Finite Group Databasebeta

← #34080894

Subgroups — #34080894

Order 19328.

454 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23753028C211yesmaximal, characteristic, complemented
2#23753023C211yesmaximal, characteristic, complemented
3#23753021C211yesmaximal, characteristic, complemented
4#23753015C211yesmaximal, characteristic, complemented
5#23752594C211yesmaximal, characteristic, complemented
6#23752485C211yesmaximal, characteristic, complemented
7#23752481C211yesmaximal, characteristic, complemented
8#23752477C211yesmaximal, characteristic, complemented
9#23752474C211yesmaximal, characteristic, complemented
10#23752391C211yesmaximal, characteristic, complemented
11#23752386C211yesmaximal, characteristic, complemented
12#23752384C211yesmaximal, characteristic, complemented
13#23752326C211yesmaximal, characteristic, complemented
14#23752326C211yesmaximal, characteristic, complemented
15#455×C151C211yesmaximal, characteristic, complemented
16#18012787C2211yescharacteristic, complemented
17#18012786C2211yescharacteristic, complemented
18#18012785C2211yescharacteristic
19#18012772C2211yescharacteristic, complemented
20#18012771—21no—
21#18012771—21no—
22#18012769—21no—
23#18012769C2211yescharacteristic
24#18012768—21no—
25#18012767C2211yescharacteristic, complemented
26#18012766—21no—
27#18012765—21no—
28#18012765—21no—
29#18012765C2211yescharacteristic
30#18012765C2211yescharacteristic, complemented
31#18012764—21no—
32#18012764C2211yescharacteristic
33#18012762—21no—
34#18012760—21no—
35#18012759—21no—
36#18012759—21no—
37#18012759C2211yescharacteristic
38#18012759C2211yescharacteristic
39C2×#14558994C2211yescharacteristic, complemented
40Q16×D151—21no—
41C2×#14558992—21no—
42C2×#14558992C2211yescharacteristic, complemented
43C2×#14558991C2211yescharacteristic, complemented
44SD16×D151—21no—
45C2×#14558989—21no—
46C2×#14558989C2211yescharacteristic
47#18012747C2211yescharacteristic, complemented
48#18012747C2211yescharacteristic, complemented
49#18012746C2211yescharacteristic
50#18012746C2211yescharacteristic, complemented
51#18012727C2211yescharacteristic, complemented
52#18012674C2211yescharacteristic, complemented
53#18012674C2211yescharacteristic, complemented
54#18012667C2211yescharacteristic, complemented
55#18012667C2211yescharacteristic, complemented
56#18012658C2211yescharacteristic, complemented
57#18012657C2211yescharacteristic, complemented
58#18012655C2211yescharacteristic, complemented
59C4×C151⋊C8C2211yescharacteristic, complemented
60H(5,𝔽2)×C151C2211yescharacteristic
61#137×C151C2211yescharacteristic
62#137×C151C2211yescharacteristic, complemented
63#124×C151C2211yescharacteristic, complemented
64#104×C151C2211yescharacteristic
65#104×C151C2211yescharacteristic, complemented
66#100×C151C2211yescharacteristic, complemented
67#14559005—21no—
68#14559005—21no—
69#14559005—21no—
70#14559004—21no—
71#14559004—21no—
72#14559004—41no—
73#14559004C2311yescharacteristic
74#14559004C2311yescharacteristic
75#14559003—21no—
76#14559003—41no—
77C2×Dic302—21no—
78C2×Dic302C2311yescharacteristic
79Q8×D151—21no—
80Q8×D151—21no—
81Q8×D151—21no—
82C2×D604—21no—
83C2×D604C2311yescharacteristic
84D4×D151—21no—
85D4×D151—41no—
86Dic604—21no—
87#14558994—21no—
88#14558994—21no—
89#14558994—21no—
90#14558994D411yescharacteristic
91#14558994D411yescharacteristic
92#14558993—21no—
93#14558993—21no—
94#14558992—21no—
95#14558992—21no—
96#14558992—21no—
97#14558992—21no—
98#14558992—21no—
99#14558992D411yescharacteristic
100#14558992D411yescharacteristic
