Finite Group Databasebeta

← #18074354

Subgroups — #18074354

Order 4864.

868 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
1C2×#11927173C211yesmaximal, characteristic
2#14563943C211yesmaximal, characteristic
3#14563940C211yesmaximal, characteristic
4C2×#11926280C211yesmaximal, characteristic
5C2×#11926269C211yesmaximal, characteristic
6#14561889C211yesmaximal, characteristic
7C2×C19×#328C211yesmaximal, characteristic
8#11927173—22no—
9#11927173—22no—
10#11927173—22no—
11#11927173C414yescomplemented
12C2×#10597334—21no—
13C2×#10597390—21no—
14C2×#10597335—21no—
15C2×#10597335—21no—
16C2×#10597370C2211yescharacteristic
17C2×#10597324—21no—
18C2×#10597323—21no—
19C22×C4⋊Dic19C2211yescharacteristic
20C22×Dic19⋊C4C2211yescharacteristic
21C2×#10597273—21no—
22C2×#10597292—21no—
23C2×C22⋊(C19⋊C8)C2211yescharacteristic
24C2×C19⋊#95—21no—
25C2×C19⋊#95—21no—
26#11926307—21no—
27#11926306—21no—
28#11926280—22no—
29#11926269—22no—
30C2×C19×C22⋊Q8C2211yescharacteristic
31C2×C19×C22⋊C8C2211yescharacteristic
32C2×C19×#95C2211yescharacteristic
33C19×#328—22no—
34C22×Q8×C19D411yescharacteristic
35C23×C4×C19—21no—
36C23×C4×C19C2311yescharacteristic
37C23×Dic19—21no—
38C23×Dic19D411yescharacteristic
39C23×Dic19D411yescharacteristic
40C22×Dic38—21no—
41C22×Dic38D411yescharacteristic
42C22×C8×C19—21no—
43C19×C22⋊Q8—21no—
44C19×C22⋊Q8—21no—
45C19×C22⋊Q8C2×C412yes—
46C19×C22⋊Q8D412yes—
47C2×C4⋊C4×C19—21no—
48C2×C4⋊C4×C19D411yescharacteristic
49C2×C22⋊C4×C19—21no—
50C2×C22⋊Dic19—21no—
51#10597390—24no—
52#10597390—24no—
53C2×C4⋊Dic19—21no—
54C2×C4⋊Dic19—21no—
55C2×C4⋊Dic19—21no—
56C2×C4⋊Dic19—42no—
57C2×C4⋊Dic19D411yescharacteristic
58#10597370—21no—
59#10597370—21no—
60#10597370C2×C412yes—
61#10597370D412yes—
62C2×Dic19⋊C4—21no—
63C2×Dic19⋊C4—21no—
64C2×Dic19⋊C4—21no—
65C2×Dic19⋊C4—21no—
66C2×Dic19⋊C4—21no—
67C2×Dic19⋊C4—21no—
68C2×Dic19⋊C4—21no—
69C2×Dic19⋊C4—21no—
70C2×Dic19⋊C4—21no—
71C2×Dic19⋊C4C2×C412yes—
72C2×Dic19⋊C4D412yes—
73C2×C4×Dic19—21no—
74C2×C4×Dic19—21no—
75C22×C19⋊C8—21no—
76#10597335—24no—
77#10597335—24no—
78#10597335—24no—
79#10597335—24no—
80#10597334—24no—
81#10597334—24no—
82#10597324—24no—
83#10597324—24no—
84#10597323—24no—
85#10597323—24no—
86C19×C22⋊C8—21no—
87C19×C22⋊C8—21no—
88C19×#95—21no—
89C19×#95—21no—
90#10597292—42no—
91C19⋊#95—42no—
92C19⋊#95—42no—
93C22⋊(C19⋊C8)—21no—
94C22⋊(C19⋊C8)—21no—
95#10597273—42no—
96C24×C19C2×D411yescharacteristic
97C2×Q8×C19—21no—
98C2×Q8×C19—41no—
99C2×Q8×C19—41no—
