Finite Group Databasebeta

← #19145596

Subgroups — #19145596

Order 5504.

400 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583453C211yesmaximal, characteristic, complemented
2#124×D43C211yesmaximal, characteristic
3#14583292C211yesmaximal, characteristic, complemented
4#14583290C211yesmaximal, characteristic, complemented
5#14583260C211yesmaximal, characteristic, complemented
6#14583257C211yesmaximal, characteristic, complemented
7#14583122C211yesmaximal, characteristic, complemented
8#14583121C211yesmaximal, characteristic, complemented
9#14583118C211yesmaximal, characteristic, complemented
10#14583056C211yesmaximal, characteristic, complemented
11#14583053C211yesmaximal, characteristic, complemented
12#14583051C211yesmaximal, characteristic
13#14583048C211yesmaximal, characteristic
14#14582955C211yesmaximal, characteristic, complemented
15C43×#464C211yesmaximal, characteristic, complemented
16C2×Q8×D43C2211yescharacteristic
17C2×D4×D43C2211yescharacteristic
18C2×Dic172C2211yescharacteristic, complemented
19C2×#10621885C2211yescharacteristic, complemented
20C2×#10621885C2211yescharacteristic, complemented
21C2×#10621873C2211yescharacteristic
22C2×#10621883C2211yescharacteristic
23C2×#10621884C2211yescharacteristic
24#13063324C2211yescharacteristic, complemented
25#13063323C2211yescharacteristic, complemented
26#13063315—21no—
27#13063314C2211yescharacteristic
28#13063313C2211yescharacteristic
29#13063312C2211yescharacteristic
30#13063311—21no—
31#13063311—21no—
32#13063305C2211yescharacteristic
33#13063303—21no—
34#13063301C2211yescharacteristic
35C4×Dic86—21no—
36C4×Dic86C2211yescharacteristic, complemented
37#13063282—21no—
38C22⋊C4×D43—21no—
39C22⋊C4×D43—21no—
40C42×D43C2211yescharacteristic
41C4⋊(C43⋊C8)C2211yescharacteristic, complemented
42#13063250C2211yescharacteristic, complemented
43#13063249C2211yescharacteristic, complemented
44#13063248C2211yescharacteristic, complemented
45#13063247C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063245C2211yescharacteristic
48(C2×D43)⋊C8C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50#13063235C2211yescharacteristic, complemented
51#13063235C2211yescharacteristic, complemented
52C2×Q16×C43C2211yescharacteristic, complemented
53C2×SD16×C43C2211yescharacteristic
54#124×C43C2211yescharacteristic
55C4×Q8×C43C2211yescharacteristic, complemented
56C4⋊C8×C43C2211yescharacteristic, complemented
57#103×C43C2211yescharacteristic, complemented
58#102×C43C2211yescharacteristic
59C23×D43—21no—
60C2×Q8×C43C2311yescharacteristic
61C2×Q8×C43C2311yescharacteristic
62C2×D4×C43C2311yescharacteristic
63C2×C22⋊D43—21no—
64Q8×D43—41no—
65Q8×D43—41no—
66D4×D43—41no—
67D4×D43—41no—
68C2×D172C2311yescharacteristic
69C2×C4×D43—21no—
70C2×C4×D43D411yescharacteristic
71C2×C4×D43D411yescharacteristic
72C2×C4×D43C2311yescharacteristic
73C2×Dic86—21no—
74C2×Dic86—21no—
75C2×Dic86C2311yescharacteristic
76C2×Dic86C2311yescharacteristic
77Q16×C43—41no—
78SD16×C43—41no—
79C2×C8×C43C2311yescharacteristic
80C2×C8×C43C2311yescharacteristic
81C4⋊C4×C43—21no—
82C4⋊C4×C43C2311yescharacteristic
83C22⋊C4×C43—21no—
84C22⋊C4×C43—21no—
85C42×C43—21no—
86C42×C43C2311yescharacteristic
87C22⋊Dic43—21no—
88C22⋊Dic43—21no—
