Finite Group Databasebeta

← #19146367

Subgroups — #19146367

Order 5504.

448 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583716C211yesmaximal, characteristic, complemented
2#14583715C211yesmaximal, characteristic, complemented
3#14583709C211yesmaximal, characteristic, complemented
4#14583705C211yesmaximal, characteristic, complemented
5#14583290C211yesmaximal, characteristic, complemented
6#14583175C211yesmaximal, characteristic, complemented
7#14583173C211yesmaximal, characteristic, complemented
8#14583161C211yesmaximal, characteristic, complemented
9#14583084C211yesmaximal, characteristic, complemented
10#14583080C211yesmaximal, characteristic, complemented
11#14583079C211yesmaximal, characteristic, complemented
12#14583070C211yesmaximal, characteristic, complemented
13#14583020C211yesmaximal, characteristic, complemented
14#14583019C211yesmaximal, characteristic, complemented
15C43×#471C211yesmaximal, characteristic, complemented
16#13063373C2211yescharacteristic
17#13063372C2211yescharacteristic
18#13063372C2211yescharacteristic, complemented
19#13063370C2211yescharacteristic
20#13063358—21no—
21#13063358—21no—
22#13063358C2211yescharacteristic
23#13063358C2211yescharacteristic
24#13063358C2211yescharacteristic
25#13063358C2211yescharacteristic, complemented
26#13063357—21no—
27#13063356C2211yescharacteristic
28#13063354—21no—
29#13063354—21no—
30#13063354—21no—
31#13063352—21no—
32#13063351C2211yescharacteristic
33#13063349—21no—
34#13063347—21no—
35#13063347C2211yescharacteristic
36#13063346—21no—
37#13063346—21no—
38#13063345C2211yescharacteristic
39#13063344—21no—
40C2×Dic172—21no—
41C2×Dic172C2211yescharacteristic, complemented
42C2×#10621885C2211yescharacteristic, complemented
43Q16×D43—21no—
44C2×#10621883C2211yescharacteristic
45SD16×D43—21no—
46SD16×D43—21no—
47#13063333C2211yescharacteristic
48#13063333C2211yescharacteristic, complemented
49#13063331C2211yescharacteristic
50#13063323C2211yescharacteristic, complemented
51#13063312C2211yescharacteristic
52#13063260C2211yescharacteristic, complemented
53#13063252C2211yescharacteristic, complemented
54#13063251C2211yescharacteristic
55#13063251C2211yescharacteristic
56#13063251C2211yescharacteristic, complemented
57#13063243C2211yescharacteristic, complemented
58#13063243C2211yescharacteristic, complemented
59#13063235C2211yescharacteristic, complemented
60#137×C43C2211yescharacteristic, complemented
61AGL(1,ℤ/8)×C43C2211yescharacteristic
62C2×SD16×C43C2211yescharacteristic
63#131×C43C2211yescharacteristic, complemented
64#108×C43C2211yescharacteristic, complemented
65#101×C43C2211yescharacteristic, complemented
66#100×C43C2211yescharacteristic
67#41×C43C2311yescharacteristic
68C2×Q8×C43C2311yescharacteristic
69C2×D4×C43C2311yescharacteristic
70C2×C22⋊D43—41no—
71#10621902—21no—
72#10621902—21no—
73Q8×D43—21no—
74Q8×D43—21no—
75Q8×D43—21no—
76Q8×D43—21no—
77#10621900—21no—
78#10621900—21no—
79#10621900—21no—
80#10621900—21no—
81#10621900—41no—
82#10621900—41no—
83D4×D43—21no—
84D4×D43—21no—
85#10621898—21no—
86#10621898—21no—
87#10621898—41no—
88#10621898C2311yescharacteristic
89#10621898C2311yescharacteristic
90#10621898C2311yescharacteristic
91C2×Dic86—21no—
92C2×Dic86—21no—
93C2×Dic86C2311yescharacteristic
94C2×Dic86C2311yescharacteristic
95Q16×C43—21no—
96SD16×C43—21no—
97SD16×C43—21no—
98SD16×C43—21no—
99SD16×C43—21no—
100D8×C43—21no—
101M16×C43—21no—
102M16×C43C2311yescharacteristic
103M16×C43C2311yescharacteristic
104M16×C43C2311yescharacteristic
105C2×C8×C43—21no—
106C2×C8×C43C2311yescharacteristic
107C22⋊Dic43—41no—
108#10621885—21no—
109#10621885—21no—
110#10621885—21no—
111#10621885D411yescharacteristic
112#10621884—21no—
