Finite Group Databasebeta

← #34078836

Subgroups — #34078836

Order 19328.

466 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#23753008C211yesmaximal, characteristic, complemented
2C2×#18012763C211yesmaximal, characteristic, complemented
3AGL(1,ℤ/8)×D151C211yesmaximal, characteristic, complemented
4#23752977C211yesmaximal, characteristic, complemented
5#23752481C211yesmaximal, characteristic, complemented
6#23752480C211yesmaximal, characteristic, complemented
7#23752479C211yesmaximal, characteristic, complemented
8#23752476C211yesmaximal, characteristic, complemented
9#23752475C211yesmaximal, characteristic, complemented
10#23752474C211yesmaximal, characteristic, complemented
11#23752473C211yesmaximal, characteristic, complemented
12#23752259C211yesmaximal, characteristic, complemented
13#23752193C211yesmaximal, characteristic, complemented
14#100×D151C211yesmaximal, characteristic, complemented
15#472×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic
17#41×D151C2211yescharacteristic
18C2×D4×D151C2211yescharacteristic
19#18012772C2211yescharacteristic, complemented
20#18012769C2211yescharacteristic, complemented
21#18012768—21no—
22#18012767C2211yescharacteristic
23#18012766—21no—
24#18012765C2211yescharacteristic
25#18012765C2211yescharacteristic, complemented
26#18012764C2211yescharacteristic
27#18012763—21no—
28#18012763—21no—
29#18012763—21no—
30#18012763—21no—
31#18012763—21no—
32#18012763—21no—
33#18012760—21no—
34#18012758—21no—
35C2×#14558993C2211yescharacteristic, complemented
36C2×#14558992C2211yescharacteristic, complemented
37SD16×D151—21no—
38C2×#14558989C2211yescharacteristic, complemented
39D8×D151—21no—
40#18012747—21no—
41#18012747C2211yescharacteristic, complemented
42#18012746C2211yescharacteristic, complemented
43#18012745—21no—
44#18012745C2211yescharacteristic, complemented
45C2×#14558987—21no—
46C2×#14558987C2211yescharacteristic
47M16×D151—21no—
48M16×D151C2211yescharacteristic
49M16×D151C2211yescharacteristic
50M16×D151C2211yescharacteristic
51#18012675C2211yescharacteristic, complemented
52#18012674C2211yescharacteristic, complemented
53#18012674C2211yescharacteristic, complemented
54#18012657C2211yescharacteristic, complemented
55#18012657C2211yescharacteristic, complemented
56#18012656C2211yescharacteristic, complemented
57#18012656C2211yescharacteristic, complemented
58#18012655C2211yescharacteristic, complemented
59#18012655C2211yescharacteristic, complemented
60AGL(1,ℤ/8)×C151C2211yescharacteristic
61AGL(1,ℤ/8)×C151C2211yescharacteristic, complemented
62C2×D8×C151C2211yescharacteristic, complemented
63#131×C151C2211yescharacteristic, complemented
64#108×C151C2211yescharacteristic, complemented
65#100×C151C2211yescharacteristic, complemented
66#100×C151C2211yescharacteristic, complemented
67C23×D151—21no—
68#14559005D411yescharacteristic
69#14559004—21no—
70#14559004C2311yescharacteristic
71#14559003—21no—
72#14559003—21no—
73#14559003—21no—
74#14559003—21no—
75#14559003—21no—
76#14559003D411yescharacteristic
77C2×Dic302C2311yescharacteristic
78Q8×D151D411yescharacteristic
79C2×D604C2311yescharacteristic
80C2×C22⋊D151—21no—
81C2×C22⋊D151—21no—
82D4×D151—21no—
83D4×D151—21no—
84D4×D151—21no—
85D4×D151—21no—
86D4×D151—21no—
87D4×D151D411yescharacteristic
88C22×Dic151—21no—
89C2×C4×D151—21no—
90C2×C4×D151C2311yescharacteristic
91Dic604—21no—
92#14558994—21no—
93#14558993—21no—
94#14558993—21no—
95#14558993—21no—
96#14558993—21no—
97#14558992—21no—
98#14558992—21no—
99#14558992—21no—
100#14558992—21no—
101#14558992—21no—
102#14558991—21no—
103D1208—21no—
104#14558989—21no—
