Finite Group Databasebeta

← #18077381

Subgroups — #18077381

Order 4864.

540 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573639C211yesmaximal, characteristic
2#14572370C211yesmaximal, characteristic
3#14564580C211yesmaximal, characteristic, complemented
4C4×#10597278C211yesmaximal, characteristic
5#14561536C211yesmaximal, characteristic, complemented
6#14561472C211yesmaximal, characteristic, complemented
7C19×#1493C211yesmaximal, characteristic, complemented
8C2×M16×D19—21no—
9C2×C4×D76C2211yescharacteristic
10#11926872—21no—
11#11926831C411yescharacteristic, complemented
12#11926831C411yescharacteristic, complemented
13#11926746C411yescharacteristic, complemented
14#11926746C411yescharacteristic, complemented
15#11926694—21no—
16C4×#64527—21no—
17C4×#64527—21no—
18#11926621—21no—
19#11926614—22no—
20#11926609—21no—
21#11926597C2211yescharacteristic
22C2×#10597278—21no—
23#11926507—21no—
24C4×#64520C2211yescharacteristic
25C4×C4⋊Dic19C2211yescharacteristic
26#11926307—21no—
27#11926303—21no—
28#11926303—21no—
29C19×#533C2211yescharacteristic
30C19×#423C2211yescharacteristic
31C2×C4×C8×C19C2211yescharacteristic
32C19×Q8⋊C8—22no—
33C22×D76D411yescharacteristic
34C22×C4×D19—21no—
35C2×M16×C19—21no—
36C22×C8×C19—21no—
37C19×C4⋊Q8C2×C411yescharacteristic
38C19×C4⋊Q8C2×C411yescharacteristic
39C19×#125—21no—
40C19×C22⋊Q8—21no—
41C19×C22⋊Q8—21no—
42C4×Q8×C19—21no—
43C4×Q8×C19—21no—
44C19×#117—21no—
45C2×C42×C19C2311yescharacteristic
46C2×#64527—21no—
47C2×#64527—21no—
48C2×(C2×D19)⋊C4—21no—
49C2×C4⋊Dic19—21no—
50C2×C4⋊Dic19D411yescharacteristic
51C2×C4×Dic19—21no—
52C2×#64520D411yescharacteristic
53C2×#64520D411yescharacteristic
54M16×D19—42no—
55M16×D19—42no—
56C2×#64515—22no—
57C2×C8×D19—22no—
58C4×D76—21no—
59C4×D76—21no—
60C4×D76C2×C411yescharacteristic
61C4×D76C2×C411yescharacteristic
62C4×D76D411yescharacteristic
63C4×D76D411yescharacteristic
64C19×C4⋊C8—21no—
65C19×C4⋊C8D412yes—
66C4×C8×C19—21no—
67C4×C8×C19—21no—
68#10597292—21no—
69#10597292—21no—
70C19⋊#95—21no—
71C22⋊(C19⋊C8)—21no—
72#10597278—24no—
73(C2×D19)⋊C8—22no—
74(C2×D19)⋊C8—22no—
75#10597266—21no—
76#10597266—21no—
77#10597265—21no—
78#10597265—21no—
79C4⋊(C19⋊C8)C2×C411yescharacteristic
80C4⋊(C19⋊C8)C2×C411yescharacteristic
81#10597260—21no—
82C4×C19⋊C8—21no—
83C4×C19⋊C8—21no—
84C23×D19—21no—
85C2×Q8×C19—21no—
86C2×Q8×C19—21no—
87C22×C4×C19C2×D411yescharacteristic
88C22×C4×C19C2×D411yescharacteristic
89C22×C4×C19#4111yescharacteristic
90C22×Dic19—21no—
91C22×Dic19—41no—
92C2×D76—22no—
93C2×D76—21no—
94C2×D76—41no—
95C2×D76C22⋊C411yescharacteristic
96C2×D76C22⋊C411yescharacteristic
97C2×C4×D19—21no—
98C2×C4×D19—21no—
