Finite Group Databasebeta

← #18079110

Subgroups — #18079110

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#14574383C211yesmaximal, characteristic
2#14566687C211yesmaximal, characteristic, complemented
3#14564470C211yesmaximal, characteristic, complemented
4C2×#11926279C211yesmaximal, characteristic, complemented
5#14561513C211yesmaximal, characteristic, complemented
6#14561482C211yesmaximal, characteristic, complemented
7C19×#1519C211yesmaximal, characteristic, complemented
8C2×#10597376C2211yescharacteristic
9C2×D4×Dic19—21no—
10#11926857—21no—
11#11926855C412yescomplemented
12#11926778—22no—
13#11926678—21no—
14#11926677C412yescomplemented
15C2×#10597263—21no—
16C2×#10597263—21no—
17C2×C22⋊(C19⋊C8)C2211yescharacteristic
18#11926437—21no—
19#11926430—21no—
20#11926424—21no—
21#11926424—21no—
22C22⋊C4×Dic19—21no—
23C4×C22⋊Dic19C2211yescharacteristic
24C2×C19⋊#95C2211yescharacteristic
25#11926279—21no—
26#11926279—21no—
27C2×C19×#121C2211yescharacteristic
28C2×C19×C22⋊C8C2211yescharacteristic
29C19×#380C2211yescharacteristic
30C19×#327—22no—
31C22×D4×C19—21no—
32C22×D4×C19D411yescharacteristic
33C23×C4×C19C2311yescharacteristic
34C22×C22⋊D19—21no—
35C23×Dic19—21no—
36C23×Dic19—21no—
37C22×D76C2×C411yescharacteristic, complemented
38C22×C8×C19—21no—
39C19×#121—21no—
40C19×#121—21no—
41C19×#121C2×C412yes—
42C19×#121D412yes—
43C2×C4⋊C4×C19—21no—
44C2×C4⋊C4×C19D411yescharacteristic
45C2×C22⋊C4×C19—21no—
46C2×C22⋊C4×C19—21no—
47C2×C22⋊Dic19—21no—
48C2×C22⋊Dic19—21no—
49C2×C22⋊Dic19—21no—
50C2×C22⋊Dic19D411yescharacteristic
51C2×C22⋊Dic19D411yescharacteristic
52D4×Dic19—42no—
53D4×Dic19—42no—
54C2×#64525—22no—
55#10597376—21no—
56#10597376—21no—
57#10597376—21no—
58#10597376—21no—
59C2×(C2×D19)⋊C4—21no—
60C2×C4⋊Dic19—21no—
61C2×C4⋊Dic19C2×C411yescharacteristic, complemented
62C2×C4×Dic19—21no—
63C2×C4×Dic19—21no—
64C22×C19⋊C8—21no—
65C19×C22⋊C8—21no—
66C19×C22⋊C8—21no—
67C19×#95—21no—
68#10597289—22no—
69C19⋊#95—21no—
70C19⋊#95—21no—
71C19⋊#95—21no—
72C19⋊#95—21no—
73C19⋊#95D411yescharacteristic
74C19⋊#95D411yescharacteristic
75C22⋊(C19⋊C8)—21no—
76C22⋊(C19⋊C8)C2×C412yescomplemented
77#10597266—22no—
78#10597264—22no—
79#10597263—42no—
80#10597263—42no—
81C24×C19—21no—
82C24×C19C2×D411yescharacteristic
83C23×D19—21no—
84C2×D4×C19—22no—
85C2×D4×C19—22no—
86C2×D4×C19—21no—
87C2×D4×C19—41no—
88C2×D4×C19—41no—
89C2×D4×C19—41no—
90C2×D4×C19—41no—
91C2×D4×C19—81no—
92C2×D4×C19C22⋊C412yes—
93C22×C4×C19—21no—
94C22×C4×C19—41no—
95C22×C4×C19—81no—
96C22×C4×C19C22×C411yescharacteristic
97C22×C4×C19C2×D411yescharacteristic
98C22×C4×C19C2×D411yescharacteristic
99C22×C4×C19C2×D411yescharacteristic
100C22×C4×C19#4111yescharacteristic
101C22×C4×C19#4111yescharacteristic
102C2×C22⋊D19—41no—
103C2×C22⋊D19—41no—
104C2×C22⋊D19—41no—
105C2×C22⋊D19—41no—
106C2×C22⋊D19—41no—
107C2×C22⋊D19—41no—
108C22×Dic19—21no—
109C22×Dic19—21no—
110C22×Dic19—21no—
111C22×Dic19—21no—
112C22×Dic19—21no—
113C22×Dic19—42no—
114C22×Dic19—42no—
115C22×Dic19—42no—
116C22×Dic19—41no—
117C22×Dic19—41no—
118C22×Dic19—81no—
119C22×Dic19—81no—
120C2×D76—21no—
121C2×D76—21no—
122C2×D76—81no—
123C2×C8×C19—41no—
124C2×C8×C19—81no—
125C4⋊C4×C19—21no—
126C4⋊C4×C19—81no—
127C4⋊C4×C19C22⋊C412yes—
128C22⋊C4×C19—22no—
129C22⋊C4×C19—22no—
130C22⋊C4×C19—41no—
131C22⋊C4×C19—41no—
132C22⋊Dic19—21no—
133C22⋊Dic19—21no—
134C22⋊Dic19—21no—
