Finite Group Databasebeta

← #19146202

Subgroups — #19146202

Order 5504.

520 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063351C211yesmaximal, characteristic, complemented
2C2×#13063350C211yesmaximal, characteristic, complemented
3#14583545C211yesmaximal, characteristic, complemented
4#14583281C211yesmaximal, characteristic, complemented
5#14583147C211yesmaximal, characteristic, complemented
6#14583143C211yesmaximal, characteristic, complemented
7#14583114C211yesmaximal, characteristic, complemented
8#14583111C211yesmaximal, characteristic, complemented
9#14583061C211yesmaximal, characteristic, complemented
10#14583059C211yesmaximal, characteristic, complemented
11#14583033C211yesmaximal, characteristic, complemented
12#14583032C211yesmaximal, characteristic, complemented
13C4×#10621882C211yesmaximal, characteristic, complemented
14#14582977C211yesmaximal, characteristic, complemented
15C43×#546C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C22×D172C2211yescharacteristic, complemented
18#13063351—24no—
19#13063350—24no—
20C2×#10621885C2211yescharacteristic, complemented
21C2×#10621883C2211yescharacteristic, complemented
22C2×#10621883C2211yescharacteristic, complemented
23C2×#10621884C2211yescharacteristic, complemented
24C2×#10621884C2211yescharacteristic, complemented
25C2×#10621882C2211yescharacteristic
26C2×#10621882C2211yescharacteristic
27C2×#10621882C2211yescharacteristic
28C2×#10621882C2211yescharacteristic
29C2×#10621877C2211yescharacteristic, complemented
30C2×#10621877C2211yescharacteristic, complemented
31#13063313C2211yescharacteristic, complemented
32#13063310—21no—
33#13063304C2211yescharacteristic, complemented
34#13063299C2211yescharacteristic
35#13063298—21no—
36#13063293—21no—
37C4×D172C2211yescharacteristic, complemented
38C22⋊C4×D43—21no—
39#13063258C2211yescharacteristic, complemented
40C4⋊(C43⋊C8)C2211yescharacteristic, complemented
41#13063249C2211yescharacteristic, complemented
42#13063248C2211yescharacteristic, complemented
43#13063246C2211yescharacteristic, complemented
44#13063246C2211yescharacteristic, complemented
45#13063245C2211yescharacteristic, complemented
46#13063245C2211yescharacteristic, complemented
47C22⋊(C43⋊C8)C2211yescharacteristic, complemented
48C22⋊(C43⋊C8)C2211yescharacteristic, complemented
49C4×C43⋊C8C2211yescharacteristic, complemented
50C2×#41×C43C2211yescharacteristic
51C22×D4×C43C2211yescharacteristic, complemented
52#124×C43C2211yescharacteristic, complemented
53#123×C43—21no—
54C22⋊Q8×C43C2211yescharacteristic, complemented
55#121×C43—21no—
56#121×C43C2211yescharacteristic
57#120×C43—21no—
58C4×D4×C43C2211yescharacteristic
59C4×D4×C43C2211yescharacteristic, complemented
60C2×C22⋊C4×C43—21no—
61C24×C43—21no—
62C23×D43—21no—
63#41×C43—22no—
64#41×C43—41no—
65C2×Q8×C43C2311yescharacteristic
