Finite Group Databasebeta

← #18078626

Subgroups — #18078626

Order 4864.

532 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573084C211yesmaximal, characteristic
2#14572591C211yesmaximal, characteristic, complemented
3#14563656C211yesmaximal, characteristic, complemented
4#14562086C211yesmaximal, characteristic, complemented
5#14561531C211yesmaximal, characteristic, complemented
6#14561476C211yesmaximal, characteristic, complemented
7C19×#1502C211yesmaximal, characteristic, complemented
8C2×#10597396—21no—
9C4×#64541C2211yescharacteristic
10#11926763—21no—
11#11926756—21no—
12#11926751C411yescharacteristic, complemented
13#11926746C411yescharacteristic, complemented
14#11926741C411yescharacteristic, complemented
15#11926736C411yescharacteristic, complemented
16#11926668—21no—
17#11926609—21no—
18(C22⋊D19)⋊C8—22no—
19#11926595—21no—
20#11926568C2211yescharacteristic
21C2×C4⋊(C19⋊C8)C2211yescharacteristic
22C2×#10597262—21no—
23#11926540—21no—
24C2×C4×C19⋊C8C2211yescharacteristic
25C4×C8×D19—21no—
26#11926304—21no—
27D4⋊(C19⋊C8)—21no—
28D4⋊(C19⋊C8)—21no—
29C19×#532C2211yescharacteristic
30C19×#431C2211yescharacteristic
31C4×C4⋊C4×C19C2211yescharacteristic
32C19×#327—22no—
33C2×#41×C19—21no—
34C2×#64541D411yescharacteristic
35C19×C4⋊Q8C2×C411yescharacteristic
36C19×#127C2×C411yescharacteristic
37C19×#124—21no—
38C19×#121—21no—
39C19×#121—21no—
40C4×D4×C19—21no—
41C4×D4×C19—21no—
42C2×C4⋊C4×C19—21no—
43C2×C42×C19—21no—
44C2×C42×C19C2311yescharacteristic
45#10597396—42no—
46#10597396—42no—
47C2×#64528—21no—
48C2×#64527—21no—
49C2×#64526—21no—
50C2×#64525—21no—
51C4×C22⋊D19—21no—
52C4×C22⋊D19—21no—
53#10597372D411yescharacteristic
54C2×#64520—21no—
55C22×C19⋊C8—21no—
56C22×C19⋊C8—21no—
57C2×C8×D19—22no—
58C4×D76C2×C411yescharacteristic
59C4×D76D411yescharacteristic
60#10597318—21no—
61C42×D19—21no—
62C4×Dic38C2×C411yescharacteristic
63C4×Dic38D411yescharacteristic
64C19×C4⋊C8—21no—
65C19×C22⋊C8D412yes—
66C4×C8×C19—21no—
67C19×#95—21no—
68#10597292—21no—
69#10597292—21no—
70#10597289—21no—
71#10597289—21no—
72(C2×D19)⋊C8—22no—
73Dic19⋊C8—22no—
74C8×Dic19—22no—
75#10597262—42no—
76C4⋊(C19⋊C8)—21no—
77C4⋊(C19⋊C8)—21no—
78C4⋊(C19⋊C8)—21no—
79C4⋊(C19⋊C8)C2×C411yescharacteristic
80C4⋊(C19⋊C8)C2×C411yescharacteristic
81C4×C19⋊C8—21no—
82C4×C19⋊C8D411yescharacteristic
83C4×C19⋊C8D411yescharacteristic
84#41×C19—41no—
85#41×C19—41no—
86#41×C19—41no—
87#41×C19—41no—
88C2×Q8×C19—21no—
89C2×D4×C19—21no—
90C2×D4×C19—21no—
91C2×D4×C19—21no—
92C2×D4×C19—41no—
93C22×C4×C19—41no—
94C22×C4×C19—41no—
95C22×C4×C19C2×D411yescharacteristic
96C22×C4×C19C2×D411yescharacteristic
