Finite Group Databasebeta

← #18074322

Subgroups — #18074322

Order 4864.

868 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14563938C212yesmaximal, complemented
2#14563933C211yesmaximal, characteristic, complemented
3C4×#10597291C211yesmaximal, characteristic, complemented
4#14562126C212yesmaximal, complemented
5C19×#3459C211yesmaximal, characteristic
6C22×#64520C2211yescharacteristic, complemented
7C2×#10597294—22no—
8C2×#10597291—21no—
9C2×C22⋊(C19⋊C8)—21no—
10C2×C22⋊(C19⋊C8)C2211yescharacteristic, complemented
11C4×C22⋊Dic19C2212yescomplemented
12#11926311—21no—
13#11926303—22no—
14#11926299—21no—
15#11926281—22no—
16#11926278—22no—
17C19×#543C411yescharacteristic, complemented
18C19×#539—22no—
19C19×#539C412yescomplemented
20C19×#538—22no—
21C19×#538—21no—
22C19×#534—21no—
23C19×#534C411yescharacteristic, complemented
24C19×#529—22no—
25C19×#529—21no—
26C19×#525—22no—
27C19×#525C2212yes—
28C2×C4×D4×C19—21no—
29C2×C4×D4×C19C2211yescharacteristic
30C2×#41×C19D412yes—
31C22×D4×C19—21no—
32C22×D4×C19D411yescharacteristic
33C23×C4×C19—21no—
34C23×C4×C19D411yescharacteristic
35C23×C4×C19C2311yescharacteristic
36C19×#126—22no—
37C19×#126—22no—
38C19×#126—22no—
39C19×#125—21no—
40C19×#125—22no—
41C19×#124—22no—
42C19×#124—21no—
43C19×#123—22no—
44C19×#123—22no—
45C19×#123—22no—
46C19×#123—22no—
47C19×#123—22no—
48C19×#123—22no—
49C19×C22⋊Q8—22no—
50C19×C22⋊Q8—22no—
51C19×C22⋊Q8—21no—
52C19×C22⋊Q8—22no—
53C19×C22⋊Q8C2×C412yes—
54C19×C22⋊Q8D412yes—
55C19×#121—22no—
56C19×#121—22no—
57C19×#121—22no—
58C19×#121—21no—
59C19×#121C2×C412yes—
60C19×#121D412yes—
61C19×#120—22no—
62C19×#120—22no—
63C19×#120—22no—
64C4×Q8×C19—21no—
65C4×D4×C19—22no—
66C4×D4×C19—22no—
67C4×D4×C19—21no—
68C4×D4×C19—22no—
69C4×D4×C19—22no—
70C4×D4×C19—22no—
71C4×D4×C19—22no—
72C4×D4×C19—22no—
73C19×#117—22no—
74C19×#117D412yes—
75C2×C4⋊C4×C19—21no—
76C2×C4⋊C4×C19C2×C411yescharacteristic
77C2×C22⋊C4×C19—21no—
78C2×C22⋊C4×C19—21no—
79C2×C22⋊C4×C19C2×C411yescharacteristic
80C2×C22⋊C4×C19D411yescharacteristic
81C2×C42×C19—21no—
82C2×C42×C19D411yescharacteristic
83C2×C22⋊Dic19—22no—
84C2×C4×Dic19—22no—
85C2×#64520—22no—
86C2×#64520—42no—
87C22×C19⋊C8—21no—
88C22×C19⋊C8—21no—
89#10597294—44no—
90#10597291—24no—
91C19⋊#95—22no—
92C22⋊(C19⋊C8)—22no—
93C22⋊(C19⋊C8)—42no—
94C24×C19—21no—
95C24×C19C22⋊C411yescharacteristic
96C24×C19C2×D411yescharacteristic
97#41×C19—42no—
98#41×C19—42no—
99C2×Q8×C19—21no—
100C2×Q8×C19C22⋊C412yes—
101C2×D4×C19—22no—
102C2×D4×C19—22no—
103C2×D4×C19—22no—
104C2×D4×C19—22no—
105C2×D4×C19—21no—
106C2×D4×C19—22no—
107C2×D4×C19—22no—
108C2×D4×C19—41no—
109C2×D4×C19—42no—
110C2×D4×C19—42no—
111C2×D4×C19C22⋊C412yes—
112C22×C4×C19—21no—
113C22×C4×C19—21no—
114C22×C4×C19—21no—
115C22×C4×C19—22no—
116C22×C4×C19—21no—
117C22×C4×C19—22no—
118C22×C4×C19—21no—
119C22×C4×C19—41no—