105#14558989—21no—
106#14558989—21no—
107#14558989—21no—
108#14558989—21no—
109#14558988—21no—
110#14558988C2311yescharacteristic
111#14558988C2311yescharacteristic
112#14558988C2311yescharacteristic
113#14558987—21no—
114#14558987—21no—
115#14558987—21no—
116#14558987—21no—
117#14558987—21no—
118#14558987D411yescharacteristic
119#14558987D411yescharacteristic
120#14558987D411yescharacteristic
121#14558987D411yescharacteristic
122C2×C151⋊C8—21no—
123C2×C151⋊C8C2311yescharacteristic
124C8×D151—21no—
125C8×D151—21no—
126C8×D151—21no—
127C8×D151—21no—
128C8×D151—21no—
129#41×C151C2311yescharacteristic
130C2×D4×C151C2311yescharacteristic
131C2×D4×C151C2311yescharacteristic
132SD16×C151—21no—
133SD16×C151—21no—
134D8×C151—21no—
135D8×C151—21no—
136D8×C151—21no—
137D8×C151—21no—
138M16×C151—21no—
139M16×C151C2311yescharacteristic
140M16×C151C2311yescharacteristic
141M16×C151C2311yescharacteristic
142C2×C8×C151—21no—
143C2×C8×C151C2311yescharacteristic
144C22×D151—21no—
145C22×D151—21no—
146C22×D151—41no—
147C22×D151—41no—
148C22×D151—82no—
149C22×D151#4111yescharacteristic
150Dic302—21no—
151Dic302—21no—
152Dic302—21no—
153Dic302C2×D411yescharacteristic
154D604—21no—
155D604—21no—
156D604—21no—
157D604C2×D411yescharacteristic
158C22⋊D151—21no—
159C22⋊D151—21no—
160C22⋊D151—21no—
161C22⋊D151—41no—
162C22⋊D151—41no—
163C22⋊D151—41no—
164C22⋊D151—41no—
165C2×Dic151—21no—
166C2×Dic151—21no—
167C2×Dic151—41no—
168C2×Dic151—41no—
169C2×Dic151#4111yescharacteristic
170C4×D151—21no—
171C4×D151—21no—
172C4×D151—21no—
173C4×D151C2×D411yescharacteristic
174C4×D151C2×D411yescharacteristic
175C4×D151C2×D411yescharacteristic
176C4×D151C2×D411yescharacteristic
177C151⋊C8—21no—
178C151⋊C8—21no—
179C151⋊C8—21no—
180C151⋊C8C2×D411yescharacteristic
181C151⋊C8C2×D411yescharacteristic
182C23×C151—21no—
183C23×C151—21no—
184Q8×C151C2×D411yescharacteristic
185D4×C151—21no—
186D4×C151—21no—
187D4×C151—21no—
188D4×C151—21no—
189D4×C151—21no—
190D4×C151C2×D411yescharacteristic
191C2×C4×C151—21no—
192C2×C4×C151C2411yescharacteristic
193C8×C151—21no—
194C8×C151—21no—
195C8×C151—21no—
196C8×C151C2×D411yescharacteristic
197C8×C151C2×D411yescharacteristic
198C22×C151—21no—
199C22×C151—41no—
200C22×C151—41no—
201C22×C151—81no—
202C22×C151—81no—
203C22×C151C2×#4111yescharacteristic
204C2×D151—21no—
205C2×D151—41no—
206C2×D151—41no—
207C2×D151—81no—
208C2×D151—82no—
209C2×D151—82no—
210C2×D151—81no—
211C2×D151#12111yescharacteristic
212C2×D151#12111yescharacteristic
213C4×C151—21no—
214C4×C151C22×D411yescharacteristic
215C4×C151C22×D411yescharacteristic
216Dic151—21no—
217Dic151—41no—
218Dic151#12111yescharacteristic
219Dic151#12111yescharacteristic
220C2×C151—21no—
221C2×C151—41no—
222C2×C151—81no—
223C2×C151—81no—
224C2×C151C2×#12111yescharacteristic
225D151—21no—
226D151—21no—
227D151—41no—
228D151—81no—
229C151#306811yescharacteristic, complemented, Sylow
230#3068—1511nomaximal, Sylow
231#575—1511no—
232C2×AGL(1,ℤ/8)—1511no—
233C2×AGL(1,ℤ/8)—1511no—
234#568—1511no—
235#472—1511no—
236#472—1511no—
237#472—1511no—
238#472D15111yescharacteristic, complemented
239#471—1511no—
240#471—1511no—
241#471—1511no—
242#471—1511no—
243#430—1511no—
244#413—1511no—
245C2×#100—1511no—
246C2×#41—1511no—
247C2×#41—1511no—
248C22×D4—1511no—
249#137—3021no—
250#137—1511no—
251#137—1511no—
252AGL(1,ℤ/8)—3021no—
253AGL(1,ℤ/8)—3021no—
254AGL(1,ℤ/8)—3021no—
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—
263AGL(1,ℤ/8)C2×D15111yescharacteristic
264AGL(1,ℤ/8)C2×D15111yescharacteristic, complemented
265#135—3021no—
266#135—3021no—
267C2×SD16—3021no—
