Finite Group Databasebeta

← #19144774

Subgroups — #19144774

Order 5504.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583516C211yesmaximal, characteristic, complemented
2#14583373C211yesmaximal, characteristic, complemented
3#14583240C211yesmaximal, characteristic, complemented
4#14583188C211yesmaximal, characteristic, complemented
5#14583178C211yesmaximal, characteristic, complemented
6#14583113C211yesmaximal, characteristic, complemented
7#14583113C211yesmaximal, characteristic, complemented
8#14583052C211yesmaximal, characteristic, complemented
9#14583032C211yesmaximal, characteristic
10#14583008C211yesmaximal, characteristic, complemented
11#14582998C211yesmaximal, characteristic, complemented
12#14582986C211yesmaximal, characteristic, complemented
13#14582979C211yesmaximal, characteristic, complemented
14#14582957C211yesmaximal, characteristic, complemented
15C43×#482C211yesmaximal, characteristic, complemented
16C22×D172C2211yescharacteristic
17C2×#10621873C2211yescharacteristic
18C2×#10621873C2211yescharacteristic
19C2×#10621882C2211yescharacteristic
20C2×#10621882C2211yescharacteristic
21#13063324C2211yescharacteristic, complemented
22#13063318—21no—
23#13063312—21no—
24#13063312C2211yescharacteristic, complemented
25#13063306—21no—
26#13063304C2211yescharacteristic
27#13063302—21no—
28#13063290C2211yescharacteristic, complemented
29C4×D172—21no—
30C4×D172—21no—
31D4×Dic43C2211yescharacteristic, complemented
32#13063287C2211yescharacteristic
33#13063287C2211yescharacteristic
34#13063287C2211yescharacteristic
35#13063287C2211yescharacteristic
36#13063284C2211yescharacteristic
37C22⋊C4×D43—21no—
38C22⋊C4×D43—21no—
39#13063258C2211yescharacteristic, complemented
40#13063256C2211yescharacteristic, complemented
41Dic43⋊C8C2211yescharacteristic, complemented
42Dic43⋊C8C2211yescharacteristic, complemented
43#13063248C2211yescharacteristic, complemented
44#13063248C2211yescharacteristic, complemented
45#13063247C2211yescharacteristic
46#13063247C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
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
63C22×Dic43—21no—
64C2×D172—21no—
65C2×D172—22no—
66C2×D172—22no—
67C2×D172C2311yescharacteristic
68C2×D172C2311yescharacteristic
69C2×C4×D43—21no—
70C2×C4×D43—21no—
71C2×C4×D43—21no—
72C2×C4×D43—21no—
73C2×Dic86—21no—
74C2×Dic86C2311yescharacteristic
75C2×C8×C43C2311yescharacteristic
76C2×C8×C43C2311yescharacteristic
77C4⋊C4×C43C2311yescharacteristic
78C4⋊C4×C43C2311yescharacteristic
79C4⋊C4×C43C2311yescharacteristic
80C22⋊C4×C43—21no—
81C22⋊C4×C43—21no—
82C42×C43—21no—
83C22⋊Dic43—21no—
84C22⋊Dic43—21no—
85C22⋊Dic43—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—
95C4⋊Dic43D411yescharacteristic
96C4⋊Dic43D411yescharacteristic
97C4⋊Dic43C2311yescharacteristic
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101C4×Dic43—21no—
102C4×Dic43C2311yescharacteristic
103C4×Dic43C2311yescharacteristic