120C22×C4×C19—41no—
121C22×C4×C19—41no—
122C22×C4×C19—41no—
123C22×C4×C19—81no—
124C22×C4×C19—81no—
125C22×C4×C19C22⋊C411yescharacteristic
126C22×C4×C19C22⋊C411yescharacteristic
127C22×C4×C19C22⋊C411yescharacteristic
128C22×C4×C19C22×C411yescharacteristic
129C22×C4×C19C2×D412yes—
130C22×C4×C19C2×D411yescharacteristic
131C22×C4×C19C2×D412yes—
132C22×Dic19—42no—
133C4⋊C4×C19—22no—
134C4⋊C4×C19—22no—
135C4⋊C4×C19—22no—
136C4⋊C4×C19—21no—
137C4⋊C4×C19—21no—
138C4⋊C4×C19—22no—
139C4⋊C4×C19—22no—
140C4⋊C4×C19—22no—
141C4⋊C4×C19—22no—
142C4⋊C4×C19C22⋊C412yes—
143C4⋊C4×C19C22⋊C412yes—
144C22⋊C4×C19—22no—
145C22⋊C4×C19—22no—
146C22⋊C4×C19—22no—
147C22⋊C4×C19—22no—
148C22⋊C4×C19—22no—
149C22⋊C4×C19—22no—
150C22⋊C4×C19—22no—
151C22⋊C4×C19—22no—
152C22⋊C4×C19—22no—
153C22⋊C4×C19—22no—
154C22⋊C4×C19—22no—
155C22⋊C4×C19—22no—
156C42×C19—22no—
157C42×C19—22no—
158C42×C19—21no—
159C42×C19—21no—
160C22⋊Dic19—24no—
161C22⋊Dic19—42no—
162C4×Dic19—42no—
163C4×Dic19—42no—
164#64520—24no—
165#64520—42no—
166C2×C19⋊C8—22no—
167C2×C19⋊C8—41no—
168C2×C19⋊C8—41no—
169C2×C19⋊C8—41no—
170C2×C19⋊C8—41no—
171C2×C19⋊C8—41no—
172#8399—191nomaximal, Sylow
173C23×C19—21no—
174C23×C19—21no—
175C23×C19—21no—
176C23×C19—21no—
177C23×C19—22no—
178C23×C19—41no—
179C23×C19—41no—
180C23×C19—41no—
181C23×C19—41no—
182C23×C19—42no—
183C23×C19—81no—
184C23×C19—81no—
185C23×C19#10412yescomplemented
186C23×C19C2×C22⋊C411yescharacteristic
187C23×C19#12012yes—
188Q8×C19—42no—
189Q8×C19—81no—
190D4×C19—42no—
191D4×C19—44no—
192D4×C19—44no—
193D4×C19—42no—
194D4×C19—42no—
195D4×C19—82no—
196D4×C19—82no—
197D4×C19—81no—
198C2×C4×C19—21no—
199C2×C4×C19—22no—
200C2×C4×C19—21no—
201C2×C4×C19—22no—
202C2×C4×C19—21no—
203C2×C4×C19—22no—
204C2×C4×C19—21no—
205C2×C4×C19—22no—
206C2×C4×C19—21no—
207C2×C4×C19—22no—
208C2×C4×C19—21no—
209C2×C4×C19—21no—
210C2×C4×C19—41no—
211C2×C4×C19—42no—
212C2×C4×C19—42no—
213C2×C4×C19—41no—
214C2×C4×C19—42no—
215C2×C4×C19—41no—
216C2×C4×C19—42no—
217C2×C4×C19—41no—
218C2×C4×C19—41no—
219C2×C4×C19—81no—
220C2×C4×C19—81no—
221C2×C4×C19—82no—
222C2×C4×C19—81no—
223C2×C4×C19C2×C22⋊C412yes—
224C2×C4×C19#12011yescharacteristic
225C2×C4×C19#12011yescharacteristic
226C2×Dic19—44no—
227C2×Dic19—82no—
228C2×Dic19—82no—
229C19⋊C8—42no—
230C19⋊C8—81no—
231#3459D1911yescharacteristic
232#1871—192no—
233#1870—191no—
234C4×#99—191no—
235#1501—192no—
236C22×C19—21no—
237C22×C19—21no—
238C22×C19—22no—
239C22×C19—22no—
240C22×C19—22no—
241C22×C19—22no—
242C22×C19—42no—
243C22×C19—41no—
244C22×C19—41no—
245C22×C19—42no—
246C22×C19—42no—
247C22×C19—42no—
248C22×C19—81no—
249C22×C19—81no—
250C22×C19—81no—
251C22×C19—84no—
252C22×C19#37911yescharacteristic
253C22×C19C2×#10411yescharacteristic
254C22×C19#42111yescharacteristic
255C4×C19—21no—
256C4×C19—22no—
257C4×C19—41no—
258C4×C19—42no—
259C4×C19—41no—
260C4×C19—42no—
