Finite Group Databasebeta

← #34080872

Subgroups — #34080872

Order 19328.

464 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23753020C211yesmaximal, characteristic, complemented
2#23753015C211yesmaximal, characteristic, complemented
3#23753014C211yesmaximal, characteristic, complemented
4#23752598C211yesmaximal, characteristic, complemented
5#23752482C211yesmaximal, characteristic, complemented
6#23752480C211yesmaximal, characteristic, complemented
7#23752477C211yesmaximal, characteristic, complemented
8#23752472C211yesmaximal, characteristic, complemented
9#23752388C211yesmaximal, characteristic, complemented
10#23752385C211yesmaximal, characteristic, complemented
11#23752380C211yesmaximal, characteristic, complemented
12#23752378C211yesmaximal, characteristic, complemented
13#23752334C211yesmaximal, characteristic, complemented
14#23752332C211yesmaximal, characteristic, complemented
15#577×C151C211yesmaximal, characteristic, complemented
16#18012785C2211yescharacteristic
17#18012785C2211yescharacteristic, complemented
18#18012770—21no—
19#18012770C2211yescharacteristic, complemented
20#18012766—21no—
21#18012766—21no—
22#18012765—21no—
23#18012765C2211yescharacteristic
24#18012764—21no—
25#18012764—21no—
26#18012764C2211yescharacteristic
27#18012764C2211yescharacteristic, complemented
28#18012764C2211yescharacteristic, complemented
29#18012764C2211yescharacteristic, complemented
30#18012762—21no—
31#18012759—21no—
32#18012759—21no—
33#18012759C2211yescharacteristic
34C2×#14558991—21no—
35C2×#14558991C2211yescharacteristic, complemented
36C2×D1208C2211yescharacteristic, complemented
37C2×#14558989—21no—
38C2×#14558989C2211yescharacteristic, complemented
39D8×D151—21no—
40#18012746C2211yescharacteristic, complemented
41#18012746C2211yescharacteristic, complemented
42#18012745C2211yescharacteristic, complemented
43#18012735C2211yescharacteristic, complemented
44#18012728C2211yescharacteristic, complemented
45#18012675C2211yescharacteristic, complemented
46#18012674C2211yescharacteristic, complemented
47#18012666C2211yescharacteristic, complemented
48#18012666C2211yescharacteristic, complemented
49#18012666C2211yescharacteristic, complemented
50#18012665C2211yescharacteristic, complemented
51#18012658C2211yescharacteristic, complemented
52#18012656C2211yescharacteristic, complemented
53#18012655C2211yescharacteristic, complemented
54#18012655C2211yescharacteristic, complemented
55#18012649C2211yescharacteristic, complemented
562−1+4×C151C2211yescharacteristic, complemented
57H(5,𝔽2)×C151C2211yescharacteristic, complemented
58#137×C151—21no—
59#137×C151C2211yescharacteristic, complemented
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#14559005—21no—
69#14559004—21no—
70#14559004—21no—
71#14559004C2311yescharacteristic
72C2×D604—21no—
73C2×D604—21no—
74C2×D604C2311yescharacteristic
75C2×D604C2311yescharacteristic
76C2×C22⋊D151—41no—
77D4×D151—21no—
78D4×D151—21no—
79D4×D151—41no—
80D4×D151—41no—
81#14558994—21no—
82#14558994D411yescharacteristic, complemented
83#14558992—21no—
84#14558992D411yescharacteristic, complemented
85#14558991—21no—
