Finite Group Databasebeta

← #19144840

Subgroups — #19144840

Order 5504.

418 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583505C211yesmaximal, characteristic, complemented
2#14583371C211yesmaximal, characteristic, complemented
3#14583226C211yesmaximal, characteristic, complemented
4#14583225C211yesmaximal, characteristic, complemented
5#14583196C211yesmaximal, characteristic, complemented
6#14583095C211yesmaximal, characteristic, complemented
7#14583094C211yesmaximal, characteristic, complemented
8#14583034C211yesmaximal, characteristic, complemented
9#14583034C211yesmaximal, characteristic, complemented
10#14583010C211yesmaximal, characteristic, complemented
11#14583008C211yesmaximal, characteristic, complemented
12#14582981C211yesmaximal, characteristic, complemented
13#14582979C211yesmaximal, characteristic, complemented
14#14582959C211yesmaximal, characteristic, complemented
15C43×#478C211yesmaximal, characteristic, complemented
16C2×D4×D43C2211yescharacteristic
17C2×D344C2211yescharacteristic
18C2×D344C2211yescharacteristic
19C2×#10621882C2211yescharacteristic
20C2×#10621882C2211yescharacteristic
21#13063322C2211yescharacteristic, complemented
22#13063310—21no—
23#13063310—21no—
24#13063300—21no—
25#13063300—21no—
26#13063300C2211yescharacteristic
27#13063300C2211yescharacteristic
28C4×D172C2211yescharacteristic
29D4×Dic43C2211yescharacteristic
30#13063287C2211yescharacteristic
31#13063287C2211yescharacteristic, complemented
32#13063287C2211yescharacteristic, complemented
33C4×C22⋊D43—21no—
34(C22⋊D43)⋊C4—21no—
35#13063283C2211yescharacteristic
36#13063282C2211yescharacteristic
37C2×(C2×D43)⋊C4—21no—
38C22⋊C4×D43—21no—
39#13063258C2211yescharacteristic, complemented
40#13063256C2211yescharacteristic, complemented
41C4⋊(C43⋊C8)C2211yescharacteristic, complemented
42#13063247C2211yescharacteristic, complemented
43#13063247C2211yescharacteristic, complemented
44#13063245C2211yescharacteristic
45#13063245C2211yescharacteristic
46#13063245C2211yescharacteristic, complemented
47#13063245C2211yescharacteristic, complemented
48(C2×D43)⋊C8C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50#13063235C2211yescharacteristic, complemented
51C8×Dic43C2211yescharacteristic, complemented
52#125×C43C2211yescharacteristic, complemented
53C4×D4×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic, complemented
55#106×C43C2211yescharacteristic, complemented
56C4⋊C8×C43C2211yescharacteristic, complemented
57#102×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic
59C23×D43—21no—
60C2×D4×C43C2311yescharacteristic
61C22×C4×C43—21no—
62C2×C22⋊D43—21no—
63C22×Dic43—21no—
64D4×D43—22no—
65D4×D43—22no—
66C2×D172—21no—
67C2×D172—21no—
68C2×D172—21no—
69C2×D172—21no—
70C2×D172C2311yescharacteristic
71C2×D172C2311yescharacteristic
72C2×D172C2311yescharacteristic
73C2×C4×D43—21no—
74C2×C4×D43—21no—
75C2×C4×D43—21no—
76C2×C4×D43—21no—
77C2×C4×D43C2311yescharacteristic
78C2×C8×C43C2311yescharacteristic
79C2×C8×C43C2311yescharacteristic
80C4⋊C4×C43—21no—
81C4⋊C4×C43—21no—
82C4⋊C4×C43C2311yescharacteristic
83C4⋊C4×C43C2311yescharacteristic
84C4⋊C4×C43C2311yescharacteristic
85C22⋊C4×C43—21no—
86C42×C43C2311yescharacteristic
87C22⋊Dic43—21no—
