Finite Group Databasebeta

← #18083267

Subgroups — #18083267

Order 4864.

686 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 686 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573631C211yesmaximal, characteristic, complemented
2#14568532C211yesmaximal, characteristic, complemented
3#14562195C211yesmaximal, characteristic, complemented
4#14562059C211yesmaximal, characteristic, complemented
5#14562026C211yesmaximal, characteristic, complemented
6#14561495C211yesmaximal, characteristic, complemented
7C19×#3036C211yesmaximal, characteristic, complemented
8C2×#10597384—21no—
9C2×C4×D76C2211yescharacteristic
10#11926855—21no—
11#11926821—21no—
12#11926736—21no—
13#11926677—21no—
14C4×#64525—22no—
15#11926597C2211yescharacteristic
16#11926597C2211yescharacteristic
17#11926469—21no—
18#11926453—21no—
19#11926423—22no—
20#11926410C2211yescharacteristic
21#11926401—21no—
22#11926278—22no—
23D4⋊(C19⋊C8)—22no—
24#11926271—22no—
25C2×C19×AGL(1,ℤ/8)—21no—
26C19×#532C2211yescharacteristic
27C2×C4×D4×C19C2211yescharacteristic
28C19×#463—22no—
29C19×#461—21no—
30C19×#459—21no—
31C19×#423C2211yescharacteristic
32C19×#417—21no—
33C2×#41×C19—21no—
34C22×D4×C19D411yescharacteristic
35C23×C4×C19—21no—
36C22×C22⋊D19—22no—
37C22×D76D411yescharacteristic
38C22×C4×D19—21no—
39C19×AGL(1,ℤ/8)—42no—
40C19×AGL(1,ℤ/8)—42no—
41C2×SD16×C19—22no—
42C2×D8×C19—22no—
43C2×M16×C19—21no—
44C19×C4⋊Q8D411yescharacteristic, complemented
45C19×#127D411yescharacteristic, complemented
46C19×#124—21no—
47C19×#121—21no—
48C19×#121—21no—
49C4×D4×C19—21no—
50C4×D4×C19—21no—
51C4×D4×C19—21no—
52C4×D4×C19—21no—
53C4×D4×C19—21no—
54C4×D4×C19—21no—
55C2×C4⋊C4×C19D411yescharacteristic
56C2×C22⋊C4×C19—21no—
57C2×C42×C19C2311yescharacteristic
58C2×C22⋊Dic19—22no—
59#10597384—42no—
60#10597384—42no—
61C2×#64525—22no—
62C2×(C2×D19)⋊C4—21no—
63C2×(C2×D19)⋊C4—22no—
64C2×C4⋊Dic19—21no—
65C2×C4⋊Dic19D411yescharacteristic
66C4×D76—21no—
67C4×D76—21no—
68C4×D76—21no—
69C4×D76—21no—
70C19×C4⋊C8—21no—
71C19×C4⋊C8D412yescomplemented
72C19×#103—22no—
73C19×#102—22no—
74#10597289—22no—
75C19⋊#95—22no—
76C19⋊#95—21no—
77C19⋊#95D412yes—
78C22⋊(C19⋊C8)—21no—
79C22⋊(C19⋊C8)—21no—
80#10597266—22no—
81#10597264—22no—
82C4⋊(C19⋊C8)—21no—
83C4⋊(C19⋊C8)—21no—
84C4×C19⋊C8—21no—
85C4×C19⋊C8D412yescomplemented
86C24×C19—21no—
87C23×D19—21no—
88#41×C19—41no—
89#41×C19—41no—
90#41×C19—41no—
91#41×C19—41no—
92C2×Q8×C19—21no—
93C2×D4×C19—21no—
94C2×D4×C19—21no—
95C2×D4×C19—21no—
96C2×D4×C19—21no—
97C2×D4×C19—21no—
98C2×D4×C19—21no—
99C2×D4×C19—21no—
100C2×D4×C19—21no—
101C2×D4×C19—41no—
102C2×D4×C19D812yescomplemented
103C22×C4×C19—21no—
104C22×C4×C19—41no—
105C22×C4×C19—41no—
106C22×C4×C19—41no—
107C22×C4×C19—82no—
108C22×C4×C19C2×D411yescharacteristic
109C22×C4×C19C2×D411yescharacteristic
110C22×C4×C19C2×D411yescharacteristic