100C2×Q8×C19C22⋊C412yes—
101C22×C4×C19—21no—
102C22×C4×C19—21no—
103C22×C4×C19—22no—
104C22×C4×C19—41no—
105C22×C4×C19—41no—
106C22×C4×C19—41no—
107C22×C4×C19—41no—
108C22×C4×C19—41no—
109C22×C4×C19—41no—
110C22×C4×C19—41no—
111C22×C4×C19—41no—
112C22×C4×C19C22×C411yescharacteristic
113C22×C4×C19C2×D411yescharacteristic
114C22×C4×C19C2×D411yescharacteristic
115C22×C4×C19C2×D411yescharacteristic
116C22×C4×C19C2×D411yescharacteristic
117C22×C4×C19C2×D411yescharacteristic
118C22×Dic19—21no—
119C22×Dic19—21no—
120C22×Dic19—21no—
121C22×Dic19—21no—
122C22×Dic19—21no—
123C22×Dic19—21no—
124C22×Dic19—21no—
125C22×Dic19—21no—
126C22×Dic19—22no—
127C22×Dic19—41no—
128C22×Dic19—41no—
129C22×Dic19—41no—
130C22×Dic19—41no—
131C22×Dic19—41no—
132C22×Dic19—41no—
133C22×Dic19—41no—
134C22×Dic19—41no—
135C22×Dic19C22⋊C412yes—
136C22×Dic19C22⋊C412yes—
137C22×Dic19SD1612yes—
138C22×Dic19Q1612yes—
139C2×Dic38—24no—
140C2×Dic38—21no—
141C2×Dic38—41no—
142C2×Dic38—41no—
143C2×Dic38—81no—
144C2×Dic38—81no—
145C2×Dic38C22⋊C412yes—
146C2×C8×C19—41no—
147C2×C8×C19—41no—
148C2×C8×C19—41no—
149C4⋊C4×C19—22no—
150C4⋊C4×C19—22no—
151C4⋊C4×C19—21no—
152C4⋊C4×C19C22⋊C412yes—
153C22⋊C4×C19—22no—
154C22⋊C4×C19—22no—
155C22⋊Dic19—22no—
156C22⋊Dic19—22no—
157C4⋊Dic19—24no—
158C4⋊Dic19—21no—
159C4⋊Dic19—22no—
160C4⋊Dic19—22no—
161C4⋊Dic19—41no—
162C4⋊Dic19—41no—
163C4⋊Dic19C22⋊C412yes—
164Dic19⋊C4—24no—
165Dic19⋊C4—24no—
166Dic19⋊C4—24no—
167Dic19⋊C4—24no—
168Dic19⋊C4—22no—
169Dic19⋊C4—22no—
170Dic19⋊C4—22no—
171Dic19⋊C4—22no—
172Dic19⋊C4—22no—
173Dic19⋊C4—22no—
174C4×Dic19—24no—
175C4×Dic19—24no—
176C2×C19⋊C8—41no—
177C2×C19⋊C8—41no—
178C2×C19⋊C8—41no—
179#8406—191nomaximal, Sylow
180C23×C19—21no—
181C23×C19—21no—
182C23×C19—21no—
183C23×C19—21no—
184C23×C19C2×C22⋊C411yescharacteristic
185C23×C19#12011yescharacteristic
186C23×C19#12011yescharacteristic
187C23×C19C2×SD1611yescharacteristic
188C23×C19C2×Q1611yescharacteristic
189C23×C19#13711yescharacteristic
190C23×C19#13711yescharacteristic
191Q8×C19—42no—
192Q8×C19—81no—
193C2×C4×C19—21no—
194C2×C4×C19—21no—
195C2×C4×C19—21no—
196C2×C4×C19—21no—
197C2×C4×C19—22no—
198C2×C4×C19—22no—
199C2×C4×C19—41no—
200C2×C4×C19—41no—
201C2×C4×C19—41no—
202C2×C4×C19—41no—
203C2×C4×C19—41no—
204C2×C4×C19—41no—
205C2×C4×C19—41no—
206C2×C4×C19—41no—
207C2×C4×C19—42no—
208C2×C4×C19—42no—
209C2×C4×C19—42no—
210C2×C4×C19—81no—
211C2×C4×C19—81no—
212C2×C4×C19—81no—
213C2×C4×C19—81no—
214C2×C4×C19C2×C22⋊C411yescharacteristic
