Finite Group Databasebeta

← #19146371

Subgroups — #19146371

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#14583713C211yesmaximal, characteristic, complemented
3#14583711C211yesmaximal, characteristic, complemented
4#14583706C211yesmaximal, characteristic, complemented
5#14583293C211yesmaximal, characteristic, complemented
6#14583175C211yesmaximal, characteristic, complemented
7#14583174C211yesmaximal, characteristic, complemented
8#14583163C211yesmaximal, characteristic, complemented
9#14583162C211yesmaximal, characteristic, complemented
10#14583083C211yesmaximal, characteristic, complemented
11#14583083C211yesmaximal, characteristic, complemented
12#14583078C211yesmaximal, characteristic, complemented
13#14583073C211yesmaximal, characteristic, complemented
14#14583022C211yesmaximal, characteristic, complemented
15C43×#444C211yesmaximal, characteristic, complemented
16#13063372C2211yescharacteristic
17#13063372C2211yescharacteristic
18#13063372C2211yescharacteristic, complemented
19#13063371C2211yescharacteristic
20#13063358—21no—
21#13063358—21no—
22#13063358—21no—
23#13063358C2211yescharacteristic
24#13063358C2211yescharacteristic
25#13063358C2211yescharacteristic, complemented
26#13063357—21no—
27#13063355C2211yescharacteristic
28#13063355C2211yescharacteristic
29#13063355C2211yescharacteristic, complemented
30#13063354—21no—
31#13063354—21no—
32#13063353—21no—
33#13063353C2211yescharacteristic
34#13063350C2211yescharacteristic
35#13063349—21no—
36#13063347—21no—
37#13063347—21no—
38#13063347C2211yescharacteristic
39#13063346—21no—
40#13063344—21no—
41C2×Dic172—21no—
42C2×Dic172C2211yescharacteristic, complemented
43C2×Dic172C2211yescharacteristic, complemented
44Q16×D43—21no—
45C2×#10621873—21no—
46C2×#10621873C2211yescharacteristic
47C2×#10621873C2211yescharacteristic
48SD16×D43—21no—
49#13063331C2211yescharacteristic
50#13063331C2211yescharacteristic, complemented
51#13063325C2211yescharacteristic, complemented
52#13063313C2211yescharacteristic
53#13063261C2211yescharacteristic, complemented
54#13063253C2211yescharacteristic
55#13063253C2211yescharacteristic, complemented
56#13063243C2211yescharacteristic, complemented
57#13063243C2211yescharacteristic, complemented
58#13063243C2211yescharacteristic, complemented
59#13063241C2211yescharacteristic
60#135×C43C2211yescharacteristic
61#131×C43C2211yescharacteristic
62#131×C43C2211yescharacteristic, complemented
63#108×C43C2211yescharacteristic, complemented
64#104×C43C2211yescharacteristic
65#104×C43C2211yescharacteristic, complemented
66#97×C43C2211yescharacteristic, complemented
67#41×C43C2311yescharacteristic
68#41×C43C2311yescharacteristic
69#10621902—21no—
70Q8×D43—21no—
71Q8×D43—21no—
72Q8×D43—21no—
73#10621900—21no—
74#10621900—21no—
75#10621900—21no—
76#10621900—41no—
77#10621900—41no—
78#10621900—41no—
79D4×D43—21no—
80D4×D43—41no—
81#10621898—21no—
82#10621898—21no—
83#10621898—21no—
84#10621898—21no—
85#10621898C2311yescharacteristic
86#10621898C2311yescharacteristic
87C2×D172—21no—
88C2×D172C2311yescharacteristic
89C2×Dic86—21no—
90C2×Dic86—21no—
91C2×Dic86—21no—
92C2×Dic86C2311yescharacteristic
93C2×Dic86C2311yescharacteristic
94C2×Dic86C2311yescharacteristic
95Q16×C43D411yescharacteristic
96SD16×C43D411yescharacteristic
97SD16×C43D411yescharacteristic
98D8×C43D411yescharacteristic
99M16×C43—21no—
100M16×C43—21no—
101M16×C43C2311yescharacteristic
