Finite Group Databasebeta

← #18076637

Subgroups — #18076637

Order 4864.

702 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14566335C211yesmaximal, characteristic
2#14563950C211yesmaximal, characteristic
3#14563827C211yesmaximal, characteristic, complemented
4C2×#11926277C211yesmaximal, characteristic
5#14561900C211yesmaximal, characteristic, complemented
6#14561477C211yesmaximal, characteristic, complemented
7C19×#1294C211yesmaximal, characteristic, complemented
8C2×#10597376C2211yescharacteristic
9C2×(C22⋊D19)⋊C4—21no—
10C22×C4⋊Dic19—21no—
11C22×C4⋊Dic19C2211yescharacteristic
12C2×#10597265—21no—
13C2×#10597278—21no—
14C2×C22⋊(C19⋊C8)C2211yescharacteristic
15#11926434—21no—
16#11926427—21no—
17#11926422—21no—
18#11926421—21no—
19#11926415—21no—
20C2×C19⋊#95—21no—
21C2×C19⋊#95C2211yescharacteristic
22#11926307—21no—
23#11926306—21no—
24#11926277C414yescomplemented
25C2×C19×C22⋊C8C2211yescharacteristic
26C19×#380C2211yescharacteristic
27C2×C19×#95C2211yescharacteristic
28C23×C4×C19—21no—
29C23×C4×C19C2311yescharacteristic
30C22×C22⋊D19—21no—
31C23×Dic19—21no—
32C23×Dic19D411yescharacteristic
33C23×Dic19D411yescharacteristic
34C22×D76D411yescharacteristic
35C22×C4×D19—21no—
36C22×C8×C19—21no—
37C2×C4⋊C4×C19D411yescharacteristic
38C2×C4⋊C4×C19D411yescharacteristic
39C2×C22⋊C4×C19—21no—
40#10597376—21no—
41#10597376—21no—
42#10597376C2×C412yes—
43#10597376Q812yes—
44C2×(C2×D19)⋊C4—21no—
45C2×(C2×D19)⋊C4—21no—
46C2×(C2×D19)⋊C4—21no—
47C2×(C2×D19)⋊C4—21no—
48C2×C4⋊Dic19—21no—
49C2×C4⋊Dic19—21no—
50C2×C4⋊Dic19—42no—
51C2×C4⋊Dic19—42no—
52C2×C4⋊Dic19—42no—
53C2×C4⋊Dic19—42no—
54C2×C4⋊Dic19D411yescharacteristic
55C2×Dic19⋊C4—21no—
56C2×C4×Dic19—21no—
57C22×C19⋊C8—21no—
58(C22⋊D19)⋊C4—42no—
59(C22⋊D19)⋊C4—42no—
60C19×C22⋊C8—21no—
61C19×C22⋊C8—21no—
62C19×#95—21no—
63C19×#95—21no—
64C19×#95C2×C412yescomplemented
65C19⋊#95—21no—
66C19⋊#95—21no—
67C19⋊#95—21no—
68C19⋊#95—21no—
69C19⋊#95—42no—
70C22⋊(C19⋊C8)—21no—
71C22⋊(C19⋊C8)C2×C412yescomplemented
72#10597278—42no—
73#10597265—42no—
74C24×C19C2×D411yescharacteristic
75C23×D19—21no—
76C22×C4×C19—22no—
77C22×C4×C19—22no—
78C22×C4×C19—22no—
79C22×C4×C19—21no—
80C22×C4×C19—21no—
81C22×C4×C19—41no—
82C22×C4×C19—41no—
83C22×C4×C19—41no—
84C22×C4×C19—41no—
85C22×C4×C19—41no—
86C22×C4×C19—41no—
87C22×C4×C19C22×C411yescharacteristic
88C22×C4×C19C2×D411yescharacteristic
89C22×C4×C19C2×D411yescharacteristic
90C22×C4×C19C2×Q811yescharacteristic
91C22×C4×C19#4111yescharacteristic
92C22×C4×C19#4111yescharacteristic
93C2×C22⋊D19—22no—
94C2×C22⋊D19—22no—
95C2×C22⋊D19—41no—
96C2×C22⋊D19—41no—
97C2×C22⋊D19—41no—
98C2×C22⋊D19—41no—
99C22×Dic19—21no—
100C22×Dic19—21no—
101C22×Dic19—21no—
102C22×Dic19—22no—
103C22×Dic19—21no—
104C22×Dic19—21no—
105C22×Dic19—21no—
106C22×Dic19—41no—
107C22×Dic19—41no—
108C22×Dic19—41no—
109C22×Dic19—41no—
110C22×Dic19—41no—
111C22×Dic19—41no—
112C22×Dic19—41no—
113C22×Dic19—41no—
114C22×Dic19—41no—
115C22×Dic19—41no—
116C22×Dic19SD1612yes—
