Finite Group Databasebeta

← #18081680

Subgroups — #18081680

Order 4864.

650 conjugacy classes of subgroups.

The subgroup lattice has 582 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#14561860C211yesmaximal, characteristic, complemented
7C2×C19×#328C211yesmaximal, characteristic, complemented
8C2×#10597393C411yescharacteristic, complemented
9C2×#10597376C2211yescharacteristic
10C22×C4×Dic19C2211yescharacteristic
11C2×Dic19⋊C8—21no—
12C2×C22⋊(C19⋊C8)C2211yescharacteristic
13#11926451C411yescharacteristic, complemented
14#11926445C411yescharacteristic, complemented
15#11926434—21no—
16#11926434—21no—
17#11926421—21no—
18#11926421—21no—
19#11926409C411yescharacteristic, complemented
20C2×C19⋊#95—21no—
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—42no—
59C2×C4×Dic19C2×C411yescharacteristic
60C2×C4×Dic19C2×C411yescharacteristic
61C2×C4×Dic19D411yescharacteristic
62C2×C4×Dic19D411yescharacteristic
63C22×C19⋊C8—21no—
64C19×C22⋊C8—21no—
65C19×C22⋊C8—21no—
66C19×#95—21no—
67C19×#95D412yes—
68C19⋊#95—21no—
69C19⋊#95—21no—
70C19⋊#95—21no—
71C19⋊#95—21no—
72C19⋊#95—21no—
73C19⋊#95—42no—
74C19⋊#95—42no—
75C19⋊#95D412yes—
76C22⋊(C19⋊C8)—21no—
77C22⋊(C19⋊C8)—21no—
78Dic19⋊C8—42no—
79C24×C19C2×D411yescharacteristic
80C23×D19—21no—
81C2×Q8×C19—21no—
82C2×Q8×C19—21no—
83C2×Q8×C19—41no—
84C2×Q8×C19—41no—
85C22×C4×C19—21no—
86C22×C4×C19—21no—
87C22×C4×C19—22no—
88C22×C4×C19—41no—
89C22×C4×C19—41no—
90C22×C4×C19—41no—
91C22×C4×C19—41no—
92C22×C4×C19—41no—
93C22×C4×C19—41no—
94C22×C4×C19—41no—
95C22×C4×C19—41no—
96C22×C4×C19C22×C411yescharacteristic
97C22×C4×C19C2×D411yescharacteristic
98C22×C4×C19C2×D411yescharacteristic
99C22×C4×C19C2×D411yescharacteristic
100C22×C4×C19#4111yescharacteristic
101C22×C4×C19#4111yescharacteristic
102C2×C22⋊D19—41no—
103C2×C22⋊D19—41no—
104C2×C22⋊D19—41no—
105C2×C22⋊D19—41no—
106C2×C22⋊D19—41no—
107C2×C22⋊D19—41no—
108C22×Dic19—21no—
109C22×Dic19—21no—
110C22×Dic19—21no—
111C22×Dic19—21no—
112C22×Dic19—22no—
113C22×Dic19—21no—
114C22×Dic19—22no—
115C22×Dic19—41no—
116C22×Dic19—41no—
117C22×Dic19—41no—
118C22×Dic19—41no—
119C22×Dic19—41no—
120C22×Dic19—41no—
121C22×Dic19—41no—
122C22×Dic19—41no—
123C22×Dic19—41no—
124C22×Dic19C22⋊C411yescharacteristic
125C22×Dic19C22⋊C411yescharacteristic
126C22×Dic19C22⋊C411yescharacteristic
127C22×Dic19C22⋊C411yescharacteristic
128C2×D76—21no—
129C2×D76—21no—
130C2×D76—41no—
131C2×D76—41no—
132C2×C8×C19—41no—
133C2×C8×C19—41no—
134C2×C8×C19—41no—
135C4⋊C4×C19—21no—
136C4⋊C4×C19—21no—
137C4⋊C4×C19—41no—
138C4⋊C4×C19—41no—
139C22⋊C4×C19—41no—
140C22⋊C4×C19—41no—
141(C2×D19)⋊C4—42no—
142(C2×D19)⋊C4—42no—
143(C2×D19)⋊C4—42no—
144(C2×D19)⋊C4—41no—
145(C2×D19)⋊C4—41no—
146(C2×D19)⋊C4—42no—
147C4⋊Dic19—21no—
148C4⋊Dic19—21no—
