Finite Group Databasebeta

← #18076089

Subgroups — #18076089

Order 4864.

530 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14566542C211yesmaximal, characteristic
2#14563620C211yesmaximal, characteristic
3#14561951C211yesmaximal, characteristic
4#14561514C211yesmaximal, characteristic, complemented
5#14561503C211yesmaximal, characteristic, complemented
6#14561502C211yesmaximal, characteristic, complemented
7C19×#1294C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊D19—21no—
9C2×C4×C22⋊D19C2211yescharacteristic
10C2×#10597263—21no—
11C2×C22⋊(C19⋊C8)C2211yescharacteristic
12#11926441—21no—
13#11926418—21no—
14#11926417—21no—
15#11926408C411yescharacteristic, complemented
16#11926404C2211yescharacteristic
17#11926404C2211yescharacteristic
18#11926403C411yescharacteristic, complemented
19#11926395C411yescharacteristic, complemented
20#95×D19C411yescharacteristic, complemented
21#11926310—21no—
22#11926269—21no—
23#11926267—21no—
24C2×C19×C22⋊C8C2211yescharacteristic
25C19×#380C2211yescharacteristic
26C2×C19×#95C2211yescharacteristic
27C23×C4×C19—21no—
28C23×C4×C19C2311yescharacteristic
29C22×C22⋊D19D411yescharacteristic
30C22×C4×D19—21no—
31C22×C4×D19C2×C411yescharacteristic
32C22×C8×C19—21no—
33C2×C4⋊C4×C19—21no—
34C2×C22⋊C4×C19—21no—
35C2×C22⋊Dic19—21no—
36C2×C22⋊Dic19—21no—
37C2×C22⋊Dic19D411yescharacteristic
38C4×C22⋊D19—21no—
39C4×C22⋊D19—21no—
40C4×C22⋊D19—21no—
41C4×C22⋊D19—21no—
42C4×C22⋊D19—42no—
43C4×C22⋊D19—42no—
44C2×(C2×D19)⋊C4—21no—
45C2×(C2×D19)⋊C4D411yescharacteristic
46C2×C4⋊Dic19—21no—
47C2×C4⋊Dic19—21no—
48C2×Dic19⋊C4—21no—
49C2×Dic19⋊C4—21no—
50C2×Dic19⋊C4—21no—
51C2×Dic19⋊C4D411yescharacteristic
52C2×C4×Dic19—21no—
53C2×C4×Dic19C2×C411yescharacteristic
54C22×C19⋊C8—21no—
55C19×C22⋊C8—21no—
56C19×C22⋊C8—21no—
57C19×#95—21no—
58C19×#95—21no—
59C19×#95C2×C411yescharacteristic
60C19×#95C2×C411yescharacteristic
61C19⋊#95—21no—
62C19⋊#95—21no—
63C19⋊#95—21no—
64C19⋊#95C2×C411yescharacteristic
65C19⋊#95C2×C411yescharacteristic
66C22⋊(C19⋊C8)—21no—
67C22⋊(C19⋊C8)—21no—
68#10597263—42no—
69C24×C19C2×D411yescharacteristic
70C23×D19C22⋊C411yescharacteristic
71C22×C4×C19—21no—
72C22×C4×C19—21no—
73C22×C4×C19—42no—
74C22×C4×C19—41no—
75C22×C4×C19—41no—
76C22×C4×C19—41no—
77C22×C4×C19—81no—
78C22×C4×C19—81no—
79C22×C4×C19C22×C411yescharacteristic
80C22×C4×C19C2×D411yescharacteristic
81C22×C4×C19#4111yescharacteristic
82C22×C4×C19#4111yescharacteristic
83C22×C4×C19#4111yescharacteristic
84C22×C4×C19#4111yescharacteristic
85C2×C22⋊D19—21no—
86C2×C22⋊D19—21no—
87C2×C22⋊D19—21no—
88C2×C22⋊D19—21no—
89C2×C22⋊D19SD1612yes—
90C2×C22⋊D19Q1612yes—
91C22×Dic19—21no—
