Finite Group Databasebeta

← #19144836

Subgroups — #19144836

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#14583503C211yesmaximal, characteristic, complemented
2#14583371C211yesmaximal, characteristic, complemented
3#14583222C211yesmaximal, characteristic, complemented
4#14583221C211yesmaximal, characteristic, complemented
5#14583200C211yesmaximal, characteristic, complemented
6#14583199C211yesmaximal, characteristic, complemented
7#14583091C211yesmaximal, characteristic, complemented
8#14583031C211yesmaximal, characteristic, complemented
9#14583031C211yesmaximal, characteristic, complemented
10#14583011C211yesmaximal, characteristic, complemented
11#14583008C211yesmaximal, characteristic, complemented
12D8×Dic43C211yesmaximal, characteristic, complemented
13#14582979C211yesmaximal, characteristic, complemented
14#14582959C211yesmaximal, characteristic, complemented
15C43×#459C211yesmaximal, characteristic, complemented
16C2×D4×D43C2211yescharacteristic
17C2×#10621882C2211yescharacteristic
18C2×#10621882C2211yescharacteristic
19#13063317C2211yescharacteristic, complemented
20#13063306—21no—
21#13063306—21no—
22#13063297—21no—
23#13063297—21no—
24#13063296C2211yescharacteristic
25#13063296C2211yescharacteristic
26C4×D172C2211yescharacteristic
27D4×Dic43C2211yescharacteristic
28D4×Dic43C2211yescharacteristic, complemented
29D4×Dic43C2211yescharacteristic, complemented
30#13063287C2211yescharacteristic
31C4×C22⋊D43—21no—
32(C22⋊D43)⋊C4—21no—
33#13063283C2211yescharacteristic
34#13063282C2211yescharacteristic
35C2×(C2×D43)⋊C4—21no—
36C22⋊C4×D43—21no—
37#13063259C2211yescharacteristic, complemented
38#13063258C2211yescharacteristic, complemented
39#13063257C2211yescharacteristic, complemented
40#13063256C2211yescharacteristic, complemented
41C4⋊(C43⋊C8)C2211yescharacteristic, complemented
42#13063247C2211yescharacteristic
43#13063247C2211yescharacteristic
44#13063246C2211yescharacteristic
45#13063246C2211yescharacteristic
46#13063246C2211yescharacteristic, complemented
47#13063246C2211yescharacteristic, complemented
48(C2×D43)⋊C8C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50#13063235C2211yescharacteristic, complemented
51C8×Dic43C2211yescharacteristic, complemented
52C2×D8×C43C2211yescharacteristic
53C2×D8×C43C2211yescharacteristic
54#127×C43C2211yescharacteristic, complemented
55C4×D4×C43C2211yescharacteristic
56C4⋊C8×C43C2211yescharacteristic, complemented
57#102×C43C2211yescharacteristic, complemented
58#102×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60C2×D4×C43—21no—
61C2×D4×C43—21no—
62C2×D4×C43C2311yescharacteristic
63C2×D4×C43C2311yescharacteristic
64C2×D4×C43C2311yescharacteristic
65C22×C4×C43—21no—
66C2×C22⋊D43—21no—
67C2×C22⋊D43—21no—
68C2×C22⋊D43—21no—
69C22×Dic43—21no—
70C22×Dic43—21no—
71C22×Dic43—21no—
72D4×D43—22no—
73D4×D43—22no—
74C2×D172C2311yescharacteristic
75C2×C4×D43—21no—
76C2×C4×D43—21no—
77C2×C4×D43C2311yescharacteristic
78D8×C43—22no—
79D8×C43—22no—
80C2×C8×C43C2311yescharacteristic
81C2×C8×C43C2311yescharacteristic
82C4⋊C4×C43C2311yescharacteristic
83C22⋊C4×C43—21no—
84C42×C43C2311yescharacteristic
85C22⋊Dic43—21no—
86C22⋊Dic43—21no—
87C22⋊Dic43—21no—
88C22⋊Dic43—21no—
89C22⋊Dic43—21no—
90#10621882—22no—
91#10621882—22no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4D411yescharacteristic
96(C2×D43)⋊C4D411yescharacteristic
97C4⋊Dic43C2311yescharacteristic
98C4⋊Dic43C2311yescharacteristic
99C4⋊Dic43C2311yescharacteristic
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102Dic43⋊C4D411yescharacteristic
103Dic43⋊C4D411yescharacteristic
104C4×Dic43—21no—
105C4×Dic43C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108C23×C43—21no—
109C23×C43—21no—
110C23×C43—21no—
111C22×D43—21no—
112C22×D43—24no—
113C22×D43—81no—
114C22×D43—81no—
115C22×D43C2×D411yescharacteristic
116D4×C43—21no—
117D4×C43—21no—
118D4×C43—21no—
119D4×C43—21no—
120D4×C43—21no—
121D4×C43—81no—
122D4×C43—81no—
123D4×C43#4112yes—
124C2×C4×C43—21no—
125C2×C4×C43—81no—
126C2×C4×C43C2×D411yescharacteristic
