Finite Group Databasebeta

← #18075261

Subgroups — #18075261

Order 4864.

742 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14566141C211yesmaximal, characteristic
2#14563613C211yesmaximal, characteristic, complemented
3C2×#11926279C211yesmaximal, characteristic
4C2×#11926277C211yesmaximal, characteristic
5Dic19⋊#95C211yesmaximal, characteristic, complemented
6#14561513C211yesmaximal, characteristic, complemented
7C19×#1294C211yesmaximal, characteristic, complemented
8C2×#10597376C2211yescharacteristic
9C2×#10597339C411yescharacteristic, complemented
10C2×(C22⋊D19)⋊C4—21no—
11C22×Dic19⋊C4—21no—
12C22×C4×Dic19C2211yescharacteristic
13C2×Dic19⋊C8—21no—
14C2×C22⋊(C19⋊C8)C2211yescharacteristic
15#11926445C411yescharacteristic, complemented
16#11926440C411yescharacteristic, complemented
17#11926433—21no—
18#11926421—21no—
19C4⋊C4×Dic19C411yescharacteristic, complemented
20#11926391—21no—
21C2×C19⋊#95—21no—
22C2×C19⋊#95C2211yescharacteristic
23#11926298—21no—
24#11926279—22no—
25#11926277—22no—
26C2×C19×C22⋊C8C2211yescharacteristic
27C19×#380C2211yescharacteristic
28C2×C19×#95C2211yescharacteristic
29C23×C4×C19—21no—
30C23×C4×C19C2311yescharacteristic
31C22×C22⋊D19—21no—
32C23×Dic19—21no—
33C23×Dic19D411yescharacteristic
34C23×Dic19D411yescharacteristic
35C22×D76C2×C411yescharacteristic
36C22×C4×D19—21no—
37C22×C8×C19—21no—
38C2×C4⋊C4×C19C2×C411yescharacteristic
39C2×C4⋊C4×C19C2×C411yescharacteristic
40C2×C22⋊C4×C19—21no—
41#10597376—21no—
42#10597376—21no—
43#10597376D412yes—
44#10597376Q812yes—
45C2×(C2×D19)⋊C4—21no—
46C2×(C2×D19)⋊C4—21no—
47C2×(C2×D19)⋊C4—21no—
48C2×(C2×D19)⋊C4—21no—
49C2×C4⋊Dic19C2×C411yescharacteristic
50C2×Dic19⋊C4—24no—
51C2×Dic19⋊C4—21no—
52C2×Dic19⋊C4—42no—
53C2×Dic19⋊C4—42no—
54C2×C4×Dic19—21no—
55C2×C4×Dic19—42no—
56C2×C4×Dic19C2×C411yescharacteristic
57C2×C4×Dic19C2×C411yescharacteristic
58C2×C4×Dic19D411yescharacteristic
59C2×C4×Dic19D411yescharacteristic
60C22×C19⋊C8—21no—
61#10597339—42no—
62(C22⋊D19)⋊C4—42no—
63(C22⋊D19)⋊C4—42no—
64C19×C22⋊C8—21no—
65C19×C22⋊C8—21no—
66C19×#95—21no—
67C19×#95—21no—
68C19×#95—21no—
69C19⋊#95—21no—
70C19⋊#95—21no—
71C19⋊#95—21no—
72C19⋊#95—21no—
73C19⋊#95—42no—
74C22⋊(C19⋊C8)—21no—
75C22⋊(C19⋊C8)—21no—
76Dic19⋊C8—42no—
77C24×C19C2×D411yescharacteristic
78C23×D19—21no—
79C22×C4×C19—22no—
80C22×C4×C19—21no—
81C22×C4×C19—21no—
82C22×C4×C19—41no—
83C22×C4×C19—41no—
84C22×C4×C19—41no—
85C22×C4×C19—41no—
86C22×C4×C19—41no—
87C22×C4×C19—41no—
88C22×C4×C19—41no—
89C22×C4×C19—41no—
90C22×C4×C19C22×C411yescharacteristic
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19C2×D411yescharacteristic
93C22×C4×C19C2×Q811yescharacteristic
94C22×C4×C19#4111yescharacteristic
95C22×C4×C19#4111yescharacteristic
96C2×C22⋊D19—22no—
97C2×C22⋊D19—22no—
98C2×C22⋊D19—41no—
99C2×C22⋊D19—41no—
100C2×C22⋊D19—41no—
101C2×C22⋊D19—41no—
102C22×Dic19—22no—
103C22×Dic19—22no—
104C22×Dic19—21no—
105C22×Dic19—21no—
106C22×Dic19—21no—
107C22×Dic19—22no—
108C22×Dic19—41no—
109C22×Dic19—41no—
110C22×Dic19—41no—
111C22×Dic19—41no—
112C22×Dic19—41no—
113C22×Dic19—41no—
114C22×Dic19—41no—
