Finite Group Databasebeta

← #18077689

Subgroups — #18077689

Order 4864.

678 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926858C211yesmaximal, characteristic
2#14566338C211yesmaximal, characteristic
3#14563722C211yesmaximal, characteristic, complemented
4C2×#11926279C211yesmaximal, characteristic
5#14561902C211yesmaximal, characteristic, complemented
6#14561515C211yesmaximal, characteristic, complemented
7C19×#1280C211yesmaximal, characteristic, complemented
8C2×#10597376C2211yescharacteristic
9C2×C4×C22⋊D19—21no—
10C22×C4⋊Dic19C2211yescharacteristic
11#11926858—22no—
12#11926858C414yescomplemented
13C2×#10597275—21no—
14C2×#10597278—21no—
15#11926436—21no—
16#11926429—21no—
17#11926423—21no—
18#11926422—21no—
19#11926418—21no—
20#11926404C2211yescharacteristic
21C2×C19⋊#95—21no—
22C2×C19⋊#95—21no—
23C2×C19⋊#95C2211yescharacteristic
24#11926307—21no—
25#11926307—21no—
26#11926279—22no—
27C2×C19×C22⋊C8C2211yescharacteristic
28C2×C19×C22⋊C8C2211yescharacteristic
29C2×C19×#95C2211yescharacteristic
30C23×C4×C19D411yescharacteristic
31C23×C4×C19D411yescharacteristic
32C23×C4×C19C2311yescharacteristic
33C22×C22⋊D19—21no—
34C23×Dic19—21no—
35C23×Dic19—21no—
36C22×D76D411yescharacteristic
37C22×C4×D19—21no—
38C22×C8×C19—21no—
39C22×C8×C19—21no—
40C2×C22⋊Dic19—21no—
41#10597376—21no—
42#10597376—21no—
43#10597376C2×C412yes—
44#10597376D412yes—
45C4×C22⋊D19—42no—
46C4×C22⋊D19—42no—
47C2×(C2×D19)⋊C4—21no—
48C2×(C2×D19)⋊C4—21no—
49C2×(C2×D19)⋊C4—21no—
50C2×(C2×D19)⋊C4—21no—
51C2×C4⋊Dic19—21no—
52C2×C4⋊Dic19—21no—
53C2×C4⋊Dic19—21no—
54C2×C4⋊Dic19—21no—
55C2×C4⋊Dic19—21no—
56C2×C4⋊Dic19C2×C412yescomplemented
57C2×C4⋊Dic19D411yescharacteristic
58C2×C4⋊Dic19D411yescharacteristic
59C2×C4⋊Dic19D411yescharacteristic
60C2×Dic19⋊C4—21no—
61C2×C4×Dic19—21no—
62C19×C22⋊C8—21no—
63C19×C22⋊C8—21no—
64C19×C22⋊C8—21no—
65C19×C22⋊C8C2×C412yescomplemented
66C19×#95—21no—
67C19×#95—21no—
68C19⋊#95—21no—
69C19⋊#95—21no—
70C19⋊#95—21no—
71C19⋊#95—21no—
72C19⋊#95—21no—
73C19⋊#95—42no—
74C19⋊#95—42no—
75#10597278—24no—
76#10597275—24no—
77C24×C19C2×D411yescharacteristic
78C23×D19—21no—
79C22×C4×C19—21no—
80C22×C4×C19—21no—
81C22×C4×C19—21no—
82C22×C4×C19—21no—
83C22×C4×C19—21no—
84C22×C4×C19—41no—
85C22×C4×C19—41no—
86C22×C4×C19—41no—
87C22×C4×C19—41no—
88C22×C4×C19—41no—
89C22×C4×C19—41no—
90C22×C4×C19D812yes—
91C22×C4×C19C22×C411yescharacteristic
92C22×C4×C19C2×D411yescharacteristic
93C22×C4×C19C2×D411yescharacteristic
94C22×C4×C19C2×D411yescharacteristic
95C22×C4×C19#4111yescharacteristic
96C22×C4×C19#4111yescharacteristic
97C2×C22⋊D19—22no—
98C2×C22⋊D19—22no—
99C2×C22⋊D19—41no—
100C2×C22⋊D19—41no—
101C2×C22⋊D19—41no—
102C2×C22⋊D19—41no—
103C22×Dic19—21no—
104C22×Dic19—22no—
105C22×Dic19—22no—
106C22×Dic19—21no—
107C22×Dic19—21no—
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×Dic19—41no—
117C22×Dic19—41no—