101#14558991—21no—
102#14558991—21no—
103#14558991—21no—
104#14558991D411yescharacteristic
105#14558991D411yescharacteristic
106D1208—21no—
107#14558989—21no—
108#14558989—21no—
109#14558989—21no—
110#14558989—21no—
111#14558989—21no—
112#14558989D411yescharacteristic
113#14558989D411yescharacteristic
114#14558988—21no—
115#14558988—21no—
116#14558988C2311yescharacteristic
117#14558988C2311yescharacteristic
118#14558987—21no—
119#14558987—21no—
120C2×C151⋊C8—21no—
121C2×C151⋊C8—21no—
122C2×C151⋊C8C2311yescharacteristic
123C2×C151⋊C8C2311yescharacteristic
124C8×D151—21no—
125C8×D151—21no—
126(C2×D151)⋊C4—41no—
127#41×C151—21no—
128#41×C151—21no—
129#41×C151C2311yescharacteristic
130#41×C151C2311yescharacteristic
131C2×Q8×C151C2311yescharacteristic
132C2×D4×C151—21no—
133C2×D4×C151—21no—
134C2×D4×C151—41no—
135C2×D4×C151C2311yescharacteristic
136Q16×C151—21no—
137Q16×C151—21no—
138SD16×C151—21no—
139SD16×C151—21no—
140M16×C151C2311yescharacteristic
141M16×C151C2311yescharacteristic
142C22⋊C4×C151—41no—
143C42×C151C2311yescharacteristic
144C22×D151—21no—
145C22×D151—41no—
146Dic302—21no—
147Dic302—21no—
148Dic302—41no—
149Dic302—41no—
150Dic302C2×D411yescharacteristic
151Dic302C2×D411yescharacteristic
152D604—21no—
153D604—21no—
154D604—41no—
155D604—41no—
156D604C2×D411yescharacteristic
157D604C2×D411yescharacteristic
158C22⋊D151—21no—
159C22⋊D151—21no—
160C22⋊D151—41no—
161C22⋊D151—41no—
162C2×Dic151—21no—
163C2×Dic151—41no—
164C4×D151—21no—
165C4×D151—21no—
166C4×D151—41no—
167C4×D151—41no—
168C4×D151—41no—
169C4×D151—41no—
170C151⋊C8—21no—
171C151⋊C8—21no—
172C151⋊C8C2×D411yescharacteristic
173C151⋊C8C2×D411yescharacteristic
174C151⋊C8C2×D411yescharacteristic
175C151⋊C8C2×D411yescharacteristic
176C23×C151—21no—
177C23×C151—41no—
178Q8×C151—21no—
179Q8×C151—21no—
180Q8×C151C2×D411yescharacteristic
181Q8×C151C2×D411yescharacteristic
182D4×C151—21no—
183D4×C151—21no—
184D4×C151—21no—
185D4×C151—21no—
186D4×C151—41no—
187D4×C151—41no—
188D4×C151C2×D411yescharacteristic
189D4×C151C2×D411yescharacteristic
190C2×C4×C151—21no—
191C2×C4×C151—21no—
192C2×C4×C151—21no—
193C2×C4×C151—21no—
194C2×C4×C151—41no—
195C2×C4×C151C2411yescharacteristic
196C8×C151—21no—
197C8×C151—21no—
198C22×C151—21no—
199C22×C151—21no—
200C22×C151—41no—
201C22×C151—81no—
202C22×C151—161no—
203C22×C151H(5,𝔽2)11yescharacteristic
204C2×D151—21no—
205C2×D151—21no—
206C2×D151—41no—
207C2×D151—81no—
208C2×D151—161no—
209C4×C151—21no—
210C4×C151—21no—
211C4×C151—41no—
212C4×C151—41no—
213C4×C151C22×D411yescharacteristic
214C4×C151C22×D411yescharacteristic
215Dic151—21no—
216Dic151—21no—
217Dic151—41no—
218C2×C151—21no—
219C2×C151—41no—
220C2×C151—41no—
221C2×C151—81no—
222C2×C151D4211yescharacteristic
223D151—41no—
224D151—41no—
225D151—81no—
226C151#329011yescharacteristic, complemented, Sylow
227#3290—1511nomaximal, Sylow
228#578—1511no—
229#577—1511no—
230#577—1511no—
231#576—1511no—
232#495—1511no—
233#473—1511no—
234#472—1511no—
235#471—1511no—
236#471—1511no—
237#455—1511no—
238#455D15111yescharacteristic, complemented
239#454—1511no—
240#454—1511no—
241#443—1511no—
242#443—1511no—
2432−1+4—1511no—
2442−1+4—1511no—
245H(5,𝔽2)—1511no—
246H(5,𝔽2)C2×D15111yescharacteristic
247#137—3021no—
248#137—3021no—
249#137—3021no—
250#137—3021no—
251#137—1511no—
252#137—1511no—
253#137C2×D15111yescharacteristic
254#137C2×D15111yescharacteristic, complemented
255AGL(1,ℤ/8)—3021no—
256AGL(1,ℤ/8)—3021no—
257AGL(1,ℤ/8)—3021no—
258AGL(1,ℤ/8)—3021no—
259AGL(1,ℤ/8)—1511no—
260AGL(1,ℤ/8)—1511no—
