Finite Group Databasebeta

← #19146365

Subgroups — #19146365

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#14583715C211yesmaximal, characteristic, complemented
2#14583714C211yesmaximal, characteristic, complemented
3#14583708C211yesmaximal, characteristic, complemented
4#14583707C211yesmaximal, characteristic, complemented
5#14583291C211yesmaximal, characteristic, complemented
6#14583173C211yesmaximal, characteristic, complemented
7#14583172C211yesmaximal, characteristic, complemented
8#14583165C211yesmaximal, characteristic, complemented
9#14583164C211yesmaximal, characteristic, complemented
10#14583081C211yesmaximal, characteristic, complemented
11#14583078C211yesmaximal, characteristic, complemented
12#14583073C211yesmaximal, characteristic, complemented
13#14583018C211yesmaximal, characteristic, complemented
14#14583018C211yesmaximal, characteristic, complemented
15C43×#456C211yesmaximal, characteristic, complemented
16#13063373C2211yescharacteristic
17#13063372C2211yescharacteristic, complemented
18#13063371C2211yescharacteristic
19#13063358C2211yescharacteristic
20#13063357—21no—
21#13063357—21no—
22#13063356—21no—
23#13063356—21no—
24#13063356C2211yescharacteristic
25#13063356C2211yescharacteristic, complemented
26#13063355—21no—
27#13063355C2211yescharacteristic
28#13063354—21no—
29#13063353C2211yescharacteristic
30#13063352—21no—
31#13063350—21no—
32#13063350C2211yescharacteristic
33#13063348—21no—
34#13063346—21no—
35#13063345—21no—
36#13063345—21no—
37#13063345C2211yescharacteristic
38#13063345C2211yescharacteristic
39C2×#10621885—21no—
40C2×#10621885C2211yescharacteristic, complemented
41C2×#10621885C2211yescharacteristic, complemented
42Q16×D43—21no—
43C2×#10621884—21no—
44C2×#10621884C2211yescharacteristic
45C2×#10621884C2211yescharacteristic
46SD16×D43—21no—
47#13063333C2211yescharacteristic
48#13063333C2211yescharacteristic, complemented
49#13063332C2211yescharacteristic
50#13063332C2211yescharacteristic, complemented
51#13063313C2211yescharacteristic
52#13063260C2211yescharacteristic, complemented
53#13063260C2211yescharacteristic, complemented
54#13063253C2211yescharacteristic
55#13063253C2211yescharacteristic, complemented
56#13063244C2211yescharacteristic, complemented
57#13063243C2211yescharacteristic, complemented
58#13063241C2211yescharacteristic
59#13063236C2211yescharacteristic, complemented
602−1+4×C43C2211yescharacteristic
61#137×C43C2211yescharacteristic
62#137×C43C2211yescharacteristic, complemented
63C4⋊Q8×C43C2211yescharacteristic, complemented
64#104×C43C2211yescharacteristic
65#104×C43C2211yescharacteristic, complemented
66#101×C43C2211yescharacteristic, complemented
67#41×C43—21no—
68#41×C43—21no—
69#41×C43—41no—
70#41×C43C2311yescharacteristic
71#41×C43C2311yescharacteristic
72C2×Q8×C43—21no—
73C2×Q8×C43—21no—
74C2×Q8×C43C2311yescharacteristic
75C2×Q8×C43C2311yescharacteristic
76#10621902—21no—
77#10621902—21no—
78#10621902—21no—
79Q8×D43—21no—
80Q8×D43—21no—
81Q8×D43—21no—
82#10621900—21no—
83#10621900—41no—
84D4×D43—21no—
85D4×D43—41no—
86#10621898—21no—
87#10621898—21no—
88#10621898—41no—
89#10621898C2311yescharacteristic
90#10621898C2311yescharacteristic
91C2×D172—21no—
92C2×D172C2311yescharacteristic
93C2×Dic86—21no—
94C2×Dic86C2311yescharacteristic
95Q16×C43—21no—
96Q16×C43—21no—
97SD16×C43—21no—
98SD16×C43—21no—
99M16×C43C2311yescharacteristic
100M16×C43C2311yescharacteristic
101C4⋊C4×C43—41no—
102C42×C43C2311yescharacteristic
103#10621885—21no—
104#10621885—21no—
105#10621885—21no—
106#10621885—21no—
107#10621885—21no—
108#10621885—21no—
109#10621885—21no—
110#10621885D411yescharacteristic
111#10621885D411yescharacteristic
112#10621884—21no—
113#10621884—21no—
114#10621884—21no—
115#10621884—21no—
116#10621884—21no—
117#10621884—21no—
118#10621884—21no—
119#10621884D411yescharacteristic
120#10621884D411yescharacteristic
121#10621883—21no—
122#10621883D411yescharacteristic
123#10621883D411yescharacteristic
124#10621882—21no—
125#10621882D411yescharacteristic
126#10621882D411yescharacteristic
127(C2×D43)⋊C4—41no—
128#10621877—21no—
129#10621877—21no—
130#10621877C2311yescharacteristic
131#10621877C2311yescharacteristic
132C2×C43⋊C8—21no—
133C2×C43⋊C8—21no—
134C2×C43⋊C8C2311yescharacteristic
135C2×C43⋊C8C2311yescharacteristic
136Dic172—21no—
137D344—21no—
138#10621873—21no—
139#10621873—21no—
140#10621872—21no—
141#10621872—21no—
142C8×D43—21no—
143C8×D43—21no—
144C22×D43—21no—
145C22×D43—41no—
146Q8×C43—21no—
147Q8×C43—21no—
148Q8×C43—21no—
149Q8×C43—21no—
150Q8×C43—41no—
151Q8×C43C2×D411yescharacteristic
152Q8×C43C2×D411yescharacteristic
153D4×C43—21no—
154D4×C43—21no—
155D4×C43—41no—
156D4×C43C2×D411yescharacteristic
157D4×C43C2×D411yescharacteristic
158C2×C4×C43—21no—
159C2×C4×C43—21no—
160C2×C4×C43—21no—
161C2×C4×C43—21no—