89#10621885—41no—
90#10621885—41no—
91#10621884—41no—
92#10621883—41no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4—21no—
97(C2×D43)⋊C4—21no—
98(C2×D43)⋊C4—21no—
99C4⋊Dic43—21no—
100C4⋊Dic43C2311yescharacteristic
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104Dic43⋊C4—21no—
105Dic43⋊C4—21no—
106C4×Dic43—21no—
107C4×Dic43D411yescharacteristic
108C4×Dic43D411yescharacteristic
109C4×Dic43C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111C2×C43⋊C8C2311yescharacteristic
112Dic172—41no—
113#10621873—41no—
114C23×C43—21no—
115C22×D43—21no—
116C22×D43—42no—
117C22×D43—42no—
118C22×D43—42no—
119C22×D43C2×D411yescharacteristic
120Q8×C43—21no—
121Q8×C43—21no—
122Q8×C43—21no—
123Q8×C43—21no—
124D4×C43—21no—
125D4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43C2×D411yescharacteristic
130C2×C4×C43C2×D411yescharacteristic
131C2×C4×C43C2411yescharacteristic
132C22⋊D43—42no—
133C2×Dic43—21no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43C2×D411yescharacteristic
137C2×Dic43C2×D411yescharacteristic
138C2×Dic43C2×D411yescharacteristic
139D172—21no—
140D172—21no—
141C4×D43—22no—
142C4×D43—21no—
143C4×D43—21no—
144C4×D43—41no—
145C4×D43—42no—
146Dic86—21no—
147Dic86—21no—
148Dic86—21no—
149Dic86—21no—
150Dic86—42no—
151Dic86—42no—
152C8×C43—21no—
153C8×C43—21no—
154C43⋊C8—21no—
155C43⋊C8—21no—
156C22×C43—41no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43C22×D411yescharacteristic
160C2×D43—21no—
161C2×D43—21no—
162C2×D43—41no—
163C2×D43—41no—
164C2×D43—41no—
165C2×D43—84no—
166C2×D43#13712yes—
167C4×C43—21no—
168C4×C43—21no—
169C4×C43—41no—
170C4×C43—41no—
171C4×C43—41no—
172C4×C43H(5,𝔽2)11yescharacteristic
173C4×C43H(5,𝔽2)11yescharacteristic
174Dic43—21no—
175Dic43—21no—
176Dic43—21no—
177Dic43—41no—
178Dic43—41no—
179Dic43—41no—
180#3215—431nomaximal, Sylow
181C2×C43—81no—
182C2×C43#53511yescharacteristic
183C2×C43C2×#13711yescharacteristic
184C2×C43#57511yescharacteristic
185D43—22no—
186D43—81no—
187#533—431no—
188C2×#124—431no—
189#497—431no—
190#497—431no—
191#489—431no—
192#489—431no—
193#464—431no—
194#464—431no—
195#464—431no—
196#464D4311yescharacteristic, complemented
197#451—431no—
198#451—431no—
199#450—431no—
200#450—431no—
201#432—431no—
202C43#321511yescharacteristic, complemented, Sylow
203C22×Q8—431no—
204C22×D4—431no—
205C2×Q16—431no—
206C2×Q16—431no—
207C2×Q16—431no—
208C2×Q16C2×D4311yescharacteristic, complemented
209C2×SD16—431no—
210C2×SD16—431no—
211C2×SD16—431no—
212C2×SD16C2×D4311yescharacteristic
213C4⋊Q8—431no—
214C4⋊Q8—431no—
215#125—861no—
216#124—431no—
217#124—431no—
218#124—431no—
219#124—861no—
220#124—861no—
221#124C2×D4311yescharacteristic
222C22⋊Q8—431no—
223C22⋊Q8—431no—
224C22⋊Q8—861no—
225C4×Q8—431no—
226C4×Q8—861no—
227C4×Q8C2×D4311yescharacteristic, complemented
228#117—861no—
229C2×C22⋊C4—861no—
230C2×C22⋊C4—861no—
231C2×C42—431no—
232C4⋊C8—431no—
233C4⋊C8C2×D4311yescharacteristic, complemented
234#103—431no—
235#103—431no—
236#103—431no—
237#103C2×D4311yescharacteristic, complemented
238#102—431no—
239#102—431no—
240#102—431no—
241#102C2×D4311yescharacteristic
242C22⋊C8—431no—
243C22⋊C8—431no—
244#97—431no—
245#97—431no—
246C24—861no—
247C2×Q8—431no—
248C2×Q8—431no—