92C22×Dic19—21no—
93C22×Dic19—41no—
94C22×Dic19C22⋊C411yescharacteristic
95C22×Dic19C22⋊C411yescharacteristic
96C22×Dic19C22⋊C411yescharacteristic
97C2×C4×D19—21no—
98C2×C4×D19—21no—
99C2×C4×D19—42no—
100C2×C4×D19—42no—
101C2×C4×D19—81no—
102C2×C4×D19—81no—
103C2×C8×C19—41no—
104C2×C8×C19—81no—
105C4⋊C4×C19—81no—
106C22⋊C4×C19—41no—
107C22⋊C4×C19—41no—
108C22⋊Dic19—21no—
109C22⋊Dic19—21no—
110C22⋊Dic19—41no—
111C22⋊Dic19—41no—
112C22⋊Dic19—41no—
113C22⋊Dic19—41no—
114(C2×D19)⋊C4—21no—
115(C2×D19)⋊C4—21no—
116(C2×D19)⋊C4—42no—
117C4⋊Dic19—81no—
118C4⋊Dic19—81no—
119Dic19⋊C4—21no—
120Dic19⋊C4—21no—
121Dic19⋊C4—42no—
122Dic19⋊C4—42no—
123Dic19⋊C4—81no—
124C4×Dic19—21no—
125C4×Dic19—21no—
126C4×Dic19—42no—
127C2×C19⋊C8—41no—
128C2×C19⋊C8—81no—
129#8761—191nomaximal, Sylow
130C23×C19—41no—
131C23×C19—41no—
132C23×C19C2×C22⋊C411yescharacteristic
133C23×C19#12311yescharacteristic
134C23×C19#12311yescharacteristic
135C23×C19C2×SD1611yescharacteristic
136C23×C19C2×Q1611yescharacteristic
137C23×C19AGL(1,ℤ/8)11yescharacteristic
138C23×C19AGL(1,ℤ/8)11yescharacteristic
139C22×D19—21no—
140C22×D19—21no—
141C22×D19—41no—
142C22×D19—41no—
143C22×D19#10312yes—
144C2×C4×C19—22no—
145C2×C4×C19—41no—
146C2×C4×C19—41no—
147C2×C4×C19—41no—
148C2×C4×C19—41no—
149C2×C4×C19—41no—
150C2×C4×C19—41no—
151C2×C4×C19—41no—
152C2×C4×C19—41no—
153C2×C4×C19—41no—
154C2×C4×C19—41no—
155C2×C4×C19—41no—
156C2×C4×C19—82no—
157C2×C4×C19—82no—
158C2×C4×C19—81no—
159C2×C4×C19—81no—
160C2×C4×C19—81no—
161C2×C4×C19#11711yescharacteristic
162C2×C4×C19#11711yescharacteristic
163C2×C4×C19#12311yescharacteristic
164C2×C4×C19#12311yescharacteristic
165C22⋊D19—22no—
166C22⋊D19—22no—
167C22⋊D19—22no—
168C22⋊D19—22no—
169C2×Dic19—21no—
170C2×Dic19—21no—
171C2×Dic19—21no—
172C2×Dic19—21no—
173C2×Dic19—41no—
174C2×Dic19—41no—
175C2×Dic19—41no—
176C2×Dic19—41no—
177C2×Dic19—41no—
178C2×Dic19—41no—
179C2×Dic19—41no—
180C2×Dic19—41no—
181C2×Dic19—81no—
182C2×Dic19—81no—
183C2×Dic19—81no—
184C2×Dic19#10312yes—
185C4×D19—81no—
186C4×D19—81no—
187C4×D19—84no—
188C8×C19—81no—
189C19⋊C8—81no—
190#2349—191no—
191#1799—191no—
192#1459—191no—
193#1294—191no—
194#1294D1911yescharacteristic, complemented
195#1289—191no—
196#1289—191no—
197C22×C19—21no—
198C22×C19—21no—
199C22×C19—21no—
200C22×C19—21no—
201C22×C19—21no—
202C22×C19—21no—
203C22×C19—41no—
204C22×C19—41no—
205C22×C19—41no—
206C22×C19—41no—
207C22×C19#38111yescharacteristic
208C22×C19C2×#10311yescharacteristic
209C22×C19#41811yescharacteristic
210C22×C19#48111yescharacteristic
211C22×C19#48111yescharacteristic
212C22×C19#48411yescharacteristic
213C22×C19#48411yescharacteristic
