Finite Group Databasebeta

← #18076544

Subgroups — #18076544

Order 4864.

692 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14566232C211yesmaximal, characteristic
2#14563830C211yesmaximal, characteristic, complemented
3#14563822C211yesmaximal, characteristic, complemented
4C2×#11926267C211yesmaximal, characteristic
5#14561881C211yesmaximal, characteristic
6#14561514C211yesmaximal, characteristic, complemented
7C19×#1294C211yesmaximal, characteristic, complemented
8C22×C4⋊Dic19C2211yescharacteristic
9C22×(C2×D19)⋊C4—21no—
10C22×(C2×D19)⋊C4C2211yescharacteristic
11C2×#10597264—21no—
12C2×#10597274—21no—
13C2×C22⋊(C19⋊C8)C2211yescharacteristic
14#11926436—21no—
15#11926436—21no—
16#11926434—21no—
17#11926434—21no—
18#11926404C2211yescharacteristic
19#11926399—21no—
20C22⋊C4×Dic19—21no—
21C2×C19⋊#95—21no—
22#11926307—21no—
23#11926306—21no—
24#11926267C414yescomplemented
25C2×C19×C22⋊C8C2211yescharacteristic
26C19×#380C2211yescharacteristic
27C2×C19×#95C2211yescharacteristic
28C24×D19D411yescharacteristic
29C23×C4×C19—21no—
30C23×C4×C19C2311yescharacteristic
31C23×Dic19—21no—
32C23×Dic19D411yescharacteristic
33C22×C8×C19—21no—
34C2×C4⋊C4×C19D411yescharacteristic
35C2×C4⋊C4×C19D411yescharacteristic
36C2×C22⋊C4×C19—21no—
37C2×C22⋊Dic19—21no—
38C2×(C2×D19)⋊C4—21no—
39C2×(C2×D19)⋊C4—21no—
40C2×(C2×D19)⋊C4—21no—
41C2×(C2×D19)⋊C4—21no—
42C2×(C2×D19)⋊C4—21no—
43C2×(C2×D19)⋊C4—21no—
44C2×(C2×D19)⋊C4—21no—
45C2×(C2×D19)⋊C4—21no—
46C2×(C2×D19)⋊C4—42no—
47C2×(C2×D19)⋊C4—42no—
48C2×(C2×D19)⋊C4—42no—
49C2×(C2×D19)⋊C4C2×C412yes—
50C2×(C2×D19)⋊C4Q812yes—
51C2×C4⋊Dic19—21no—
52C2×C4⋊Dic19—21no—
53C2×C4⋊Dic19—42no—
54C2×C4⋊Dic19D411yescharacteristic
55C2×C4⋊Dic19D411yescharacteristic
56C2×C4×Dic19—21no—
57C2×C4×Dic19—21no—
58C22×C19⋊C8—21no—
59C19×C22⋊C8—21no—
60C19×C22⋊C8C2×C412yes—
61C19×#95—21no—
62C19×#95—21no—
63C19×#95—21no—
64C19⋊#95—21no—
65C19⋊#95—21no—
66C19⋊#95—21no—
67C19⋊#95—42no—
68C22⋊(C19⋊C8)—21no—
69C22⋊(C19⋊C8)C2×C412yes—
70#10597274—42no—
71#10597264—42no—
72C24×C19C2×D411yescharacteristic
73C23×D19—21no—
74C23×D19—21no—
75C23×D19—21no—
76C23×D19—21no—
77C23×D19—21no—
78C23×D19—21no—
79C23×D19—41no—
80C23×D19—41no—
81C23×D19—41no—
82C23×D19—41no—
83C23×D19C4⋊C412yes—
84C22×C4×C19—22no—
85C22×C4×C19—21no—
86C22×C4×C19—21no—
87C22×C4×C19—41no—
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×C19C22×C411yescharacteristic
96C22×C4×C19C2×D411yescharacteristic
97C22×C4×C19C2×D411yescharacteristic
98C22×C4×C19C2×Q811yescharacteristic
99C22×C4×C19#4111yescharacteristic
100C22×C4×C19#4111yescharacteristic
101C22×Dic19—21no—
102C22×Dic19—21no—
103C22×Dic19—22no—
104C22×Dic19—21no—
105C22×Dic19—21no—
106C22×Dic19—41no—
107C22×Dic19—41no—
108C22×Dic19—41no—
109C22×Dic19—41no—
110C22×Dic19—41no—
111C22×Dic19—41no—
112C22×Dic19—41no—
113C22×Dic19—41no—
114C22×Dic19C4⋊C412yes—
115C2×C8×C19—22no—
116C2×C8×C19—41no—
117C2×C8×C19—41no—
118C4⋊C4×C19—41no—
119C4⋊C4×C19—41no—
