Finite Group Databasebeta

← #19146229

Subgroups — #19146229

Order 5504.

498 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063356C211yesmaximal, characteristic, complemented
2C2×#13063352C211yesmaximal, characteristic, complemented
3#14583560C211yesmaximal, characteristic, complemented
4#14583546C211yesmaximal, characteristic, complemented
5#14583280C211yesmaximal, characteristic, complemented
6#14583156C211yesmaximal, characteristic, complemented
7#14583150C211yesmaximal, characteristic, complemented
8#14583119C211yesmaximal, characteristic, complemented
9#14583117C211yesmaximal, characteristic, complemented
10#14583064C211yesmaximal, characteristic, complemented
11#14583048C211yesmaximal, characteristic, complemented
12#14583046C211yesmaximal, characteristic, complemented
13#14582984C211yesmaximal, characteristic, complemented
14#14582974C211yesmaximal, characteristic, complemented
15C43×#448C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×#10621898C2211yescharacteristic
18C2×D4×D43C2211yescharacteristic
19#13063356—24no—
20#13063352—24no—
21C2×#10621885C2211yescharacteristic, complemented
22C2×#10621885C2211yescharacteristic, complemented
23C2×#10621873C2211yescharacteristic, complemented
24C2×#10621884C2211yescharacteristic
25C2×#10621884C2211yescharacteristic
26C2×D344C2211yescharacteristic
27C2×#10621882C2211yescharacteristic
28C2×#10621877C2211yescharacteristic, complemented
29C2×#10621872C2211yescharacteristic
30#13063314—21no—
31#13063314C2211yescharacteristic, complemented
32#13063312C2211yescharacteristic
33#13063307—21no—
34#13063305C2211yescharacteristic
35#13063301—21no—
36#13063301C2211yescharacteristic
37#13063299—21no—
38#13063299C2211yescharacteristic, complemented
39#13063296—21no—
40#13063293—21no—
41Q8×Dic43C2211yescharacteristic, complemented
42#13063287C2211yescharacteristic
43C4×C22⋊D43—21no—
44C4×C22⋊D43C2211yescharacteristic
45C22⋊C4×D43—21no—
46#13063256C2211yescharacteristic, complemented
47Dic43⋊C8C2211yescharacteristic, complemented
48#13063250C2211yescharacteristic, complemented
49#13063247C2211yescharacteristic
50#13063246C2211yescharacteristic
51#13063245C2211yescharacteristic, complemented
52(C2×D43)⋊C8C2211yescharacteristic
53C8×Dic43C2211yescharacteristic, complemented
54C22×Q8×C43C2211yescharacteristic, complemented
55C2×SD16×C43C2211yescharacteristic
56C2×SD16×C43C2211yescharacteristic
57#121×C43C2211yescharacteristic
58#103×C43C2211yescharacteristic, complemented
59#103×C43C2211yescharacteristic, complemented
60C22⋊C8×C43C2211yescharacteristic, complemented
61C23×D43—21no—
62C2×Q8×C43—21no—
63C2×Q8×C43—22no—
64C2×Q8×C43—41no—
65C2×Q8×C43C2311yescharacteristic
66C2×Q8×C43C2311yescharacteristic
67C2×D4×C43—21no—
68C2×D4×C43C2311yescharacteristic
69C22×C4×C43—21no—
70C22×C4×C43C2311yescharacteristic
71C2×C22⋊D43—21no—
72C2×C22⋊D43—21no—
73C2×C22⋊D43—21no—
74C2×C22⋊D43D411yescharacteristic
75#10621902—22no—
76#10621902—41no—
77D4×D43—22no—
78D4×D43—41no—
79#10621898—22no—
80#10621898—41no—
81C2×D172—21no—
82C2×D172C2311yescharacteristic
83C2×D172C2311yescharacteristic
84C2×C4×D43—21no—
85C2×C4×D43—21no—
86C2×C4×D43—21no—
87C2×C4×D43C2311yescharacteristic
88C2×Dic86C2311yescharacteristic
89SD16×C43—22no—
90SD16×C43—41no—
91C2×C8×C43C2311yescharacteristic
92C2×C8×C43C2311yescharacteristic
93C4⋊C4×C43C2311yescharacteristic
94C22⋊C4×C43—21no—
95C22⋊Dic43—21no—
96C22⋊Dic43—21no—
97C22⋊Dic43D411yescharacteristic
98#10621885—22no—
99#10621885—22no—
100#10621884—22no—
