Finite Group Databasebeta

← #19144832

Subgroups — #19144832

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#14583374C211yesmaximal, characteristic, complemented
3#14583224C211yesmaximal, characteristic, complemented
4#14583220C211yesmaximal, characteristic, complemented
5#14583201C211yesmaximal, characteristic, complemented
6#14583197C211yesmaximal, characteristic, complemented
7#14583092C211yesmaximal, characteristic, complemented
8#14583092C211yesmaximal, characteristic, complemented
9#14583033C211yesmaximal, characteristic, complemented
10#14583011C211yesmaximal, characteristic, complemented
11#14583008C211yesmaximal, characteristic, complemented
12D8×Dic43C211yesmaximal, characteristic, complemented
13#14582979C211yesmaximal, characteristic, complemented
14#14582957C211yesmaximal, characteristic, complemented
15C43×#447C211yesmaximal, characteristic, complemented
16C2×#10621882C2211yescharacteristic
17C2×#10621882C2211yescharacteristic
18#13063321C2211yescharacteristic, complemented
19#13063316C2211yescharacteristic, complemented
20#13063309—21no—
21#13063307—21no—
22#13063299C2211yescharacteristic
23#13063297—21no—
24#13063296—21no—
25D4×Dic43—21no—
26D4×Dic43—21no—
27D4×Dic43C2211yescharacteristic
28D4×Dic43C2211yescharacteristic
29D4×Dic43C2211yescharacteristic
30D4×Dic43C2211yescharacteristic
31D4×Dic43C2211yescharacteristic, complemented
32#13063287C2211yescharacteristic, complemented
33#13063284C2211yescharacteristic
34#13063284C2211yescharacteristic
35C2×C22⋊Dic43—21no—
36C2×C22⋊Dic43—21no—
37#13063259C2211yescharacteristic, complemented
38#13063258C2211yescharacteristic, complemented
39#13063257C2211yescharacteristic, complemented
40#13063256C2211yescharacteristic, complemented
41Dic43⋊C8C2211yescharacteristic, complemented
42Dic43⋊C8C2211yescharacteristic, complemented
43#13063247C2211yescharacteristic, complemented
44#13063247C2211yescharacteristic, complemented
45#13063246C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063246C2211yescharacteristic, complemented
48#13063246C2211yescharacteristic, complemented
49C22⋊(C43⋊C8)C2211yescharacteristic
50#13063235C2211yescharacteristic, complemented
51C8×Dic43C2211yescharacteristic, complemented
52C22×D4×C43C2211yescharacteristic
53C2×D8×C43C2211yescharacteristic
54C2×D8×C43C2211yescharacteristic
55#121×C43C2211yescharacteristic
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59C24×C43—21no—
60C2×D4×C43—22no—
61C2×D4×C43—22no—
62C2×D4×C43—21no—
63C2×D4×C43—21no—
64C2×D4×C43C2311yescharacteristic
65C2×D4×C43C2311yescharacteristic
66C2×D4×C43C2311yescharacteristic
67C22×C4×C43C2311yescharacteristic
68C2×C22⋊D43—21no—
69C2×C22⋊D43—21no—
70C2×C22⋊D43—21no—
71C22×Dic43—21no—
72C22×Dic43—21no—
73C22×Dic43—21no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76C2×D172C2311yescharacteristic
77C2×C4×D43—21no—
78D8×C43—22no—
79D8×C43—22no—
80C2×C8×C43C2311yescharacteristic
81C2×C8×C43C2311yescharacteristic
82C4⋊C4×C43C2311yescharacteristic
83C22⋊C4×C43—21no—
84C22⋊Dic43—21no—
85C22⋊Dic43—21no—
86C22⋊Dic43—21no—
87C22⋊Dic43—21no—
88C22⋊Dic43—21no—
89C22⋊Dic43—21no—
90C22⋊Dic43D411yescharacteristic
91C22⋊Dic43D411yescharacteristic
92#10621882—22no—
93#10621882—22no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4—21no—
96C4⋊Dic43—21no—
97C4⋊Dic43D411yescharacteristic
98C4⋊Dic43D411yescharacteristic
99C4⋊Dic43C2311yescharacteristic
100C4⋊Dic43C2311yescharacteristic
101C4⋊Dic43C2311yescharacteristic
102Dic43⋊C4—21no—
103C4×Dic43—21no—
104C4×Dic43C2311yescharacteristic
105C4×Dic43C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108C23×C43—24no—
109C23×C43—21no—
110C23×C43—21no—
111C23×C43—21no—
112C23×C43—81no—
113C23×C43—81no—
114C23×C43C2×D411yescharacteristic
115C22×D43—21no—
116D4×C43—24no—
117D4×C43—21no—
118D4×C43—21no—
119D4×C43—21no—
120D4×C43—21no—
121D4×C43—81no—
122D4×C43#4112yes—
123D4×C43#4112yes—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43C2×D411yescharacteristic
128C2×C4×C43C2411yescharacteristic
129C22⋊D43—81no—
130C22⋊D43—81no—
131C22⋊D43—81no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—21no—
135C2×Dic43—81no—
136C2×Dic43—81no—
137C2×Dic43—81no—
138C2×Dic43—81no—
139C2×Dic43—81no—
140C2×Dic43C2×D411yescharacteristic
141C2×Dic43C2×D411yescharacteristic