118C22×Dic19—41no—
119C22×Dic19—41no—
120C2×D76—21no—
121C2×D76—41no—
122C2×D76—41no—
123C2×D76C22⋊C412yes—
124C2×C4×D19—42no—
125C2×C4×D19—81no—
126C2×C4×D19—81no—
127C2×C8×C19—22no—
128C2×C8×C19—41no—
129C2×C8×C19—41no—
130C2×C8×C19—41no—
131C2×C8×C19—41no—
132C2×C8×C19—41no—
133C22⋊Dic19—41no—
134C22⋊Dic19—41no—
135(C2×D19)⋊C4—22no—
136(C2×D19)⋊C4—22no—
137(C2×D19)⋊C4—42no—
138(C2×D19)⋊C4—81no—
139(C2×D19)⋊C4—81no—
140C4⋊Dic19—21no—
141C4⋊Dic19—22no—
142C4⋊Dic19—22no—
143C4⋊Dic19—41no—
144C4⋊Dic19—41no—
145C4⋊Dic19—41no—
146C4⋊Dic19—41no—
147C4⋊Dic19C22⋊C412yes—
148Dic19⋊C4—42no—
149C4×Dic19—42no—
150#9043—191nomaximal, Sylow
151C23×C19—21no—
152C23×C19—21no—
153C23×C19—21no—
154C23×C19—21no—
155C23×C19C4×D411yescharacteristic
156C23×C19#12011yescharacteristic
157C23×C19#12111yescharacteristic
158C23×C19C2×D811yescharacteristic
159C23×C19#13511yescharacteristic
160C23×C19AGL(1,ℤ/8)11yescharacteristic
161C23×C19AGL(1,ℤ/8)11yescharacteristic
162C22×D19—22no—
163C22×D19—41no—
164C22×D19—41no—
165C22×D19—41no—
166C22×D19—41no—
167C22×D19—41no—
168C22×D19—41no—
169C2×C4×C19—21no—
170C2×C4×C19—21no—
171C2×C4×C19—21no—
172C2×C4×C19—21no—
173C2×C4×C19—22no—
174C2×C4×C19—41no—
175C2×C4×C19—41no—
176C2×C4×C19—41no—
177C2×C4×C19—41no—
178C2×C4×C19—41no—
179C2×C4×C19—41no—
180C2×C4×C19—42no—
181C2×C4×C19—42no—
182C2×C4×C19—41no—
183C2×C4×C19—41no—
184C2×C4×C19—41no—
185C2×C4×C19—81no—
186C2×C4×C19—81no—
187C2×C4×C19C2×C22⋊C411yescharacteristic
188C2×C4×C19C4×D411yescharacteristic
189C2×C4×C19#12111yescharacteristic
190C2×C4×C19#12311yescharacteristic
191C22⋊D19—42no—
192C22⋊D19—42no—
193C22⋊D19—42no—
194C22⋊D19—42no—
195C2×Dic19—22no—
196C2×Dic19—41no—
197C2×Dic19—41no—
198C2×Dic19—42no—
199C2×Dic19—42no—
200C2×Dic19—42no—
201C2×Dic19—42no—
202C2×Dic19—42no—
203C2×Dic19—42no—
204C2×Dic19—41no—
205C2×Dic19—41no—
206C2×Dic19—41no—
207C2×Dic19—41no—
208C2×Dic19—41no—
209C2×Dic19—41no—
210C2×Dic19—81no—
211C2×Dic19—81no—
212C2×Dic19—81no—
213C2×Dic19—81no—
214C2×Dic19—81no—
215C2×Dic19—81no—
216C2×Dic19—81no—
217C2×Dic19—81no—
218D76—42no—
219D76—81no—
220C4×D19—84no—
221C8×C19—42no—
222C8×C19—81no—
223C2×#480—191no—
224#2325—191no—
225#1823—191no—
226C2×#327—191no—
227#1445—191no—
228#1294—191no—
229#1280D1911yescharacteristic, complemented
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—21no—
241C22×C19—21no—
242C22×C19#38611yescharacteristic
243C22×C19C4×D811yescharacteristic
244C22×C19#44211yescharacteristic
245C22×C19#44711yescharacteristic
246C22×C19#44911yescharacteristic
247C22×C19#45511yescharacteristic
248C22×C19#45611yescharacteristic
249C22×C19#45811yescharacteristic
250C22×C19#45811yescharacteristic
251C22×C19#45911yescharacteristic
252C22×C19#46311yescharacteristic
253C2×D19—42no—
254C2×D19—42no—
255C2×D19—42no—
256C2×D19—81no—
257C2×D19—81no—
258C2×D19—81no—
259C2×D19—81no—
260C4×C19—21no—
261C4×C19—21no—