268C2×SD16—1511no—
269C2×SD16—1511no—
270C2×D8—3021no—
271C2×D8—1511no—
272C2×D8C2×D15111yescharacteristic, complemented
273#131—3021no—
274#131—3021no—
275#131—1511no—
276#131—1511no—
277#131—1511no—
278#131C2×D15111yescharacteristic, complemented
279C2×M16—3021no—
280C2×M16—3021no—
281C2×M16—1511no—
282C2×M16—1511no—
283C2×M16—1511no—
284C2×M16—1511no—
285#108—1511no—
286#108—1511no—
287#108—1511no—
288#108C2×D15111yescharacteristic, complemented
289#101—1511no—
290#101—1511no—
291#100—1511no—
292#100—1511no—
293#100—1511no—
294#100—1511no—
295#100C2×D15111yescharacteristic, complemented
296#100C2×D15111yescharacteristic, complemented
297C24—3021no—
298#41—3021no—
299#41—3021no—
300#41—3021no—
301#41—3021no—
302#41—3021no—
303#41—3021no—
304#41—1511no—
305#41—1511no—
306#41—1511no—
307#41C22×D15111yescharacteristic
308C2×Q8—1511no—
309C2×Q8—1511no—
310C2×D4—3021no—
311C2×D4—3021no—
312C2×D4—3021no—
313C2×D4—3021no—
314C2×D4—3021no—
315C2×D4—3021no—
316C2×D4—3021no—
317C2×D4—1511no—
318C2×D4—1511no—
319C2×D4C22×D15111yescharacteristic
320C2×D4C22×D15111yescharacteristic
321C22×C4—3021no—
322C22×C4—3021no—
323C22×C4—1511no—
324Q16—3021no—
325Q16—3021no—
326SD16—21no—
327SD16—21no—
328SD16—3021no—
329SD16—3021no—
330SD16—3021no—
331SD16—3021no—
332SD16—3021no—
333SD16—3021no—
334SD16—3021no—
335SD16—3021no—
336SD16—3021no—
337SD16—3021no—
338D8—21no—
339D8—21no—
340D8—21no—
341D8—21no—
342D8—3021no—
343D8—3021no—
344D8—3021no—
345D8—3021no—
346D8—3021no—
347D8—3021no—
348M16—21no—
349M16—3021no—
350M16—3021no—
351M16—3021no—
352M16—3021no—
353M16—3021no—
354M16—3021no—
355M16—1511no—
356M16—1511no—
357M16—1511no—
358M16—1511no—
359M16—1511no—
360M16—1511no—
361M16—1511no—
362M16C22×D15111yescharacteristic
363M16C22×D15111yescharacteristic
364M16C22×D15111yescharacteristic
365C2×C8—21no—
366C2×C8—3021no—
367C2×C8—3021no—
368C2×C8—3021no—
369C2×C8—3021no—
370C2×C8—3021no—
371C2×C8—3021no—
372C2×C8—1511no—
373C2×C8C22×D15111yescharacteristic
374C23—21no—
375C23—21no—
376C23—3021no—
377C23—3021no—
378C23—6041no—
379C23—6041no—
380C23—1511no—
381C23—12082no—
382Q8—3021no—
383Q8—3021no—
384Q8—3021no—
385Q8—1511no—
386Q8D4×D15111yescharacteristic
387D4—21no—
388D4—21no—
389D4—21no—
390D4—21no—
391D4—21no—
392D4—3021no—
393D4—3021no—
394D4—3021no—
395D4—3021no—
396D4—3021no—
397D4—3021no—
398D4—6041no—
399D4—6041no—
400D4—6041no—
401D4—6041no—
402D4—1511no—
403D4D4×D15111yescharacteristic
404C2×C4—21no—
405C2×C4—3021no—
406C2×C4—3021no—
407C2×C4—3021no—
408C2×C4—3021no—
409C2×C4—3021no—
410C2×C4—6041no—
411C2×C4—6041no—
412C2×C4—1511no—
413C2×C4—1511no—
414C2×C4—1511no—
415C2×C4—1511no—
416C2×C4—1511no—
417C2×C4C23×D15111yescharacteristic
418C8—21no—
419C8—21no—
420C8—21no—
421C8—3021no—
422C8—3021no—
423C8—3021no—
424C8—1511no—
425C8—1511no—
426C8D4×D15111yescharacteristic
427C8D4×D15111yescharacteristic
428C22—21no—
429C22—41no—
430C22—41no—
431C22—81no—
432C22—81no—
433C22—3021no—
434C22—6041no—
435C22—6041no—
436C22—1511no—
437C22—1511no—
438C22—12081no—
439C22—12081no—
440C22—12082no—
441C22—12082no—
442C22#41×D15111yescharacteristic
443C4—21no—
444C4—3021no—
445C4—6041no—
446C4—1511no—
447C4—1511no—
448C4C2×D4×D15111yescharacteristic
449C4C2×D4×D15111yescharacteristic
450C2—21no—
451C2—41no—
452C2—81no—
453C2—81no—
454C2—3021no—
455C2—3021no—
456C2—6041no—
457C2—12081no—
458C2#121×D15111yescharacteristic
subgroupG/H
centerC2#121×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#472×C151C2
socleC2×C151C2×#121
hypercenter#472D151
hypocenterC151#3068
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ #472