215C2×C4×C19C2×C22⋊C411yescharacteristic
216C2×C4×C19#12011yescharacteristic
217C2×C4×C19#12011yescharacteristic
218C2×Dic19—22no—
219C2×Dic19—22no—
220C2×Dic19—22no—
221C2×Dic19—22no—
222C2×Dic19—22no—
223C2×Dic19—22no—
224C2×Dic19—22no—
225C2×Dic19—22no—
226C2×Dic19—22no—
227C2×Dic19—41no—
228C2×Dic19—41no—
229C2×Dic19—41no—
230C2×Dic19—41no—
231C2×Dic19—41no—
232C2×Dic19—41no—
233C2×Dic19—42no—
234C2×Dic19—42no—
235C2×Dic19—42no—
236C2×Dic19—42no—
237C2×Dic19—81no—
238C2×Dic19—81no—
239C2×Dic19—81no—
240C2×Dic19—81no—
241C2×Dic19—81no—
242C2×Dic19#10314yescomplemented
243Dic38—42no—
244Dic38—81no—
245Dic38—84no—
246C8×C19—81no—
247C19⋊C8—81no—
248C2×#544—191no—
249#1872—191no—
250#1872—191no—
251C2×#328—191no—
252C2×#328D1911yescharacteristic
253C2×#324—191no—
254#1441—191no—
255C22×C19—21no—
256C22×C19—21no—
257C22×C19—21no—
258C22×C19—21no—
259C22×C19—21no—
260C22×C19—21no—
261C22×C19—21no—
262C22×C19—21no—
263C22×C19—21no—
264C22×C19—21no—
265C22×C19—21no—
266C22×C19—21no—
267C22×C19#37911yescharacteristic
268C22×C19C2×#10311yescharacteristic
269C22×C19#41911yescharacteristic
270C22×C19#44811yescharacteristic
271C22×C19#44811yescharacteristic
272C22×C19#45111yescharacteristic
273C22×C19#45111yescharacteristic
274C22×C19#45411yescharacteristic
275C22×C19#45611yescharacteristic
276C22×C19B(4,𝔽2)11yescharacteristic
277C22×C19#45811yescharacteristic
278C4×C19—21no—
279C4×C19—21no—
280C4×C19—21no—
281C4×C19—21no—
282C4×C19—42no—
283C4×C19—42no—
284C4×C19—82no—
285Dic19—24no—
286Dic19—42no—
287Dic19—42no—
288Dic19—42no—
289Dic19—82no—
290#544—194no—
291#544—382no—
292#544—382no—
293#544—382no—
294C2×C4⋊Q8—381no—
295C2×C4⋊Q8—381no—
296C2×#125—381no—
297C2×#125—381no—
298C2×C22⋊Q8—191no—
299C2×C22⋊Q8—381no—
300C2×C22⋊Q8C2×D1911yescharacteristic
301C2×#117—381no—
302C22×C4⋊C4—191no—
303C22×C4⋊C4—191no—
304C2×#103—381no—
305C2×#103—381no—
306C2×C22⋊C8—191no—
307C2×C22⋊C8C2×D1911yescharacteristic
308C2×#95—381no—
309C2×#95—381no—
310C2×#95C2×D1911yescharacteristic
311#340—381no—
312#340—381no—
313#328—22no—
314#328—382no—
315#324—382no—
316C2×C19—21no—
317C2×C19—21no—
318C2×C19—21no—
319C2×C19—21no—
320C2×C19#159911yescharacteristic
321C2×C19#160511yescharacteristic
322C2×C19#161111yescharacteristic
323C2×C19#161711yescharacteristic
324C2×C19#178711yescharacteristic
325C2×C19#179011yescharacteristic
326C2×C19#179311yescharacteristic
327C22×Q8—191no—
328C22×Q8—381no—
329C22×Q8D7611yescharacteristic
330C23×C4—21no—