86#14558991—21no—
87#14558991—21no—
88#14558991—21no—
89#14558991—21no—
90#14558991—21no—
91#14558991—21no—
92#14558991D411yescharacteristic, complemented
93D1208—21no—
94D1208—21no—
95#14558989—21no—
96#14558989—21no—
97#14558989—21no—
98#14558989—21no—
99#14558989—21no—
100#14558989—21no—
101#14558989—21no—
102#14558989D411yescharacteristic, complemented
103#14558988—21no—
104#14558988—21no—
105#14558988C2311yescharacteristic
106#14558988C2311yescharacteristic
107#14558988C2311yescharacteristic
108#14558987—21no—
109C2×C151⋊C8—21no—
110C2×C151⋊C8—21no—
111C2×C151⋊C8C2311yescharacteristic
112C8×D151—21no—
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, complemented
132SD16×C151—21no—
133SD16×C151—21no—
134SD16×C151—21no—
135SD16×C151—21no—
136SD16×C151D411yescharacteristic, complemented
137SD16×C151D411yescharacteristic, complemented
138D8×C151—21no—
139D8×C151D411yescharacteristic, complemented
140M16×C151—21no—
141M16×C151C2311yescharacteristic
142C2×C8×C151—21no—
143C2×C8×C151C2311yescharacteristic
144C22×D151—21no—
145C22×D151—21no—
146C22×D151—41no—
147C22×D151—41no—
148Dic302C2×D411yescharacteristic
149D604—21no—
150D604—21no—
151D604—21no—
152D604—21no—
153D604—41no—
154D604—41no—
155D604C2×D411yescharacteristic
156C22⋊D151—21no—
157C22⋊D151—41no—
158C22⋊D151—41no—
159C22⋊D151—82no—
160C2×Dic151—21no—
161C4×D151—21no—
162C4×D151—41no—
163C4×D151—41no—
164C151⋊C8—21no—
165C151⋊C8—21no—
166C151⋊C8—21no—
167C151⋊C8C2×D411yescharacteristic
168C151⋊C8C2×D411yescharacteristic
169C23×C151—21no—
170C23×C151—41no—
171Q8×C151—21no—
172Q8×C151—21no—
173Q8×C151—41no—
174Q8×C151C2×D411yescharacteristic
175Q8×C151C2×D411yescharacteristic
176Q8×C151C2×D411yescharacteristic
177D4×C151—21no—
178D4×C151—21no—
179D4×C151—21no—
180D4×C151—21no—
181D4×C151—21no—
182D4×C151—41no—
183D4×C151—41no—
184D4×C151—41no—
185D4×C151C2×D411yescharacteristic
186D4×C151C2×D411yescharacteristic
187D4×C151C2×D411yescharacteristic
188C2×C4×C151—21no—
189C2×C4×C151—21no—
190C2×C4×C151—21no—
191C2×C4×C151—21no—
192C2×C4×C151—41no—
193C2×C4×C151—41no—
194C2×C4×C151—41no—
195C2×C4×C151C2411yescharacteristic
196C8×C151—21no—
197C8×C151C2×D411yescharacteristic
198C8×C151C2×D411yescharacteristic
199C22×C151—21no—
200C22×C151—21no—
201C22×C151—21no—
202C22×C151—41no—
203C22×C151—81no—
204C22×C151—161no—
205C22×C151H(5,𝔽2)11yescharacteristic
206C2×D151—21no—
207C2×D151—41no—
208C2×D151—41no—
209C2×D151—81no—
210C2×D151—81no—
211C2×D151—161no—
212C2×D151—161no—
213C4×C151—21no—
214C4×C151—21no—
215C4×C151—21no—
216C4×C151—41no—
217C4×C151C22×D411yescharacteristic
218C4×C151C22×D411yescharacteristic
219Dic151—21no—
220Dic151—41no—
221C2×C151—21no—
222C2×C151—41no—
223C2×C151—41no—
224C2×C151—41no—
225C2×C151—81no—
226C2×C151D4211yescharacteristic
227D151—41no—
228D151—81no—
229D151—81no—
230C151#328811yescharacteristic, complemented, Sylow
231#3288—1511nomaximal, Sylow
232#577—1511no—
233#577D15111yescharacteristic, complemented
234#576—1511no—
235#576—1511no—
236#496—1511no—
237#472—1511no—
238#472—1511no—
239#471—1511no—
240#471—1511no—
241#455—1511no—
242#454—1511no—
243#453—1511no—