149C4×Dic19—22no—
150C4×Dic19—22no—
151C4×Dic19—41no—
152C4×Dic19—41no—
153C2×C19⋊C8—41no—
154C2×C19⋊C8—41no—
155C2×C19⋊C8—41no—
156#9716—191nomaximal, Sylow
157C23×C19—21no—
158C23×C19—21no—
159C23×C19—21no—
160C23×C19—21no—
161C23×C19C2×C22⋊C411yescharacteristic
162C23×C19#12111yescharacteristic
163C23×C19#12111yescharacteristic
164C23×C19#13511yescharacteristic
165C23×C19#13511yescharacteristic
166C23×C19AGL(1,ℤ/8)11yescharacteristic
167C23×C19#13711yescharacteristic
168C22×D19—41no—
169C22×D19—41no—
170C22×D19—41no—
171C22×D19—41no—
172C22×D19—41no—
173C22×D19—41no—
174C22×D19—41no—
175Q8×C19—81no—
176Q8×C19—81no—
177C2×C4×C19—21no—
178C2×C4×C19—21no—
179C2×C4×C19—21no—
180C2×C4×C19—21no—
181C2×C4×C19—41no—
182C2×C4×C19—41no—
183C2×C4×C19—41no—
184C2×C4×C19—41no—
185C2×C4×C19—42no—
186C2×C4×C19—42no—
187C2×C4×C19—41no—
188C2×C4×C19—41no—
189C2×C4×C19—41no—
190C2×C4×C19—41no—
191C2×C4×C19—41no—
192C2×C4×C19—41no—
193C2×C4×C19—42no—
194C2×C4×C19—81no—
195C2×C4×C19—81no—
196C2×C4×C19—81no—
197C2×C4×C19—81no—
198C2×C4×C19C4×D411yescharacteristic
199C2×C4×C19C4×D411yescharacteristic
200C2×C4×C19#12411yescharacteristic
201C2×C4×C19#12711yescharacteristic
202C22⋊D19—81no—
203C22⋊D19—81no—
204C22⋊D19—81no—
205C22⋊D19—81no—
206C2×Dic19—21no—
207C2×Dic19—21no—
208C2×Dic19—21no—
209C2×Dic19—21no—
210C2×Dic19—21no—
211C2×Dic19—21no—
212C2×Dic19—21no—
213C2×Dic19—21no—
214C2×Dic19—21no—
215C2×Dic19—21no—
216C2×Dic19—21no—
217C2×Dic19—42no—
218C2×Dic19—42no—
219C2×Dic19—42no—
220C2×Dic19—42no—
221C2×Dic19—42no—
222C2×Dic19—42no—
223C2×Dic19—41no—
224C2×Dic19—41no—
225C2×Dic19—41no—
226C2×Dic19—42no—
227C2×Dic19—81no—
228C2×Dic19—81no—
229C2×Dic19—81no—
230C2×Dic19—81no—
231C2×Dic19#9912yes—
232D76—81no—
233D76—81no—
234C8×C19—81no—
235C19⋊C8—81no—
236#2850—191no—
237#1797—191no—
238C2×#328—191no—
239C2×#328D1911yescharacteristic, complemented
240C2×#327—191no—
241C2×#327—191no—
242#1434—191no—
243C22×C19—21no—
244C22×C19—21no—
245C22×C19—21no—
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#39011yescharacteristic
256C22×C19C2×#9911yescharacteristic
257C22×C19#41011yescharacteristic
258C22×C19#41611yescharacteristic
259C22×C19#41711yescharacteristic
260C22×C19#42111yescharacteristic
261C22×C19#42111yescharacteristic
262C22×C19#46311yescharacteristic
263C22×C19#46311yescharacteristic
264C22×C19#46411yescharacteristic
265C22×C19#46411yescharacteristic
266C2×D19—81no—
267C2×D19—81no—
268C2×D19—81no—
269C2×D19—81no—
270C2×D19—81no—
271C2×D19—81no—
272C2×D19—81no—
273C4×C19—21no—
274C4×C19—21no—
275C4×C19—21no—
276C4×C19—21no—
277C4×C19—82no—
278C4×C19—81no—
279C4×C19—81no—
280Dic19—22no—
281Dic19—41no—
282Dic19—41no—
283Dic19—41no—
284Dic19—82no—
285Dic19—81no—
286C2×#124—191no—
287C2×C22⋊Q8C2×D1911yescharacteristic