120C22⋊C4×C19—41no—
121C22⋊C4×C19—41no—
122C22⋊Dic19—41no—
123C22⋊Dic19—41no—
124(C2×D19)⋊C4—22no—
125(C2×D19)⋊C4—22no—
126(C2×D19)⋊C4—22no—
127(C2×D19)⋊C4—22no—
128(C2×D19)⋊C4—48no—
129(C2×D19)⋊C4—81no—
130(C2×D19)⋊C4—81no—
131(C2×D19)⋊C4—81no—
132(C2×D19)⋊C4—81no—
133C4⋊Dic19—22no—
134C4⋊Dic19—22no—
135C4⋊Dic19—41no—
136C4⋊Dic19—41no—
137C4⋊Dic19—41no—
138C4⋊Dic19—41no—
139C4×Dic19—81no—
140C4×Dic19—81no—
141C2×C19⋊C8—22no—
142C2×C19⋊C8—41no—
143C2×C19⋊C8—41no—
144#8858—191nomaximal, Sylow
145C23×C19—21no—
146C23×C19—21no—
147C23×C19—21no—
148C23×C19—21no—
149C23×C19C2×C4⋊C411yescharacteristic
150C23×C19#12011yescharacteristic
151C23×C19#12311yescharacteristic
152C23×C19#13511yescharacteristic
153C23×C19#13511yescharacteristic
154C23×C19AGL(1,ℤ/8)11yescharacteristic
155C23×C19#13711yescharacteristic
156C22×D19—22no—
157C22×D19—22no—
158C22×D19—22no—
159C22×D19—42no—
160C22×D19—42no—
161C22×D19—42no—
162C22×D19—42no—
163C22×D19—42no—
164C22×D19—42no—
165C22×D19—41no—
166C22×D19—41no—
167C22×D19—41no—
168C22×D19—41no—
169C22×D19—41no—
170C22×D19—41no—
171C22×D19—41no—
172C22×D19—41no—
173C22×D19—81no—
174C22×D19—81no—
175C22×D19—81no—
176C22×D19—81no—
177C22×D19—81no—
178C22×D19—81no—
179C2×C4×C19—21no—
180C2×C4×C19—21no—
181C2×C4×C19—21no—
182C2×C4×C19—21no—
183C2×C4×C19—41no—
184C2×C4×C19—41no—
185C2×C4×C19—41no—
186C2×C4×C19—41no—
187C2×C4×C19—42no—
188C2×C4×C19—42no—
189C2×C4×C19—42no—
190C2×C4×C19—41no—
191C2×C4×C19—41no—
192C2×C4×C19—41no—
193C2×C4×C19—41no—
194C2×C4×C19—41no—
195C2×C4×C19—41no—
196C2×C4×C19—81no—
197C2×C4×C19—81no—
198C2×C4×C19—81no—
199C2×C4×C19—81no—
200C2×C4×C19C4×D411yescharacteristic
201C2×C4×C19C4×D411yescharacteristic
202C2×C4×C19C22⋊Q811yescharacteristic
203C2×C4×C19C22⋊Q811yescharacteristic
204C2×Dic19—22no—
205C2×Dic19—41no—
206C2×Dic19—41no—
207C2×Dic19—42no—
208C2×Dic19—42no—
209C2×Dic19—42no—
210C2×Dic19—41no—
211C2×Dic19—41no—
212C2×Dic19—41no—
213C2×Dic19—41no—
214C2×Dic19—42no—
215C2×Dic19—41no—
216C2×Dic19—41no—
217C2×Dic19—81no—
218C2×Dic19—81no—
219C2×Dic19—81no—
220C2×Dic19—81no—
221C2×Dic19—81no—
222C8×C19—42no—
223C19⋊C8—42no—
224#2312—191no—
225#1853—191no—
226#1852—191no—
227C2×#323—191no—
228#1439—191no—
229#1294—191no—
230#1294D1911yescharacteristic, complemented
231C22×C19—21no—
232C22×C19—21no—
233C22×C19—21no—
234C22×C19—21no—
235C22×C19—21no—
236C22×C19—21no—
237C22×C19—21no—
238C22×C19—21no—
239C22×C19—21no—
240C22×C19—21no—
241C22×C19—21no—
242C22×C19—21no—
243C22×C19#38511yescharacteristic
244C22×C19#42711yescharacteristic
245C22×C19#42811yescharacteristic
246C22×C19#44911yescharacteristic
247C22×C19#45211yescharacteristic
248C22×C19#45311yescharacteristic
249C22×C19#45511yescharacteristic
250C22×C19B(4,𝔽2)11yescharacteristic
251C22×C19#45811yescharacteristic
252C22×C19#48211yescharacteristic
253C22×C19#48511yescharacteristic
254C2×D19—44no—
255C2×D19—42no—
256C2×D19—42no—
257C2×D19—42no—
258C2×D19—82no—
259C2×D19—82no—
