Finite Group Databasebeta

← #18085876

Subgroups — #18085876

Order 4864.

602 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14569563C211yesmaximal, characteristic
2#14563950C211yesmaximal, characteristic
3#14563940C211yesmaximal, characteristic, complemented
4C2×#11926282C211yesmaximal, characteristic, complemented
5C2×#11926279C211yesmaximal, characteristic
6#14561891C211yesmaximal, characteristic, complemented
7C19×#1280C211yesmaximal, characteristic, complemented
8C2×#10597370C2211yescharacteristic
9C2×#10597376C2211yescharacteristic
10C22×C4⋊Dic19C2211yescharacteristic
11C2×#10597273—21no—
12C2×#10597278—21no—
13#11926484—21no—
14#11926471—21no—
15#11926462—21no—
16#11926457—21no—
17#11926423—21no—
18#11926423—21no—
19C2×C19⋊#95—21no—
20C2×C19⋊#95—21no—
21C2×C19⋊#95C2211yescharacteristic
22#11926307—21no—
23#11926307—21no—
24#11926282—22no—
25#11926279—22no—
26C2×C19×C22⋊C8C2211yescharacteristic
27C2×C19×C22⋊C8C2211yescharacteristic
28C2×C19×#95C2211yescharacteristic
29C23×C4×C19D411yescharacteristic
30C23×C4×C19D411yescharacteristic
31C23×C4×C19C2311yescharacteristic
32C22×C22⋊D19—21no—
33C23×Dic19—21no—
34C23×Dic19—21no—
35C22×D76D411yescharacteristic
36C22×Dic38D411yescharacteristic
37C22×C8×C19—21no—
38C22×C8×C19—21no—
39C2×C22⋊Dic19—21no—
40#10597376—21no—
41#10597376—21no—
42#10597376—21no—
43#10597376—21no—
44C2×(C2×D19)⋊C4—21no—
45C2×(C2×D19)⋊C4—21no—
46C2×(C2×D19)⋊C4—21no—
47C2×(C2×D19)⋊C4—21no—
48C2×(C2×D19)⋊C4—21no—
49C2×C4⋊Dic19—21no—
50C2×C4⋊Dic19—21no—
51C2×C4⋊Dic19—42no—
52C2×C4⋊Dic19D411yescharacteristic
53C2×C4⋊Dic19D411yescharacteristic
54#10597370—21no—
55#10597370—21no—
56#10597370—21no—
57#10597370—21no—
58C2×Dic19⋊C4—21no—
59C19×C22⋊C8—21no—
60C19×C22⋊C8—21no—
61C19×C22⋊C8—21no—
62C19×C22⋊C8—21no—
63C19×#95—21no—
64C19×#95—21no—
65C19⋊#95—21no—
66C19⋊#95—21no—
67C19⋊#95—21no—
68C19⋊#95—21no—
69C19⋊#95—21no—
70C19⋊#95—42no—
71C19⋊#95—42no—
72C19⋊#95D412yes—
73#10597278—42no—
74#10597273—42no—
75C24×C19C2×D411yescharacteristic
76C23×D19—21no—
77C22×C4×C19—21no—
78C22×C4×C19—21no—
79C22×C4×C19—21no—
80C22×C4×C19—21no—
81C22×C4×C19—21no—
82C22×C4×C19—21no—
83C22×C4×C19—41no—
84C22×C4×C19—41no—
85C22×C4×C19—41no—
86C22×C4×C19—41no—
87C22×C4×C19—41no—
88C22×C4×C19—41no—
89C22×C4×C19C2×D411yescharacteristic
90C22×C4×C19C2×D411yescharacteristic
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19#4111yescharacteristic
93C22×C4×C19#4111yescharacteristic
94C22×C4×C19#4111yescharacteristic
95C2×C22⋊D19—41no—
96C2×C22⋊D19—41no—
97C2×C22⋊D19—41no—
98C2×C22⋊D19—41no—
99C2×C22⋊D19—41no—
100C2×C22⋊D19—41no—
101C22×Dic19—22no—
102C22×Dic19—21no—
103C22×Dic19—21no—
104C22×Dic19—21no—
105C22×Dic19—22no—
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×Dic19—41no—
