Finite Group Databasebeta

← #27182894

Subgroups — #27182894

Order 12928.

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#20265985C211yesmaximal, characteristic, complemented
2#20265980C211yesmaximal, characteristic, complemented
3#20265979C211yesmaximal, characteristic, complemented
4#20265563C211yesmaximal, characteristic, complemented
5#20265447C211yesmaximal, characteristic, complemented
6#20265445C211yesmaximal, characteristic, complemented
7#20265442C211yesmaximal, characteristic, complemented
8#20265437C211yesmaximal, characteristic, complemented
9#20265353C211yesmaximal, characteristic, complemented
10#20265350C211yesmaximal, characteristic, complemented
11#20265345C211yesmaximal, characteristic, complemented
12#20265343C211yesmaximal, characteristic, complemented
13#20265299C211yesmaximal, characteristic, complemented
14#20265297C211yesmaximal, characteristic, complemented
15#577×C101C211yesmaximal, characteristic, complemented
16#15692301C2211yescharacteristic
17#15692301C2211yescharacteristic, complemented
18#15692286—21no—
19#15692286C2211yescharacteristic, complemented
20#15692282—21no—
21#15692282—21no—
22#15692281—21no—
23#15692281C2211yescharacteristic
24#15692280—21no—
25#15692280—21no—
26#15692280C2211yescharacteristic
27#15692280C2211yescharacteristic, complemented
28#15692280C2211yescharacteristic, complemented
29#15692280C2211yescharacteristic, complemented
30#15692278—21no—
31#15692275—21no—
32#15692275—21no—
33#15692275C2211yescharacteristic
34C2×#13108061—21no—
35C2×#13108061C2211yescharacteristic, complemented
36C2×D808C2211yescharacteristic, complemented
37C2×#13108059—21no—
38C2×#13108059C2211yescharacteristic, complemented
39D8×D101—21no—
40#15692262C2211yescharacteristic, complemented
41#15692262C2211yescharacteristic, complemented
42#15692261C2211yescharacteristic, complemented
43#15692251C2211yescharacteristic, complemented
44#15692244C2211yescharacteristic, complemented
45#15692191C2211yescharacteristic, complemented
46#15692190C2211yescharacteristic, complemented
47#15692182C2211yescharacteristic, complemented
48#15692182C2211yescharacteristic, complemented
49#15692182C2211yescharacteristic, complemented
50#15692181C2211yescharacteristic, complemented
51#15692174C2211yescharacteristic, complemented
52#15692172C2211yescharacteristic, complemented
53#15692171C2211yescharacteristic, complemented
54#15692171C2211yescharacteristic, complemented
55#15692165C2211yescharacteristic, complemented
562−1+4×C101C2211yescharacteristic, complemented
57H(5,𝔽2)×C101C2211yescharacteristic, complemented
58#137×C101—21no—
59#137×C101C2211yescharacteristic, complemented
60AGL(1,ℤ/8)×C101—21no—
61AGL(1,ℤ/8)×C101C2211yescharacteristic, complemented
62#135×C101—21no—
63#135×C101C2211yescharacteristic
64C2×SD16×C101—21no—
65C2×SD16×C101C2211yescharacteristic, complemented
66#131×C101C2211yescharacteristic, complemented
67#13108075—21no—
68#13108075—21no—
69#13108074—21no—
70#13108074—21no—
71#13108074C2311yescharacteristic
72C2×D404—21no—
73C2×D404—21no—
74C2×D404C2311yescharacteristic
75C2×D404C2311yescharacteristic
76C2×C22⋊D101—41no—
77D4×D101—21no—
78D4×D101—21no—
79D4×D101—41no—
80D4×D101—41no—
81#13108064—21no—
82#13108064D411yescharacteristic, complemented
83#13108062—21no—
84#13108062D411yescharacteristic, complemented
85#13108061—21no—
86#13108061—21no—
87#13108061—21no—
88#13108061—21no—
89#13108061—21no—
90#13108061—21no—
91#13108061—21no—
92#13108061D411yescharacteristic, complemented
93D808—21no—
94D808—21no—
95#13108059—21no—
96#13108059—21no—
97#13108059—21no—
98#13108059—21no—
99#13108059—21no—
100#13108059—21no—
101#13108059—21no—
102#13108059D411yescharacteristic, complemented
103#13108058—21no—
