Finite Group Databasebeta

← #18074435

Subgroups — #18074435

Order 4864.

772 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564580C211yesmaximal, characteristic, complemented
2#14563460C211yesmaximal, characteristic, complemented
3#14562250C211yesmaximal, characteristic, complemented
4#14562223C211yesmaximal, characteristic, complemented
5#14562160C211yesmaximal, characteristic, complemented
6#14562078C211yesmaximal, characteristic, complemented
7C19×#3520C211yesmaximal, characteristic
8#11926601C2211yescharacteristic
9C2×#10597289—21no—
10C4×#64520C2211yescharacteristic
11C2×#10597260C2211yescharacteristic
12C4×C4⋊Dic19C2211yescharacteristic
13#11926306—21no—
14#11926303—22no—
15#11926286—21no—
16#11926286—22no—
17#11926284—21no—
18#11926281—21no—
19#11926278—21no—
20D4⋊(C19⋊C8)—21no—
21D4⋊(C19⋊C8)—21no—
22C19×#556C411yescharacteristic, complemented
23C19×#554—21no—
24C19×#552—21no—
25C19×#551—22no—
26D4×Q8×C19C411yescharacteristic, complemented
27C19×#548—21no—
28C19×#547C411yescharacteristic, complemented
29C19×#547C411yescharacteristic, complemented
30C19×#546—21no—
31C19×#542—21no—
32C19×#539—22no—
33C19×#533C2211yescharacteristic
34C19×#529C2211yescharacteristic
35C19×#525—21no—
36C2×C19×C22⋊Q8—21no—
37C19×#520—21no—
38C2×C4×D4×C19C2211yescharacteristic
39C2×#41×C19—21no—
40C2×#41×C19—21no—
41C22×Q8×C19—21no—
42C22×D4×C19D411yescharacteristic
43C23×C4×C19—21no—
44C19×C4⋊Q8—21no—
45C19×C4⋊Q8C2×C411yescharacteristic
46C19×C4⋊Q8C2×C411yescharacteristic
47C19×#126—22no—
48C19×#126—22no—
49C19×#126—21no—
50C19×#125—22no—
51C19×#125D411yescharacteristic
52C19×#125D412yes—
53C19×#124—22no—
54C19×#124—21no—
55C19×#124D411yescharacteristic
56C19×#123—22no—
57C19×#123—22no—
58C19×#123—21no—
59C19×#123—22no—
60C19×#123—22no—
61C19×C22⋊Q8—22no—
62C19×C22⋊Q8—22no—
63C19×C22⋊Q8—22no—
64C19×C22⋊Q8—21no—
65C19×C22⋊Q8—21no—
66C19×C22⋊Q8—21no—
67C19×C22⋊Q8—21no—
68C19×C22⋊Q8—21no—
69C19×C22⋊Q8—22no—
70C19×C22⋊Q8—21no—
71C19×C22⋊Q8D411yescharacteristic
72C19×#121—22no—
73C19×#121—21no—
74C19×#121—21no—
75C19×#121D411yescharacteristic
76C19×#120—22no—
77C4×Q8×C19—21no—
78C4×Q8×C19—21no—
79C4×Q8×C19—21no—
80C4×Q8×C19C2×C411yescharacteristic
81C4×D4×C19—22no—
82C4×D4×C19—22no—
83C4×D4×C19—22no—
84C4×D4×C19—21no—
85C4×D4×C19—21no—
86C4×D4×C19—21no—
87C4×D4×C19—21no—
88C4×D4×C19C2×C411yescharacteristic
89C4×D4×C19C2×C411yescharacteristic
90C4×D4×C19C2×C411yescharacteristic
91C4×D4×C19D411yescharacteristic
92C4×D4×C19D411yescharacteristic
93C19×#117—22no—
94C19×#117—21no—
95C19×#117—21no—
96C19×#117D412yes—
97C2×C4⋊C4×C19—22no—
98C2×C4⋊C4×C19—21no—
99C2×C4⋊C4×C19—21no—
100C2×C4⋊C4×C19D411yescharacteristic
101C2×C22⋊C4×C19—22no—
102C2×C22⋊C4×C19—21no—
103C2×C42×C19C2311yescharacteristic
104C2×C4⋊Dic19—21no—
105C2×C4×Dic19—21no—
106C2×#64520—21no—
107C22×C19⋊C8—21no—
108#10597289—24no—
109C19⋊#95—21no—
110C22⋊(C19⋊C8)—21no—
111C4⋊(C19⋊C8)—21no—
112#10597260—21no—
113#10597260—21no—
114#10597260—21no—
115#10597260—21no—
116C4×C19⋊C8—21no—
117C24×C19—21no—
118#41×C19—42no—
119#41×C19—42no—
120#41×C19—82no—
121C2×Q8×C19—22no—
122C2×Q8×C19—21no—
123C2×Q8×C19—21no—
124C2×Q8×C19—82no—
125C2×Q8×C19C22⋊C411yescharacteristic
126C2×D4×C19—22no—
127C2×D4×C19—22no—
