Finite Group Databasebeta

← #31818184

Subgroups — #31818184

Order 17792.

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#22581768C211yesmaximal, characteristic, complemented
2#22581760C211yesmaximal, characteristic, complemented
3#22581756C211yesmaximal, characteristic, complemented
4#22581334C211yesmaximal, characteristic, complemented
5#22581226C211yesmaximal, characteristic, complemented
6#22581221C211yesmaximal, characteristic, complemented
7#22581216C211yesmaximal, characteristic, complemented
8#22581213C211yesmaximal, characteristic, complemented
9#22581131C211yesmaximal, characteristic, complemented
10#22581129C211yesmaximal, characteristic, complemented
11#22581126C211yesmaximal, characteristic, complemented
12#22581124C211yesmaximal, characteristic, complemented
13#22581070C211yesmaximal, characteristic, complemented
14#22581068C211yesmaximal, characteristic, complemented
15#577×C139C211yesmaximal, characteristic, complemented
16#17984889C2211yescharacteristic, complemented
17#17984888C2211yescharacteristic
18#17984874—21no—
19#17984873—21no—
20#17984873C2211yescharacteristic, complemented
21#17984872—21no—
22#17984872C2211yescharacteristic
23#17984872C2211yescharacteristic, complemented
24#17984868—21no—
25#17984868C2211yescharacteristic
26#17984867—21no—
27#17984867C2211yescharacteristic
28#17984867C2211yescharacteristic, complemented
29#17984866—21no—
30#17984863—21no—
31#17984862—21no—
32#17984862—21no—
33#17984862C2211yescharacteristic
34C2×#14555775—21no—
35C2×#14555775C2211yescharacteristic, complemented
36C2×#14555774C2211yescharacteristic, complemented
37SD16×D139—21no—
38C2×#14555770—21no—
39C2×#14555770C2211yescharacteristic
40#17984849C2211yescharacteristic
41#17984849C2211yescharacteristic, complemented
42#17984848C2211yescharacteristic, complemented
43#17984831C2211yescharacteristic, complemented
44#17984829C2211yescharacteristic, complemented
45#17984778C2211yescharacteristic, complemented
46#17984777C2211yescharacteristic, complemented
47#17984769C2211yescharacteristic
48#17984769C2211yescharacteristic, complemented
49#17984769C2211yescharacteristic, complemented
50#17984768C2211yescharacteristic, complemented
51#17984761C2211yescharacteristic, complemented
52#17984760C2211yescharacteristic, complemented
53#17984759C2211yescharacteristic, complemented
54#17984758C2211yescharacteristic, complemented
55C8×Dic139C2211yescharacteristic, complemented
562−1+4×C139C2211yescharacteristic, complemented
57H(5,𝔽2)×C139C2211yescharacteristic
58#137×C139—21no—
59#137×C139C2211yescharacteristic
60AGL(1,ℤ/8)×C139—21no—
61AGL(1,ℤ/8)×C139C2211yescharacteristic, complemented
62#135×C139—21no—
63#135×C139C2211yescharacteristic
64C2×SD16×C139—21no—
65C2×SD16×C139C2211yescharacteristic, complemented
66#131×C139C2211yescharacteristic, complemented
67#14555786—21no—
68#14555785—21no—
69#14555785—21no—
70#14555785C2311yescharacteristic
71#14555784—21no—
72#14555784—41no—
73C2×Dic278—21no—
74C2×Dic278C2311yescharacteristic
75Q8×D139—21no—
76C2×D556—21no—
77C2×D556C2311yescharacteristic
78D4×D139—21no—
79D4×D139—41no—
80#14555775—21no—
81#14555775—21no—
82#14555775—21no—
83#14555775—21no—
84#14555775—21no—
85#14555775D411yescharacteristic
86#14555774—21no—
87#14555774—21no—
88#14555773—21no—
89#14555773—21no—
90#14555773—21no—
91#14555773D411yescharacteristic
92#14555772—21no—
93#14555772—21no—
94#14555772—21no—
95#14555772D411yescharacteristic
96#14555770—21no—
97#14555770—21no—
98#14555770—21no—
99#14555770—21no—
100#14555770—21no—
101#14555770D411yescharacteristic
102#14555769—21no—