66C2×D4×C43—21no—
67C2×D4×C43—21no—
68C2×D4×C43—21no—
69C2×D4×C43—22no—
70C2×D4×C43—41no—
71C2×D4×C43D411yescharacteristic
72C2×D4×C43C2311yescharacteristic
73C2×D4×C43C2311yescharacteristic
74C22×C4×C43—21no—
75C22×C4×C43—21no—
76C22×C4×C43C2311yescharacteristic
77C22×C4×C43C2311yescharacteristic
78C2×C22⋊D43—21no—
79C2×C22⋊D43—21no—
80#10621898—22no—
81#10621898—41no—
82C2×D172—21no—
83C2×D172—22no—
84C2×D172—41no—
85C2×D172C2311yescharacteristic
86C2×D172C2311yescharacteristic
87C2×C4×D43—21no—
88C2×C4×D43—21no—
89C2×Dic86C2311yescharacteristic
90C4⋊C4×C43—21no—
91C4⋊C4×C43D411yescharacteristic
92C4⋊C4×C43C2311yescharacteristic
93C22⋊C4×C43—21no—
94C22⋊C4×C43—21no—
95C22⋊C4×C43—21no—
96C22⋊C4×C43—21no—
97C22⋊C4×C43—21no—
98C22⋊C4×C43D411yescharacteristic
99C22⋊C4×C43D411yescharacteristic
100C42×C43C2311yescharacteristic
101C22⋊Dic43—21no—
102#10621885—41no—
103#10621884—22no—
104#10621884—22no—
105#10621883—22no—
106#10621883—22no—
107#10621882—22no—
108#10621882—22no—
109#10621882—41no—
110#10621882D414yescomplemented
111(C2×D43)⋊C4—21no—
112(C2×D43)⋊C4—21no—
113(C2×D43)⋊C4—21no—
114(C2×D43)⋊C4—21no—
115C4⋊Dic43C2311yescharacteristic
116Dic43⋊C4—21no—
117#10621877—22no—
118#10621877—22no—
119C2×C43⋊C8C2311yescharacteristic
120C2×C43⋊C8C2311yescharacteristic
121C2×C43⋊C8C2311yescharacteristic
122C2×C43⋊C8C2311yescharacteristic
123C23×C43—21no—
124C23×C43—21no—
125C23×C43—42no—
126C23×C43—42no—
127C23×C43—81no—
128C23×C43C2×D411yescharacteristic
129C23×C43C2×D411yescharacteristic
130C22×D43—21no—
131C22×D43—21no—
132C22×D43—42no—
133C22×D43—42no—
134C22×D43—81no—
135Q8×C43—21no—
136Q8×C43—21no—
137D4×C43—21no—
138D4×C43—21no—
139D4×C43—21no—
140D4×C43—41no—
141D4×C43—42no—
142D4×C43—42no—
143D4×C43—81no—
144D4×C43C2×D412yes—
145C2×C4×C43—21no—
146C2×C4×C43—21no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—42no—
152C2×C4×C43—81no—
153C2×C4×C43C2×D411yescharacteristic
154C2×C4×C43C2×D411yescharacteristic
155C2×C4×C43C2×D411yescharacteristic
156C2×C4×C43C2×D411yescharacteristic
157C2×C4×C43C2411yescharacteristic
158C22⋊D43—42no—
159C22⋊D43—81no—
160C2×Dic43—21no—
161C2×Dic43—21no—
162D172—21no—
163D172—21no—
164D172—21no—
165D172—42no—
166D172C2×D412yes—
167C4×D43—42no—
168C4×D43—81no—
169Dic86—21no—
170Dic86—21no—
171C43⋊C8—21no—
172C43⋊C8—21no—
173C43⋊C8—21no—
174C43⋊C8C2×D412yes—
175C22×C43—21no—
176C22×C43—22no—
177C22×C43—21no—
178C22×C43—21no—
179C22×C43—21no—
180C22×C43—21no—
181C22×C43—21no—
182C22×C43—41no—
183C22×C43—41no—
184C22×C43—41no—
185C22×C43—41no—
186C22×C43—41no—
187C22×C43—84no—
188C22×C43C22×D411yescharacteristic
189C2×D43—22no—
190C2×D43—41no—
191C2×D43—41no—
192C2×D43—41no—
193C2×D43—41no—
194C2×D43—41no—
195C2×D43—84no—
196C4×C43—21no—
197C4×C43—21no—
198C4×C43—21no—
199C4×C43—21no—
200C4×C43—41no—
201C4×C43—41no—
