Finite Group Databasebeta

← #18075211

Subgroups — #18075211

Order 4864.

678 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
1C2×#11926433C211yesmaximal, characteristic
2#14563613C211yesmaximal, characteristic, complemented
3#14563613C211yesmaximal, characteristic, complemented
4C2×#11926267C211yesmaximal, characteristic
5C2×#11926267C211yesmaximal, characteristic
6#14561478C211yesmaximal, characteristic, complemented
7C19×#1280C211yesmaximal, characteristic, complemented
8C22×Dic19⋊C4C411yescharacteristic
9C22×(C2×D19)⋊C4C411yescharacteristic
10C22×(C2×D19)⋊C4C411yescharacteristic
11C22×(C2×D19)⋊C4C2211yescharacteristic
12C22×C4×Dic19C2211yescharacteristic
13C2×Dic19⋊C8—21no—
14C2×Dic19⋊C8—21no—
15C2×C22⋊(C19⋊C8)C2211yescharacteristic
16C2×C22⋊(C19⋊C8)C2211yescharacteristic
17#11926433—21no—
18#11926433—21no—
19#11926433—21no—
20#11926433—21no—
21C2×C19⋊#95C411yescharacteristic
22#11926298—21no—
23#11926298—21no—
24#11926267—22no—
25#11926267—22no—
26C2×C19×C22⋊C8C2211yescharacteristic
27C2×C19×C22⋊C8C2211yescharacteristic
28C2×C19×#95C2211yescharacteristic
29C24×D19C2×C411yescharacteristic
30C23×C4×C19C2×C411yescharacteristic
31C23×C4×C19C2×C411yescharacteristic
32C23×C4×C19C2311yescharacteristic
33C23×Dic19C2×C411yescharacteristic
34C23×Dic19C2×C411yescharacteristic
35C23×Dic19C2×C411yescharacteristic
36C22×C8×C19—21no—
37C22×C8×C19—21no—
38C2×(C2×D19)⋊C4—21no—
39C2×(C2×D19)⋊C4—21no—
40C2×(C2×D19)⋊C4—21no—
41C2×(C2×D19)⋊C4—21no—
42C2×(C2×D19)⋊C4—21no—
43C2×(C2×D19)⋊C4—21no—
44C2×(C2×D19)⋊C4—21no—
45C2×(C2×D19)⋊C4—21no—
46C2×(C2×D19)⋊C4—42no—
47C2×(C2×D19)⋊C4—42no—
48C2×(C2×D19)⋊C4D412yes—
49C2×(C2×D19)⋊C4Q812yes—
50C2×Dic19⋊C4—21no—
51C2×Dic19⋊C4—21no—
52C2×Dic19⋊C4—42no—
53C2×C4×Dic19—42no—
54C2×C4×Dic19D411yescharacteristic
55C2×C4×Dic19D411yescharacteristic
56C2×C4×Dic19D411yescharacteristic
57C2×C4×Dic19D411yescharacteristic
58C22×C19⋊C8—21no—
59C22×C19⋊C8—21no—
60C19×C22⋊C8—21no—
61C19×C22⋊C8—21no—
62C19×C22⋊C8—21no—
63C19×C22⋊C8—21no—
64C19×#95—21no—
65C19×#95—21no—
66C19⋊#95—21no—
67C19⋊#95—21no—
68C22⋊(C19⋊C8)—21no—
69C22⋊(C19⋊C8)—21no—
70C22⋊(C19⋊C8)—21no—
71C22⋊(C19⋊C8)—21no—
72Dic19⋊C8—42no—
73Dic19⋊C8—42no—
74C24×C19C22×C411yescharacteristic
75C23×D19—21no—
76C23×D19—21no—
77C23×D19—21no—
78C23×D19—21no—
79C23×D19—21no—
80C23×D19—21no—
81C23×D19—41no—
82C23×D19—41no—
83C23×D19—41no—
84C23×D19—41no—
85C23×D19C4⋊C412yes—
86C22×C4×C19—21no—
87C22×C4×C19—21no—
88C22×C4×C19—21no—
89C22×C4×C19—21no—
90C22×C4×C19—21no—
91C22×C4×C19—21no—
92C22×C4×C19—41no—
93C22×C4×C19—41no—
94C22×C4×C19—41no—
95C22×C4×C19—41no—
96C22×C4×C19—41no—
97C22×C4×C19—41no—
98C22×C4×C19C2×D411yescharacteristic
99C22×C4×C19C2×D411yescharacteristic
100C22×C4×C19C2×D411yescharacteristic
101C22×C4×C19C2×Q811yescharacteristic
102C22×C4×C19#4111yescharacteristic
103C22×C4×C19#4111yescharacteristic
104C22×Dic19—21no—
105C22×Dic19—21no—
106C22×Dic19—21no—
107C22×Dic19—21no—
108C22×Dic19—21no—
109C22×Dic19—21no—
110C22×Dic19—22no—
111C22×Dic19—22no—
112C22×Dic19—41no—
