Finite Group Databasebeta

← #34080893

Subgroups — #34080893

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#23753024C211yesmaximal, characteristic, complemented
3#23753018C211yesmaximal, characteristic, complemented
4#23753016C211yesmaximal, characteristic, complemented
5#23752593C211yesmaximal, characteristic, complemented
6#23752486C211yesmaximal, characteristic, complemented
7#23752481C211yesmaximal, characteristic, complemented
8#23752476C211yesmaximal, characteristic, complemented
9#23752392C211yesmaximal, characteristic, complemented
10#23752388C211yesmaximal, characteristic, complemented
11#23752387C211yesmaximal, characteristic, complemented
12#23752383C211yesmaximal, characteristic, complemented
13#23752328C211yesmaximal, characteristic, complemented
14#23752327C211yesmaximal, characteristic, complemented
15#471×C151C211yesmaximal, characteristic, complemented
16#18012787C2211yescharacteristic, complemented
17#18012786C2211yescharacteristic, complemented
18#18012785C2211yescharacteristic
19#18012784C2211yescharacteristic
20#18012772—21no—
21#18012772C2211yescharacteristic
22#18012772C2211yescharacteristic, complemented
23#18012771—21no—
24#18012770C2211yescharacteristic
25#18012768—21no—
26#18012768—21no—
27#18012767—21no—
28#18012767C2211yescharacteristic
29#18012767C2211yescharacteristic, complemented
30#18012766—21no—
31#18012766—21no—
32#18012765C2211yescharacteristic, complemented
33#18012763—21no—
34#18012761—21no—
35#18012761C2211yescharacteristic
36#18012760—21no—
37#18012760—21no—
38#18012760—21no—
39#18012759C2211yescharacteristic
40C2×#14558994C2211yescharacteristic, complemented
41Q16×D151—21no—
42C2×#14558993—21no—
43C2×#14558993C2211yescharacteristic, complemented
44SD16×D151—21no—
45C2×#14558989C2211yescharacteristic
46D8×D151—21no—
47#18012747C2211yescharacteristic
48#18012747C2211yescharacteristic, complemented
49#18012745C2211yescharacteristic, complemented
50#18012728C2211yescharacteristic, complemented
51#18012726C2211yescharacteristic, complemented
52#18012674C2211yescharacteristic, complemented
53#18012666C2211yescharacteristic, complemented
54#18012665C2211yescharacteristic
55#18012665C2211yescharacteristic, complemented
56#18012665C2211yescharacteristic, complemented
57#18012657C2211yescharacteristic, complemented
58#18012655C2211yescharacteristic, complemented
59C8×Dic151C2211yescharacteristic, complemented
60#137×C151C2211yescharacteristic, complemented
61AGL(1,ℤ/8)×C151C2211yescharacteristic
62C2×SD16×C151C2211yescharacteristic, complemented
63#131×C151C2211yescharacteristic, complemented
64#108×C151C2211yescharacteristic, complemented
65#101×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#14559004C2311yescharacteristic
76#14559003—21no—
77#14559003—21no—
78#14559003—21no—
79#14559003—41no—
80C2×Dic302—21no—
81C2×Dic302C2311yescharacteristic
82Q8×D151—21no—
83Q8×D151—21no—
84Q8×D151—21no—
85C2×D604—21no—
86C2×D604C2311yescharacteristic
87C2×C22⋊D151—41no—
88D4×D151—21no—
89D4×D151—21no—
90D4×D151—21no—
91D4×D151—41no—
92Dic604—21no—
93Dic604—21no—
94Dic604D411yescharacteristic
95#14558994—21no—
96#14558994—21no—
97#14558994—21no—
98#14558994D411yescharacteristic
99#14558993—21no—
100#14558993—21no—
101#14558993—21no—
102#14558993—21no—
103#14558993—21no—
104#14558993—21no—
105#14558993D411yescharacteristic
106#14558993D411yescharacteristic