260C2×D19—81no—
261C2×D19—81no—
262C2×D19—81no—
263C2×D19—81no—
264C2×D19—82no—
265C4×C19—21no—
266C4×C19—21no—
267C4×C19—21no—
268C4×C19—21no—
269C4×C19—82no—
270C4×C19—81no—
271C4×C19—81no—
272Dic19—42no—
273Dic19—82no—
274Dic19—81no—
275Dic19—81no—
276C22×C4⋊C4—191no—
277C22×C22⋊C4—191no—
278C22×C22⋊C4—381no—
279C2×#107—381no—
280C2×#106—381no—
281C2×C22⋊C8—191no—
282C2×C22⋊C8C2×D1911yescharacteristic
283#388—381no—
284#388—381no—
285#388—381no—
286#388—381no—
287#380—191no—
288#380C2×D1911yescharacteristic
289#379—381no—
290C4×C22⋊C4—381no—
291C2×#95—381no—
292C2×#95C2×D1911yescharacteristic
293#340—381no—
294#340—381no—
295#323—194no—
296C2×C19—21no—
297C2×C19—21no—
298C2×C19—21no—
299C2×C19—21no—
300C2×C19#160011yescharacteristic
301C2×C19#160611yescharacteristic
302C2×C19#161211yescharacteristic
303C2×C19#161811yescharacteristic
304C2×C19#185411yescharacteristic
305C2×C19#185611yescharacteristic
306C2×C19#186711yescharacteristic
307D19—82no—
308C25—191no—
309C23×C4—21no—
310C23×C4—191no—
311C23×C4—381no—
312C23×C4C22×D1911yescharacteristic
313C22×C8—21no—
314C22×C8—381no—
315C2×C4⋊C4—191no—
316C2×C4⋊C4—191no—
317C2×C4⋊C4—381no—
318C2×C4⋊C4—381no—
319C2×C4⋊C4—762no—
320C2×C4⋊C4D7611yescharacteristic
321C2×C4⋊C4D7611yescharacteristic
322C2×C22⋊C4—21no—
323C2×C22⋊C4—192no—
324C2×C22⋊C4—192no—
325C2×C22⋊C4—381no—
326C2×C22⋊C4—381no—
327C2×C22⋊C4—381no—
328C2×C22⋊C4—381no—
329C2×C22⋊C4—381no—
330C2×C22⋊C4—381no—
331C2×C22⋊C4—381no—
332C2×C22⋊C4—381no—
333C2×C22⋊C4—381no—
334C2×C22⋊C4—762no—
335C2×C22⋊C4—762no—
336C2×C22⋊C4—762no—
337C2×C42—381no—
338C2×C42—381no—
339#107—762no—
340#106—762no—
341C22⋊C8—21no—
342C22⋊C8—192no—
343C22⋊C8—381no—
344C22⋊C8C4×D1912yes—
345#95—21no—
346#95—21no—
347#95—21no—
348#95—381no—
349#95—381no—
350#95—381no—
351#95—762no—
352C19#885811yescharacteristic, complemented, Sylow
353C24—192no—
354C24—381no—
355C24—381no—
356C24—381no—
357C24—381no—
358C24—381no—
359C24—381no—
360C24—761no—
361C24—761no—
362C24—761no—
363C24—761no—
364C24D4×D1911yescharacteristic
365C22×C4—22no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—192no—
377C22×C4—381no—
378C22×C4—381no—
379C22×C4—382no—
380C22×C4—381no—
381C22×C4—381no—
382C22×C4—761no—
383C22×C4—761no—
384C22×C4—761no—
385C22×C4—761no—
386C22×C4—761no—
387C22×C4—761no—
388C22×C4—761no—
389C22×C4—761no—
390C22×C4C2×C4×D1911yescharacteristic
391C22×C4C2×D7611yescharacteristic
392C22×C4#6454111yescharacteristic
393C22×C4D4×D1911yescharacteristic
394C22×C4#6454311yescharacteristic
395C22×C4Q8×D1911yescharacteristic
396C2×C8—22no—
397C2×C8—41no—
398C2×C8—41no—
399C2×C8—382no—
400C2×C8—761no—
401C2×C8—761no—
402C4⋊C4—41no—
403C4⋊C4—41no—
404C4⋊C4—382no—
405C4⋊C4—382no—
406C4⋊C4—761no—
407C4⋊C4—761no—
408C4⋊C4—761no—
409C4⋊C4—761no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—382no—
413C22⋊C4—382no—
414C22⋊C4—382no—
415C22⋊C4—382no—
416C22⋊C4—768no—
417C22⋊C4—761no—
418C22⋊C4—761no—