104C2×C43⋊C8C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106#10621873—22no—
107#10621873—22no—
108C23×C43—21no—
109C23×C43C2×D411yescharacteristic
110C22×D43—21no—
111C22×D43—21no—
112C22×D43—24no—
113C22×D43—81no—
114C22×D43—81no—
115D4×C43—21no—
116D4×C43—21no—
117D4×C43—81no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43C2×D411yescharacteristic
124C2×C4×C43C2411yescharacteristic
125C2×Dic43—21no—
126C2×Dic43—21no—
127C2×Dic43—81no—
128C2×Dic43C2×D411yescharacteristic
129C2×Dic43C2×D411yescharacteristic
130C2×Dic43C2×D411yescharacteristic
131C2×Dic43C2×D411yescharacteristic
132D172—24no—
133D172—21no—
134D172—21no—
135D172#4112yes—
136D172#4112yes—
137C4×D43—81no—
138C4×D43—81no—
139C4×D43—81no—
140C4×D43—81no—
141Dic86—21no—
142Dic86—21no—
143Dic86—81no—
144C8×C43—21no—
145C8×C43—21no—
146C43⋊C8—21no—
147C43⋊C8—21no—
148C22×C43—21no—
149C22×C43—21no—
150C22×C43—21no—
151C22×C43—41no—
152C22×C43—41no—
153C22×C43—41no—
154C22×C43C22×D411yescharacteristic
155C2×D43—22no—
156C2×D43—22no—
157C2×D43—41no—
158C2×D43—41no—
159C2×D43—41no—
160C2×D43—41no—
161C2×D43—84no—
162C4×C43—21no—
163C4×C43—41no—
164C4×C43—41no—
165C4×C43—41no—
166C4×C43C2×#4111yescharacteristic
167C4×C43C2×#4111yescharacteristic
168Dic43—21no—
169Dic43—21no—
170Dic43—21no—
171Dic43—21no—
172Dic43—41no—
173Dic43—41no—
174#3118—431nomaximal, Sylow
175C2×C43—41no—
176C2×C43—81no—
177C2×C43#52511yescharacteristic
178C2×C43#57611yescharacteristic
179C2×C43#57711yescharacteristic
180D43—42no—
181D43—42no—
182#542—431no—
183#518—431no—
184#485—431no—
185#482D4311yescharacteristic, complemented
186#476—431no—
187#474—431no—
188#463—431no—
189#463—431no—
190#450—431no—
191#447—431no—
192#442—431no—
193#440—431no—
194C4×SD16—431no—
195C4×D8—431no—
196#433—431no—
197C43#311811yescharacteristic, complemented, Sylow
198C22×D4—431no—
199C2×SD16—431no—
200C2×SD16—431no—
201C2×D8—431no—
202C2×D8—431no—
203C4⋊Q8—431no—
204#126—861no—
205#124—431no—
206#124—861no—
207#123—861no—
208C22⋊Q8—431no—
209C22⋊Q8—861no—
210#121C2×D4311yescharacteristic
211C4×Q8—431no—
212C4×D4—431no—
213C4×D4—431no—
214C4×D4—431no—
215C4×D4—431no—
216C4×D4—431no—
217C4×D4—861no—
218C4×D4—861no—
219#117—431no—
220#117C2×D4311yescharacteristic
221C2×C22⋊C4—861no—
222C2×C22⋊C4—861no—
223#107—431no—
224#107C2×D4311yescharacteristic, complemented
225#106—431no—
226#106C2×D4311yescharacteristic, complemented
227C4⋊C8—431no—
228C4⋊C8—431no—
229#103—431no—
230#103—431no—
231#102—431no—
232#102—431no—
233#102—431no—
234#102—431no—
235#102C2×D4311yescharacteristic, complemented
236#102C2×D4311yescharacteristic, complemented
237C22⋊C8—431no—
238C22⋊C8C2×D4311yescharacteristic
239#97—431no—
240C4×C8—431no—
241C24—861no—
242C2×Q8—431no—
243C2×Q8—861no—
244C2×D4—21no—
245C2×D4—431no—
246C2×D4—431no—
247C2×D4—862no—
248C2×D4—862no—
249C2×D4—861no—
250C2×D4C22×D4311yescharacteristic
251C22×C4—861no—
252C22×C4—861no—
