Finite Group Databasebeta

← #19144834

Subgroups — #19144834

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#14583502C211yesmaximal, characteristic, complemented
2#14583373C211yesmaximal, characteristic, complemented
3#14583223C211yesmaximal, characteristic, complemented
4#14583202C211yesmaximal, characteristic, complemented
5#14583198C211yesmaximal, characteristic, complemented
6#14583093C211yesmaximal, characteristic, complemented
7#14583093C211yesmaximal, characteristic, complemented
8#14583035C211yesmaximal, characteristic, complemented
9#14583032C211yesmaximal, characteristic, complemented
10#14583010C211yesmaximal, characteristic, complemented
11#14583008C211yesmaximal, characteristic, complemented
12#14582981C211yesmaximal, characteristic, complemented
13#14582979C211yesmaximal, characteristic, complemented
14#14582957C211yesmaximal, characteristic, complemented
15C43×#482C211yesmaximal, characteristic, complemented
16C22×D172C2211yescharacteristic
17C2×D344C2211yescharacteristic
18C2×D344C2211yescharacteristic
19C2×#10621882C2211yescharacteristic
20C2×#10621882C2211yescharacteristic
21#13063321C2211yescharacteristic, complemented
22#13063316C2211yescharacteristic, complemented
23#13063309—21no—
24#13063307—21no—
25#13063299C2211yescharacteristic
26#13063297—21no—
27#13063296—21no—
28C4×D172—21no—
29C4×D172—21no—
30D4×Dic43C2211yescharacteristic, complemented
31#13063287C2211yescharacteristic
32#13063287C2211yescharacteristic
33#13063287C2211yescharacteristic
34#13063287C2211yescharacteristic
35#13063287C2211yescharacteristic, complemented
36#13063284C2211yescharacteristic
37C22⋊C4×D43—21no—
38C22⋊C4×D43—21no—
39#13063258C2211yescharacteristic, complemented
40#13063256C2211yescharacteristic, complemented
41Dic43⋊C8C2211yescharacteristic, complemented
42Dic43⋊C8C2211yescharacteristic, complemented
43#13063247C2211yescharacteristic
44#13063247C2211yescharacteristic
45#13063245C2211yescharacteristic
46#13063245C2211yescharacteristic
47#13063245C2211yescharacteristic, complemented
48#13063245C2211yescharacteristic, complemented
49C22⋊(C43⋊C8)C2211yescharacteristic
50#13063235C2211yescharacteristic, complemented
51C8×Dic43C2211yescharacteristic, complemented
52#121×C43C2211yescharacteristic
53#117×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic, complemented
55#106×C43C2211yescharacteristic, complemented
56#102×C43C2211yescharacteristic, complemented
57#102×C43C2211yescharacteristic, complemented
58C22⋊C8×C43C2211yescharacteristic
59C23×D43—21no—
60C2×D4×C43—21no—
61C2×D4×C43C2311yescharacteristic
62C22×C4×C43C2311yescharacteristic
63C2×C22⋊D43—21no—
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66C22×Dic43—21no—
67C2×D172—21no—
68C2×D172—22no—
69C2×D172—22no—
70C2×D172C2311yescharacteristic
71C2×D172C2311yescharacteristic
72C2×D172C2311yescharacteristic
73C2×C4×D43—21no—
74C2×C4×D43—21no—
75C2×C4×D43—21no—
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C8×C43C2311yescharacteristic
79C2×C8×C43C2311yescharacteristic
80C4⋊C4×C43C2311yescharacteristic
81C4⋊C4×C43C2311yescharacteristic
82C4⋊C4×C43C2311yescharacteristic
83C22⋊C4×C43—21no—
84C22⋊C4×C43—21no—
85C42×C43—21no—
86C22⋊Dic43—21no—
87C22⋊Dic43D411yescharacteristic
88C22⋊Dic43D411yescharacteristic
89#10621882—22no—
90#10621882—22no—
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—
97C4⋊Dic43—21no—
98C4⋊Dic43D411yescharacteristic
99C4⋊Dic43D411yescharacteristic
100C4⋊Dic43C2311yescharacteristic
101Dic43⋊C4—21no—
102C4×Dic43C2311yescharacteristic
103C4×Dic43C2311yescharacteristic
104C2×C43⋊C8C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106D344—22no—
107D344—22no—
108C23×C43—21no—
109C23×C43C2×D411yescharacteristic
110C22×D43—21no—
111C22×D43—21no—
112C22×D43—24no—
113C22×D43—21no—
114C22×D43—81no—
115C22×D43—81no—
116D4×C43—21no—
117D4×C43—21no—
118D4×C43—81no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43C2×D411yescharacteristic
125C2×C4×C43C2411yescharacteristic
126C22⋊D43—81no—
127C22⋊D43—81no—
128C22⋊D43—81no—
129C2×Dic43—21no—
130C2×Dic43—81no—
131C2×Dic43C2×D411yescharacteristic
132C2×Dic43C2×D411yescharacteristic
133C2×Dic43C2×D411yescharacteristic
134C2×Dic43C2×D411yescharacteristic
135D172—24no—
136D172—21no—
137D172—21no—
138D172—21no—
139D172—21no—
140D172#4112yes—
141D172#4112yes—
142C4×D43—81no—
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—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—41no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43C22×D411yescharacteristic
