Finite Group Databasebeta

← #18085878

Subgroups — #18085878

Order 4864.

646 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14569569C211yesmaximal, characteristic
2#14563952C211yesmaximal, characteristic
3C2×#11926281C211yesmaximal, characteristic, complemented
4C2×#11926279C211yesmaximal, characteristic
5#14561898C211yesmaximal, characteristic, complemented
6#14561477C211yesmaximal, characteristic, complemented
7C19×#1872C211yesmaximal, characteristic, complemented
8C2×#10597376C2211yescharacteristic
9C22×Dic19⋊C4—21no—
10C2×#10597266—21no—
11C2×C22⋊(C19⋊C8)C2211yescharacteristic
12#11926483—21no—
13#11926470—21no—
14#11926461—21no—
15#11926455—21no—
16#11926421—21no—
17#11926421—21no—
18C2×C19⋊#95—21no—
19C2×C19⋊#95C2211yescharacteristic
20C2×C19⋊#95C2211yescharacteristic
21#11926306—21no—
22#11926281—22no—
23#11926279—22no—
24C2×C19×C22⋊Q8C2211yescharacteristic
25C22×C4⋊C4×C19C2211yescharacteristic
26C2×C19×#103—21no—
27C2×C19×C22⋊C8C2211yescharacteristic
28C19×#340—21no—
29C22×Q8×C19D411yescharacteristic
30C23×C4×C19—21no—
31C23×C4×C19C2311yescharacteristic
32C22×C22⋊D19—21no—
33C23×Dic19—21no—
34C23×Dic19D411yescharacteristic
35C23×Dic19D411yescharacteristic
36C22×D76D411yescharacteristic
37C22×C8×C19—21no—
38C19×C22⋊Q8—21no—
39C19×C22⋊Q8—21no—
40C19×C22⋊Q8—21no—
41C19×C22⋊Q8—21no—
42C2×C4⋊C4×C19—21no—
43C2×C4⋊C4×C19—21no—
44C2×C4⋊C4×C19—21no—
45C2×C4⋊C4×C19—42no—
46C2×C4⋊C4×C19D411yescharacteristic
47C2×C22⋊C4×C19—21no—
48#10597376—21no—
49#10597376—21no—
50#10597376—21no—
51#10597376—21no—
52C2×(C2×D19)⋊C4—21no—
53C2×(C2×D19)⋊C4—21no—
54C2×(C2×D19)⋊C4—21no—
55C2×(C2×D19)⋊C4—21no—
56C2×(C2×D19)⋊C4—21no—
57C2×C4⋊Dic19D411yescharacteristic
58C2×Dic19⋊C4—42no—
59C2×Dic19⋊C4—42no—
60C2×Dic19⋊C4—42no—
61C22×C19⋊C8—21no—
62C19×#103—42no—
63C19×C22⋊C8—21no—
64C19×C22⋊C8—21no—
65C19⋊#95—21no—
66C19⋊#95—21no—
67C19⋊#95—21no—
68C19⋊#95—21no—
69C19⋊#95—21no—
70C19⋊#95—21no—
71C19⋊#95—21no—
72C19⋊#95—42no—
73C19⋊#95D412yes—
74C22⋊(C19⋊C8)—21no—
75C22⋊(C19⋊C8)—21no—
76#10597266—42no—
77C24×C19C2×D411yescharacteristic
78C23×D19—21no—
79C2×Q8×C19—21no—
80C2×Q8×C19—21no—
81C2×Q8×C19—41no—
82C2×Q8×C19—41no—
83C22×C4×C19—22no—
84C22×C4×C19—21no—
85C22×C4×C19—21no—
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×C19—41no—
94C22×C4×C19C2×D411yescharacteristic
95C22×C4×C19C2×D411yescharacteristic
96C22×C4×C19C2×D411yescharacteristic
97C22×C4×C19#4111yescharacteristic
98C22×C4×C19#4111yescharacteristic
99C22×C4×C19#4111yescharacteristic
100C2×C22⋊D19—41no—
101C2×C22⋊D19—41no—
102C2×C22⋊D19—41no—
103C2×C22⋊D19—41no—
104C2×C22⋊D19—41no—
105C2×C22⋊D19—41no—
106C22×Dic19—22no—
107C22×Dic19—22no—
108C22×Dic19—22no—
109C22×Dic19—21no—
110C22×Dic19—21no—
111C22×Dic19—21no—
112C22×Dic19—21no—
113C22×Dic19—21no—
114C22×Dic19—21no—