102M16×C43C2311yescharacteristic
103C2×C8×C43—21no—
104C2×C8×C43—21no—
105C2×C8×C43C2311yescharacteristic
106C2×C8×C43C2311yescharacteristic
107C42×C43C2311yescharacteristic
108#10621885—21no—
109#10621885—21no—
110#10621885—21no—
111#10621884—21no—
112#10621883—21no—
113#10621883—21no—
114#10621883—21no—
115#10621882—21no—
116(C2×D43)⋊C4—41no—
117C4⋊Dic43—41no—
118#10621877C2311yescharacteristic
119#10621877C2311yescharacteristic
120Dic172—21no—
121Dic172—21no—
122Dic172—21no—
123Dic172—21no—
124Dic172—21no—
125Dic172—21no—
126Dic172—21no—
127Dic172D411yescharacteristic
128D344—21no—
129D344D411yescharacteristic
130#10621873—21no—
131#10621873—21no—
132#10621873—21no—
133#10621873—21no—
134#10621873—21no—
135#10621873—21no—
136#10621873—21no—
137#10621873—21no—
138#10621873D411yescharacteristic
139#10621873D411yescharacteristic
140#10621872—21no—
141#10621872—21no—
142C8×D43—21no—
143C8×D43—21no—
144C22×D43—21no—
145C22×D43—41no—
146Q8×C43C2×D411yescharacteristic
147Q8×C43C2×D411yescharacteristic
148D4×C43—21no—
149D4×C43—21no—
150D4×C43C2×D411yescharacteristic
151D4×C43C2×D411yescharacteristic
152C2×C4×C43—21no—
153C2×C4×C43—21no—
154C2×C4×C43—21no—
155C2×C4×C43C2411yescharacteristic
156C22⋊D43—21no—
157C22⋊D43—21no—
158C22⋊D43—41no—
159C22⋊D43—41no—
160C22⋊D43—41no—
161C22⋊D43—41no—
162C2×Dic43—21no—
163C2×Dic43—21no—
164C2×Dic43—21no—
165C2×Dic43—41no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168D172—21no—
169D172—21no—
170D172—41no—
171D172C2×D411yescharacteristic
172D172C2×D411yescharacteristic
173C4×D43—21no—
174C4×D43—21no—
175C4×D43—41no—
176C4×D43—41no—
177C4×D43—41no—
178C4×D43—41no—
179Dic86—21no—
180Dic86—21no—
181Dic86—21no—
182Dic86—21no—
183Dic86—21no—
184Dic86—21no—
185Dic86—41no—
186Dic86—41no—
187Dic86—41no—
188Dic86C2×D411yescharacteristic
189Dic86C2×D411yescharacteristic
190C8×C43—21no—
191C8×C43—21no—
192C8×C43C2×D411yescharacteristic
193C8×C43C2×D411yescharacteristic
194C8×C43C2×D411yescharacteristic
195C8×C43C2×D411yescharacteristic
196C43⋊C8—21no—
197C43⋊C8—21no—
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×C43C22×D411yescharacteristic
210C4×C43C22×D411yescharacteristic
211Dic43—21no—
212Dic43—21no—
213Dic43—41no—
214Dic43—41no—
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#456—431no—
235#455—431no—
236#454—431no—
237#444—431no—
238#444D4311yescharacteristic, complemented
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—431no—
250#137—861no—
251#137—861no—
252#137—861no—
253#137—861no—
254#137—861no—
255#137—861no—
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—861no—
262#135—861no—
263#135—861no—
264#135—861no—
265#135C2×D4311yescharacteristic
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#131C2×D4311yescharacteristic
277#131C2×D4311yescharacteristic, complemented
278C4⋊Q8—431no—
279#124—431no—
280#108—431no—
281#108C2×D4311yescharacteristic, complemented
282#104—431no—
283#104—431no—
284#104C2×D4311yescharacteristic
285#104C2×D4311yescharacteristic, complemented
286#101—431no—
287#101—431no—
288#101—431no—
289#100—431no—
290#97C2×D4311yescharacteristic, complemented
291#41—431no—
292#41—431no—
293#41—861no—
294#41—861no—
295#41—861no—
296#41—861no—
297#41—861no—
298#41—861no—
299#41—861no—
300#41—861no—
301#41—1721no—
302#41—1721no—
303#41—1721no—
304#41C22×D4311yescharacteristic
305#41C22×D4311yescharacteristic
306C2×Q8—431no—
307C2×Q8—431no—
308C2×Q8—431no—
309C2×Q8—861no—
