Finite Group Databasebeta

← #27206908

Subgroups — #27206908

Order 13184.

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#20268602C211yesmaximal, characteristic, complemented
2#20268598C211yesmaximal, characteristic, complemented
3#20268594C211yesmaximal, characteristic, complemented
4#20268179C211yesmaximal, characteristic, complemented
5#20268059C211yesmaximal, characteristic, complemented
6#20268058C211yesmaximal, characteristic, complemented
7#20268054C211yesmaximal, characteristic, complemented
8#20268052C211yesmaximal, characteristic, complemented
9#20267969C211yesmaximal, characteristic, complemented
10#20267962C211yesmaximal, characteristic, complemented
11#20267959C211yesmaximal, characteristic, complemented
12#20267957C211yesmaximal, characteristic, complemented
13#20267913C211yesmaximal, characteristic, complemented
14#20267911C211yesmaximal, characteristic, complemented
15#576×C103C211yesmaximal, characteristic, complemented
16#15693068C2211yescharacteristic, complemented
17#15693067C2211yescharacteristic, complemented
18#15693053—21no—
19#15693051—21no—
20#15693051C2211yescharacteristic, complemented
21#15693051C2211yescharacteristic, complemented
22#15693047—21no—
23#15693047—21no—
24#15693047C2211yescharacteristic, complemented
25#15693047C2211yescharacteristic, complemented
26#15693046—21no—
27#15693046C2211yescharacteristic
28#15693046C2211yescharacteristic, complemented
29#15693045—21no—
30#15693042—21no—
31#15693041—21no—
32#15693041—21no—
33#15693041C2211yescharacteristic
34C2×#13110094C2211yescharacteristic, complemented
35C2×#13110093—21no—
36C2×#13110093C2211yescharacteristic, complemented
37SD16×D103—21no—
38C2×#13110090—21no—
39C2×#13110090C2211yescharacteristic, complemented
40#15693028C2211yescharacteristic, complemented
41#15693028C2211yescharacteristic, complemented
42#15693027C2211yescharacteristic, complemented
43#15693017C2211yescharacteristic, complemented
44#15693008C2211yescharacteristic, complemented
45#15692957C2211yescharacteristic, complemented
46#15692956C2211yescharacteristic, complemented
47#15692948C2211yescharacteristic, complemented
48#15692948C2211yescharacteristic, complemented
49#15692948C2211yescharacteristic, complemented
50#15692947C2211yescharacteristic, complemented
51#15692939C2211yescharacteristic, complemented
52#15692938C2211yescharacteristic, complemented
53#15692938C2211yescharacteristic, complemented
54#15692937C2211yescharacteristic, complemented
55#15692931C2211yescharacteristic, complemented
56H(5,𝔽2)×C103C2211yescharacteristic
57H(5,𝔽2)×C103C2211yescharacteristic, complemented
58AGL(1,ℤ/8)×C103—21no—
59AGL(1,ℤ/8)×C103—21no—
60AGL(1,ℤ/8)×C103C2211yescharacteristic
61AGL(1,ℤ/8)×C103C2211yescharacteristic, complemented
62#135×C103—21no—
63#135×C103C2211yescharacteristic
64C2×D8×C103—21no—
65C2×D8×C103C2211yescharacteristic, complemented
66#131×C103C2211yescharacteristic, complemented
67#13110106—21no—
68#13110105—21no—
69#13110105—21no—
70#13110105C2311yescharacteristic
71#13110104—21no—
72#13110104—41no—
73C2×Dic206—21no—
74C2×Dic206C2311yescharacteristic
75Q8×D103—21no—
76C2×D412—21no—
77C2×D412C2311yescharacteristic
78C2×C22⋊D103—41no—
79D4×D103—21no—
80D4×D103—41no—
81#13110095—21no—
82#13110095—21no—
83#13110095D411yescharacteristic, complemented
84#13110094—21no—
85#13110094—21no—
86#13110093—21no—
87#13110093—21no—
88#13110093—21no—
89#13110093—21no—
90#13110093—21no—
91#13110093—21no—
92#13110093D411yescharacteristic, complemented
93#13110092—21no—
94#13110092—21no—
95#13110092D411yescharacteristic, complemented
96#13110090—21no—
97#13110090—21no—
98#13110090—21no—
99#13110090—21no—
100#13110090—21no—
101#13110090—21no—
102#13110090D411yescharacteristic, complemented