158C2×D43—22no—
159C2×D43—22no—
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—41no—
170C4×C43—41no—
171C4×C43—41no—
172C4×C43C2×#4111yescharacteristic
173C4×C43C2×#4111yescharacteristic
174Dic43—21no—
175Dic43—21no—
176Dic43—21no—
177Dic43—21no—
178Dic43—41no—
179#3122—431nomaximal, Sylow
180C2×C43—41no—
181C2×C43—81no—
182C2×C43#52511yescharacteristic
183C2×C43#57611yescharacteristic
184C2×C43#57611yescharacteristic
185D43—42no—
186D43—42no—
187D43—81no—
188#540—431no—
189#518—431no—
190#482—431no—
191#482D4311yescharacteristic, complemented
192#478—431no—
193#478—431no—
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#125—431no—
211#123—861no—
212#123—861no—
213#121—431no—
214#121—861no—
215#121—861no—
216#121C2×D4311yescharacteristic
217C4×D4—431no—
218C4×D4—431no—
219C4×D4—431no—
220C4×D4—431no—
221C4×D4—431no—
222C4×D4—431no—
223C4×D4—861no—
224C4×D4—861no—
225#117—431no—
226#117C2×D4311yescharacteristic
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⋊C8—431no—
235#102—431no—
236#102—431no—
237#102—431no—
238#102—431no—
239#102—431no—
240#102—431no—
241#102C2×D4311yescharacteristic, complemented
242#102C2×D4311yescharacteristic, complemented
243C22⋊C8—431no—
244C22⋊C8C2×D4311yescharacteristic
245#97—431no—
246C4×C8—431no—
247C24—861no—
248C2×D4—21no—
249C2×D4—431no—
250C2×D4—431no—
251C2×D4—431no—
252C2×D4—862no—
253C2×D4—862no—
254C2×D4—861no—
255C2×D4—861no—
256C2×D4—861no—
257C2×D4—861no—
258C2×D4C22×D4311yescharacteristic
259C22×C4—861no—
260C22×C4—861no—
261C22×C4—861no—
262C22×C4—861no—
263C22×C4—861no—
264C22×C4—861no—
265C22×C4C22×D4311yescharacteristic
266D8—862no—
267D8—862no—
268D8—862no—
269D8—862no—
270C2×C8—431no—
271C2×C8—431no—
272C2×C8C22×D4311yescharacteristic
273C2×C8C22×D4311yescharacteristic
274C4⋊C4—431no—
275C4⋊C4—431no—
276C4⋊C4—431no—
277C4⋊C4—861no—
278C4⋊C4—861no—
279C4⋊C4C22×D4311yescharacteristic
280C4⋊C4C22×D4311yescharacteristic
281C4⋊C4C22×D4311yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—431no—
285C22⋊C4—431no—
286C22⋊C4—861no—
287C22⋊C4—861no—
288C22⋊C4—861no—
289C22⋊C4—861no—
290C22⋊C4—861no—
291C22⋊C4—861no—
292C22⋊C4—861no—
293C42—21no—
294C42—431no—
295C42—431no—
296C23—21no—
297C23—864no—
298C23—861no—
299C23—861no—
300C23—861no—
301C23—3441no—
302C23—3441no—
303C23D4×D4311yescharacteristic
304D4—21no—
305D4—21no—
306D4—81no—
307D4—432no—
308D4—432no—
309D4—864no—
310D4—861no—
311D4—861no—
312D4—861no—
313D4—861no—
314D4—3441no—
315D4—3441no—
316D4—3441no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—431no—
323C2×C4—431no—
324C2×C4—431no—
325C2×C4—431no—
326C2×C4—861no—
327C2×C4—3441no—
328C2×C4—3441no—
329C2×C4—3441no—
330C2×C4—3441no—
331C2×C4—3441no—
332C2×C4—3441no—
333C2×C4D4×D4311yescharacteristic
334C2×C4C23×D4311yescharacteristic
335C8—21no—
336C8—21no—
337C8—861no—
338C8—861no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—862no—
346C22—862no—
347C22—3444no—
348C22—1721no—
349C22—1721no—
350C22—1721no—
351C22—1721no—
352C22—1721no—
353C22—1721no—
354C22—1721no—
355C22C2×D4×D4311yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—861no—
361C4—861no—
362C4—861no—
363C4—861no—
364C4—1721no—
365C4#41×D4311yescharacteristic
366C4#41×D4311yescharacteristic
367C2—41no—
368C2—81no—
369C2—3441no—
370C2—1722no—
371C2—1722no—
372C2#1458340711yescharacteristic
373C2#1458370111yescharacteristic
374C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#482C2
socleC22×C43C22×D4
hypercenter#482D43
hypocenterC43#3122
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #14583502C2semidirect
2. #14583373C2semidirect
3. #14583223C2semidirect
4. #14583202C2semidirect
5. #14583198C2semidirect
6. #14583093C2semidirect
7. #14583093C2semidirect
8. #14583035C2semidirect
9. #14583032C2semidirect
10. #14583010C2semidirect
11. #14583008C2semidirect
12. #14582981C2semidirect
13. #14582979C2semidirect
14. #14582957C2semidirect
15. C43×#482C2semidirect
21. #13063321C22semidirect
22. #13063316C22semidirect
30. D4×Dic43C22semidirect
35. #13063287C22semidirect
39. #13063258C22semidirect
40. #13063256C22semidirect
41. Dic43⋊C8C22semidirect
42. Dic43⋊C8C22semidirect
47. #13063245C22semidirect
48. #13063245C22semidirect
50. #13063235C22semidirect
51. C8×Dic43C22semidirect
54. #107×C43C22semidirect
55. #106×C43C22semidirect
56. #102×C43C22semidirect
57. #102×C43C22semidirect
191. #482D43semidirect
203. C43#3122semidirect
230. #107C2×D43semidirect
232. #106C2×D43semidirect
241. #102C2×D43semidirect
242. #102C2×D43semidirect