103#14555769—21no—
104#14555769C2311yescharacteristic
105#14555769C2311yescharacteristic
106#14555769C2311yescharacteristic
107#14555768—21no—
108C2×C139⋊C8—21no—
109C2×C139⋊C8—21no—
110C2×C139⋊C8C2311yescharacteristic
111C8×D139—21no—
112C22⋊Dic139—41no—
113(C2×D139)⋊C4—41no—
114C4×Dic139C2311yescharacteristic
115#41×C139—21no—
116#41×C139—21no—
117#41×C139—21no—
118#41×C139—21no—
119#41×C139—41no—
120#41×C139C2311yescharacteristic
121#41×C139C2311yescharacteristic
122#41×C139C2311yescharacteristic
123C2×Q8×C139—21no—
124C2×Q8×C139—21no—
125C2×Q8×C139C2311yescharacteristic
126C2×D4×C139—21no—
127C2×D4×C139—21no—
128C2×D4×C139—41no—
129C2×D4×C139C2311yescharacteristic
130Q16×C139—21no—
131Q16×C139D411yescharacteristic
132SD16×C139—21no—
133SD16×C139—21no—
134SD16×C139—21no—
135SD16×C139—21no—
136SD16×C139D411yescharacteristic
137SD16×C139D411yescharacteristic
138D8×C139—21no—
139D8×C139D411yescharacteristic
140M16×C139—21no—
141M16×C139C2311yescharacteristic
142C2×C8×C139—21no—
143C2×C8×C139C2311yescharacteristic
144C22×D139—21no—
145C22×D139—41no—
146Dic278—21no—
147Dic278—21no—
148Dic278—41no—
149Dic278C2×D411yescharacteristic
150D556—21no—
151D556—21no—
152D556—41no—
153D556C2×D411yescharacteristic
154C22⋊D139—21no—
155C22⋊D139—41no—
156C22⋊D139—41no—
157C2×Dic139—21no—
158C2×Dic139—21no—
159C2×Dic139—41no—
160C4×D139—21no—
161C4×D139—41no—
162C4×D139—41no—
163C139⋊C8—21no—
164C139⋊C8—21no—
165C139⋊C8—21no—
166C139⋊C8C2×D411yescharacteristic
167C139⋊C8C2×D411yescharacteristic
168C23×C139—21no—
169C23×C139—41no—
170Q8×C139—21no—
171Q8×C139—21no—
172Q8×C139—41no—
173Q8×C139C2×D411yescharacteristic
174Q8×C139C2×D411yescharacteristic
175Q8×C139C2×D411yescharacteristic
176D4×C139—21no—
177D4×C139—21no—
178D4×C139—21no—
179D4×C139—21no—
180D4×C139—21no—
181D4×C139—41no—
182D4×C139—41no—
183D4×C139—41no—
184D4×C139C2×D411yescharacteristic
185D4×C139C2×D411yescharacteristic
186D4×C139C2×D411yescharacteristic
187C2×C4×C139—21no—
188C2×C4×C139—21no—
189C2×C4×C139—21no—
190C2×C4×C139—21no—
191C2×C4×C139—41no—
192C2×C4×C139—41no—
193C2×C4×C139—41no—
194C2×C4×C139C2411yescharacteristic
195C8×C139—21no—
196C8×C139C2×D411yescharacteristic
197C8×C139C2×D411yescharacteristic
198C22×C139—21no—
199C22×C139—21no—
200C22×C139—21no—
201C22×C139—41no—
202C22×C139—81no—
203C22×C139—161no—
204C22×C139H(5,𝔽2)11yescharacteristic
205C2×D139—21no—
206C2×D139—41no—
207C2×D139—81no—
208C2×D139—161no—
209C4×C139—21no—
210C4×C139—21no—
211C4×C139—21no—
212C4×C139—41no—
213C4×C139C22×D411yescharacteristic
214C4×C139C22×D411yescharacteristic
215Dic139—21no—
216Dic139—41no—
217Dic139—41no—
218C2×C139—21no—
219C2×C139—41no—
220C2×C139—41no—
221C2×C139—41no—
222C2×C139—81no—
223C2×C139D4211yescharacteristic
224D139—41no—
225D139—81no—
226C139#329011yescharacteristic, complemented, Sylow
227#3290—1391nomaximal, Sylow
228#578—1391no—
229#577—1391no—
230#577D13911yescharacteristic, complemented
231#576—1391no—
232#495—1391no—
233#473—1391no—
234#472—1391no—
235#471—1391no—
236#471—1391no—
237#455—1391no—
238#455—1391no—
239#454—1391no—
240#454—1391no—
241#443—1391no—
242#443—1391no—
2432−1+4—1391no—
2442−1+4C2×D13911yescharacteristic, complemented
245H(5,𝔽2)—1391no—
246H(5,𝔽2)C2×D13911yescharacteristic
247#137—21no—
248#137—2781no—
249#137—2781no—
250#137—2781no—
251#137—1391no—
252#137—1391no—
253#137—1391no—
254#137C2×D13911yescharacteristic
255AGL(1,ℤ/8)—21no—
256AGL(1,ℤ/8)—2781no—
257AGL(1,ℤ/8)—2781no—
258AGL(1,ℤ/8)—2781no—
259AGL(1,ℤ/8)—1391no—
260AGL(1,ℤ/8)—1391no—
261AGL(1,ℤ/8)—1391no—
262AGL(1,ℤ/8)C2×D13911yescharacteristic, complemented