117C22×Dic19—41no—
118C2×D76—21no—
119C2×D76—21no—
120C2×D76—41no—
121C2×D76—41no—
122C2×Dic38—21no—
123C2×Dic38—21no—
124C2×Dic38—41no—
125C2×Dic38—41no—
126C2×C8×C19—41no—
127C2×C8×C19—41no—
128C2×C8×C19—41no—
129C2×C8×C19—41no—
130C2×C8×C19—41no—
131C2×C8×C19—41no—
132C22⋊Dic19—41no—
133C22⋊Dic19—41no—
134(C2×D19)⋊C4—41no—
135(C2×D19)⋊C4—41no—
136(C2×D19)⋊C4—81no—
137(C2×D19)⋊C4—81no—
138(C2×D19)⋊C4—81no—
139(C2×D19)⋊C4—81no—
140C4⋊Dic19—22no—
141C4⋊Dic19—22no—
142C4⋊Dic19—21no—
143C4⋊Dic19—21no—
144C4⋊Dic19—21no—
145C4⋊Dic19—21no—
146C4⋊Dic19—41no—
147C4⋊Dic19—41no—
148Dic19⋊C4—41no—
149Dic19⋊C4—41no—
150#10404—191nomaximal, Sylow
151C23×C19—21no—
152C23×C19—21no—
153C23×C19—21no—
154C23×C19—21no—
155C23×C19#12011yescharacteristic
156C23×C19#12111yescharacteristic
157C23×C19#12411yescharacteristic
158C23×C19#13511yescharacteristic
159C23×C19#13511yescharacteristic
160C23×C19AGL(1,ℤ/8)11yescharacteristic
161C23×C19#13711yescharacteristic
162C22×D19—41no—
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—41no—
174C2×C4×C19—41no—
175C2×C4×C19—41no—
176C2×C4×C19—41no—
177C2×C4×C19—42no—
178C2×C4×C19—42no—
179C2×C4×C19—41no—
180C2×C4×C19—41no—
181C2×C4×C19—41no—
182C2×C4×C19—41no—
183C2×C4×C19—41no—
184C2×C4×C19—41no—
185C2×C4×C19—81no—
186C2×C4×C19—81no—
187C2×C4×C19#12111yescharacteristic
188C2×C4×C19#12111yescharacteristic
189C2×C4×C19#12311yescharacteristic
190C2×C4×C19#12311yescharacteristic
191C22⋊D19—81no—
192C22⋊D19—81no—
193C22⋊D19—81no—
194C22⋊D19—81no—
195C2×Dic19—42no—
196C2×Dic19—42no—
197C2×Dic19—42no—
198C2×Dic19—42no—
199C2×Dic19—41no—
200C2×Dic19—41no—
201C2×Dic19—41no—
202C2×Dic19—41no—
203C2×Dic19—41no—
204C2×Dic19—41no—
205C2×Dic19—41no—
206C2×Dic19—42no—
207C2×Dic19—41no—
208C2×Dic19—41no—
209C2×Dic19—42no—
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—
220Dic38—42no—
221Dic38—81no—
222C8×C19—81no—
223C8×C19—81no—
224#2639—191no—
225#1874—191no—
226#1872—191no—
227C2×#328—191no—
228C2×#327—191no—
229#1442—191no—
230#1280D1911yescharacteristic, complemented
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—21no—
243C22×C19#39411yescharacteristic
244C22×C19#44911yescharacteristic
245C22×C19#45211yescharacteristic
246C22×C19#45411yescharacteristic
247C22×C19#45511yescharacteristic
248C22×C19B(4,𝔽2)11yescharacteristic
249C22×C19#45811yescharacteristic
250C22×C19#46311yescharacteristic
251C22×C19#46411yescharacteristic
252C22×C19#48811yescharacteristic
253C22×C19#48911yescharacteristic
254C2×D19—81no—
255C2×D19—81no—
256C2×D19—81no—
257C2×D19—81no—
258C2×D19—81no—
259C2×D19—81no—
260C2×D19—81no—
261C4×C19—21no—
262C4×C19—21no—
263C4×C19—21no—
264C4×C19—21no—
265C4×C19—81no—
266C4×C19—81no—
267Dic19—82no—
268Dic19—82no—
269Dic19—81no—
