Finite Group Databasebeta

← #34080901

Subgroups — #34080901

Order 19328.

460 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23753023C211yesmaximal, characteristic, complemented
2#23753020C211yesmaximal, characteristic, complemented
3#23753019C211yesmaximal, characteristic, complemented
4#23752583C211yesmaximal, characteristic, complemented
5#23752477C211yesmaximal, characteristic, complemented
6#23752475C211yesmaximal, characteristic, complemented
7#23752473C211yesmaximal, characteristic, complemented
8#23752472C211yesmaximal, characteristic, complemented
9#23752395C211yesmaximal, characteristic, complemented
10#23752393C211yesmaximal, characteristic, complemented
11#23752380C211yesmaximal, characteristic, complemented
12#23752378C211yesmaximal, characteristic, complemented
13#23752329C211yesmaximal, characteristic, complemented
14#23752327C211yesmaximal, characteristic, complemented
15#577×C151C211yesmaximal, characteristic, complemented
16#18012786C2211yescharacteristic
17#18012785C2211yescharacteristic, complemented
18#18012771—21no—
19#18012770—21no—
20#18012770C2211yescharacteristic, complemented
21#18012769—21no—
22#18012769C2211yescharacteristic, complemented
23#18012769C2211yescharacteristic, complemented
24#18012765—21no—
25#18012765C2211yescharacteristic
26#18012764—21no—
27#18012764C2211yescharacteristic
28#18012764C2211yescharacteristic
29#18012763—21no—
30#18012760—21no—
31#18012759—21no—
32#18012759—21no—
33#18012759C2211yescharacteristic
34C2×#14558993C2211yescharacteristic, complemented
35C2×#14558992—21no—
36C2×#14558992C2211yescharacteristic, complemented
37C2×#14558991—21no—
38C2×#14558991C2211yescharacteristic, complemented
39SD16×D151—21no—
40#18012746C2211yescharacteristic, complemented
41#18012746C2211yescharacteristic, complemented
42#18012745C2211yescharacteristic, complemented
43#18012737C2211yescharacteristic, complemented
44#18012735C2211yescharacteristic
45#18012675C2211yescharacteristic, complemented
46#18012674C2211yescharacteristic, complemented
47#18012666C2211yescharacteristic, complemented
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
57H(5,𝔽2)×C151C2211yescharacteristic, complemented
58#137×C151—21no—
59#137×C151C2211yescharacteristic, complemented
60AGL(1,ℤ/8)×C151—21no—
61AGL(1,ℤ/8)×C151C2211yescharacteristic
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
78C2×C22⋊D151—41no—
79D4×D151—21no—
80D4×D151—41no—
81#14558994—21no—
82#14558994—21no—
83#14558994—21no—
84#14558994D411yescharacteristic, complemented
85#14558993—21no—
86#14558993—21no—
87#14558992—21no—
88#14558992—21no—
89#14558992—21no—
90#14558992—21no—
91#14558992—21no—
92#14558992D411yescharacteristic, complemented
93#14558991—21no—
94#14558991—21no—
95#14558991—21no—
96#14558991—21no—
97#14558991—21no—
98#14558991D411yescharacteristic, complemented
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—
113Dic151⋊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—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—
157C22⋊D151—82no—
158C2×Dic151—21no—
159C2×Dic151—21no—
160C2×Dic151—41no—
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—81no—
209C2×D151—161no—
210C4×C151—21no—
211C4×C151—21no—
212C4×C151—21no—
213C4×C151—41no—
