Finite Group Databasebeta

← #18074749

Subgroups — #18074749

Order 4864.

722 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564621C211yesmaximal, characteristic, complemented
2#14563734C211yesmaximal, characteristic, complemented
3#14563730C211yesmaximal, characteristic, complemented
4#14562178C211yesmaximal, characteristic
5#14562126C211yesmaximal, characteristic
6#14561999C211yesmaximal, characteristic, complemented
7C19×#3495C211yesmaximal, characteristic
8#11926508C2211yescharacteristic
9C2×C22⋊(C19⋊C8)C2211yescharacteristic
10#11926404C2211yescharacteristic
11C4×C22⋊Dic19C2211yescharacteristic
12#11926311—22no—
13#11926306—21no—
14#11926306—21no—
15#11926303—21no—
16#11926303—21no—
17#11926281—21no—
18#11926281—21no—
19#11926278—21no—
20#11926278—21no—
21#11926270—22no—
22C19×#556—21no—
23C19×#554—21no—
24C19×#552—21no—
25C19×#552—22no—
26C19×#552—21no—
27C19×#551—22no—
28C19×#544C411yescharacteristic, complemented
29C19×#542—21no—
30C19×#541—21no—
31C19×#536C411yescharacteristic, complemented
32C19×#533—21no—
33C19×#529—21no—
34C19×#525C2211yescharacteristic
35C2×C19×C22⋊Q8C2211yescharacteristic
36C19×#520C411yescharacteristic, complemented
37C19×#519C411yescharacteristic, complemented
38C2×C19×#117C2211yescharacteristic
39C2×#41×C19C2×C411yescharacteristic
40C22×Q8×C19C2×C411yescharacteristic
41C23×C4×C19C2311yescharacteristic
42C19×C4⋊Q8—21no—
43C19×C4⋊Q8—21no—
44C19×C4⋊Q8—21no—
45C19×#126—22no—
46C19×#126—22no—
47C19×#126—22no—
48C19×#126—22no—
49C19×#125—22no—
50C19×#125—22no—
51C19×#125—22no—
52C19×#125—21no—
53C19×#125—21no—
54C19×#124—22no—
55C19×#124—21no—
56C19×#123—22no—
57C19×#123—22no—
58C19×#123—22no—
59C19×#123—21no—
60C19×C22⋊Q8—22no—
61C19×C22⋊Q8—22no—
62C19×C22⋊Q8—22no—
63C19×C22⋊Q8—21no—
64C19×C22⋊Q8—21no—
65C19×C22⋊Q8—21no—
66C19×C22⋊Q8—21no—
67C19×C22⋊Q8—21no—
68C19×C22⋊Q8—21no—
69C19×C22⋊Q8D411yescharacteristic
70C19×C22⋊Q8D411yescharacteristic
71C19×#121D411yescharacteristic
72C19×#121D411yescharacteristic
73C19×#120—21no—
74C4×Q8×C19—22no—
75C4×Q8×C19—21no—
76C4×Q8×C19—21no—
77C4×Q8×C19—21no—
78C4×Q8×C19—21no—
79C4×Q8×C19—21no—
80C4×D4×C19—22no—
81C4×D4×C19—21no—
82C4×D4×C19—22no—
83C4×D4×C19—21no—
84C4×D4×C19—21no—
85C19×#117—22no—
86C19×#117—22no—
87C19×#117—22no—
88C19×#117—21no—
89C19×#117—21no—
90C19×#117—21no—
91C19×#117C2×C411yescharacteristic
92C19×#117C2×C411yescharacteristic
93C19×#117C2×C411yescharacteristic
94C19×#117D411yescharacteristic
95C19×#117D411yescharacteristic
96C2×C4⋊C4×C19—21no—
97C2×C4⋊C4×C19C2×C411yescharacteristic
98C2×C4⋊C4×C19D412yes—
99C2×C4⋊C4×C19D411yescharacteristic
100C2×C4⋊C4×C19D411yescharacteristic
101C2×C22⋊C4×C19—21no—
102C2×C22⋊C4×C19D412yes—
103C2×C42×C19—21no—
104C2×C22⋊Dic19—21no—
105C2×C22⋊Dic19—21no—
106C2×C4⋊Dic19—21no—
107C2×C4×Dic19—21no—
108C2×#64520—21no—
109C22×C19⋊C8—21no—
110C19⋊#95—21no—
111C19⋊#95—21no—
112C22⋊(C19⋊C8)—21no—
113C22⋊(C19⋊C8)—21no—
114C22⋊(C19⋊C8)—21no—
115C22⋊(C19⋊C8)—21no—
116C24×C19C2×D411yescharacteristic
117#41×C19—42no—
118C2×Q8×C19—22no—
119C2×Q8×C19—21no—
120C2×Q8×C19—21no—
121C2×Q8×C19—42no—
