Finite Group Databasebeta

← #34080890

Subgroups — #34080890

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#23753027C211yesmaximal, characteristic, complemented
2#23753019C211yesmaximal, characteristic, complemented
3#23753015C211yesmaximal, characteristic, complemented
4#23752593C211yesmaximal, characteristic, complemented
5#23752485C211yesmaximal, characteristic, complemented
6#23752480C211yesmaximal, characteristic, complemented
7#23752475C211yesmaximal, characteristic, complemented
8#23752472C211yesmaximal, characteristic, complemented
9#23752390C211yesmaximal, characteristic, complemented
10#23752388C211yesmaximal, characteristic, complemented
11#23752385C211yesmaximal, characteristic, complemented
12#23752383C211yesmaximal, characteristic, complemented
13#23752329C211yesmaximal, characteristic, complemented
14#23752327C211yesmaximal, characteristic, complemented
15#577×C151C211yesmaximal, characteristic, complemented
16#18012786C2211yescharacteristic, complemented
17#18012785C2211yescharacteristic
18#18012771—21no—
19#18012770—21no—
20#18012770C2211yescharacteristic, complemented
21#18012769—21no—
22#18012769C2211yescharacteristic
23#18012769C2211yescharacteristic, complemented
24#18012765—21no—
25#18012765C2211yescharacteristic
26#18012764—21no—
27#18012764C2211yescharacteristic
28#18012764C2211yescharacteristic, complemented
29#18012763—21no—
30#18012760—21no—
31#18012759—21no—
32#18012759—21no—
33#18012759C2211yescharacteristic
34C2×#14558994—21no—
35C2×#14558994C2211yescharacteristic, complemented
36C2×#14558993C2211yescharacteristic, complemented
37SD16×D151—21no—
38C2×#14558989—21no—
39C2×#14558989C2211yescharacteristic
40#18012746C2211yescharacteristic
41#18012746C2211yescharacteristic, complemented
42#18012745C2211yescharacteristic, complemented
43#18012728C2211yescharacteristic, complemented
44#18012726C2211yescharacteristic, complemented
45#18012675C2211yescharacteristic, complemented
46#18012674C2211yescharacteristic, complemented
47#18012666C2211yescharacteristic
48#18012666C2211yescharacteristic, complemented
49#18012666C2211yescharacteristic, complemented
50#18012665C2211yescharacteristic, complemented
51#18012658C2211yescharacteristic, complemented
52#18012657C2211yescharacteristic, complemented
53#18012656C2211yescharacteristic, complemented
54#18012655C2211yescharacteristic, complemented
55C8×Dic151C2211yescharacteristic, complemented
562−1+4×C151C2211yescharacteristic, complemented
57H(5,𝔽2)×C151C2211yescharacteristic
58#137×C151—21no—
59#137×C151C2211yescharacteristic
60AGL(1,ℤ/8)×C151—21no—
61AGL(1,ℤ/8)×C151C2211yescharacteristic, complemented
62#135×C151—21no—
63#135×C151C2211yescharacteristic
64C2×SD16×C151—21no—
65C2×SD16×C151C2211yescharacteristic, complemented
66#131×C151C2211yescharacteristic, complemented
67#14559005—21no—
68#14559004—21no—
69#14559004—21no—
70#14559004C2311yescharacteristic
71#14559003—21no—
72#14559003—41no—
73C2×Dic302—21no—
74C2×Dic302C2311yescharacteristic