253C22×C4—861no—
254C22×C4—861no—
255C22×C4—861no—
256C22×C4C22×D4311yescharacteristic
257SD16—862no—
258SD16—862no—
259D8—862no—
260D8—862no—
261C2×C8—431no—
262C2×C8—431no—
263C2×C8C22×D4311yescharacteristic
264C2×C8C22×D4311yescharacteristic
265C4⋊C4—431no—
266C4⋊C4—431no—
267C4⋊C4—431no—
268C4⋊C4—861no—
269C4⋊C4—861no—
270C4⋊C4—861no—
271C4⋊C4C22×D4311yescharacteristic
272C4⋊C4C22×D4311yescharacteristic
273C4⋊C4C22×D4311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—431no—
277C22⋊C4—431no—
278C22⋊C4—861no—
279C22⋊C4—861no—
280C22⋊C4—861no—
281C22⋊C4—861no—
282C22⋊C4—861no—
283C22⋊C4—861no—
284C22⋊C4—861no—
285C22⋊C4—861no—
286C42—21no—
287C42—431no—
288C42—431no—
289C42—861no—
290C23—21no—
291C23—864no—
292C23—861no—
293C23—861no—
294C23—3441no—
295C23—3441no—
296C23D4×D4311yescharacteristic
297Q8—861no—
298Q8—861no—
299Q8—3441no—
300D4—21no—
301D4—21no—
302D4—81no—
303D4—432no—
304D4—432no—
305D4—864no—
306D4—861no—
307D4—861no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—431no—
314C2×C4—431no—
315C2×C4—431no—
316C2×C4—431no—
317C2×C4—861no—
318C2×C4—861no—
319C2×C4—3441no—
320C2×C4—3441no—
321C2×C4—3441no—
322C2×C4—3441no—
323C2×C4—3441no—
324C2×C4D4×D4311yescharacteristic
325C2×C4C23×D4311yescharacteristic
326C8—21no—
327C8—21no—
328C8—861no—
329C8—861no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—862no—
337C22—862no—
338C22—3444no—
339C22—1721no—
340C22—1721no—
341C22—1721no—
342C22—1721no—
343C22C2×D4×D4311yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—861no—
349C4—861no—
350C4—861no—
351C4—861no—
352C4—1721no—
353C4—1721no—
354C4#41×D4311yescharacteristic
355C4#41×D4311yescharacteristic
356C2—41no—
357C2—81no—
358C2—1722no—
359C2—1722no—
360C2#1458340711yescharacteristic
361C2#1458370311yescharacteristic
362C2#1458370611yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#482C2
socleC22×C43C22×D4
hypercenter#482D43
hypocenterC43#3118
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. #14583516C2semidirect
2. #14583373C2semidirect
3. #14583240C2semidirect
4. #14583188C2semidirect
5. #14583178C2semidirect
6. #14583113C2semidirect
7. #14583113C2semidirect
8. #14583052C2semidirect
10. #14583008C2semidirect
11. #14582998C2semidirect
12. #14582986C2semidirect
13. #14582979C2semidirect
14. #14582957C2semidirect
15. C43×#482C2semidirect
21. #13063324C22semidirect
24. #13063312C22semidirect
28. #13063290C22semidirect
31. D4×Dic43C22semidirect
39. #13063258C22semidirect
40. #13063256C22semidirect
41. Dic43⋊C8C22semidirect
42. Dic43⋊C8C22semidirect
43. #13063248C22semidirect
44. #13063248C22semidirect
50. #13063235C22semidirect
51. C8×Dic43C22semidirect
54. #107×C43C22semidirect
55. #106×C43C22semidirect
56. #102×C43C22semidirect
57. #102×C43C22semidirect
185. #482D43semidirect
197. C43#3118semidirect
224. #107C2×D43semidirect
226. #106C2×D43semidirect
235. #102C2×D43semidirect
236. #102C2×D43semidirect