128C2×D4×C19—21no—
129C2×D4×C19—22no—
130C2×D4×C19—21no—
131C2×D4×C19—41no—
132C2×D4×C19C22⋊C411yescharacteristic
133C2×D4×C19C22⋊C411yescharacteristic
134C2×D4×C19C22⋊C411yescharacteristic
135C22×C4×C19—22no—
136C22×C4×C19—22no—
137C22×C4×C19—22no—
138C22×C4×C19—21no—
139C22×C4×C19—21no—
140C22×C4×C19—21no—
141C22×C4×C19—21no—
142C22×C4×C19—21no—
143C22×C4×C19—21no—
144C22×C4×C19—82no—
145C22×C4×C19C2×D411yescharacteristic
146C22×C4×C19C2×D411yescharacteristic
147C22×C4×C19C2×D411yescharacteristic
148C22×Dic19—41no—
149C4⋊C4×C19—22no—
150C4⋊C4×C19—22no—
151C4⋊C4×C19—22no—
152C4⋊C4×C19—22no—
153C4⋊C4×C19—21no—
154C4⋊C4×C19—21no—
155C4⋊C4×C19—21no—
156C4⋊C4×C19—21no—
157C4⋊C4×C19—22no—
158C4⋊C4×C19—21no—
159C4⋊C4×C19—21no—
160C4⋊C4×C19—21no—
161C4⋊C4×C19—22no—
162C4⋊C4×C19C22⋊C411yescharacteristic
163C4⋊C4×C19C22⋊C411yescharacteristic
164C4⋊C4×C19C22⋊C411yescharacteristic
165C4⋊C4×C19C22⋊C411yescharacteristic
166C4⋊C4×C19C22⋊C412yes—
167C4⋊C4×C19C22⋊C412yes—
168C22⋊C4×C19—22no—
169C22⋊C4×C19—22no—
170C22⋊C4×C19—22no—
171C22⋊C4×C19—22no—
172C22⋊C4×C19—22no—
173C22⋊C4×C19—21no—
174C22⋊C4×C19—22no—
175C22⋊C4×C19—21no—
176C22⋊C4×C19—21no—
177C22⋊C4×C19—21no—
178C22⋊C4×C19—21no—
179C22⋊C4×C19—21no—
180C22⋊C4×C19—21no—
181C22⋊C4×C19—21no—
182C22⋊C4×C19—21no—
183C42×C19—22no—
184C42×C19—21no—
185C42×C19—22no—
186C42×C19C22×C411yescharacteristic
187C42×C19C2×D411yescharacteristic
188C42×C19C2×D411yescharacteristic
189C42×C19C2×D411yescharacteristic
190C4⋊Dic19—22no—
191C4⋊Dic19—41no—
192C4×Dic19—42no—
193#64520—22no—
194#64520—41no—
195C2×C19⋊C8—22no—
196C2×C19⋊C8—41no—
197C2×C19⋊C8—41no—
198C2×C19⋊C8—41no—
199C2×C19⋊C8—41no—
200#8418—191nomaximal, Sylow
201C23×C19—21no—
202C23×C19—21no—
203C23×C19—21no—
204C23×C19—42no—
205C23×C19—41no—
206C23×C19—41no—
207C23×C19—81no—
208C23×C19#12011yescharacteristic
209Q8×C19—41no—
210Q8×C19—42no—
211Q8×C19—41no—
212Q8×C19—41no—
213Q8×C19—82no—
214D4×C19—21no—
215D4×C19—21no—
216D4×C19—21no—
217D4×C19—42no—
218D4×C19—41no—
219D4×C19—44no—
220D4×C19—41no—
221D4×C19—41no—
222D4×C19—82no—
223D4×C19#10412yes—
224C2×C4×C19—21no—
225C2×C4×C19—21no—
226C2×C4×C19—21no—
227C2×C4×C19—21no—
228C2×C4×C19—21no—
229C2×C4×C19—22no—
230C2×C4×C19—21no—
231C2×C4×C19—21no—
232C2×C4×C19—22no—
233C2×C4×C19—21no—
234C2×C4×C19—21no—
235C2×C4×C19—41no—
236C2×C4×C19—42no—
237C2×C4×C19—42no—
238C2×C4×C19—44no—
239C2×C4×C19—41no—
240C2×C4×C19—41no—
241C2×C4×C19—81no—
242C2×C4×C19—81no—
243C2×C4×C19—81no—
244C2×C4×C19—82no—
245C2×C4×C19—82no—
246C2×C4×C19C2×C22⋊C411yescharacteristic
247C2×C4×C19C2×C22⋊C411yescharacteristic
248C2×C4×C19C2×C22⋊C411yescharacteristic
249C2×C4×C19#12011yescharacteristic
250C2×C4×C19#12011yescharacteristic
251C2×C4×C19#12011yescharacteristic
252C2×Dic19—42no—
253C2×Dic19—81no—
254C2×Dic19—81no—
255C19⋊C8—42no—
256C19⋊C8—42no—
257C19⋊C8—81no—
258#3520D1911yescharacteristic
259#1986—191no—
260#1762—191no—
261#1531—191no—
262#1524—191no—
263#1509—191no—
264#1490—191no—
265C22×C19—21no—
266C22×C19—21no—
267C22×C19—22no—
268C22×C19—41no—
269C22×C19—41no—
270C22×C19—41no—
271C22×C19—41no—
272C22×C19—41no—
273C22×C19—41no—
274C22×C19—41no—
275C22×C19—41no—
276C22×C19—82no—
277C22×C19—82no—
278C22×C19#37911yescharacteristic