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×Dic19—41no—
124C2×D76—21no—
125C2×D76—21no—
126C2×D76—41no—
127C2×D76—41no—
128C2×C8×C19—41no—
129C2×C8×C19—41no—
130C2×C8×C19—41no—
131C4⋊C4×C19—22no—
132C4⋊C4×C19—22no—
133C4⋊C4×C19—21no—
134C4⋊C4×C19—21no—
135C4⋊C4×C19—41no—
136C4⋊C4×C19—41no—
137C4⋊C4×C19—41no—
138C4⋊C4×C19—41no—
139C22⋊C4×C19—41no—
140C22⋊C4×C19—41no—
141(C2×D19)⋊C4—41no—
142(C2×D19)⋊C4—41no—
143(C2×D19)⋊C4—81no—
144(C2×D19)⋊C4—81no—
145(C2×D19)⋊C4—81no—
146(C2×D19)⋊C4—81no—
147C4⋊Dic19—21no—
148C4⋊Dic19—21no—
149Dic19⋊C4—48no—
150C2×C19⋊C8—41no—
151C2×C19⋊C8—41no—
152C2×C19⋊C8—41no—
153#10405—191nomaximal, Sylow
154C23×C19—21no—
155C23×C19—21no—
156C23×C19—21no—
157C23×C19—21no—
158C23×C19#12011yescharacteristic
159C23×C19#12111yescharacteristic
160C23×C19#12411yescharacteristic
161C23×C19#13511yescharacteristic
162C23×C19#13511yescharacteristic
163C23×C19AGL(1,ℤ/8)11yescharacteristic
164C23×C19#13711yescharacteristic
165C22×D19—41no—
166C22×D19—41no—
167C22×D19—41no—
168C22×D19—41no—
169C22×D19—41no—
170C22×D19—41no—
171C22×D19—41no—
172Q8×C19—42no—
173Q8×C19—81no—
174C2×C4×C19—21no—
175C2×C4×C19—21no—
176C2×C4×C19—21no—
177C2×C4×C19—21no—
178C2×C4×C19—41no—
179C2×C4×C19—41no—
180C2×C4×C19—41no—
181C2×C4×C19—41no—
182C2×C4×C19—42no—
183C2×C4×C19—42no—
184C2×C4×C19—41no—
185C2×C4×C19—41no—
186C2×C4×C19—41no—
187C2×C4×C19—41no—
188C2×C4×C19—41no—
189C2×C4×C19—42no—
190C2×C4×C19—41no—
191C2×C4×C19—81no—
192C2×C4×C19—81no—
193C2×C4×C19—81no—
194C2×C4×C19—81no—
195C2×C4×C19#12111yescharacteristic
196C2×C4×C19#12111yescharacteristic
197C2×C4×C19#12311yescharacteristic
198C2×C4×C19#12311yescharacteristic
199C22⋊D19—81no—
200C22⋊D19—81no—
201C22⋊D19—81no—
202C22⋊D19—81no—
203C2×Dic19—24no—
204C2×Dic19—42no—
205C2×Dic19—42no—
206C2×Dic19—42no—
207C2×Dic19—42no—
208C2×Dic19—42no—
209C2×Dic19—42no—
210C2×Dic19—42no—
211C2×Dic19—42no—
212C2×Dic19—41no—
213C2×Dic19—41no—
214C2×Dic19—41no—
215C2×Dic19—41no—
216C2×Dic19—41no—
217C2×Dic19—41no—
218C2×Dic19—41no—
219C2×Dic19—41no—
220C2×Dic19—41no—
221C2×Dic19—81no—
222C2×Dic19—81no—
223D76—42no—
224D76—81no—
225C8×C19—81no—
226C19⋊C8—81no—
227#2639—191no—
228#1874—191no—
229#1872D1911yescharacteristic, complemented
230C2×#328—191no—
231C2×#327—191no—
232#1444—191no—
233#1280—191no—
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—21no—
244C22×C19—21no—
245C22×C19—21no—
246C22×C19#39411yescharacteristic
247C22×C19#44911yescharacteristic
248C22×C19#45211yescharacteristic
249C22×C19#45311yescharacteristic
250C22×C19#45611yescharacteristic
251C22×C19B(4,𝔽2)11yescharacteristic
252C22×C19#45811yescharacteristic
253C22×C19#46311yescharacteristic
254C22×C19#46411yescharacteristic
255C22×C19#48811yescharacteristic
256C22×C19#48911yescharacteristic
257C2×D19—81no—
258C2×D19—81no—
259C2×D19—81no—
260C2×D19—81no—
261C2×D19—81no—