113C22×Dic19—41no—
114C22×Dic19—41no—
115C22×Dic19—41no—
116C22×Dic19C22⋊C411yescharacteristic
117C22×Dic19C22⋊C411yescharacteristic
118C22×Dic19C22⋊C411yescharacteristic
119C22×Dic19C22⋊C411yescharacteristic
120C22×Dic19C4⋊C412yes—
121C2×C8×C19—41no—
122C2×C8×C19—41no—
123C2×C8×C19—41no—
124C2×C8×C19—41no—
125C2×C8×C19—41no—
126C2×C8×C19—41no—
127(C2×D19)⋊C4—22no—
128(C2×D19)⋊C4—22no—
129(C2×D19)⋊C4—22no—
130(C2×D19)⋊C4—22no—
131(C2×D19)⋊C4—42no—
132(C2×D19)⋊C4—42no—
133(C2×D19)⋊C4—42no—
134(C2×D19)⋊C4—42no—
135Dic19⋊C4—42no—
136Dic19⋊C4—42no—
137C4×Dic19—22no—
138C4×Dic19—22no—
139C4×Dic19—41no—
140C4×Dic19—41no—
141C2×C19⋊C8—41no—
142C2×C19⋊C8—41no—
143C2×C19⋊C8—41no—
144C2×C19⋊C8—41no—
145C2×C19⋊C8—41no—
146C2×C19⋊C8—41no—
147#8561—191nomaximal, Sylow
148C23×C19—21no—
149C23×C19—21no—
150C23×C19—21no—
151C23×C19—21no—
152C23×C19C2×C22⋊C411yescharacteristic
153C23×C19C2×C4⋊C411yescharacteristic
154C23×C19#11711yescharacteristic
155C23×C19#13111yescharacteristic
156C23×C19#13111yescharacteristic
157C23×C19#13111yescharacteristic
158C23×C19#13111yescharacteristic
159C22×D19—22no—
160C22×D19—22no—
161C22×D19—22no—
162C22×D19—42no—
163C22×D19—42no—
164C22×D19—41no—
165C22×D19—41no—
166C22×D19—41no—
167C22×D19—41no—
168C22×D19—41no—
169C22×D19—41no—
170C22×D19—41no—
171C22×D19—41no—
172C22×D19—42no—
173C22×D19—42no—
174C22×D19—81no—
175C22×D19—81no—
176C22×D19—81no—
177C22×D19—81no—
178C22×D19—81no—
179C22×D19—81no—
180C22×D19—81no—
181C22×D19—81no—
182C2×C4×C19—21no—
183C2×C4×C19—21no—
184C2×C4×C19—21no—
185C2×C4×C19—21no—
186C2×C4×C19—41no—
187C2×C4×C19—41no—
188C2×C4×C19—41no—
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—41no—
196C2×C4×C19—81no—
197C2×C4×C19—81no—
198C2×C4×C19—81no—
199C2×C4×C19—81no—
200C2×C4×C19#12111yescharacteristic
201C2×C4×C19#12111yescharacteristic
202C2×C4×C19C22⋊Q811yescharacteristic
203C2×C4×C19C22⋊Q811yescharacteristic
204C2×Dic19—21no—
205C2×Dic19—21no—
206C2×Dic19—21no—
207C2×Dic19—21no—
208C2×Dic19—22no—
209C2×Dic19—21no—
210C2×Dic19—21no—
211C2×Dic19—21no—
212C2×Dic19—21no—
213C2×Dic19—21no—
214C2×Dic19—21no—
215C2×Dic19—42no—
216C2×Dic19—42no—
217C2×Dic19—42no—
218C2×Dic19—42no—
219C2×Dic19—42no—
220C2×Dic19—41no—
221C2×Dic19—41no—
222C2×Dic19—42no—
223C2×Dic19#9912yes—
224C2×Dic19#10012yes—
225C8×C19—81no—
226C8×C19—81no—
227C19⋊C8—81no—
228C19⋊C8—81no—
229C2×#388—191no—
230#1797—191no—
231#1797—191no—
232C2×#323—191no—
233C2×#323—191no—
234#1280—191no—
235#1280D1911yescharacteristic, complemented
236C22×C19—21no—
237C22×C19—21no—
238C22×C19—21no—
239C22×C19—21no—
240C22×C19—21no—
241C22×C19—21no—
242C22×C19—21no—
243C22×C19—21no—
244C22×C19—21no—
245C22×C19—21no—
246C22×C19—21no—
247C22×C19—21no—
248C22×C19#38011yescharacteristic
249C22×C19#40811yescharacteristic
250C22×C19#40811yescharacteristic
251C22×C19C2×#9911yescharacteristic
252C22×C19#41011yescharacteristic
253C22×C19C2×#10011yescharacteristic
254C22×C19#41311yescharacteristic
255C22×C19#42411yescharacteristic
256C22×C19#42411yescharacteristic
