Finite Group Databasebeta

← #18074407

Subgroups — #18074407

Order 4864.

758 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14563445C211yesmaximal, characteristic, complemented
2#14562242C211yesmaximal, characteristic, complemented
3#14562143C211yesmaximal, characteristic, complemented
4#14562121C211yesmaximal, characteristic, complemented
5#14562069C211yesmaximal, characteristic, complemented
6#14562052C211yesmaximal, characteristic, complemented
7C19×#3517C211yesmaximal, characteristic
8#11926601C2211yescharacteristic
9#11926597C2211yescharacteristic
10C2×#10597294—21no—
11C4×#64520C2211yescharacteristic
12#11926390C2211yescharacteristic
13#11926303—21no—
14#11926286—21no—
15#11926284—21no—
16#11926281—21no—
17#11926278—21no—
18#11926278—22no—
19Q8⋊(C19⋊C8)—21no—
20D4⋊(C19⋊C8)—22no—
21D4⋊(C19⋊C8)—21no—
22C19×#557C411yescharacteristic, complemented
23C19×#553—22no—
24C19×#553—21no—
25C19×#550—21no—
26C19×#550—21no—
27C19×#550C411yescharacteristic, complemented
28C19×#550C411yescharacteristic, complemented
29C19×#547—21no—
30C19×#547C411yescharacteristic, complemented
31C19×#540—22no—
32C19×#540—21no—
33C19×#532—21no—
34C19×#532C2211yescharacteristic
35C19×#529—21no—
36C19×#529C2211yescharacteristic
37C19×#520—21no—
38C4×#41×C19C2211yescharacteristic
39C2×#41×C19—21no—
40C2×#41×C19—21no—
41C2×#41×C19—21no—
42C2×#41×C19—21no—
43C2×#41×C19D411yescharacteristic
44C19×C4⋊Q8—21no—
45C19×C4⋊Q8C2×C411yescharacteristic
46C19×#127—22no—
47C19×#127—21no—
48C19×#127—21no—
49C19×#127C2×C411yescharacteristic
50C19×#126—22no—
51C19×#126—21no—
52C19×#125—22no—
53C19×#125—21no—
54C19×#125D411yescharacteristic
55C19×#124—21no—
56C19×#124D411yescharacteristic
57C19×#123—22no—
58C19×#123—22no—
59C19×#123—22no—
60C19×#123—21no—
61C19×#123—22no—
62C19×C22⋊Q8—21no—
63C19×C22⋊Q8D411yescharacteristic
64C19×#121—22no—
65C19×#121—22no—
66C19×#121—22no—
67C19×#121—22no—
68C19×#121—22no—
69C19×#121—21no—
70C19×#121—22no—
71C19×#121—22no—
72C19×#121—21no—
73C19×#121—21no—
74C19×#121—21no—
75C19×#121D411yescharacteristic
76C19×#121D412yes—
77C4×Q8×C19—21no—
78C4×Q8×C19—21no—
79C4×Q8×C19C2×C411yescharacteristic
80C4×Q8×C19C2×C411yescharacteristic
81C4×Q8×C19D411yescharacteristic
82C4×D4×C19—22no—
83C4×D4×C19—22no—
84C4×D4×C19—22no—
85C4×D4×C19—22no—
86C4×D4×C19—21no—
87C4×D4×C19—21no—
88C4×D4×C19—21no—
89C4×D4×C19—21no—
90C4×D4×C19—21no—
91C4×D4×C19—21no—
92C4×D4×C19C2×C411yescharacteristic
93C4×D4×C19C2×C411yescharacteristic
94C4×D4×C19D411yescharacteristic
95C4×D4×C19D412yes—
96C19×#117—22no—
97C19×#117—21no—
98C19×#117—21no—
99C19×#117D411yescharacteristic
100C2×C4⋊C4×C19—22no—
101C2×C4⋊C4×C19—21no—
102C2×C42×C19—21no—
103C2×C42×C19C2311yescharacteristic
104C2×C4×Dic19—21no—
105C2×#64520—21no—
106#10597294—24no—
107C19⋊#95—21no—
108C19⋊#95—21no—
109C22⋊(C19⋊C8)—21no—
110C22⋊(C19⋊C8)—21no—
111C4⋊(C19⋊C8)—21no—
112C4⋊(C19⋊C8)—21no—
113#10597260—21no—
114#10597260—21no—
115C4×C19⋊C8—21no—
116C4×C19⋊C8—21no—
117#41×C19—22no—
118#41×C19—41no—
119#41×C19—42no—
120#41×C19—42no—
121#41×C19—82no—
122#41×C19—82no—
123#41×C19—82no—
124C2×Q8×C19—21no—
125C2×Q8×C19C22⋊C411yescharacteristic
