Finite Group Databasebeta

← #18081667

Subgroups — #18081667

Order 4864.

742 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14571938C211yesmaximal, characteristic
2#14563613C211yesmaximal, characteristic, complemented
3C2×#11926281C211yesmaximal, characteristic, complemented
4C2×#11926279C211yesmaximal, characteristic
5C2×#11926277C211yesmaximal, characteristic
6#95×Dic19C211yesmaximal, characteristic, complemented
7C2×C19×#328C211yesmaximal, characteristic, complemented
8C2×#10597393C411yescharacteristic, complemented
9C2×#10597376C2211yescharacteristic
10C22×C4×Dic19—21no—
11C22×C4×Dic19C2211yescharacteristic
12C2×Dic19⋊C8—21no—
13C2×C22⋊(C19⋊C8)C2211yescharacteristic
14#11926451C411yescharacteristic, complemented
15#11926445C411yescharacteristic, complemented
16#11926434—21no—
17#11926434—21no—
18#11926421—21no—
19#11926421—21no—
20#11926409C411yescharacteristic, complemented
21C2×C19⋊#95—21no—
22C2×C19⋊#95C2211yescharacteristic
23#11926298—21no—
24#11926281—22no—
25#11926279—22no—
26#11926277—22no—
27C2×C19×C22⋊Q8C2211yescharacteristic
28C2×C19×C22⋊C8C2211yescharacteristic
29C2×C19×#95C2211yescharacteristic
30C19×#328—22no—
31C22×Q8×C19C2×C411yescharacteristic
32C23×C4×C19—21no—
33C23×C4×C19C2311yescharacteristic
34C22×C22⋊D19—21no—
35C23×Dic19—21no—
36C23×Dic19D411yescharacteristic
37C23×Dic19D411yescharacteristic
38C22×D76C2×C411yescharacteristic
39C22×C8×C19—21no—
40C19×C22⋊Q8—21no—
41C19×C22⋊Q8—21no—
42C19×C22⋊Q8—21no—
43C19×C22⋊Q8—21no—
44C2×C4⋊C4×C19—21no—
45C2×C4⋊C4×C19C2×C411yescharacteristic
46C2×C22⋊C4×C19—21no—
47#10597393—42no—
48#10597376—21no—
49#10597376—21no—
50#10597376—21no—
51#10597376—21no—
52C2×(C2×D19)⋊C4—21no—
53C2×(C2×D19)⋊C4—21no—
54C2×(C2×D19)⋊C4—21no—
55C2×(C2×D19)⋊C4—21no—
56C2×(C2×D19)⋊C4—21no—
57C2×C4⋊Dic19C2×C411yescharacteristic
58C2×C4×Dic19—24no—
59C2×C4×Dic19—42no—
60C2×C4×Dic19—42no—
61C2×C4×Dic19—42no—
62C2×C4×Dic19C2×C411yescharacteristic
63C2×C4×Dic19C2×C411yescharacteristic
64C2×C4×Dic19D411yescharacteristic
65C2×C4×Dic19D411yescharacteristic
66C22×C19⋊C8—21no—
67C19×C22⋊C8—21no—
68C19×C22⋊C8—21no—
69C19×#95—21no—
70C19×#95D412yes—
71C19⋊#95—24no—
72C19⋊#95—21no—
73C19⋊#95—21no—
74C19⋊#95—21no—
75C19⋊#95—21no—
76C19⋊#95—21no—
77C19⋊#95D412yes—
78C22⋊(C19⋊C8)—21no—
79C22⋊(C19⋊C8)—21no—
80Dic19⋊C8—42no—
81C24×C19C2×D411yescharacteristic
82C23×D19—21no—
83C2×Q8×C19—21no—
84C2×Q8×C19—21no—
85C2×Q8×C19—41no—
86C2×Q8×C19—41no—
87C22×C4×C19—22no—
88C22×C4×C19—22no—
89C22×C4×C19—22no—
90C22×C4×C19—21no—
91C22×C4×C19—21no—
92C22×C4×C19—41no—
93C22×C4×C19—41no—
94C22×C4×C19—41no—
95C22×C4×C19—41no—
96C22×C4×C19—41no—
97C22×C4×C19—41no—
98C22×C4×C19C22×C411yescharacteristic
99C22×C4×C19C2×D411yescharacteristic
100C22×C4×C19C2×D411yescharacteristic
101C22×C4×C19C2×D411yescharacteristic
102C22×C4×C19#4111yescharacteristic
103C22×C4×C19#4111yescharacteristic
104C2×C22⋊D19—41no—
105C2×C22⋊D19—41no—
106C2×C22⋊D19—41no—
107C2×C22⋊D19—41no—
108C2×C22⋊D19—41no—
109C2×C22⋊D19—41no—
110C22×Dic19—21no—
111C22×Dic19—21no—
112C22×Dic19—22no—
113C22×Dic19—22no—
114C22×Dic19—22no—
115C22×Dic19—22no—
116C22×Dic19—22no—
117C22×Dic19—21no—