331C23×C4—191no—
332C23×C4—191no—
333C23×C4—381no—
334C23×C4C22×D1911yescharacteristic
335C22×C8—21no—
336C22×C8—381no—
337C4⋊Q8—384no—
338C4⋊Q8—384no—
339C4⋊Q8—384no—
340C4⋊Q8—384no—
341#125—384no—
342#125—384no—
343#125—384no—
344#125—384no—
345C22⋊Q8—21no—
346C22⋊Q8—21no—
347C22⋊Q8—192no—
348C22⋊Q8—192no—
349C22⋊Q8—384no—
350C22⋊Q8—384no—
351C22⋊Q8—381no—
352C22⋊Q8—381no—
353C22⋊Q8C4×D1912yes—
354C22⋊Q8C22⋊D1912yes—
355#117—384no—
356#117—384no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—191no—
359C2×C4⋊C4—192no—
360C2×C4⋊C4—192no—
361C2×C4⋊C4—381no—
362C2×C4⋊C4—381no—
363C2×C4⋊C4—381no—
364C2×C4⋊C4—381no—
365C2×C4⋊C4—381no—
366C2×C4⋊C4—381no—
367C2×C4⋊C4—381no—
368C2×C4⋊C4—381no—
369C2×C4⋊C4—381no—
370C2×C4⋊C4—381no—
371C2×C4⋊C4—381no—
372C2×C4⋊C4—381no—
373C2×C4⋊C4—762no—
374C2×C4⋊C4D7611yescharacteristic
375C2×C22⋊C4—21no—
376C2×C22⋊C4—381no—
377C2×C42—381no—
378C2×C42—381no—
379#103—762no—
380#103—762no—
381C22⋊C8—21no—
382C22⋊C8—21no—
383C22⋊C8—381no—
384C22⋊C8—381no—
385#95—21no—
386#95—21no—
387#95—762no—
388#95—762no—
389C19#840611yescharacteristic, complemented, Sylow
390C24D4×D1911yescharacteristic
391C2×Q8—21no—
392C2×Q8—41no—
393C2×Q8—41no—
394C2×Q8—192no—
395C2×Q8—384no—
396C2×Q8—381no—
397C2×Q8—761no—
398C2×Q8—761no—
399C2×Q8—1521no—
400C2×Q8—1521no—
401C2×Q8(C2×D19)⋊C412yes—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—192no—
414C22×C4—192no—
415C22×C4—192no—
416C22×C4—192no—
417C22×C4—381no—
418C22×C4—381no—
419C22×C4—381no—
420C22×C4—381no—
421C22×C4—381no—
422C22×C4—381no—
423C22×C4—381no—
424C22×C4—381no—
425C22×C4—382no—
426C22×C4—761no—
427C22×C4—761no—
428C22×C4—761no—
429C22×C4—761no—
430C22×C4—761no—
431C22×C4—761no—
432C22×C4—761no—
433C22×C4—761no—
434C22×C4C2×C4×D1911yescharacteristic
435C22×C4C2×D7611yescharacteristic
436C22×C4D4×D1911yescharacteristic
437C22×C4D4×D1911yescharacteristic
438C22×C4D4×D1911yescharacteristic
439C22×C4C2×C22⋊D1911yescharacteristic
440C2×C8—41no—
441C2×C8—41no—
442C2×C8—41no—
443C2×C8—761no—
444C2×C8—761no—
445C2×C8—761no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—21no—
449C4⋊C4—192no—
450C4⋊C4—384no—
451C4⋊C4—384no—
452C4⋊C4—384no—
453C4⋊C4—384no—
454C4⋊C4—384no—
455C4⋊C4—382no—
456C4⋊C4—382no—
457C4⋊C4—382no—
458C4⋊C4—381no—
459C4⋊C4—382no—
460C4⋊C4—382no—
461C4⋊C4—382no—
462C4⋊C4—382no—
463C4⋊C4—382no—
464C4⋊C4—761no—
465C4⋊C4—761no—
466C4⋊C4(C2×D19)⋊C412yes—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—382no—
470C22⋊C4—382no—