288C2×#121—191no—
289C22×C42—191no—
290C2×C4⋊C8—381no—
291C2×C22⋊C8—191no—
292C2×C22⋊C8C2×D1911yescharacteristic
293#391—191no—
294#390—191no—
295#388—381no—
296#388—381no—
297#386—381no—
298#386—381no—
299#382—191no—
300C2×#95—191no—
301C2×#95—381no—
302C2×#95—381no—
303C2×#95C2×D1911yescharacteristic
304#336—381no—
305#328—22no—
306#328—382no—
307#327—382no—
308#327—382no—
309C2×C19—21no—
310C2×C19—21no—
311C2×C19—21no—
312C2×C19—21no—
313C2×C19#151211yescharacteristic
314C2×C19#151311yescharacteristic
315C2×C19#151611yescharacteristic
316C2×C19#152111yescharacteristic
317C2×C19#196311yescharacteristic
318C2×C19#196411yescharacteristic
319C2×C19#198311yescharacteristic
320D19—161no—
321C22×Q8C4×D1911yescharacteristic
322C22×D4—191no—
323C22×D4—381no—
324C23×C4—21no—
325C23×C4—191no—
326C23×C4—191no—
327C23×C4—381no—
328C23×C4C22×D1911yescharacteristic
329C22×C8—21no—
330C22×C8—381no—
331#124—762no—
332C22⋊Q8—21no—
333C22⋊Q8—21no—
334C22⋊Q8—21no—
335C22⋊Q8—21no—
336#121—381no—
337#121—381no—
338#121—381no—
339#121—381no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—191no—
342C2×C4⋊C4C4×D1911yescharacteristic
343C2×C22⋊C4—21no—
344C2×C22⋊C4—381no—
345C2×C22⋊C4—381no—
346C2×C22⋊C4—381no—
347C2×C22⋊C4—381no—
348C2×C22⋊C4—381no—
349C2×C42—191no—
350C2×C42—191no—
351C2×C42—191no—
352C2×C42—191no—
353C2×C42—762no—
354C4⋊C8—762no—
355C22⋊C8—21no—
356C22⋊C8—21no—
357C22⋊C8—381no—
358C22⋊C8—381no—
359#95—21no—
360#95—192no—
361#95—381no—
362#95—381no—
363#95—381no—
364#95—381no—
365#95—381no—
366#95—762no—
367#95—762no—
368#95C22⋊D1912yes—
369C19#971611yescharacteristic, complemented, Sylow
370C24—381no—
371C24D4×D1911yescharacteristic
372C2×Q8—21no—
373C2×Q8—21no—
374C2×Q8—41no—
375C2×Q8—41no—
376C2×D4—381no—
377C2×D4—381no—
378C2×D4—761no—
379C2×D4—761no—
380C2×D4—761no—
381C2×D4—761no—
382C2×D4—761no—
383C2×D4—761no—
384C2×D4—761no—
385C2×D4—761no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—191no—
398C22×C4—191no—
399C22×C4—191no—
400C22×C4—191no—
401C22×C4—382no—
402C22×C4—381no—
403C22×C4—381no—
404C22×C4—381no—
405C22×C4—381no—
406C22×C4—381no—
407C22×C4—382no—
408C22×C4—761no—
409C22×C4—761no—
410C22×C4—761no—
411C22×C4—761no—
412C22×C4—761no—
413C22×C4—761no—
414C22×C4—761no—
415C22×C4—761no—
416C22×C4—761no—
417C22×C4C2×C4×D1911yescharacteristic
418C22×C4#6454111yescharacteristic
419C22×C4D4×D1911yescharacteristic
420C22×C4D4×D1911yescharacteristic
421C22×C4#6454311yescharacteristic
422C22×C4C2×C22⋊D1911yescharacteristic
423C2×C8—41no—
424C2×C8—41no—
425C2×C8—41no—
426C2×C8—761no—
427C2×C8—761no—
428C2×C8—761no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—41no—
432C4⋊C4—41no—
433C4⋊C4—381no—
434C4⋊C4—381no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—762no—