111C2×C22⋊D19—44no—
112C2×C22⋊D19—44no—
113C2×C22⋊D19—82no—
114C22×Dic19—21no—
115C22×Dic19—22no—
116C2×D76—21no—
117C2×D76—21no—
118C2×D76—42no—
119C2×C4×D19—41no—
120C2×C4×D19—41no—
121C2×C4×D19—41no—
122C2×C4×D19—41no—
123C2×C4×D19—41no—
124C2×C4×D19—41no—
125SD16×C19—44no—
126D8×C19—44no—
127M16×C19—41no—
128M16×C19—41no—
129C2×C8×C19—22no—
130C4⋊C4×C19—21no—
131C4⋊C4×C19—21no—
132C4⋊C4×C19—21no—
133C4⋊C4×C19—21no—
134C22⋊C4×C19—41no—
135C22⋊C4×C19—41no—
136C22⋊C4×C19—41no—
137C22⋊C4×C19—41no—
138C42×C19C2×D411yescharacteristic
139C42×C19C2×D411yescharacteristic
140C42×C19C2×D411yescharacteristic
141C42×C19#4111yescharacteristic
142C22⋊Dic19—44no—
143#64525—44no—
144(C2×D19)⋊C4—41no—
145(C2×D19)⋊C4—41no—
146(C2×D19)⋊C4—82no—
147C4⋊Dic19—21no—
148C4⋊Dic19—21no—
149C4⋊Dic19—41no—
150C4⋊Dic19—41no—
151C2×C19⋊C8—22no—
152C2×C19⋊C8—41no—
153#9996—191nomaximal, Sylow
154C23×C19—22no—
155C23×C19—42no—
156C23×C19—42no—
157C23×C19—41no—
158C23×C19—41no—
159C23×C19—41no—
160C23×C19#12011yescharacteristic
161C22×D19—22no—
162C22×D19—41no—
163C22×D19—41no—
164C22×D19—41no—
165C22×D19—41no—
166C22×D19—41no—
167C22×D19—41no—
168Q8×C19—41no—
169Q8×C19—41no—
170D4×C19—22no—
171D4×C19—22no—
172D4×C19—42no—
173D4×C19—41no—
174D4×C19—41no—
175D4×C19—41no—
176D4×C19—41no—
177D4×C19—81no—
178D4×C19—81no—
179D4×C19—81no—
180C2×C4×C19—41no—
181C2×C4×C19—41no—
182C2×C4×C19—42no—
183C2×C4×C19—41no—
184C2×C4×C19—41no—
185C2×C4×C19—82no—
186C2×C4×C19—82no—
187C2×C4×C19—81no—
188C2×C4×C19—81no—
189C2×C4×C19#12011yescharacteristic
190C2×C4×C19#12011yescharacteristic
191C2×C4×C19#12111yescharacteristic
192C2×C4×C19#12111yescharacteristic
193C2×C4×C19#12111yescharacteristic
194C2×C4×C19#12711yescharacteristic
195C2×C4×C19C2×D811yescharacteristic
196C2×C4×C19#13511yescharacteristic
197C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
198C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
199C22⋊D19—88no—
200C2×Dic19—42no—
201C2×Dic19—42no—
202C2×Dic19—41no—
203C2×Dic19—42no—
204C2×Dic19—41no—
205C2×Dic19—41no—
206D76—22no—
207D76—22no—
208D76—41no—
209D76—41no—
210C4×D19—81no—
211C4×D19—81no—
212C4×D19—81no—
213C4×D19—81no—
214C8×C19—42no—
215C19⋊C8—42no—
216C19⋊C8—81no—
217#3100—191no—
218#3036D1911yescharacteristic, complemented
219#2535—191no—
220#1517—191no—
221#1486—191no—
222#1478—191no—
223#1286—191no—
224C22×C19—21no—
225C22×C19—21no—
226C22×C19—44no—
227C22×C19—42no—
228C22×C19—82no—
229C22×C19—81no—
230C22×C19—81no—
231C22×C19—81no—
232C22×C19—81no—
233C22×C19—81no—
234C22×C19#39211yescharacteristic
235C22×C19#44711yescharacteristic
236C22×C19#44911yescharacteristic
237C2×D19—42no—
238C2×D19—42no—
239C2×D19—42no—
240C2×D19—81no—
241C2×D19—81no—
242C2×D19—81no—
243C2×D19—81no—
244C4×C19—21no—
245C4×C19—21no—
246C4×C19—21no—
247C4×C19—21no—
248C4×C19—81no—
249C4×C19—81no—
250C4×C19#44711yescharacteristic