202C4×C43C22×D411yescharacteristic
203C4×C43H(5,𝔽2)11yescharacteristic
204Dic43—41no—
205Dic43—41no—
206#3273—431nomaximal, Sylow
207C2×C43—41no—
208C2×C43—41no—
209C2×C43—42no—
210C2×C43—81no—
211C2×C43D4211yescharacteristic
212C2×C43#57511yescharacteristic
213C2×C43#57611yescharacteristic
214D43—42no—
215D43—81no—
216C2×AGL(1,ℤ/8)—431no—
217C2×AGL(1,ℤ/8)—431no—
218#546—431no—
219#546D4311yescharacteristic, complemented
220#495—431no—
221#468—431no—
222#468—431no—
223#463—431no—
224#463—431no—
225#452—431no—
226#452—431no—
227#447—431no—
228#447—431no—
229C4×D8—431no—
230#436—431no—
231C43#327311yescharacteristic, complemented, Sylow
232C2×#41—431no—
233C2×#41C2×D4311yescharacteristic
234C22×D4—431no—
235C22×D4C2×D4311yescharacteristic, complemented
236AGL(1,ℤ/8)—864no—
237AGL(1,ℤ/8)—864no—
238C2×Q16—431no—
239C2×SD16—431no—
240C2×SD16—431no—
241C2×SD16—431no—
242C2×SD16—431no—
243C2×D8—431no—
244C2×D8—431no—
245C2×D8—431no—
246C2×D8—431no—
247C2×M16—431no—
248C2×M16—431no—
249#124—431no—
250#124C2×D4311yescharacteristic, complemented
251#123—21no—
252#123—861no—
253C22⋊Q8—431no—
254C22⋊Q8C2×D4311yescharacteristic, complemented
255#121—21no—
256#121—431no—
257#121—861no—
258#121C2×D4311yescharacteristic
259#120—21no—
260#120—861no—
261C4×D4—431no—
262C4×D4C2×D4311yescharacteristic
263C4×D4C2×D4311yescharacteristic, complemented
264C2×C22⋊C4—21no—
265C2×C22⋊C4—861no—
266#107—431no—
267C4⋊C8—431no—
268#103—431no—
269#103—431no—
270#102—431no—
271#102—431no—
272#102—431no—
273#102—431no—
274C22⋊C8—431no—
275C22⋊C8—431no—
276C4×C8—431no—
277C24—21no—
278C24—861no—
279#41—22no—
280#41—41no—
281#41—862no—
282#41—1721no—
283C2×Q8—431no—
284C2×Q8C22×D4311yescharacteristic
285C2×D4—22no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—41no—
290C2×D4—431no—
291C2×D4—431no—
292C2×D4—862no—
293C2×D4—861no—
294C2×D4—861no—
295C2×D4—861no—
296C2×D4—1721no—
297C2×D4C22⋊D4311yescharacteristic
298C2×D4C22×D4311yescharacteristic
299C2×D4C22×D4311yescharacteristic
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—861no—
303C22×C4—861no—
304C22×C4C22×D4311yescharacteristic
305C22×C4C22×D4311yescharacteristic
306Q16—1721no—
307SD16—862no—
308SD16—862no—
309SD16—862no—
310SD16—862no—
311D8—434no—
312D8—862no—
313D8—862no—
314D8—1721no—
315M16—862no—
316M16—862no—
317C2×C8—431no—
318C2×C8—431no—
319C2×C8—431no—
320C2×C8—431no—
321C4⋊C4—21no—
322C4⋊C4—431no—
323C4⋊C4—861no—
324C4⋊C4C22⋊D4311yescharacteristic
325C4⋊C4C22×D4311yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—21no—
330C22⋊C4—21no—
331C22⋊C4—861no—
332C22⋊C4—861no—
333C22⋊C4—861no—
334C22⋊C4—861no—
335C22⋊C4—861no—
336C22⋊C4C22⋊D4311yescharacteristic
337C22⋊C4C22⋊D4311yescharacteristic
338C42C22×D4311yescharacteristic
339C23—21no—
340C23—21no—
341C23—42no—
342C23—42no—
343C23—81no—
344C23—861no—