126C2×Q8×C19C22⋊C411yescharacteristic
127C2×D4×C19—22no—
128C2×D4×C19—21no—
129C2×D4×C19—22no—
130C2×D4×C19—22no—
131C2×D4×C19—22no—
132C2×D4×C19—22no—
133C2×D4×C19—21no—
134C2×D4×C19—22no—
135C2×D4×C19—21no—
136C2×D4×C19—21no—
137C2×D4×C19C22⋊C411yescharacteristic
138C2×D4×C19C22⋊C411yescharacteristic
139C2×D4×C19C22⋊C412yes—
140C22×C4×C19—22no—
141C22×C4×C19—22no—
142C22×C4×C19—22no—
143C22×C4×C19—21no—
144C22×C4×C19—21no—
145C22×C4×C19—21no—
146C22×C4×C19—21no—
147C22×C4×C19—22no—
148C22×C4×C19C2×D411yescharacteristic
149C22×C4×C19C2×D411yescharacteristic
150C22×C4×C19C2×D411yescharacteristic
151C22×Dic19—41no—
152C4⋊C4×C19—22no—
153C4⋊C4×C19—22no—
154C4⋊C4×C19—22no—
155C4⋊C4×C19—22no—
156C4⋊C4×C19—21no—
157C4⋊C4×C19—21no—
158C4⋊C4×C19—21no—
159C4⋊C4×C19—21no—
160C4⋊C4×C19—21no—
161C4⋊C4×C19—21no—
162C4⋊C4×C19—21no—
163C4⋊C4×C19C22⋊C411yescharacteristic
164C4⋊C4×C19C22⋊C411yescharacteristic
165C4⋊C4×C19C22⋊C411yescharacteristic
166C4⋊C4×C19C22⋊C412yes—
167C4⋊C4×C19C22⋊C411yescharacteristic
168C22⋊C4×C19—22no—
169C22⋊C4×C19—22no—
170C22⋊C4×C19—22no—
171C22⋊C4×C19—21no—
172C22⋊C4×C19—21no—
173C22⋊C4×C19—21no—
174C22⋊C4×C19—21no—
175C22⋊C4×C19—21no—
176C22⋊C4×C19—21no—
177C22⋊C4×C19—22no—
178C22⋊C4×C19—21no—
179C22⋊C4×C19—21no—
180C22⋊C4×C19—22no—
181C42×C19—22no—
182C42×C19—21no—
183C42×C19—21no—
184C42×C19—21no—
185C42×C19—21no—
186C42×C19C22×C411yescharacteristic
187C42×C19C2×D411yescharacteristic
188C42×C19C2×D411yescharacteristic
189C42×C19C2×D411yescharacteristic
190C4×Dic19—22no—
191C4×Dic19—41no—
192#64520—22no—
193#64520—41no—
194C2×C19⋊C8—41no—
195C2×C19⋊C8—41no—
196C2×C19⋊C8—41no—
197#8414—191nomaximal, Sylow
198C23×C19—21no—
199C23×C19—22no—
200C23×C19—21no—
201C23×C19#12011yescharacteristic
202Q8×C19—21no—
203Q8×C19—41no—
204Q8×C19—42no—
205Q8×C19#10412yes—
206D4×C19—21no—
207D4×C19—21no—
208D4×C19—42no—
209D4×C19—42no—
210D4×C19—41no—
211D4×C19—44no—
212D4×C19—42no—
213D4×C19—41no—
214D4×C19—41no—
215D4×C19—81no—
216D4×C19—82no—
217D4×C19—82no—
218D4×C19—82no—
219D4×C19—82no—
220D4×C19—82no—
221C2×C4×C19—21no—
222C2×C4×C19—21no—
223C2×C4×C19—21no—
224C2×C4×C19—21no—
225C2×C4×C19—21no—
226C2×C4×C19—21no—
227C2×C4×C19—21no—
228C2×C4×C19—22no—
229C2×C4×C19—21no—
230C2×C4×C19—41no—
231C2×C4×C19—41no—
232C2×C4×C19—42no—
233C2×C4×C19—44no—
234C2×C4×C19—42no—
235C2×C4×C19—41no—
236C2×C4×C19—41no—
237C2×C4×C19—81no—
238C2×C4×C19—82no—
239C2×C4×C19—82no—
240C2×C4×C19—82no—
241C2×C4×C19C2×C22⋊C411yescharacteristic
242C2×C4×C19C2×C22⋊C411yescharacteristic
243C2×C4×C19C2×C22⋊C411yescharacteristic
244C2×C4×C19#12011yescharacteristic
245C2×C4×C19#12011yescharacteristic
246C2×C4×C19#12011yescharacteristic
247C2×Dic19—42no—
248C2×Dic19—81no—
249C2×Dic19—81no—
250C19⋊C8—42no—
251C19⋊C8—81no—
252C19⋊C8—81no—
253#3517D1911yescharacteristic
254#1759—191no—
255#1529—191no—
256#1505—191no—
257#1500—191no—
258#1488—191no—
259#1484—191no—
260C22×C19—21no—
261C22×C19—21no—
262C22×C19—21no—
263C22×C19—41no—
264C22×C19—42no—
265C22×C19—41no—
266C22×C19—41no—
267C22×C19—42no—
268C22×C19—41no—
269C22×C19—41no—
270C22×C19—42no—
271C22×C19—41no—
272C22×C19#37911yescharacteristic