118C22×Dic19—21no—
119C22×Dic19—22no—
120C22×Dic19—21no—
121C22×Dic19—41no—
122C22×Dic19—41no—
123C22×Dic19—41no—
124C22×Dic19—41no—
125C22×Dic19—41no—
126C22×Dic19C22⋊C411yescharacteristic
127C22×Dic19C22⋊C411yescharacteristic
128C22×Dic19C22⋊C411yescharacteristic
129C22×Dic19C22⋊C411yescharacteristic
130C2×D76—21no—
131C2×D76—21no—
132C2×D76—41no—
133C2×D76—41no—
134C2×C8×C19—41no—
135C2×C8×C19—41no—
136C2×C8×C19—41no—
137C4⋊C4×C19—21no—
138C4⋊C4×C19—21no—
139C4⋊C4×C19—41no—
140C4⋊C4×C19—41no—
141C22⋊C4×C19—41no—
142C22⋊C4×C19—41no—
143(C2×D19)⋊C4—42no—
144(C2×D19)⋊C4—41no—
145(C2×D19)⋊C4—41no—
146(C2×D19)⋊C4—42no—
147(C2×D19)⋊C4—42no—
148(C2×D19)⋊C4—42no—
149C4⋊Dic19—21no—
150C4⋊Dic19—21no—
151C4×Dic19—22no—
152C4×Dic19—22no—
153C4×Dic19—41no—
154C4×Dic19—41no—
155C4×Dic19—48no—
156C2×C19⋊C8—41no—
157C2×C19⋊C8—41no—
158C2×C19⋊C8—41no—
159#9713—191nomaximal, Sylow
160C23×C19—21no—
161C23×C19—21no—
162C23×C19—21no—
163C23×C19—21no—
164C23×C19C2×C22⋊C411yescharacteristic
165C23×C19#12111yescharacteristic
166C23×C19#12111yescharacteristic
167C23×C19#13511yescharacteristic
168C23×C19#13511yescharacteristic
169C23×C19AGL(1,ℤ/8)11yescharacteristic
170C23×C19#13711yescharacteristic
171C22×D19—41no—
172C22×D19—41no—
173C22×D19—41no—
174C22×D19—41no—
175C22×D19—41no—
176C22×D19—41no—
177C22×D19—41no—
178Q8×C19—81no—
179Q8×C19—81no—
180C2×C4×C19—21no—
181C2×C4×C19—21no—
182C2×C4×C19—21no—
183C2×C4×C19—21no—
184C2×C4×C19—24no—
185C2×C4×C19—41no—
186C2×C4×C19—41no—
187C2×C4×C19—41no—
188C2×C4×C19—41no—
189C2×C4×C19—42no—
190C2×C4×C19—42no—
191C2×C4×C19—42no—
192C2×C4×C19—42no—
193C2×C4×C19—42no—
194C2×C4×C19—42no—
195C2×C4×C19—41no—
196C2×C4×C19—41no—
197C2×C4×C19—41no—
198C2×C4×C19—41no—
199C2×C4×C19—41no—
200C2×C4×C19—41no—
201C2×C4×C19C4×D411yescharacteristic
202C2×C4×C19C4×D411yescharacteristic
203C2×C4×C19#12411yescharacteristic
204C2×C4×C19#12711yescharacteristic
205C22⋊D19—81no—
206C22⋊D19—81no—
207C22⋊D19—81no—
208C22⋊D19—81no—
209C2×Dic19—24no—
210C2×Dic19—24no—
211C2×Dic19—21no—
212C2×Dic19—21no—
213C2×Dic19—21no—
214C2×Dic19—21no—
215C2×Dic19—21no—
216C2×Dic19—21no—
217C2×Dic19—24no—
218C2×Dic19—21no—
219C2×Dic19—21no—
220C2×Dic19—21no—
221C2×Dic19—42no—
222C2×Dic19—42no—
223C2×Dic19—42no—
224C2×Dic19—42no—
225C2×Dic19—42no—
226C2×Dic19—42no—
227C2×Dic19—42no—
228C2×Dic19—42no—
229C2×Dic19—41no—
230C2×Dic19—41no—
231C2×Dic19—41no—
232C2×Dic19#9912yes—
233C2×Dic19#10412yes—
234C2×Dic19#10412yes—
235D76—81no—
236D76—81no—
237C8×C19—81no—
238C19⋊C8—81no—
239#2850—191no—
240#1797—191no—
241C2×#328—191no—
242C2×#328D1911yescharacteristic, complemented
243C2×#327—191no—
244C2×#327—191no—
245C4×#95—191no—
246C22×C19—21no—
247C22×C19—21no—
248C22×C19—21no—
249C22×C19—21no—
250C22×C19—21no—
251C22×C19—21no—
252C22×C19—21no—
253C22×C19—21no—
254C22×C19—21no—
255C22×C19—21no—
256C22×C19—21no—
257C22×C19—21no—
258C22×C19#39011yescharacteristic
259C22×C19C2×#9911yescharacteristic
260C22×C19#41011yescharacteristic
261C22×C19#41611yescharacteristic
262C22×C19#41711yescharacteristic
263C22×C19C2×#10411yescharacteristic
264C22×C19C2×#10411yescharacteristic
265C22×C19#46311yescharacteristic
