Finite Group Databasebeta

← #18078128

Subgroups — #18078128

Order 4864.

674 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926598C211yesmaximal, characteristic, complemented
2#14571967C211yesmaximal, characteristic
3C2×#11926279C211yesmaximal, characteristic
4C2×#11926277C211yesmaximal, characteristic
5#14561859C211yesmaximal, characteristic, complemented
6#14561513C211yesmaximal, characteristic, complemented
7C19×#1294C211yesmaximal, characteristic, complemented
8C2×#10597332—21no—
9C2×#10597376C2211yescharacteristic
10C22×C4×Dic19C2211yescharacteristic
11#11926598—22no—
12#11926598—22no—
13C2×Dic19⋊C8—21no—
14C2×C22⋊(C19⋊C8)C2211yescharacteristic
15C2×#10597272—21no—
16#11926445C411yescharacteristic, complemented
17#11926445C411yescharacteristic, complemented
18#11926443C411yescharacteristic, complemented
19#11926443C411yescharacteristic, complemented
20#11926436—21no—
21#11926436—21no—
22#11926421—21no—
23C2×C19⋊#95—21no—
24C2×C19⋊#95—21no—
25C2×C19⋊#95C2211yescharacteristic
26#11926279—22no—
27#11926277—22no—
28C2×C19×C22⋊C8C2211yescharacteristic
29C19×#380C2211yescharacteristic
30C2×C19×#95C2211yescharacteristic
31C23×C4×C19—21no—
32C23×C4×C19C2311yescharacteristic
33C22×C22⋊D19—21no—
34C23×Dic19—21no—
35C23×Dic19D411yescharacteristic
36C23×Dic19D411yescharacteristic
37C22×D76C2×C411yescharacteristic
38C22×C8×C19—21no—
39C2×C4⋊C4×C19C2×C411yescharacteristic
40C2×C4⋊C4×C19C2×C411yescharacteristic
41C2×C22⋊C4×C19—21no—
42#10597376—21no—
43#10597376—21no—
44#10597376—21no—
45#10597376—21no—
46C2×(C2×D19)⋊C4—21no—
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⋊Dic19C2×C411yescharacteristic
54C2×C4×Dic19—21no—
55C2×C4×Dic19—21no—
56C2×C4×Dic19—21no—
57C2×C4×Dic19—21no—
58C2×C4×Dic19C2×C411yescharacteristic
59C2×C4×Dic19C2×C411yescharacteristic
60C2×C4×Dic19D411yescharacteristic
61C2×C4×Dic19D411yescharacteristic
62C22×C19⋊C8—21no—
63#10597332—42no—
64#10597332—42no—
65C19×C22⋊C8—21no—
66C19×C22⋊C8D412yes—
67C19×#95—21no—
68C19×#95—21no—
69C19×#95—21no—
70C19⋊#95—24no—
71C19⋊#95—21no—
72C19⋊#95—21no—
73C19⋊#95—21no—
74C19⋊#95—21no—
75C19⋊#95—42no—
76C22⋊(C19⋊C8)—21no—
77C22⋊(C19⋊C8)D412yes—
78#10597272—24no—
79Dic19⋊C8—24no—
80C24×C19C2×D411yescharacteristic
81C23×D19—21no—
82C22×C4×C19—22no—
83C22×C4×C19—21no—
84C22×C4×C19—21no—
85C22×C4×C19—41no—
86C22×C4×C19—41no—
87C22×C4×C19—41no—
88C22×C4×C19—41no—
89C22×C4×C19—41no—
90C22×C4×C19—41no—
91C22×C4×C19—41no—
92C22×C4×C19—41no—
93C22×C4×C19C22×C411yescharacteristic
94C22×C4×C19C2×D411yescharacteristic
95C22×C4×C19C2×D411yescharacteristic
96C22×C4×C19C2×D411yescharacteristic
97C22×C4×C19#4111yescharacteristic
98C22×C4×C19#4111yescharacteristic
99C2×C22⋊D19—41no—
100C2×C22⋊D19—41no—
101C2×C22⋊D19—41no—
102C2×C22⋊D19—41no—
103C2×C22⋊D19—41no—
104C2×C22⋊D19—41no—
105C22×Dic19—21no—
106C22×Dic19—21no—
107C22×Dic19—21no—
108C22×Dic19—21no—
109C22×Dic19—21no—
110C22×Dic19—21no—
111C22×Dic19—21no—
112C22×Dic19—21no—
113C22×Dic19—22no—
114C22×Dic19—22no—
115C22×Dic19—21no—
116C22×Dic19—41no—
117C22×Dic19—41no—
118C22×Dic19—41no—
119C22×Dic19—41no—
120C22×Dic19—41no—
121C22×Dic19—41no—
