Finite Group Databasebeta

← #19144129

Subgroups — #19144129

Order 5504.

504 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063349C211yesmaximal, characteristic, complemented
2C2×#13063344C211yesmaximal, characteristic, complemented
3#14583462C211yesmaximal, characteristic, complemented
4#14583378C211yesmaximal, characteristic, complemented
5#14583122C211yesmaximal, characteristic, complemented
6#14583120C211yesmaximal, characteristic, complemented
7#14583114C211yesmaximal, characteristic, complemented
8#14583112C211yesmaximal, characteristic, complemented
9#14583098C211yesmaximal, characteristic, complemented
10#14583096C211yesmaximal, characteristic, complemented
11#14583092C211yesmaximal, characteristic, complemented
12#14582924C211yesmaximal, characteristic, complemented
13#14582897C211yesmaximal, characteristic, complemented
14#102×D43C211yesmaximal, characteristic, complemented
15C43×#459C211yesmaximal, characteristic, complemented
16C2×#10621900C2211yescharacteristic
17C2×#10621900C2211yescharacteristic
18C2×D4×D43C2211yescharacteristic
19#13063349—24no—
20#13063344—24no—
21C2×Dic172C2211yescharacteristic, complemented
22C2×#10621873C2211yescharacteristic
23C2×#10621883C2211yescharacteristic
24C2×#10621883C2211yescharacteristic, complemented
25C2×#10621883C2211yescharacteristic, complemented
26C2×#10621882C2211yescharacteristic
27C2×#10621872C2211yescharacteristic
28C2×C8×D43C2211yescharacteristic
29#13063321C2211yescharacteristic
30#13063313C2211yescharacteristic
31#13063312C2211yescharacteristic
32#13063297—21no—
33#13063297—21no—
34#13063293—21no—
35#13063293—21no—
36C4×Dic86C2211yescharacteristic, complemented
37#13063290C2211yescharacteristic, complemented
38D4×Dic43C2211yescharacteristic, complemented
39C4×C22⋊D43—21no—
40(C22⋊D43)⋊C4—21no—
41#13063282C2211yescharacteristic
42#13063281—21no—
43C2×Dic43⋊C4—21no—
44C4⋊C4×D43C2211yescharacteristic
45C4⋊(C43⋊C8)C2211yescharacteristic, complemented
46Dic43⋊C8C2211yescharacteristic, complemented
47Dic43⋊C8C2211yescharacteristic, complemented
48#13063250C2211yescharacteristic, complemented
49#13063248C2211yescharacteristic, complemented
50#13063247C2211yescharacteristic
51#13063246C2211yescharacteristic
52#13063246C2211yescharacteristic, complemented
53#13063245C2211yescharacteristic
54C2×D8×C43C2211yescharacteristic
55C2×D8×C43C2211yescharacteristic, complemented
56#127×C43C2211yescharacteristic
57C4×D4×C43C2211yescharacteristic, complemented
58C4⋊C8×C43C2211yescharacteristic, complemented
59#102×C43C2211yescharacteristic
60#102×C43C2211yescharacteristic, complemented
61C23×D43—21no—
62C2×D4×C43—21no—
63C2×D4×C43—21no—
64C2×D4×C43C2311yescharacteristic
65C2×D4×C43C2311yescharacteristic
66C2×D4×C43C2311yescharacteristic
67C22×C4×C43—21no—
68C2×C22⋊D43—21no—
69C2×C22⋊D43—21no—
70C2×C22⋊D43—21no—
71C2×C22⋊D43—21no—
72C2×C22⋊D43—21no—
73C22×Dic43—21no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76#10621900—22no—
77#10621900—22no—
78#10621900—22no—
79#10621900D414yescomplemented
80D4×D43—22no—
81D4×D43—22no—
82C2×D172C2311yescharacteristic
83C2×C4×D43—21no—
84C2×C4×D43C2311yescharacteristic
85C2×Dic86C2311yescharacteristic
86C2×Dic86C2311yescharacteristic
87D8×C43—22no—
88D8×C43—22no—
89C2×C8×C43C2311yescharacteristic
90C2×C8×C43C2311yescharacteristic
91C4⋊C4×C43C2311yescharacteristic
92C22⋊C4×C43—21no—
93C42×C43C2311yescharacteristic
94C22⋊Dic43—21no—
95C22⋊Dic43—21no—
96C22⋊Dic43—21no—
97#10621883—22no—
98#10621883—22no—