97C22×C4×C19#4111yescharacteristic
98C2×C22⋊D19—21no—
99#64541—21no—
100#64541—21no—
101#64541D812yes—
102#64541SD1612yes—
103C2×D76C22⋊C411yescharacteristic
104C2×C4×D19—21no—
105C2×C4×D19—21no—
106C2×C4×D19—21no—
107C2×Dic38C22⋊C411yescharacteristic
108C2×C8×C19—22no—
109C4⋊C4×C19—22no—
110C4⋊C4×C19—21no—
111C4⋊C4×C19—21no—
112C4⋊C4×C19—41no—
113C22⋊C4×C19—41no—
114C22⋊C4×C19—41no—
115C42×C19—41no—
116C42×C19—41no—
117C42×C19C22×C411yescharacteristic
118C42×C19C2×D411yescharacteristic
119C42×C19C2×D411yescharacteristic
120C42×C19#4111yescharacteristic
121C22⋊Dic19—21no—
122#64528—42no—
123#64527—42no—
124#64526—42no—
125#64525—42no—
126(C2×D19)⋊C4—21no—
127(C2×D19)⋊C4—21no—
128C4⋊Dic19C22⋊C411yescharacteristic
129C4⋊Dic19C22⋊C411yescharacteristic
130Dic19⋊C4—21no—
131Dic19⋊C4—21no—
132C4×Dic19—21no—
133C4×Dic19—21no—
134C4×Dic19—21no—
135#64520—41no—
136#64520—41no—
137C2×C19⋊C8—21no—
138C2×C19⋊C8—21no—
139C2×C19⋊C8—21no—
140C2×C19⋊C8—21no—
141C2×C19⋊C8—42no—
142C2×C19⋊C8—41no—
143C2×C19⋊C8—41no—
144C2×C19⋊C8—41no—
145C8×D19—44no—
146#9208—191nomaximal, Sylow
147C23×C19—41no—
148C23×C19#12111yescharacteristic
149C22×D19—21no—
150Q8×C19—41no—
151Q8×C19—41no—
152D4×C19—41no—
153D4×C19—41no—
154D4×C19—41no—
155D4×C19—41no—
156D4×C19—81no—
157D4×C19—81no—
158D4×C19—81no—
159C2×C4×C19—21no—
160C2×C4×C19—21no—
161C2×C4×C19—41no—
162C2×C4×C19—42no—
163C2×C4×C19—41no—
164C2×C4×C19—81no—
165C2×C4×C19—81no—
166C2×C4×C19—81no—
167C2×C4×C19—81no—
168C2×C4×C19C2×C22⋊C411yescharacteristic
169C2×C4×C19C4×D411yescharacteristic
170C2×C4×C19C4×D411yescharacteristic
171C2×C4×C19#12011yescharacteristic
172C2×C4×C19#12111yescharacteristic
173C2×C4×C19#12311yescharacteristic
174C2×C4×C19C2×D811yescharacteristic
175C2×C4×C19C2×SD1611yescharacteristic
176C2×C4×C19#13511yescharacteristic
177C2×C4×C19#13511yescharacteristic
178C22⋊D19—22no—
179C22⋊D19—22no—
180C2×Dic19—21no—
181C2×Dic19—21no—
182C2×Dic19—21no—
183D76—21no—
184D76#10212yes—
185C4×D19—22no—
186C4×D19—22no—
187C4×D19—42no—
188C4×D19—41no—
189C4×D19—41no—
190Dic38—21no—
191Dic38#10212yes—
192C8×C19—42no—
193C19⋊C8—22no—
194C19⋊C8—41no—
195C19⋊C8—41no—
196C19⋊C8—41no—
197C19⋊C8—81no—
198#3035—191no—
199C8×#41—191no—
200#1806—191no—
201#1502D1911yescharacteristic, complemented
202#1492—191no—
203#1301—191no—
204#1279—191no—
205C22×C19—21no—
206C22×C19—21no—
207C22×C19—81no—
208C22×C19—81no—
209C22×C19—81no—
210C22×C19#38611yescharacteristic
211C22×C19#46511yescharacteristic
212C22×C19#46611yescharacteristic
213C2×D19—22no—
214C2×D19—41no—
215C2×D19—41no—
216C4×C19—21no—
217C4×C19—21no—
218C4×C19—21no—
219C4×C19—82no—
220C4×C19—81no—