101#10621884D414yescomplemented
102#10621882—22no—
103(C2×D43)⋊C4—21no—
104(C2×D43)⋊C4—21no—
105(C2×D43)⋊C4—21no—
106(C2×D43)⋊C4—21no—
107(C2×D43)⋊C4—21no—
108(C2×D43)⋊C4—21no—
109(C2×D43)⋊C4D411yescharacteristic
110C4⋊Dic43—21no—
111C4⋊Dic43—21no—
112C4⋊Dic43C2311yescharacteristic
113Dic43⋊C4—21no—
114Dic43⋊C4D411yescharacteristic
115C4×Dic43—21no—
116C4×Dic43C2311yescharacteristic
117#10621877—22no—
118C2×C43⋊C8C2311yescharacteristic
119C2×C43⋊C8C2311yescharacteristic
120D344—22no—
121#10621873—41no—
122#10621872—22no—
123C23×C43—21no—
124C23×C43C2×D411yescharacteristic
125C22×D43—21no—
126C22×D43—21no—
127C22×D43—42no—
128C22×D43—42no—
129C22×D43—81no—
130C22×D43C2×D411yescharacteristic
131Q8×C43—21no—
132Q8×C43—21no—
133Q8×C43—21no—
134Q8×C43—42no—
135Q8×C43C2×D412yes—
136D4×C43—21no—
137D4×C43—21no—
138D4×C43—81no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—42no—
145C2×C4×C43C2×D411yescharacteristic
146C2×C4×C43C2411yescharacteristic
147C22⋊D43—41no—
148C22⋊D43—42no—
149C22⋊D43—42no—
150C22⋊D43—42no—
151C2×Dic43—21no—
152C2×Dic43—21no—
153C2×Dic43C2×D411yescharacteristic
154C2×Dic43C2×D411yescharacteristic
155C2×Dic43C2×D411yescharacteristic
156D172—21no—
157D172—21no—
158D172—21no—
159D172—42no—
160D172C2×D412yes—
161C4×D43—21no—
162C4×D43—21no—
163C4×D43—42no—
164C4×D43—42no—
165C4×D43—81no—
166Dic86—21no—
167Dic86—21no—
168C8×C43—21no—
169C8×C43—21no—
170C43⋊C8—21no—
171C43⋊C8C2×D412yes—
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—41no—
176C22×C43—41no—
177C22×C43—41no—
178C22×C43C22×D411yescharacteristic
179C2×D43—22no—
180C2×D43—21no—
181C2×D43—21no—
182C2×D43—21no—
183C2×D43—41no—
184C2×D43—41no—
185C2×D43—41no—
186C2×D43—41no—
187C2×D43—41no—
188C2×D43—84no—
189C4×C43—21no—
190C4×C43—22no—
191C4×C43—41no—
192C4×C43—41no—
193C4×C43C22×D411yescharacteristic
194C4×C43H(5,𝔽2)11yescharacteristic
195Dic43—21no—
196Dic43—21no—
197Dic43—21no—
198Dic43—41no—
199Dic43—41no—
200#3275—431nomaximal, Sylow
201C2×C43—41no—
202C2×C43—81no—
203C2×C43D4211yescharacteristic
204C2×C43#57511yescharacteristic
205C2×C43#57711yescharacteristic
206D43—41no—
207D43—42no—
208D43—81no—
209C2×#137—431no—
210C2×AGL(1,ℤ/8)—431no—
211#548—431no—
212#546—431no—
213#495—431no—
214#470—431no—
215#469—431no—
216#464—431no—
217#463—431no—
218#452—431no—
219#450—431no—
220#449—431no—
221#448D4311yescharacteristic, complemented
222C4×SD16—431no—
223#436—431no—
224C43#327511yescharacteristic, complemented, Sylow
225C2×#41—431no—
226C2×#41—431no—
227C22×Q8C2×D4311yescharacteristic, complemented
228C22×D4—431no—
229#137—864no—
230AGL(1,ℤ/8)—864no—
231C2×Q16—431no—
232C2×Q16—431no—
233C2×SD16—431no—
234C2×SD16—431no—
235C2×SD16—431no—
236C2×SD16C2×D4311yescharacteristic
237C2×SD16C2×D4311yescharacteristic
238C2×D8—431no—
239C2×D8—431no—
240C2×M16—431no—
241C2×M16—431no—
242#124—431no—
243#124—431no—
244#124—861no—
245#123—861no—
246C22⋊Q8—431no—
247C22⋊Q8—431no—
248C22⋊Q8—861no—
249#121—431no—
250#121—861no—
251#121—861no—
252#121C2×D4311yescharacteristic
253#120—861no—
254C4×Q8—431no—
255C4×D4—431no—
256C4×D4—431no—
257C4×D4—861no—
258C2×C22⋊C4—861no—
259#106—431no—
260C4⋊C8—431no—
261#103—431no—
262#103C2×D4311yescharacteristic, complemented
263#103C2×D4311yescharacteristic, complemented
264#102—431no—
265#102—431no—
266#102—431no—
267C22⋊C8—431no—
268C22⋊C8C2×D4311yescharacteristic, complemented
269C4×C8—431no—
270C24—861no—
271#41—862no—
272#41—862no—
273#41—1721no—
274#41—1721no—