127C2×C4×C43C2×D411yescharacteristic
128C2×C4×C43C2411yescharacteristic
129C22⋊D43—24no—
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×Dic43C2×D411yescharacteristic
139C2×Dic43C2×D411yescharacteristic
140C2×Dic43C2×D411yescharacteristic
141D172—21no—
142D172#4112yes—
143C4×D43—21no—
144C4×D43—21no—
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×C43—41no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43C22×D411yescharacteristic
161C2×D43—21no—
162C2×D43—22no—
163C2×D43—21no—
164C2×D43—21no—
165C2×D43—41no—
166C2×D43—41no—
167C2×D43—84no—
168C4×C43—21no—
169C4×C43—21no—
170C4×C43—41no—
171C4×C43C2×#4111yescharacteristic
172C4×C43C2×#4111yescharacteristic
173Dic43—21no—
174Dic43—21no—
175Dic43—21no—
176Dic43—41no—
177Dic43—41no—
178Dic43—41no—
179#3122—431nomaximal, Sylow
180C2×C43—42no—
181C2×C43—81no—
182C2×C43—81no—
183C2×C43#52511yescharacteristic
184C2×C43#57611yescharacteristic
185C2×C43#57611yescharacteristic
186D43—41no—
187D43—42no—
188#540—431no—
189#518—431no—
190#482—431no—
191#482—431no—
192#478—431no—
193#478—431no—
194#459—431no—
195#459D4311yescharacteristic, complemented
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×D8C2×D4311yescharacteristic
208C2×D8C2×D4311yescharacteristic
209#127C2×D4311yescharacteristic, complemented
210#125—431no—
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#107—431no—
231#106—431no—
232#106—431no—
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, complemented
242#102C2×D4311yescharacteristic, complemented
243C22⋊C8—431no—
244C22⋊C8—431no—
245#97—431no—
246C4×C8—431no—
247C24—861no—
248C2×D4—21no—
249C2×D4—21no—
250C2×D4—431no—
251C2×D4—861no—
252C2×D4—862no—
253C2×D4—862no—
254C2×D4—861no—
255C2×D4—861no—
256C2×D4C22×D4311yescharacteristic
257C2×D4C22×D4311yescharacteristic
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—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—861no—
295C42C22×D4311yescharacteristic
296C23—21no—
297C23—21no—
298C23—21no—
299C23—431no—
300C23—864no—
301C23—861no—
302C23—3441no—
303C23—3441no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—81no—
310D4—81no—
311D4—432no—
312D4—864no—
313D4—861no—
314D4—3441no—
315D4—3441no—
316D4#1062190012yes—
317C2×C4—21no—
318C2×C4—81no—
319C2×C4—431no—
320C2×C4—431no—
321C2×C4—431no—
322C2×C4—861no—
323C2×C4—861no—
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—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—861no—
349C22—862no—
350C22—861no—
351C22—861no—
352C22—3444no—
353C22—1721no—
354C22—1721no—
355C22C2×D4×D4311yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—861no—
360C4—861no—
361C4—861no—
362C4—1721no—
363C4—1721no—
364C4—1721no—
365C4#41×D4311yescharacteristic
366C4C2×#1062190011yescharacteristic
367C2—42no—
368C2—81no—
369C2—81no—
370C2—1721no—
371C2—1722no—
372C2#1458340911yescharacteristic
373C2#1458370011yescharacteristic
374C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#459C2
socleC22×C43C22×D4
hypercenter#459D43
hypocenterC43#3122
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. #14583503C2semidirect
2. #14583371C2semidirect
3. #14583222C2semidirect
4. #14583221C2semidirect
5. #14583200C2semidirect
6. #14583199C2semidirect
7. #14583091C2semidirect
8. #14583031C2semidirect
9. #14583031C2semidirect
10. #14583011C2semidirect
11. #14583008C2semidirect
12. D8×Dic43C2semidirect
13. #14582979C2semidirect
14. #14582959C2semidirect
15. C43×#459C2semidirect
19. #13063317C22semidirect
28. D4×Dic43C22semidirect
29. D4×Dic43C22semidirect
37. #13063259C22semidirect
38. #13063258C22semidirect
39. #13063257C22semidirect
40. #13063256C22semidirect
41. C4⋊(C43⋊C8)C22semidirect
46. #13063246C22semidirect
47. #13063246C22semidirect
50. #13063235C22semidirect
51. C8×Dic43C22semidirect
54. #127×C43C22semidirect
56. C4⋊C8×C43C22semidirect
57. #102×C43C22semidirect
58. #102×C43C22semidirect
195. #459D43semidirect
203. C43#3122semidirect
209. #127C2×D43semidirect
234. C4⋊C8C2×D43semidirect
241. #102C2×D43semidirect
242. #102C2×D43semidirect