Finite Group Databasebeta

← #19146134

Subgroups — #19146134

Order 5504.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063349C211yesmaximal, characteristic, complemented
2C2×#13063346C211yesmaximal, characteristic, complemented
3#14583569C211yesmaximal, characteristic, complemented
4#14583542C211yesmaximal, characteristic, complemented
5#14583142C211yesmaximal, characteristic, complemented
6#14583132C211yesmaximal, characteristic, complemented
7#14583118C211yesmaximal, characteristic, complemented
8#14583091C211yesmaximal, characteristic, complemented
9#14583058C211yesmaximal, characteristic, complemented
10#14583043C211yesmaximal, characteristic, complemented
11#14583041C211yesmaximal, characteristic, complemented
12#14583031C211yesmaximal, characteristic, complemented
13#14583001C211yesmaximal, characteristic, complemented
14#14582972C211yesmaximal, characteristic, complemented
15C43×#496C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×#10621900C2211yescharacteristic
18C2×#10621900C2211yescharacteristic, complemented
19C2×D4×D43C2211yescharacteristic
20#13063349—24no—
21#13063346—24no—
22C2×#10621885C2211yescharacteristic, complemented
23C2×#10621873C2211yescharacteristic
24C2×#10621883C2211yescharacteristic
25C2×#10621882C2211yescharacteristic
26C2×#10621882C2211yescharacteristic
27C2×#10621872C2211yescharacteristic
28C2×C8×D43C2211yescharacteristic, complemented
29#13063321—21no—
30#13063307—21no—
31#13063301C2211yescharacteristic
32#13063298—21no—
33#13063297—21no—
34#13063297—21no—
35#13063296C2211yescharacteristic
36#13063296C2211yescharacteristic
37#13063296C2211yescharacteristic, complemented
38#13063295—21no—
39C4×Dic86C2211yescharacteristic, complemented
40C4×D172C2211yescharacteristic
41C4×D172C2211yescharacteristic
42D4×Dic43—21no—
43C22⋊C4×D43—21no—
44#13063259C2211yescharacteristic, complemented
45C4⋊(C43⋊C8)C2211yescharacteristic, complemented
46#13063250C2211yescharacteristic, complemented
47#13063249C2211yescharacteristic, complemented
48#13063247C2211yescharacteristic
49#13063246C2211yescharacteristic
50#13063246C2211yescharacteristic, complemented
51#13063246C2211yescharacteristic, complemented
52(C2×D43)⋊C8C2211yescharacteristic
53(C2×D43)⋊C8C2211yescharacteristic, complemented
54C2×SD16×C43C2211yescharacteristic, complemented
55C2×SD16×C43C2211yescharacteristic, complemented
56C2×D8×C43C2211yescharacteristic
57C2×D8×C43C2211yescharacteristic
58#127×C43C2211yescharacteristic, complemented
59#124×C43C2211yescharacteristic
60#97×C43C2211yescharacteristic, complemented
61C23×D43—21no—
62C2×Q8×C43C2311yescharacteristic
63C2×D4×C43—21no—
64C2×D4×C43—21no—
65C2×D4×C43C2311yescharacteristic
66C2×D4×C43C2311yescharacteristic
67C2×D4×C43C2311yescharacteristic
68C2×C22⋊D43—21no—
69C2×C22⋊D43—21no—
70C2×C22⋊D43—21no—
71C2×C22⋊D43—21no—
72C2×C22⋊D43—21no—
73C2×C22⋊D43—21no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76#10621902—22no—
77#10621902—41no—
78#10621900—22no—
79#10621900—22no—
80#10621900—41no—
81#10621900—41no—
82D4×D43—22no—
83D4×D43—41no—
84C2×D172—21no—
85C2×D172D411yescharacteristic
86C2×D172C2311yescharacteristic
87C2×C4×D43—21no—
88C2×C4×D43—21no—
89C2×C4×D43C2311yescharacteristic
90C2×C4×D43C2311yescharacteristic
91C2×Dic86C2311yescharacteristic
92SD16×C43—22no—
93SD16×C43—41no—
94D8×C43—22no—
95D8×C43—41no—
96C2×C8×C43C2311yescharacteristic
97C2×C8×C43C2311yescharacteristic
98C22⋊C4×C43—21no—
99C22⋊C4×C43—21no—
100C42×C43C2311yescharacteristic
101C22⋊Dic43—21no—
102C22⋊Dic43—21no—
103C22⋊Dic43—21no—
104#10621885—22no—