122C22×Dic19—41no—
123C22×Dic19C22⋊C411yescharacteristic
124C22×Dic19C22⋊C411yescharacteristic
125C22×Dic19C22⋊C411yescharacteristic
126C22×Dic19C22⋊C411yescharacteristic
127C2×D76—21no—
128C2×D76—21no—
129C2×D76—41no—
130C2×D76—41no—
131C2×C8×C19—22no—
132C2×C8×C19—41no—
133C2×C8×C19—41no—
134C4⋊C4×C19—41no—
135C4⋊C4×C19—41no—
136C22⋊C4×C19—41no—
137C22⋊C4×C19—41no—
138(C2×D19)⋊C4—42no—
139(C2×D19)⋊C4—42no—
140(C2×D19)⋊C4—42no—
141(C2×D19)⋊C4—41no—
142(C2×D19)⋊C4—41no—
143(C2×D19)⋊C4—42no—
144C4⋊Dic19—21no—
145C4⋊Dic19—21no—
146C4⋊Dic19—42no—
147C4⋊Dic19—42no—
148C4×Dic19—21no—
149C4×Dic19—21no—
150C4×Dic19—21no—
151C4×Dic19—21no—
152C4×Dic19—21no—
153C4×Dic19—21no—
154C4×Dic19—21no—
155C4×Dic19—21no—
156C2×C19⋊C8—22no—
157C2×C19⋊C8—41no—
158C2×C19⋊C8—41no—
159#9118—191nomaximal, Sylow
160C23×C19—21no—
161C23×C19—21no—
162C23×C19—21no—
163C23×C19—21no—
164C23×C19C2×C22⋊C411yescharacteristic
165C23×C19#12111yescharacteristic
166C23×C19#12111yescharacteristic
167C23×C19AGL(1,ℤ/8)11yescharacteristic
168C23×C19AGL(1,ℤ/8)11yescharacteristic
169C23×C19AGL(1,ℤ/8)11yescharacteristic
170C23×C19#13711yescharacteristic
171C22×D19—41no—
172C22×D19—41no—
173C22×D19—41no—
174C22×D19—41no—
175C22×D19—41no—
176C22×D19—41no—
177C22×D19—41no—
178C2×C4×C19—21no—
179C2×C4×C19—21no—
180C2×C4×C19—21no—
181C2×C4×C19—21no—
182C2×C4×C19—41no—
183C2×C4×C19—41no—
184C2×C4×C19—41no—
185C2×C4×C19—41no—
186C2×C4×C19—42no—
187C2×C4×C19—42no—
188C2×C4×C19—42no—
189C2×C4×C19—41no—
190C2×C4×C19—41no—
191C2×C4×C19—41no—
192C2×C4×C19—41no—
193C2×C4×C19—41no—
194C2×C4×C19—41no—
195C2×C4×C19—81no—
196C2×C4×C19—81no—
197C2×C4×C19—81no—
198C2×C4×C19—81no—
199C2×C4×C19C4×D411yescharacteristic
200C2×C4×C19C4×D411yescharacteristic
201C2×C4×C19#12011yescharacteristic
202C2×C4×C19#12311yescharacteristic
203C22⋊D19—81no—
204C22⋊D19—81no—
205C22⋊D19—81no—
206C22⋊D19—81no—
207C2×Dic19—21no—
208C2×Dic19—21no—
209C2×Dic19—21no—
210C2×Dic19—21no—
211C2×Dic19—21no—
212C2×Dic19—21no—
213C2×Dic19—21no—
214C2×Dic19—21no—
215C2×Dic19—21no—
216C2×Dic19—21no—
217C2×Dic19—21no—
218C2×Dic19—42no—
219C2×Dic19—42no—
220C2×Dic19—41no—
221C2×Dic19—41no—
222C2×Dic19—41no—
223C2×Dic19—41no—
224C2×Dic19—42no—
225C2×Dic19—42no—
226C2×Dic19—42no—
227C2×Dic19—41no—
228C2×Dic19—41no—
229C2×Dic19—41no—
230C2×Dic19—81no—
231C2×Dic19—81no—
232C2×Dic19—81no—
233C2×Dic19—81no—
234C2×Dic19#10412yes—
235D76—81no—
236D76—81no—
237C8×C19—42no—
238C19⋊C8—42no—
239C2×#432—191no—
240#2854—191no—
241C2×#327—191no—
242C2×#327—191no—
243#1434—191no—
244#1294—191no—
245#1294D1911yescharacteristic, complemented
246C22×C19—21no—
247C22×C19—21no—
248C22×C19—21no—
249C22×C19—21no—
250C22×C19—21no—
251C22×C19—21no—
252C22×C19—21no—
253C22×C19—21no—
254C22×C19—21no—
255C22×C19—21no—
256C22×C19—21no—
257C22×C19—21no—
258C22×C19#38611yescharacteristic
259C22×C19#41011yescharacteristic
260C22×C19#41011yescharacteristic
261C22×C19#41711yescharacteristic
262C22×C19#41811yescharacteristic
263C22×C19C2×#10411yescharacteristic
264C22×C19#42111yescharacteristic
265C22×C19#46811yescharacteristic
266C22×C19#46811yescharacteristic