88#10621882—22no—
89#10621882—22no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4—21no—
97(C2×D43)⋊C4D411yescharacteristic
98(C2×D43)⋊C4D411yescharacteristic
99C4⋊Dic43C2311yescharacteristic
100Dic43⋊C4D411yescharacteristic
101Dic43⋊C4D411yescharacteristic
102C4×Dic43—21no—
103C4×Dic43C2311yescharacteristic
104C2×C43⋊C8C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106D344—22no—
107D344—22no—
108C23×C43—21no—
109C22×D43—21no—
110C22×D43—24no—
111C22×D43—21no—
112C22×D43—21no—
113C22×D43—81no—
114C22×D43—81no—
115C22×D43C2×D411yescharacteristic
116D4×C43—21no—
117D4×C43#4112yes—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—81no—
122C2×C4×C43C2×D411yescharacteristic
123C2×C4×C43C2×D411yescharacteristic
124C2×C4×C43C2411yescharacteristic
125C22⋊D43—24no—
126C2×Dic43—21no—
127C2×Dic43—81no—
128C2×Dic43C2×D411yescharacteristic
129C2×Dic43C2×D411yescharacteristic
130C2×Dic43C2×D411yescharacteristic
131D172—21no—
132D172—21no—
133D172—21no—
134D172—21no—
135D172—21no—
136D172—81no—
137D172—81no—
138D172—81no—
139D172—81no—
140D172#4112yes—
141C4×D43—21no—
142C4×D43—21no—
143C4×D43—81no—
144C4×D43—81no—
145C4×D43—81no—
146C4×D43—81no—
147C8×C43—21no—
148C8×C43—21no—
149C43⋊C8—21no—
150C43⋊C8—21no—
151C22×C43—22no—
152C22×C43—41no—
153C22×C43—41no—
154C22×C43C22×D411yescharacteristic
155C2×D43—21no—
156C2×D43—22no—
157C2×D43—21no—
158C2×D43—21no—
159C2×D43—41no—
160C2×D43—41no—
161C2×D43—41no—
162C2×D43—41no—
163C2×D43—41no—
164C2×D43—41no—
165C2×D43—41no—
166C2×D43—41no—
167C2×D43—84no—
168C4×C43—21no—
169C4×C43—21no—
170C4×C43—41no—
171C4×C43—41no—
172C4×C43—41no—
173C4×C43C2×#4111yescharacteristic
174C4×C43C2×#4111yescharacteristic
175Dic43—21no—
176Dic43—21no—
177Dic43—21no—
178Dic43—41no—
179#3122—431nomaximal, Sylow
180C2×C43—42no—
181C2×C43#52511yescharacteristic
182C2×C43#57611yescharacteristic
183C2×C43#57611yescharacteristic
184D43—41no—
185D43—42no—
186D43—81no—
187D43—81no—
188#540—431no—
189#518—431no—
190#482—431no—
191#482—431no—
192#478—431no—
193#478D4311yescharacteristic, complemented
194#459—431no—
195#459—431no—
196#447—431no—
197#447—431no—
198#442—431no—
199#442—431no—
200C4×D8—431no—
201C4×D8—431no—
202#433—431no—
203C43#312211yescharacteristic, complemented, Sylow
204C22×D4—431no—
205C2×D8—431no—
206C2×D8—431no—
207C2×D8—431no—
208C2×D8—431no—
209#127—431no—
210#125C2×D4311yescharacteristic, complemented
211#123—861no—
212#123—861no—
213#121—431no—
214#121—431no—
215#121—861no—
216#121—861no—
217C4×D4—431no—
218C4×D4—431no—
219C4×D4—431no—
220C4×D4—431no—
221C4×D4—431no—
222C4×D4—861no—
223C4×D4—861no—
224C4×D4C2×D4311yescharacteristic
225#117—431no—
226#117—431no—
227C2×C22⋊C4—861no—
228C2×C22⋊C4—861no—
229#107—431no—
230#107C2×D4311yescharacteristic, complemented
231#106—431no—
232#106C2×D4311yescharacteristic, complemented
233C4⋊C8—431no—
234C4⋊C8C2×D4311yescharacteristic, complemented
235#102—431no—
236#102—431no—
237#102—431no—
238#102—431no—
239#102—431no—
240#102—431no—
241#102C2×D4311yescharacteristic
242#102C2×D4311yescharacteristic
243C22⋊C8—431no—
244C22⋊C8—431no—
245#97—431no—
246C4×C8—431no—
247C24—861no—
248C2×D4—431no—
249C2×D4—431no—
250C2×D4—431no—
251C2×D4—861no—
252C2×D4—861no—
253C2×D4—861no—