142C2×Dic43C2×D411yescharacteristic
143C2×Dic43C2×D411yescharacteristic
144D172—21no—
145D172—21no—
146C4×D43—81no—
147C8×C43—21no—
148C8×C43—21no—
149C43⋊C8—21no—
150C43⋊C8—21no—
151C22×C43—21no—
152C22×C43—22no—
153C22×C43—22no—
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—41no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43—41no—
161C22×C43—41no—
162C22×C43—41no—
163C22×C43—84no—
164C22×C43C22×D411yescharacteristic
165C2×D43—41no—
166C2×D43—41no—
167C2×D43—41no—
168C4×C43—21no—
169C4×C43—41no—
170C4×C43C2×#4111yescharacteristic
171C4×C43C2×#4111yescharacteristic
172Dic43—21no—
173Dic43—21no—
174Dic43—21no—
175Dic43—21no—
176Dic43—41no—
177Dic43—41no—
178Dic43—41no—
179#3122—431nomaximal, Sylow
180C2×C43—41no—
181C2×C43—42no—
182C2×C43—42no—
183C2×C43—81no—
184C2×C43#52511yescharacteristic
185C2×C43#57611yescharacteristic
186C2×C43#57611yescharacteristic
187D43—81no—
188#540—431no—
189#518—431no—
190#482—431no—
191#482—431no—
192#478—431no—
193#478—431no—
194#459—431no—
195#459—431no—
196#447—431no—
197#447D4311yescharacteristic, complemented
198#442—431no—
199#442—431no—
200C4×D8—431no—
201C4×D8—431no—
202#433—431no—
203C43#312211yescharacteristic, complemented, Sylow
204C22×D4C2×D4311yescharacteristic
205C2×D8—431no—
206C2×D8—431no—
207C2×D8C2×D4311yescharacteristic
208C2×D8C2×D4311yescharacteristic
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#117—431no—
227C2×C22⋊C4—861no—
228C2×C22⋊C4—861no—
229#107—431no—
230#107—431no—
231#106—431no—
232#106—431no—
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
242#102C2×D4311yescharacteristic
243C22⋊C8—431no—
244C22⋊C8C2×D4311yescharacteristic
245#97—431no—
246C4×C8—431no—
247C24—21no—
248C2×D4—22no—
249C2×D4—22no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—431no—
253C2×D4—861no—
254C2×D4—861no—
255C2×D4—861no—
256C2×D4C22×D4311yescharacteristic
257C2×D4C22×D4311yescharacteristic
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—22no—
267D8—22no—
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—431no—
278C4⋊C4—431no—
279C4⋊C4—861no—
280C4⋊C4—861no—
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—431no—
295C42—861no—
296C23—24no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—81no—
301C23—81no—
302C23—861no—
303C23D4×D4311yescharacteristic
304D4—24no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—81no—
310D4—861no—
311D4—861no—
312D4—3441no—
313D4—3441no—
314D4—3441no—
315D4#1062190012yes—
316D4#1062190012yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—431no—
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×C4—3441no—
333C2×C4D4×D4311yescharacteristic
334C2×C4C23×D4311yescharacteristic
335C8—21no—
336C8—21no—
337C8—861no—
338C8—861no—
339C22—21no—
340C22—22no—
341C22—22no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—84no—
352C22—1721no—
353C22—1721no—
354C22—1721no—
355C22C2×D4×D4311yescharacteristic
356C4—21no—
357C4—41no—
358C4—861no—
359C4—861no—
360C4—861no—
361C4—861no—
362C4—1721no—
363C4—1721no—
364C4—1721no—
365C4C2×#1062190011yescharacteristic
366C4C2×#1062190011yescharacteristic
367C2—41no—
368C2—42no—
369C2—42no—
370C2—81no—
371C2—3441no—
372C2#1458340511yescharacteristic
373C2#1458370011yescharacteristic
374C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#447C2
socleC22×C43C22×D4
hypercenter#447D43
hypocenterC43#3122
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #14583502C2semidirect
2. #14583374C2semidirect
3. #14583224C2semidirect
4. #14583220C2semidirect
5. #14583201C2semidirect
6. #14583197C2semidirect
7. #14583092C2semidirect
8. #14583092C2semidirect
9. #14583033C2semidirect
10. #14583011C2semidirect
11. #14583008C2semidirect
12. D8×Dic43C2semidirect
13. #14582979C2semidirect
14. #14582957C2semidirect
15. C43×#447C2semidirect
18. #13063321C22semidirect
19. #13063316C22semidirect
31. D4×Dic43C22semidirect
32. #13063287C22semidirect
37. #13063259C22semidirect
38. #13063258C22semidirect
39. #13063257C22semidirect
40. #13063256C22semidirect
41. Dic43⋊C8C22semidirect
42. Dic43⋊C8C22semidirect
43. #13063247C22semidirect
44. #13063247C22semidirect
47. #13063246C22semidirect
48. #13063246C22semidirect
50. #13063235C22semidirect
51. C8×Dic43C22semidirect
197. #447D43semidirect
203. C43#3122semidirect