438C22⋊C4—762no—
439C22⋊C4—762no—
440C22⋊C4—762no—
441C22⋊C4—761no—
442C22⋊C4—761no—
443C42—382no—
444C42—382no—
445C42—761no—
446C42—761no—
447C23—21no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—761no—
452C23—761no—
453C23—761no—
454C23—761no—
455C23—761no—
456C23—761no—
457C23—761no—
458C23C22⋊C4×D1911yescharacteristic
459C23#1059733011yescharacteristic
460C23#1059736011yescharacteristic
461C23#1059736211yescharacteristic
462C23#1059736411yescharacteristic
463C23#1059736511yescharacteristic
464C23#1059738511yescharacteristic
465Q8—81no—
466Q8—81no—
467D4—1521no—
468D4—1521no—
469D4—1521no—
470D4—1521no—
471D4—1521no—
472D4—1521no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—81no—
491C2×C4—81no—
492C2×C4—81no—
493C2×C4—81no—
494C2×C4—192no—
495C2×C4—381no—
496C2×C4—381no—
497C2×C4—381no—
498C2×C4—381no—
499C2×C4—381no—
500C2×C4—381no—
501C2×C4—381no—
502C2×C4—381no—
503C2×C4—381no—
504C2×C4—381no—
505C2×C4—381no—
506C2×C4—762no—
507C2×C4—762no—
508C2×C4—762no—
509C2×C4—762no—
510C2×C4—762no—
511C2×C4—762no—
512C2×C4—761no—
513C2×C4—761no—
514C2×C4—761no—
515C2×C4—762no—
516C2×C4—1521no—
517C2×C4—1521no—
518C2×C4—1521no—
519C2×C4—1521no—
520C2×C4(C22⋊D19)⋊C411yescharacteristic
521C2×C4#1059733111yescharacteristic
522C2×C4C4×C22⋊D1911yescharacteristic
523C2×C4#1059738611yescharacteristic
524C8—81no—
525C8—1521no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—1521no—
539C22—1521no—
540C22—1521no—
541C22—1521no—
542C22—1521no—
543C22—1521no—
544C22—1521no—
545C22#1192644411yescharacteristic
546C22#99×D1911yescharacteristic
547C22#1192651611yescharacteristic
548C22#1192653911yescharacteristic
549C22#1192654411yescharacteristic
550C22#1192655911yescharacteristic
551C22#1192655911yescharacteristic
552C22#1192676111yescharacteristic
553C22#1192676211yescharacteristic
554C22#1192676811yescharacteristic
555C22#1192676911yescharacteristic
556C4—21no—
557C4—21no—
558C4—21no—
559C4—21no—
560C4—82no—
561C4—81no—
562C4—81no—
563C4—382no—
564C4—761no—
565C4—761no—
566C4—761no—
567C4—1522no—
568C4—1521no—
569C2—21no—
570C2—21no—
571C2—21no—
572C2—21no—
573C2—3041no—
574C2#1456217211yescharacteristic
575C2#1456217711yescharacteristic
576C2#1456219011yescharacteristic
577C2#1456221111yescharacteristic
578C2#1456446511yescharacteristic
579C2#1456446911yescharacteristic
580C2#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#9716
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. #14561860C2semidirect
7. C2×C19×#328C2semidirect
8. C2×#10597393C4semidirect
13. #11926451C4semidirect
14. #11926445C4semidirect
19. #11926409C4semidirect
239. C2×#328D19semidirect
369. C19#9716semidirect

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
#145618602
C2×C19×#3282
#971619