162C2×C4×C43—21no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43C2411yescharacteristic
166C22⋊D43—21no—
167C22⋊D43—21no—
168C22⋊D43—41no—
169C22⋊D43—41no—
170C2×Dic43—21no—
171C2×Dic43—41no—
172D172—21no—
173D172—21no—
174D172—41no—
175D172—41no—
176D172C2×D411yescharacteristic
177D172C2×D411yescharacteristic
178C4×D43—21no—
179C4×D43—21no—
180C4×D43—41no—
181C4×D43—41no—
182C4×D43—41no—
183C4×D43—41no—
184Dic86—21no—
185Dic86—21no—
186Dic86—41no—
187Dic86—41no—
188Dic86C2×D411yescharacteristic
189Dic86C2×D411yescharacteristic
190C8×C43—21no—
191C8×C43—21no—
192C43⋊C8—21no—
193C43⋊C8—21no—
194C43⋊C8C2×D411yescharacteristic
195C43⋊C8C2×D411yescharacteristic
196C43⋊C8C2×D411yescharacteristic
197C43⋊C8C2×D411yescharacteristic
198C22×C43—21no—
199C22×C43—21no—
200C22×C43H(5,𝔽2)11yescharacteristic
201C2×D43—21no—
202C2×D43—21no—
203C2×D43—41no—
204C2×D43—81no—
205C2×D43—161no—
206C4×C43—21no—
207C4×C43—21no—
208C4×C43—41no—
209C4×C43—41no—
210C4×C43—41no—
211C4×C43C22×D411yescharacteristic
212C4×C43C22×D411yescharacteristic
213Dic43—21no—
214Dic43—21no—
215Dic43—41no—
216#3289—431nomaximal, Sylow
217C2×C43—21no—
218C2×C43—41no—
219C2×C43—41no—
220C2×C43D4211yescharacteristic
221D43—41no—
222D43—41no—
223D43—81no—
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#471—431no—
233#456—431no—
234#456D4311yescharacteristic, complemented
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+4C2×D4311yescharacteristic
243H(5,𝔽2)—431no—
244#137—431no—
245#137—431no—
246#137—431no—
247#137—431no—
248#137—861no—
249#137—861no—
250#137—861no—
251#137—861no—
252#137—861no—
253#137—861no—
254#137C2×D4311yescharacteristic
255#137C2×D4311yescharacteristic, complemented
256AGL(1,ℤ/8)—431no—
257AGL(1,ℤ/8)—431no—
258AGL(1,ℤ/8)—861no—
259AGL(1,ℤ/8)—861no—
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—431no—
272C2×SD16—861no—
273C2×SD16—861no—
274#131—431no—
275#131—431no—
276#131—431no—
277#131—431no—
278C4⋊Q8C2×D4311yescharacteristic, complemented
279#124—431no—
280#108—431no—
281#108—431no—
282#104—431no—
283#104—431no—
284#104C2×D4311yescharacteristic
285#104C2×D4311yescharacteristic, complemented
286#101—431no—
287#101—431no—
288#101C2×D4311yescharacteristic, complemented
289#100—431no—
290#97—431no—
291#41—21no—
292#41—21no—
293#41—41no—
294#41—431no—
295#41—431no—
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#41C22×D4311yescharacteristic
305#41C22×D4311yescharacteristic
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—431no—
309C2×Q8—861no—
310C2×Q8—861no—
311C2×Q8—861no—
312C2×Q8—861no—
313C2×Q8C22×D4311yescharacteristic
314C2×Q8C22×D4311yescharacteristic
315C2×D4—431no—
316C2×D4—861no—
317C2×D4—861no—
318C2×D4—1721no—
319Q16—21no—
320Q16—21no—
321Q16—431no—
322Q16—431no—
323Q16—861no—
324Q16—861no—
325Q16—861no—
326Q16—861no—
327Q16—861no—
328Q16—861no—
329Q16—861no—
330Q16—861no—
331SD16—21no—
332SD16—21no—
333SD16—431no—
334SD16—431no—
335SD16—431no—
336SD16—431no—
337SD16—861no—
338SD16—861no—
339SD16—861no—
340SD16—861no—
341SD16—861no—
342SD16—861no—
343SD16—861no—
344SD16—861no—
345SD16—861no—
346SD16—861no—
347D8—431no—
348D8—431no—
349D8—861no—
350D8—861no—
351M16—431no—
352M16—431no—
353M16—861no—
354M16—861no—
355M16—861no—
356M16—861no—
357M16C22×D4311yescharacteristic
358M16C22×D4311yescharacteristic
359C2×C8—431no—
360C2×C8—431no—
361C2×C8—861no—
362C2×C8—861no—
363C2×C8—861no—
364C2×C8—861no—
365C4⋊C4—41no—
366C22⋊C4—1721no—
367C42C22×D4311yescharacteristic
368C23—861no—
369C23—1721no—
370Q8—21no—
371Q8—21no—
372Q8—21no—
373Q8—21no—
374Q8—41no—
375Q8—431no—
376Q8—431no—
377Q8—861no—
378Q8—861no—
379Q8—1721no—
380Q8—1721no—
381Q8D4×D4311yescharacteristic
382Q8D4×D4311yescharacteristic
383D4—21no—
384D4—21no—
385D4—41no—
386D4—431no—
387D4—431no—
388D4—861no—
389D4—861no—
390D4—861no—
391D4—861no—
392D4—1721no—
393D4—1721no—
394D4—1721no—
395D4—1721no—
396D4D4×D4311yescharacteristic
397D4D4×D4311yescharacteristic
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—861no—
406C2×C4—861no—
407C2×C4—861no—
408C2×C4—1721no—
409C2×C4—1721no—
410C2×C4—1721no—
411C2×C4—1721no—
412C2×C4—1721no—
413C2×C4C23×D4311yescharacteristic
414C8—21no—
415C8—21no—
416C8—431no—
417C8—431no—
418C8—431no—
419C8—431no—
420C8—861no—
421C8—861no—
422C22—21no—
423C22—21no—
424C22—861no—
425C22—861no—
426C22—3441no—
427C22—1721no—
428C22—6881no—
429C22#1306337011yescharacteristic
430C4—21no—
431C4—21no—
432C4—41no—
433C4—41no—
434C4—41no—
435C4—861no—
436C4—861no—
437C4—1721no—
438C4C2×D4×D4311yescharacteristic
439C4C2×D4×D4311yescharacteristic
440C2—21no—
441C2—41no—
442C2—41no—
443C2—3441no—
444C2—1721no—
445C2—1721no—
446C2#1458353111yescharacteristic
subgroupG/H
centerC2#14583531
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#456C2
socleC2×C43D42
hypercenter#456D43
hypocenterC43#3289
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #456

