Finite Group Databasebeta

← #19144546

Subgroups — #19144546

Order 5504.

418 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583465C211yesmaximal, characteristic
2#14583380C211yesmaximal, characteristic, complemented
3#14583226C211yesmaximal, characteristic, complemented
4#14583224C211yesmaximal, characteristic, complemented
5#14583221C211yesmaximal, characteristic, complemented
6#14583220C211yesmaximal, characteristic, complemented
7#14583217C211yesmaximal, characteristic, complemented
8#14583216C211yesmaximal, characteristic, complemented
9#14583214C211yesmaximal, characteristic, complemented
10#14582940C211yesmaximal, characteristic, complemented
11#14582936C211yesmaximal, characteristic, complemented
12#14582902C211yesmaximal, characteristic, complemented
13#102×D43C211yesmaximal, characteristic, complemented
14#14582864C211yesmaximal, characteristic, complemented
15C43×#480C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×D4×D43C2211yescharacteristic
18C2×#10621872C2211yescharacteristic
19C2×C8×D43C2211yescharacteristic
20#13063321—21no—
21#13063311—21no—
22#13063300C2211yescharacteristic
23#13063299C2211yescharacteristic
24#13063296C2211yescharacteristic
25#13063295—21no—
26#13063293—21no—
27#13063290—21no—
28#13063287—21no—
29C4×C22⋊D43—21no—
30C4×C22⋊D43—21no—
31#13063284C2211yescharacteristic, complemented
32#13063283C2211yescharacteristic
33#13063283C2211yescharacteristic
34#13063283C2211yescharacteristic, complemented
35C4⋊C4×D43C2211yescharacteristic
36C4⋊C4×D43C2211yescharacteristic, complemented
37#13063259C2211yescharacteristic, complemented
38#13063258C2211yescharacteristic, complemented
39#13063257C2211yescharacteristic, complemented
40#13063256C2211yescharacteristic, complemented
41#13063256C2211yescharacteristic, complemented
42#13063256C2211yescharacteristic, complemented
43#13063247C2211yescharacteristic
44#13063247C2211yescharacteristic
45#13063246C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic, complemented
50(C2×D43)⋊C8C2211yescharacteristic, complemented
51(C2×D43)⋊C8C2211yescharacteristic, complemented
52#121×C43C2211yescharacteristic
53C2×C4⋊C4×C43C2211yescharacteristic, complemented
54#107×C43C2211yescharacteristic, complemented
55#107×C43C2211yescharacteristic, complemented
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60C2×D4×C43—21no—
61C2×D4×C43C2311yescharacteristic
62C22×C4×C43—21no—
63C22×C4×C43C2311yescharacteristic
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C2×C22⋊D43D411yescharacteristic
68C2×C22⋊D43D411yescharacteristic
69D4×D43—22no—
70D4×D43—22no—
71#10621898—22no—
72#10621898—22no—
73C2×D172—21no—
74C2×D172D411yescharacteristic
75C2×D172C2311yescharacteristic
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C4×D43C2311yescharacteristic
79C2×C4×D43C2311yescharacteristic
80C2×Dic86D411yescharacteristic
81C2×C8×C43C2311yescharacteristic
82C2×C8×C43C2311yescharacteristic
83C4⋊C4×C43—21no—
84C4⋊C4×C43C2311yescharacteristic
85C4⋊C4×C43C2311yescharacteristic
86C4⋊C4×C43C2311yescharacteristic
87C22⋊C4×C43—21no—
88C22⋊Dic43—21no—
89C22⋊Dic43—21no—
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—