221C4×C19C2×#10211yescharacteristic
222C4×C19#41611yescharacteristic
223C4×C19#44311yescharacteristic
224C4×C19#44411yescharacteristic
225C4×C19#46511yescharacteristic
226C4×C19#46611yescharacteristic
227Dic19—22no—
228Dic19—41no—
229Dic19—41no—
230C2×#135—381no—
231#532C2×D1911yescharacteristic
232C4×#41—191no—
233#464—381no—
234#463—381no—
235#462—191no—
236#461—191no—
237#460—191no—
238#459—191no—
239C8×Q8—381no—
240C8×D4—381no—
241C8×D4—382no—
242#431—381no—
243#431C2×D1911yescharacteristic
244#423—191no—
245C2×C4⋊C8—191no—
246C2×#104—381no—
247#416—381no—
248C2×C4×C8—191no—
249C2×C4×C8—381no—
250C4×C4⋊C4C2×D1911yescharacteristic
251#339—381no—
252#327—22no—
253D4⋊C8—381no—
254D4⋊C8—381no—
255C2×C19—21no—
256C2×C19—21no—
257C2×C19—161no—
258C2×C19#187611yescharacteristic
259C2×C19#189311yescharacteristic
260C2×C19#190611yescharacteristic
261D19—42no—
262C2×#41—21no—
263C2×#41—191no—
264#135—762no—
265#135—762no—
266C2×Q16—381no—
267C2×SD16—381no—
268C2×SD16—381no—
269C2×D8—381no—
270C2×M16—381no—
271C22×C8—382no—
272C22×C8—381no—
273C22×C8—381no—
274C4⋊Q8C4×D1911yescharacteristic
275#127C4×D1911yescharacteristic
276#124—21no—
277#121—21no—
278#121—21no—
279C4×Q8—191no—
280C4×Q8—191no—
281C4×D4—21no—
282C4×D4—21no—
283C4×D4—191no—
284C4×D4—191no—
285C4×D4—381no—
286C4×D4—381no—
287#117—191no—
288#117—381no—
289C2×C4⋊C4—21no—
290C2×C42—21no—
291C2×C42—381no—
292C2×C42C22×D1911yescharacteristic
293C4⋊C8—21no—
294C4⋊C8—191no—
295C4⋊C8—191no—
296C4⋊C8—382no—
297C4⋊C8—381no—
298C4⋊C8—381no—
299C4⋊C8—381no—
300#104—762no—
301#103—381no—
302#103—381no—
303#102—381no—
304#102—381no—
305C22⋊C8—382no—
306C22⋊C8C22⋊D1912yes—
307C4×C8—21no—
308C4×C8—191no—
309C4×C8—191no—
310C4×C8—382no—
311C4×C8—381no—
312#95—21no—
313C19#920811yescharacteristic, complemented, Sylow
314#41—41no—
315#41—41no—
316#41—41no—
317#41—41no—
318#41—192no—
319#41—192no—
320#41—381no—
321#41—381no—
322C2×Q8—21no—
323C2×Q8—191no—
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—41no—
328C2×D4—191no—
329C2×D4—381no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—381no—
333C22×C4—381no—
334C22×C4—381no—
335C22×C4D4×D1911yescharacteristic
336C22×C4#6454311yescharacteristic
337C22×C4C2×C22⋊D1911yescharacteristic
338Q16—762no—
339SD16—762no—
340SD16—762no—
341D8—762no—
342M16—761no—
343M16—761no—
344C2×C8—22no—
345C2×C8—381no—
346C2×C8—381no—
347C2×C8—381no—
348C2×C8—381no—
349C2×C8—764no—
350C2×C8—762no—
351C2×C8—761no—
352C2×C8—761no—
353C2×C8—761no—
354C4⋊C4—22no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—41no—
358C4⋊C4—191no—
359C4⋊C4—191no—
360C4⋊C4—381no—
361C4⋊C4—381no—
362C22⋊C4—41no—