261C4×C19—41no—
262C4×C19—42no—
263C4×C19B(4,𝔽2)11yescharacteristic
264C4×C19#45811yescharacteristic
265Dic19—84no—
266C22×M16—191no—
267#543Dic1911yescharacteristic, complemented
268#539—22no—
269#539Dic1912yescomplemented
270#538—22no—
271#538—21no—
272#534—21no—
273#534Dic1911yescharacteristic, complemented
274#529—22no—
275#529—21no—
276#525—22no—
277#525C2×D1912yes—
278C2×C4×D4—21no—
279C2×C4×D4C2×D1911yescharacteristic
280C2×#104—382no—
281C2×#99—381no—
282C2×C22⋊C8—191no—
283C2×C22⋊C8—381no—
284C4×C22⋊C4—192no—
285#342—381no—
286#339—382no—
287#336—381no—
288#328—382no—
289#327—382no—
290C2×C19—21no—
291C2×C19—21no—
292C2×C19—42no—
293C2×C19—42no—
294C2×C19—82no—
295C2×C19#178911yescharacteristic
296C2×C19#179011yescharacteristic
297C2×C19#179411yescharacteristic
298C2×#41C22⋊D1912yes—
299C22×D4—21no—
300C22×D4C22⋊D1911yescharacteristic
301C23×C4—21no—
302C23×C4C22⋊D1911yescharacteristic
303C23×C4C22×D1911yescharacteristic
304C2×M16—382no—
305C2×M16—762no—
306C22×C8—381no—
307C22×C8—381no—
308#126—22no—
309#126—22no—
310#126—22no—
311#125—21no—
312#125—22no—
313#124—22no—
314#124—21no—
315#123—22no—
316#123—22no—
317#123—22no—
318#123—22no—
319#123—22no—
320#123—22no—
321C22⋊Q8—22no—
322C22⋊Q8—22no—
323C22⋊Q8—21no—
324C22⋊Q8—22no—
325C22⋊Q8C2×Dic1912yes—
326C22⋊Q8C22⋊D1912yes—
327#121—22no—
328#121—22no—
329#121—22no—
330#121—21no—
331#121C2×Dic1912yes—
332#121C22⋊D1912yes—
333#120—22no—
334#120—22no—
335#120—22no—
336C4×Q8—21no—
337C4×D4—22no—
338C4×D4—22no—
339C4×D4—21no—
340C4×D4—22no—
341C4×D4—22no—
342C4×D4—22no—
343C4×D4—22no—
344C4×D4—22no—
345#117—22no—
346#117C22⋊D1912yes—
347C2×C4⋊C4—21no—
348C2×C4⋊C4C2×Dic1911yescharacteristic
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—382no—
352C2×C22⋊C4C2×Dic1911yescharacteristic
353C2×C22⋊C4C22⋊D1911yescharacteristic
354C2×C42—21no—
355C2×C42—382no—
356C2×C42C22⋊D1911yescharacteristic
357#104—764no—
358#99—384no—
359C22⋊C8—382no—
360C22⋊C8—762no—
361#95—382no—
362C19#839911yescharacteristic, complemented, Sylow
363C24—21no—
364C24C22⋊Dic1911yescharacteristic
365C24C2×C22⋊D1911yescharacteristic
366#41—42no—
367#41—42no—
368C2×Q8—21no—
369C2×Q8C22⋊Dic1912yes—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—21no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—41no—
378C2×D4—42no—
379C2×D4—42no—
380C2×D4C22⋊Dic1912yes—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—22no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—81no—
393C22×C4—81no—
394C22×C4—762no—
395C22×C4C22⋊Dic1911yescharacteristic
396C22×C4C22⋊Dic1911yescharacteristic
397C22×C4C22⋊Dic1911yescharacteristic
398C22×C4C22×Dic1911yescharacteristic
399C22×C4C2×C22⋊D1912yes—
400C22×C4C2×C22⋊D1911yescharacteristic
401C22×C4C2×C22⋊D1912yes—
402M16—384no—
403M16—762no—
404C2×C8—382no—
405C2×C8—761no—
406C2×C8—761no—
407C2×C8—761no—