Complements

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

NH ≅ G/Ntype
1. #14583715C2semidirect
2. #14583714C2semidirect
3. #14583708C2semidirect
4. #14583707C2semidirect
5. #14583291C2semidirect
6. #14583173C2semidirect
7. #14583172C2semidirect
8. #14583165C2semidirect
9. #14583164C2semidirect
10. #14583081C2semidirect
11. #14583078C2semidirect
12. #14583073C2semidirect
13. #14583018C2semidirect
14. #14583018C2semidirect
15. C43×#456C2semidirect
17. #13063372C22semidirect
25. #13063356C22semidirect
40. C2×#10621885C22semidirect
41. C2×#10621885C22semidirect
48. #13063333C22semidirect
50. #13063332C22semidirect
52. #13063260C22semidirect
53. #13063260C22semidirect
55. #13063253C22semidirect
56. #13063244C22semidirect
57. #13063243C22semidirect
59. #13063236C22semidirect
62. #137×C43C22semidirect
63. C4⋊Q8×C43C22semidirect
65. #104×C43C22semidirect
66. #101×C43C22semidirect
234. #456D43semidirect
239. C43#3289semidirect
255. #137C2×D43semidirect
278. C4⋊Q8C2×D43semidirect
285. #104C2×D43semidirect
288. #101C2×D43semidirect