95C4⋊Dic43C2311yescharacteristic
96C4⋊Dic43C2311yescharacteristic
97C4⋊Dic43C2311yescharacteristic
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100C4×Dic43—21no—
101C4×Dic43—21no—
102C4×Dic43—21no—
103C4×Dic43—21no—
104C2×C43⋊C8C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106#10621872—22no—
107C8×D43—22no—
108C23×C43—21no—
109C23×C43C2×D411yescharacteristic
110C22×D43—21no—
111C22×D43—42no—
112C22×D43—81no—
113C22×D43—81no—
114C22×D43C2×D411yescharacteristic
115C22×D43C2×D411yescharacteristic
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×C43—81no—
125C2×C4×C43C2×D411yescharacteristic
126C2×C4×C43C2411yescharacteristic
127C22⋊D43—22no—
128C22⋊D43—22no—
129C22⋊D43—42no—
130C22⋊D43—81no—
131C22⋊D43—81no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—21no—
135C2×Dic43C2×D411yescharacteristic
136C2×Dic43C2×D411yescharacteristic
137D172—22no—
138D172—21no—
139D172—21no—
140D172—81no—
141C4×D43—21no—
142C4×D43—21no—
143C4×D43—81no—
144C4×D43—81no—
145C4×D43#4112yes—
146C4×D43#4112yes—
147Dic86—22no—
148C8×C43—21no—
149C8×C43—21no—
150C43⋊C8—21no—
151C43⋊C8—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43—41no—
158C22×C43C22×D411yescharacteristic
159C2×D43—21no—
160C2×D43—21no—
161C2×D43—21no—
162C2×D43—21no—
163C2×D43—21no—
164C2×D43—41no—
165C2×D43—41no—
166C2×D43—41no—
167C2×D43—84no—
168C2×D43#12312yes—
169C4×C43—21no—
170C4×C43—41no—
171C4×C43—41no—
172C4×C43—41no—
173C4×C43C2×#4111yescharacteristic
174C4×C43C2×#4111yescharacteristic
175Dic43—21no—
176Dic43—41no—
177Dic43—41no—
178Dic43—41no—
179Dic43#12312yes—
180#3096—431nomaximal, Sylow
181C2×C43—41no—
182C2×C43—81no—
183C2×C43C2×#12311yescharacteristic
184C2×C43#57611yescharacteristic
185C2×C43#57711yescharacteristic
186D43—22no—
187D43—41no—
188D43—81no—
189#535—431no—
190#520—431no—
191#482—431no—
192#482—431no—
193#482—431no—
194#482—431no—
195#481—431no—
196#481—431no—
197#480—431no—
198#480D4311yescharacteristic, complemented
199#428—431no—
200#427—431no—
201#418—431no—
202C2×#102—431no—
203#408—431no—
204C43#309611yescharacteristic, complemented, Sylow
205C2×#41—431no—
206C22×D4—431no—
207C2×M16—431no—
208C22×C8—431no—
209#127—861no—
210#124—861no—
211#121—431no—
212#121—431no—
213#121—431no—
214#121C2×D4311yescharacteristic
215#120—861no—
216#120—861no—
217C4×Q8—861no—
218C4×D4—861no—
219C4×D4—861no—
220C4×D4—861no—
221#117—431no—
222#117—431no—
223#117—431no—
224#117—431no—
225C2×C4⋊C4—431no—
226C2×C4⋊C4—431no—
227C2×C4⋊C4C2×D4311yescharacteristic, complemented
228#107—431no—
229#107—431no—
230#107C2×D4311yescharacteristic, complemented
231#107C2×D4311yescharacteristic, complemented
232#106—431no—
233#106—431no—
234#106—431no—
235#106—431no—
236#102—431no—
237#102—431no—
238#102—431no—
239#102—431no—
240#102—431no—
241#102—431no—
242#102C2×D4311yescharacteristic
243#102C2×D4311yescharacteristic
244C22⋊C8—431no—
245C22⋊C8—431no—
246C22⋊C8—431no—
247C22⋊C8C2×D4311yescharacteristic, complemented
248C24—861no—
249#41—862no—
250#41—862no—
251C2×Q8—431no—
252C2×D4—21no—
253C2×D4—431no—
254C2×D4—431no—
255C2×D4—431no—
256C2×D4—431no—
257C2×D4—861no—