99C2×C4×D19—21no—
100C2×C4×D19—21no—
101C2×C4×D19—41no—
102C2×C4×D19—41no—
103C2×C4×D19—41no—
104C2×C4×D19—41no—
105M16×C19—41no—
106M16×C19—41no—
107C2×C8×C19—22no—
108C2×C8×C19—22no—
109C2×C8×C19—41no—
110C2×C8×C19—41no—
111C4⋊C4×C19—21no—
112C4⋊C4×C19—21no—
113C4⋊C4×C19—21no—
114C4⋊C4×C19—21no—
115C4⋊C4×C19—41no—
116C4⋊C4×C19—41no—
117C22⋊C4×C19—41no—
118C42×C19—41no—
119C42×C19C22×C411yescharacteristic
120C42×C19C2×D411yescharacteristic
121C42×C19C2×D411yescharacteristic
122C42×C19#4111yescharacteristic
123#64527—42no—
124#64527—42no—
125(C2×D19)⋊C4—21no—
126(C2×D19)⋊C4—21no—
127(C2×D19)⋊C4—21no—
128(C2×D19)⋊C4—21no—
129C4⋊Dic19—21no—
130C4⋊Dic19—22no—
131C4⋊Dic19—41no—
132C4⋊Dic19C22⋊C411yescharacteristic
133C4⋊Dic19C22⋊C411yescharacteristic
134C4×Dic19—41no—
135C4×Dic19—41no—
136#64520—21no—
137#64520—21no—
138#64520—21no—
139#64520SD1612yescomplemented
140C2×C19⋊C8—21no—
141C2×C19⋊C8—21no—
142C2×C19⋊C8—21no—
143C2×C19⋊C8—21no—
144#64515—44no—
145C8×D19—44no—
146#8989—191nomaximal, Sylow
147C23×C19#12111yescharacteristic
148C22×D19—21no—
149C22×D19—21no—
150C22×D19—42no—
151C22×D19—41no—
152C22×D19—41no—
153C22×D19—81no—
154Q8×C19—42no—
155Q8×C19—41no—
156Q8×C19—41no—
157C2×C4×C19—21no—
158C2×C4×C19—21no—
159C2×C4×C19—41no—
160C2×C4×C19—41no—
161C2×C4×C19—41no—
162C2×C4×C19C2×C22⋊C411yescharacteristic
163C2×C4×C19C4×D411yescharacteristic
164C2×C4×C19C4×D411yescharacteristic
165C2×C4×C19#12011yescharacteristic
166C2×C4×C19#12111yescharacteristic
167C2×C4×C19#12311yescharacteristic
168C2×C4×C19C2×SD1611yescharacteristic
169C2×C4×C19#13511yescharacteristic
170C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C19#13711yescharacteristic
172C2×Dic19—21no—
173C2×Dic19—21no—
174C2×Dic19—41no—
175C2×Dic19—41no—
176C2×Dic19—42no—
177C2×Dic19—81no—
178C2×Dic19—81no—
179D76—21no—
180D76—21no—
181D76—21no—
182D76—42no—
183D76#10412yes—
184C4×D19—41no—
185C4×D19—41no—
186C4×D19—41no—
187C4×D19—41no—
188C4×D19—41no—
189C4×D19—41no—
190C4×D19—41no—
191C4×D19—41no—
192C8×C19—42no—
193C8×C19—42no—
194C19⋊C8—22no—
195C19⋊C8—41no—
196C19⋊C8—41no—
197C19⋊C8—41no—
198#3101—191no—
199D4×M16—191no—
200#1986—191no—
201C4×#102—191no—
202#1493D1911yescharacteristic, complemented
203#1303—191no—
204#1278—191no—
205C22×C19—21no—
206C22×C19—21no—
207C22×C19#38611yescharacteristic
208C22×C19#46111yescharacteristic
209C22×C19#46311yescharacteristic
210C2×D19—22no—
211C2×D19—41no—
212C2×D19—41no—
213C2×D19—41no—
214C2×D19—41no—
215C2×D19—41no—
216C2×D19—82no—
217C2×D19—82no—
218C4×C19—21no—
219C4×C19—21no—
220C4×C19—21no—
221C4×C19—81no—
222C4×C19—81no—
223C4×C19C2×#10411yescharacteristic
224C4×C19#42111yescharacteristic