103#13110089—21no—
104#13110089—21no—
105#13110089C2311yescharacteristic
106#13110089C2311yescharacteristic
107#13110089C2311yescharacteristic
108#13110088—21no—
109C2×C103⋊C8—21no—
110C2×C103⋊C8—21no—
111C2×C103⋊C8C2311yescharacteristic
112C8×D103—21no—
113C22⋊Dic103—41no—
114C4×Dic103C2311yescharacteristic
115#41×C103—21no—
116#41×C103—21no—
117#41×C103—21no—
118#41×C103—21no—
119#41×C103C2311yescharacteristic
120#41×C103C2311yescharacteristic
121#41×C103C2311yescharacteristic
122C2×D4×C103—21no—
123C2×D4×C103—21no—
124C2×D4×C103—21no—
125C2×D4×C103—21no—
126C2×D4×C103—41no—
127C2×D4×C103—41no—
128C2×D4×C103C2311yescharacteristic
129C2×D4×C103C2311yescharacteristic
130Q16×C103D411yescharacteristic, complemented
131SD16×C103—21no—
132SD16×C103—21no—
133SD16×C103D411yescharacteristic, complemented
134SD16×C103D411yescharacteristic, complemented
135D8×C103—21no—
136D8×C103—21no—
137D8×C103—21no—
138D8×C103—21no—
139D8×C103D411yescharacteristic, complemented
140M16×C103—21no—
141M16×C103C2311yescharacteristic
142C2×C8×C103—21no—
143C2×C8×C103C2311yescharacteristic
144C23×C103—21no—
145C23×C103—21no—
146C23×C103—41no—
147C23×C103—41no—
148C22×D103—21no—
149C22×D103—41no—
150Q8×C103C2×D411yescharacteristic
151Q8×C103C2×D411yescharacteristic
152Q8×C103C2×D411yescharacteristic
153D4×C103—21no—
154D4×C103—21no—
155D4×C103—21no—
156D4×C103—21no—
157D4×C103—21no—
158D4×C103—21no—
159D4×C103—21no—
160D4×C103—41no—
161D4×C103—41no—
162D4×C103—41no—
163D4×C103—41no—
164D4×C103C2×D411yescharacteristic
165D4×C103C2×D411yescharacteristic
166D4×C103C2×D411yescharacteristic
167C2×C4×C103—21no—
168C2×C4×C103—21no—
169C2×C4×C103—21no—
170C2×C4×C103—41no—
171C2×C4×C103—41no—
172C2×C4×C103C2411yescharacteristic
173C22⋊D103—21no—
174C22⋊D103—41no—
175C22⋊D103—41no—
176C22⋊D103—82no—
177C2×Dic103—21no—
178C2×Dic103—21no—
179C2×Dic103—41no—
180D412—21no—
181D412—21no—
182D412—41no—
183D412C2×D411yescharacteristic
184C4×D103—21no—
185C4×D103—41no—
186C4×D103—41no—
187Dic206—21no—
188Dic206—21no—
189Dic206—41no—
190Dic206C2×D411yescharacteristic
191C8×C103—21no—
192C8×C103C2×D411yescharacteristic
193C8×C103C2×D411yescharacteristic
194C103⋊C8—21no—
195C103⋊C8—21no—
196C103⋊C8—21no—
197C103⋊C8C2×D411yescharacteristic
198C103⋊C8C2×D411yescharacteristic
199C22×C103—21no—
200C22×C103—21no—
201C22×C103—21no—
202C22×C103—41no—
203C22×C103—41no—
204C22×C103—81no—
205C22×C103—81no—
206C22×C103—161no—
207C22×C103—161no—
208C22×C103H(5,𝔽2)11yescharacteristic
209C2×D103—21no—
210C2×D103—41no—
211C2×D103—81no—
212C2×D103—161no—
213C4×C103—21no—
214C4×C103—21no—
215C4×C103—21no—
216C4×C103C22×D411yescharacteristic
217C4×C103C22×D411yescharacteristic
218Dic103—21no—
219Dic103—41no—
220Dic103—41no—
221C2×C103—21no—
222C2×C103—41no—
223C2×C103—41no—
224C2×C103—41no—
225C2×C103—81no—
226C2×C103—81no—
227C2×C103D4211yescharacteristic
228D103—41no—
229D103—81no—
230#3288—1031nomaximal, Sylow
231C103#328811yescharacteristic, complemented, Sylow
232#577—1031no—
233#577—1031no—
234#576—1031no—
235#576D10311yescharacteristic, complemented
236#496—1031no—
237#472—1031no—
238#472—1031no—
239#471—1031no—
240#471—1031no—
241#455—1031no—
242#454—1031no—
243#453—1031no—
244#453—1031no—
245#444—1031no—
246#444—1031no—
2472−1+4—1031no—
248H(5,𝔽2)—1031no—
249H(5,𝔽2)C2×D10311yescharacteristic
250H(5,𝔽2)C2×D10311yescharacteristic, complemented
251#137—1031no—
252#137—1031no—
253#137—2061no—
254#137—2061no—
255AGL(1,ℤ/8)—21no—
256AGL(1,ℤ/8)—21no—
257AGL(1,ℤ/8)—1031no—
258AGL(1,ℤ/8)—1031no—
259AGL(1,ℤ/8)—1031no—
260AGL(1,ℤ/8)—1031no—
261AGL(1,ℤ/8)—2061no—
262AGL(1,ℤ/8)—2061no—
263AGL(1,ℤ/8)—2061no—
264AGL(1,ℤ/8)—2061no—
265AGL(1,ℤ/8)C2×D10311yescharacteristic