99#10621883—22no—
100#10621882—22no—
101(C2×D43)⋊C4—21no—
102(C2×D43)⋊C4—21no—
103(C2×D43)⋊C4D411yescharacteristic
104(C2×D43)⋊C4D411yescharacteristic
105C4⋊Dic43C2311yescharacteristic
106Dic43⋊C4—21no—
107Dic43⋊C4—21no—
108Dic43⋊C4—21no—
109Dic43⋊C4D411yescharacteristic
110Dic43⋊C4D411yescharacteristic
111C4×Dic43—21no—
112C4×Dic43—21no—
113C4×Dic43C2311yescharacteristic
114C2×C43⋊C8C2311yescharacteristic
115C2×C43⋊C8C2311yescharacteristic
116Dic172—22no—
117#10621873—22no—
118#10621872—22no—
119C8×D43—22no—
120C23×C43—21no—
121C23×C43—21no—
122C23×C43—21no—
123C22×D43—21no—
124C22×D43—42no—
125C22×D43—81no—
126C22×D43—81no—
127C22×D43C2×D411yescharacteristic
128D4×C43—21no—
129D4×C43—21no—
130D4×C43—21no—
131D4×C43—21no—
132D4×C43—21no—
133D4×C43—81no—
134D4×C43—81no—
135D4×C43C2×D412yes—
136C2×C4×C43—21no—
137C2×C4×C43—81no—
138C2×C4×C43C2×D411yescharacteristic
139C2×C4×C43C2×D411yescharacteristic
140C2×C4×C43C2411yescharacteristic
141C22⋊D43—24no—
142C22⋊D43—42no—
143C22⋊D43—42no—
144C22⋊D43—81no—
145C22⋊D43—81no—
146C2×Dic43—21no—
147C2×Dic43—24no—
148C2×Dic43—21no—
149C2×Dic43—21no—
150C2×Dic43—42no—
151C2×Dic43—81no—
152C2×Dic43C2×D411yescharacteristic
153C2×Dic43C2×D411yescharacteristic
154C2×Dic43C2×D411yescharacteristic
155D172—21no—
156D172—21no—
157C4×D43—81no—
158C4×D43C2×D412yes—
159C4×D43#4112yes—
160Dic86—21no—
161Dic86—21no—
162Dic86—21no—
163Dic86C2×D412yes—
164C8×C43—21no—
165C8×C43—21no—
166C43⋊C8—21no—
167C43⋊C8—21no—
168C22×C43—22no—
169C22×C43—41no—
170C22×C43—41no—
171C22×C43—41no—
172C22×C43—41no—
173C22×C43—41no—
174C22×C43—41no—
175C22×C43—41no—
176C22×C43—41no—
177C22×C43C22×D411yescharacteristic
178C2×D43—21no—
179C2×D43—21no—
180C2×D43—41no—
181C2×D43—41no—
182C2×D43—41no—
183C2×D43—84no—
184C2×D43#12112yes—
185C4×C43—21no—
186C4×C43—21no—
187C4×C43—41no—
188C4×C43C22×D411yescharacteristic
189C4×C43C2×#4111yescharacteristic
190Dic43—22no—
191Dic43—21no—
192Dic43—21no—
193Dic43—41no—
194Dic43—41no—
195Dic43#12112yes—
196#3045—431nomaximal, Sylow
197C2×C43—42no—
198C2×C43—81no—
199C2×C43—81no—
200C2×C43C2×#12111yescharacteristic
201C2×C43#57611yescharacteristic
202C2×C43#57711yescharacteristic
203D43—22no—
204D43—81no—
205C2×AGL(1,ℤ/8)—431no—
206C2×#135—431no—
207#535—431no—
208#520—431no—
209#464—431no—
210#464—431no—
211#463—431no—
212#463—431no—
213#460—431no—
214#460—431no—
215#459—431no—
216#459D4311yescharacteristic, complemented
217#424—431no—
218#417—431no—
219C2×#102—431no—
220C43#304511yescharacteristic, complemented, Sylow
221C2×#41—431no—
222C2×#41—431no—
223C22×D4—431no—
224AGL(1,ℤ/8)—864no—
225#135—864no—
226C2×Q16—431no—
227C2×SD16—431no—
228C2×SD16—431no—
229C2×SD16—431no—
230C2×SD16—431no—
231C2×D8—431no—
232C2×D8C2×D4311yescharacteristic
233C2×D8C2×D4311yescharacteristic, complemented
234C2×M16—431no—
235C22×C8—431no—
236#127—431no—
237#127C2×D4311yescharacteristic
238#124—431no—
239#124—431no—
240#121—861no—
241#121—861no—
242#120—861no—
243#120—861no—
244C4×Q8—431no—
245C4×Q8—431no—
246C4×D4—431no—
247C4×D4—861no—
248C4×D4—861no—
249C4×D4C2×D4311yescharacteristic, complemented
250#117—431no—
251#117—861no—
252C2×C4⋊C4—431no—
253C2×C4⋊C4—861no—
254C4⋊C8—431no—
255C4⋊C8—431no—
256C4⋊C8—431no—
257C4⋊C8C2×D4311yescharacteristic, complemented
258#103—431no—
259#103—431no—
260#102—431no—
261#102—431no—
262#102—431no—
263#102—431no—
264#102C2×D4311yescharacteristic
265#102C2×D4311yescharacteristic, complemented
266C24—861no—
267#41—434no—
268#41—862no—