262C2×D19—81no—
263C2×D19—81no—
264C4×C19—21no—
265C4×C19—21no—
266C4×C19—21no—
267C4×C19—21no—
268C4×C19—82no—
269C4×C19—81no—
270C4×C19—81no—
271Dic19—44no—
272Dic19—81no—
273Dic19—81no—
274Dic19—81no—
275C2×C22⋊Q8C2×D1911yescharacteristic
276C2×#121—191no—
277C22×C4⋊C4—381no—
278C22×C4⋊C4C2×D1911yescharacteristic
279C2×#103—21no—
280C2×#102—381no—
281C2×C22⋊C8—191no—
282C2×C22⋊C8C2×D1911yescharacteristic
283#400—381no—
284#397—381no—
285#394—381no—
286#393—381no—
287#386—381no—
288#386—381no—
289C2×#95—191no—
290C2×#95—191no—
291C2×#95—381no—
292#340—21no—
293#340—381no—
294#328—382no—
295#327—382no—
296C2×C19—21no—
297C2×C19—21no—
298C2×C19—21no—
299C2×C19—21no—
300C2×C19#160011yescharacteristic
301C2×C19#160311yescharacteristic
302C2×C19#160911yescharacteristic
303C2×C19#161811yescharacteristic
304C2×C19#203911yescharacteristic
305C2×C19#204211yescharacteristic
306C2×C19#204411yescharacteristic
307D19—161no—
308C22×Q8C22⋊D1911yescharacteristic
309C22×D4—191no—
310C22×D4—381no—
311C23×C4—21no—
312C23×C4—191no—
313C23×C4—191no—
314C23×C4—381no—
315C23×C4C22×D1911yescharacteristic
316C22×C8—21no—
317C22×C8—381no—
318C22⋊Q8—21no—
319C22⋊Q8—21no—
320C22⋊Q8—21no—
321C22⋊Q8—21no—
322#121—381no—
323#121—381no—
324#121—381no—
325#121—381no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—191no—
331C2×C4⋊C4—762no—
332C2×C4⋊C4—762no—
333C2×C4⋊C4—762no—
334C2×C4⋊C4C22⋊D1911yescharacteristic
335C2×C22⋊C4—21no—
336C2×C22⋊C4—381no—
337C2×C22⋊C4—381no—
338C2×C22⋊C4—381no—
339C2×C22⋊C4—381no—
340C2×C22⋊C4—381no—
341#103—42no—
342#102—762no—
343C22⋊C8—21no—
344C22⋊C8—21no—
345C22⋊C8—381no—
346C22⋊C8—381no—
347#95—192no—
348#95—381no—
349#95—381no—
350#95—381no—
351#95—381no—
352#95—381no—
353#95—381no—
354#95—381no—
355#95—762no—
356C19#1040511yescharacteristic, complemented, Sylow
357C24—381no—
358C24D4×D1911yescharacteristic
359C2×Q8—21no—
360C2×Q8—21no—
361C2×Q8—41no—
362C2×Q8—41no—
363C2×D4—381no—
364C2×D4—381no—
365C2×D4—761no—
366C2×D4—761no—
367C2×D4—761no—
368C2×D4—761no—
369C2×D4—761no—
370C2×D4—761no—
371C2×D4—761no—
372C2×D4—761no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—382no—
385C22×C4—382no—
386C22×C4—382no—
387C22×C4—381no—
388C22×C4—381no—
389C22×C4—381no—
390C22×C4—381no—
391C22×C4—381no—
392C22×C4—381no—
393C22×C4—381no—
394C22×C4—761no—
395C22×C4—761no—
396C22×C4—761no—
397C22×C4—761no—
398C22×C4—761no—
399C22×C4—761no—
400C22×C4—761no—
401C22×C4—761no—
402C22×C4#6454111yescharacteristic
403C22×C4#6454111yescharacteristic
404C22×C4D4×D1911yescharacteristic
405C22×C4D4×D1911yescharacteristic
406C22×C4#6454311yescharacteristic
407C22×C4C2×C22⋊D1911yescharacteristic
408C2×C8—41no—
409C2×C8—41no—
410C2×C8—41no—
411C2×C8—761no—
412C2×C8—761no—
413C2×C8—761no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—41no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C4⋊C4—41no—