225C4×C19C4×SD1611yescharacteristic
226C4×C19#44011yescharacteristic
227C4×C19#45011yescharacteristic
228C4×C19#45211yescharacteristic
229Dic19—41no—
230Dic19—41no—
231Dic19—82no—
232C22×M16—381no—
233#533C2×D1911yescharacteristic
234C2×C4×D4—191no—
235#483—381no—
236#476—191no—
237#476—191no—
238#461—191no—
239#461—191no—
240#450—381no—
241C4×SD16—381no—
242C4×SD16—381no—
243#436—381no—
244#435—382no—
245C8×D4—381no—
246#431—191no—
247#423C2×D1911yescharacteristic
248C2×#102—381no—
249#407—381no—
250C4×M16—191no—
251C2×C4×C8C2×D1911yescharacteristic
252C4×C4⋊C4—191no—
253#340—381no—
254#339—381no—
255#339—381no—
256Q8⋊C8—22no—
257C2×C19—21no—
258C2×C19—21no—
259C2×C19#187111yescharacteristic
260C2×C19#187711yescharacteristic
261C2×C19#188111yescharacteristic
262D19—42no—
263D19—81no—
264C22×D4—191no—
265C23×C4—381no—
266C2×SD16—381no—
267C2×SD16—381no—
268C2×M16—21no—
269C2×M16—191no—
270C2×M16—191no—
271C2×M16—382no—
272C2×M16—762no—
273C2×M16—762no—
274C22×C8—21no—
275C22×C8—382no—
276C4⋊Q8C4×D1911yescharacteristic
277C4⋊Q8C4×D1911yescharacteristic
278#125—21no—
279C22⋊Q8—21no—
280C22⋊Q8—21no—
281C4×Q8—21no—
282C4×Q8—21no—
283C4×D4—191no—
284C4×D4—191no—
285C4×D4—191no—
286C4×D4—191no—
287C4×D4—381no—
288C4×D4—381no—
289#117—21no—
290C2×C4⋊C4—191no—
291C2×C4⋊C4—381no—
292C2×C22⋊C4—381no—
293C2×C42—381no—
294C2×C42C22×D1911yescharacteristic
295#106—381no—
296#106—381no—
297C4⋊C8—21no—
298C4⋊C8—191no—
299C4⋊C8—191no—
300C4⋊C8C22⋊D1912yes—
301#103—381no—
302#103—381no—
303#102—381no—
304#102—381no—
305#102—384no—
306C22⋊C8—382no—
307C22⋊C8—382no—
308C22⋊C8—381no—
309#97—381no—
310C4×C8—21no—
311C4×C8—21no—
312C4×C8—381no—
313C4×C8—381no—
314#95—381no—
315C19#898911yescharacteristic, complemented, Sylow
316C24—381no—
317C2×Q8—21no—
318C2×Q8—21no—
319C2×D4—191no—
320C2×D4—191no—
321C2×D4—382no—
322C2×D4—381no—
323C2×D4—761no—
324C22×C4—381no—
325C22×C4—381no—
326C22×C4—381no—
327C22×C4—381no—
328C22×C4—381no—
329C22×C4—761no—
330C22×C4—761no—
331C22×C4—761no—
332C22×C4—761no—
333C22×C4—761no—
334C22×C4#6454111yescharacteristic
335C22×C4D4×D1911yescharacteristic
336C22×C4D4×D1911yescharacteristic
337SD16—762no—
338SD16—762no—
339M16—41no—
340M16—41no—
341M16—192no—
342M16—381no—
343M16—381no—
344M16—381no—
345M16—764no—
346C2×C8—22no—
347C2×C8—22no—
348C2×C8—41no—
349C2×C8—41no—
350C2×C8—381no—
351C2×C8—381no—
352C2×C8—381no—
353C2×C8—381no—
354C2×C8—764no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—41no—
360C4⋊C4—41no—
361C4⋊C4—191no—
362C4⋊C4—191no—
363C4⋊C4—382no—
364C4⋊C4—381no—
365C4⋊C4—761no—
366C22⋊C4—41no—
367C22⋊C4—381no—
368C22⋊C4—381no—
369C22⋊C4—381no—