105#10621883—22no—
106#10621882—22no—
107#10621882—22no—
108(C2×D43)⋊C4—21no—
109(C2×D43)⋊C4—21no—
110(C2×D43)⋊C4D411yescharacteristic
111(C2×D43)⋊C4D411yescharacteristic
112C4⋊Dic43D411yescharacteristic
113C4⋊Dic43C2311yescharacteristic
114C4⋊Dic43C2311yescharacteristic
115Dic43⋊C4—21no—
116Dic43⋊C4—21no—
117C4×Dic43—21no—
118C2×C43⋊C8C2311yescharacteristic
119C2×C43⋊C8C2311yescharacteristic
120#10621873D414yescomplemented
121#10621872—22no—
122C8×D43—22no—
123C23×C43—21no—
124C23×C43—21no—
125C23×C43—21no—
126C22×D43—21no—
127C22×D43—42no—
128C22×D43—42no—
129C22×D43—81no—
130C22×D43C2×D411yescharacteristic
131C22×D43C2×D411yescharacteristic
132Q8×C43—21no—
133Q8×C43—21no—
134D4×C43—21no—
135D4×C43—21no—
136D4×C43—21no—
137D4×C43—21no—
138D4×C43—21no—
139D4×C43—21no—
140D4×C43—42no—
141D4×C43—81no—
142C2×C4×C43—21no—
143C2×C4×C43C2×D411yescharacteristic
144C2×C4×C43C2×D411yescharacteristic
145C2×C4×C43C2411yescharacteristic
146C22⋊D43—42no—
147C22⋊D43—42no—
148C22⋊D43—42no—
149C22⋊D43—81no—
150C22⋊D43—81no—
151C22⋊D43—81no—
152C2×Dic43—21no—
153C2×Dic43—21no—
154C2×Dic43—21no—
155C2×Dic43—42no—
156C2×Dic43—42no—
157C2×Dic43C2×D411yescharacteristic
158C2×Dic43C2×D411yescharacteristic
159D172—21no—
160D172—41no—
161D172—42no—
162D172C2×D412yes—
163C4×D43—21no—
164C4×D43—21no—
165C4×D43—21no—
166C4×D43—21no—
167C4×D43—42no—
168C4×D43—81no—
169Dic86—21no—
170Dic86C2×D412yes—
171C8×C43—21no—
172C8×C43C2×D412yes—
173C43⋊C8—21no—
174C43⋊C8—21no—
175C22×C43—41no—
176C22×C43—41no—
177C22×C43—41no—
178C22×C43—41no—
179C22×C43—41no—
180C22×C43—41no—
181C22×C43—41no—
182C22×C43—41no—
183C22×C43—41no—
184C22×C43C22×D411yescharacteristic
185C2×D43—22no—
186C2×D43—21no—
187C2×D43—21no—
188C2×D43—21no—
189C2×D43—21no—
190C2×D43—21no—
191C2×D43—21no—
192C2×D43—41no—
193C2×D43—41no—
194C2×D43—84no—
195C4×C43—21no—
196C4×C43—21no—
197C4×C43—41no—
198C4×C43C22×D411yescharacteristic
199C4×C43H(5,𝔽2)11yescharacteristic
200Dic43—22no—
201Dic43—21no—
202Dic43—21no—
203Dic43—41no—
204Dic43—41no—
205#3268—431nomaximal, Sylow
206C2×C43—81no—
207C2×C43—81no—
208C2×C43—81no—
209C2×C43D4211yescharacteristic
210C2×C43#57511yescharacteristic
211C2×C43#57611yescharacteristic
212D43—41no—
213D43—41no—
214D43—42no—
215C2×AGL(1,ℤ/8)—431no—
216C2×#135—431no—
217#550—431no—
218#546—431no—
219#496D4311yescharacteristic, complemented
220#468—431no—
221#466—431no—
222#464—431no—
223#459—431no—
224#452—431no—
225#449—431no—
226#449—431no—
227#447—431no—
228#440—431no—
229#435—431no—
230C43#326811yescharacteristic, complemented, Sylow
231C2×#41—431no—
232C2×#41—431no—
233C2×#41—431no—
234C22×D4—431no—
235AGL(1,ℤ/8)—864no—
236#135—864no—
237C2×Q16—431no—
238C2×SD16—431no—
239C2×SD16—431no—
240C2×SD16C2×D4311yescharacteristic, complemented
241C2×SD16C2×D4311yescharacteristic, complemented
242C2×D8—431no—
243C2×D8—431no—
244C2×D8C2×D4311yescharacteristic
245C2×D8C2×D4311yescharacteristic
246C2×M16—431no—
247C22×C8—431no—
248#127—861no—
249#127C2×D4311yescharacteristic, complemented
250#124C2×D4311yescharacteristic
251#123—861no—
252C22⋊Q8—431no—
253#121—431no—
254#121—431no—
255#121—431no—
256#121—861no—
257#121—861no—
258#121—861no—
259#120—861no—
260C4×Q8—431no—
261C4×D4—431no—
262C4×D4—431no—
263C4×D4—861no—
264C2×C22⋊C4—861no—
265#107—431no—
266C4⋊C8—431no—
267#103—431no—
268#103—431no—
269#102—431no—
270#102—431no—
271#102—431no—
272#102—431no—
273C22⋊C8—431no—
274C22⋊C8—431no—
275#97C2×D4311yescharacteristic, complemented
276C24—861no—
277#41—862no—
278#41—862no—
279#41—862no—
280#41—1721no—
281#41—1721no—
282#41—1721no—