214C4×C151C22×D411yescharacteristic
215C4×C151C22×D411yescharacteristic
216Dic151—22no—
217Dic151—21no—
218Dic151—41no—
219C2×C151—21no—
220C2×C151—41no—
221C2×C151—41no—
222C2×C151—41no—
223C2×C151—81no—
224C2×C151D4211yescharacteristic
225D151—41no—
226D151—81no—
227C151#329111yescharacteristic, complemented, Sylow
228#3291—1511nomaximal, Sylow
229#577—1511no—
230#577—1511no—
231#577—1511no—
232#577D15111yescharacteristic, complemented
233#492—1511no—
234#471—1511no—
235#471—1511no—
236#471—1511no—
237#471—1511no—
238#456—1511no—
239#456—1511no—
240#453—1511no—
241#453—1511no—
242#443—1511no—
243#443—1511no—
2442−1+4—1511no—
2452−1+4C2×D15111yescharacteristic
246H(5,𝔽2)—1511no—
247H(5,𝔽2)C2×D15111yescharacteristic, complemented
248#137—21no—
249#137—3021no—
250#137—3021no—
251#137—3021no—
252#137—1511no—
253#137—1511no—
254#137—1511no—
255#137C2×D15111yescharacteristic, complemented
256AGL(1,ℤ/8)—21no—
257AGL(1,ℤ/8)—3021no—
258AGL(1,ℤ/8)—3021no—
259AGL(1,ℤ/8)—3021no—
260AGL(1,ℤ/8)—1511no—
261AGL(1,ℤ/8)—1511no—
262AGL(1,ℤ/8)—1511no—
263AGL(1,ℤ/8)C2×D15111yescharacteristic
264#135—21no—
265#135—3021no—
266#135—3021no—
267#135—3021no—
268#135—1511no—
269#135C2×D15111yescharacteristic
270C2×SD16—21no—
271C2×SD16—3021no—
272C2×SD16—3021no—
273C2×SD16—3021no—
274C2×SD16—1511no—
275C2×SD16—1511no—
276C2×SD16—1511no—
277C2×SD16C2×D15111yescharacteristic, complemented
278#131—1511no—
279#131—1511no—
280#131—1511no—
281#131C2×D15111yescharacteristic, complemented
282C4⋊Q8—1511no—
283#127—1511no—
284#108—1511no—
285#108—1511no—
286#104—1511no—
287#104—1511no—
288#104—1511no—
289#104—1511no—
290#101—1511no—
291#101—1511no—
292#100—1511no—
293#100—1511no—
294C4×C8—1511no—
295#41—21no—
296#41—21no—
297#41—21no—
298#41—21no—
299#41—41no—
300#41—3021no—
301#41—3021no—
302#41—3021no—
303#41—3021no—
304#41—6041no—
305#41—1511no—
306#41C22×D15111yescharacteristic
307#41C22×D15111yescharacteristic
308#41C22×D15111yescharacteristic
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—3021no—
312C2×Q8—3021no—
313C2×Q8—1511no—
314C2×Q8C22×D15111yescharacteristic
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—41no—
318C2×D4—3021no—
319C2×D4—3021no—
320C2×D4—6041no—
321C2×D4—6041no—
322C2×D4—1511no—
323C2×D4C22×D15111yescharacteristic
324Q16—21no—
325Q16—3021no—
326Q16—3021no—
327Q16—3021no—
328Q16—1511no—
329Q16C22⋊D15111yescharacteristic, complemented
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—3021no—
343SD16—3021no—
344SD16—3021no—
345SD16—3021no—
346SD16—1511no—
347SD16—1511no—
348SD16C22⋊D15111yescharacteristic, complemented
349SD16C22⋊D15111yescharacteristic, complemented
350D8—21no—
351D8—3021no—
352D8—3021no—
353D8—3021no—
354D8—1511no—
355D8C22⋊D15111yescharacteristic, complemented
356M16—21no—
357M16—3021no—
358M16—3021no—
359M16—3021no—
360M16—1511no—
361M16—1511no—
362M16—1511no—
363M16C22×D15111yescharacteristic
364C2×C8—21no—
365C2×C8—3021no—
366C2×C8—3021no—
367C2×C8—3021no—
368C2×C8—1511no—
369C2×C8C22×D15111yescharacteristic
370C4⋊C4—6041no—
371C42—1511no—
372C23—21no—
373C23—41no—
374C23—3021no—
375C23—6041no—
376Q8—21no—
377Q8—21no—
378Q8—41no—
379Q8—3021no—
380Q8—3021no—
381Q8—6041no—
382Q8—1511no—
383Q8D4×D15111yescharacteristic