262C4×C19—21no—
263C4×C19—21no—
264C4×C19—42no—
265C4×C19—81no—
266Dic19—42no—
267Dic19—82no—
268Dic19—81no—
269Dic19—81no—
270Dic19—82no—
271C2×#121—191no—
272C2×C4×D4—381no—
273C22×C4⋊C4—191no—
274#480—194no—
275#480—382no—
276C2×#107—381no—
277C2×#102—381no—
278C2×C22⋊C8C2×D1911yescharacteristic
279C2×C22⋊C8C2×D1911yescharacteristic
280#388—381no—
281#387—381no—
282#386—381no—
283#386—381no—
284#385—381no—
285#380—191no—
286C2×#95—191no—
287C2×#95—381no—
288C2×#95—381no—
289C2×#95C2×D1911yescharacteristic
290#340—381no—
291#340—381no—
292#327—382no—
293C2×C19—21no—
294C2×C19—21no—
295C2×C19—21no—
296C2×C19—21no—
297C2×C19#160711yescharacteristic
298C2×C19#160911yescharacteristic
299C2×C19#161011yescharacteristic
300C2×C19#161211yescharacteristic
301C2×C19#187911yescharacteristic
302C2×C19#188211yescharacteristic
303C2×C19#189011yescharacteristic
304D19—82no—
305C22×D4—191no—
306C22×D4—381no—
307C23×C4—381no—
308C23×C4—381no—
309C23×C4—381no—
310C23×C4D7611yescharacteristic
311C23×C4D7611yescharacteristic
312C23×C4C22×D1911yescharacteristic
313C22×C8—21no—
314C22×C8—21no—
315#121—192no—
316#121—192no—
317#121—381no—
318#121—381no—
319C4×D4—762no—
320C4×D4—762no—
321C2×C4⋊C4—191no—
322C2×C4⋊C4—192no—
323C2×C4⋊C4—191no—
324C2×C4⋊C4—191no—
325C2×C4⋊C4—381no—
326C2×C4⋊C4—381no—
327C2×C4⋊C4—381no—
328C2×C4⋊C4—381no—
329C2×C4⋊C4—381no—
330C2×C4⋊C4—381no—
331C2×C22⋊C4—381no—
332C2×C22⋊C4—381no—
333C2×C22⋊C4—381no—
334C2×C22⋊C4—381no—
335C2×C22⋊C4—381no—
336C2×C42—381no—
337#107—384no—
338#102—384no—
339C22⋊C8—21no—
340C22⋊C8—21no—
341C22⋊C8—21no—
342C22⋊C8C4×D1912yescomplemented
343#95—21no—
344#95—21no—
345#95—381no—
346#95—381no—
347#95—381no—
348#95—381no—
349#95—381no—
350#95—762no—
351#95—762no—
352C19#904311yescharacteristic, complemented, Sylow
353C24—381no—
354C24C2×D7611yescharacteristic
355C2×D4—192no—
356C2×D4—382no—
357C2×D4—382no—
358C2×D4—381no—
359C2×D4—761no—
360C2×D4—761no—
361C2×D4—761no—
362C2×D4—761no—
363C2×D4—761no—
364C2×D4—761no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—381no—
377C22×C4—382no—
378C22×C4—382no—
379C22×C4—381no—
380C22×C4—381no—
381C22×C4—762no—
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—761no—
391C22×C4—761no—
392C22×C4—761no—
393C22×C4—761no—
394C22×C4—1521no—
395C22×C4—1521no—
396C22×C4D15212yes—
397C22×C4C2×C4×D1911yescharacteristic
398C22×C4#6454111yescharacteristic
399C22×C4D4×D1911yescharacteristic
400C22×C4D4×D1911yescharacteristic
401C22×C4D4×D1911yescharacteristic
402C22×C4#6454511yescharacteristic
403C2×C8—22no—
404C2×C8—41no—
405C2×C8—41no—
406C2×C8—41no—
407C2×C8—41no—
408C2×C8—41no—
409C4⋊C4—192no—
410C4⋊C4—381no—
411C4⋊C4—382no—
412C4⋊C4—382no—
413C4⋊C4—761no—
414C4⋊C4—761no—
415C4⋊C4—762no—
416C4⋊C4—761no—
417C4⋊C4—761no—
418C22⋊C4—382no—
419C22⋊C4—382no—
420C22⋊C4—762no—
421C22⋊C4—761no—
422C22⋊C4—761no—
423C22⋊C4—1521no—