104#13108058—21no—
105#13108058C2311yescharacteristic
106#13108058C2311yescharacteristic
107#13108058C2311yescharacteristic
108#13108057—21no—
109C2×#11717579—21no—
110C2×#11717579—21no—
111C2×#11717579C2311yescharacteristic
112C8×D101—21no—
113#13108051—41no—
114C4×Dic101C2311yescharacteristic
115#41×C101—21no—
116#41×C101—21no—
117#41×C101—21no—
118#41×C101—21no—
119#41×C101—41no—
120#41×C101C2311yescharacteristic
121#41×C101C2311yescharacteristic
122#41×C101C2311yescharacteristic
123C2×Q8×C101—21no—
124C2×Q8×C101—21no—
125C2×Q8×C101C2311yescharacteristic
126C2×D4×C101—21no—
127C2×D4×C101—21no—
128C2×D4×C101—41no—
129C2×D4×C101C2311yescharacteristic
130Q16×C101—21no—
131Q16×C101D411yescharacteristic, complemented
132SD16×C101—21no—
133SD16×C101—21no—
134SD16×C101—21no—
135SD16×C101—21no—
136SD16×C101D411yescharacteristic, complemented
137SD16×C101D411yescharacteristic, complemented
138D8×C101—21no—
139D8×C101D411yescharacteristic, complemented
140M16×C101—21no—
141M16×C101C2311yescharacteristic
142C2×C8×C101—21no—
143C2×C8×C101C2311yescharacteristic
144C23×C101—21no—
145C23×C101—41no—
146C22×D101—21no—
147C22×D101—21no—
148C22×D101—41no—
149C22×D101—41no—
150Q8×C101—21no—
151Q8×C101—21no—
152Q8×C101—41no—
153Q8×C101C2×D411yescharacteristic
154Q8×C101C2×D411yescharacteristic
155Q8×C101C2×D411yescharacteristic
156D4×C101—21no—
157D4×C101—21no—
158D4×C101—21no—
159D4×C101—21no—
160D4×C101—21no—
161D4×C101—41no—
162D4×C101—41no—
163D4×C101—41no—
164D4×C101C2×D411yescharacteristic
165D4×C101C2×D411yescharacteristic
166D4×C101C2×D411yescharacteristic
167C2×C4×C101—21no—
168C2×C4×C101—21no—
169C2×C4×C101—21no—
170C2×C4×C101—21no—
171C2×C4×C101—41no—
172C2×C4×C101—41no—
173C2×C4×C101—41no—
174C2×C4×C101C2411yescharacteristic
175C22⋊D101—21no—
176C22⋊D101—41no—
177C22⋊D101—41no—
178C22⋊D101—82no—
179C2×Dic101—21no—
180D404—21no—
181D404—21no—
182D404—21no—
183D404—21no—
184D404—41no—
185D404—41no—
186D404C2×D411yescharacteristic
187C4×D101—21no—
188C4×D101—41no—
189C4×D101—41no—
190Dic202C2×D411yescharacteristic
191C8×C101—21no—
192C8×C101C2×D411yescharacteristic
193C8×C101C2×D411yescharacteristic
194#11717579—21no—
195#11717579—21no—
196#11717579—21no—
197#11717579C2×D411yescharacteristic
198#11717579C2×D411yescharacteristic
199C22×C101—21no—
200C22×C101—21no—
201C22×C101—21no—
202C22×C101—41no—
203C22×C101—81no—
204C22×C101—161no—
205C22×C101H(5,𝔽2)11yescharacteristic
206C2×D101—21no—
207C2×D101—41no—
208C2×D101—41no—
209C2×D101—81no—
210C2×D101—81no—
211C2×D101—161no—
212C2×D101—161no—
213C4×C101—21no—
214C4×C101—21no—
215C4×C101—21no—
216C4×C101—41no—
217C4×C101C22×D411yescharacteristic
218C4×C101C22×D411yescharacteristic
219Dic101—21no—
220Dic101—41no—
221C2×C101—21no—
222C2×C101—41no—
223C2×C101—41no—
224C2×C101—41no—
225C2×C101—81no—
226C2×C101D4211yescharacteristic
227D101—41no—
228D101—81no—
229D101—81no—
230#3288—1011nomaximal, Sylow
231C101#328811yescharacteristic, complemented, Sylow
232#577—1011no—
233#577D10111yescharacteristic, complemented
234#576—1011no—
235#576—1011no—
236#496—1011no—
237#472—1011no—
238#472—1011no—
239#471—1011no—
240#471—1011no—
241#455—1011no—
242#454—1011no—
243#453—1011no—
244#453—1011no—
245#444—1011no—
246#444—1011no—
2472−1+4C2×D10111yescharacteristic, complemented
248H(5,𝔽2)—1011no—
249H(5,𝔽2)—1011no—
250H(5,𝔽2)C2×D10111yescharacteristic, complemented
251#137—21no—
252#137—1011no—
253#137—2021no—
254#137C2×D10111yescharacteristic, complemented
255AGL(1,ℤ/8)—21no—
256AGL(1,ℤ/8)—1011no—
257AGL(1,ℤ/8)—1011no—
258AGL(1,ℤ/8)—1011no—
259AGL(1,ℤ/8)—1011no—
260AGL(1,ℤ/8)—1011no—
261AGL(1,ℤ/8)—2021no—
262AGL(1,ℤ/8)—2021no—
263AGL(1,ℤ/8)—2021no—
264AGL(1,ℤ/8)—2021no—
265AGL(1,ℤ/8)—2021no—