266C22×C19#46311yescharacteristic
267C22×C19#46411yescharacteristic
268C22×C19#46411yescharacteristic
269C2×D19—81no—
270C2×D19—81no—
271C2×D19—81no—
272C2×D19—81no—
273C2×D19—81no—
274C2×D19—81no—
275C2×D19—81no—
276C4×C19—21no—
277C4×C19—21no—
278C4×C19—21no—
279C4×C19—21no—
280C4×C19—44no—
281C4×C19—81no—
282C4×C19—81no—
283Dic19—22no—
284Dic19—22no—
285Dic19—22no—
286Dic19—44no—
287Dic19—41no—
288Dic19—81no—
289C2×#124—191no—
290C2×C22⋊Q8C2×D1911yescharacteristic
291C2×#121—191no—
292C22×C42—191no—
293C22×C42—381no—
294C2×C4⋊C8—381no—
295C2×C22⋊C8—191no—
296C2×C22⋊C8C2×D1911yescharacteristic
297#391—191no—
298#390—191no—
299#388—381no—
300#388—381no—
301#386—381no—
302#386—381no—
303#382—191no—
304C2×#95—191no—
305C2×#95—381no—
306C2×#95C2×D1911yescharacteristic
307#336—381no—
308#328—22no—
309#328—382no—
310#327—382no—
311#327—382no—
312C2×C19—21no—
313C2×C19—21no—
314C2×C19—21no—
315C2×C19—21no—
316C2×C19#150011yescharacteristic
317C2×C19#150111yescharacteristic
318C2×C19#150411yescharacteristic
319C2×C19#150911yescharacteristic
320C2×C19#196211yescharacteristic
321C2×C19#196411yescharacteristic
322C2×C19#198311yescharacteristic
323D19—161no—
324C22×Q8C4×D1911yescharacteristic
325C22×D4—191no—
326C22×D4—381no—
327C23×C4—21no—
328C23×C4—191no—
329C23×C4—191no—
330C23×C4—381no—
331C23×C4C22×D1911yescharacteristic
332C22×C8—21no—
333C22×C8—381no—
334#124—762no—
335C22⋊Q8—21no—
336C22⋊Q8—21no—
337C22⋊Q8—21no—
338C22⋊Q8—21no—
339#121—381no—
340#121—381no—
341#121—381no—
342#121—381no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—191no—
345C2×C4⋊C4C4×D1911yescharacteristic
346C2×C22⋊C4—21no—
347C2×C22⋊C4—381no—
348C2×C22⋊C4—381no—
349C2×C22⋊C4—381no—
350C2×C22⋊C4—381no—
351C2×C22⋊C4—381no—
352C2×C42—191no—
353C2×C42—191no—
354C2×C42—191no—
355C2×C42—191no—
356C2×C42—384no—
357C2×C42—762no—
358C2×C42—762no—
359C2×C42—762no—
360C4⋊C8—762no—
361C22⋊C8—21no—
362C22⋊C8—21no—
363C22⋊C8—381no—
364C22⋊C8—381no—
365#95—21no—
366#95—192no—
367#95—381no—
368#95—381no—
369#95—381no—
370#95—381no—
371#95—384no—
372#95—381no—
373#95C22⋊D1912yes—
374C19#971311yescharacteristic, complemented, Sylow
375C24—381no—
376C24D4×D1911yescharacteristic
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—41no—
380C2×Q8—41no—
381C2×D4—381no—
382C2×D4—381no—
383C2×D4—761no—
384C2×D4—761no—
385C2×D4—761no—
386C2×D4—761no—
387C2×D4—761no—
388C2×D4—761no—
389C2×D4—761no—
390C2×D4—761no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—191no—
403C22×C4—191no—
404C22×C4—191no—
405C22×C4—191no—
406C22×C4—382no—
407C22×C4—382no—
408C22×C4—382no—
409C22×C4—381no—
410C22×C4—381no—
411C22×C4—382no—
412C22×C4—382no—
413C22×C4—382no—
414C22×C4—381no—
415C22×C4—381no—
416C22×C4—381no—
417C22×C4—761no—
418C22×C4—761no—
419C22×C4—761no—
420C22×C4—761no—
421C22×C4—761no—
422C22×C4C2×C4×D1911yescharacteristic
423C22×C4#6454111yescharacteristic
424C22×C4D4×D1911yescharacteristic
425C22×C4D4×D1911yescharacteristic
426C22×C4#6454311yescharacteristic
427C22×C4C2×C22⋊D1911yescharacteristic
428C2×C8—41no—
429C2×C8—41no—
430C2×C8—41no—
431C2×C8—761no—
432C2×C8—761no—
433C2×C8—761no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—41no—