345C23—861no—
346C23—3441no—
347C23—1722no—
348C23—1722no—
349C23C2×C22⋊D4311yescharacteristic
350C23C2×C22⋊D4311yescharacteristic
351Q8—21no—
352Q8—21no—
353Q8—861no—
354Q8—861no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—41no—
359D4—42no—
360D4—42no—
361D4—81no—
362D4—432no—
363D4—861no—
364D4—861no—
365D4—861no—
366D4—3441no—
367D4—1722no—
368D4—1722no—
369D4D4×D4312yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—42no—
377C2×C4—81no—
378C2×C4—861no—
379C2×C4—861no—
380C2×C4—3441no—
381C2×C4—1722no—
382C2×C4C2×C22⋊D4311yescharacteristic
383C2×C4C2×C22⋊D4311yescharacteristic
384C2×C4C2×C22⋊D4311yescharacteristic
385C2×C4C2×C22⋊D4311yescharacteristic
386C2×C4C23×D4311yescharacteristic
387C8—432no—
388C8—861no—
389C8—861no—
390C8—861no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—22no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—84no—
404C22—862no—
405C22—3444no—
406C22—1721no—
407C22—1721no—
408C22—1721no—
409C22—1721no—
410C22—1721no—
411C22C22×C22⋊D4311yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—41no—
417C4—41no—
418C4—1721no—
419C4—1721no—
420C4C2×D4×D4311yescharacteristic
421C4#1306337011yescharacteristic
422C2—41no—
423C2—41no—
424C2—42no—
425C2—81no—
426C2—3441no—
427C2—1722no—
428C2D4×C22⋊D4311yescharacteristic
429C2#1458369711yescharacteristic
430C2#1458370211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#546C2
socleC22×C43C22×D4
hypercenter#546D43
hypocenterC43#3273
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C2×#13063351C2semidirect
2. C2×#13063350C2semidirect
3. #14583545C2semidirect
4. #14583281C2semidirect
5. #14583147C2semidirect
6. #14583143C2semidirect
7. #14583114C2semidirect
8. #14583111C2semidirect
9. #14583061C2semidirect
10. #14583059C2semidirect
11. #14583033C2semidirect
12. #14583032C2semidirect
13. C4×#10621882C2semidirect
14. #14582977C2semidirect
15. C43×#546C2semidirect
17. C22×D172C22semidirect
20. C2×#10621885C22semidirect
21. C2×#10621883C22semidirect
22. C2×#10621883C22semidirect
23. C2×#10621884C22semidirect
24. C2×#10621884C22semidirect
29. C2×#10621877C22semidirect
30. C2×#10621877C22semidirect
31. #13063313C22semidirect
33. #13063304C22semidirect
37. C4×D172C22semidirect
39. #13063258C22semidirect
40. C4⋊(C43⋊C8)C22semidirect
41. #13063249C22semidirect
42. #13063248C22semidirect
43. #13063246C22semidirect
44. #13063246C22semidirect
45. #13063245C22semidirect
46. #13063245C22semidirect
47. C22⋊(C43⋊C8)C22semidirect
48. C22⋊(C43⋊C8)C22semidirect
49. C4×C43⋊C8C22semidirect
51. C22×D4×C43C22semidirect
52. #124×C43C22semidirect
54. C22⋊Q8×C43C22semidirect
59. C4×D4×C43C22semidirect
110. #10621882D4semidirect
219. #546D43semidirect
231. C43#3273semidirect
235. C22×D4C2×D43semidirect
250. #124C2×D43semidirect
254. C22⋊Q8C2×D43semidirect
263. C4×D4C2×D43semidirect