75Q8×D151—21no—
76C2×D604—21no—
77C2×D604C2311yescharacteristic
78D4×D151—21no—
79D4×D151—41no—
80#14558994—21no—
81#14558994—21no—
82#14558994—21no—
83#14558994—21no—
84#14558994—21no—
85#14558994D411yescharacteristic
86#14558993—21no—
87#14558993—21no—
88#14558992—21no—
89#14558992—21no—
90#14558992—21no—
91#14558992D411yescharacteristic
92#14558991—21no—
93#14558991—21no—
94#14558991—21no—
95#14558991D411yescharacteristic
96#14558989—21no—
97#14558989—21no—
98#14558989—21no—
99#14558989—21no—
100#14558989—21no—
101#14558989D411yescharacteristic
102#14558988—21no—
103#14558988—21no—
104#14558988C2311yescharacteristic
105#14558988C2311yescharacteristic
106#14558988C2311yescharacteristic
107#14558987—21no—
108C2×C151⋊C8—21no—
109C2×C151⋊C8—21no—
110C2×C151⋊C8C2311yescharacteristic
111C8×D151—21no—
112C22⋊Dic151—41no—
113(C2×D151)⋊C4—41no—
114C4×Dic151C2311yescharacteristic
115#41×C151—21no—
116#41×C151—21no—
117#41×C151—21no—
118#41×C151—21no—
119#41×C151—41no—
120#41×C151C2311yescharacteristic
121#41×C151C2311yescharacteristic
122#41×C151C2311yescharacteristic
123C2×Q8×C151—21no—
124C2×Q8×C151—21no—
125C2×Q8×C151C2311yescharacteristic
126C2×D4×C151—21no—
127C2×D4×C151—21no—
128C2×D4×C151—41no—
129C2×D4×C151C2311yescharacteristic
130Q16×C151—21no—
131Q16×C151D411yescharacteristic
132SD16×C151—21no—
133SD16×C151—21no—
134SD16×C151—21no—
135SD16×C151—21no—
136SD16×C151D411yescharacteristic
137SD16×C151D411yescharacteristic
138D8×C151—21no—
139D8×C151D411yescharacteristic
140M16×C151—21no—
141M16×C151C2311yescharacteristic
142C2×C8×C151—21no—
143C2×C8×C151C2311yescharacteristic
144C22×D151—21no—
145C22×D151—41no—
146Dic302—21no—
147Dic302—21no—
148Dic302—41no—
149Dic302C2×D411yescharacteristic
150D604—21no—
151D604—21no—
152D604—41no—
153D604C2×D411yescharacteristic
154C22⋊D151—21no—
155C22⋊D151—41no—
156C22⋊D151—41no—
157C2×Dic151—21no—
158C2×Dic151—21no—
159C2×Dic151—41no—
160C4×D151—21no—
161C4×D151—41no—
162C4×D151—41no—
163C151⋊C8—21no—
164C151⋊C8—21no—
165C151⋊C8—21no—
166C151⋊C8C2×D411yescharacteristic
167C151⋊C8C2×D411yescharacteristic
168C23×C151—21no—
169C23×C151—41no—
170Q8×C151—21no—
171Q8×C151—21no—
172Q8×C151—41no—
173Q8×C151C2×D411yescharacteristic
174Q8×C151C2×D411yescharacteristic
175Q8×C151C2×D411yescharacteristic
176D4×C151—21no—
177D4×C151—21no—
178D4×C151—21no—
179D4×C151—21no—
180D4×C151—21no—
181D4×C151—41no—
182D4×C151—41no—
183D4×C151—41no—
184D4×C151C2×D411yescharacteristic
185D4×C151C2×D411yescharacteristic
186D4×C151C2×D411yescharacteristic
187C2×C4×C151—21no—
188C2×C4×C151—21no—
189C2×C4×C151—21no—
190C2×C4×C151—21no—
191C2×C4×C151—41no—
192C2×C4×C151—41no—
193C2×C4×C151—41no—
194C2×C4×C151C2411yescharacteristic
195C8×C151—21no—
196C8×C151C2×D411yescharacteristic
197C8×C151C2×D411yescharacteristic
198C22×C151—21no—
199C22×C151—21no—
200C22×C151—21no—
201C22×C151—41no—
202C22×C151—81no—
203C22×C151—161no—
204C22×C151H(5,𝔽2)11yescharacteristic
205C2×D151—21no—
206C2×D151—41no—