257C22×C19#43311yescharacteristic
258C22×C19#43311yescharacteristic
259C2×D19—42no—
260C2×D19—42no—
261C2×D19—42no—
262C2×D19—82no—
263C2×D19—82no—
264C2×D19—81no—
265C2×D19—81no—
266C2×D19—81no—
267C2×D19—81no—
268C2×D19—82no—
269C2×D19—82no—
270C4×C19—21no—
271C4×C19—21no—
272C4×C19—21no—
273C4×C19—21no—
274C4×C19—81no—
275C4×C19—81no—
276Dic19—22no—
277Dic19—22no—
278Dic19—42no—
279Dic19—41no—
280Dic19—41no—
281C22×C4⋊C4—191no—
282C22×C22⋊C4—191no—
283C22×C22⋊C4—191no—
284C22×C22⋊C4—191no—
285C22×C42—191no—
286C2×C4⋊C8—381no—
287C2×C4⋊C8—381no—
288C2×C22⋊C8—191no—
289C2×C22⋊C8—191no—
290C2×C22⋊C8C2×D1911yescharacteristic
291C2×C22⋊C8C2×D1911yescharacteristic
292#388—381no—
293#388—381no—
294#388—381no—
295#388—381no—
296C2×#95—191no—
297C2×#95C2×D1911yescharacteristic
298#336—381no—
299#336—381no—
300#323—382no—
301#323—382no—
302C2×C19—21no—
303C2×C19—21no—
304C2×C19—21no—
305C2×C19—21no—
306C2×C19#146811yescharacteristic
307C2×C19#146911yescharacteristic
308C2×C19#147111yescharacteristic
309C2×C19#147311yescharacteristic
310C2×C19#179811yescharacteristic
311C2×C19#179911yescharacteristic
312C2×C19#180011yescharacteristic
313D19—82no—
314C25—191no—
315C23×C4—191no—
316C23×C4—191no—
317C23×C4—191no—
318C23×C4C4×D1911yescharacteristic
319C23×C4C4×D1911yescharacteristic
320C23×C4C22×D1911yescharacteristic
321C22×C8—21no—
322C22×C8—21no—
323C22×C8—381no—
324C22×C8—381no—
325C2×C4⋊C4—381no—
326C2×C4⋊C4—381no—
327C2×C4⋊C4—762no—
328C2×C22⋊C4—192no—
329C2×C22⋊C4—192no—
330C2×C22⋊C4—381no—
331C2×C22⋊C4—381no—
332C2×C22⋊C4—381no—
333C2×C22⋊C4—381no—
334C2×C22⋊C4—381no—
335C2×C22⋊C4—381no—
336C2×C22⋊C4—381no—
337C2×C22⋊C4—381no—
338C2×C22⋊C4—762no—
339C2×C22⋊C4—762no—
340C2×C42—191no—
341C2×C42—191no—
342C2×C42—191no—
343C2×C42—191no—
344C2×C42—762no—
345C4⋊C8—762no—
346C4⋊C8—762no—
347C22⋊C8—21no—
348C22⋊C8—21no—
349C22⋊C8—21no—
350C22⋊C8—21no—
351C22⋊C8—381no—
352C22⋊C8—381no—
353C22⋊C8—381no—
354C22⋊C8—381no—
355#95—21no—
356#95—21no—
357#95—381no—
358#95—381no—
359C19#856111yescharacteristic, complemented, Sylow
360C24—192no—
361C24—381no—
362C24—381no—
363C24—381no—
364C24—381no—
365C24—381no—
366C24—381no—
367C24—761no—
368C24—761no—
369C24—761no—
370C24—761no—
371C24C2×C4×D1911yescharacteristic
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—191no—
385C22×C4—191no—
386C22×C4—191no—
387C22×C4—191no—
388C22×C4—192no—
389C22×C4—382no—
390C22×C4—382no—
391C22×C4—381no—
392C22×C4—381no—
393C22×C4—381no—
394C22×C4—381no—
395C22×C4—381no—
396C22×C4—381no—
397C22×C4—761no—
398C22×C4—761no—
399C22×C4—761no—
400C22×C4—761no—
401C22×C4#6454111yescharacteristic
402C22×C4#6454111yescharacteristic
403C22×C4D4×D1911yescharacteristic
404C22×C4D4×D1911yescharacteristic
405C22×C4D4×D1911yescharacteristic
406C22×C4Q8×D1911yescharacteristic
407C2×C8—41no—
408C2×C8—41no—
409C2×C8—41no—
410C2×C8—41no—
411C2×C8—41no—
412C2×C8—41no—
413C2×C8—761no—
414C2×C8—761no—
415C2×C8—761no—
416C2×C8—761no—
417C2×C8—761no—
418C2×C8—761no—
419C4⋊C4—762no—
420C4⋊C4—762no—