279C22×C19#45411yescharacteristic
280C22×C19#45611yescharacteristic
281C4×C19—21no—
282C4×C19—21no—
283C4×C19—21no—
284C4×C19—21no—
285C4×C19—21no—
286C4×C19—41no—
287C4×C19—41no—
288C4×C19—41no—
289C4×C19—42no—
290C4×C19—41no—
291C4×C19—41no—
292C4×C19—42no—
293C4×C19C2×#10411yescharacteristic
294C4×C19#42111yescharacteristic
295Dic19—82no—
296#556Dic1911yescharacteristic, complemented
297#554—21no—
298#552—21no—
299#551—22no—
300D4×Q8Dic1911yescharacteristic, complemented
301#548—21no—
302#547Dic1911yescharacteristic, complemented
303#547Dic1911yescharacteristic, complemented
304#546—21no—
305#542—21no—
306#539—22no—
307#533C2×D1911yescharacteristic
308#529C2×D1911yescharacteristic
309#525—21no—
310C2×C22⋊Q8—21no—
311#520—21no—
312C2×C4×D4C2×D1911yescharacteristic
313#432—191no—
314C2×#102—381no—
315C4×M16—191no—
316C2×#97—191no—
317C4×C4⋊C4—191no—
318#340—381no—
319#339—382no—
320#330—381no—
321#330—382no—
322#329—381no—
323#328—381no—
324#327—381no—
325D4⋊C8—381no—
326D4⋊C8—381no—
327C2×C19—21no—
328C2×C19—21no—
329C2×C19—42no—
330C2×C19—81no—
331C2×C19—81no—
332C2×C19#178911yescharacteristic
333C2×C19#179311yescharacteristic
334C2×C19#179511yescharacteristic
335C2×#41—21no—
336C2×#41—21no—
337C22×Q8—21no—
338C22×D4C22⋊D1911yescharacteristic
339C23×C4—21no—
340C2×M16—381no—
341C22×C8—381no—
342C4⋊Q8—21no—
343C4⋊Q8C2×Dic1911yescharacteristic
344C4⋊Q8C2×Dic1911yescharacteristic
345#126—22no—
346#126—22no—
347#126—21no—
348#125—22no—
349#125C22⋊D1911yescharacteristic
350#125C22⋊D1912yes—
351#124—22no—
352#124—21no—
353#124C22⋊D1911yescharacteristic
354#123—22no—
355#123—22no—
356#123—21no—
357#123—22no—
358#123—22no—
359C22⋊Q8—22no—
360C22⋊Q8—22no—
361C22⋊Q8—22no—
362C22⋊Q8—21no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—22no—
368C22⋊Q8—21no—
369C22⋊Q8C22⋊D1911yescharacteristic
370#121—22no—
371#121—21no—
372#121—21no—
373#121C22⋊D1911yescharacteristic
374#120—22no—
375C4×Q8—21no—
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8C2×Dic1911yescharacteristic
379C4×D4—22no—
380C4×D4—22no—
381C4×D4—22no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4C2×Dic1911yescharacteristic
387C4×D4C2×Dic1911yescharacteristic
388C4×D4C2×Dic1911yescharacteristic
389C4×D4C22⋊D1911yescharacteristic
390C4×D4C22⋊D1911yescharacteristic
391#117—22no—
392#117—21no—
393#117—21no—
394#117C22⋊D1912yes—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—381no—
399C2×C4⋊C4C22⋊D1911yescharacteristic
400C2×C22⋊C4—22no—
401C2×C22⋊C4—21no—
402C2×C42—381no—
403C2×C42C22×D1911yescharacteristic
404C4⋊C8—381no—
405#102—384no—
406C22⋊C8—381no—
407#97—381no—
408#97—381no—
409#97—381no—
410#97—381no—
411C4×C8—381no—
412#95—381no—
413C19#841811yescharacteristic, complemented, Sylow
414C24—21no—
415#41—42no—
416#41—42no—
417#41—82no—
418C2×Q8—22no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—82no—
422C2×Q8C22⋊Dic1911yescharacteristic
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—21no—
426C2×D4—22no—
427C2×D4—21no—
428C2×D4—41no—
429C2×D4C22⋊Dic1911yescharacteristic
430C2×D4C22⋊Dic1911yescharacteristic
431C2×D4C22⋊Dic1911yescharacteristic
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—82no—
442C22×C4—761no—
443C22×C4C2×C22⋊D1911yescharacteristic