270Dic19—81no—
271Dic19—81no—
272C2×C22⋊Q8—191no—
273C2×#121—191no—
274C22×C4⋊C4—191no—
275C2×#103—381no—
276C2×#102—381no—
277C2×C22⋊C8C2×D1911yescharacteristic
278C2×C22⋊C8C2×D1911yescharacteristic
279#400—381no—
280#397—381no—
281#394—381no—
282#393—381no—
283#386—381no—
284#386—381no—
285C2×#95—191no—
286C2×#95—381no—
287C2×#95—381no—
288C2×#95C2×D1911yescharacteristic
289#340—381no—
290#340—381no—
291#328—382no—
292#327—382no—
293C2×C19—21no—
294C2×C19—21no—
295C2×C19—21no—
296C2×C19—21no—
297C2×C19#159711yescharacteristic
298C2×C19#160611yescharacteristic
299C2×C19#161211yescharacteristic
300C2×C19#161511yescharacteristic
301C2×C19#204011yescharacteristic
302C2×C19#204211yescharacteristic
303C2×C19#204411yescharacteristic
304D19—161no—
305C22×Q8—191no—
306C22×D4—191no—
307C22×D4—381no—
308C23×C4—381no—
309C23×C4—381no—
310C23×C4D7611yescharacteristic
311C23×C4D7611yescharacteristic
312C23×C4C22×D1911yescharacteristic
313C22×C8—21no—
314C22×C8—21no—
315C22⋊Q8—381no—
316C22⋊Q8—381no—
317C22⋊Q8—381no—
318C22⋊Q8—381no—
319#121—381no—
320#121—381no—
321#121—381no—
322#121—381no—
323C2×C4⋊C4—191no—
324C2×C4⋊C4—191no—
325C2×C4⋊C4—381no—
326C2×C4⋊C4—381no—
327C2×C4⋊C4—381no—
328C2×C4⋊C4—762no—
329C2×C22⋊C4—381no—
330C2×C22⋊C4—381no—
331C2×C22⋊C4—381no—
332C2×C22⋊C4—381no—
333C2×C22⋊C4—381no—
334C2×C22⋊C4—381no—
335#103—762no—
336#102—762no—
337C22⋊C8—21no—
338C22⋊C8—21no—
339C22⋊C8—21no—
340C22⋊C8—21no—
341#95—21no—
342#95—21no—
343#95—192no—
344#95—381no—
345#95—381no—
346#95—381no—
347#95—381no—
348#95—381no—
349#95—762no—
350#95—762no—
351C19#1040411yescharacteristic, complemented, Sylow
352C24—381no—
353C24C2×D7611yescharacteristic
354C2×Q8—381no—
355C2×Q8—381no—
356C2×Q8—761no—
357C2×Q8—761no—
358C2×D4—381no—
359C2×D4—381no—
360C2×D4—761no—
361C2×D4—761no—
362C2×D4—761no—
363C2×D4—761no—
364C2×D4—761no—
365C2×D4—761no—
366C2×D4—761no—
367C2×D4—761no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—382no—
381C22×C4—381no—
382C22×C4—381no—
383C22×C4—381no—
384C22×C4—382no—
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—761no—
395C22×C4—761no—
396C22×C4—761no—
397C22×C4#6454111yescharacteristic
398C22×C4#6454111yescharacteristic
399C22×C4D4×D1911yescharacteristic
400C22×C4D4×D1911yescharacteristic
401C22×C4D4×D1911yescharacteristic
402C22×C4#6454511yescharacteristic
403C2×C8—41no—
404C2×C8—41no—
405C2×C8—41no—
406C2×C8—41no—
407C2×C8—41no—
408C2×C8—41no—
409C4⋊C4—382no—
410C4⋊C4—382no—
411C4⋊C4—381no—
412C4⋊C4—381no—
413C4⋊C4—381no—
414C4⋊C4—381no—
415C4⋊C4—761no—
416C4⋊C4—761no—
417C4⋊C4—761no—
418C4⋊C4—761no—
419C22⋊C4—761no—
420C22⋊C4—761no—
421C22⋊C4—761no—
422C22⋊C4—761no—
423C22⋊C4—1521no—
424C22⋊C4—1521no—
425C22⋊C4—1521no—