266AGL(1,ℤ/8)C2×D10311yescharacteristic, complemented
267#135—21no—
268#135—1031no—
269#135—2061no—
270#135—2061no—
271#135—2061no—
272#135C2×D10311yescharacteristic
273C2×SD16—1031no—
274C2×SD16—1031no—
275C2×SD16—2061no—
276C2×SD16—2061no—
277C2×D8—21no—
278C2×D8—1031no—
279C2×D8—2061no—
280C2×D8C2×D10311yescharacteristic, complemented
281#131—1031no—
282#131—1031no—
283#131—1031no—
284#131C2×D10311yescharacteristic, complemented
285#127—1031no—
286#124—1031no—
287#108—1031no—
288#108—1031no—
289#104—1031no—
290#104—1031no—
291#104—1031no—
292#104—1031no—
293#101—1031no—
294#100—1031no—
295#100—1031no—
296#100—1031no—
297#97—1031no—
298#41—21no—
299#41—21no—
300#41—21no—
301#41—21no—
302#41—1031no—
303#41—4121no—
304#41—2061no—
305#41—2061no—
306#41—2061no—
307#41—2061no—
308#41C22×D10311yescharacteristic
309#41C22×D10311yescharacteristic
310#41C22×D10311yescharacteristic
311C2×Q8—1031no—
312C2×Q8—2061no—
313C2×Q8—2061no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—21no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—1031no—
321C2×D4—4121no—
322C2×D4—4121no—
323C2×D4—2061no—
324C2×D4—2061no—
325C2×D4C22×D10311yescharacteristic
326C2×D4C22×D10311yescharacteristic
327Q16—1031no—
328Q16—2061no—
329Q16—2061no—
330Q16C22⋊D10311yescharacteristic, complemented
331SD16—21no—
332SD16—21no—
333SD16—1031no—
334SD16—1031no—
335SD16—2061no—
336SD16—2061no—
337SD16—2061no—
338SD16—2061no—
339SD16—2061no—
340SD16—2061no—
341SD16—2061no—
342SD16—2061no—
343SD16—2061no—
344SD16—2061no—
345SD16C22⋊D10311yescharacteristic, complemented
346SD16C22⋊D10311yescharacteristic, complemented
347D8—21no—
348D8—21no—
349D8—21no—
350D8—21no—
351D8—1031no—
352D8—2061no—
353D8—2061no—
354D8—2061no—
355D8—2061no—
356D8—2061no—
357D8—2061no—
358D8C22⋊D10311yescharacteristic, complemented
359M16—21no—
360M16—1031no—
361M16—1031no—
362M16—1031no—
363M16—2061no—
364M16—2061no—
365M16—2061no—
366M16C22×D10311yescharacteristic
367C2×C8—21no—
368C2×C8—1031no—
369C2×C8—2061no—
370C2×C8—2061no—
371C2×C8—2061no—
372C2×C8C22×D10311yescharacteristic
373C22⋊C4—4121no—
374C42—1031no—
375C23—21no—
376C23—21no—
377C23—41no—
378C23—41no—
379C23—4121no—
380C23—2061no—
381Q8—1031no—
382Q8—4121no—
383Q8—2061no—
384Q8—2061no—
385Q8D4×D10311yescharacteristic
386Q8C2×C22⋊D10311yescharacteristic
387Q8C2×C22⋊D10311yescharacteristic
388D4—21no—
389D4—21no—
390D4—21no—
391D4—21no—
392D4—21no—
393D4—21no—
394D4—21no—
395D4—41no—
396D4—41no—
397D4—41no—
398D4—41no—
399D4—8242no—
400D4—1031no—
401D4—4121no—
402D4—4121no—
403D4—4121no—
404D4—2061no—
405D4—2061no—
406D4—2061no—
407D4D4×D10311yescharacteristic
408D4C2×C22⋊D10311yescharacteristic
409D4C2×C22⋊D10311yescharacteristic
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—4121no—
416C2×C4—4121no—
417C2×C4—4121no—
418C2×C4—2061no—
419C2×C4—2061no—
420C2×C4—2061no—
421C2×C4C23×D10311yescharacteristic
422C8—21no—
423C8—1031no—
424C8—1031no—
425C8—2061no—
426C8—2061no—
427C8—2061no—
428C8C2×C22⋊D10311yescharacteristic
429C8C2×C22⋊D10311yescharacteristic
430C22—21no—
431C22—21no—
432C22—21no—
433C22—41no—
434C22—41no—
435C22—81no—
436C22—81no—
437C22—161no—
438C22—161no—
439C22—8241no—
440C22—16481no—
441C22—4121no—
442C22—2061no—
443C22#1569306611yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—4121no—
448C4—4121no—
449C4—2061no—
450C4C2×D4×D10311yescharacteristic
451C4C22×C22⋊D10311yescharacteristic
452C2—21no—
453C2—41no—
454C2—41no—
455C2—41no—
456C2—81no—
457C2—81no—
458C2—8241no—
459C2—4121no—
460C2D4×C22⋊D10311yescharacteristic
subgroupG/H
centerC2D4×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#576×C103C2
socleC2×C103D42
hypercenter#576D103
hypocenterC103#3288
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C2×C4 ◁ #576