267C22×C19#46911yescharacteristic
268C22×C19#46911yescharacteristic
269C2×D19—81no—
270C2×D19—81no—
271C2×D19—81no—
272C2×D19—81no—
273C2×D19—81no—
274C2×D19—81no—
275C2×D19—81no—
276C4×C19—21no—
277C4×C19—21no—
278C4×C19—21no—
279C4×C19—21no—
280C4×C19—82no—
281C4×C19—81no—
282C4×C19—81no—
283Dic19—22no—
284Dic19—41no—
285Dic19—41no—
286Dic19—41no—
287Dic19—82no—
288Dic19—81no—
289C2×#123—381no—
290C2×#121—191no—
291C22×C42—191no—
292#432—382no—
293#432—382no—
294C2×C4⋊C8—381no—
295C2×C22⋊C8—191no—
296C2×C22⋊C8C2×D1911yescharacteristic
297C2×#97—381no—
298#390—191no—
299#390—191no—
300#389—191no—
301#389—191no—
302#388—381no—
303#388—381no—
304#386—381no—
305#380C2×D1911yescharacteristic
306C2×#95—191no—
307C2×#95—381no—
308C2×#95—381no—
309C2×#95C2×D1911yescharacteristic
310#327—382no—
311#327—382no—
312C2×C19—21no—
313C2×C19—21no—
314C2×C19—21no—
315C2×C19—21no—
316C2×C19#150511yescharacteristic
317C2×C19#150911yescharacteristic
318C2×C19#151211yescharacteristic
319C2×C19#151411yescharacteristic
320C2×C19#187111yescharacteristic
321C2×C19#189511yescharacteristic
322C2×C19#189911yescharacteristic
323D19—161no—
324C22×D4—191no—
325C22×D4—381no—
326C23×C4—21no—
327C23×C4—191no—
328C23×C4—191no—
329C23×C4—381no—
330C23×C4C22×D1911yescharacteristic
331C22×C8—21no—
332C22×C8—381no—
333#123—762no—
334#123—762no—
335#121—381no—
336#121—381no—
337#121—381no—
338#121—381no—
339C2×C4⋊C4—191no—
340C2×C4⋊C4—381no—
341C2×C4⋊C4—381no—
342C2×C4⋊C4C4×D1911yescharacteristic
343C2×C4⋊C4C4×D1911yescharacteristic
344C2×C22⋊C4—21no—
345C2×C22⋊C4—381no—
346C2×C22⋊C4—381no—
347C2×C22⋊C4—381no—
348C2×C22⋊C4—381no—
349C2×C22⋊C4—381no—
350C2×C42—191no—
351C2×C42—191no—
352C2×C42—191no—
353C2×C42—191no—
354C2×C42—381no—
355C2×C42—381no—
356C2×C42—381no—
357C2×C42—381no—
358C4⋊C8—384no—
359C22⋊C8—21no—
360C22⋊C8—192no—
361C22⋊C8—381no—
362C22⋊C8D7612yes—
363#97—384no—
364#95—21no—
365#95—21no—
366#95—21no—
367#95—381no—
368#95—381no—
369#95—384no—
370#95—381no—
371#95—381no—
372#95—762no—
373C19#911811yescharacteristic, complemented, Sylow
374C24—381no—
375C24D4×D1911yescharacteristic
376C2×D4—381no—
377C2×D4—381no—
378C2×D4—761no—
379C2×D4—761no—
380C2×D4—761no—
381C2×D4—761no—
382C2×D4—761no—
383C2×D4—761no—
384C2×D4—761no—
385C2×D4—761no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—191no—
398C22×C4—191no—
399C22×C4—191no—
400C22×C4—191no—
401C22×C4—382no—
402C22×C4—381no—
403C22×C4—381no—
404C22×C4—381no—
405C22×C4—381no—
406C22×C4—381no—
407C22×C4—381no—
408C22×C4—381no—
409C22×C4—381no—
410C22×C4—382no—
411C22×C4—381no—
412C22×C4—761no—
413C22×C4—761no—
414C22×C4—761no—
415C22×C4—761no—
416C22×C4—761no—
417C22×C4—761no—
418C22×C4—761no—
419C22×C4C2×C4×D1911yescharacteristic
420C22×C4C2×D7611yescharacteristic
421C22×C4#6454111yescharacteristic
422C22×C4D4×D1911yescharacteristic
423C22×C4D4×D1911yescharacteristic
424C22×C4#6454511yescharacteristic
425C2×C8—22no—
426C2×C8—41no—
427C2×C8—41no—
428C2×C8—382no—
429C2×C8—761no—
430C2×C8—761no—
431C4⋊C4—41no—
432C4⋊C4—41no—
433C4⋊C4—381no—
434C4⋊C4—381no—
435C4⋊C4—762no—
436C4⋊C4—762no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—762no—