261AGL(1,ℤ/8)—1511no—
262AGL(1,ℤ/8)—1511no—
263#135—3021no—
264#135—3021no—
265#135—3021no—
266#135—3021no—
267#135—1511no—
268#135—1511no—
269C2×Q16—3021no—
270C2×Q16—1511no—
271C2×SD16—3021no—
272C2×SD16—3021no—
273C2×SD16—1511no—
274C2×SD16—1511no—
275C2×D8—3021no—
276C2×D8—1511no—
277#131—1511no—
278#131—1511no—
279#131—1511no—
280#131—1511no—
281#124—1511no—
282#124C2×D15111yescharacteristic, complemented
283#108—1511no—
284#108—1511no—
285#104—1511no—
286#104—1511no—
287#104C2×D15111yescharacteristic
288#104C2×D15111yescharacteristic, complemented
289#101—1511no—
290#101—1511no—
291#100—1511no—
292#100C2×D15111yescharacteristic, complemented
293C4×C8—1511no—
294#41—21no—
295#41—21no—
296#41—3021no—
297#41—3021no—
298#41—3021no—
299#41—3021no—
300#41—3021no—
301#41—3021no—
302#41—6041no—
303#41—6041no—
304#41—1511no—
305#41—1511no—
306#41C22×D15111yescharacteristic
307#41C22×D15111yescharacteristic
308C2×Q8—3021no—
309C2×Q8—3021no—
310C2×Q8—3021no—
311C2×Q8—3021no—
312C2×Q8—1511no—
313C2×Q8C22×D15111yescharacteristic
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4—3021no—
318C2×D4—3021no—
319C2×D4—6041no—
320C2×D4—1511no—
321C2×D4C22×D15111yescharacteristic
322Q16—21no—
323Q16—21no—
324Q16—3021no—
325Q16—3021no—
326Q16—3021no—
327Q16—3021no—
328Q16—1511no—
329Q16—1511no—
330SD16—21no—
331SD16—21no—
332SD16—3021no—
333SD16—3021no—
334SD16—3021no—
335SD16—3021no—
336SD16—3021no—
337SD16—3021no—
338SD16—3021no—
339SD16—3021no—
340SD16—3021no—
341SD16—3021no—
342SD16—1511no—
343SD16—1511no—
344SD16—1511no—
345SD16—1511no—
346D8—3021no—
347D8—3021no—
348D8—3021no—
349D8—3021no—
350D8—3021no—
351D8—3021no—
352D8—1511no—
353D8—1511no—
354M16—3021no—
355M16—3021no—
356M16—3021no—
357M16—3021no—
358M16—1511no—
359M16—1511no—
360M16C22×D15111yescharacteristic
361M16C22×D15111yescharacteristic
362C2×C8—3021no—
363C2×C8—3021no—
364C2×C8—3021no—
365C2×C8—3021no—
366C2×C8—1511no—
367C2×C8—1511no—
368C22⋊C4—41no—
369C22⋊C4—6041no—
370C42C22×D15111yescharacteristic
371C23—21no—
372C23—41no—
373C23—3021no—
374C23—6041no—
375Q8—21no—
376Q8—21no—
377Q8—3021no—
378Q8—3021no—
379Q8—6041no—
380Q8—6041no—
381Q8—1511no—
382Q8—1511no—
383Q8D4×D15111yescharacteristic
384Q8D4×D15111yescharacteristic
385D4—21no—
386D4—21no—
387D4—21no—
388D4—21no—
389D4—41no—
390D4—41no—
391D4—3021no—
392D4—3021no—
393D4—3021no—
394D4—3021no—
395D4—6041no—
396D4—6041no—
397D4—6041no—
398D4—6041no—
399D4—1511no—
400D4—1511no—
401D4D4×D15111yescharacteristic
402D4D4×D15111yescharacteristic
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—41no—
408C2×C4—3021no—
409C2×C4—3021no—
410C2×C4—3021no—
411C2×C4—6041no—
412C2×C4—6041no—
413C2×C4—6041no—
414C2×C4—6041no—
415C2×C4—6041no—
416C2×C4C23×D15111yescharacteristic
417C8—21no—
418C8—21no—
419C8—3021no—
420C8—3021no—
421C8—1511no—
422C8—1511no—
423C8—1511no—
424C8—1511no—
425C22—21no—
426C22—21no—
427C22—41no—
428C22—81no—
429C22—161no—
430C22—3021no—
431C22—3021no—
432C22—6041no—
433C22—24161no—
434C22—12081no—
435C22#1801278411yescharacteristic
436C4—21no—
437C4—21no—
438C4—41no—
439C4—41no—
440C4—3021no—
441C4—3021no—
442C4—6041no—
443C4C2×D4×D15111yescharacteristic
444C4C2×D4×D15111yescharacteristic
445C2—21no—
446C2—41no—
447C2—41no—
448C2—81no—
449C2—6041no—
450C2—6041no—
451C2—12081no—
452C2#2375284411yescharacteristic
subgroupG/H
centerC2#23752844
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#455×C151C2
socleC2×C151D42
hypercenter#455D151
hypocenterC151#3290
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ #455