263#135—21no—
264#135—2781no—
265#135—2781no—
266#135—2781no—
267#135—1391no—
268#135C2×D13911yescharacteristic
269C2×Q16—2781no—
270C2×Q16—1391no—
271C2×SD16—21no—
272C2×SD16—2781no—
273C2×SD16—1391no—
274C2×SD16C2×D13911yescharacteristic, complemented
275C2×D8—2781no—
276C2×D8—1391no—
277#131—1391no—
278#131—1391no—
279#131—1391no—
280#131C2×D13911yescharacteristic, complemented
281#124—1391no—
282#124—1391no—
283#108—1391no—
284#108—1391no—
285#104—1391no—
286#104—1391no—
287#104—1391no—
288#104—1391no—
289#101—1391no—
290#101—1391no—
291#100—1391no—
292#100—1391no—
293C4×C8—1391no—
294#41—21no—
295#41—21no—
296#41—21no—
297#41—21no—
298#41—41no—
299#41—2781no—
300#41—2781no—
301#41—2781no—
302#41—2781no—
303#41—5561no—
304#41—1391no—
305#41C22×D13911yescharacteristic
306#41C22×D13911yescharacteristic
307#41C22×D13911yescharacteristic
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—2781no—
311C2×Q8—2781no—
312C2×Q8—1391no—
313C2×Q8C22×D13911yescharacteristic
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4—2781no—
318C2×D4—2781no—
319C2×D4—5561no—
320C2×D4—1391no—
321C2×D4C22×D13911yescharacteristic
322Q16—21no—
323Q16—2781no—
324Q16—2781no—
325Q16—2781no—
326Q16—2781no—
327Q16—2781no—
328Q16—1391no—
329Q16C22⋊D13911yescharacteristic
330SD16—21no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—2781no—
335SD16—2781no—
336SD16—2781no—
337SD16—2781no—
338SD16—2781no—
339SD16—2781no—
340SD16—2781no—
341SD16—2781no—
342SD16—1391no—
343SD16—1391no—
344SD16C22⋊D13911yescharacteristic
345SD16C22⋊D13911yescharacteristic
346D8—21no—
347D8—2781no—
348D8—2781no—
349D8—2781no—
350D8—2781no—
351D8—2781no—
352D8—1391no—
353D8C22⋊D13911yescharacteristic
354M16—21no—
355M16—2781no—
356M16—2781no—
357M16—2781no—
358M16—1391no—
359M16—1391no—
360M16—1391no—
361M16C22×D13911yescharacteristic
362C2×C8—21no—
363C2×C8—2781no—
364C2×C8—2781no—
365C2×C8—2781no—
366C2×C8—1391no—
367C2×C8C22×D13911yescharacteristic
368C22⋊C4—5561no—
369C22⋊C4—5561no—
370C42—1391no—
371C23—21no—
372C23—41no—
373C23—2781no—
374C23—5561no—
375Q8—21no—
376Q8—21no—
377Q8—41no—
378Q8—2781no—
379Q8—2781no—
380Q8—5561no—
381Q8—1391no—
382Q8D4×D13911yescharacteristic
383Q8C2×C22⋊D13911yescharacteristic
384Q8C2×C22⋊D13911yescharacteristic
385D4—21no—
386D4—21no—
387D4—21no—
388D4—21no—
389D4—21no—
390D4—41no—
391D4—41no—
392D4—41no—
393D4—2781no—
394D4—2781no—
395D4—2781no—
396D4—5561no—
397D4—5561no—
398D4—5561no—
399D4—1391no—
400D4D4×D13911yescharacteristic
401D4C2×C22⋊D13911yescharacteristic
402D4C2×C22⋊D13911yescharacteristic
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—2781no—
411C2×C4—2781no—
412C2×C4—2781no—
413C2×C4—5561no—
414C2×C4—5561no—
415C2×C4—5561no—
416C2×C4C23×D13911yescharacteristic
417C8—21no—
418C8—2781no—
419C8—2781no—
420C8—2781no—
421C8—1391no—
422C8—1391no—
423C8C2×C22⋊D13911yescharacteristic
424C8C2×C22⋊D13911yescharacteristic
425C22—21no—
426C22—21no—
427C22—21no—
428C22—41no—
429C22—81no—
430C22—161no—
431C22—2781no—
432C22—5561no—
433C22—11121no—
434C22—22241no—
435C22#1798488711yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—41no—
440C4—2781no—
441C4—5561no—
442C4—5561no—
443C4C2×D4×D13911yescharacteristic
444C4C22×C22⋊D13911yescharacteristic
445C2—21no—
446C2—41no—
447C2—41no—
448C2—41no—
449C2—81no—
450C2—5561no—
451C2—11121no—
452C2D4×C22⋊D13911yescharacteristic
subgroupG/H
centerC2D4×C22⋊D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#577×C139C2
socleC2×C139D42
hypercenter#577D139
hypocenterC139#3290
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C2×C4 ◁ #577

