Finite Group Databasebeta

← #18081376

Subgroups — #18081376

Order 4864.

704 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926434C211yesmaximal, characteristic
2#14563613C211yesmaximal, characteristic, complemented
3#14563399C211yesmaximal, characteristic, complemented
4C2×#11926270C211yesmaximal, characteristic, complemented
5C2×#11926267C211yesmaximal, characteristic
6C2×#11926267C211yesmaximal, characteristic
7C2×C19×#324C211yesmaximal, characteristic, complemented
8C22×(C2×D19)⋊C4C411yescharacteristic
9C22×(C2×D19)⋊C4C411yescharacteristic
10C22×(C2×D19)⋊C4C2211yescharacteristic
11C22×C4×Dic19C2211yescharacteristic
12C2×Dic19⋊C8—21no—
13C2×C22⋊(C19⋊C8)C2211yescharacteristic
14C2×C22⋊(C19⋊C8)C2211yescharacteristic
15C2×#10597272—21no—
16#11926434—21no—
17#11926434—21no—
18#11926434—21no—
19#11926434—21no—
20C2×C19⋊#95C411yescharacteristic
21C2×C19⋊#95C411yescharacteristic
22#11926298—21no—
23#11926298—21no—
24#11926270—22no—
25#11926267—22no—
26#11926267—22no—
27C22×C4⋊C4×C19C2211yescharacteristic
28C2×C19×C22⋊C8C2211yescharacteristic
29C2×C19×C22⋊C8C2211yescharacteristic
30C19×#324—22no—
31C24×D19C2×C411yescharacteristic
32C23×C4×C19C2×C411yescharacteristic
33C23×C4×C19C2×C411yescharacteristic
34C23×C4×C19C2311yescharacteristic
35C23×Dic19C2×C411yescharacteristic
36C23×Dic19C2×C411yescharacteristic
37C23×Dic19C2×C411yescharacteristic
38C22×C8×C19—21no—
39C22×C8×C19—21no—
40C2×C4⋊C4×C19—21no—
41C2×C4⋊C4×C19—21no—
42C2×C4⋊C4×C19—21no—
43C2×C4⋊C4×C19—21no—
44C2×C4⋊C4×C19—21no—
45C2×C4⋊C4×C19—21no—
46C2×(C2×D19)⋊C4—22no—
47C2×(C2×D19)⋊C4—22no—
48C2×(C2×D19)⋊C4—21no—
49C2×(C2×D19)⋊C4—21no—
50C2×(C2×D19)⋊C4—21no—
51C2×(C2×D19)⋊C4—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×(C2×D19)⋊C4—21no—
58C2×(C2×D19)⋊C4—42no—
59C2×C4×Dic19—42no—
60C2×C4×Dic19D411yescharacteristic
61C2×C4×Dic19D411yescharacteristic
62C2×C4×Dic19D411yescharacteristic
63C2×C4×Dic19D411yescharacteristic
64C22×C19⋊C8—21no—
65C22×C19⋊C8—21no—
66C19×C22⋊C8—21no—
67C19×C22⋊C8—21no—
68C19×C22⋊C8—21no—
69C19×C22⋊C8D412yes—
70C19⋊#95—21no—
71C19⋊#95—21no—
72C19⋊#95—21no—
73C19⋊#95—21no—
74C22⋊(C19⋊C8)—21no—
75C22⋊(C19⋊C8)—21no—
76C22⋊(C19⋊C8)—21no—
77C22⋊(C19⋊C8)D412yes—
78#10597272—42no—
79Dic19⋊C8—42no—
80C24×C19C22×C411yescharacteristic
81C23×D19—21no—
82C23×D19—21no—
83C23×D19—21no—
84C23×D19—21no—
85C23×D19—21no—
86C23×D19—21no—
87C23×D19—41no—
88C23×D19—41no—
89C23×D19—41no—
90C23×D19—41no—
91C23×D19M1612yes—
92C22×C4×C19—21no—
93C22×C4×C19—21no—
94C22×C4×C19—21no—
95C22×C4×C19—21no—
96C22×C4×C19—21no—
97C22×C4×C19—21no—
98C22×C4×C19—21no—
99C22×C4×C19—21no—
100C22×C4×C19—21no—
101C22×C4×C19—41no—
102C22×C4×C19—41no—
103C22×C4×C19—41no—
104C22×C4×C19—41no—
105C22×C4×C19M1612yes—
106C22×C4×C19C2×D411yescharacteristic
107C22×C4×C19C2×D411yescharacteristic
108C22×C4×C19C2×D411yescharacteristic
109C22×C4×C19C2×D411yescharacteristic
110C22×C4×C19#4111yescharacteristic
111C22×C4×C19#4111yescharacteristic
112C22×Dic19—21no—
113C22×Dic19—21no—
114C22×Dic19—21no—
115C22×Dic19—21no—
116C22×Dic19—22no—