214C2×D19—22no—
215C2×D19—42no—
216C2×D19—41no—
217C2×D19—41no—
218C2×D19—42no—
219C4×C19—21no—
220C4×C19—21no—
221C4×C19—21no—
222C4×C19—21no—
223C4×C19—42no—
224C4×C19—81no—
225C4×C19—161no—
226Dic19—22no—
227Dic19—41no—
228Dic19—41no—
229Dic19—81no—
230Dic19—81no—
231Dic19—161no—
232C2×C4×D4—191no—
233C2×C4×D4—381no—
234C2×#99—381no—
235C2×C22⋊C8—191no—
236C2×C22⋊C8C2×D1911yescharacteristic
237#389—381no—
238#385—381no—
239#385—381no—
240#382—191no—
241#380—191no—
242#380—191no—
243#380—191no—
244#380C2×D1911yescharacteristic
245C4×C4⋊C4—191no—
246C2×#95—191no—
247C2×#95C2×D1911yescharacteristic
248#342—381no—
249#324—381no—
250#323—381no—
251C2×C19—21no—
252C2×C19—21no—
253C2×C19—21no—
254C2×C19—21no—
255C2×C19—21no—
256C2×C19—21no—
257C2×C19#182411yescharacteristic
258C2×C19#182711yescharacteristic
259C2×C19#182811yescharacteristic
260D19—42no—
261C22×D4—191no—
262C23×C4—21no—
263C23×C4—191no—
264C23×C4—381no—
265C23×C4C22×D1911yescharacteristic
266C22×C8—21no—
267C22×C8—381no—
268C4×D4—381no—
269C4×D4—381no—
270C4×D4—381no—
271C4×D4—381no—
272C4×D4—762no—
273C4×D4—762no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—191no—
276C2×C4⋊C4—381no—
277C2×C4⋊C4—381no—
278C2×C4⋊C4—381no—
279C2×C4⋊C4—381no—
280C2×C4⋊C4—381no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—191no—
283C2×C22⋊C4—191no—
284C2×C22⋊C4—381no—
285C2×C22⋊C4—381no—
286C2×C22⋊C4—381no—
287C2×C42—191no—
288C2×C42—381no—
289#99—762no—
290C22⋊C8—21no—
291C22⋊C8—21no—
292C22⋊C8—381no—
293C22⋊C8—381no—
294#95—21no—
295#95—21no—
296#95—191no—
297#95—191no—
298#95—381no—
299#95—381no—
300#95—381no—
301#95C4×D1911yescharacteristic
302#95C4×D1911yescharacteristic
303C19#876111yescharacteristic, complemented, Sylow
304C24—191no—
305C24D4×D1911yescharacteristic
306C2×D4—192no—
307C2×D4—192no—
308C2×D4—381no—
309C2×D4—381no—
310C2×D4—381no—
311C2×D4—381no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—42no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—81no—
319C22×C4—81no—
320C22×C4—191no—
321C22×C4—191no—
322C22×C4—191no—
323C22×C4—381no—
324C22×C4—381no—
325C22×C4—381no—
326C22×C4—381no—
327C22×C4—762no—
328C22×C4—762no—
329C22×C4—761no—
330C22×C4—1521no—
331C22×C4—1521no—
332C22×C4C2×C4×D1911yescharacteristic
333C22×C4#6454111yescharacteristic
334C22×C4#6454111yescharacteristic
335C22×C4D4×D1911yescharacteristic
336C22×C4#6454311yescharacteristic
337C22×C4#6454511yescharacteristic
338C2×C8—41no—
339C2×C8—81no—
340C2×C8—761no—
341C2×C8—1521no—
342C4⋊C4—81no—
343C4⋊C4—381no—
344C4⋊C4—381no—
345C4⋊C4—762no—
346C4⋊C4—762no—
347C4⋊C4—1521no—
348C4⋊C4—1521no—