115C22×Dic19—41no—
116C22×Dic19C22⋊C411yescharacteristic
117C22×Dic19C22⋊C411yescharacteristic
118C22×Dic19C22⋊C411yescharacteristic
119C22×Dic19C22⋊C411yescharacteristic
120C22×Dic19D812yes—
121C22×Dic19SD1612yes—
122C2×D76—21no—
123C2×D76—41no—
124C2×D76—41no—
125C2×D76C4⋊C412yescomplemented
126C2×C4×D19—42no—
127C2×C4×D19—42no—
128C2×C4×D19—42no—
129C2×C8×C19—41no—
130C2×C8×C19—41no—
131C2×C8×C19—41no—
132C4⋊C4×C19—41no—
133C4⋊C4×C19—41no—
134C22⋊C4×C19—41no—
135C22⋊C4×C19—41no—
136(C2×D19)⋊C4—22no—
137(C2×D19)⋊C4—22no—
138(C2×D19)⋊C4—42no—
139(C2×D19)⋊C4—42no—
140(C2×D19)⋊C4—42no—
141C4⋊Dic19—21no—
142C4⋊Dic19C4⋊C412yescomplemented
143Dic19⋊C4—48no—
144Dic19⋊C4—42no—
145C4×Dic19—22no—
146C4×Dic19—22no—
147C4×Dic19—41no—
148C4×Dic19—41no—
149C4×Dic19—42no—
150C2×C19⋊C8—41no—
151C2×C19⋊C8—41no—
152C2×C19⋊C8—41no—
153#8571—191nomaximal, Sylow
154C23×C19—21no—
155C23×C19—21no—
156C23×C19—21no—
157C23×C19—21no—
158C23×C19C2×C22⋊C411yescharacteristic
159C23×C19#12111yescharacteristic
160C23×C19C22⋊Q811yescharacteristic
161C23×C19C2×D811yescharacteristic
162C23×C19C2×SD1611yescharacteristic
163C23×C19AGL(1,ℤ/8)11yescharacteristic
164C23×C19#13711yescharacteristic
165C22×D19—22no—
166C22×D19—41no—
167C22×D19—41no—
168C22×D19—41no—
169C22×D19—41no—
170C22×D19—41no—
171C22×D19—41no—
172C2×C4×C19—21no—
173C2×C4×C19—21no—
174C2×C4×C19—21no—
175C2×C4×C19—21no—
176C2×C4×C19—41no—
177C2×C4×C19—41no—
178C2×C4×C19—41no—
179C2×C4×C19—41no—
180C2×C4×C19—42no—
181C2×C4×C19—42no—
182C2×C4×C19—42no—
183C2×C4×C19—41no—
184C2×C4×C19—41no—
185C2×C4×C19—41no—
186C2×C4×C19—41no—
187C2×C4×C19—41no—
188C2×C4×C19—41no—
189C2×C4×C19—81no—
190C2×C4×C19—81no—
191C2×C4×C19—81no—
192C2×C4×C19—81no—
193C2×C4×C19C2×C4⋊C411yescharacteristic
194C2×C4×C19#11711yescharacteristic
195C2×C4×C19#12111yescharacteristic
196C2×C4×C19C22⋊Q811yescharacteristic
197C22⋊D19—42no—
198C22⋊D19—42no—
199C22⋊D19—42no—
200C22⋊D19—42no—
201C2×Dic19—21no—
202C2×Dic19—21no—
203C2×Dic19—24no—
204C2×Dic19—24no—
205C2×Dic19—22no—
206C2×Dic19—21no—
207C2×Dic19—21no—
208C2×Dic19—21no—
209C2×Dic19—21no—
210C2×Dic19—21no—
211C2×Dic19—21no—
212C2×Dic19—42no—
213C2×Dic19—42no—
214C2×Dic19—41no—
215C2×Dic19—41no—
216C2×Dic19—42no—
217C2×Dic19—42no—
218C2×Dic19—42no—
219C2×Dic19—81no—
220C2×Dic19—81no—
221C2×Dic19—81no—
222C2×Dic19—81no—
223C2×Dic19#9912yes—
224C2×Dic19#10212yes—
225C2×Dic19#10212yes—
226C2×Dic19#10412yes—
227D76—42no—
228D76—42no—
229C4×D19—84no—
230C8×C19—81no—
231C19⋊C8—81no—
232C4×#121—191no—
233#1797—191no—
234C2×#327—191no—
235C2×#327—191no—
236C4⋊#95—191no—
237#1294—191no—
238#1294D1911yescharacteristic, complemented
239C22×C19—21no—
240C22×C19—21no—
241C22×C19—21no—
242C22×C19—21no—
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#38011yescharacteristic
252C22×C19C2×#9911yescharacteristic
253C22×C19#41011yescharacteristic
254C22×C19C2×#10211yescharacteristic
255C22×C19#41711yescharacteristic
256C22×C19C2×#10411yescharacteristic
257C22×C19#42111yescharacteristic
258C22×C19#45911yescharacteristic
259C22×C19#46111yescharacteristic
260C22×C19#47411yescharacteristic