310C2×Q8—861no—
311C2×Q8—861no—
312C2×Q8—861no—
313C2×Q8—861no—
314C2×Q8—861no—
315C2×D4—431no—
316C2×D4—861no—
317C2×D4—861no—
318C2×D4—1721no—
319Q16—431no—
320Q16—861no—
321Q16—861no—
322Q16—861no—
323Q16—861no—
324Q16—861no—
325Q16—861no—
326Q16—861no—
327Q16—861no—
328Q16—861no—
329Q16—861no—
330Q16D17211yescharacteristic
331SD16—431no—
332SD16—431no—
333SD16—861no—
334SD16—861no—
335SD16—861no—
336SD16—861no—
337SD16—861no—
338SD16—861no—
339SD16—861no—
340SD16—861no—
341SD16—861no—
342SD16—861no—
343SD16—861no—
344SD16—861no—
345SD16D17211yescharacteristic
346SD16D17211yescharacteristic
347D8—431no—
348D8—861no—
349D8—861no—
350D8D17211yescharacteristic
351M16—21no—
352M16—21no—
353M16—431no—
354M16—431no—
355M16—861no—
356M16—861no—
357M16C22×D4311yescharacteristic
358M16C22×D4311yescharacteristic
359C2×C8—21no—
360C2×C8—21no—
361C2×C8—861no—
362C2×C8—861no—
363C2×C8C22×D4311yescharacteristic
364C2×C8C22×D4311yescharacteristic
365C4⋊C4—1721no—
366C22⋊C4—1721no—
367C42C22×D4311yescharacteristic
368C23—861no—
369C23—1721no—
370Q8—431no—
371Q8—431no—
372Q8—861no—
373Q8—861no—
374Q8—861no—
375Q8—861no—
376Q8—861no—
377Q8—861no—
378Q8—1721no—
379Q8—1721no—
380Q8—1721no—
381Q8C2×D17211yescharacteristic
382Q8C2×D17211yescharacteristic
383D4—21no—
384D4—21no—
385D4—431no—
386D4—431no—
387D4—861no—
388D4—861no—
389D4—861no—
390D4—861no—
391D4—1721no—
392D4—1721no—
393D4—1721no—
394D4—1721no—
395D4—1721no—
396D4C2×D17211yescharacteristic
397D4C2×D17211yescharacteristic
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
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—861no—
417C8—861no—
418C8C2×D17211yescharacteristic
419C8C2×D17211yescharacteristic
420C8D4×D4311yescharacteristic
421C8D4×D4311yescharacteristic
422C22—21no—
423C22—21no—
424C22—861no—
425C22—861no—
426C22—3441no—
427C22—1721no—
428C22—6881no—
429C22#1306337111yescharacteristic
430C4—21no—
431C4—21no—
432C4—41no—
433C4—861no—
434C4—861no—
435C4—1721no—
436C4—1721no—
437C4—1721no—
438C4C2×D4×D4311yescharacteristic
439C4C22×D17211yescharacteristic
440C2—21no—
441C2—41no—
442C2—41no—
443C2—3441no—
444C2—1721no—
445C2—1721no—
446C2D4×D17211yescharacteristic
subgroupG/H
centerC2D4×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#444C2
socleC2×C43D42
hypercenter#444D43
hypocenterC43#3289
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #444

Complements

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

NH ≅ G/Ntype
1. #14583716C2semidirect
2. #14583713C2semidirect
3. #14583711C2semidirect
4. #14583706C2semidirect
5. #14583293C2semidirect
6. #14583175C2semidirect
7. #14583174C2semidirect
8. #14583163C2semidirect
9. #14583162C2semidirect
10. #14583083C2semidirect
11. #14583083C2semidirect
12. #14583078C2semidirect
13. #14583073C2semidirect
14. #14583022C2semidirect
15. C43×#444C2semidirect
18. #13063372C22semidirect
25. #13063358C22semidirect
29. #13063355C22semidirect
42. C2×Dic172C22semidirect
43. C2×Dic172C22semidirect
50. #13063331C22semidirect
51. #13063325C22semidirect
53. #13063261C22semidirect
55. #13063253C22semidirect
56. #13063243C22semidirect
57. #13063243C22semidirect
58. #13063243C22semidirect
62. #131×C43C22semidirect
63. #108×C43C22semidirect
65. #104×C43C22semidirect
66. #97×C43C22semidirect
238. #444D43semidirect
239. C43#3289semidirect
277. #131C2×D43semidirect
281. #108C2×D43semidirect
285. #104C2×D43semidirect
290. #97C2×D43semidirect