384Q8C2×C22⋊D15111yescharacteristic
385Q8C2×C22⋊D15111yescharacteristic
386D4—21no—
387D4—21no—
388D4—21no—
389D4—21no—
390D4—21no—
391D4—41no—
392D4—41no—
393D4—41no—
394D4—3021no—
395D4—3021no—
396D4—3021no—
397D4—6041no—
398D4—6041no—
399D4—6041no—
400D4—1511no—
401D4—12082no—
402D4D4×D15111yescharacteristic
403D4C2×C22⋊D15111yescharacteristic
404D4C2×C22⋊D15111yescharacteristic
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—3021no—
413C2×C4—3021no—
414C2×C4—3021no—
415C2×C4—6041no—
416C2×C4—6041no—
417C2×C4—6041no—
418C2×C4C23×D15111yescharacteristic
419C8—21no—
420C8—3021no—
421C8—3021no—
422C8—3021no—
423C8—1511no—
424C8—1511no—
425C8C2×C22⋊D15111yescharacteristic
426C8C2×C22⋊D15111yescharacteristic
427C22—21no—
428C22—21no—
429C22—21no—
430C22—41no—
431C22—81no—
432C22—161no—
433C22—3021no—
434C22—6041no—
435C22—24161no—
436C22—12081no—
437C22#1801278411yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—41no—
442C4—3022no—
443C4—3021no—
444C4—6041no—
445C4C2×D4×D15111yescharacteristic
446C4C22×C22⋊D15111yescharacteristic
447C2—21no—
448C2—41no—
449C2—41no—
450C2—41no—
451C2—81no—
452C2—6041no—
453C2—12081no—
454C2D4×C22⋊D15111yescharacteristic
subgroupG/H
centerC2D4×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#577×C151C2
socleC2×C151D42
hypercenter#577D151
hypocenterC151#3291
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. #23753023C2semidirect
2. #23753020C2semidirect
3. #23753019C2semidirect
4. #23752583C2semidirect
5. #23752477C2semidirect
6. #23752475C2semidirect
7. #23752473C2semidirect
8. #23752472C2semidirect
9. #23752395C2semidirect
10. #23752393C2semidirect
11. #23752380C2semidirect
12. #23752378C2semidirect
13. #23752329C2semidirect
14. #23752327C2semidirect
15. #577×C151C2semidirect
17. #18012785C22semidirect
20. #18012770C22semidirect
22. #18012769C22semidirect
23. #18012769C22semidirect
34. C2×#14558993C22semidirect
36. C2×#14558992C22semidirect
38. C2×#14558991C22semidirect
40. #18012746C22semidirect
41. #18012746C22semidirect
42. #18012745C22semidirect
43. #18012737C22semidirect
45. #18012675C22semidirect
46. #18012674C22semidirect
47. #18012666C22semidirect
48. #18012666C22semidirect
49. #18012666C22semidirect
50. #18012665C22semidirect
51. #18012658C22semidirect
52. #18012657C22semidirect
53. #18012656C22semidirect
54. #18012655C22semidirect
55. C8×Dic151C22semidirect
57. H(5,𝔽2)×C151C22semidirect
59. #137×C151C22semidirect
65. C2×SD16×C151C22semidirect
66. #131×C151C22semidirect
84. #14558994D4semidirect
92. #14558992D4semidirect
98. #14558991D4semidirect
102. #14558989D4semidirect
131. Q16×C151D4semidirect
136. SD16×C151D4semidirect
137. SD16×C151D4semidirect
139. D8×C151D4semidirect
227. C151#3291semidirect
232. #577D151semidirect
247. H(5,𝔽2)C2×D151semidirect
255. #137C2×D151semidirect
277. C2×SD16C2×D151semidirect
281. #131C2×D151semidirect
329. Q16C22⋊D151semidirect
348. SD16C22⋊D151semidirect
349. SD16C22⋊D151semidirect
355. D8C22⋊D151semidirect

Maximal subgroups

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

subgroupindex
#237530232
#237530202
#237530192
#237525832
#237524772
#237524752
#237524732
#237524722
#237523952
#237523932
#237523802
#237523782
#237523292
#237523272
#577×C1512
#3291151