Finite Group Databasebeta

← #18085822

Subgroups — #18085822

Order 4864.

632 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14569377C211yesmaximal, characteristic
2#14563950C211yesmaximal, characteristic
3#14563830C211yesmaximal, characteristic, complemented
4C2×#11926279C211yesmaximal, characteristic
5#14561888C211yesmaximal, characteristic, complemented
6#14561515C211yesmaximal, characteristic, complemented
7C2×C19×#324C211yesmaximal, characteristic, complemented
8C2×#10597375—21no—
9C2×#10597376C2211yescharacteristic
10C22×C4⋊Dic19C2211yescharacteristic
11C2×#10597274—21no—
12C2×#10597278—21no—
13#11926474—21no—
14#11926466—21no—
15#11926466—21no—
16#11926461—21no—
17#11926423—21no—
18#11926404C2211yescharacteristic
19C2×C19⋊#95—21no—
20C2×C19⋊#95—21no—
21C2×C19⋊#95C2211yescharacteristic
22#11926307—21no—
23#11926307—21no—
24#11926279—22no—
25C22×C4⋊C4×C19C2211yescharacteristic
26C2×C19×C22⋊C8C2211yescharacteristic
27C2×C19×C22⋊C8C2211yescharacteristic
28C19×#324—22no—
29C23×C4×C19D411yescharacteristic
30C23×C4×C19D411yescharacteristic
31C23×C4×C19C2311yescharacteristic
32C22×C22⋊D19—21no—
33C23×Dic19—21no—
34C23×Dic19—21no—
35C22×D76D411yescharacteristic
36C22×C8×C19—21no—
37C22×C8×C19—21no—
38C2×C4⋊C4×C19—21no—
39C2×C4⋊C4×C19—21no—
40C2×C4⋊C4×C19—21no—
41C2×C4⋊C4×C19—21no—
42C2×C4⋊C4×C19—21no—
43C2×C4⋊C4×C19—21no—
44C2×C22⋊Dic19—21no—
45#10597376—21no—
46#10597376—21no—
47#10597376—21no—
48#10597376—21no—
49#10597375—42no—
50#10597375—42no—
51C2×(C2×D19)⋊C4—21no—
52C2×(C2×D19)⋊C4—21no—
53C2×(C2×D19)⋊C4—21no—
54C2×(C2×D19)⋊C4—21no—
55C2×(C2×D19)⋊C4—21no—
56C2×C4⋊Dic19—21no—
57C2×C4⋊Dic19—21no—
58C2×C4⋊Dic19—42no—
59C2×C4⋊Dic19D411yescharacteristic
60C2×C4⋊Dic19D411yescharacteristic
61C2×C4⋊Dic19D411yescharacteristic
62C2×Dic19⋊C4—21no—
63C2×Dic19⋊C4—21no—
64C19×C22⋊C8—21no—
65C19×C22⋊C8—21no—
66C19×C22⋊C8—21no—
67C19×C22⋊C8D412yes—
68C19⋊#95—21no—
69C19⋊#95—21no—
70C19⋊#95—21no—
71C19⋊#95—21no—
72C19⋊#95—21no—
73C19⋊#95—42no—
74C19⋊#95—42no—
75#10597278—42no—
76#10597274—42no—
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—21no—
85C22×C4×C19—21no—
86C22×C4×C19—21no—
87C22×C4×C19—21no—
88C22×C4×C19—41no—
89C22×C4×C19—41no—
90C22×C4×C19—41no—
91C22×C4×C19—41no—
92C22×C4×C19SD1612yes—
93C22×C4×C19C2×D411yescharacteristic
94C22×C4×C19C2×D411yescharacteristic
95C22×C4×C19C2×D411yescharacteristic
96C22×C4×C19#4111yescharacteristic
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—22no—
106C22×Dic19—22no—
107C22×Dic19—21no—
108C22×Dic19—21no—
109C22×Dic19—21no—
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—
120C22×Dic19—41no—
121C22×Dic19—41no—
122C2×D76—21no—
123C2×D76—21no—
124C2×D76—41no—
125C2×D76—41no—
126C2×C8×C19—22no—
127C2×C8×C19—41no—