117C22×Dic19—21no—
118C22×Dic19—21no—
119C22×Dic19—21no—
120C22×Dic19—41no—
121C22×Dic19—41no—
122C22×Dic19—41no—
123C22×Dic19—41no—
124C22×Dic19—41no—
125C22×Dic19C22⋊C411yescharacteristic
126C22×Dic19C22⋊C411yescharacteristic
127C22×Dic19C22⋊C411yescharacteristic
128C22×Dic19C22⋊C411yescharacteristic
129C2×C8×C19—22no—
130C2×C8×C19—41no—
131C2×C8×C19—41no—
132C2×C8×C19—41no—
133C2×C8×C19—41no—
134C2×C8×C19—41no—
135C4⋊C4×C19—41no—
136C4⋊C4×C19—41no—
137C4⋊C4×C19—41no—
138C4⋊C4×C19—41no—
139(C2×D19)⋊C4—24no—
140(C2×D19)⋊C4—24no—
141(C2×D19)⋊C4—42no—
142(C2×D19)⋊C4—41no—
143(C2×D19)⋊C4—41no—
144(C2×D19)⋊C4—41no—
145(C2×D19)⋊C4—41no—
146(C2×D19)⋊C4—42no—
147C4×Dic19—22no—
148C4×Dic19—22no—
149C4×Dic19—41no—
150C4×Dic19—41no—
151C2×C19⋊C8—22no—
152C2×C19⋊C8—41no—
153C2×C19⋊C8—41no—
154C2×C19⋊C8—41no—
155C2×C19⋊C8—41no—
156C2×C19⋊C8—41no—
157#9652—191nomaximal, Sylow
158C23×C19—21no—
159C23×C19—21no—
160C23×C19—21no—
161C23×C19—21no—
162C23×C19C2×C22⋊C411yescharacteristic
163C23×C19C4×D411yescharacteristic
164C23×C19C4×D411yescharacteristic
165C23×C19C2×M1611yescharacteristic
166C23×C19C2×M1611yescharacteristic
167C23×C19#13111yescharacteristic
168C23×C19#13111yescharacteristic
169C22×D19—22no—
170C22×D19—22no—
171C22×D19—22no—
172C22×D19—42no—
173C22×D19—42no—
174C22×D19—41no—
175C22×D19—41no—
176C22×D19—41no—
177C22×D19—41no—
178C22×D19—41no—
179C22×D19—41no—
180C22×D19—41no—
181C22×D19—41no—
182C22×D19—42no—
183C22×D19—42no—
184C22×D19—81no—
185C22×D19—81no—
186C22×D19—81no—
187C22×D19—81no—
188C22×D19—81no—
189C22×D19—81no—
190C22×D19—81no—
191C22×D19—81no—
192C2×C4×C19—21no—
193C2×C4×C19—21no—
194C2×C4×C19—21no—
195C2×C4×C19—21no—
196C2×C4×C19—22no—
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—41no—
208C2×C4×C19—41no—
209C2×C4×C19—41no—
210C2×C4×C19—81no—
211C2×C4×C19—81no—
212C2×C4×C19#12111yescharacteristic
213C2×C4×C19#12111yescharacteristic
214C2×C4×C19#12411yescharacteristic
215C2×C4×C19#12711yescharacteristic
216C2×Dic19—21no—
217C2×Dic19—21no—
218C2×Dic19—21no—
219C2×Dic19—21no—
220C2×Dic19—21no—
221C2×Dic19—21no—
222C2×Dic19—21no—
223C2×Dic19—21no—
224C2×Dic19—21no—
225C2×Dic19—21no—
226C2×Dic19—21no—
227C2×Dic19—42no—
228C2×Dic19—42no—
229C2×Dic19—42no—
230C2×Dic19—42no—
231C2×Dic19—41no—
232C2×Dic19—41no—
233C2×Dic19—41no—
234C2×Dic19—81no—
235C2×Dic19—81no—
236C2×Dic19#9912yes—
237C8×C19—42no—
238C8×C19—81no—
239C19⋊C8—42no—
240C19⋊C8—81no—
241C2×#388—191no—
242#1797—191no—
243#1749—191no—
244C2×#324—191no—
245C2×#324D1911yescharacteristic, complemented
246C2×#323—191no—
247C2×#323—191no—
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—21no—
259C22×C19—21no—
260C22×C19#39011yescharacteristic
261C22×C19#40711yescharacteristic
262C22×C19#40811yescharacteristic
263C22×C19C2×#9911yescharacteristic
264C22×C19#41011yescharacteristic
265C22×C19#41311yescharacteristic
266C22×C19#41311yescharacteristic
267C22×C19#43511yescharacteristic
268C22×C19#43511yescharacteristic
269C22×C19#43511yescharacteristic
270C22×C19#43511yescharacteristic