207C2×D151—81no—
208C2×D151—161no—
209C4×C151—21no—
210C4×C151—21no—
211C4×C151—21no—
212C4×C151—41no—
213C4×C151C22×D411yescharacteristic
214C4×C151C22×D411yescharacteristic
215Dic151—21no—
216Dic151—41no—
217Dic151—41no—
218C2×C151—21no—
219C2×C151—41no—
220C2×C151—41no—
221C2×C151—41no—
222C2×C151—81no—
223C2×C151D4211yescharacteristic
224D151—41no—
225D151—81no—
226C151#329011yescharacteristic, complemented, Sylow
227#3290—1511nomaximal, Sylow
228#578—1511no—
229#577—1511no—
230#577D15111yescharacteristic, complemented
231#576—1511no—
232#495—1511no—
233#473—1511no—
234#472—1511no—
235#471—1511no—
236#471—1511no—
237#455—1511no—
238#455—1511no—
239#454—1511no—
240#454—1511no—
241#443—1511no—
242#443—1511no—
2432−1+4—1511no—
2442−1+4C2×D15111yescharacteristic, complemented
245H(5,𝔽2)—1511no—
246H(5,𝔽2)C2×D15111yescharacteristic
247#137—21no—
248#137—3021no—
249#137—3021no—
250#137—3021no—
251#137—1511no—
252#137—1511no—
253#137—1511no—
254#137C2×D15111yescharacteristic
255AGL(1,ℤ/8)—21no—
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)C2×D15111yescharacteristic, complemented
263#135—21no—
264#135—3021no—
265#135—3021no—
266#135—3021no—
267#135—1511no—
268#135C2×D15111yescharacteristic
269C2×Q16—3021no—
270C2×Q16—1511no—
271C2×SD16—21no—
272C2×SD16—3021no—
273C2×SD16—1511no—
274C2×SD16C2×D15111yescharacteristic, complemented
275C2×D8—3021no—
276C2×D8—1511no—
277#131—1511no—
278#131—1511no—
279#131—1511no—
280#131C2×D15111yescharacteristic, complemented
281#124—1511no—
282#124—1511no—
283#108—1511no—
284#108—1511no—
285#104—1511no—
286#104—1511no—
287#104—1511no—
288#104—1511no—
289#101—1511no—
290#101—1511no—
291#100—1511no—
292#100—1511no—
293C4×C8—1511no—
294#41—21no—
295#41—21no—
296#41—21no—
297#41—21no—
298#41—41no—
299#41—3021no—
300#41—3021no—
301#41—3021no—
302#41—3021no—
303#41—6041no—
304#41—1511no—
305#41C22×D15111yescharacteristic
306#41C22×D15111yescharacteristic
307#41C22×D15111yescharacteristic
308C2×Q8—21no—
309C2×Q8—21no—
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—3021no—
324Q16—3021no—
325Q16—3021no—
326Q16—3021no—
327Q16—3021no—
328Q16—1511no—
329Q16C22⋊D15111yescharacteristic
330SD16—21no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—3021no—
335SD16—3021no—
336SD16—3021no—
337SD16—3021no—
338SD16—3021no—
339SD16—3021no—
340SD16—3021no—
341SD16—3021no—
342SD16—1511no—
343SD16—1511no—
344SD16C22⋊D15111yescharacteristic
345SD16C22⋊D15111yescharacteristic
346D8—21no—
347D8—3021no—
348D8—3021no—
349D8—3021no—
350D8—3021no—
351D8—3021no—
352D8—1511no—
353D8C22⋊D15111yescharacteristic
354M16—21no—
355M16—3021no—
356M16—3021no—
357M16—3021no—
358M16—1511no—
359M16—1511no—
360M16—1511no—
361M16C22×D15111yescharacteristic
362C2×C8—21no—
363C2×C8—3021no—
364C2×C8—3021no—
365C2×C8—3021no—
366C2×C8—1511no—
367C2×C8C22×D15111yescharacteristic
368C22⋊C4—6041no—
369C22⋊C4—6041no—
370C42—1511no—
371C23—21no—
372C23—41no—
373C23—3021no—
374C23—6041no—
375Q8—21no—
376Q8—21no—
377Q8—41no—