266AGL(1,ℤ/8)C2×D10111yescharacteristic, complemented
267#135—21no—
268#135—1011no—
269#135—2021no—
270#135—2021no—
271#135—2021no—
272#135C2×D10111yescharacteristic
273C2×SD16—21no—
274C2×SD16—1011no—
275C2×SD16—2021no—
276C2×SD16C2×D10111yescharacteristic, complemented
277C2×D8—1011no—
278C2×D8—1011no—
279C2×D8—2021no—
280C2×D8—2021no—
281#131—1011no—
282#131—1011no—
283#131—1011no—
284#131C2×D10111yescharacteristic, complemented
285#127—1011no—
286#124—1011no—
287#108—1011no—
288#108—1011no—
289#104—1011no—
290#104—1011no—
291#104—1011no—
292#104—1011no—
293#101—1011no—
294#100—1011no—
295#100—1011no—
296#100—1011no—
297#97—1011no—
298#41—21no—
299#41—21no—
300#41—21no—
301#41—21no—
302#41—41no—
303#41—1011no—
304#41—2021no—
305#41—2021no—
306#41—2021no—
307#41—2021no—
308#41C22×D10111yescharacteristic
309#41C22×D10111yescharacteristic
310#41C22×D10111yescharacteristic
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8C22×D10111yescharacteristic
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4—1011no—
318C2×D4—1011no—
319C2×D4—4041no—
320C2×D4—4041no—
321C2×D4—4041no—
322C2×D4—2021no—
323C2×D4—2021no—
324C2×D4—2021no—
325C2×D4—2021no—
326C2×D4C22×D10111yescharacteristic
327Q16—21no—
328Q16—1011no—
329Q16—2021no—
330Q16C22⋊D10111yescharacteristic, complemented
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—21no—
335SD16—1011no—
336SD16—1011no—
337SD16—2021no—
338SD16—2021no—
339SD16—2021no—
340SD16—2021no—
341SD16—2021no—
342SD16—2021no—
343SD16—2021no—
344SD16—2021no—
345SD16C22⋊D10111yescharacteristic, complemented
346SD16C22⋊D10111yescharacteristic, complemented
347D8—21no—
348D8—1011no—
349D8—2021no—
350D8—2021no—
351D8—2021no—
352D8—2021no—
353D8—2021no—
354D8—2021no—
355D8—2021no—
356D8—2021no—
357D8—2021no—
358D8C22⋊D10111yescharacteristic, complemented
359M16—21no—
360M16—1011no—
361M16—1011no—
362M16—1011no—
363M16—2021no—
364M16—2021no—
365M16—2021no—
366M16C22×D10111yescharacteristic
367C2×C8—21no—
368C2×C8—1011no—
369C2×C8—2021no—
370C2×C8—2021no—
371C2×C8—2021no—
372C2×C8C22×D10111yescharacteristic
373C22⋊C4—4041no—
374C42—1011no—
375C23—21no—
376C23—41no—
377C23—4041no—
378C23—4041no—
379C23—2021no—
380C23—2021no—
381Q8—21no—
382Q8—21no—
383Q8—41no—
384Q8—1011no—
385Q8D4×D10111yescharacteristic
386Q8C2×C22⋊D10111yescharacteristic
387Q8C2×C22⋊D10111yescharacteristic
388D4—21no—
389D4—21no—
390D4—21no—
391D4—21no—
392D4—21no—
393D4—41no—
394D4—41no—
395D4—41no—
396D4—8082no—
397D4—1011no—
398D4—4041no—
399D4—4041no—
400D4—4041no—
401D4—4041no—
402D4—2021no—
403D4—2021no—
404D4—2021no—
405D4—2021no—
406D4—2021no—
407D4D4×D10111yescharacteristic
408D4C2×C22⋊D10111yescharacteristic
409D4C2×C22⋊D10111yescharacteristic
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—4041no—
418C2×C4—4041no—
419C2×C4—2021no—
420C2×C4—2021no—
421C2×C4C23×D10111yescharacteristic
422C8—21no—
423C8—1011no—
424C8—1011no—
425C8—2021no—
426C8—2021no—
427C8—2021no—
428C8C2×C22⋊D10111yescharacteristic
429C8C2×C22⋊D10111yescharacteristic
430C22—21no—
431C22—21no—
432C22—21no—
433C22—41no—
434C22—81no—
435C22—161no—
436C22—8081no—
437C22—8081no—
438C22—16161no—
439C22—16161no—
440C22—4041no—
441C22—4041no—
442C22—2021no—
443C22#1569230011yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—41no—
448C4—4041no—
449C4—2021no—
450C4C2×D4×D10111yescharacteristic
451C4C22×C22⋊D10111yescharacteristic
452C2—21no—
453C2—41no—
454C2—41no—
455C2—41no—
456C2—81no—
457C2—8081no—
458C2—8081no—
459C2—4041no—
460C2D4×C22⋊D10111yescharacteristic
subgroupG/H
centerC2D4×C22⋊D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#577×C101C2
socleC2×C101D42
hypercenter#577D101
hypocenterC101#3288
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C2×C4 ◁ #577