251C4×C19#44911yescharacteristic
252C4×C19#46611yescharacteristic
253C4×C19#46911yescharacteristic
254Dic19—82no—
255Dic19—81no—
256C2×AGL(1,ℤ/8)—21no—
257#532C2×D1911yescharacteristic
258C2×#121—381no—
259C2×C4×D4—191no—
260C2×C4×D4C2×D1911yescharacteristic
261#480—381no—
262#474—381no—
263#463—22no—
264#461—21no—
265#459—21no—
266#459—381no—
267#447—381no—
268C4×D8—382no—
269#431—191no—
270#431—191no—
271#423C2×D1911yescharacteristic
272#417—21no—
273#397—381no—
274#392—381no—
275#386—382no—
276#382—191no—
277#380—381no—
278#327—382no—
279D4⋊C8—382no—
280D4⋊C8—382no—
281C2×C19—21no—
282C2×C19—21no—
283C2×C19—82no—
284C2×C19—161no—
285C2×C19#199911yescharacteristic
286C2×C19#200811yescharacteristic
287C2×C19#201011yescharacteristic
288D19—82no—
289C2×#41—21no—
290C22×D4—191no—
291C22×D4—382no—
292C22×D4C22⋊D1911yescharacteristic
293C23×C4—21no—
294C23×C4—381no—
295AGL(1,ℤ/8)—42no—
296AGL(1,ℤ/8)—42no—
297C2×SD16—22no—
298C2×D8—22no—
299C2×D8—382no—
300C2×M16—21no—
301C4⋊Q8C22⋊D1911yescharacteristic, complemented
302#127C22⋊D1911yescharacteristic, complemented
303#124—21no—
304#121—21no—
305#121—21no—
306#121—762no—
307#121—762no—
308C4×D4—21no—
309C4×D4—21no—
310C4×D4—21no—
311C4×D4—21no—
312C4×D4—21no—
313C4×D4—21no—
314C4×D4—381no—
315C4×D4—381no—
316C4×D4—381no—
317C4×D4—381no—
318C2×C4⋊C4—191no—
319C2×C4⋊C4—381no—
320C2×C4⋊C4C22⋊D1911yescharacteristic
321C2×C22⋊C4—21no—
322C2×C22⋊C4—382no—
323C2×C22⋊C4—381no—
324C2×C22⋊C4—382no—
325C2×C42C22×D1911yescharacteristic
326#107—382no—
327C4⋊C8—21no—
328C4⋊C8—381no—
329C4⋊C8—381no—
330C4⋊C8C22⋊D1912yescomplemented
331#103—22no—
332#102—22no—
333#102—382no—
334#102—382no—
335C22⋊C8—381no—
336C22⋊C8—381no—
337C4×C8—192no—
338C4×C8—381no—
339#95—192no—
340#95—382no—
341#95—381no—
342C19#999611yescharacteristic, complemented, Sylow
343C24—21no—
344C24—381no—
345#41—41no—
346#41—41no—
347#41—41no—
348#41—41no—
349C2×Q8—21no—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—41no—
359C2×D4—381no—
360C2×D4—381no—
361C2×D4—762no—
362C2×D4—764no—
363C2×D4—764no—
364C2×D4—1522no—
365C2×D4#6452512yescomplemented
366C22×C4—21no—
367C22×C4—41no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—82no—
371C22×C4—382no—
372C22×C4—381no—
373C22×C4—761no—
374C22×C4—761no—
375C22×C4—761no—
376C22×C4—761no—
377C22×C4—761no—
378C22×C4—761no—
379C22×C4D4×D1911yescharacteristic
380C22×C4D4×D1911yescharacteristic
381C22×C4C2×C22⋊D1911yescharacteristic
382SD16—44no—
383D8—44no—
384D8—764no—
385M16—41no—
386M16—41no—
387C2×C8—22no—
388C2×C8—382no—
389C2×C8—761no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—381no—
395C4⋊C4—381no—
396C4⋊C4—761no—
397C4⋊C4—761no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—41no—
402C22⋊C4—764no—
403C22⋊C4—761no—
404C22⋊C4—761no—
405C22⋊C4—1522no—
406C42D4×D1911yescharacteristic