128C2×C8×C19—41no—
129C2×C8×C19—41no—
130C2×C8×C19—41no—
131C2×C8×C19—41no—
132C4⋊C4×C19—41no—
133C4⋊C4×C19—41no—
134C4⋊C4×C19—41no—
135C4⋊C4×C19—41no—
136C22⋊Dic19—41no—
137C22⋊Dic19—41no—
138(C2×D19)⋊C4—42no—
139(C2×D19)⋊C4—42no—
140(C2×D19)⋊C4—41no—
141(C2×D19)⋊C4—41no—
142(C2×D19)⋊C4—81no—
143(C2×D19)⋊C4—81no—
144C4⋊Dic19—22no—
145C4⋊Dic19—22no—
146C4⋊Dic19—21no—
147C4⋊Dic19—21no—
148C4⋊Dic19—41no—
149C4⋊Dic19—41no—
150C4⋊Dic19—41no—
151C4⋊Dic19—41no—
152Dic19⋊C4—42no—
153Dic19⋊C4—42no—
154#10396—191nomaximal, Sylow
155C23×C19—21no—
156C23×C19—21no—
157C23×C19—21no—
158C23×C19—21no—
159C23×C19#12011yescharacteristic
160C23×C19#12111yescharacteristic
161C23×C19#12311yescharacteristic
162C23×C19C2×SD1611yescharacteristic
163C23×C19#13511yescharacteristic
164C23×C19AGL(1,ℤ/8)11yescharacteristic
165C23×C19AGL(1,ℤ/8)11yescharacteristic
166C22×D19—41no—
167C22×D19—41no—
168C22×D19—41no—
169C22×D19—41no—
170C22×D19—41no—
171C22×D19—41no—
172C22×D19—41no—
173C2×C4×C19—21no—
174C2×C4×C19—21no—
175C2×C4×C19—21no—
176C2×C4×C19—21no—
177C2×C4×C19—22no—
178C2×C4×C19—22no—
179C2×C4×C19—22no—
180C2×C4×C19—41no—
181C2×C4×C19—41no—
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×C19—42no—
189C2×C4×C19—41no—
190C2×C4×C19—41no—
191C2×C4×C19—41no—
192C2×C4×C19—81no—
193C2×C4×C19#12111yescharacteristic
194C2×C4×C19#12111yescharacteristic
195C2×C4×C19#12311yescharacteristic
196C2×C4×C19#12411yescharacteristic
197C22⋊D19—81no—
198C22⋊D19—81no—
199C22⋊D19—81no—
200C22⋊D19—81no—
201C2×Dic19—42no—
202C2×Dic19—42no—
203C2×Dic19—42no—
204C2×Dic19—42no—
205C2×Dic19—42no—
206C2×Dic19—41no—
207C2×Dic19—41no—
208C2×Dic19—41no—
209C2×Dic19—41no—
210C2×Dic19—41no—
211C2×Dic19—41no—
212C2×Dic19—41no—
213C2×Dic19—42no—
214C2×Dic19—41no—
215C2×Dic19—41no—
216C2×Dic19—81no—
217C2×Dic19—81no—
218C2×Dic19—81no—
219C2×Dic19—81no—
220C2×Dic19—81no—
221C2×Dic19—81no—
222C2×Dic19—81no—
223C2×Dic19—81no—
224D76—42no—
225D76—81no—
226C8×C19—42no—
227C8×C19—81no—
228#2618—191no—
229#1874—191no—
230#1853—191no—
231C2×#327—191no—
232C2×#324D1911yescharacteristic, complemented
233#1441—191no—
234#1294—191no—
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—21no—
244C22×C19—21no—
245C22×C19—21no—
246C22×C19—21no—
247C22×C19#39411yescharacteristic
248C22×C19#44911yescharacteristic
249C22×C19#45011yescharacteristic
250C22×C19#45411yescharacteristic
251C22×C19#45611yescharacteristic
252C22×C19B(4,𝔽2)11yescharacteristic
253C22×C19#45811yescharacteristic
254C22×C19#46511yescharacteristic
255C22×C19#46911yescharacteristic
256C22×C19#48111yescharacteristic
257C22×C19#48211yescharacteristic
258C2×D19—81no—
259C2×D19—81no—
260C2×D19—81no—
261C2×D19—81no—
262C2×D19—81no—
263C2×D19—81no—
264C2×D19—81no—
265C4×C19—21no—