117C2×D76—21no—
118C2×D76—41no—
119C2×D76—41no—
120C2×D76C4⋊C412yescomplemented
121C2×C4×D19—42no—
122C2×C4×D19—81no—
123C2×C4×D19—81no—
124C2×C8×C19—41no—
125C2×C8×C19—41no—
126C2×C8×C19—41no—
127C4⋊C4×C19—41no—
128C4⋊C4×C19—41no—
129C22⋊C4×C19—41no—
130C22⋊C4×C19—41no—
131(C2×D19)⋊C4—22no—
132(C2×D19)⋊C4—22no—
133(C2×D19)⋊C4—42no—
134(C2×D19)⋊C4—81no—
135(C2×D19)⋊C4—81no—
136C4⋊Dic19—21no—
137C4⋊Dic19—22no—
138C4⋊Dic19—22no—
139C4⋊Dic19—41no—
140C4⋊Dic19—41no—
141C4⋊Dic19—48no—
142C4⋊Dic19C4⋊C412yescomplemented
143Dic19⋊C4—42no—
144C4×Dic19—42no—
145C2×C19⋊C8—22no—
146C2×C19⋊C8—41no—
147C2×C19⋊C8—41no—
148#8873—191nomaximal, Sylow
149C23×C19—21no—
150C23×C19—21no—
151C23×C19—21no—
152C23×C19—21no—
153C23×C19C4×D411yescharacteristic
154C23×C19#12011yescharacteristic
155C23×C19C22⋊Q811yescharacteristic
156C23×C19C2×SD1611yescharacteristic
157C23×C19#13511yescharacteristic
158C23×C19AGL(1,ℤ/8)11yescharacteristic
159C23×C19AGL(1,ℤ/8)11yescharacteristic
160C22×D19—22no—
161C22×D19—41no—
162C22×D19—41no—
163C22×D19—41no—
164C22×D19—41no—
165C22×D19—41no—
166C22×D19—41no—
167C2×C4×C19—21no—
168C2×C4×C19—21no—
169C2×C4×C19—21no—
170C2×C4×C19—21no—
171C2×C4×C19—24no—
172C2×C4×C19—41no—
173C2×C4×C19—41no—
174C2×C4×C19—41no—
175C2×C4×C19—41no—
176C2×C4×C19—42no—
177C2×C4×C19—42no—
178C2×C4×C19—42no—
179C2×C4×C19—42no—
180C2×C4×C19—42no—
181C2×C4×C19—42no—
182C2×C4×C19—41no—
183C2×C4×C19—41no—
184C2×C4×C19—41no—
185C2×C4×C19—41no—
186C2×C4×C19—41no—
187C2×C4×C19—41no—
188C2×C4×C19C2×C4⋊C411yescharacteristic
189C2×C4×C19C4×D411yescharacteristic
190C2×C4×C19C22⋊Q811yescharacteristic
191C2×C4×C19#12311yescharacteristic
192C22⋊D19—42no—
193C22⋊D19—42no—
194C22⋊D19—42no—
195C22⋊D19—42no—
196C2×Dic19—22no—
197C2×Dic19—22no—
198C2×Dic19—41no—
199C2×Dic19—41no—
200C2×Dic19—41no—
201C2×Dic19—41no—
202C2×Dic19—42no—
203C2×Dic19—42no—
204C2×Dic19—42no—
205C2×Dic19—42no—
206C2×Dic19—41no—
207C2×Dic19—41no—
208C2×Dic19—42no—
209C2×Dic19—41no—
210C2×Dic19—81no—
211C2×Dic19—81no—
212C2×Dic19—81no—
213C2×Dic19—81no—
214C2×Dic19—81no—
215C2×Dic19—81no—
216D76—42no—
217D76—81no—
218C4×D19—84no—
219C8×C19—81no—
220C19⋊C8—42no—
221#2325—191no—
222#1874—191no—
223#1853—191no—
224C2×#327—191no—
225#1444—191no—
226#1294D1911yescharacteristic, complemented
227#1280—191no—
228C22×C19—21no—
229C22×C19—21no—
230C22×C19—21no—
231C22×C19—21no—
232C22×C19—21no—
233C22×C19—21no—
234C22×C19—21no—
235C22×C19—21no—
236C22×C19—21no—
237C22×C19—21no—
238C22×C19—21no—
239C22×C19—21no—
240C22×C19#38511yescharacteristic
241C22×C19C4×SD1611yescharacteristic
242C22×C19#44211yescharacteristic
243C22×C19#44911yescharacteristic
244C22×C19#45011yescharacteristic
245C22×C19#45311yescharacteristic
246C22×C19#45611yescharacteristic
247C22×C19B(4,𝔽2)11yescharacteristic
248C22×C19#45811yescharacteristic
249C22×C19#47611yescharacteristic
250C22×C19#47811yescharacteristic
251C2×D19—42no—
252C2×D19—42no—
253C2×D19—42no—
254C2×D19—81no—
255C2×D19—81no—