370C22⋊C4—381no—
371C42—41no—
372C42—761no—
373C42—761no—
374C42C2×C4×D1911yescharacteristic
375C42D4×D1911yescharacteristic
376C42#6454311yescharacteristic
377C42C2×C22⋊D1911yescharacteristic
378C23—381no—
379C23—381no—
380C23—762no—
381C23—761no—
382C23—761no—
383C23—1521no—
384C23#1059733011yescharacteristic
385Q8—42no—
386Q8—41no—
387Q8—41no—
388D4—192no—
389D4—381no—
390D4—381no—
391D4—381no—
392D4—762no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—381no—
399C2×C4—381no—
400C2×C4—761no—
401C2×C4—761no—
402C2×C4—761no—
403C2×C4—761no—
404C2×C4—761no—
405C2×C4—761no—
406C2×C4—761no—
407C2×C4—761no—
408C2×C4—761no—
409C2×C4—761no—
410C2×C4—762no—
411C2×C4—1521no—
412C2×C4—1521no—
413C2×C4C22⋊C4×D1911yescharacteristic
414C2×C4(C22⋊D19)⋊C411yescharacteristic
415C2×C4#1059732911yescharacteristic
416C2×C4SD16×D1911yescharacteristic
417C2×C4#1059736011yescharacteristic
418C2×C4#1059736411yescharacteristic
419C2×C4#1059736511yescharacteristic
420C2×C4C4×C22⋊D1911yescharacteristic
421C2×C4#1059738311yescharacteristic
422C2×C4#1059738411yescharacteristic
423C8—42no—
424C8—42no—
425C8—382no—
426C8—761no—
427C8—761no—
428C8—761no—
429C22—21no—
430C22—21no—
431C22—382no—
432C22—761no—
433C22—761no—
434C22—761no—
435C22—761no—
436C22—761no—
437C22—1522no—
438C22—1522no—
439C22#1192642011yescharacteristic
440C22#1192674811yescharacteristic
441C22#1192676211yescharacteristic
442C4—21no—
443C4—21no—
444C4—21no—
445C4—81no—
446C4—81no—
447C4—761no—
448C4—761no—
449C4—1522no—
450C4#104×D1911yescharacteristic
451C4#1192655911yescharacteristic
452C4#1192662911yescharacteristic
453C4#1192664711yescharacteristic
454C4#1192669311yescharacteristic
455C4#1192670511yescharacteristic
456C2—21no—
457C2—21no—
458C2—762no—
459C2—1521no—
460C2#1456393411yescharacteristic
461C2#1456396611yescharacteristic
462C2#1456400011yescharacteristic
subgroupG/H
centerC2×C4#10597383
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1493C2
socleC22×C19#386
prime radicalC22×D76D4
cosocleC2×C42×C19C23
hypercenter#1493D19
hypocenterC19#8989
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1493

Complements

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

NH ≅ G/Ntype
3. #14564580C2semidirect
5. #14561536C2semidirect
6. #14561472C2semidirect
7. C19×#1493C2semidirect
11. #11926831C4semidirect
12. #11926831C4semidirect
13. #11926746C4semidirect
14. #11926746C4semidirect
139. #64520SD16semidirect
202. #1493D19semidirect
315. C19#8989semidirect

Maximal subgroups

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

subgroupindex
#145736392
#145723702
#145645802
C4×#105972782
#145615362
#145614722
C19×#14932
#898919