424C22⋊C4—1521no—
425C42—762no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—382no—
431C23—761no—
432C23—761no—
433C23—761no—
434C23—761no—
435C23—761no—
436C23—761no—
437C23C4×D7611yescharacteristic
438C23#1059732811yescharacteristic
439C23#1059734111yescharacteristic
440C23C2×D15211yescharacteristic
441C23#1059735011yescharacteristic
442C23#1059735411yescharacteristic
443C23#1059735411yescharacteristic
444D4—762no—
445D4—762no—
446D4—762no—
447D4—762no—
448D4—762no—
449D4—1521no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—22no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—81no—
467C2×C4—81no—
468C2×C4—382no—
469C2×C4—761no—
470C2×C4—761no—
471C2×C4—762no—
472C2×C4—762no—
473C2×C4—762no—
474C2×C4—762no—
475C2×C4—762no—
476C2×C4—762no—
477C2×C4—761no—
478C2×C4—761no—
479C2×C4—761no—
480C2×C4—761no—
481C2×C4—761no—
482C2×C4—761no—
483C2×C4—1524no—
484C2×C4—1521no—
485C2×C4—1521no—
486C2×C4—1521no—
487C2×C4—1521no—
488C2×C4—1521no—
489C2×C4—1521no—
490C2×C4—1521no—
491C2×C4—1521no—
492C2×C4C22⋊C4×D1911yescharacteristic
493C2×C4#1059733011yescharacteristic
494C2×C4#1059733911yescharacteristic
495C2×C4#1059734011yescharacteristic
496C8—42no—
497C8—81no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—762no—
511C22—762no—
512C22—762no—
513C22—1521no—
514C22—1521no—
515C22—1521no—
516C22—1521no—
517C22#1192642211yescharacteristic
518C22C4×D15211yescharacteristic
519C22#1192665711yescharacteristic
520C22#1192668011yescharacteristic
521C22#1192669111yescharacteristic
522C22#1192672411yescharacteristic
523C22#1192672911yescharacteristic
524C22#1192673511yescharacteristic
525C22#1192673511yescharacteristic
526C22#1192674011yescharacteristic
527C22#1192676011yescharacteristic
528C4—21no—
529C4—21no—
530C4—21no—
531C4—21no—
532C4—42no—
533C4—81no—
534C4—762no—
535C4—1522no—
536C4—1521no—
537C4—1521no—
538C4—1522no—
539C2—21no—
540C2—21no—
541C2—21no—
542C2—21no—
543C2—1522no—
544C2#1456262311yescharacteristic
545C2#1456263411yescharacteristic
546C2#1456264011yescharacteristic
547C2#1456265111yescharacteristic
548C2#1456398211yescharacteristic
549C2#1456400311yescharacteristic
550C2#1456404711yescharacteristic
subgroupG/H
centerC23#10597328
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1280C2
socleC23×C19#120
prime radicalC2×#10597376C22
cosocleC23×C4×C19C23
hypercenter#1280D19
hypocenterC19#9043
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
3. #14563722C2semidirect
5. #14561902C2semidirect
6. #14561515C2semidirect
7. C19×#1280C2semidirect
12. #11926858C4semidirect
56. C2×C4⋊Dic19C2×C4semidirect
65. C19×C22⋊C8C2×C4semidirect
229. #1280D19semidirect
342. C22⋊C8C4×D19semidirect
352. C19#9043semidirect

Maximal subgroups

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

subgroupindex
C2×#119268582
#145663382
#145637222
C2×#119262792
#145619022
#145615152
C19×#12802
#904319