244#453—1511no—
245#444—1511no—
246#444—1511no—
2472−1+4C2×D15111yescharacteristic, complemented
248H(5,𝔽2)—1511no—
249H(5,𝔽2)—1511no—
250H(5,𝔽2)C2×D15111yescharacteristic, complemented
251#137—21no—
252#137—3021no—
253#137—1511no—
254#137C2×D15111yescharacteristic, complemented
255AGL(1,ℤ/8)—21no—
256AGL(1,ℤ/8)—3021no—
257AGL(1,ℤ/8)—3021no—
258AGL(1,ℤ/8)—3021no—
259AGL(1,ℤ/8)—3021no—
260AGL(1,ℤ/8)—3021no—
261AGL(1,ℤ/8)—1511no—
262AGL(1,ℤ/8)—1511no—
263AGL(1,ℤ/8)—1511no—
264AGL(1,ℤ/8)—1511no—
265AGL(1,ℤ/8)—1511no—
266AGL(1,ℤ/8)C2×D15111yescharacteristic, complemented
267#135—21no—
268#135—3021no—
269#135—3021no—
270#135—3021no—
271#135—1511no—
272#135C2×D15111yescharacteristic
273C2×SD16—21no—
274C2×SD16—3021no—
275C2×SD16—1511no—
276C2×SD16C2×D15111yescharacteristic, complemented
277C2×D8—3021no—
278C2×D8—3021no—
279C2×D8—1511no—
280C2×D8—1511no—
281#131—1511no—
282#131—1511no—
283#131—1511no—
284#131C2×D15111yescharacteristic, complemented
285#127—1511no—
286#124—1511no—
287#108—1511no—
288#108—1511no—
289#104—1511no—
290#104—1511no—
291#104—1511no—
292#104—1511no—
293#101—1511no—
294#100—1511no—
295#100—1511no—
296#100—1511no—
297#97—1511no—
298#41—21no—
299#41—21no—
300#41—21no—
301#41—21no—
302#41—41no—
303#41—3021no—
304#41—3021no—
305#41—3021no—
306#41—3021no—
307#41—1511no—
308#41C22×D15111yescharacteristic
309#41C22×D15111yescharacteristic
310#41C22×D15111yescharacteristic
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8C22×D15111yescharacteristic
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4—3021no—
318C2×D4—3021no—
319C2×D4—3021no—
320C2×D4—3021no—
321C2×D4—6041no—
322C2×D4—6041no—
323C2×D4—6041no—
324C2×D4—1511no—
325C2×D4—1511no—
326C2×D4C22×D15111yescharacteristic
327Q16—21no—
328Q16—3021no—
329Q16—1511no—
330Q16C22⋊D15111yescharacteristic, complemented
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—21no—
335SD16—3021no—
336SD16—3021no—
337SD16—3021no—
338SD16—3021no—
339SD16—3021no—
340SD16—3021no—
341SD16—3021no—
342SD16—3021no—
343SD16—1511no—
344SD16—1511no—
345SD16C22⋊D15111yescharacteristic, complemented
346SD16C22⋊D15111yescharacteristic, complemented
347D8—21no—
348D8—3021no—
349D8—3021no—
350D8—3021no—
351D8—3021no—
352D8—3021no—
353D8—3021no—
354D8—3021no—
355D8—3021no—
356D8—3021no—
357D8—1511no—
358D8C22⋊D15111yescharacteristic, complemented
359M16—21no—
360M16—3021no—
361M16—3021no—
362M16—3021no—
363M16—1511no—
364M16—1511no—
365M16—1511no—
366M16C22×D15111yescharacteristic
367C2×C8—21no—
368C2×C8—3021no—
369C2×C8—3021no—
370C2×C8—3021no—
371C2×C8—1511no—
372C2×C8C22×D15111yescharacteristic
373C22⋊C4—6041no—
374C42—1511no—
375C23—21no—
376C23—41no—
377C23—3021no—
378C23—3021no—
379C23—6041no—
380C23—6041no—
381Q8—21no—
382Q8—21no—
383Q8—41no—
384Q8—1511no—
385Q8D4×D15111yescharacteristic
386Q8C2×C22⋊D15111yescharacteristic
387Q8C2×C22⋊D15111yescharacteristic
388D4—21no—
389D4—21no—
390D4—21no—
391D4—21no—
392D4—21no—
393D4—41no—
394D4—41no—
395D4—41no—
396D4—3021no—
397D4—3021no—
398D4—3021no—
399D4—3021no—
400D4—3021no—
401D4—6041no—
402D4—6041no—
403D4—6041no—
404D4—6041no—
405D4—1511no—
406D4—12082no—