258C2×D4—862no—
259C2×D4—862no—
260C2×D4—861no—
261C2×D4—861no—
262C2×D4—861no—
263C2×D4C22×D4311yescharacteristic
264C22×C4—21no—
265C22×C4—431no—
266C22×C4—431no—
267C22×C4—861no—
268C22×C4—861no—
269C22×C4C22×D4311yescharacteristic
270M16—862no—
271C2×C8—431no—
272C2×C8—431no—
273C2×C8—862no—
274C2×C8C22×D4311yescharacteristic
275C2×C8C22×D4311yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—431no—
278C4⋊C4—431no—
279C4⋊C4—431no—
280C4⋊C4—861no—
281C4⋊C4—861no—
282C4⋊C4C22×D4311yescharacteristic
283C4⋊C4C22×D4311yescharacteristic
284C4⋊C4C22×D4311yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—861no—
287C22⋊C4—861no—
288C22⋊C4—861no—
289C22⋊C4—861no—
290C22⋊C4—861no—
291C22⋊C4—861no—
292C22⋊C4—861no—
293C42—861no—
294C42—861no—
295C42—861no—
296C42—861no—
297C23—21no—
298C23—431no—
299C23—431no—
300C23—861no—
301C23—3441no—
302C23—3441no—
303C23—1722no—
304C23D4×D4311yescharacteristic
305Q8—862no—
306D4—21no—
307D4—21no—
308D4—81no—
309D4—862no—
310D4—862no—
311D4—862no—
312D4—861no—
313D4—861no—
314D4—3441no—
315D4—3441no—
316D4—3441no—
317D4—1722no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—81no—
324C2×C4—431no—
325C2×C4—432no—
326C2×C4—432no—
327C2×C4—431no—
328C2×C4—861no—
329C2×C4—861no—
330C2×C4—861no—
331C2×C4—861no—
332C2×C4—861no—
333C2×C4—3441no—
334C2×C4—3441no—
335C2×C4D4×D4311yescharacteristic
336C2×C4C23×D4311yescharacteristic
337C8—21no—
338C8—21no—
339C8—861no—
340C8—861no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—432no—
348C22—861no—
349C22—861no—
350C22—861no—
351C22—861no—
352C22—861no—
353C22—3444no—
354C22—1721no—
355C22—1721no—
356C22—1721no—
357C22C2×D4×D4311yescharacteristic
358C4—21no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—432no—
363C4—861no—
364C4—1721no—
365C4—1721no—
366C4—1721no—
367C4#41×D4311yescharacteristic
368C4#41×D4311yescharacteristic
369C2—41no—
370C2—81no—
371C2—862no—
372C2—3441no—
373C2—1721no—
374C2#123×D4311yescharacteristic
375C2#1458370011yescharacteristic
376C2#1458370811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#480C2
socleC22×C43C22×D4
hypercenter#480D43
hypocenterC43#3096
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #14583380C2semidirect
3. #14583226C2semidirect
4. #14583224C2semidirect
5. #14583221C2semidirect
6. #14583220C2semidirect
7. #14583217C2semidirect
8. #14583216C2semidirect
9. #14583214C2semidirect
10. #14582940C2semidirect
11. #14582936C2semidirect
12. #14582902C2semidirect
13. #102×D43C2semidirect
14. #14582864C2semidirect
15. C43×#480C2semidirect
31. #13063284C22semidirect
34. #13063283C22semidirect
36. C4⋊C4×D43C22semidirect
37. #13063259C22semidirect
38. #13063258C22semidirect
39. #13063257C22semidirect
40. #13063256C22semidirect
41. #13063256C22semidirect
42. #13063256C22semidirect
49. C22⋊(C43⋊C8)C22semidirect
50. (C2×D43)⋊C8C22semidirect
51. (C2×D43)⋊C8C22semidirect
53. C2×C4⋊C4×C43C22semidirect
54. #107×C43C22semidirect
55. #107×C43C22semidirect
58. C22⋊C8×C43C22semidirect
198. #480D43semidirect
204. C43#3096semidirect
227. C2×C4⋊C4C2×D43semidirect
230. #107C2×D43semidirect
231. #107C2×D43semidirect
247. C22⋊C8C2×D43semidirect