Complements

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

NH ≅ G/Ntype
1. #20265985C2semidirect
2. #20265980C2semidirect
3. #20265979C2semidirect
4. #20265563C2semidirect
5. #20265447C2semidirect
6. #20265445C2semidirect
7. #20265442C2semidirect
8. #20265437C2semidirect
9. #20265353C2semidirect
10. #20265350C2semidirect
11. #20265345C2semidirect
12. #20265343C2semidirect
13. #20265299C2semidirect
14. #20265297C2semidirect
15. #577×C101C2semidirect
17. #15692301C22semidirect
19. #15692286C22semidirect
27. #15692280C22semidirect
28. #15692280C22semidirect
29. #15692280C22semidirect
35. C2×#13108061C22semidirect
36. C2×D808C22semidirect
38. C2×#13108059C22semidirect
40. #15692262C22semidirect
41. #15692262C22semidirect
42. #15692261C22semidirect
43. #15692251C22semidirect
44. #15692244C22semidirect
45. #15692191C22semidirect
46. #15692190C22semidirect
47. #15692182C22semidirect
48. #15692182C22semidirect
49. #15692182C22semidirect
50. #15692181C22semidirect
51. #15692174C22semidirect
52. #15692172C22semidirect
53. #15692171C22semidirect
54. #15692171C22semidirect
55. #15692165C22semidirect
56. 2−1+4×C101C22semidirect
57. H(5,𝔽2)×C101C22semidirect
59. #137×C101C22semidirect
61. AGL(1,ℤ/8)×C101C22semidirect
65. C2×SD16×C101C22semidirect
66. #131×C101C22semidirect
82. #13108064D4semidirect
84. #13108062D4semidirect
92. #13108061D4semidirect
102. #13108059D4semidirect
131. Q16×C101D4semidirect
136. SD16×C101D4semidirect
137. SD16×C101D4semidirect
139. D8×C101D4semidirect
231. C101#3288semidirect
233. #577D101semidirect
247. 2−1+4C2×D101semidirect
250. H(5,𝔽2)C2×D101semidirect
254. #137C2×D101semidirect
266. AGL(1,ℤ/8)C2×D101semidirect
276. C2×SD16C2×D101semidirect
284. #131C2×D101semidirect
330. Q16C22⋊D101semidirect
345. SD16C22⋊D101semidirect
346. SD16C22⋊D101semidirect
358. D8C22⋊D101semidirect

Maximal subgroups

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

subgroupindex
#202659852
#202659802
#202659792
#202655632
#202654472
#202654452
#202654422
#202654372
#202653532
#202653502
#202653452
#202653432
#202652992
#202652972
#577×C1012
#3288101