Complements

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

NH ≅ G/Ntype
1. #20268602C2semidirect
2. #20268598C2semidirect
3. #20268594C2semidirect
4. #20268179C2semidirect
5. #20268059C2semidirect
6. #20268058C2semidirect
7. #20268054C2semidirect
8. #20268052C2semidirect
9. #20267969C2semidirect
10. #20267962C2semidirect
11. #20267959C2semidirect
12. #20267957C2semidirect
13. #20267913C2semidirect
14. #20267911C2semidirect
15. #576×C103C2semidirect
16. #15693068C22semidirect
17. #15693067C22semidirect
20. #15693051C22semidirect
21. #15693051C22semidirect
24. #15693047C22semidirect
25. #15693047C22semidirect
28. #15693046C22semidirect
34. C2×#13110094C22semidirect
36. C2×#13110093C22semidirect
39. C2×#13110090C22semidirect
40. #15693028C22semidirect
41. #15693028C22semidirect
42. #15693027C22semidirect
43. #15693017C22semidirect
44. #15693008C22semidirect
45. #15692957C22semidirect
46. #15692956C22semidirect
47. #15692948C22semidirect
48. #15692948C22semidirect
49. #15692948C22semidirect
50. #15692947C22semidirect
51. #15692939C22semidirect
52. #15692938C22semidirect
53. #15692938C22semidirect
54. #15692937C22semidirect
55. #15692931C22semidirect
57. H(5,𝔽2)×C103C22semidirect
61. AGL(1,ℤ/8)×C103C22semidirect
65. C2×D8×C103C22semidirect
66. #131×C103C22semidirect
83. #13110095D4semidirect
92. #13110093D4semidirect
95. #13110092D4semidirect
102. #13110090D4semidirect
130. Q16×C103D4semidirect
133. SD16×C103D4semidirect
134. SD16×C103D4semidirect
139. D8×C103D4semidirect
231. C103#3288semidirect
235. #576D103semidirect
250. H(5,𝔽2)C2×D103semidirect
266. AGL(1,ℤ/8)C2×D103semidirect
280. C2×D8C2×D103semidirect
284. #131C2×D103semidirect
330. Q16C22⋊D103semidirect
345. SD16C22⋊D103semidirect
346. SD16C22⋊D103semidirect
358. D8C22⋊D103semidirect

Maximal subgroups

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

subgroupindex
#202686022
#202685982
#202685942
#202681792
#202680592
#202680582
#202680542
#202680522
#202679692
#202679622
#202679592
#202679572
#202679132
#202679112
#576×C1032
#3288103