269#41—862no—
270#41—862no—
271C2×Q8—431no—
272C2×Q8—431no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—431no—
276C2×D4—862no—
277C2×D4—862no—
278C2×D4—861no—
279C2×D4—861no—
280C2×D4—861no—
281C2×D4—861no—
282C2×D4—861no—
283C2×D4C22×D4311yescharacteristic
284C2×D4C22×D4311yescharacteristic
285C2×D4C22×D4311yescharacteristic
286C22×C4—21no—
287C22×C4—431no—
288C22×C4—861no—
289C22×C4—861no—
290C22×C4—861no—
291C22×C4—861no—
292Q16—862no—
293SD16—862no—
294SD16—862no—
295SD16—862no—
296SD16—862no—
297D8—22no—
298D8—22no—
299D8—862no—
300M16—862no—
301C2×C8—431no—
302C2×C8—431no—
303C2×C8—862no—
304C2×C8C22×D4311yescharacteristic
305C2×C8C22×D4311yescharacteristic
306C4⋊C4—431no—
307C4⋊C4—431no—
308C4⋊C4—431no—
309C4⋊C4—861no—
310C4⋊C4—861no—
311C4⋊C4—861no—
312C4⋊C4C22×D4311yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—431no—
315C22⋊C4—431no—
316C22⋊C4—861no—
317C22⋊C4—861no—
318C22⋊C4—861no—
319C22⋊C4—861no—
320C22⋊C4—861no—
321C42—431no—
322C42—861no—
323C42—861no—
324C42C22×D4311yescharacteristic
325C23—21no—
326C23—21no—
327C23—21no—
328C23—431no—
329C23—861no—
330C23—3441no—
331C23—3441no—
332C23—1722no—
333Q8—432no—
334Q8—861no—
335Q8—861no—
336Q8—861no—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—21no—
342D4—81no—
343D4—81no—
344D4—864no—
345D4—861no—
346D4—861no—
347D4—3441no—
348D4—3441no—
349D4—1722no—
350D4—1722no—
351D4D4×D4312yes—
352C2×C4—21no—
353C2×C4—81no—
354C2×C4—431no—
355C2×C4—432no—
356C2×C4—432no—
357C2×C4—431no—
358C2×C4—431no—
359C2×C4—864no—
360C2×C4—861no—
361C2×C4—861no—
362C2×C4—861no—
363C2×C4—3441no—
364C2×C4—3441no—
365C2×C4—1722no—
366C2×C4D4×D4311yescharacteristic
367C2×C4D4×D4311yescharacteristic
368C2×C4C23×D4311yescharacteristic
369C8—21no—
370C8—21no—
371C8—861no—
372C8—861no—
373C22—22no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—432no—
383C22—861no—
384C22—861no—
385C22—3444no—
386C22—1721no—
387C22—1721no—
388C22—1721no—
389C22C2×D4×D4311yescharacteristic
390C4—21no—
391C4—21no—
392C4—41no—
393C4—432no—
394C4—862no—
395C4—861no—
396C4—861no—
397C4—1721no—
398C4—1721no—
399C4C2×D4×D4311yescharacteristic
400C4#41×D4311yescharacteristic
401C2—42no—
402C2—81no—
403C2—81no—
404C2—862no—
405C2—3441no—
406C2#121×D4311yescharacteristic
407C2#1458370011yescharacteristic
408C2#1458370911yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#459C2
socleC22×C43C22×D4
hypercenter#459D43
hypocenterC43#3045
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#13063349C2semidirect
2. C2×#13063344C2semidirect
3. #14583462C2semidirect
4. #14583378C2semidirect
5. #14583122C2semidirect
6. #14583120C2semidirect
7. #14583114C2semidirect
8. #14583112C2semidirect
9. #14583098C2semidirect
10. #14583096C2semidirect
11. #14583092C2semidirect
12. #14582924C2semidirect
13. #14582897C2semidirect
14. #102×D43C2semidirect
15. C43×#459C2semidirect
21. C2×Dic172C22semidirect
24. C2×#10621883C22semidirect
25. C2×#10621883C22semidirect
36. C4×Dic86C22semidirect
37. #13063290C22semidirect
38. D4×Dic43C22semidirect
45. C4⋊(C43⋊C8)C22semidirect
46. Dic43⋊C8C22semidirect
47. Dic43⋊C8C22semidirect
48. #13063250C22semidirect
49. #13063248C22semidirect
52. #13063246C22semidirect
55. C2×D8×C43C22semidirect
57. C4×D4×C43C22semidirect
58. C4⋊C8×C43C22semidirect
60. #102×C43C22semidirect
79. #10621900D4semidirect
216. #459D43semidirect
220. C43#3045semidirect
233. C2×D8C2×D43semidirect
249. C4×D4C2×D43semidirect
257. C4⋊C8C2×D43semidirect
265. #102C2×D43semidirect