437C4⋊C4—41no—
438C4⋊C4—381no—
439C4⋊C4—381no—
440C22⋊C4—41no—
441C22⋊C4—41no—
442C22⋊C4—762no—
443C22⋊C4—762no—
444C22⋊C4—762no—
445C22⋊C4—762no—
446C22⋊C4—761no—
447C22⋊C4—761no—
448C42—382no—
449C42—382no—
450C42—761no—
451C42—761no—
452C42—768no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—761no—
458C23—761no—
459C23—761no—
460C23—761no—
461C23—761no—
462C23—761no—
463C23—761no—
464C23C22⋊C4×D1911yescharacteristic
465C23#1059733011yescharacteristic
466C23#1059736011yescharacteristic
467C23#1059736211yescharacteristic
468C23#1059736411yescharacteristic
469C23#1059736511yescharacteristic
470C23#1059738511yescharacteristic
471Q8—81no—
472Q8—81no—
473D4—1521no—
474D4—1521no—
475D4—1521no—
476D4—1521no—
477D4—1521no—
478D4—1521no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—24no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—192no—
501C2×C4—192no—
502C2×C4—192no—
503C2×C4—384no—
504C2×C4—384no—
505C2×C4—381no—
506C2×C4—381no—
507C2×C4—381no—
508C2×C4—381no—
509C2×C4—381no—
510C2×C4—381no—
511C2×C4—384no—
512C2×C4—381no—
513C2×C4—381no—
514C2×C4—381no—
515C2×C4—762no—
516C2×C4—762no—
517C2×C4—762no—
518C2×C4—762no—
519C2×C4—762no—
520C2×C4—762no—
521C2×C4—762no—
522C2×C4—762no—
523C2×C4—761no—
524C2×C4—761no—
525C2×C4—761no—
526C2×C4(C22⋊D19)⋊C411yescharacteristic
527C2×C4#1059733111yescharacteristic
528C2×C4C4×C22⋊D1911yescharacteristic
529C2×C4#1059738611yescharacteristic
530C8—81no—
531C8—1521no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—1521no—
545C22—1521no—
546C22—1521no—
547C22—1521no—
548C22—1521no—
549C22—1521no—
550C22—1521no—
551C22#1192644411yescharacteristic
552C22#99×D1911yescharacteristic
553C22#1192651611yescharacteristic
554C22#1192653911yescharacteristic
555C22#1192654411yescharacteristic
556C22#104×D1911yescharacteristic
557C22#104×D1911yescharacteristic
558C22#1192676111yescharacteristic
559C22#1192676211yescharacteristic
560C22#1192676811yescharacteristic
561C22#1192676911yescharacteristic
562C4—21no—
563C4—21no—
564C4—21no—
565C4—21no—
566C4—44no—
567C4—81no—
568C4—81no—
569C4—382no—
570C4—382no—
571C4—382no—
572C4—764no—
573C4—761no—
574C4—1521no—
575C2—21no—
576C2—21no—
577C2—21no—
578C2—21no—
579C2—3041no—
580C2#1456212011yescharacteristic
581C2#1456212511yescharacteristic
582C2#1456213811yescharacteristic
583C2#1456215911yescharacteristic
584C2#1456446111yescharacteristic
585C2#1456446911yescharacteristic
586C2#1456456411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC2×C19×#328C2
socleC23×C19C2×C22⋊C4
prime radicalC2×#10597376C22
cosocleC23×C4×C19C23
hypercenterC2×#328D19
hypocenterC19#9713
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
2. #14563613C2semidirect
3. C2×#11926281C2semidirect
6. #95×Dic19C2semidirect
7. C2×C19×#328C2semidirect
8. C2×#10597393C4semidirect
14. #11926451C4semidirect
15. #11926445C4semidirect
20. #11926409C4semidirect
242. C2×#328D19semidirect
374. C19#9713semidirect

Maximal subgroups

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

subgroupindex
#145719382
#145636132
C2×#119262812
C2×#119262792
C2×#119262772
#95×Dic192
C2×C19×#3282
#971319