363C22⋊C4—41no—
364C22⋊C4—381no—
365C22⋊C4—381no—
366C22⋊C4—381no—
367C42—41no—
368C42—41no—
369C42—381no—
370C42—381no—
371C42—381no—
372C42C2×C4×D1911yescharacteristic
373C42#6454111yescharacteristic
374C42D4×D1911yescharacteristic
375C42D4×D1911yescharacteristic
376C23—41no—
377C23—381no—
378C23#1059738411yescharacteristic
379Q8—41no—
380Q8—41no—
381Q8—192no—
382Q8—381no—
383D4—41no—
384D4—41no—
385D4—41no—
386D4—41no—
387D4—81no—
388D4—81no—
389D4—81no—
390D4—192no—
391D4—382no—
392D4—382no—
393D4—381no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—381no—
404C2×C4—382no—
405C2×C4—382no—
406C2×C4—381no—
407C2×C4—381no—
408C2×C4—762no—
409C2×C4—761no—
410C2×C4—761no—
411C2×C4C22⋊C4×D1911yescharacteristic
412C2×C4(C22⋊D19)⋊C411yescharacteristic
413C2×C4#1059732911yescharacteristic
414C2×C4#1059733011yescharacteristic
415C2×C4D8×D1911yescharacteristic
416C2×C4#1059735811yescharacteristic
417C2×C4SD16×D1911yescharacteristic
418C2×C4#1059736211yescharacteristic
419C2×C4C4×C22⋊D1911yescharacteristic
420C2×C4#1059738311yescharacteristic
421C8—42no—
422C8—382no—
423C8—761no—
424C8—761no—
425C8—761no—
426C8—1521no—
427C22—21no—
428C22—21no—
429C22—81no—
430C22—81no—
431C22—81no—
432C22—382no—
433C22—761no—
434C22—761no—
435C22#1192642011yescharacteristic
436C22#1192677011yescharacteristic
437C22#1192677711yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—82no—
442C4—81no—
443C4—382no—
444C4—761no—
445C4—761no—
446C4#102×D1911yescharacteristic
447C4#1192653711yescharacteristic
448C4#1192665811yescharacteristic
449C4#1192666311yescharacteristic
450C4#1192677211yescharacteristic
451C4#1192677911yescharacteristic
452C2—21no—
453C2—21no—
454C2—161no—
455C2—762no—
456C2#1456395911yescharacteristic
457C2#1456406011yescharacteristic
458C2#1456413311yescharacteristic
subgroupG/H
centerC2×C4#10597330
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1502C2
socleC22×C19#386
prime radical#14573084C2
cosocleC2×C42×C19C23
hypercenter#1502D19
hypocenterC19#9208
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1502

Complements

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

NH ≅ G/Ntype
2. #14572591C2semidirect
3. #14563656C2semidirect
4. #14562086C2semidirect
5. #14561531C2semidirect
6. #14561476C2semidirect
7. C19×#1502C2semidirect
12. #11926751C4semidirect
13. #11926746C4semidirect
14. #11926741C4semidirect
15. #11926736C4semidirect
201. #1502D19semidirect
313. C19#9208semidirect

Maximal subgroups

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

subgroupindex
#145730842
#145725912
#145636562
#145620862
#145615312
#145614762
C19×#15022
#920819