261C22×C19#47611yescharacteristic
262C2×D19—42no—
263C2×D19—42no—
264C2×D19—42no—
265C2×D19—81no—
266C2×D19—81no—
267C2×D19—81no—
268C2×D19—81no—
269C4×C19—21no—
270C4×C19—21no—
271C4×C19—21no—
272C4×C19—21no—
273C4×C19—82no—
274C4×C19—81no—
275C4×C19—81no—
276Dic19—22no—
277Dic19—42no—
278Dic19—41no—
279Dic19—41no—
280Dic19—82no—
281Dic19#32714yescomplemented
282C2×#121—191no—
283C2×C4×D4—191no—
284C2×C4×D4—381no—
285C22×C4⋊C4—381no—
286C22×C42—191no—
287C2×C4⋊C8—381no—
288C2×C22⋊C8—191no—
289C2×C22⋊C8C2×D1911yescharacteristic
290#390—191no—
291#389—191no—
292#388—381no—
293#386—381no—
294#380C2×D1911yescharacteristic
295C4×C4⋊C4—191no—
296C4×C22⋊C4—381no—
297C2×#95—191no—
298C2×#95—381no—
299C2×#95C2×D1911yescharacteristic
300#336—381no—
301#327—382no—
302#327—382no—
303C2×C19—21no—
304C2×C19—21no—
305C2×C19—21no—
306C2×C19—21no—
307C2×C19C2×#32711yescharacteristic
308C2×C19#150911yescharacteristic
309C2×C19#151311yescharacteristic
310C2×C19#151711yescharacteristic
311C2×C19#179911yescharacteristic
312C2×C19#180211yescharacteristic
313C2×C19#180611yescharacteristic
314D19—82no—
315C22×D4—191no—
316C22×D4—381no—
317C23×C4—21no—
318C23×C4—191no—
319C23×C4—191no—
320C23×C4—381no—
321C23×C4—381no—
322C23×C4C22×D1911yescharacteristic
323C22×C8—21no—
324C22×C8—381no—
325#121—192no—
326#121—192no—
327#121—381no—
328#121—381no—
329C4×D4—762no—
330C4×D4—762no—
331C4×D4—762no—
332C2×C4⋊C4—191no—
333C2×C4⋊C4—381no—
334C2×C4⋊C4—384no—
335C2×C4⋊C4—762no—
336C2×C4⋊C4—762no—
337C2×C4⋊C4C4×D1911yescharacteristic
338C2×C4⋊C4C4×D1911yescharacteristic
339C2×C22⋊C4—21no—
340C2×C22⋊C4—381no—
341C2×C22⋊C4—381no—
342C2×C22⋊C4—381no—
343C2×C22⋊C4—381no—
344C2×C42—191no—
345C2×C42—191no—
346C2×C42—191no—
347C2×C42—191no—
348C2×C42—381no—
349C2×C42—762no—
350C4⋊C8—762no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C22⋊C8—381no—
354C22⋊C8—381no—
355#95—21no—
356#95—21no—
357#95—21no—
358#95—381no—
359#95—381no—
360#95—381no—
361#95—381no—
362#95—762no—
363C19#857111yescharacteristic, complemented, Sylow
364C24—381no—
365C24D4×D1911yescharacteristic
366C2×D4—192no—
367C2×D4—382no—
368C2×D4—382no—
369C2×D4—381no—
370C2×D4—761no—
371C2×D4—761no—
372C2×D4—761no—
373C2×D4—761no—
374C2×D4—761no—
375C2×D4—761no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—191no—
388C22×C4—191no—
389C22×C4—192no—
390C22×C4—192no—
391C22×C4—191no—
392C22×C4—191no—
393C22×C4—382no—
394C22×C4—382no—
395C22×C4—381no—
396C22×C4—381no—
397C22×C4—381no—
398C22×C4—382no—
399C22×C4—762no—
400C22×C4—762no—
401C22×C4—762no—
402C22×C4—761no—
403C22×C4—761no—
404C22×C4—761no—
405C22×C4—761no—
406C22×C4—761no—
407C22×C4—761no—
408C22×C4—761no—
409C22×C4—761no—
410C22×C4C2×C4×D1911yescharacteristic
411C22×C4#6454111yescharacteristic
412C22×C4#6454111yescharacteristic
413C22×C4D4×D1911yescharacteristic
414C22×C4D4×D1911yescharacteristic
415C22×C4Q8×D1911yescharacteristic
416C2×C8—41no—
417C2×C8—41no—
418C2×C8—41no—
419C2×C8—761no—
420C2×C8—761no—
421C2×C8—761no—
422C4⋊C4—41no—
423C4⋊C4—41no—
424C4⋊C4—192no—
425C4⋊C4—381no—
426C4⋊C4—762no—
427C4⋊C4—768no—
428C22⋊C4—41no—