283C2×Q8—431no—
284C2×Q8C22×D4311yescharacteristic
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—431no—
288C2×D4—431no—
289C2×D4—861no—
290C2×D4—861no—
291C2×D4—862no—
292C2×D4—861no—
293C2×D4—861no—
294C2×D4—861no—
295C2×D4—861no—
296C2×D4—861no—
297C2×D4—1721no—
298C2×D4C22×D4311yescharacteristic
299C2×D4C22×D4311yescharacteristic
300C2×D4C22×D4311yescharacteristic
301C22×C4—431no—
302C22×C4—431no—
303C22×C4—861no—
304C22×C4—861no—
305C22×C4—861no—
306C22×C4—861no—
307Q16—862no—
308SD16—22no—
309SD16—41no—
310SD16—434no—
311SD16—862no—
312D8—22no—
313D8—41no—
314D8—862no—
315D8—862no—
316M16—862no—
317C2×C8—431no—
318C2×C8—431no—
319C2×C8—862no—
320C2×C8C22×D4311yescharacteristic
321C2×C8C22×D4311yescharacteristic
322C4⋊C4—431no—
323C4⋊C4—431no—
324C4⋊C4—431no—
325C4⋊C4—861no—
326C4⋊C4—861no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—431no—
330C22⋊C4—431no—
331C22⋊C4—861no—
332C22⋊C4—861no—
333C22⋊C4—861no—
334C22⋊C4—861no—
335C22⋊C4—861no—
336C42—861no—
337C42C22×D4311yescharacteristic
338C23—21no—
339C23—21no—
340C23—21no—
341C23—431no—
342C23—431no—
343C23—861no—
344C23—3441no—
345C23—1722no—
346C23—1722no—
347Q8—21no—
348Q8—21no—
349Q8—432no—
350Q8—861no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—21no—
356D4—21no—
357D4—42no—
358D4—81no—
359D4—432no—
360D4—861no—
361D4—3441no—
362D4—3441no—
363D4—3441no—
364D4—1721no—
365D4—1722no—
366D4—1722no—
367D4—1722no—
368D4—1722no—
369C2×C4—21no—
370C2×C4—431no—
371C2×C4—431no—
372C2×C4—861no—
373C2×C4—861no—
374C2×C4—861no—
375C2×C4—861no—
376C2×C4—861no—
377C2×C4—861no—
378C2×C4—861no—
379C2×C4—3441no—
380C2×C4—1722no—
381C2×C4—1722no—
382C2×C4—1722no—
383C2×C4D4×D4311yescharacteristic
384C2×C4D4×D4311yescharacteristic
385C2×C4C23×D4311yescharacteristic
386C8—21no—
387C8—861no—
388C8—861no—
389C8D4×D4312yes—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—861no—
400C22—861no—
401C22—861no—
402C22—861no—
403C22—861no—
404C22—861no—
405C22—862no—
406C22—3444no—
407C22—1721no—
408C22—1721no—
409C22C2×D4×D4311yescharacteristic
410C4—21no—
411C4—21no—
412C4—41no—
413C4—861no—
414C4—861no—
415C4—862no—
416C4—1721no—
417C4—1721no—
418C4C2×D4×D4311yescharacteristic
419C4#1306337011yescharacteristic
420C2—81no—
421C2—81no—
422C2—81no—
423C2—1721no—
424C2—1721no—
425C2—1722no—
426C2#1458353411yescharacteristic
427C2#1458369511yescharacteristic
428C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#496C2
socleC22×C43C22×D4
hypercenter#496D43
hypocenterC43#3268
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×#13063349C2semidirect
2. C2×#13063346C2semidirect
3. #14583569C2semidirect
4. #14583542C2semidirect
5. #14583142C2semidirect
6. #14583132C2semidirect
7. #14583118C2semidirect
8. #14583091C2semidirect
9. #14583058C2semidirect
10. #14583043C2semidirect
11. #14583041C2semidirect
12. #14583031C2semidirect
13. #14583001C2semidirect
14. #14582972C2semidirect
15. C43×#496C2semidirect
18. C2×#10621900C22semidirect
22. C2×#10621885C22semidirect
28. C2×C8×D43C22semidirect
37. #13063296C22semidirect
39. C4×Dic86C22semidirect
44. #13063259C22semidirect
45. C4⋊(C43⋊C8)C22semidirect
46. #13063250C22semidirect
47. #13063249C22semidirect
50. #13063246C22semidirect
51. #13063246C22semidirect
53. (C2×D43)⋊C8C22semidirect
54. C2×SD16×C43C22semidirect
55. C2×SD16×C43C22semidirect
58. #127×C43C22semidirect
60. #97×C43C22semidirect
120. #10621873D4semidirect
219. #496D43semidirect
230. C43#3268semidirect
240. C2×SD16C2×D43semidirect
241. C2×SD16C2×D43semidirect
249. #127C2×D43semidirect
275. #97C2×D43semidirect