378Q8—3021no—
379Q8—3021no—
380Q8—6041no—
381Q8—1511no—
382Q8D4×D15111yescharacteristic
383Q8C2×C22⋊D15111yescharacteristic
384Q8C2×C22⋊D15111yescharacteristic
385D4—21no—
386D4—21no—
387D4—21no—
388D4—21no—
389D4—21no—
390D4—41no—
391D4—41no—
392D4—41no—
393D4—3021no—
394D4—3021no—
395D4—3021no—
396D4—6041no—
397D4—6041no—
398D4—6041no—
399D4—1511no—
400D4D4×D15111yescharacteristic
401D4C2×C22⋊D15111yescharacteristic
402D4C2×C22⋊D15111yescharacteristic
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—3021no—
411C2×C4—3021no—
412C2×C4—3021no—
413C2×C4—6041no—
414C2×C4—6041no—
415C2×C4—6041no—
416C2×C4C23×D15111yescharacteristic
417C8—21no—
418C8—3021no—
419C8—3021no—
420C8—3021no—
421C8—1511no—
422C8—1511no—
423C8C2×C22⋊D15111yescharacteristic
424C8C2×C22⋊D15111yescharacteristic
425C22—21no—
426C22—21no—
427C22—21no—
428C22—41no—
429C22—81no—
430C22—161no—
431C22—3021no—
432C22—6041no—
433C22—24161no—
434C22—12081no—
435C22#1801278411yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—41no—
440C4—3021no—
441C4—6041no—
442C4—6041no—
443C4C2×D4×D15111yescharacteristic
444C4C22×C22⋊D15111yescharacteristic
445C2—21no—
446C2—41no—
447C2—41no—
448C2—41no—
449C2—81no—
450C2—6041no—
451C2—12081no—
452C2D4×C22⋊D15111yescharacteristic
subgroupG/H
centerC2D4×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#577×C151C2
socleC2×C151D42
hypercenter#577D151
hypocenterC151#3290
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ #577

Complements

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

NH ≅ G/Ntype
1. #23753027C2semidirect
2. #23753019C2semidirect
3. #23753015C2semidirect
4. #23752593C2semidirect
5. #23752485C2semidirect
6. #23752480C2semidirect
7. #23752475C2semidirect
8. #23752472C2semidirect
9. #23752390C2semidirect
10. #23752388C2semidirect
11. #23752385C2semidirect
12. #23752383C2semidirect
13. #23752329C2semidirect
14. #23752327C2semidirect
15. #577×C151C2semidirect
16. #18012786C22semidirect
20. #18012770C22semidirect
23. #18012769C22semidirect
28. #18012764C22semidirect
35. C2×#14558994C22semidirect
36. C2×#14558993C22semidirect
41. #18012746C22semidirect
42. #18012745C22semidirect
43. #18012728C22semidirect
44. #18012726C22semidirect
45. #18012675C22semidirect
46. #18012674C22semidirect
48. #18012666C22semidirect
49. #18012666C22semidirect
50. #18012665C22semidirect
51. #18012658C22semidirect
52. #18012657C22semidirect
53. #18012656C22semidirect
54. #18012655C22semidirect
55. C8×Dic151C22semidirect
56. 2−1+4×C151C22semidirect
61. AGL(1,ℤ/8)×C151C22semidirect
65. C2×SD16×C151C22semidirect
66. #131×C151C22semidirect
226. C151#3290semidirect
230. #577D151semidirect
244. 2−1+4C2×D151semidirect
262. AGL(1,ℤ/8)C2×D151semidirect
274. C2×SD16C2×D151semidirect
280. #131C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237530272
#237530192
#237530152
#237525932
#237524852
#237524802
#237524752
#237524722
#237523902
#237523882
#237523852
#237523832
#237523292
#237523272
#577×C1512
#3290151