Finite Group Databasebeta

← #18079114

Subgroups — #18079114

Order 4864.

648 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14566687C211yesmaximal, characteristic, complemented
2#14564472C211yesmaximal, characteristic, complemented
3#14562203C211yesmaximal, characteristic, complemented
4C2×#11926278C211yesmaximal, characteristic, complemented
5#14561515C211yesmaximal, characteristic, complemented
6#14561481C211yesmaximal, characteristic, complemented
7C19×#3186C211yesmaximal, characteristic
8C2×D4×Dic19—21no—
9C2×#10597291—21no—
10C2×#10597291—21no—
11C2×C22⋊(C19⋊C8)C2211yescharacteristic
12#11926437—21no—
13#11926430—21no—
14#11926424—21no—
15#11926424—21no—
16#11926404C2211yescharacteristic
17C22⋊C4×Dic19—21no—
18C4×C22⋊Dic19C2211yescharacteristic
19C2×C19⋊#95C2211yescharacteristic
20#11926278—21no—
21#11926278—21no—
22#11926278—22no—
23C2×C19×#121C2211yescharacteristic
24C2×C19×#121C2211yescharacteristic
25C19×#480—21no—
26C19×#480C412yescomplemented
27C19×#466—22no—
28C19×#447—21no—
29C19×#447C412yescomplemented
30C2×C19×C22⋊C8C2211yescharacteristic
31C22×D4×C19—21no—
32C22×D4×C19—21no—
33C22×D4×C19C2×C411yescharacteristic, complemented
34C22×D4×C19D411yescharacteristic
35C23×C4×C19C2311yescharacteristic
36C23×Dic19—21no—
37C23×Dic19—21no—
38C2×D8×C19—22no—
39C22×C8×C19—21no—
40C19×#121—21no—
41C19×#121—21no—
42C19×#121—21no—
43C19×#121—21no—
44C19×#121—21no—
45C19×#121—21no—
46C19×#121C2×C412yes—
47C19×#121D412yes—
48C2×C4⋊C4×C19C2×C411yescharacteristic, complemented
49C2×C4⋊C4×C19D411yescharacteristic
50C2×C22⋊C4×C19—21no—
51C2×C22⋊C4×C19—21no—
52C2×C22⋊Dic19—21no—
53C2×C22⋊Dic19—21no—
54C2×C22⋊Dic19—21no—
55C2×C22⋊Dic19—21no—
56C2×C22⋊Dic19D411yescharacteristic
57C2×C22⋊Dic19D411yescharacteristic
58D4×Dic19—42no—
59D4×Dic19—42no—
60C2×C4⋊Dic19—21no—
61C2×C4⋊Dic19—21no—
62C2×C4×Dic19—21no—
63C2×C4×Dic19—21no—
64C22×C19⋊C8—21no—
65C19×#107—22no—
66C19×#102—22no—
67C19×#102—22no—
68C19×C22⋊C8—21no—
69C19×C22⋊C8C2×C412yescomplemented
70#10597291—42no—
71#10597291—42no—
72C19⋊#95—21no—
73C19⋊#95—21no—
74C19⋊#95—21no—
75C19⋊#95—21no—
76C19⋊#95—21no—
77C19⋊#95D411yescharacteristic
78C19⋊#95D411yescharacteristic
79C22⋊(C19⋊C8)—21no—
80C22⋊(C19⋊C8)—21no—
81C24×C19—21no—
82C24×C19—21no—
83C24×C19C2×D411yescharacteristic
84C2×D4×C19—22no—
85C2×D4×C19—22no—
86C2×D4×C19—21no—
87C2×D4×C19—21no—
88C2×D4×C19—21no—
89C2×D4×C19—41no—
90C2×D4×C19—41no—
91C2×D4×C19—41no—
92C2×D4×C19—41no—
93C2×D4×C19—41no—
94C2×D4×C19—41no—
95C2×D4×C19—41no—
96C2×D4×C19—41no—
97C2×D4×C19—41no—
98C2×D4×C19—41no—
99C2×D4×C19—81no—
100C2×D4×C19—81no—
101C2×D4×C19C22⋊C412yes—
102C22×C4×C19—21no—
103C22×C4×C19—21no—
104C22×C4×C19—81no—
105C22×C4×C19C22×C411yescharacteristic
106C22×C4×C19C2×D411yescharacteristic
107C22×C4×C19C2×D411yescharacteristic
108C22×C4×C19C2×D411yescharacteristic
109C22×C4×C19#4111yescharacteristic
110C22×C4×C19#4111yescharacteristic