440C22⋊C4—762no—
441C22⋊C4—762no—
442C22⋊C4—762no—
443C22⋊C4—761no—
444C22⋊C4—761no—
445C42—381no—
446C42—381no—
447C42—381no—
448C42—381no—
449C42—381no—
450C42—381no—
451C42—381no—
452C42—381no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—761no—
458C23—761no—
459C23—761no—
460C23—761no—
461C23—761no—
462C23—761no—
463C23—761no—
464C23C22⋊C4×D1911yescharacteristic
465C23#1059733011yescharacteristic
466C23#1059734111yescharacteristic
467C23#1059735711yescharacteristic
468C23#1059736011yescharacteristic
469C23#1059736011yescharacteristic
470C23#1059736411yescharacteristic
471D4—1521no—
472D4—1521no—
473D4—1521no—
474D4—1521no—
475D4—1521no—
476D4—1521no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—81no—
495C2×C4—81no—
496C2×C4—81no—
497C2×C4—81no—
498C2×C4—192no—
499C2×C4—381no—
500C2×C4—381no—
501C2×C4—381no—
502C2×C4—381no—
503C2×C4—381no—
504C2×C4—381no—
505C2×C4—381no—
506C2×C4—381no—
507C2×C4—381no—
508C2×C4—381no—
509C2×C4—381no—
510C2×C4—762no—
511C2×C4—762no—
512C2×C4—761no—
513C2×C4—761no—
514C2×C4—761no—
515C2×C4—761no—
516C2×C4—762no—
517C2×C4—762no—
518C2×C4—762no—
519C2×C4—761no—
520C2×C4—761no—
521C2×C4—761no—
522C2×C4—1521no—
523C2×C4—1521no—
524C2×C4—1521no—
525C2×C4—1521no—
526C2×C4C4×D7611yescharacteristic
527C2×C4#1059732811yescharacteristic
528C2×C4#1059733911yescharacteristic
529C2×C4#1059734011yescharacteristic
530C8—42no—
531C8—762no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—1521no—
545C22—1521no—
546C22—1521no—
547C22—1521no—
548C22—1521no—
549C22—1521no—
550C22—1521no—
551C22#1192642211yescharacteristic
552C22#1192651611yescharacteristic
553C22#1192651611yescharacteristic
554C22#1192654411yescharacteristic
555C22#1192654711yescharacteristic
556C22#104×D1911yescharacteristic
557C22#1192655911yescharacteristic
558C22#1192679111yescharacteristic
559C22#1192679311yescharacteristic
560C22#1192679611yescharacteristic
561C22#1192679811yescharacteristic
562C4—21no—
563C4—21no—
564C4—21no—
565C4—21no—
566C4—82no—
567C4—81no—
568C4—81no—
569C4—382no—
570C4—761no—
571C4—761no—
572C4—761no—
573C4—1522no—
574C4—1521no—
575C2—21no—
576C2—21no—
577C2—21no—
578C2—21no—
579C2—3041no—
580C2#1456214111yescharacteristic
581C2#1456215911yescharacteristic
582C2#1456217211yescharacteristic
583C2#1456218011yescharacteristic
584C2#1456393611yescharacteristic
585C2#1456407211yescharacteristic
586C2#1456409211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1294C2
socleC23×C19C2×C22⋊C4
prime radicalC2×#10597376C22
cosocleC23×C4×C19C23
hypercenter#1294D19
hypocenterC19#9118
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
1. C2×#11926598C2semidirect
5. #14561859C2semidirect
6. #14561513C2semidirect
7. C19×#1294C2semidirect
16. #11926445C4semidirect
17. #11926445C4semidirect
18. #11926443C4semidirect
19. #11926443C4semidirect
245. #1294D19semidirect
373. C19#9118semidirect

Maximal subgroups

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

subgroupindex
C2×#119265982
#145719672
C2×#119262792
C2×#119262772
#145618592
#145615132
C19×#12942
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