1912yes—
376C22⋊Q8C22⋊D1911yescharacteristic
377#121C2×Dic1911yescharacteristic
378#121C22⋊D1911yescharacteristic
379#120—21no—
380C4×Q8—21no—
381C4×Q8—21no—
382C4×D4—22no—
383C4×D4—22no—
384C4×D4—21no—
385C4×D4—21no—
386#117—21no—
387#117—22no—
388#117—22no—
389#117C22⋊D1911yescharacteristic
390C2×C4⋊C4—21no—
391C2×C4⋊C4—381no—
392C2×C4⋊C4C2×Dic1912yes—
393C2×C4⋊C4C22⋊D1911yescharacteristic
394C2×C4⋊C4C22⋊D1911yescharacteristic
395C2×C22⋊C4—21no—
396C2×C22⋊C4—381no—
397C2×C22⋊C4—381no—
398C2×C22⋊C4C22⋊D1912yes—
399C2×C42—381no—
400#104—762no—
401#103—762no—
402#101—762no—
403C22⋊C8—381no—
404C22⋊C8—381no—
405#95—381no—
406#95—381no—
407C19#848211yescharacteristic, complemented, Sylow
408C24C2×C22⋊D1911yescharacteristic
409#41—41no—
410#41—41no—
411C2×Q8—22no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—41no—
416C2×Q8—41no—
417C2×Q8—41no—
418C2×Q8—41no—
419C2×Q8—81no—
420C2×Q8—81no—
421C2×Q8C22⋊Dic1912yes—
422C2×Q8C22⋊Dic1911yescharacteristic
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4C22⋊Dic1911yescharacteristic
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—761no—
434C22×C4—761no—
435C22×C4C22⋊Dic1912yes—
436C22×C4C22⋊Dic1912yes—
437C22×C4C22×Dic1911yescharacteristic
438C22×C4C2×C22⋊D1911yescharacteristic
439C22×C4C2×C22⋊D1911yescharacteristic
440C22×C4C2×C22⋊D1911yescharacteristic
441C22×C4C2×C22⋊D1911yescharacteristic
442C22×C4C2×C22⋊D1911yescharacteristic
443M16—382no—
444M16—382no—
445M16—761no—
446M16—761no—
447M16—761no—
448M16—761no—
449C2×C8—382no—
450C2×C8—761no—
451C2×C8—761no—
452C2×C8—761no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—21no—
465C4⋊C4—22no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—761no—
471C4⋊C4—761no—
472C4⋊C4C22⋊Dic1912yes—
473C4⋊C4C22⋊Dic1911yescharacteristic
474C4⋊C4C22⋊Dic1911yescharacteristic
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—22no—
479C22⋊C4—21no—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—382no—
488C22⋊C4—761no—
489C22⋊C4—762no—
490C42—22no—
491C42—22no—
492C42—22no—
493C42—21no—
494C42—761no—
495C42—761no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—41no—
500C23—41no—
501C23C2×C22⋊Dic1911yescharacteristic
502C23#1059739911yescharacteristic
503C23#1059739911yescharacteristic
504Q8—42no—
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—81no—
511Q8—82no—
512D4—41no—
513D4—42no—
514D4—41no—
515D4—41no—
516D4—81no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—81no—
540C2×C4—82no—
541C2×C4—762no—
542C2×C4—1521no—
543C2×C4—1521no—
544C2×C4—1521no—
545C2×C4—1521no—
546C2×C4—1521no—
547C2×C4C2×C22⋊Dic1911yescharacteristic
548C2×C4C2×C22⋊Dic1911yescharacteristic
549C2×C4#1059739911yescharacteristic
550C2×C4#1059739911yescharacteristic
551C8—762no—
552C8—1521no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—81no—
565C22—81no—
566C22#1192640011yescharacteristic
567C22#1192671711yescharacteristic
568C22#1192672711yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—42no—
573C4—41no—
574C4—42no—
575C4—41no—
576C4—41no—
577C4—42no—
578C4—42no—
579C4—3041no—
580C4—1522no—
581C4#1192673111yescharacteristic
582C4#1192673411yescharacteristic
583C2—21no—
584C2—21no—
585C2—41no—
586C2—41no—
587C2—81no—
588C2#1456358311yescharacteristic
589C2#1456359411yescharacteristic
590C2#1456361011yescharacteristic
subgroupG/H
centerC22#11926400
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#3538C2
socleC22×C19#379
prime radicalC19×#525C22
cosocleC23×C4×C19C23
hypercenter#3538D19
hypocenterC19#8482
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3538

Complements

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

NH ≅ G/Ntype
1. #14564621C2semidirect
2. #14564104C2semidirect
3. #14564069C2semidirect
6. #14562155C2semidirect
29. C19×#544C4semidirect
32. C19×#539C4semidirect
303. #544Dic19semidirect
306. #539Dic19semidirect
407. C19#8482semidirect

Maximal subgroups

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

subgroupindex
#145646212
#145641042
#145640692
#145639382
#145621782
#145621552
C19×#35382
#848219