266C4×C19—21no—
267C4×C19—21no—
268C4×C19—21no—
269C4×C19—42no—
270C4×C19—81no—
271Dic19—82no—
272Dic19—82no—
273Dic19—81no—
274Dic19—81no—
275Dic19—81no—
276C2×#123—381no—
277C2×#121—191no—
278C22×C4⋊C4—191no—
279C22×C4⋊C4C2×D1911yescharacteristic
280C2×#106—381no—
281C2×#102—381no—
282C2×C22⋊C8C2×D1911yescharacteristic
283C2×C22⋊C8C2×D1911yescharacteristic
284#398—381no—
285#396—381no—
286#396—381no—
287#394—381no—
288#386—381no—
289#380—191no—
290C2×#95—191no—
291C2×#95—381no—
292C2×#95—381no—
293#340—381no—
294#340—381no—
295#327—382no—
296#324—22no—
297C2×C19—21no—
298C2×C19—21no—
299C2×C19—21no—
300C2×C19—21no—
301C2×C19#159711yescharacteristic
302C2×C19#160411yescharacteristic
303C2×C19#160911yescharacteristic
304C2×C19#161611yescharacteristic
305C2×C19#203411yescharacteristic
306C2×C19#203811yescharacteristic
307C2×C19#204411yescharacteristic
308D19—161no—
309C22×D4—191no—
310C22×D4—381no—
311C23×C4—381no—
312C23×C4—381no—
313C23×C4D7611yescharacteristic
314C23×C4D7611yescharacteristic
315C23×C4C22×D1911yescharacteristic
316C22×C8—21no—
317C22×C8—21no—
318#123—762no—
319#123—762no—
320#121—381no—
321#121—381no—
322#121—381no—
323#121—381no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—191no—
331C2×C4⋊C4—191no—
332C2×C4⋊C4—191no—
333C2×C4⋊C4—381no—
334C2×C4⋊C4—381no—
335C2×C4⋊C4—381no—
336C2×C4⋊C4—381no—
337C2×C4⋊C4—762no—
338C2×C22⋊C4—381no—
339C2×C22⋊C4—381no—
340C2×C22⋊C4—381no—
341C2×C22⋊C4—381no—
342C2×C22⋊C4—381no—
343C2×C22⋊C4—381no—
344#106—762no—
345#102—762no—
346C22⋊C8—21no—
347C22⋊C8—21no—
348C22⋊C8—21no—
349C22⋊C8C22⋊D1912yes—
350#95—381no—
351#95—381no—
352#95—381no—
353#95—381no—
354#95—381no—
355#95—762no—
356#95—762no—
357C19#1039611yescharacteristic, complemented, Sylow
358C24—381no—
359C24C2×D7611yescharacteristic
360C2×D4—381no—
361C2×D4—381no—
362C2×D4—761no—
363C2×D4—761no—
364C2×D4—761no—
365C2×D4—761no—
366C2×D4—761no—
367C2×D4—761no—
368C2×D4—761no—
369C2×D4—761no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—382no—
384C22×C4—382no—
385C22×C4—381no—
386C22×C4—381no—
387C22×C4—381no—
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—761no—
398C22×C4—761no—
399C22×C4—761no—
400C22×C4#6451612yes—
401C22×C4#6454111yescharacteristic
402C22×C4D4×D1911yescharacteristic
403C22×C4D4×D1911yescharacteristic
404C22×C4#6454311yescharacteristic
405C22×C4#6454311yescharacteristic
406C22×C4C2×C22⋊D1911yescharacteristic
407C2×C8—22no—
408C2×C8—41no—
409C2×C8—41no—
410C2×C8—41no—
411C2×C8—41no—
412C2×C8—41no—
413C4⋊C4—41no—
414C4⋊C4—41no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4—382no—
418C4⋊C4—382no—
419C4⋊C4—381no—
420C4⋊C4—381no—
421C4⋊C4—761no—
422C4⋊C4—761no—
423C4⋊C4—762no—
424C4⋊C4—762no—
425C4⋊C4—761no—
426C4⋊C4—761no—