275C2×Q8—21no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—431no—
279C2×Q8C22×D4311yescharacteristic
280C2×Q8C22×D4311yescharacteristic
281C2×D4—21no—
282C2×D4—431no—
283C2×D4—431no—
284C2×D4—431no—
285C2×D4—861no—
286C2×D4—861no—
287C2×D4—862no—
288C2×D4—861no—
289C2×D4—861no—
290C2×D4—1721no—
291C2×D4C22×D4311yescharacteristic
292C22×C4—21no—
293C22×C4—431no—
294C22×C4—861no—
295C22×C4—861no—
296C22×C4—861no—
297C22×C4C22×D4311yescharacteristic
298Q16—862no—
299Q16—862no—
300SD16—22no—
301SD16—41no—
302SD16—434no—
303SD16—862no—
304SD16—1721no—
305D8—862no—
306D8—862no—
307M16—862no—
308M16—862no—
309C2×C8—431no—
310C2×C8—431no—
311C2×C8C22×D4311yescharacteristic
312C2×C8C22×D4311yescharacteristic
313C4⋊C4—431no—
314C4⋊C4—431no—
315C4⋊C4—861no—
316C4⋊C4—861no—
317C4⋊C4—861no—
318C4⋊C4C22×D4311yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—431no—
321C22⋊C4—431no—
322C22⋊C4—861no—
323C22⋊C4—861no—
324C22⋊C4—861no—
325C22⋊C4—861no—
326C22⋊C4—861no—
327C22⋊C4—861no—
328C22⋊C4—861no—
329C22⋊C4—861no—
330C42—431no—
331C42—861no—
332C23—21no—
333C23—431no—
334C23—861no—
335C23—861no—
336C23—3441no—
337C23—1722no—
338C23—1722no—
339C23D4×D4311yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—42no—
344Q8—861no—
345Q8—861no—
346Q8D4×D4312yes—
347D4—21no—
348D4—21no—
349D4—81no—
350D4—432no—
351D4—861no—
352D4—861no—
353D4—861no—
354D4—1722no—
355D4—1721no—
356D4—1722no—
357D4—1722no—
358D4—1722no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—42no—
365C2×C4—431no—
366C2×C4—431no—
367C2×C4—431no—
368C2×C4—861no—
369C2×C4—861no—
370C2×C4—861no—
371C2×C4—861no—
372C2×C4—3441no—
373C2×C4—1722no—
374C2×C4—1722no—
375C2×C4D4×D4311yescharacteristic
376C2×C4C23×D4311yescharacteristic
377C8—21no—
378C8—21no—
379C8—432no—
380C8—861no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—861no—
388C22—861no—
389C22—861no—
390C22—862no—
391C22—3444no—
392C22—1721no—
393C22—1721no—
394C22—1721no—
395C22—1721no—
396C22—1721no—
397C22C2×D4×D4311yescharacteristic
398C4—21no—
399C4—22no—
400C4—41no—
401C4—41no—
402C4—861no—
403C4—861no—
404C4—861no—
405C4—1721no—
406C4—1721no—
407C4C2×D4×D4311yescharacteristic
408C4#1306337011yescharacteristic
409C2—41no—
410C2—81no—
411C2—3441no—
412C2—1721no—
413C2—1722no—
414C2#1458353111yescharacteristic
415C2#1458369811yescharacteristic
416C2#1458370511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#448C2
socleC22×C43C22×D4
hypercenter#448D43
hypocenterC43#3275
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C2×#13063356C2semidirect
2. C2×#13063352C2semidirect
3. #14583560C2semidirect
4. #14583546C2semidirect
5. #14583280C2semidirect
6. #14583156C2semidirect
7. #14583150C2semidirect
8. #14583119C2semidirect
9. #14583117C2semidirect
10. #14583064C2semidirect
11. #14583048C2semidirect
12. #14583046C2semidirect
13. #14582984C2semidirect
14. #14582974C2semidirect
15. C43×#448C2semidirect
21. C2×#10621885C22semidirect
22. C2×#10621885C22semidirect
23. C2×#10621873C22semidirect
28. C2×#10621877C22semidirect
31. #13063314C22semidirect
38. #13063299C22semidirect
41. Q8×Dic43C22semidirect
46. #13063256C22semidirect
47. Dic43⋊C8C22semidirect
48. #13063250C22semidirect
51. #13063245C22semidirect
53. C8×Dic43C22semidirect
54. C22×Q8×C43C22semidirect
58. #103×C43C22semidirect
59. #103×C43C22semidirect
60. C22⋊C8×C43C22semidirect
101. #10621884D4semidirect
221. #448D43semidirect
224. C43#3275semidirect
227. C22×Q8C2×D43semidirect
262. #103C2×D43semidirect
263. #103C2×D43semidirect
268. C22⋊C8C2×D43semidirect