421C22⋊C4—382no—
422C22⋊C4—382no—
423C22⋊C4—382no—
424C22⋊C4—382no—
425C22⋊C4—762no—
426C22⋊C4—762no—
427C22⋊C4—762no—
428C22⋊C4—762no—
429C42—382no—
430C42—382no—
431C42—761no—
432C42—761no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—382no—
438C23—382no—
439C23—382no—
440C23—762no—
441C23—762no—
442C23—762no—
443C23—762no—
444C23—761no—
445C23—761no—
446C23—761no—
447C23—761no—
448C23—761no—
449C23—761no—
450C23—761no—
451C23—761no—
452C23—1521no—
453C23—1521no—
454C23—1521no—
455C23—1521no—
456C23—1521no—
457C23—1521no—
458C23—1521no—
459C23—1521no—
460C23#1059731811yescharacteristic
461C23C22⋊C4×D1911yescharacteristic
462C23C4⋊C4×D1911yescharacteristic
463C23#1059734711yescharacteristic
464C23#1059734711yescharacteristic
465C23#1059735311yescharacteristic
466C23#1059735311yescharacteristic
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—81no—
482C2×C4—81no—
483C2×C4—81no—
484C2×C4—81no—
485C2×C4—192no—
486C2×C4—192no—
487C2×C4—381no—
488C2×C4—381no—
489C2×C4—381no—
490C2×C4—381no—
491C2×C4—382no—
492C2×C4—381no—
493C2×C4—381no—
494C2×C4—381no—
495C2×C4—381no—
496C2×C4—381no—
497C2×C4—381no—
498C2×C4—762no—
499C2×C4—762no—
500C2×C4—762no—
501C2×C4—762no—
502C2×C4—762no—
503C2×C4—761no—
504C2×C4—761no—
505C2×C4—762no—
506C2×C4#1059733011yescharacteristic
507C2×C4#1059733011yescharacteristic
508C2×C4#1059734211yescharacteristic
509C2×C4#1059734211yescharacteristic
510C8—81no—
511C8—81no—
512C8—1521no—
513C8—1521no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—762no—
527C22—762no—
528C22—762no—
529C22—1522no—
530C22—1522no—
531C22—1522no—
532C22—1522no—
533C22—1521no—
534C22—1521no—
535C22—1521no—
536C22—1521no—
537C22#1192640311yescharacteristic
538C22#1192650911yescharacteristic
539C22#1192650911yescharacteristic
540C22#99×D1911yescharacteristic
541C22#1192651611yescharacteristic
542C22#100×D1911yescharacteristic
543C22#1192652711yescharacteristic
544C22#1192656911yescharacteristic
545C22#1192656911yescharacteristic
546C22#1192660311yescharacteristic
547C22#1192660611yescharacteristic
548C4—21no—
549C4—21no—
550C4—21no—
551C4—21no—
552C4—81no—
553C4—81no—
554C4—382no—
555C4—382no—
556C4—762no—
557C4—761no—
558C4—761no—
559C2—21no—
560C2—21no—
561C2—21no—
562C2—21no—
563C2—1522no—
564C2#1456198211yescharacteristic
565C2#1456198511yescharacteristic
566C2#1456199311yescharacteristic
567C2#1456200311yescharacteristic
568C2#1456361811yescharacteristic
569C2#1456362211yescharacteristic
570C2#1456362611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1280C2
socleC23×C19C2×C22⋊C4
prime radicalC24×D19C2×C4
cosocleC23×C4×C19C23
hypercenter#1280D19
hypocenterC19#8561
LCSG ▷ C24×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
2. #14563613C2semidirect
3. #14563613C2semidirect
6. #14561478C2semidirect
7. C19×#1280C2semidirect
235. #1280D19semidirect
359. C19#8561semidirect

Maximal subgroups

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

subgroupindex
C2×#119264332
#145636132
C2×#119262672
#145614782
C19×#12802
#856119