Complements

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

NH ≅ G/Ntype
1. #23753028C2semidirect
2. #23753023C2semidirect
3. #23753021C2semidirect
4. #23753015C2semidirect
5. #23752594C2semidirect
6. #23752485C2semidirect
7. #23752481C2semidirect
8. #23752477C2semidirect
9. #23752474C2semidirect
10. #23752391C2semidirect
11. #23752386C2semidirect
12. #23752384C2semidirect
13. #23752326C2semidirect
14. #23752326C2semidirect
15. #455×C151C2semidirect
16. #18012787C22semidirect
17. #18012786C22semidirect
19. #18012772C22semidirect
25. #18012767C22semidirect
30. #18012765C22semidirect
39. C2×#14558994C22semidirect
42. C2×#14558992C22semidirect
43. C2×#14558991C22semidirect
47. #18012747C22semidirect
48. #18012747C22semidirect
50. #18012746C22semidirect
51. #18012727C22semidirect
52. #18012674C22semidirect
53. #18012674C22semidirect
54. #18012667C22semidirect
55. #18012667C22semidirect
56. #18012658C22semidirect
57. #18012657C22semidirect
58. #18012655C22semidirect
59. C4×C151⋊C8C22semidirect
62. #137×C151C22semidirect
63. #124×C151C22semidirect
65. #104×C151C22semidirect
66. #100×C151C22semidirect
226. C151#3290semidirect
238. #455D151semidirect
254. #137C2×D151semidirect
282. #124C2×D151semidirect
288. #104C2×D151semidirect
292. #100C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237530282
#237530232
#237530212
#237530152
#237525942
#237524852
#237524812
#237524772
#237524742
#237523912
#237523862
#237523842
#237523262
#455×C1512
#3290151