408C2×C8—761no—
409C2×C8—761no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4C22⋊Dic1912yes—
420C4⋊C4C22⋊Dic1912yes—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C22⋊C4—22no—
424C22⋊C4—22no—
425C22⋊C4—22no—
426C22⋊C4—22no—
427C22⋊C4—22no—
428C22⋊C4—22no—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—384no—
434C22⋊C4—762no—
435C42—22no—
436C42—21no—
437C42—22no—
438C42—21no—
439C42—762no—
440C42—762no—
441C23—21no—
442C23—21no—
443C23—21no—
444C23—21no—
445C23—22no—
446C23—41no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—42no—
451C23—81no—
452C23—81no—
453C23#1059729412yescomplemented
454C23C2×C22⋊Dic1911yescharacteristic
455C23#1059739912yes—
456Q8—42no—
457Q8—81no—
458D4—42no—
459D4—44no—
460D4—44no—
461D4—42no—
462D4—42no—
463D4—82no—
464D4—82no—
465D4—81no—
466C2×C4—22no—
467C2×C4—21no—
468C2×C4—22no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—22no—
474C2×C4—21no—
475C2×C4—22no—
476C2×C4—21no—
477C2×C4—22no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—81no—
488C2×C4—82no—
489C2×C4—81no—
490C2×C4—81no—
491C2×C4—764no—
492C2×C4—1522no—
493C2×C4—1522no—
494C2×C4C2×C22⋊Dic1912yes—
495C2×C4#1059739911yescharacteristic
496C2×C4#1059739911yescharacteristic
497C8—762no—
498C8—1521no—
499C22—21no—
500C22—21no—
501C22—22no—
502C22—22no—
503C22—22no—
504C22—22no—
505C22—42no—
506C22—41no—
507C22—41no—
508C22—42no—
509C22—42no—
510C22—42no—
511C22—81no—
512C22—81no—
513C22—81no—
514C22—84no—
515C22#1192640011yescharacteristic
516C22C2×#1059729411yescharacteristic
517C22#1192656111yescharacteristic
518C4—21no—
519C4—22no—
520C4—41no—
521C4—42no—
522C4—41no—
523C4—42no—
524C4—41no—
525C4—42no—
526C4—1524no—
527C4#1192673111yescharacteristic
528C4#1192673411yescharacteristic
529C2—21no—
530C2—21no—
531C2—42no—
532C2—42no—
533C2—82no—
534C2#1456357911yescharacteristic
535C2#1456358311yescharacteristic
536C2#1456359911yescharacteristic
subgroupG/H
centerC2×C4#10597399
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
Fitting, prime radicalC19×#3459C2
socleC22×C19#379
cosocleC23×C4×C19C23
hypercenter#3459D19
hypocenterC19#8399
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3459

Complements

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

NH ≅ G/Ntype
1. #14563938C2semidirect
2. #14563933C2semidirect
3. C4×#10597291C2semidirect
4. #14562126C2semidirect
6. C22×#64520C22semidirect
10. C2×C22⋊(C19⋊C8)C22semidirect
11. C4×C22⋊Dic19C22semidirect
17. C19×#543C4semidirect
19. C19×#539C4semidirect
23. C19×#534C4semidirect
185. C23×C19#104semidirect
267. #543Dic19semidirect
269. #539Dic19semidirect
273. #534Dic19semidirect
362. C19#8399semidirect
453. C23#10597294semidirect

Maximal subgroups

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

subgroupindex
#145639382
#145639332
C4×#105972912
#145621262
C19×#34592
#839919