107#14558992—21no—
108#14558992D411yescharacteristic
109#14558991—21no—
110#14558991D411yescharacteristic
111D1208—21no—
112D1208—21no—
113D1208D411yescharacteristic
114#14558989—21no—
115#14558989—21no—
116#14558989—21no—
117#14558989D411yescharacteristic
118#14558988C2311yescharacteristic
119#14558987—21no—
120#14558987—21no—
121#14558987—21no—
122C2×C151⋊C8C2311yescharacteristic
123C8×D151—21no—
124C8×D151—21no—
125C8×D151—21no—
126C22⋊Dic151—41no—
127(C2×D151)⋊C4—41no—
128C4×Dic151C2311yescharacteristic
129#41×C151C2311yescharacteristic
130C2×Q8×C151C2311yescharacteristic
131C2×D4×C151C2311yescharacteristic
132Q16×C151—21no—
133SD16×C151—21no—
134SD16×C151—21no—
135SD16×C151—21no—
136SD16×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—41no—
146C22×D151—41no—
147Dic302—21no—
148Dic302—21no—
149Dic302—41no—
150Dic302—41no—
151Dic302C2×D411yescharacteristic
152Dic302C2×D411yescharacteristic
153Dic302C2×D411yescharacteristic
154D604—21no—
155D604—21no—
156D604—41no—
157D604—41no—
158D604C2×D411yescharacteristic
159D604C2×D411yescharacteristic
160D604C2×D411yescharacteristic
161C22⋊D151—21no—
162C22⋊D151—21no—
163C22⋊D151—21no—
164C22⋊D151—41no—
165C22⋊D151—41no—
166C22⋊D151—41no—
167C22⋊D151—41no—
168C2×Dic151—21no—
169C2×Dic151—21no—
170C2×Dic151—41no—
171C2×Dic151—41no—
172C4×D151—21no—
173C4×D151—21no—
174C4×D151—21no—
175C4×D151—41no—
176C4×D151—41no—
177C4×D151—41no—
178C4×D151—41no—
179C151⋊C8—21no—
180C151⋊C8C2×D411yescharacteristic
181C151⋊C8C2×D411yescharacteristic
182C23×C151—21no—
183Q8×C151—21no—
184Q8×C151—21no—
185Q8×C151C2×D411yescharacteristic
186D4×C151—21no—
187D4×C151—21no—
188D4×C151—21no—
189D4×C151C2×D411yescharacteristic
190C2×C4×C151—21no—
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—81no—
201C22×C151H(5,𝔽2)11yescharacteristic
202C2×D151—21no—
203C2×D151—21no—
204C2×D151—21no—
205C2×D151—41no—
206C2×D151—81no—
207C2×D151—161no—
208C2×D151—161no—
209C4×C151—21no—
210C4×C151—41no—
211C4×C151C22×D411yescharacteristic
212C4×C151C22×D411yescharacteristic
213Dic151—21no—
214Dic151—21no—
215Dic151—21no—
216Dic151—41no—
217Dic151—41no—
218C2×C151—21no—
219C2×C151—41no—
220C2×C151—81no—
221C2×C151D4211yescharacteristic
222D151—41no—
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#471D15111yescharacteristic, complemented
237#455—1511no—
238#455—1511no—
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)—1511no—
247#137—3021no—
248#137—3021no—
249#137—3021no—
250#137—3021no—
251#137—1511no—
252#137—1511no—
253#137—1511no—
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)C2×D15111yescharacteristic
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×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#108C2×D15111yescharacteristic, complemented
285#104—1511no—
286#104—1511no—
287#104—1511no—
288#104—1511no—
289#101—1511no—
290#101C2×D15111yescharacteristic, complemented
291#100—1511no—
292#100C2×D15111yescharacteristic, complemented
293C4×C8—1511no—
294#41—3021no—
295#41—3021no—
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#41—1511no—
307#41C22×D15111yescharacteristic
308C2×Q8—3021no—
309C2×Q8—3021no—
310C2×Q8—3021no—
311C2×Q8—3021no—
312C2×Q8—1511no—
313C2×Q8C22×D15111yescharacteristic
314C2×D4—3021no—
315C2×D4—3021no—
316C2×D4—3021no—
317C2×D4—3021no—
318C2×D4—6041no—
319C2×D4—6041no—
320C2×D4—1511no—
321C2×D4C22×D15111yescharacteristic
322Q16—21no—