111C22×Dic19—21no—
112C22×Dic19—21no—
113C22×Dic19—21no—
114C22×Dic19—21no—
115C22×Dic19—42no—
116C22×Dic19—42no—
117C22×Dic19—42no—
118C22×Dic19—41no—
119C22×Dic19—41no—
120C22×Dic19—41no—
121C22×Dic19—81no—
122C22×Dic19—81no—
123D8×C19—82no—
124C2×C8×C19—22no—
125C2×C8×C19—81no—
126C4⋊C4×C19—21no—
127C4⋊C4×C19—21no—
128C4⋊C4×C19—21no—
129C4⋊C4×C19C22⋊C412yes—
130C22⋊C4×C19—22no—
131C22⋊C4×C19—22no—
132C22⋊C4×C19—41no—
133C22⋊C4×C19—41no—
134C22⋊Dic19—21no—
135C22⋊Dic19—21no—
136C22⋊Dic19—21no—
137C22⋊Dic19—42no—
138C22⋊Dic19—42no—
139C22⋊Dic19—41no—
140C22⋊Dic19—41no—
141C22⋊Dic19—81no—
142C22⋊Dic19D812yescomplemented
143C4⋊Dic19—42no—
144C4⋊Dic19—81no—
145C4×Dic19—42no—
146C4×Dic19—81no—
147C2×C19⋊C8—41no—
148C2×C19⋊C8—81no—
149#9277—191nomaximal, Sylow
150C23×C19—22no—
151C23×C19—41no—
152C23×C19—41no—
153C23×C19—41no—
154C23×C19—41no—
155C23×C19—41no—
156C23×C19—41no—
157C23×C19—41no—
158C23×C19—41no—
159C23×C19—41no—
160C23×C19—41no—
161C23×C19—41no—
162C23×C19—81no—
163C23×C19—81no—
164C23×C19C4×D411yescharacteristic
165C23×C19#12011yescharacteristic
166C23×C19#12111yescharacteristic
167C23×C19C2×D811yescharacteristic
168C23×C19#13511yescharacteristic
169C23×C19AGL(1,ℤ/8)11yescharacteristic
170C23×C19AGL(1,ℤ/8)11yescharacteristic
171D4×C19—42no—
172D4×C19—42no—
173D4×C19—42no—
174D4×C19—42no—
175D4×C19—42no—
176D4×C19—42no—
177D4×C19—81no—
178D4×C19—81no—
179D4×C19—81no—
180D4×C19—81no—
181D4×C19—81no—
182D4×C19—81no—
183C2×C4×C19—22no—
184C2×C4×C19—41no—
185C2×C4×C19—41no—
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×C19C2×C22⋊C411yescharacteristic
196C2×C4×C19C4×D411yescharacteristic
197C2×C4×C19#12111yescharacteristic
198C2×C4×C19#12311yescharacteristic
199C2×Dic19—22no—
200C2×Dic19—22no—
201C2×Dic19—41no—
202C2×Dic19—41no—
203C2×Dic19—41no—
204C2×Dic19—41no—
205C2×Dic19—41no—
206C2×Dic19—41no—
207C2×Dic19—41no—
208C2×Dic19—41no—
209C2×Dic19—41no—
210C2×Dic19—41no—
211C2×Dic19—84no—
212C2×Dic19—82no—
213C2×Dic19—82no—
214C2×Dic19—81no—
215C2×Dic19—81no—
216C2×Dic19—81no—
217C8×C19—42no—
218C19⋊C8—81no—
219#3186D1911yescharacteristic
220#2364—191no—
221#1964—191no—
222#1519—191no—
223C2×#327—191no—
224#1294—191no—
225#1282—191no—
226C22×C19—21no—
227C22×C19—21no—
228C22×C19—21no—
229C22×C19—21no—
230C22×C19—21no—
231C22×C19—21no—
232C22×C19—41no—
233C22×C19—41no—
234C22×C19—41no—
235C22×C19—41no—
236C22×C19—42no—
237C22×C19—42no—
238C22×C19—42no—
239C22×C19—81no—
240C22×C19—81no—
241C22×C19—81no—
242C22×C19—81no—
243C22×C19—81no—
244C22×C19—81no—
245C22×C19—81no—
246C22×C19—161no—
247C22×C19—161no—
248C22×C19#38611yescharacteristic
249C22×C19C4×D811yescharacteristic
250C22×C19#44211yescharacteristic
251C22×C19#44711yescharacteristic
252C22×C19#44911yescharacteristic
253C22×C19#45911yescharacteristic
254C22×C19#46311yescharacteristic
255C4×C19—21no—
256C4×C19—21no—
257C4×C19—21no—
258C4×C19—21no—