427C22⋊C4—762no—
428C22⋊C4—762no—
429C22⋊C4—761no—
430C22⋊C4—761no—
431C22⋊C4—761no—
432C22⋊C4—761no—
433C22⋊C4—1521no—
434C22⋊C4—1521no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—761no—
440C23—761no—
441C23—761no—
442C23—761no—
443C23—761no—
444C23—761no—
445C23—761no—
446C23#1059732811yescharacteristic
447C23#1059733211yescharacteristic
448C23C2×#6451611yescharacteristic
449C23#1059735011yescharacteristic
450C23#1059735411yescharacteristic
451C23#1059735411yescharacteristic
452C23#1059737611yescharacteristic
453D4—762no—
454D4—1521no—
455D4—1521no—
456D4—1521no—
457D4—1521no—
458D4—1521no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—81no—
479C2×C4—762no—
480C2×C4—762no—
481C2×C4—762no—
482C2×C4—762no—
483C2×C4—762no—
484C2×C4—761no—
485C2×C4—761no—
486C2×C4—761no—
487C2×C4—761no—
488C2×C4—761no—
489C2×C4—761no—
490C2×C4—761no—
491C2×C4—761no—
492C2×C4—762no—
493C2×C4—761no—
494C2×C4—1521no—
495C2×C4—1521no—
496C2×C4—1521no—
497C2×C4—1521no—
498C2×C4—1521no—
499C2×C4—1521no—
500C2×C4—1521no—
501C2×C4—1521no—
502C2×C4#1059732911yescharacteristic
503C2×C4#1059733111yescharacteristic
504C2×C4#1059738411yescharacteristic
505C2×C4#1059738511yescharacteristic
506C8—42no—
507C8—81no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—1521no—
521C22—1521no—
522C22—1521no—
523C22—1521no—
524C22—1521no—
525C22—1521no—
526C22—1521no—
527C22#1192646011yescharacteristic
528C22#1192669111yescharacteristic
529C22#1192669711yescharacteristic
530C22#1192671911yescharacteristic
531C22#1192672911yescharacteristic
532C22#1192673211yescharacteristic
533C22#1192673511yescharacteristic
534C22#1192677311yescharacteristic
535C22#1192679711yescharacteristic
536C22#1192686311yescharacteristic
537C22#1192686911yescharacteristic
538C4—21no—
539C4—21no—
540C4—21no—
541C4—21no—
542C4—42no—
543C4—81no—
544C4—1522no—
545C4—1522no—
546C4—1521no—
547C4—1521no—
548C4—1521no—
549C2—21no—
550C2—21no—
551C2—21no—
552C2—21no—
553C2—3041no—
554C2#1456256611yescharacteristic
555C2#1456260611yescharacteristic
556C2#1456263411yescharacteristic
557C2#1456267411yescharacteristic
558C2#1456482511yescharacteristic
559C2#1456485311yescharacteristic
560C2#1456488511yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC2×C19×#324C2
socleC23×C19#120
prime radicalC2×#10597376C22
hypercenterC2×#324D19
hypocenterC19#10396
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
3. #14563830C2semidirect
5. #14561888C2semidirect
6. #14561515C2semidirect
7. C2×C19×#324C2semidirect
232. C2×#324D19semidirect
357. C19#10396semidirect

Maximal subgroups

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

subgroupindex
#145693772
#145639502
#145638302
C2×#119262792
#145618882
#145615152
C2×C19×#3242
#1039619