419C22⋊C4—1521no—
420C22⋊C4—1521no—
421C22⋊C4—1521no—
422C22⋊C4—1521no—
423C42—1521no—
424C42—1521no—
425C23—21no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—382no—
430C23—382no—
431C23—382no—
432C23—762no—
433C23—762no—
434C23—762no—
435C23—762no—
436C23—762no—
437C23—762no—
438C23—761no—
439C23—761no—
440C23—761no—
441C23—761no—
442C23—761no—
443C23—761no—
444C23—761no—
445C23—761no—
446C23—1521no—
447C23—1521no—
448C23—1521no—
449C23—1521no—
450C23—1521no—
451C23—1521no—
452C23#1059732811yescharacteristic
453C23#1059732911yescharacteristic
454C23C4⋊C4×D1911yescharacteristic
455C23#1059735711yescharacteristic
456C23#1059736211yescharacteristic
457C23#1059736211yescharacteristic
458C23#1059736411yescharacteristic
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—81no—
477C2×C4—81no—
478C2×C4—81no—
479C2×C4—81no—
480C2×C4—382no—
481C2×C4—761no—
482C2×C4—761no—
483C2×C4—762no—
484C2×C4—762no—
485C2×C4—762no—
486C2×C4—761no—
487C2×C4—761no—
488C2×C4—761no—
489C2×C4—761no—
490C2×C4—761no—
491C2×C4—762no—
492C2×C4—761no—
493C2×C4—1521no—
494C2×C4—1521no—
495C2×C4—1521no—
496C2×C4—1521no—
497C2×C4—1521no—
498C2×C4C4×D7611yescharacteristic
499C2×C4(C22⋊D19)⋊C411yescharacteristic
500C2×C4#1059734211yescharacteristic
501C2×C4#1059734311yescharacteristic
502C8—42no—
503C8—762no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—764no—
517C22—762no—
518C22—762no—
519C22—762no—
520C22—1522no—
521C22—1522no—
522C22—1522no—
523C22—1521no—
524C22—1521no—
525C22—1521no—
526C22—1521no—
527C22#1192641811yescharacteristic
528C22#1192657911yescharacteristic
529C22#1192658511yescharacteristic
530C22#1192669011yescharacteristic
531C22#1192670911yescharacteristic
532C22#1192671311yescharacteristic
533C22#1192672311yescharacteristic
534C22#1192673211yescharacteristic
535C22#1192673511yescharacteristic
536C22#1192686711yescharacteristic
537C22#1192688311yescharacteristic
538C4—21no—
539C4—21no—
540C4—21no—
541C4—21no—
542C4—82no—
543C4—81no—
544C4—81no—
545C4—762no—
546C4—1522no—
547C4—1521no—
548C4—1521no—
549C2—21no—
550C2—21no—
551C2—21no—
552C2—21no—
553C2—1522no—
554C2#1456258211yescharacteristic
555C2#1456261811yescharacteristic
556C2#1456265011yescharacteristic
557C2#1456268611yescharacteristic
558C2#1456383511yescharacteristic
559C2#1456384611yescharacteristic
560C2#1456391711yescharacteristic
subgroupG/H
centerC23#10597328
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1294C2
socleC23×C19#120
prime radicalC24×D19D4
cosocleC23×C4×C19C23
hypercenter#1294D19
hypocenterC19#8858
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. #14563830C2semidirect
3. #14563822C2semidirect
6. #14561514C2semidirect
7. C19×#1294C2semidirect
24. #11926267C4semidirect
230. #1294D19semidirect
352. C19#8858semidirect

Maximal subgroups

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

subgroupindex
#145662322
#145638302
#145638222
C2×#119262672
#145618812
#145615142
C19×#12942
#885819