271C2×D19—42no—
272C2×D19—42no—
273C2×D19—42no—
274C2×D19—82no—
275C2×D19—82no—
276C2×D19—81no—
277C2×D19—81no—
278C2×D19—81no—
279C2×D19—81no—
280C2×D19—82no—
281C2×D19—82no—
282C4×C19—21no—
283C4×C19—21no—
284C4×C19—21no—
285C4×C19—21no—
286C4×C19—42no—
287C4×C19—81no—
288Dic19—22no—
289Dic19—41no—
290Dic19—41no—
291Dic19—41no—
292Dic19—81no—
293C22×C4⋊C4C2×D1911yescharacteristic
294C22×C22⋊C4—191no—
295C22×C22⋊C4—191no—
296C22×C22⋊C4—191no—
297C22×C42—191no—
298C2×C4⋊C8—381no—
299C2×C22⋊C8—191no—
300C2×C22⋊C8—191no—
301C2×C22⋊C8C2×D1911yescharacteristic
302C2×C22⋊C8C2×D1911yescharacteristic
303C2×#97—381no—
304#388—381no—
305#388—381no—
306#388—381no—
307#388—381no—
308C2×#95—191no—
309C2×#95—191no—
310#336—381no—
311#336—381no—
312#324—22no—
313#324—382no—
314#323—382no—
315#323—382no—
316C2×C19—21no—
317C2×C19—21no—
318C2×C19—21no—
319C2×C19—21no—
320C2×C19#146411yescharacteristic
321C2×C19#146511yescharacteristic
322C2×C19#146811yescharacteristic
323C2×C19#147311yescharacteristic
324C2×C19#195511yescharacteristic
325C2×C19#196411yescharacteristic
326C2×C19#196711yescharacteristic
327D19—82no—
328C25—191no—
329C23×C4—191no—
330C23×C4—191no—
331C23×C4—191no—
332C23×C4C4×D1911yescharacteristic
333C23×C4C4×D1911yescharacteristic
334C23×C4C22×D1911yescharacteristic
335C22×C8—21no—
336C22×C8—21no—
337C22×C8—381no—
338C22×C8—381no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C22⋊C4—381no—
346C2×C22⋊C4—381no—
347C2×C22⋊C4—382no—
348C2×C22⋊C4—382no—
349C2×C22⋊C4—381no—
350C2×C22⋊C4—381no—
351C2×C22⋊C4—381no—
352C2×C22⋊C4—381no—
353C2×C22⋊C4—381no—
354C2×C22⋊C4—381no—
355C2×C22⋊C4—381no—
356C2×C22⋊C4—381no—
357C2×C22⋊C4—762no—
358C2×C42—191no—
359C2×C42—191no—
360C2×C42—191no—
361C2×C42—191no—
362C2×C42—762no—
363C4⋊C8—762no—
364C22⋊C8—21no—
365C22⋊C8—21no—
366C22⋊C8—21no—
367C22⋊C8—192no—
368C22⋊C8—381no—
369C22⋊C8—381no—
370C22⋊C8—381no—
371C22⋊C8C22⋊D1912yes—
372#97—762no—
373#95—381no—
374#95—381no—
375#95—381no—
376#95—381no—
377C19#965211yescharacteristic, complemented, Sylow
378C24—192no—
379C24—381no—
380C24—381no—
381C24—381no—
382C24—381no—
383C24—381no—
384C24—381no—
385C24—761no—
386C24—761no—
387C24—761no—
388C24—761no—
389C24C2×C4×D1911yescharacteristic
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—41no—
403C22×C4—191no—
404C22×C4—191no—
405C22×C4—191no—
406C22×C4—191no—
407C22×C4—382no—
408C22×C4—381no—
409C22×C4—381no—
410C22×C4—381no—
411C22×C4—381no—
412C22×C4—381no—
413C22×C4—381no—
414C22×C4—381no—
415C22×C4—761no—
416C22×C4—761no—
417C22×C4—761no—
418C22×C4—761no—
419C22×C4—761no—
420C22×C4#6451512yes—
421C22×C4#6454111yescharacteristic
422C22×C4D4×D1911yescharacteristic
423C22×C4D4×D1911yescharacteristic
424C22×C4D4×D1911yescharacteristic
425C22×C4#6454311yescharacteristic
426C22×C4C2×C22⋊D1911yescharacteristic
427C2×C8—22no—
428C2×C8—41no—
429C2×C8—41no—
430C2×C8—41no—
431C2×C8—41no—
432C2×C8—41no—
433C2×C8—382no—
434C2×C8—761no—
435C2×C8—761no—
436C2×C8—761no—
437C2×C8—761no—
438C2×C8—761no—
439C4⋊C4—41no—
440C4⋊C4—41no—
441C4⋊C4—41no—
