Finite Group Databasebeta

← #18075006

Subgroups — #18075006

Order 4864.

728 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564580C211yesmaximal, characteristic, complemented
2#14564568C211yesmaximal, characteristic, complemented
3#14562335C211yesmaximal, characteristic, complemented
4#14562233C211yesmaximal, characteristic, complemented
5#14562160C211yesmaximal, characteristic, complemented
6#14562048C211yesmaximal, characteristic, complemented
7C19×#3561C211yesmaximal, characteristic
8#11926601C2211yescharacteristic
9C2×C4⋊(C19⋊C8)C2211yescharacteristic
10C2×#10597292—21no—
11C2×#10597289—21no—
12C4×#64520C2211yescharacteristic
13C4×C4⋊Dic19C2211yescharacteristic
14#11926303—22no—
15#11926290—21no—
16#11926290—21no—
17#11926284—22no—
18#11926281—21no—
19#11926278—21no—
20Q8⋊(C19⋊C8)—21no—
21D4⋊(C19⋊C8)—21no—
22C19×#563C412yescomplemented
23C19×#562C412yescomplemented
24C19×#556—21no—
25C19×#551—22no—
26D4×Q8×C19—21no—
27C19×#548—21no—
28C19×#546—21no—
29C19×#543—21no—
30C19×#542—21no—
31C19×#542—22no—
32C19×#538—21no—
33C19×#536—21no—
34C19×#533C2211yescharacteristic
35C19×#529C2211yescharacteristic
36C2×C19×#124C2211yescharacteristic
37C2×#41×C19—21no—
38C22×Q8×C19—21no—
39C22×Q8×C19D411yescharacteristic
40C22×D4×C19D411yescharacteristic
41C19×C4⋊Q8—21no—
42C19×C4⋊Q8—22no—
43C19×C4⋊Q8D411yescharacteristic
44C19×C4⋊Q8D411yescharacteristic
45C19×#126—22no—
46C19×#126—22no—
47C19×#126—22no—
48C19×#126—21no—
49C19×#125C2×C411yescharacteristic
50C19×#125C2×C412yes—
51C19×#124—21no—
52C19×#124—22no—
53C19×#124—22no—
54C19×#124—21no—
55C19×#124—21no—
56C19×#124C2×C412yes—
57C19×#124C2×C411yescharacteristic
58C19×#124D412yes—
59C19×#123—22no—
60C19×#123—22no—
61C19×#123—21no—
62C19×#123—22no—
63C19×#123—22no—
64C19×C22⋊Q8—22no—
65C19×C22⋊Q8—22no—
66C19×C22⋊Q8—21no—
67C19×C22⋊Q8—22no—
68C19×C22⋊Q8—22no—
69C19×C22⋊Q8—22no—
70C19×C22⋊Q8—21no—
71C19×C22⋊Q8—21no—
72C19×C22⋊Q8—22no—
73C19×C22⋊Q8—22no—
74C19×C22⋊Q8D411yescharacteristic
75C19×#121—21no—
76C19×#121—22no—
77C19×#121—22no—
78C19×#121D411yescharacteristic
79C19×#120—22no—
80C4×Q8×C19—21no—
81C4×Q8×C19—21no—
82C4×Q8×C19—21no—
83C4×Q8×C19D411yescharacteristic
84C4×D4×C19—22no—
85C4×D4×C19—21no—
86C4×D4×C19—22no—
87C4×D4×C19—21no—
88C4×D4×C19D411yescharacteristic
89C19×#117—22no—
90C19×#117—21no—
91C19×#117D412yes—
92C2×C22⋊C4×C19—22no—
93C2×C22⋊C4×C19—21no—
94C2×C22⋊C4×C19—21no—
95C2×C42×C19C2311yescharacteristic
96C2×C4⋊Dic19—21no—
97C2×C4×Dic19—21no—
98C2×#64520—21no—
99C22×C19⋊C8—21no—
100#10597292—42no—
101#10597289—42no—
102C19⋊#95—21no—
103C22⋊(C19⋊C8)—21no—
104C4⋊(C19⋊C8)—21no—
105C4⋊(C19⋊C8)—21no—
106C4⋊(C19⋊C8)—21no—
107#10597260—21no—
108#10597260—21no—
109C4×C19⋊C8—21no—
110C24×C19—21no—
111#41×C19—81no—
112#41×C19—81no—
113C2×Q8×C19—22no—
114C2×Q8×C19—21no—
115C2×Q8×C19—21no—
116C2×Q8×C19—21no—
117C2×Q8×C19—41no—
118C2×Q8×C19—41no—
119C2×Q8×C19—81no—
120C2×Q8×C19—81no—
121C2×Q8×C19C22⋊C411yescharacteristic