471C42—384no—
472C42—384no—
473C23—21no—
474C23—21no—
475C23—21no—
476C23—21no—
477C23C22⋊C4×D1911yescharacteristic
478C23#1059732811yescharacteristic
479C23SD16×D1911yescharacteristic
480C23#1059736111yescharacteristic
481C23Q16×D1911yescharacteristic
482C23#1059736411yescharacteristic
483C23#1059738311yescharacteristic
484Q8—42no—
485Q8—81no—
486Q8—762no—
487Q8—1521no—
488Q8—1524no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—81no—
507C2×C4—81no—
508C2×C4—81no—
509C2×C4—81no—
510C2×C4—194no—
511C2×C4—382no—
512C2×C4—382no—
513C2×C4—382no—
514C2×C4—382no—
515C2×C4—382no—
516C2×C4—382no—
517C2×C4—382no—
518C2×C4—382no—
519C2×C4—382no—
520C2×C4—761no—
521C2×C4—761no—
522C2×C4—761no—
523C2×C4—761no—
524C2×C4—761no—
525C2×C4—761no—
526C2×C4—762no—
527C2×C4—762no—
528C2×C4—762no—
529C2×C4—762no—
530C2×C4—1521no—
531C2×C4—1521no—
532C2×C4—1521no—
533C2×C4—1521no—
534C2×C4—1521no—
535C2×C4C22⋊C4×D1911yescharacteristic
536C2×C4#1059732811yescharacteristic
537C2×C4C2×(C2×D19)⋊C411yescharacteristic
538C2×C4#1059738311yescharacteristic
539C8—81no—
540C8—1521no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22#1192639911yescharacteristic
554C22#103×D1911yescharacteristic
555C22#1192655111yescharacteristic
556C22#1192668111yescharacteristic
557C22#1192668411yescharacteristic
558C22#1192669811yescharacteristic
559C22#1192670111yescharacteristic
560C22#1192671811yescharacteristic
561C22#1192672811yescharacteristic
562C22#1192673211yescharacteristic
563C22#1192673511yescharacteristic
564C4—21no—
565C4—21no—
566C4—21no—
567C4—21no—
568C4—42no—
569C4—42no—
570C4—82no—
571C4—384no—
572C4—762no—
573C4—762no—
574C4—762no—
575C4—1522no—
576C2—21no—
577C2—21no—
578C2—21no—
579C2—21no—
580C2#1456257611yescharacteristic
581C2#1456261011yescharacteristic
582C2#1456264411yescharacteristic
583C2#1456267811yescharacteristic
584C2#1456356811yescharacteristic
585C2#1456358111yescharacteristic
586C2#1456359511yescharacteristic
subgroupG/H
centerC23#10597328
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC2×C19×#328C2
socleC23×C19#120
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenterC2×#328D19
hypocenterC19#8406
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
11. #11927173C4semidirect
242. C2×Dic19#103semidirect
389. C19#8406semidirect

Maximal subgroups

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

subgroupindex
C2×#119271732
#145639432
#145639402
C2×#119262802
C2×#119262692
#145618892
C2×C19×#3282
#840619