323Q16—3021no—
324Q16—3021no—
325Q16—3021no—
326Q16—3021no—
327Q16—3021no—
328Q16—1511no—
329Q16—1511no—
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—
344SD16—1511no—
345SD16—1511no—
346D8—21no—
347D8—3021no—
348D8—3021no—
349D8—3021no—
350D8—3021no—
351D8—3021no—
352D8—1511no—
353D8—1511no—
354M16—21no—
355M16—3021no—
356M16—3021no—
357M16—3021no—
358M16—1511no—
359M16C22×D15111yescharacteristic
360M16C22×D15111yescharacteristic
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—3021no—
373C23—6041no—
374C23—6041no—
375Q8—21no—
376Q8—21no—
377Q8—3021no—
378Q8—3021no—
379Q8—6041no—
380Q8—6041no—
381Q8—1511no—
382Q8—1511no—
383Q8—1511no—
384Q8D4×D15111yescharacteristic
385D4—21no—
386D4—21no—
387D4—21no—
388D4—3021no—
389D4—3021no—
390D4—3021no—
391D4—3021no—
392D4—3021no—
393D4—6041no—
394D4—6041no—
395D4—6041no—
396D4—6041no—
397D4—6041no—
398D4—6041no—
399D4—1511no—
400D4—1511no—
401D4—1511no—
402D4D4×D15111yescharacteristic
403C2×C4—21no—
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—6041no—
413C2×C4—6041no—
414C2×C4—6041no—
415C2×C4—6041no—
416C2×C4C23×D15111yescharacteristic
417C8—21no—
418C8—21no—
419C8—21no—
420C8—3021no—
421C8—1511no—
422C8—1511no—
423C8D4×D15111yescharacteristic
424C8D4×D15111yescharacteristic
425C22—21no—
426C22—41no—
427C22—81no—
428C22—3021no—
429C22—3021no—
430C22—3021no—
431C22—6041no—
432C22—24161no—
433C22—24161no—
434C22—12081no—
435C22#1801278511yescharacteristic
436C4—21no—
437C4—41no—
438C4—3021no—
439C4—3021no—
440C4—3021no—
441C4—6041no—
442C4—6041no—
443C4C2×D4×D15111yescharacteristic
444C4C2×D4×D15111yescharacteristic
445C2—21no—
446C2—41no—
447C2—81no—
448C2—6041no—
449C2—6041no—
450C2—6041no—
451C2—12081no—
452C2#2375284611yescharacteristic
subgroupG/H
centerC2#23752846
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#471×C151C2
socleC2×C151D42
hypercenter#471D151
hypocenterC151#3290
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. #23753028C2semidirect
2. #23753024C2semidirect
3. #23753018C2semidirect
4. #23753016C2semidirect
5. #23752593C2semidirect
6. #23752486C2semidirect
7. #23752481C2semidirect
8. #23752476C2semidirect
9. #23752392C2semidirect
10. #23752388C2semidirect
11. #23752387C2semidirect
12. #23752383C2semidirect
13. #23752328C2semidirect
14. #23752327C2semidirect
15. #471×C151C2semidirect
16. #18012787C22semidirect
17. #18012786C22semidirect
22. #18012772C22semidirect
29. #18012767C22semidirect
32. #18012765C22semidirect
40. C2×#14558994C22semidirect
43. C2×#14558993C22semidirect
48. #18012747C22semidirect
49. #18012745C22semidirect
50. #18012728C22semidirect
51. #18012726C22semidirect
52. #18012674C22semidirect
53. #18012666C22semidirect
55. #18012665C22semidirect
56. #18012665C22semidirect
57. #18012657C22semidirect
58. #18012655C22semidirect
59. C8×Dic151C22semidirect
60. #137×C151C22semidirect
62. C2×SD16×C151C22semidirect
63. #131×C151C22semidirect
64. #108×C151C22semidirect
65. #101×C151C22semidirect
66. #100×C151C22semidirect
226. C151#3290semidirect
236. #471D151semidirect
254. #137C2×D151semidirect
274. C2×SD16C2×D151semidirect
280. #131C2×D151semidirect
284. #108C2×D151semidirect
290. #101C2×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
#237530242
#237530182
#237530162
#237525932
#237524862
#237524812
#237524762
#237523922
#237523882
#237523872
#237523832
#237523282
#237523272
#471×C1512
#3290151