249C2×Q8—861no—
250C2×Q8—861no—
251C2×Q8—1721no—
252C2×Q8—1721no—
253C2×Q8C22×D4311yescharacteristic
254C2×Q8C22×D4311yescharacteristic
255C2×D4—431no—
256C2×D4—861no—
257C2×D4—1721no—
258C2×D4—1721no—
259C2×D4C22×D4311yescharacteristic
260C22×C4—431no—
261C22×C4—431no—
262C22×C4—431no—
263C22×C4—861no—
264Q16—41no—
265Q16—1721no—
266Q16—1721no—
267Q16—1721no—
268SD16—41no—
269SD16—1721no—
270SD16—1721no—
271SD16—1721no—
272C2×C8—431no—
273C2×C8—431no—
274C2×C8C22×D4311yescharacteristic
275C2×C8C22×D4311yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—431no—
278C4⋊C4—861no—
279C4⋊C4—861no—
280C4⋊C4—861no—
281C4⋊C4—861no—
282C4⋊C4—861no—
283C4⋊C4—861no—
284C4⋊C4C22×D4311yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—861no—
288C22⋊C4—861no—
289C22⋊C4—861no—
290C22⋊C4—861no—
291C22⋊C4—861no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C22⋊C4—861no—
295C42—21no—
296C42—431no—
297C42—431no—
298C42—431no—
299C42—861no—
300C42C22×D4311yescharacteristic
301C23—21no—
302C23—431no—
303C23—861no—
304C23—1722no—
305C23—1722no—
306C23—1722no—
307Q8—21no—
308Q8—21no—
309Q8—21no—
310Q8—21no—
311Q8—861no—
312Q8—861no—
313Q8—861no—
314Q8—861no—
315Q8—1722no—
316Q8—1722no—
317D4—21no—
318D4—21no—
319D4—861no—
320D4—861no—
321D4—1722no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—431no—
326C2×C4—431no—
327C2×C4—431no—
328C2×C4—862no—
329C2×C4—861no—
330C2×C4—861no—
331C2×C4—861no—
332C2×C4—861no—
333C2×C4—861no—
334C2×C4—1721no—
335C2×C4—1722no—
336C2×C4D4×D4311yescharacteristic
337C2×C4D4×D4311yescharacteristic
338C2×C4C23×D4311yescharacteristic
339C8—21no—
340C8—21no—
341C8—861no—
342C8—861no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—432no—
347C22—861no—
348C22—861no—
349C22—3444no—
350C22—1721no—
351C22—1721no—
352C22—1721no—
353C22C2×D4×D4311yescharacteristic
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—861no—
360C4—861no—
361C4—861no—
362C4—1721no—
363C4—1721no—
364C4—1721no—
365C4#1306337011yescharacteristic
366C4#1306337111yescharacteristic
367C2—81no—
368C2—862no—
369C2—3441no—
370C2#1458346511yescharacteristic
371C2#137×D4311yescharacteristic
372C2#1458369611yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#464C2
socleC22×C43C22×D4
hypercenter#464D43
hypocenterC43#3215
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #14583453C2semidirect
3. #14583292C2semidirect
4. #14583290C2semidirect
5. #14583260C2semidirect
6. #14583257C2semidirect
7. #14583122C2semidirect
8. #14583121C2semidirect
9. #14583118C2semidirect
10. #14583056C2semidirect
11. #14583053C2semidirect
14. #14582955C2semidirect
15. C43×#464C2semidirect
18. C2×Dic172C22semidirect
19. C2×#10621885C22semidirect
20. C2×#10621885C22semidirect
24. #13063324C22semidirect
25. #13063323C22semidirect
36. C4×Dic86C22semidirect
41. C4⋊(C43⋊C8)C22semidirect
42. #13063250C22semidirect
43. #13063249C22semidirect
44. #13063248C22semidirect
50. #13063235C22semidirect
51. #13063235C22semidirect
52. C2×Q16×C43C22semidirect
55. C4×Q8×C43C22semidirect
56. C4⋊C8×C43C22semidirect
57. #103×C43C22semidirect
196. #464D43semidirect
202. C43#3215semidirect
208. C2×Q16C2×D43semidirect
227. C4×Q8C2×D43semidirect
233. C4⋊C8C2×D43semidirect
237. #103C2×D43semidirect