259C4×C19—42no—
260C4×C19—81no—
261Dic19—42no—
262Dic19—42no—
263Dic19—81no—
264Dic19—81no—
265Dic19—161no—
266C2×#121C2×D1911yescharacteristic
267C2×#121C2×D1911yescharacteristic
268C2×C4×D4—381no—
269#480—21no—
270#480Dic1912yescomplemented
271#466—22no—
272#447—21no—
273#447Dic1912yescomplemented
274C2×#99—381no—
275C2×#99—381no—
276C2×C22⋊C8—191no—
277C2×C22⋊C8C2×D1911yescharacteristic
278#388—381no—
279#387—381no—
280#386—381no—
281#386—381no—
282#380—191no—
283C4×C22⋊C4—191no—
284C4×C22⋊C4—381no—
285C2×#95—191no—
286#327—381no—
287#327—381no—
288#327—382no—
289C2×C19—21no—
290C2×C19—21no—
291C2×C19—21no—
292C2×C19—21no—
293C2×C19—21no—
294C2×C19—21no—
295C2×C19—82no—
296C2×C19—161no—
297C2×C19#187911yescharacteristic
298C2×C19#190611yescharacteristic
299C2×C19#191311yescharacteristic
300C22×D4—21no—
301C22×D4—21no—
302C22×D4C2×Dic1911yescharacteristic, complemented
303C22×D4C22⋊D1911yescharacteristic
304C23×C4—381no—
305C23×C4—381no—
306C23×C4C22×D1911yescharacteristic
307C2×D8—22no—
308C22×C8—21no—
309C22×C8—381no—
310#121—21no—
311#121—21no—
312#121—21no—
313#121—21no—
314#121—21no—
315#121—21no—
316#121C2×Dic1912yes—
317#121C22⋊D1912yes—
318C4×D4—762no—
319C4×D4—762no—
320C2×C4⋊C4—381no—
321C2×C4⋊C4—381no—
322C2×C4⋊C4C2×Dic1911yescharacteristic, complemented
323C2×C4⋊C4C22⋊D1911yescharacteristic
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—191no—
327C2×C22⋊C4—191no—
328C2×C22⋊C4—381no—
329C2×C22⋊C4—381no—
330C2×C22⋊C4—381no—
331C2×C22⋊C4—381no—
332C2×C42—381no—
333C2×C42—381no—
334#107—22no—
335#102—22no—
336#102—22no—
337#99—762no—
338#99—762no—
339C22⋊C8—21no—
340C22⋊C8—381no—
341C22⋊C8—381no—
342C22⋊C8C2×Dic1912yescomplemented
343#95—191no—
344#95—191no—
345#95—381no—
346#95—381no—
347#95—381no—
348#95—381no—
349#95—381no—
350C19#927711yescharacteristic, complemented, Sylow
351C24—21no—
352C24—21no—
353C24D4×D1911yescharacteristic
354C2×D4—22no—
355C2×D4—22no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—41no—
360C2×D4—41no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—81no—
370C2×D4—81no—
371C2×D4C22⋊Dic1912yes—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—81no—
375C22×C4—381no—
376C22×C4—381no—
377C22×C4—381no—
378C22×C4—381no—
379C22×C4—762no—
380C22×C4—762no—
381C22×C4—762no—
382C22×C4—761no—
383C22×C4—761no—
384C22×C4—761no—
385C22×C4—1521no—
386C22×C4—1521no—
387C22×C4D4×D1911yescharacteristic
388C22×C4#6454311yescharacteristic
389C22×C4#6454311yescharacteristic
390C22×C4C22×Dic1911yescharacteristic
391C22×C4C2×C22⋊D1911yescharacteristic
392C22×C4C2×C22⋊D1911yescharacteristic
393D8—82no—
394C2×C8—22no—
395C2×C8—81no—
396C2×C8—761no—
397C2×C8—1521no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—762no—
402C4⋊C4—1521no—
403C4⋊C4C22⋊Dic1912yes—
404C22⋊C4—22no—
405C22⋊C4—22no—
406C22⋊C4—41no—
407C22⋊C4—41no—
408C22⋊C4—192no—
409C22⋊C4—381no—
410C22⋊C4—381no—
411C22⋊C4—381no—