113#10621884D411yescharacteristic
114#10621883—21no—
115#10621883—21no—
116#10621883—21no—
117#10621883D411yescharacteristic
118#10621882—21no—
119#10621882D411yescharacteristic
120Dic43⋊C4—41no—
121C4×Dic43C2311yescharacteristic
122#10621877C2311yescharacteristic
123C2×C43⋊C8C2311yescharacteristic
124Dic172—21no—
125Dic172—21no—
126Dic172—21no—
127Dic172—21no—
128Dic172—21no—
129Dic172—21no—
130Dic172D411yescharacteristic
131D344D411yescharacteristic
132#10621873—21no—
133#10621873—21no—
134#10621873—21no—
135#10621873—21no—
136#10621873D411yescharacteristic
137#10621873D411yescharacteristic
138#10621872—21no—
139#10621872—21no—
140#10621872—21no—
141C8×D43—21no—
142C8×D43—21no—
143C8×D43—21no—
144C23×C43—21no—
145C22×D43—41no—
146Q8×C43—21no—
147Q8×C43—21no—
148Q8×C43C2×D411yescharacteristic
149D4×C43—21no—
150D4×C43—21no—
151D4×C43—21no—
152D4×C43C2×D411yescharacteristic
153C2×C4×C43—21no—
154C2×C4×C43—21no—
155C2×C4×C43C2411yescharacteristic
156C22⋊D43—21no—
157C22⋊D43—21no—
158C22⋊D43—21no—
159C22⋊D43—41no—
160C22⋊D43—41no—
161C22⋊D43—41no—
162C22⋊D43—41no—
163C2×Dic43—21no—
164C2×Dic43—21no—
165C2×Dic43—21no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168C2×Dic43—41no—
169D172—41no—
170D172C2×D411yescharacteristic
171D172C2×D411yescharacteristic
172D172C2×D411yescharacteristic
173C4×D43—21no—
174C4×D43—21no—
175C4×D43—21no—
176C4×D43—41no—
177C4×D43—41no—
178C4×D43—41no—
179C4×D43—41no—
180Dic86—21no—
181Dic86—21no—
182Dic86—21no—
183Dic86—21no—
184Dic86—41no—
185Dic86—41no—
186Dic86—41no—
187Dic86C2×D411yescharacteristic
188Dic86C2×D411yescharacteristic
189Dic86C2×D411yescharacteristic
190C8×C43—21no—
191C8×C43—21no—
192C8×C43—21no—
193C8×C43C2×D411yescharacteristic
194C8×C43C2×D411yescharacteristic
195C43⋊C8—21no—
196C43⋊C8C2×D411yescharacteristic
197C43⋊C8C2×D411yescharacteristic
198C22×C43—21no—
199C22×C43—41no—
200C22×C43—81no—
201C22×C43H(5,𝔽2)11yescharacteristic
202C2×D43—21no—
203C2×D43—21no—
204C2×D43—21no—
205C2×D43—161no—
206C4×C43—21no—
207C4×C43—41no—
208C4×C43C22×D411yescharacteristic
209C4×C43C22×D411yescharacteristic
210Dic43—21no—
211Dic43—21no—
212Dic43—21no—
213Dic43—41no—
214Dic43—41no—
215Dic43—41no—
216#3289—431nomaximal, Sylow
217C2×C43—21no—
218C2×C43—41no—
219C2×C43—81no—
220C2×C43D4211yescharacteristic
221D43—41no—
222D43—41no—
223D43—41no—
224#578—431no—
225#578—431no—
226#577—431no—
227#577—431no—
228#497—431no—
229#473—431no—
230#473—431no—
231#471—431no—
232#471D4311yescharacteristic, complemented
233#456—431no—
234#456—431no—
235#455—431no—
236#454—431no—
237#444—431no—
238#444—431no—
239C43#328911yescharacteristic, complemented, Sylow
2402−1+4—431no—
2412−1+4—431no—
2422−1+4—431no—
243H(5,𝔽2)—431no—
244#137—431no—
245#137—431no—
246#137—431no—
247#137—431no—
248#137—431no—
249#137—861no—
250#137—861no—
251#137—861no—
252#137—861no—
253#137—861no—
254#137—861no—
255#137C2×D4311yescharacteristic, complemented
256AGL(1,ℤ/8)—431no—
257AGL(1,ℤ/8)—861no—
258AGL(1,ℤ/8)—861no—
259AGL(1,ℤ/8)C2×D4311yescharacteristic
260#135—431no—
261#135—431no—
262#135—861no—
263#135—861no—
264#135—861no—
265#135—861no—
266C2×Q16—431no—
267C2×Q16—431no—
268C2×Q16—861no—
269C2×Q16—861no—
270C2×SD16—431no—
271C2×SD16—861no—
272C2×SD16—861no—
273C2×SD16C2×D4311yescharacteristic
274#131—431no—
275#131—431no—
276#131—431no—
277#131C2×D4311yescharacteristic, complemented
278C4⋊Q8—431no—
279#124—431no—
280#108—431no—
281#108C2×D4311yescharacteristic, complemented
282#104—431no—
283#104—431no—
284#104—431no—
285#104—431no—
286#101—431no—
287#101—431no—
288#101C2×D4311yescharacteristic, complemented
289#100C2×D4311yescharacteristic
290#97—431no—
291#41—431no—
292#41—431no—