122C2×Q8×C19C22⋊C412yes—
123C2×D4×C19—21no—
124C2×D4×C19—22no—
125C2×D4×C19—22no—
126C2×D4×C19—21no—
127C2×D4×C19—41no—
128C2×D4×C19—41no—
129C2×D4×C19C22⋊C411yescharacteristic
130C2×D4×C19C22⋊C412yes—
131C22×C4×C19—22no—
132C22×C4×C19—22no—
133C22×C4×C19—22no—
134C22×C4×C19—21no—
135C22×C4×C19—21no—
136C22×C4×C19C2×D411yescharacteristic
137C22×C4×C19C2×D411yescharacteristic
138C22×C4×C19C2×D411yescharacteristic
139C22×Dic19—41no—
140C4⋊C4×C19—22no—
141C4⋊C4×C19—22no—
142C4⋊C4×C19—22no—
143C4⋊C4×C19—22no—
144C4⋊C4×C19—21no—
145C4⋊C4×C19—21no—
146C4⋊C4×C19—22no—
147C4⋊C4×C19—22no—
148C4⋊C4×C19—21no—
149C4⋊C4×C19—21no—
150C4⋊C4×C19—21no—
151C4⋊C4×C19—21no—
152C4⋊C4×C19C22⋊C412yes—
153C4⋊C4×C19C22⋊C412yes—
154C4⋊C4×C19C22⋊C411yescharacteristic
155C4⋊C4×C19C22⋊C411yescharacteristic
156C22⋊C4×C19—22no—
157C22⋊C4×C19—22no—
158C22⋊C4×C19—22no—
159C22⋊C4×C19—22no—
160C22⋊C4×C19—22no—
161C22⋊C4×C19—21no—
162C22⋊C4×C19—22no—
163C22⋊C4×C19—22no—
164C22⋊C4×C19—22no—
165C22⋊C4×C19—21no—
166C22⋊C4×C19—21no—
167C22⋊C4×C19—22no—
168C22⋊C4×C19—22no—
169C22⋊C4×C19—21no—
170C22⋊C4×C19—21no—
171C42×C19—22no—
172C42×C19—22no—
173C42×C19—21no—
174C42×C19C22×C411yescharacteristic
175C42×C19C2×D411yescharacteristic
176C42×C19C2×D411yescharacteristic
177C42×C19C2×D411yescharacteristic
178C4⋊Dic19—22no—
179C4⋊Dic19—41no—
180C4×Dic19—42no—
181#64520—22no—
182#64520—41no—
183C2×C19⋊C8—41no—
184C2×C19⋊C8—41no—
185C2×C19⋊C8—41no—
186C2×C19⋊C8—41no—
187C2×C19⋊C8—41no—
188#8511—191nomaximal, Sylow
189C23×C19—22no—
190C23×C19—21no—
191C23×C19—41no—
192C23×C19—41no—
193C23×C19—81no—
194C23×C19—81no—
195C23×C19#12011yescharacteristic
196Q8×C19—42no—
197Q8×C19—41no—
198Q8×C19—41no—
199Q8×C19—41no—
200Q8×C19—41no—
201Q8×C19—41no—
202Q8×C19—81no—
203Q8×C19—82no—
204D4×C19—42no—
205D4×C19—41no—
206D4×C19—41no—
207D4×C19—41no—
208D4×C19—41no—
209D4×C19—41no—
210D4×C19—82no—
211D4×C19—82no—
212C2×C4×C19—21no—
213C2×C4×C19—21no—
214C2×C4×C19—21no—
215C2×C4×C19—21no—
216C2×C4×C19—21no—
217C2×C4×C19—22no—
218C2×C4×C19—21no—
219C2×C4×C19—22no—
220C2×C4×C19—22no—
221C2×C4×C19—21no—
222C2×C4×C19—41no—
223C2×C4×C19—41no—
224C2×C4×C19—41no—
225C2×C4×C19—81no—
226C2×C4×C19—82no—
227C2×C4×C19—82no—
228C2×C4×C19—82no—
229C2×C4×C19C2×C22⋊C411yescharacteristic
230C2×C4×C19C2×C22⋊C411yescharacteristic
231C2×C4×C19C2×C22⋊C411yescharacteristic
232C2×C4×C19#12011yescharacteristic
233C2×C4×C19#12011yescharacteristic
234C2×C4×C19#12011yescharacteristic
235C2×Dic19—42no—
236C2×Dic19—81no—
237C2×Dic19—81no—
238C19⋊C8—42no—
239C19⋊C8—81no—
240C19⋊C8—81no—
241#3561D1911yescharacteristic
242#1986—191no—
243#1983—191no—
244#1552—191no—
245#1527—191no—
246#1509—191no—
247#1483—191no—
248C22×C19—21no—
249C22×C19—21no—
250C22×C19—41no—
251C22×C19—42no—
252C22×C19—41no—
253C22×C19—42no—
254C22×C19—42no—
255C22×C19—41no—
256C22×C19—161no—
257C22×C19—161no—
258C22×C19#37911yescharacteristic
259C22×C19#45411yescharacteristic
260C22×C19#45611yescharacteristic