412C22⋊C4—762no—
413C22⋊C4—762no—
414C22⋊C4—761no—
415C22⋊C4—761no—
416C22⋊C4—1521no—
417C42—762no—
418C42—1521no—
419C23—22no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—41no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—81no—
432C23—81no—
433C23D8×D1911yescharacteristic
434C23#1059735711yescharacteristic
435C23#1059735711yescharacteristic
436C23#1059735811yescharacteristic
437C23D4×Dic1911yescharacteristic
438C23#1059738311yescharacteristic
439C23#1059738511yescharacteristic
440D4—42no—
441D4—42no—
442D4—42no—
443D4—42no—
444D4—42no—
445D4—42no—
446D4—81no—
447D4—81no—
448D4—81no—
449D4—81no—
450D4—81no—
451D4—81no—
452C2×C4—22no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—382no—
465C2×C4—382no—
466C2×C4—761no—
467C2×C4—761no—
468C2×C4—761no—
469C2×C4—761no—
470C2×C4—761no—
471C2×C4—761no—
472C2×C4—761no—
473C2×C4—761no—
474C2×C4—761no—
475C2×C4—761no—
476C2×C4—1521no—
477C2×C4—1521no—
478C2×C4—1521no—
479C2×C4—1524no—
480C2×C4—1522no—
481C2×C4—1522no—
482C2×C4D4×Dic1911yescharacteristic
483C2×C4#1059738111yescharacteristic
484C2×C4#1059738511yescharacteristic
485C2×C4C2×C22⋊Dic1911yescharacteristic
486C8—42no—
487C8—1521no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—42no—
499C22—42no—
500C22—42no—
501C22—81no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22—161no—
509C22—161no—
510C22#1192642411yescharacteristic
511C22D8×Dic1911yescharacteristic
512C22#1192665611yescharacteristic
513C22#1192667611yescharacteristic
514C22#1192668611yescharacteristic
515C22#1192673711yescharacteristic
516C22#1192675711yescharacteristic
517C4—21no—
518C4—21no—
519C4—21no—
520C4—21no—
521C4—42no—
522C4—81no—
523C4—3041no—
524C4—762no—
525C4—762no—
526C4—1521no—
527C4—1521no—
528C2—21no—
529C2—21no—
530C2—21no—
531C2—21no—
532C2—21no—
533C2—21no—
534C2—82no—
535C2—161no—
536C2#1456398511yescharacteristic
537C2#1456413811yescharacteristic
538C2#1456417811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
Fitting, prime radicalC19×#3186C2
socleC22×C19#386
cosocleC23×C4×C19C23
hypercenter#3186D19
hypocenterC19#9277
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3186

Complements

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

NH ≅ G/Ntype
1. #14566687C2semidirect
2. #14564472C2semidirect
3. #14562203C2semidirect
4. C2×#11926278C2semidirect
5. #14561515C2semidirect
6. #14561481C2semidirect
26. C19×#480C4semidirect
29. C19×#447C4semidirect
33. C22×D4×C19C2×C4semidirect
48. C2×C4⋊C4×C19C2×C4semidirect
69. C19×C22⋊C8C2×C4semidirect
142. C22⋊Dic19D8semidirect
270. #480Dic19semidirect
273. #447Dic19semidirect
302. C22×D4C2×Dic19semidirect
322. C2×C4⋊C4C2×Dic19semidirect
342. C22⋊C8C2×Dic19semidirect
350. C19#9277semidirect

Maximal subgroups

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

subgroupindex
#145666872
#145644722
#145622032
C2×#119262782
#145615152
#145614812
C19×#31862
#927719