Complements

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

NH ≅ G/Ntype
1. #22581768C2semidirect
2. #22581760C2semidirect
3. #22581756C2semidirect
4. #22581334C2semidirect
5. #22581226C2semidirect
6. #22581221C2semidirect
7. #22581216C2semidirect
8. #22581213C2semidirect
9. #22581131C2semidirect
10. #22581129C2semidirect
11. #22581126C2semidirect
12. #22581124C2semidirect
13. #22581070C2semidirect
14. #22581068C2semidirect
15. #577×C139C2semidirect
16. #17984889C22semidirect
20. #17984873C22semidirect
23. #17984872C22semidirect
28. #17984867C22semidirect
35. C2×#14555775C22semidirect
36. C2×#14555774C22semidirect
41. #17984849C22semidirect
42. #17984848C22semidirect
43. #17984831C22semidirect
44. #17984829C22semidirect
45. #17984778C22semidirect
46. #17984777C22semidirect
48. #17984769C22semidirect
49. #17984769C22semidirect
50. #17984768C22semidirect
51. #17984761C22semidirect
52. #17984760C22semidirect
53. #17984759C22semidirect
54. #17984758C22semidirect
55. C8×Dic139C22semidirect
56. 2−1+4×C139C22semidirect
61. AGL(1,ℤ/8)×C139C22semidirect
65. C2×SD16×C139C22semidirect
66. #131×C139C22semidirect
226. C139#3290semidirect
230. #577D139semidirect
244. 2−1+4C2×D139semidirect
262. AGL(1,ℤ/8)C2×D139semidirect
274. C2×SD16C2×D139semidirect
280. #131C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225817682
#225817602
#225817562
#225813342
#225812262
#225812212
#225812162
#225812132
#225811312
#225811292
#225811262
#225811242
#225810702
#225810682
#577×C1392
#3290139