293#41—431no—
294#41—861no—
295#41—861no—
296#41—861no—
297#41—861no—
298#41—861no—
299#41—861no—
300#41—861no—
301#41—861no—
302#41—1721no—
303#41—1721no—
304#41—1721no—
305#41C22×D4311yescharacteristic
306C2×Q8—431no—
307C2×Q8—431no—
308C2×Q8—861no—
309C2×Q8—861no—
310C2×Q8—861no—
311C2×Q8—861no—
312C2×Q8—861no—
313C2×Q8—861no—
314C2×Q8C22×D4311yescharacteristic
315C2×D4—861no—
316C2×D4—861no—
317C2×D4—1721no—
318C2×D4C22×D4311yescharacteristic
319Q16—21no—
320Q16—431no—
321Q16—431no—
322Q16—861no—
323Q16—861no—
324Q16—861no—
325Q16—861no—
326Q16—861no—
327Q16—861no—
328Q16—861no—
329Q16—861no—
330Q16—861no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—21no—
335SD16—431no—
336SD16—431no—
337SD16—431no—
338SD16—431no—
339SD16—861no—
340SD16—861no—
341SD16—861no—
342SD16—861no—
343SD16—861no—
344SD16—861no—
345SD16—861no—
346SD16—861no—
347D8—21no—
348D8—431no—
349D8—431no—
350D8—861no—
351M16—21no—
352M16—431no—
353M16—861no—
354M16—861no—
355M16—861no—
356M16C22×D4311yescharacteristic
357M16C22×D4311yescharacteristic
358M16C22×D4311yescharacteristic
359C2×C8—21no—
360C2×C8—431no—
361C2×C8—861no—
362C2×C8—861no—
363C2×C8—861no—
364C2×C8C22×D4311yescharacteristic
365C4⋊C4—1721no—
366C22⋊C4—1721no—
367C42—431no—
368C23—21no—
369C23—1721no—
370Q8—21no—
371Q8—21no—
372Q8—431no—
373Q8—431no—
374Q8—431no—
375Q8—861no—
376Q8—861no—
377Q8—861no—
378Q8—861no—
379Q8—1721no—
380Q8—1721no—
381Q8—1721no—
382Q8D4×D4311yescharacteristic
383D4—21no—
384D4—21no—
385D4—21no—
386D4—431no—
387D4—431no—
388D4—431no—
389D4—861no—
390D4—861no—
391D4—861no—
392D4—1721no—
393D4—1721no—
394D4—1721no—
395D4—1721no—
396D4—1721no—
397D4D4×D4311yescharacteristic
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—861no—
401C2×C4—861no—
402C2×C4—861no—
403C2×C4—861no—
404C2×C4—861no—
405C2×C4—861no—
406C2×C4—1721no—
407C2×C4—1721no—
408C2×C4—1721no—
409C2×C4—1721no—
410C2×C4—1721no—
411C2×C4—1721no—
412C2×C4—1721no—
413C2×C4C23×D4311yescharacteristic
414C8—21no—
415C8—21no—
416C8—21no—
417C8—431no—
418C8—431no—
419C8—861no—
420C8D4×D4311yescharacteristic
421C8D4×D4311yescharacteristic
422C22—21no—
423C22—41no—
424C22—81no—
425C22—861no—
426C22—861no—
427C22—861no—
428C22—6881no—
429C22#1306337111yescharacteristic
430C4—21no—
431C4—41no—
432C4—861no—
433C4—861no—
434C4—861no—
435C4—1721no—
436C4—1721no—
437C4—1721no—
438C4C2×D4×D4311yescharacteristic
439C4C2×D4×D4311yescharacteristic
440C2—21no—
441C2—41no—
442C2—81no—
443C2—1721no—
444C2—1721no—
445C2—1721no—
446C2#1458353311yescharacteristic
subgroupG/H
centerC2#14583533
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#471C2
socleC2×C43D42
hypercenter#471D43
hypocenterC43#3289
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. #14583716C2semidirect
2. #14583715C2semidirect
3. #14583709C2semidirect
4. #14583705C2semidirect
5. #14583290C2semidirect
6. #14583175C2semidirect
7. #14583173C2semidirect
8. #14583161C2semidirect
9. #14583084C2semidirect
10. #14583080C2semidirect
11. #14583079C2semidirect
12. #14583070C2semidirect
13. #14583020C2semidirect
14. #14583019C2semidirect
15. C43×#471C2semidirect
18. #13063372C22semidirect
25. #13063358C22semidirect
41. C2×Dic172C22semidirect
42. C2×#10621885C22semidirect
48. #13063333C22semidirect
50. #13063323C22semidirect
52. #13063260C22semidirect
53. #13063252C22semidirect
56. #13063251C22semidirect
57. #13063243C22semidirect
58. #13063243C22semidirect
59. #13063235C22semidirect
60. #137×C43C22semidirect
63. #131×C43C22semidirect
64. #108×C43C22semidirect
65. #101×C43C22semidirect
232. #471D43semidirect
239. C43#3289semidirect
255. #137C2×D43semidirect
277. #131C2×D43semidirect
281. #108C2×D43semidirect
288. #101C2×D43semidirect