261C4×C19—21no—
262C4×C19—21no—
263C4×C19—21no—
264C4×C19—21no—
265C4×C19—21no—
266C4×C19—41no—
267C4×C19—42no—
268C4×C19—42no—
269C4×C19—41no—
270C4×C19—41no—
271C4×C19—42no—
272C4×C19#45311yescharacteristic
273C4×C19#45511yescharacteristic
274Dic19—82no—
275#563Dic1912yescomplemented
276#562Dic1912yescomplemented
277#556—21no—
278#551—22no—
279D4×Q8—21no—
280#548—21no—
281#546—21no—
282#543—21no—
283#542—21no—
284#542—22no—
285#538—21no—
286#536—21no—
287#533C2×D1911yescharacteristic
288#529C2×D1911yescharacteristic
289C2×#124C2×D1911yescharacteristic
290#432—191no—
291C2×C4⋊C8—191no—
292C2×#103—381no—
293C2×#102—381no—
294C4×M16—191no—
295C4×C4⋊C4—191no—
296#339—382no—
297#332—381no—
298#332—381no—
299#329—382no—
300#328—381no—
301#327—381no—
302Q8⋊C8—381no—
303D4⋊C8—381no—
304C2×C19—21no—
305C2×C19—21no—
306C2×C19—81no—
307C2×C19—82no—
308C2×C19#179211yescharacteristic
309C2×C19#179311yescharacteristic
310C2×C19#179411yescharacteristic
311C2×#41—21no—
312C22×Q8—21no—
313C22×Q8C22⋊D1911yescharacteristic
314C22×D4C22⋊D1911yescharacteristic
315C2×M16—381no—
316C22×C8—381no—
317C4⋊Q8—21no—
318C4⋊Q8—22no—
319C4⋊Q8C22⋊D1911yescharacteristic
320C4⋊Q8C22⋊D1911yescharacteristic
321#126—22no—
322#126—22no—
323#126—22no—
324#126—21no—
325#125C2×Dic1911yescharacteristic
326#125C2×Dic1912yes—
327#124—21no—
328#124—22no—
329#124—22no—
330#124—21no—
331#124—21no—
332#124C2×Dic1912yes—
333#124C2×Dic1911yescharacteristic
334#124C22⋊D1912yes—
335#123—22no—
336#123—22no—
337#123—21no—
338#123—22no—
339#123—22no—
340C22⋊Q8—22no—
341C22⋊Q8—22no—
342C22⋊Q8—21no—
343C22⋊Q8—22no—
344C22⋊Q8—22no—
345C22⋊Q8—22no—
346C22⋊Q8—21no—
347C22⋊Q8—21no—
348C22⋊Q8—22no—
349C22⋊Q8—22no—
350C22⋊Q8C22⋊D1911yescharacteristic
351#121—21no—
352#121—22no—
353#121—22no—
354#121C22⋊D1911yescharacteristic
355#120—22no—
356C4×Q8—21no—
357C4×Q8—21no—
358C4×Q8—21no—
359C4×Q8C22⋊D1911yescharacteristic
360C4×D4—22no—
361C4×D4—21no—
362C4×D4—22no—
363C4×D4—21no—
364C4×D4C22⋊D1911yescharacteristic
365#117—22no—
366#117—21no—
367#117C22⋊D1912yes—
368C2×C4⋊C4—381no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C42—381no—
373C2×C42C22×D1911yescharacteristic
374C4⋊C8—381no—
375C4⋊C8—381no—
376C4⋊C8—381no—
377#103—762no—
378#102—762no—
379C22⋊C8—381no—
380#97—381no—
381#97—381no—
382C4×C8—381no—
383#95—381no—
384C19#851111yescharacteristic, complemented, Sylow
385C24—21no—
386#41—81no—
387#41—81no—
388C2×Q8—22no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—41no—
393C2×Q8—41no—
394C2×Q8—81no—
395C2×Q8—81no—
396C2×Q8C22⋊Dic1911yescharacteristic
397C2×Q8C22⋊Dic1912yes—
398C2×D4—21no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—21no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4C22⋊Dic1911yescharacteristic
405C2×D4C22⋊Dic1912yes—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—761no—
412C22×C4C2×C22⋊D1911yescharacteristic
413C22×C4C2×C22⋊D1911yescharacteristic
414C22×C4C2×C22⋊D1911yescharacteristic
415M16—382no—