256C2×D19—81no—
257C2×D19—81no—
258C4×C19—21no—
259C4×C19—21no—
260C4×C19—21no—
261C4×C19—21no—
262C4×C19—44no—
263C4×C19—81no—
264C4×C19—81no—
265Dic19—42no—
266Dic19—42no—
267Dic19—81no—
268Dic19—82no—
269C2×#121—191no—
270C2×C4×D4—381no—
271C22×C4⋊C4—191no—
272C22×C4⋊C4—381no—
273C2×#106—381no—
274C2×#102—381no—
275C2×C22⋊C8—191no—
276C2×C22⋊C8C2×D1911yescharacteristic
277#388—381no—
278#387—381no—
279#386—381no—
280#386—381no—
281#385—381no—
282#380C2×D1911yescharacteristic
283C2×#95—191no—
284C2×#95—381no—
285C2×#95C2×D1911yescharacteristic
286#340—381no—
287#340—381no—
288#327—194no—
289C2×C19—21no—
290C2×C19—21no—
291C2×C19—21no—
292C2×C19—21no—
293C2×C19#160011yescharacteristic
294C2×C19#160411yescharacteristic
295C2×C19#160911yescharacteristic
296C2×C19#161311yescharacteristic
297C2×C19#185911yescharacteristic
298C2×C19#186411yescharacteristic
299C2×C19#186711yescharacteristic
300D19—82no—
301C22×D4—191no—
302C22×D4—381no—
303C23×C4—21no—
304C23×C4—191no—
305C23×C4—191no—
306C23×C4—381no—
307C23×C4—381no—
308C23×C4C22×D1911yescharacteristic
309C22×C8—21no—
310C22×C8—381no—
311#121—192no—
312#121—192no—
313#121—381no—
314#121—381no—
315C4×D4—762no—
316C4×D4—762no—
317C2×C4⋊C4—191no—
318C2×C4⋊C4—381no—
319C2×C4⋊C4—381no—
320C2×C4⋊C4—381no—
321C2×C4⋊C4—762no—
322C2×C4⋊C4—762no—
323C2×C4⋊C4—762no—
324C2×C4⋊C4—762no—
325C2×C4⋊C4D7611yescharacteristic
326C2×C4⋊C4D7611yescharacteristic
327C2×C22⋊C4—21no—
328C2×C22⋊C4—381no—
329C2×C22⋊C4—381no—
330C2×C22⋊C4—381no—
331C2×C22⋊C4—381no—
332C2×C42—381no—
333#106—762no—
334#102—762no—
335C22⋊C8—21no—
336C22⋊C8—21no—
337C22⋊C8—192no—
338C22⋊C8—381no—
339#95—21no—
340#95—21no—
341#95—381no—
342#95—381no—
343#95—381no—
344#95—381no—
345#95—762no—
346#95C4×D1912yescomplemented
347C19#887311yescharacteristic, complemented, Sylow
348C24—381no—
349C24D4×D1911yescharacteristic
350C2×D4—192no—
351C2×D4—382no—
352C2×D4—382no—
353C2×D4—381no—
354C2×D4—761no—
355C2×D4—761no—
356C2×D4—761no—
357C2×D4—761no—
358C2×D4—761no—
359C2×D4—761no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4—41no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—41no—
371C22×C4—192no—
372C22×C4—381no—
373C22×C4—381no—
374C22×C4—381no—
375C22×C4—382no—
376C22×C4—381no—
377C22×C4—381no—
378C22×C4—381no—
379C22×C4—762no—
380C22×C4—761no—
381C22×C4—761no—
382C22×C4—761no—
383C22×C4—761no—
384C22×C4—761no—
385C22×C4—761no—
386C22×C4—761no—
387C22×C4—761no—
388C22×C4—761no—
389C22×C4—761no—
390C22×C4—1521no—
391C22×C4—1521no—
392C22×C4C2×C4×D1911yescharacteristic
393C22×C4C2×D7611yescharacteristic
394C22×C4#6454111yescharacteristic
395C22×C4D4×D1911yescharacteristic
396C22×C4#6454311yescharacteristic
397C22×C4Q8×D1911yescharacteristic
398C2×C8—41no—
399C2×C8—41no—
400C2×C8—41no—
401C2×C8—382no—
402C2×C8—761no—
403C2×C8—761no—
404C4⋊C4—41no—
405C4⋊C4—41no—
406C4⋊C4—192no—
407C4⋊C4—382no—
408C4⋊C4—382no—
409C4⋊C4—381no—
410C4⋊C4—761no—
411C4⋊C4—761no—
412C4⋊C4—762no—