122C2×Q8×C19C22⋊C411yescharacteristic
123C2×D4×C19—21no—
124C2×D4×C19—21no—
125C2×D4×C19—21no—
126C2×D4×C19C22⋊C411yescharacteristic
127C22×C4×C19—21no—
128C22×C4×C19—22no—
129C22×C4×C19—21no—
130C22×C4×C19—21no—
131C22×C4×C19—42no—
132C22×C4×C19C22⋊C412yes—
133C22×C4×C19C22⋊C412yes—
134C22×C4×C19C22×C411yescharacteristic
135C22×C4×C19C2×D411yescharacteristic
136C22×C4×C19C2×D411yescharacteristic
137C22×C4×C19C2×D411yescharacteristic
138C22×C4×C19C2×D411yescharacteristic
139C22×C4×C19C2×D411yescharacteristic
140C22×Dic19—41no—
141C22×Dic19—41no—
142C4⋊C4×C19—22no—
143C4⋊C4×C19—22no—
144C4⋊C4×C19—22no—
145C4⋊C4×C19—22no—
146C4⋊C4×C19—22no—
147C4⋊C4×C19—22no—
148C4⋊C4×C19—22no—
149C4⋊C4×C19—22no—
150C4⋊C4×C19—21no—
151C4⋊C4×C19—21no—
152C4⋊C4×C19—21no—
153C4⋊C4×C19—21no—
154C4⋊C4×C19—22no—
155C4⋊C4×C19—22no—
156C4⋊C4×C19—21no—
157C4⋊C4×C19—21no—
158C4⋊C4×C19C22⋊C411yescharacteristic
159C4⋊C4×C19C22⋊C411yescharacteristic
160C4⋊C4×C19C22⋊C411yescharacteristic
161C4⋊C4×C19C22⋊C411yescharacteristic
162C4⋊C4×C19C22⋊C411yescharacteristic
163C4⋊C4×C19C22⋊C411yescharacteristic
164C22⋊C4×C19—22no—
165C22⋊C4×C19—22no—
166C22⋊C4×C19—22no—
167C22⋊C4×C19—21no—
168C22⋊C4×C19—21no—
169C22⋊C4×C19—21no—
170C22⋊C4×C19—21no—
171C22⋊C4×C19—21no—
172C22⋊C4×C19—22no—
173C22⋊C4×C19—22no—
174C22⋊C4×C19—21no—
175C22⋊C4×C19—21no—
176C22⋊C4×C19—21no—
177C22⋊C4×C19—21no—
178C42×C19—22no—
179C42×C19—22no—
180C42×C19—22no—
181C42×C19—21no—
182C42×C19—21no—
183C42×C19—21no—
184C42×C19—21no—
185C42×C19—21no—
186C22⋊Dic19—22no—
187C22⋊Dic19—41no—
188C22⋊Dic19—42no—
189C4⋊Dic19—42no—
190C4×Dic19—42no—
191#64520—42no—
192C2×C19⋊C8—42no—
193C2×C19⋊C8—41no—
194C2×C19⋊C8—41no—
195#8468—191nomaximal, Sylow
196C23×C19—21no—
197C23×C19—21no—
198C23×C19—21no—
199C23×C19—41no—
200C23×C19—41no—
201C23×C19C2×C22⋊C411yescharacteristic
202C23×C19#12011yescharacteristic
203C23×C19#12011yescharacteristic
204Q8×C19—41no—
205Q8×C19—42no—
206Q8×C19—42no—
207Q8×C19—82no—
208D4×C19—41no—
209D4×C19—42no—
210D4×C19—41no—
211D4×C19—41no—
212D4×C19—81no—
213C2×C4×C19—22no—
214C2×C4×C19—22no—
215C2×C4×C19—22no—
216C2×C4×C19—21no—
217C2×C4×C19—21no—
218C2×C4×C19—21no—
219C2×C4×C19—21no—
220C2×C4×C19—21no—
221C2×C4×C19—22no—
222C2×C4×C19—21no—
223C2×C4×C19—21no—
224C2×C4×C19—22no—
225C2×C4×C19—41no—
226C2×C4×C19—41no—
227C2×C4×C19—41no—
228C2×C4×C19—41no—
229C2×C4×C19—41no—
230C2×C4×C19—42no—
231C2×C4×C19—42no—
232C2×C4×C19—42no—
233C2×C4×C19—81no—
234C2×C4×C19—82no—
235C2×C4×C19C2×C22⋊C411yescharacteristic
236C2×C4×C19C2×C22⋊C411yescharacteristic
237C2×C4×C19#12011yescharacteristic
238C2×C4×C19#12011yescharacteristic
239C2×Dic19—42no—
240C2×Dic19—81no—
241C2×Dic19—81no—
242C2×Dic19—81no—
243C2×Dic19—81no—
244C2×Dic19—81no—
245C19⋊C8—81no—
246C19⋊C8—81no—
247#3495D1911yescharacteristic
248#1996—191no—
249#1826—191no—
250#1825—191no—
251#1513—191no—
252#1501—191no—
253#1472—191no—
254C22×C19—21no—
255C22×C19—21no—
256C22×C19—21no—
257C22×C19—21no—
258C22×C19—21no—
259C22×C19—21no—
260C22×C19—21no—
261C22×C19—21no—
262C22×C19—41no—
263C22×C19—41no—
264C22×C19—41no—
265C22×C19—81no—