416M16—761no—
417C2×C8—761no—
418C2×C8—761no—
419C2×C8—761no—
420C2×C8—761no—
421C2×C8—761no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—382no—
435C4⋊C4—761no—
436C4⋊C4C22⋊Dic1912yes—
437C4⋊C4C22⋊Dic1912yes—
438C4⋊C4C22⋊Dic1911yescharacteristic
439C4⋊C4C22⋊Dic1911yescharacteristic
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—21no—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—21no—
450C22⋊C4—21no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—21no—
454C22⋊C4—21no—
455C42—22no—
456C42—22no—
457C42—21no—
458C42—762no—
459C42C22×Dic1911yescharacteristic
460C42C2×C22⋊D1911yescharacteristic
461C42C2×C22⋊D1911yescharacteristic
462C42C2×C22⋊D1911yescharacteristic
463C23—22no—
464C23—21no—
465C23—41no—
466C23—41no—
467C23—81no—
468C23—81no—
469C23#1059739911yescharacteristic
470Q8—42no—
471Q8—41no—
472Q8—41no—
473Q8—41no—
474Q8—41no—
475Q8—41no—
476Q8—81no—
477Q8—82no—
478D4—42no—
479D4—41no—
480D4—41no—
481D4—41no—
482D4—41no—
483D4—41no—
484D4—82no—
485D4—82no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—22no—
492C2×C4—21no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—21no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—81no—
500C2×C4—82no—
501C2×C4—82no—
502C2×C4—82no—
503C2×C4—762no—
504C2×C4—1521no—
505C2×C4—1521no—
506C2×C4C2×C22⋊Dic1911yescharacteristic
507C2×C4C2×C22⋊Dic1911yescharacteristic
508C2×C4C2×C22⋊Dic1911yescharacteristic
509C2×C4#1059739911yescharacteristic
510C2×C4#1059739911yescharacteristic
511C2×C4#1059739911yescharacteristic
512C8—762no—
513C8—1521no—
514C8—1521no—
515C22—21no—
516C22—21no—
517C22—41no—
518C22—42no—
519C22—41no—
520C22—42no—
521C22—42no—
522C22—41no—
523C22—161no—
524C22—161no—
525C22#1192640011yescharacteristic
526C22#1192671711yescharacteristic
527C22#1192672711yescharacteristic
528C4—21no—
529C4—21no—
530C4—21no—
531C4—21no—
532C4—21no—
533C4—41no—
534C4—42no—
535C4—42no—
536C4—41no—
537C4—41no—
538C4—42no—
539C4—1522no—
540C4#1192671211yescharacteristic
541C4#1192672211yescharacteristic
542C2—21no—
543C2—21no—
544C2—82no—
545C2—81no—
546C2#1456358911yescharacteristic
547C2#1456359411yescharacteristic
548C2#1456359911yescharacteristic
subgroupG/H
centerC22#11926400
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
Fitting, prime radicalC19×#3561C2
socleC22×C19#379
cosocleC2×C42×C19C23
hypercenter#3561D19
hypocenterC19#8511
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3561

Complements

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

NH ≅ G/Ntype
1. #14564580C2semidirect
2. #14564568C2semidirect
3. #14562335C2semidirect
4. #14562233C2semidirect
5. #14562160C2semidirect
6. #14562048C2semidirect
22. C19×#563C4semidirect
23. C19×#562C4semidirect
275. #563Dic19semidirect
276. #562Dic19semidirect
384. C19#8511semidirect

Maximal subgroups

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

subgroupindex
#145645802
#145645682
#145623352
#145622332
#145621602
#145620482
C19×#35612
#851119