349C4⋊C4—1521no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—381no—
353C22⋊C4—381no—
354C22⋊C4—381no—
355C22⋊C4—381no—
356C22⋊C4—762no—
357C22⋊C4—761no—
358C22⋊C4—761no—
359C22⋊C4—761no—
360C22⋊C4—761no—
361C42—381no—
362C42—381no—
363C42—762no—
364C23—41no—
365C23—41no—
366C23—192no—
367C23—381no—
368C23—381no—
369C23—761no—
370C23—761no—
371C23C22⋊C4×D1911yescharacteristic
372C23#1059732911yescharacteristic
373C23#1059734011yescharacteristic
374C23#1059735711yescharacteristic
375C23SD16×D1911yescharacteristic
376C23#1059736011yescharacteristic
377C23Q16×D1911yescharacteristic
378D4—382no—
379D4—382no—
380D4—382no—
381D4—382no—
382C2×C4—22no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—82no—
395C2×C4—82no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—192no—
400C2×C4—381no—
401C2×C4—381no—
402C2×C4—381no—
403C2×C4—381no—
404C2×C4—761no—
405C2×C4—761no—
406C2×C4—761no—
407C2×C4—761no—
408C2×C4—761no—
409C2×C4—761no—
410C2×C4—761no—
411C2×C4—761no—
412C2×C4—1521no—
413C2×C4—1521no—
414C2×C4—1524no—
415C2×C4—1521no—
416C2×C4—1521no—
417C2×C4—1521no—
418C2×C4#1059731811yescharacteristic
419C2×C4#1059732911yescharacteristic
420C2×C4#1059733811yescharacteristic
421C2×C4#1059734011yescharacteristic
422C8—81no—
423C8—1521no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—382no—
435C22—762no—
436C22—762no—
437C22—761no—
438C22—761no—
439C22#1192640611yescharacteristic
440C22#103×D1911yescharacteristic
441C22#1192654711yescharacteristic
442C22#1192686111yescharacteristic
443C22#1192686411yescharacteristic
444C22#1192687811yescharacteristic
445C22#1192688111yescharacteristic
446C4—21no—
447C4—21no—
448C4—21no—
449C4—21no—
450C4—42no—
451C4—81no—
452C4—161no—
453C4—382no—
454C4—3041no—
455C4—761no—
456C4—761no—
457C4—1521no—
458C4—1521no—
459C2—21no—
460C2—21no—
461C2—21no—
462C2—21no—
463C2—21no—
464C2—21no—
465C2—762no—
466C2#1456372411yescharacteristic
467C2#1456373811yescharacteristic
468C2#1456374211yescharacteristic
subgroupG/H
centerC22#11926406
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1294C2
socleC22×C19#381
prime radicalC22×C22⋊D19D4
cosocleC23×C4×C19C23
hypercenter#1294D19
hypocenterC19#8761
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
4. #14561514C2semidirect
5. #14561503C2semidirect
6. #14561502C2semidirect
7. C19×#1294C2semidirect
15. #11926408C4semidirect
18. #11926403C4semidirect
19. #11926395C4semidirect
20. #95×D19C4semidirect
194. #1294D19semidirect
303. C19#8761semidirect

Maximal subgroups

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

subgroupindex
#145665422
#145636202
#145619512
#145615142
#145615032
#145615022
C19×#12942
#876119