429C22⋊C4—41no—
430C22⋊C4—382no—
431C22⋊C4—382no—
432C22⋊C4—762no—
433C22⋊C4—762no—
434C22⋊C4—762no—
435C42—382no—
436C42—382no—
437C42—761no—
438C42—761no—
439C42—762no—
440C23—21no—
441C23—21no—
442C23—21no—
443C23—21no—
444C23—382no—
445C23—761no—
446C23—761no—
447C23—761no—
448C23—761no—
449C23—761no—
450C23—761no—
451C23C22⋊C4×D1911yescharacteristic
452C23#1059733011yescharacteristic
453C23#1059734211yescharacteristic
454C23D8×D1911yescharacteristic
455C23SD16×D1911yescharacteristic
456C23#1059736011yescharacteristic
457C23#1059736411yescharacteristic
458D4—762no—
459D4—762no—
460D4—762no—
461D4—762no—
462D4—762no—
463D4—762no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—81no—
482C2×C4—81no—
483C2×C4—81no—
484C2×C4—81no—
485C2×C4—192no—
486C2×C4—192no—
487C2×C4—192no—
488C2×C4—192no—
489C2×C4—384no—
490C2×C4—384no—
491C2×C4—381no—
492C2×C4—381no—
493C2×C4—381no—
494C2×C4—381no—
495C2×C4—381no—
496C2×C4—381no—
497C2×C4—382no—
498C2×C4—381no—
499C2×C4—381no—
500C2×C4—762no—
501C2×C4—762no—
502C2×C4—761no—
503C2×C4—761no—
504C2×C4—762no—
505C2×C4—762no—
506C2×C4—762no—
507C2×C4—1524no—
508C2×C4—1521no—
509C2×C4—1521no—
510C2×C4—1521no—
511C2×C4—1521no—
512C2×C4#1059731811yescharacteristic
513C2×C4#1059733011yescharacteristic
514C2×C4C4⋊C4×D1911yescharacteristic
515C2×C4#1059734211yescharacteristic
516C8—81no—
517C8—1521no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—762no—
531C22—762no—
532C22—762no—
533C22—1521no—
534C22—1521no—
535C22—1521no—
536C22—1521no—
537C22#1192640311yescharacteristic
538C22#99×D1911yescharacteristic
539C22#1192651611yescharacteristic
540C22#102×D1911yescharacteristic
541C22#1192654411yescharacteristic
542C22#104×D1911yescharacteristic
543C22#1192655911yescharacteristic
544C22#1192673811yescharacteristic
545C22#1192674811yescharacteristic
546C22#1192682311yescharacteristic
547C22#1192683311yescharacteristic
548C4—21no—
549C4—21no—
550C4—21no—
551C4—21no—
552C4—82no—
553C4—81no—
554C4—81no—
555C4—194no—
556C4—382no—
557C4—762no—
558C4—761no—
559C4—761no—
560C4—1522no—
561C2—21no—
562C2—21no—
563C2—21no—
564C2—21no—
565C2—1522no—
566C2D19×#32711yescharacteristic
567C2#1456215911yescharacteristic
568C2#1456217711yescharacteristic
569C2#1456219311yescharacteristic
570C2#1456362211yescharacteristic
571C2#1456363411yescharacteristic
572C2#1456365411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1294C2
socleC23×C19C2×C22⋊C4
prime radicalC2×#10597376C22
cosocleC23×C4×C19C23
hypercenter#1294D19
hypocenterC19#8571
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
2. #14563613C2semidirect
5. Dic19⋊#95C2semidirect
6. #14561513C2semidirect
7. C19×#1294C2semidirect
9. C2×#10597339C4semidirect
15. #11926445C4semidirect
16. #11926440C4semidirect
19. C4⋊C4×Dic19C4semidirect
125. C2×D76C4⋊C4semidirect
142. C4⋊Dic19C4⋊C4semidirect
238. #1294D19semidirect
281. Dic19#327semidirect
363. C19#8571semidirect

Maximal subgroups

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

subgroupindex
#145661412
#145636132
C2×#119262792
C2×#119262772
Dic19⋊#952
#145615132
C19×#12942
#857119