266C22×C19—81no—
267C22×C19#37911yescharacteristic
268C22×C19#45411yescharacteristic
269C22×C19#45611yescharacteristic
270C4×C19—21no—
271C4×C19—21no—
272C4×C19—21no—
273C4×C19—41no—
274C4×C19—41no—
275C4×C19—41no—
276C4×C19—42no—
277C4×C19—41no—
278C4×C19—41no—
279C4×C19—41no—
280C4×C19—41no—
281C4×C19—42no—
282C4×C19#41012yes—
283Dic19—82no—
284Dic19—161no—
285#556—21no—
286#554—21no—
287#552—21no—
288#552—22no—
289#552—21no—
290#551—22no—
291#544Dic1911yescharacteristic, complemented
292#542—21no—
293#541—21no—
294#536Dic1911yescharacteristic, complemented
295#533—21no—
296#529—21no—
297#525C2×D1911yescharacteristic
298C2×C22⋊Q8C2×D1911yescharacteristic
299#520Dic1911yescharacteristic, complemented
300#519Dic1911yescharacteristic, complemented
301C2×#117C2×D1911yescharacteristic
302#407—191no—
303C2×C22⋊C8—191no—
304#380—191no—
305C4×C22⋊C4—191no—
306#342—382no—
307#340—381no—
308#340—381no—
309#339—381no—
310#339—381no—
311#328—381no—
312#328—381no—
313#327—381no—
314#327—381no—
315#324—382no—
316C2×C19—21no—
317C2×C19—21no—
318C2×C19—41no—
319C2×C19—41no—
320C2×C19—81no—
321C2×C19#178211yescharacteristic
322C2×C19#179311yescharacteristic
323C2×C19#179411yescharacteristic
324C2×#41C2×Dic1911yescharacteristic
325C22×Q8C2×Dic1911yescharacteristic
326C23×C4C22×D1911yescharacteristic
327C2×M16—381no—
328C22×C8—381no—
329C4⋊Q8—21no—
330C4⋊Q8—21no—
331C4⋊Q8—21no—
332#126—22no—
333#126—22no—
334#126—22no—
335#126—22no—
336#125—22no—
337#125—22no—
338#125—22no—
339#125—21no—
340#125—21no—
341#124—22no—
342#124—21no—
343#123—22no—
344#123—22no—
345#123—22no—
346#123—21no—
347C22⋊Q8—22no—
348C22⋊Q8—22no—
349C22⋊Q8—22no—
350C22⋊Q8—21no—
351C22⋊Q8—21no—
352C22⋊Q8—21no—
353C22⋊Q8—21no—
354C22⋊Q8—21no—
355C22⋊Q8—21no—
356C22⋊Q8C22⋊D1911yescharacteristic
357C22⋊Q8C22⋊D1911yescharacteristic
358#121C22⋊D1911yescharacteristic
359#121C22⋊D1911yescharacteristic
360#120—21no—
361C4×Q8—22no—
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×D4—22no—
368C4×D4—21no—
369C4×D4—22no—
370C4×D4—21no—
371C4×D4—21no—
372#117—22no—
373#117—22no—
374#117—22no—
375#117—21no—
376#117—21no—
377#117—21no—
378#117C2×Dic1911yescharacteristic
379#117C2×Dic1911yescharacteristic
380#117C2×Dic1911yescharacteristic
381#117C22⋊D1911yescharacteristic
382#117C22⋊D1911yescharacteristic
383C2×C4⋊C4—21no—
384C2×C4⋊C4—381no—
385C2×C4⋊C4C2×Dic1911yescharacteristic
386C2×C4⋊C4C22⋊D1912yes—
387C2×C4⋊C4C22⋊D1911yescharacteristic
388C2×C4⋊C4C22⋊D1911yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—381no—
391C2×C22⋊C4—381no—
392C2×C22⋊C4C22⋊D1912yes—
393C2×C42—21no—
394C2×C42—381no—
395C22⋊C8—381no—
396C22⋊C8—381no—
397C22⋊C8—381no—
398C22⋊C8—381no—
399#95—381no—
400#95—381no—
401C19#846811yescharacteristic, complemented, Sylow
402C24C2×C22⋊D1911yescharacteristic
403#41—42no—
404C2×Q8—22no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—42no—
408C2×Q8C22⋊Dic1911yescharacteristic
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4C22⋊Dic1911yescharacteristic
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—42no—
418C22×C4—761no—
419C22×C4—761no—