273C4×C19—21no—
274C4×C19—21no—
275C4×C19—21no—
276C4×C19—21no—
277C4×C19—21no—
278C4×C19—22no—
279C4×C19—41no—
280C4×C19—41no—
281C4×C19—41no—
282C4×C19—41no—
283C4×C19—42no—
284C4×C19—41no—
285C4×C19C2×#10411yescharacteristic
286C4×C19#42111yescharacteristic
287Dic19—82no—
288#557Dic1911yescharacteristic, complemented
289#553—22no—
290#553—21no—
291#550—21no—
292#550—21no—
293#550Dic1911yescharacteristic, complemented
294#550Dic1911yescharacteristic, complemented
295#547—21no—
296#547Dic1911yescharacteristic, complemented
297#540—22no—
298#540—21no—
299#532—21no—
300#532C2×D1911yescharacteristic
301#529—21no—
302#529C2×D1911yescharacteristic
303#520—21no—
304C4×#41C2×D1911yescharacteristic
305#432—191no—
306#431—191no—
307C2×#104—381no—
308C4×M16—191no—
309#376—191no—
310#339—381no—
311#330—381no—
312#329—381no—
313#328—381no—
314#327—381no—
315#327—382no—
316Q8⋊C8—381no—
317D4⋊C8—382no—
318D4⋊C8—381no—
319C2×C19—41no—
320C2×C19—81no—
321C2×C19—82no—
322C2×C19—81no—
323C2×C19#178911yescharacteristic
324C2×C19#179411yescharacteristic
325C2×C19#179511yescharacteristic
326C2×#41—21no—
327C2×#41—21no—
328C2×#41—21no—
329C2×#41—21no—
330C2×#41C22⋊D1911yescharacteristic
331C2×M16—381no—
332C4⋊Q8—21no—
333C4⋊Q8C2×Dic1911yescharacteristic
334#127—22no—
335#127—21no—
336#127—21no—
337#127C2×Dic1911yescharacteristic
338#126—22no—
339#126—21no—
340#125—22no—
341#125—21no—
342#125C22⋊D1911yescharacteristic
343#124—21no—
344#124C22⋊D1911yescharacteristic
345#123—22no—
346#123—22no—
347#123—22no—
348#123—21no—
349#123—22no—
350C22⋊Q8—21no—
351C22⋊Q8C22⋊D1911yescharacteristic
352#121—22no—
353#121—22no—
354#121—22no—
355#121—22no—
356#121—22no—
357#121—21no—
358#121—22no—
359#121—22no—
360#121—21no—
361#121—21no—
362#121—21no—
363#121C22⋊D1911yescharacteristic
364#121C22⋊D1912yes—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8C2×Dic1911yescharacteristic
368C4×Q8C2×Dic1911yescharacteristic
369C4×Q8C22⋊D1911yescharacteristic
370C4×D4—22no—
371C4×D4—22no—
372C4×D4—22no—
373C4×D4—22no—
374C4×D4—21no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4C2×Dic1911yescharacteristic
381C4×D4C2×Dic1911yescharacteristic
382C4×D4C22⋊D1911yescharacteristic
383C4×D4C22⋊D1912yes—
384#117—22no—
385#117—21no—
386#117—21no—
387#117C22⋊D1911yescharacteristic
388C2×C4⋊C4—22no—
389C2×C4⋊C4—21no—
390C2×C42—21no—
391C2×C42—381no—
392C2×C42C22×D1911yescharacteristic
393C4⋊C8—381no—
394C4⋊C8—381no—
395#104—384no—
396C22⋊C8—381no—
397C22⋊C8—381no—
398#97—381no—
399#97—381no—
400C4×C8—381no—
401C4×C8—381no—
402#95—381no—
403#95—381no—
404C19#841411yescharacteristic, complemented, Sylow
405#41—22no—
406#41—41no—
407#41—42no—
408#41—42no—
409#41—82no—
410#41—82no—
411#41—82no—
412C2×Q8—21no—
413C2×Q8C22⋊Dic1911yescharacteristic
414C2×Q8C22⋊Dic1911yescharacteristic
415C2×D4—22no—
416C2×D4—21no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—21no—
422C2×D4—22no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4C22⋊Dic1911yescharacteristic
426C2×D4C22⋊Dic1911yescharacteristic
427C2×D4C22⋊Dic1912yes—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—761no—