407C42#6454311yescharacteristic
408C42C2×C22⋊D1911yescharacteristic
409C42C2×C22⋊D1911yescharacteristic
410C23—22no—
411C23—42no—
412C23—42no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—382no—
417C23—761no—
418C23—761no—
419C23—761no—
420C23—761no—
421C23—761no—
422C23—761no—
423C23#1059738311yescharacteristic
424Q8—41no—
425Q8—41no—
426D4—22no—
427D4—22no—
428D4—42no—
429D4—41no—
430D4—41no—
431D4—41no—
432D4—41no—
433D4—81no—
434D4—81no—
435D4—81no—
436D4—382no—
437D4—382no—
438D4—761no—
439D4—761no—
440D4—1528no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—82no—
447C2×C4—82no—
448C2×C4—81no—
449C2×C4—81no—
450C2×C4—762no—
451C2×C4—762no—
452C2×C4—761no—
453C2×C4—762no—
454C2×C4—761no—
455C2×C4—761no—
456C2×C4—1521no—
457C2×C4—1521no—
458C2×C4—1521no—
459C2×C4—1521no—
460C2×C4C2×#6452511yescharacteristic
461C2×C4#1059737811yescharacteristic
462C2×C4#1059738311yescharacteristic
463C2×C4#1059738411yescharacteristic
464C2×C4#1059738511yescharacteristic
465C2×C4#1059738511yescharacteristic
466C2×C4#1059738611yescharacteristic
467C2×C4#1059739511yescharacteristic
468C2×C4#1059739611yescharacteristic
469C2×C4#1059739911yescharacteristic
470C8—42no—
471C8—762no—
472C8—1521no—
473C22—21no—
474C22—21no—
475C22—44no—
476C22—42no—
477C22—82no—
478C22—81no—
479C22—81no—
480C22—81no—
481C22—81no—
482C22—81no—
483C22—762no—
484C22—762no—
485C22—762no—
486C22—1521no—
487C22—1521no—
488C22—1521no—
489C22—1521no—
490C22#1192645211yescharacteristic
491C22#1192667711yescharacteristic
492C22#1192668711yescharacteristic
493C4—21no—
494C4—21no—
495C4—21no—
496C4—21no—
497C4—81no—
498C4—81no—
499C4—1522no—
500C4—1521no—
501C4#1192667811yescharacteristic
502C4#1192668911yescharacteristic
503C4#1192677811yescharacteristic
504C4#1192679511yescharacteristic
505C2—21no—
506C2—21no—
507C2—82no—
508C2—161no—
509C2—1522no—
510C2#1456463111yescharacteristic
511C2#1456468611yescharacteristic
512C2#1456469911yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#3036C2
socleC22×C19#392
hypercenter#3036D19
hypocenterC19#9996
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3036

Complements

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

NH ≅ G/Ntype
1. #14573631C2semidirect
2. #14568532C2semidirect
3. #14562195C2semidirect
4. #14562059C2semidirect
5. #14562026C2semidirect
6. #14561495C2semidirect
7. C19×#3036C2semidirect
44. C19×C4⋊Q8D4semidirect
45. C19×#127D4semidirect
71. C19×C4⋊C8D4semidirect
85. C4×C19⋊C8D4semidirect
102. C2×D4×C19D8semidirect
218. #3036D19semidirect
301. C4⋊Q8C22⋊D19semidirect
302. #127C22⋊D19semidirect
330. C4⋊C8C22⋊D19semidirect
342. C19#9996semidirect
365. C2×D4#64525semidirect

Maximal subgroups

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

subgroupindex
#145736312
#145685322
#145621952
#145620592
#145620262
#145614952
C19×#30362
#999619