254C2×D4—862no—
255C2×D4—862no—
256C2×D4—861no—
257C2×D4—861no—
258C2×D4C22×D4311yescharacteristic
259C22×C4—21no—
260C22×C4—431no—
261C22×C4—861no—
262C22×C4—861no—
263C22×C4—861no—
264C22×C4—861no—
265C22×C4—861no—
266D8—862no—
267D8—862no—
268D8—862no—
269D8—862no—
270C2×C8—431no—
271C2×C8—431no—
272C2×C8C22×D4311yescharacteristic
273C2×C8C22×D4311yescharacteristic
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—431no—
277C4⋊C4—431no—
278C4⋊C4—431no—
279C4⋊C4C22×D4311yescharacteristic
280C4⋊C4C22×D4311yescharacteristic
281C4⋊C4C22×D4311yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—431no—
284C22⋊C4—431no—
285C22⋊C4—861no—
286C22⋊C4—861no—
287C22⋊C4—861no—
288C22⋊C4—861no—
289C22⋊C4—861no—
290C22⋊C4—861no—
291C22⋊C4—861no—
292C22⋊C4—861no—
293C42—431no—
294C42—861no—
295C42C22×D4311yescharacteristic
296C23—21no—
297C23—431no—
298C23—864no—
299C23—861no—
300C23—861no—
301C23—861no—
302C23—3441no—
303C23—3441no—
304D4—21no—
305D4—432no—
306D4—864no—
307D4—861no—
308D4—861no—
309D4—861no—
310D4—861no—
311D4—861no—
312D4—3441no—
313D4—3441no—
314D4—3441no—
315D4—3441no—
316D4#1062190212yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—81no—
321C2×C4—431no—
322C2×C4—431no—
323C2×C4—431no—
324C2×C4—861no—
325C2×C4—861no—
326C2×C4—861no—
327C2×C4—3441no—
328C2×C4—3441no—
329C2×C4—3441no—
330C2×C4—3441no—
331C2×C4—3441no—
332C2×C4D4×D4311yescharacteristic
333C2×C4D4×D4311yescharacteristic
334C2×C4C23×D4311yescharacteristic
335C8—21no—
336C8—21no—
337C8—861no—
338C8—861no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—861no—
343C22—862no—
344C22—861no—
345C22—861no—
346C22—3444no—
347C22—1721no—
348C22—1721no—
349C22—1721no—
350C22—1721no—
351C22—1721no—
352C22—1721no—
353C22—1721no—
354C22—1721no—
355C22C2×D4×D4311yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—861no—
362C4—861no—
363C4—861no—
364C4—1721no—
365C4#41×D4311yescharacteristic
366C4C2×#1062190211yescharacteristic
367C2—42no—
368C2—3441no—
369C2—3441no—
370C2—1721no—
371C2—1722no—
372C2#1458341211yescharacteristic
373C2#1458370111yescharacteristic
374C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#478C2
socleC22×C43C22×D4
hypercenter#478D43
hypocenterC43#3122
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #14583505C2semidirect
2. #14583371C2semidirect
3. #14583226C2semidirect
4. #14583225C2semidirect
5. #14583196C2semidirect
6. #14583095C2semidirect
7. #14583094C2semidirect
8. #14583034C2semidirect
9. #14583034C2semidirect
10. #14583010C2semidirect
11. #14583008C2semidirect
12. #14582981C2semidirect
13. #14582979C2semidirect
14. #14582959C2semidirect
15. C43×#478C2semidirect
21. #13063322C22semidirect
31. #13063287C22semidirect
32. #13063287C22semidirect
39. #13063258C22semidirect
40. #13063256C22semidirect
41. C4⋊(C43⋊C8)C22semidirect
42. #13063247C22semidirect
43. #13063247C22semidirect
46. #13063245C22semidirect
47. #13063245C22semidirect
50. #13063235C22semidirect
51. C8×Dic43C22semidirect
52. #125×C43C22semidirect
54. #107×C43C22semidirect
55. #106×C43C22semidirect
56. C4⋊C8×C43C22semidirect
193. #478D43semidirect
203. C43#3122semidirect
210. #125C2×D43semidirect
230. #107C2×D43semidirect
232. #106C2×D43semidirect
234. C4⋊C8C2×D43semidirect