135C22⋊Dic19—42no—
136C22⋊Dic19—42no—
137C22⋊Dic19—81no—
138C22⋊Dic19D812yescomplemented
139#64525—82no—
140(C2×D19)⋊C4—41no—
141(C2×D19)⋊C4—41no—
142C4⋊Dic19—21no—
143C4⋊Dic19—21no—
144C4⋊Dic19—42no—
145C4×Dic19—42no—
146C4×Dic19—81no—
147C2×C19⋊C8—22no—
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×C19C4×D411yescharacteristic
160C23×C19#12011yescharacteristic
161C23×C19#12111yescharacteristic
162C23×C19C2×D811yescharacteristic
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—81no—
170C22×D19—81no—
171D4×C19—42no—
172D4×C19—42no—
173D4×C19—42no—
174D4×C19—42no—
175D4×C19—42no—
176D4×C19—81no—
177C2×C4×C19—22no—
178C2×C4×C19—41no—
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—41no—
186C2×C4×C19—81no—
187C2×C4×C19—81no—
188C2×C4×C19—81no—
189C2×C4×C19C2×C22⋊C411yescharacteristic
190C2×C4×C19C4×D411yescharacteristic
191C2×C4×C19#12111yescharacteristic
192C2×C4×C19#12311yescharacteristic
193C22⋊D19—81no—
194C22⋊D19—81no—
195C22⋊D19—81no—
196C22⋊D19—81no—
197C2×Dic19—22no—
198C2×Dic19—22no—
199C2×Dic19—41no—
200C2×Dic19—41no—
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—41no—
212C2×Dic19—84no—
213C2×Dic19—82no—
214C2×Dic19—82no—
215D76—42no—
216D76—81no—
217C8×C19—81no—
218C19⋊C8—42no—
219#3186—191no—
220#2364—191no—
221#1964—191no—
222#1519D1911yescharacteristic, complemented
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#38611yescharacteristic
244C22×C19C4×D811yescharacteristic
245C22×C19#44211yescharacteristic
246C22×C19#44711yescharacteristic
247C22×C19#44911yescharacteristic
248C22×C19#45911yescharacteristic
249C22×C19#46311yescharacteristic
250C2×D19—81no—
251C2×D19—81no—
252C2×D19—81no—
253C2×D19—161no—
254C2×D19—161no—
255C4×C19—21no—
256C4×C19—21no—
257C4×C19—21no—
258C4×C19—21no—
259C4×C19—42no—
260C4×C19—161no—
261Dic19—42no—
262Dic19—42no—
263Dic19—81no—
264Dic19—81no—
265Dic19—81no—
266C2×#121—191no—
267C2×#121C2×D1911yescharacteristic
268C2×C4×D4—381no—
269#480—192no—
270#480—381no—
271#466—382no—
272#447—192no—
273#447—381no—
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#380C2×D1911yescharacteristic
283C4×C22⋊C4—191no—
284C4×C22⋊C4—381no—
285C2×#95—191no—
286#327—22no—
287#327—381no—
288#327—381no—
289C2×C19—21no—
290C2×C19—21no—
291C2×C19—21no—
292C2×C19—21no—
293C2×C19—21no—
294C2×C19—21no—
295C2×C19—82no—
296C2×C19#187911yescharacteristic
297C2×C19#190611yescharacteristic
298C2×C19#191311yescharacteristic
299D19—161no—
300C22×D4—21no—
301C22×D4—191no—
302C22×D4—381no—
303C22×D4D7611yescharacteristic
304C23×C4—381no—
305C23×C4—381no—
306C23×C4C22×D1911yescharacteristic
307C2×D8—382no—
308C22×C8—21no—
309C22×C8—381no—
310#121—21no—
311#121—21no—
312#121—381no—
313#121—381no—
314#121—381no—
315#121—381no—
316#121C4×D1912yes—
317#121C22⋊D1912yes—
318C4×D4—762no—
319C4×D4—762no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—191no—
322C2×C4⋊C4—381no—
323C2×C4⋊C4D7611yescharacteristic
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—382no—
335#102—382no—
336#102—382no—
337#99—762no—
338#99—762no—
339C22⋊C8—21no—
340C22⋊C8—21no—
341C22⋊C8—192no—
342C22⋊C8—381no—
343#95—21no—
344#95—191no—
345#95—191no—
346#95—381no—
347#95—381no—
348#95—381no—
349#95—381no—
350C19#927711yescharacteristic, complemented, Sylow
351C24—21no—
352C24—381no—
353C24D4×D1911yescharacteristic
354C2×D4—22no—
355C2×D4—22no—
356C2×D4—21no—
357C2×D4—41no—
358C2×D4—41no—