444C22×C4C2×C22⋊D1911yescharacteristic
445C22×C4C2×C22⋊D1911yescharacteristic
446M16—382no—
447M16—761no—
448C2×C8—382no—
449C2×C8—761no—
450C2×C8—761no—
451C2×C8—761no—
452C2×C8—761no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—22no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—22no—
466C4⋊C4—382no—
467C4⋊C4—761no—
468C4⋊C4C22⋊Dic1911yescharacteristic
469C4⋊C4C22⋊Dic1911yescharacteristic
470C4⋊C4C22⋊Dic1911yescharacteristic
471C4⋊C4C22⋊Dic1911yescharacteristic
472C4⋊C4C22⋊Dic1912yes—
473C4⋊C4C22⋊Dic1912yes—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—22no—
479C22⋊C4—21no—
480C22⋊C4—22no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C42—22no—
490C42—21no—
491C42—22no—
492C42—762no—
493C42C22×Dic1911yescharacteristic
494C42C2×C22⋊D1911yescharacteristic
495C42C2×C22⋊D1911yescharacteristic
496C42C2×C22⋊D1911yescharacteristic
497C23—21no—
498C23—21no—
499C23—21no—
500C23—42no—
501C23—41no—
502C23—41no—
503C23—81no—
504C23#1059739911yescharacteristic
505Q8—41no—
506Q8—42no—
507Q8—41no—
508Q8—41no—
509Q8—82no—
510D4—21no—
511D4—21no—
512D4—21no—
513D4—42no—
514D4—41no—
515D4—44no—
516D4—41no—
517D4—41no—
518D4—82no—
519D4#1059729412yes—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—44no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—81no—
538C2×C4—81no—
539C2×C4—81no—
540C2×C4—82no—
541C2×C4—82no—
542C2×C4—762no—
543C2×C4—1521no—
544C2×C4—1521no—
545C2×C4C2×C22⋊Dic1911yescharacteristic
546C2×C4C2×C22⋊Dic1911yescharacteristic
547C2×C4C2×C22⋊Dic1911yescharacteristic
548C2×C4#1059739911yescharacteristic
549C2×C4#1059739911yescharacteristic
550C2×C4#1059739911yescharacteristic
551C8—762no—
552C8—762no—
553C8—1521no—
554C22—21no—
555C22—21no—
556C22—22no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—82no—
566C22—82no—
567C22#1192640011yescharacteristic
568C22#1192671711yescharacteristic
569C22#1192672711yescharacteristic
570C4—21no—
571C4—21no—
572C4—21no—
573C4—21no—
574C4—21no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—42no—
579C4—41no—
580C4—41no—
581C4—42no—
582C4—1522no—
583C4C2×#1059729411yescharacteristic
584C4#1192656111yescharacteristic
585C2—21no—
586C2—21no—
587C2—42no—
588C2—81no—
589C2—81no—
590C2#1456357911yescharacteristic
591C2#1456359411yescharacteristic
592C2#1456360511yescharacteristic
subgroupG/H
centerC22#11926400
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
Fitting, prime radicalC19×#3520C2
socleC22×C19#379
cosocleC2×C42×C19C23
hypercenter#3520D19
hypocenterC19#8418
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3520

Complements

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

NH ≅ G/Ntype
1. #14564580C2semidirect
2. #14563460C2semidirect
3. #14562250C2semidirect
4. #14562223C2semidirect
5. #14562160C2semidirect
6. #14562078C2semidirect
22. C19×#556C4semidirect
26. D4×Q8×C19C4semidirect
28. C19×#547C4semidirect
29. C19×#547C4semidirect
296. #556Dic19semidirect
300. D4×Q8Dic19semidirect
302. #547Dic19semidirect
303. #547Dic19semidirect
413. C19#8418semidirect

Maximal subgroups

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

subgroupindex
#145645802
#145634602
#145622502
#145622232
#145621602
#145620782
C19×#35202
#841819