437C22×C4C2×C22⋊D1911yescharacteristic
438C22×C4C2×C22⋊D1911yescharacteristic
439C22×C4C2×C22⋊D1911yescharacteristic
440M16—382no—
441M16—761no—
442C2×C8—761no—
443C2×C8—761no—
444C2×C8—761no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4C22⋊Dic1911yescharacteristic
457C4⋊C4C22⋊Dic1911yescharacteristic
458C4⋊C4C22⋊Dic1911yescharacteristic
459C4⋊C4C22⋊Dic1912yes—
460C4⋊C4C22⋊Dic1911yescharacteristic
461C22⋊C4—22no—
462C22⋊C4—22no—
463C22⋊C4—22no—
464C22⋊C4—21no—
465C22⋊C4—21no—
466C22⋊C4—21no—
467C22⋊C4—21no—
468C22⋊C4—21no—
469C22⋊C4—21no—
470C22⋊C4—22no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—22no—
474C42—22no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—382no—
480C42—761no—
481C42C22×Dic1911yescharacteristic
482C42C2×C22⋊D1911yescharacteristic
483C42C2×C22⋊D1911yescharacteristic
484C42C2×C22⋊D1911yescharacteristic
485C23—21no—
486C23—22no—
487C23—21no—
488C23#1059739911yescharacteristic
489Q8—21no—
490Q8—41no—
491Q8—42no—
492Q8#1059729412yes—
493D4—21no—
494D4—21no—
495D4—42no—
496D4—41no—
497D4—42no—
498D4—44no—
499D4—42no—
500D4—41no—
501D4—41no—
502D4—82no—
503D4—81no—
504D4—82no—
505D4—82no—
506D4—82no—
507D4—82no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—44no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—82no—
525C2×C4—81no—
526C2×C4—82no—
527C2×C4—82no—
528C2×C4—762no—
529C2×C4—1521no—
530C2×C4—1521no—
531C2×C4C2×C22⋊Dic1911yescharacteristic
532C2×C4C2×C22⋊Dic1911yescharacteristic
533C2×C4C2×C22⋊Dic1911yescharacteristic
534C2×C4#1059739911yescharacteristic
535C2×C4#1059739911yescharacteristic
536C2×C4#1059739911yescharacteristic
537C8—762no—
538C8—1521no—
539C8—1521no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—41no—
544C22—42no—
545C22—41no—
546C22—41no—
547C22—42no—
548C22—41no—
549C22—41no—
550C22—42no—
551C22—41no—
552C22#1192640011yescharacteristic
553C4—21no—
554C4—21no—
555C4—21no—
556C4—21no—
557C4—21no—
558C4—22no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—42no—
563C4—41no—
564C4—41no—
565C4—1522no—
566C4C2×#1059729411yescharacteristic
567C4#1192656111yescharacteristic
568C2—41no—
569C2—81no—
570C2—82no—
571C2—81no—
572C2#1456357911yescharacteristic
573C2#1456359911yescharacteristic
574C2#1456360511yescharacteristic
subgroupG/H
centerC22#11926400
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
Fitting, prime radicalC19×#3517C2
socleC22×C19#379
cosocleC2×C42×C19C23
hypercenter#3517D19
hypocenterC19#8414
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3517

Complements

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

NH ≅ G/Ntype
1. #14563445C2semidirect
2. #14562242C2semidirect
3. #14562143C2semidirect
4. #14562121C2semidirect
5. #14562069C2semidirect
6. #14562052C2semidirect
22. C19×#557C4semidirect
27. C19×#550C4semidirect
28. C19×#550C4semidirect
30. C19×#547C4semidirect
288. #557Dic19semidirect
293. #550Dic19semidirect
294. #550Dic19semidirect
296. #547Dic19semidirect
404. C19#8414semidirect

Maximal subgroups

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

subgroupindex
#145634452
#145622422
#145621432
#145621212
#145620692
#145620522
C19×#35172
#841419