359C2×D4—41no—
360C2×D4—41no—
361C2×D4—81no—
362C2×D4—381no—
363C2×D4—381no—
364C2×D4—761no—
365C2×D4—761no—
366C2×D4—761no—
367C2×D4—761no—
368C2×D4—761no—
369C2×D4—761no—
370C2×D4—1521no—
371C2×D4(C2×D19)⋊C412yes—
372C22×C4—21no—
373C22×C4—41no—
374C22×C4—81no—
375C22×C4—381no—
376C22×C4—381no—
377C22×C4—381no—
378C22×C4—381no—
379C22×C4—381no—
380C22×C4—762no—
381C22×C4—762no—
382C22×C4—762no—
383C22×C4—761no—
384C22×C4—761no—
385C22×C4—1521no—
386C22×C4—1521no—
387C22×C4C2×C4×D1911yescharacteristic
388C22×C4C2×D7611yescharacteristic
389C22×C4D4×D1911yescharacteristic
390C22×C4#6454311yescharacteristic
391C22×C4#6454311yescharacteristic
392C22×C4C2×C22⋊D1911yescharacteristic
393D8—1522no—
394C2×C8—41no—
395C2×C8—81no—
396C2×C8—382no—
397C2×C8—1521no—
398C4⋊C4—21no—
399C4⋊C4—81no—
400C4⋊C4—381no—
401C4⋊C4—381no—
402C4⋊C4—762no—
403C4⋊C4(C2×D19)⋊C412yes—
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—761no—
429C23—761no—
430C23—761no—
431C23—1521no—
432C23—1521no—
433C23(C22⋊D19)⋊C411yescharacteristic
434C23#1059732811yescharacteristic
435C23D8×D1911yescharacteristic
436C23#1059735711yescharacteristic
437C23#1059736011yescharacteristic
438C23#1059736211yescharacteristic
439C23#1059738511yescharacteristic
440D4—42no—
441D4—42no—
442D4—42no—
443D4—42no—
444D4—42no—
445D4—81no—
446D4—762no—
447D4—1521no—
448D4—1521no—
449D4—1521no—
450D4—1521no—
451D4—1521no—
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—81no—
462C2×C4—81no—
463C2×C4—81no—
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—761no—
477C2×C4—761no—
478C2×C4—761no—
479C2×C4—1524no—
480C2×C4—1522no—
481C2×C4—1522no—
482C2×C4(C22⋊D19)⋊C411yescharacteristic
483C2×C4#1059733211yescharacteristic
484C2×C4C2×(C2×D19)⋊C411yescharacteristic
485C2×C4#1059738511yescharacteristic
486C8—81no—
487C8—762no—
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—3041no—
506C22—3041no—
507C22—1521no—
508C22—1521no—
509C22—1521no—
510C22#1192642111yescharacteristic
511C22#1192662411yescharacteristic
512C22#1192665311yescharacteristic
513C22#1192667911yescharacteristic
514C22#1192669011yescharacteristic
515C22#1192673711yescharacteristic
516C22#1192676111yescharacteristic
517C4—21no—
518C4—21no—
519C4—21no—
520C4—21no—
521C4—42no—
522C4—161no—
523C4—762no—
524C4—762no—
525C4—1521no—
526C4—1521no—
527C4—1521no—
528C2—21no—
529C2—21no—
530C2—21no—
531C2—21no—
532C2—21no—
533C2—21no—
534C2—82no—
535C2—3041no—
536C2#1456398111yescharacteristic
537C2#1456413411yescharacteristic
538C2#1456417511yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1519C2
socleC22×C19#386
prime radical#14574383C2
cosocleC23×C4×C19C23
hypercenter#1519D19
hypocenterC19#9277
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1519

Complements

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

NH ≅ G/Ntype
2. #14566687C2semidirect
3. #14564470C2semidirect
4. C2×#11926279C2semidirect
5. #14561513C2semidirect
6. #14561482C2semidirect
7. C19×#1519C2semidirect
11. #11926855C4semidirect
14. #11926677C4semidirect
37. C22×D76C2×C4semidirect
61. C2×C4⋊Dic19C2×C4semidirect
76. C22⋊(C19⋊C8)C2×C4semidirect
138. C22⋊Dic19D8semidirect
222. #1519D19semidirect
350. C19#9277semidirect

Maximal subgroups

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

subgroupindex
#145743832
#145666872
#145644702
C2×#119262792
#145615132
#145614822
C19×#15192
#927719