Complements

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

NH ≅ G/Ntype
1. #23753008C2semidirect
2. C2×#18012763C2semidirect
3. AGL(1,ℤ/8)×D151C2semidirect
4. #23752977C2semidirect
5. #23752481C2semidirect
6. #23752480C2semidirect
7. #23752479C2semidirect
8. #23752476C2semidirect
9. #23752475C2semidirect
10. #23752474C2semidirect
11. #23752473C2semidirect
12. #23752259C2semidirect
13. #23752193C2semidirect
14. #100×D151C2semidirect
15. #472×C151C2semidirect
19. #18012772C22semidirect
20. #18012769C22semidirect
25. #18012765C22semidirect
35. C2×#14558993C22semidirect
36. C2×#14558992C22semidirect
38. C2×#14558989C22semidirect
41. #18012747C22semidirect
42. #18012746C22semidirect
44. #18012745C22semidirect
51. #18012675C22semidirect
52. #18012674C22semidirect
53. #18012674C22semidirect
54. #18012657C22semidirect
55. #18012657C22semidirect
56. #18012656C22semidirect
57. #18012656C22semidirect
58. #18012655C22semidirect
59. #18012655C22semidirect
61. AGL(1,ℤ/8)×C151C22semidirect
62. C2×D8×C151C22semidirect
63. #131×C151C22semidirect
64. #108×C151C22semidirect
65. #100×C151C22semidirect
66. #100×C151C22semidirect
229. C151#3068semidirect
238. #472D151semidirect
264. AGL(1,ℤ/8)C2×D151semidirect
272. C2×D8C2×D151semidirect
278. #131C2×D151semidirect
288. #108C2×D151semidirect
295. #100C2×D151semidirect
296. #100C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237530082
C2×#180127632
AGL(1,ℤ/8)×D1512
#237529772
#237524812
#237524802
#237524792
#237524762
#237524752
#237524742
#237524732
#237522592
#237521932
#100×D1512
#472×C1512
#3068151