442C4⋊C4—41no—
443C22⋊C4—384no—
444C22⋊C4—384no—
445C22⋊C4—762no—
446C22⋊C4—762no—
447C22⋊C4—761no—
448C22⋊C4—761no—
449C22⋊C4—761no—
450C22⋊C4—761no—
451C42—382no—
452C42—382no—
453C42—761no—
454C42—761no—
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—382no—
460C23—382no—
461C23—382no—
462C23—762no—
463C23—762no—
464C23—762no—
465C23—762no—
466C23—761no—
467C23—761no—
468C23—761no—
469C23—761no—
470C23—761no—
471C23—761no—
472C23—761no—
473C23—761no—
474C23—1521no—
475C23—1521no—
476C23—1521no—
477C23—1521no—
478C23—1521no—
479C23—1521no—
480C23—1521no—
481C23—1521no—
482C23C22⋊C4×D1911yescharacteristic
483C23(C22⋊D19)⋊C411yescharacteristic
484C23C2×#6451511yescharacteristic
485C23#1059734711yescharacteristic
486C23M16×D1911yescharacteristic
487C23#1059735311yescharacteristic
488C23C4×C22⋊D1911yescharacteristic
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—81no—
508C2×C4—81no—
509C2×C4—192no—
510C2×C4—381no—
511C2×C4—381no—
512C2×C4—381no—
513C2×C4—381no—
514C2×C4—381no—
515C2×C4—381no—
516C2×C4—381no—
517C2×C4—381no—
518C2×C4—381no—
519C2×C4—381no—
520C2×C4—381no—
521C2×C4—762no—
522C2×C4—762no—
523C2×C4—762no—
524C2×C4—762no—
525C2×C4—761no—
526C2×C4—761no—
527C2×C4—761no—
528C2×C4—1521no—
529C2×C4—1521no—
530C2×C4#1059733011yescharacteristic
531C2×C4#1059733111yescharacteristic
532C2×C4#1059738511yescharacteristic
533C2×C4#1059738611yescharacteristic
534C8—42no—
535C8—81no—
536C8—762no—
537C8—1521no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—762no—
551C22—762no—
552C22—762no—
553C22—1522no—
554C22—1522no—
555C22—1522no—
556C22—1522no—
557C22—1521no—
558C22—1521no—
559C22—1521no—
560C22—1521no—
561C22#1192644411yescharacteristic
562C22#1192650611yescharacteristic
563C22#1192650911yescharacteristic
564C22#99×D1911yescharacteristic
565C22#1192651611yescharacteristic
566C22#1192652711yescharacteristic
567C22#1192652711yescharacteristic
568C22#1192661211yescharacteristic
569C22#1192661311yescharacteristic
570C22#1192661511yescharacteristic
571C22#1192661811yescharacteristic
572C4—21no—
573C4—21no—
574C4—21no—
575C4—21no—
576C4—42no—
577C4—81no—
578C4—382no—
579C4—761no—
580C4—761no—
581C4—761no—
582C4—1521no—
583C2—21no—
584C2—21no—
585C2—21no—
586C2—21no—
587C2—1522no—
588C2#1456196811yescharacteristic
589C2#1456197211yescharacteristic
590C2#1456198211yescharacteristic
591C2#1456200311yescharacteristic
592C2#1456443111yescharacteristic
593C2#1456446911yescharacteristic
594C2#1456448311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC2×C19×#324C2
socleC23×C19C2×C22⋊C4
prime radicalC24×D19C2×C4
cosocleC23×C4×C19C23
hypercenterC2×#324D19
hypocenterC19#9652
LCSG ▷ C24×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. #14563613C2semidirect
3. #14563399C2semidirect
4. C2×#11926270C2semidirect
7. C2×C19×#324C2semidirect
245. C2×#324D19semidirect
377. C19#9652semidirect

Maximal subgroups

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

subgroupindex
C2×#119264342
#145636132
#145633992
C2×#119262702
C2×#119262672
C2×C19×#3242
#965219