426C22⋊C4—1521no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—761no—
432C23—761no—
433C23—761no—
434C23—761no—
435C23—761no—
436C23—761no—
437C23—761no—
438C23#1059732111yescharacteristic
439C23#1059732811yescharacteristic
440C23#1059734111yescharacteristic
441C23#1059735011yescharacteristic
442C23#1059735011yescharacteristic
443C23#1059735411yescharacteristic
444C23#1059735511yescharacteristic
445Q8—762no—
446Q8—1521no—
447D4—762no—
448D4—1521no—
449D4—1521no—
450D4—1521no—
451D4—1521no—
452D4—1521no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
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—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—81no—
470C2×C4—81no—
471C2×C4—762no—
472C2×C4—762no—
473C2×C4—762no—
474C2×C4—762no—
475C2×C4—761no—
476C2×C4—761no—
477C2×C4—761no—
478C2×C4—761no—
479C2×C4—761no—
480C2×C4—761no—
481C2×C4—761no—
482C2×C4—761no—
483C2×C4—762no—
484C2×C4—761no—
485C2×C4—762no—
486C2×C4—1521no—
487C2×C4—1521no—
488C2×C4—1521no—
489C2×C4—1521no—
490C2×C4—1521no—
491C2×C4—1521no—
492C2×C4—1521no—
493C2×C4—1521no—
494C2×C4#1059733011yescharacteristic
495C2×C4#1059733011yescharacteristic
496C2×C4#1059734011yescharacteristic
497C2×C4#1059734011yescharacteristic
498C8—81no—
499C8—81no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—1521no—
513C22—1521no—
514C22—1521no—
515C22—1521no—
516C22—1521no—
517C22—1521no—
518C22—1521no—
519C22#1192646211yescharacteristic
520C22#1192669111yescharacteristic
521C22#1192670811yescharacteristic
522C22#1192671911yescharacteristic
523C22#1192672411yescharacteristic
524C22#1192673211yescharacteristic
525C22#1192673511yescharacteristic
526C22#1192676011yescharacteristic
527C22#1192676711yescharacteristic
528C22#1192689911yescharacteristic
529C22#1192690411yescharacteristic
530C4—21no—
531C4—21no—
532C4—21no—
533C4—21no—
534C4—81no—
535C4—81no—
536C4—1522no—
537C4—1521no—
538C4—1522no—
539C4—1521no—
540C4—1521no—
541C2—21no—
542C2—21no—
543C2—21no—
544C2—21no—
545C2—3041no—
546C2#1456256611yescharacteristic
547C2#1456261711yescharacteristic
548C2#1456265111yescharacteristic
549C2#1456266811yescharacteristic
550C2#1456486511yescharacteristic
551C2#1456487711yescharacteristic
552C2#1456488711yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1280C2
socleC23×C19#120
prime radicalC2×#10597376C22
hypercenter#1280D19
hypocenterC19#10404
LCSG ▷ C23×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. #14563940C2semidirect
4. C2×#11926282C2semidirect
6. #14561891C2semidirect
7. C19×#1280C2semidirect
230. #1280D19semidirect
351. C19#10404semidirect

Maximal subgroups

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

subgroupindex
#145695632
#145639502
#145639402
C2×#119262822
C2×#119262792
#145618912
C19×#12802
#1040419