422C4⋊C4—381no—
423C4⋊C4—381no—
424C4⋊C4—768no—
425C22⋊C4—41no—
426C22⋊C4—41no—
427C22⋊C4—761no—
428C22⋊C4—761no—
429C22⋊C4—1521no—
430C22⋊C4—1521no—
431C22⋊C4—1521no—
432C22⋊C4—1521no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—761no—
438C23—761no—
439C23—761no—
440C23—761no—
441C23—761no—
442C23—761no—
443C23—761no—
444C23#1059733011yescharacteristic
445C23#1059733111yescharacteristic
446C23#1059736011yescharacteristic
447C23#1059736211yescharacteristic
448C23#1059736411yescharacteristic
449C23#1059736511yescharacteristic
450C23#1059738311yescharacteristic
451Q8—42no—
452Q8—81no—
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—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—41no—
476C2×C4—81no—
477C2×C4—81no—
478C2×C4—81no—
479C2×C4—81no—
480C2×C4—384no—
481C2×C4—762no—
482C2×C4—762no—
483C2×C4—762no—
484C2×C4—762no—
485C2×C4—762no—
486C2×C4—762no—
487C2×C4—762no—
488C2×C4—762no—
489C2×C4—761no—
490C2×C4—761no—
491C2×C4—761no—
492C2×C4—761no—
493C2×C4—761no—
494C2×C4—761no—
495C2×C4—761no—
496C2×C4—761no—
497C2×C4—761no—
498C2×C4—1521no—
499C2×C4—1521no—
500C2×C4#1059732911yescharacteristic
501C2×C4#1059733011yescharacteristic
502C2×C4#1059737511yescharacteristic
503C2×C4#1059738511yescharacteristic
504C8—81no—
505C8—1521no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—1521no—
519C22—1521no—
520C22—1521no—
521C22—1521no—
522C22—1521no—
523C22—1521no—
524C22—1521no—
525C22#1192645911yescharacteristic
526C22#1192668811yescharacteristic
527C22#1192670511yescharacteristic
528C22#1192671011yescharacteristic
529C22#1192672511yescharacteristic
530C22#1192673011yescharacteristic
531C22#1192673311yescharacteristic
532C22#1192676211yescharacteristic
533C22#1192676911yescharacteristic
534C22#1192690011yescharacteristic
535C22#1192690511yescharacteristic
536C4—21no—
537C4—21no—
538C4—21no—
539C4—21no—
540C4—82no—
541C4—81no—
542C4—81no—
543C4—764no—
544C4—1521no—
545C4—1521no—
546C4—1521no—
547C2—21no—
548C2—21no—
549C2—21no—
550C2—21no—
551C2—3041no—
552C2#1456258011yescharacteristic
553C2#1456259711yescharacteristic
554C2#1456263111yescharacteristic
555C2#1456268211yescharacteristic
556C2#1456485711yescharacteristic
557C2#1456487211yescharacteristic
558C2#1456488411yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1872C2
socleC23×C19#120
prime radicalC2×#10597376C22
hypercenter#1872D19
hypocenterC19#10405
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
3. C2×#11926281C2semidirect
5. #14561898C2semidirect
6. #14561477C2semidirect
7. C19×#1872C2semidirect
229. #1872D19semidirect
356. C19#10405semidirect

Maximal subgroups

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

subgroupindex
#145695692
#145639522
C2×#119262812
C2×#119262792
#145618982
#145614772
C19×#18722
#1040519