413C4⋊C4—768no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—382no—
417C22⋊C4—382no—
418C22⋊C4—762no—
419C22⋊C4—1521no—
420C22⋊C4—1521no—
421C42—762no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—21no—
426C23—382no—
427C23—761no—
428C23—761no—
429C23—761no—
430C23—761no—
431C23—761no—
432C23—761no—
433C23(C22⋊D19)⋊C411yescharacteristic
434C23#1059732811yescharacteristic
435C23#1059734211yescharacteristic
436C23#1059735711yescharacteristic
437C23SD16×D1911yescharacteristic
438C23#1059736011yescharacteristic
439C23#1059736511yescharacteristic
440D4—762no—
441D4—762no—
442D4—762no—
443D4—762no—
444D4—762no—
445D4—1521no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—24no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—382no—
468C2×C4—382no—
469C2×C4—761no—
470C2×C4—761no—
471C2×C4—761no—
472C2×C4—761no—
473C2×C4—762no—
474C2×C4—762no—
475C2×C4—762no—
476C2×C4—762no—
477C2×C4—761no—
478C2×C4—761no—
479C2×C4—761no—
480C2×C4—762no—
481C2×C4—1524no—
482C2×C4—1521no—
483C2×C4—1521no—
484C2×C4—1521no—
485C2×C4—1521no—
486C2×C4—1521no—
487C2×C4—1521no—
488C2×C4C4×D7611yescharacteristic
489C2×C4#1059732911yescharacteristic
490C2×C4C4⋊C4×D1911yescharacteristic
491C2×C4#1059734311yescharacteristic
492C8—81no—
493C8—762no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—762no—
507C22—762no—
508C22—762no—
509C22—1521no—
510C22—1521no—
511C22—1521no—
512C22—1521no—
513C22#1192641811yescharacteristic
514C22#1192662911yescharacteristic
515C22#1192665311yescharacteristic
516C22#1192669211yescharacteristic
517C22#1192669611yescharacteristic
518C22#1192671311yescharacteristic
519C22#1192672811yescharacteristic
520C22#1192673211yescharacteristic
521C22#1192673511yescharacteristic
522C22#1192683311yescharacteristic
523C22#1192684711yescharacteristic
524C4—21no—
525C4—21no—
526C4—21no—
527C4—21no—
528C4—44no—
529C4—81no—
530C4—81no—
531C4—762no—
532C4—762no—
533C4—1521no—
534C4—1522no—
535C2—21no—
536C2—21no—
537C2—21no—
538C2—21no—
539C2—1522no—
540C2#1456258411yescharacteristic
541C2#1456260511yescharacteristic
542C2#1456263511yescharacteristic
543C2#1456265611yescharacteristic
544C2#1456386211yescharacteristic
545C2#1456389711yescharacteristic
546C2#1456391711yescharacteristic
subgroupG/H
centerC23#10597328
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1294C2
socleC23×C19#120
prime radicalC2×#10597376C22
cosocleC23×C4×C19C23
hypercenter#1294D19
hypocenterC19#8873
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
3. #14563827C2semidirect
5. #14561900C2semidirect
6. #14561477C2semidirect
7. C19×#1294C2semidirect
24. #11926277C4semidirect
64. C19×#95C2×C4semidirect
71. C22⋊(C19⋊C8)C2×C4semidirect
120. C2×D76C4⋊C4semidirect
142. C4⋊Dic19C4⋊C4semidirect
226. #1294D19semidirect
346. #95C4×D19semidirect
347. C19#8873semidirect

Maximal subgroups

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

subgroupindex
#145663352
#145639502
#145638272
C2×#119262772
#145619002
#145614772
C19×#12942
#887319