420C22×C4C22⋊Dic1912yes—
421C22×C4C22⋊Dic1912yes—
422C22×C4C22×Dic1911yescharacteristic
423C22×C4C2×C22⋊D1911yescharacteristic
424C22×C4C2×C22⋊D1911yescharacteristic
425C22×C4C2×C22⋊D1911yescharacteristic
426C22×C4C2×C22⋊D1911yescharacteristic
427C22×C4C2×C22⋊D1911yescharacteristic
428M16—762no—
429C2×C8—762no—
430C2×C8—761no—
431C2×C8—761no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—762no—
449C4⋊C4C22⋊Dic1911yescharacteristic
450C4⋊C4C22⋊Dic1911yescharacteristic
451C4⋊C4C22⋊Dic1911yescharacteristic
452C4⋊C4C22⋊Dic1911yescharacteristic
453C4⋊C4C22⋊Dic1911yescharacteristic
454C4⋊C4C22⋊Dic1911yescharacteristic
455C22⋊C4—22no—
456C22⋊C4—22no—
457C22⋊C4—22no—
458C22⋊C4—21no—
459C22⋊C4—21no—
460C22⋊C4—21no—
461C22⋊C4—21no—
462C22⋊C4—21no—
463C22⋊C4—22no—
464C22⋊C4—22no—
465C22⋊C4—21no—
466C22⋊C4—21no—
467C22⋊C4—21no—
468C22⋊C4—21no—
469C22⋊C4—382no—
470C22⋊C4—761no—
471C22⋊C4—762no—
472C42—22no—
473C42—22no—
474C42—22no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—762no—
481C23—21no—
482C23—21no—
483C23—21no—
484C23—41no—
485C23—41no—
486C23C2×C22⋊Dic1911yescharacteristic
487C23#1059739911yescharacteristic
488C23#1059739911yescharacteristic
489Q8—41no—
490Q8—42no—
491Q8—42no—
492Q8—82no—
493D4—41no—
494D4—42no—
495D4—41no—
496D4—41no—
497D4—81no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—22no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—81no—
519C2×C4—82no—
520C2×C4—762no—
521C2×C4—1521no—
522C2×C4—1521no—
523C2×C4—1521no—
524C2×C4—1521no—
525C2×C4—1521no—
526C2×C4C2×C22⋊Dic1911yescharacteristic
527C2×C4C2×C22⋊Dic1911yescharacteristic
528C2×C4#1059739911yescharacteristic
529C2×C4#1059739911yescharacteristic
530C8—1521no—
531C8—1521no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—81no—
544C22—81no—
545C22#1192640011yescharacteristic
546C22#1192671711yescharacteristic
547C22#1192672711yescharacteristic
548C4—21no—
549C4—21no—
550C4—21no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—42no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4—41no—
559C4—42no—
560C4—3041no—
561C4—1522no—
562C4#1192651812yes—
563C2—21no—
564C2—21no—
565C2—41no—
566C2—41no—
567C2—81no—
568C2#1456355311yescharacteristic
569C2#1456359411yescharacteristic
570C2#1456359911yescharacteristic
subgroupG/H
centerC22#11926400
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#3495C2
socleC22×C19#379
prime radicalC19×#525C22
cosocleC23×C4×C19C23
hypercenter#3495D19
hypocenterC19#8468
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3495

Complements

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

NH ≅ G/Ntype
1. #14564621C2semidirect
2. #14563734C2semidirect
3. #14563730C2semidirect
6. #14561999C2semidirect
28. C19×#544C4semidirect
31. C19×#536C4semidirect
36. C19×#520C4semidirect
37. C19×#519C4semidirect
291. #544Dic19semidirect
294. #536Dic19semidirect
299. #520Dic19semidirect
300. #519Dic19semidirect
401. C19#8468semidirect

Maximal subgroups

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

subgroupindex
#145646212
#145637342
#145637302
#145621782
#145621262
#145619992
C19×#34952
#846819