407D4D4×D15111yescharacteristic
408D4C2×C22⋊D15111yescharacteristic
409D4C2×C22⋊D15111yescharacteristic
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—3021no—
418C2×C4—3021no—
419C2×C4—6041no—
420C2×C4—6041no—
421C2×C4C23×D15111yescharacteristic
422C8—21no—
423C8—3021no—
424C8—3021no—
425C8—3021no—
426C8—1511no—
427C8—1511no—
428C8C2×C22⋊D15111yescharacteristic
429C8C2×C22⋊D15111yescharacteristic
430C22—21no—
431C22—21no—
432C22—21no—
433C22—41no—
434C22—81no—
435C22—161no—
436C22—3021no—
437C22—6041no—
438C22—6041no—
439C22—24161no—
440C22—24161no—
441C22—12081no—
442C22—12081no—
443C22#1801278411yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—41no—
448C4—3021no—
449C4—6041no—
450C4C2×D4×D15111yescharacteristic
451C4C22×C22⋊D15111yescharacteristic
452C2—21no—
453C2—41no—
454C2—41no—
455C2—41no—
456C2—81no—
457C2—6041no—
458C2—12081no—
459C2—12081no—
460C2D4×C22⋊D15111yescharacteristic
subgroupG/H
centerC2D4×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#577×C151C2
socleC2×C151D42
hypercenter#577D151
hypocenterC151#3288
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. #23753020C2semidirect
2. #23753015C2semidirect
3. #23753014C2semidirect
4. #23752598C2semidirect
5. #23752482C2semidirect
6. #23752480C2semidirect
7. #23752477C2semidirect
8. #23752472C2semidirect
9. #23752388C2semidirect
10. #23752385C2semidirect
11. #23752380C2semidirect
12. #23752378C2semidirect
13. #23752334C2semidirect
14. #23752332C2semidirect
15. #577×C151C2semidirect
17. #18012785C22semidirect
19. #18012770C22semidirect
27. #18012764C22semidirect
28. #18012764C22semidirect
29. #18012764C22semidirect
35. C2×#14558991C22semidirect
36. C2×D1208C22semidirect
38. C2×#14558989C22semidirect
40. #18012746C22semidirect
41. #18012746C22semidirect
42. #18012745C22semidirect
43. #18012735C22semidirect
44. #18012728C22semidirect
45. #18012675C22semidirect
46. #18012674C22semidirect
47. #18012666C22semidirect
48. #18012666C22semidirect
49. #18012666C22semidirect
50. #18012665C22semidirect
51. #18012658C22semidirect
52. #18012656C22semidirect
53. #18012655C22semidirect
54. #18012655C22semidirect
55. #18012649C22semidirect
56. 2−1+4×C151C22semidirect
57. H(5,𝔽2)×C151C22semidirect
59. #137×C151C22semidirect
61. AGL(1,ℤ/8)×C151C22semidirect
65. C2×SD16×C151C22semidirect
66. #131×C151C22semidirect
82. #14558994D4semidirect
84. #14558992D4semidirect
92. #14558991D4semidirect
102. #14558989D4semidirect
131. Q16×C151D4semidirect
136. SD16×C151D4semidirect
137. SD16×C151D4semidirect
139. D8×C151D4semidirect
230. C151#3288semidirect
233. #577D151semidirect
247. 2−1+4C2×D151semidirect
250. H(5,𝔽2)C2×D151semidirect
254. #137C2×D151semidirect
266. AGL(1,ℤ/8)C2×D151semidirect
276. C2×SD16C2×D151semidirect
284. #131C2×D151semidirect
330. Q16C22⋊D151semidirect
345. SD16C22⋊D151semidirect
346. SD16C22⋊D151semidirect
358. D8C22⋊D151semidirect

Maximal subgroups

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

subgroupindex
#237530202
#237530152
#237530142
#237525982
#237524822
#237524802
#237524772
#237524722
#237523882
#237523852
#237523802
#237523782
#237523342
#237523322
#577×C1512
#3288151