Finite Group Databasebeta

← #19146673

Subgroups — #19146673

Order 5504.

410 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#14583610C211yesmaximal, characteristic, complemented
2#14583544C211yesmaximal, characteristic
3#14583261C211yesmaximal, characteristic, complemented
4#14583236C211yesmaximal, characteristic, complemented
5#14583214C211yesmaximal, characteristic, complemented
6#14583146C211yesmaximal, characteristic, complemented
7#14583141C211yesmaximal, characteristic, complemented
8#14583122C211yesmaximal, characteristic, complemented
9#14583062C211yesmaximal, characteristic, complemented
10#14583051C211yesmaximal, characteristic, complemented
11#14582999C211yesmaximal, characteristic, complemented
12#14582969C211yesmaximal, characteristic, complemented
13#14582897C211yesmaximal, characteristic, complemented
14#102×D43C211yesmaximal, characteristic, complemented
15C43×#474C211yesmaximal, characteristic, complemented
16C2×#10621900C2211yescharacteristic
17C2×D4×D43C2211yescharacteristic
18C2×Dic172C2211yescharacteristic, complemented
19C2×#10621873C2211yescharacteristic
20C2×#10621883C2211yescharacteristic
21C2×#10621872C2211yescharacteristic, complemented
22C2×C8×D43C2211yescharacteristic
23#13063316—21no—
24#13063313C2211yescharacteristic
25#13063309—21no—
26#13063305C2211yescharacteristic
27#13063305C2211yescharacteristic
28#13063305C2211yescharacteristic, complemented
29#13063301—21no—
30#13063301—21no—
31#13063300C2211yescharacteristic
32#13063299—21no—
33#13063295—21no—
34C4×Dic86C2211yescharacteristic, complemented
35C4×D172C2211yescharacteristic
36#13063287—21no—
37C4⋊C4×D43C2211yescharacteristic
38C4⋊C4×D43C2211yescharacteristic, complemented
39C2×(C2×D43)⋊C4—21no—
40#13063258C2211yescharacteristic, complemented
41#13063250C2211yescharacteristic, complemented
42#13063248C2211yescharacteristic, complemented
43#13063248C2211yescharacteristic, complemented
44#13063248C2211yescharacteristic, complemented
45#13063247C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic, complemented
51#13063236C2211yescharacteristic, complemented
52C4⋊Q8×C43C2211yescharacteristic, complemented
53C4×D4×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic, complemented
55#107×C43C2211yescharacteristic, complemented
56C4⋊C8×C43C2211yescharacteristic, complemented
57#102×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic
59C23×D43—21no—
60C2×Q8×C43—21no—
61C2×D4×C43C2311yescharacteristic
62C22×C4×C43—21no—
63C2×C22⋊D43—21no—
64C2×C22⋊D43—21no—
65C22×Dic43—21no—
66#10621900—22no—
67#10621900—41no—
68D4×D43—22no—
69D4×D43—41no—
70C2×D172—21no—
71C2×D172D411yescharacteristic
72C2×D172C2311yescharacteristic
73C2×C4×D43—21no—
74C2×C4×D43—21no—
75C2×C4×D43C2311yescharacteristic
76C2×C4×D43C2311yescharacteristic
77C2×Dic86C2311yescharacteristic
78C2×Dic86C2311yescharacteristic
79C2×C8×C43C2311yescharacteristic
80C2×C8×C43C2311yescharacteristic
81C4⋊C4×C43—21no—
82C4⋊C4×C43C2311yescharacteristic
83C4⋊C4×C43C2311yescharacteristic
84C4⋊C4×C43C2311yescharacteristic
85C22⋊C4×C43—21no—
86C42×C43C2311yescharacteristic
87#10621883—22no—
88(C2×D43)⋊C4—21no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4D411yescharacteristic
95(C2×D43)⋊C4D411yescharacteristic
96C4⋊Dic43—21no—
97C4⋊Dic43—21no—
98C4⋊Dic43—21no—
99C4⋊Dic43D411yescharacteristic
100C4⋊Dic43C2311yescharacteristic
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104C4×Dic43—21no—
105C2×C43⋊C8C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107Dic172—41no—
108#10621873—41no—
109#10621872—41no—
110C8×D43—41no—
111C23×C43—21no—
112C22×D43—21no—
113C22×D43—42no—
114C22×D43—42no—
115C22×D43—81no—
116C22×D43C2×D411yescharacteristic
117C22×D43C2×D411yescharacteristic
118Q8×C43—81no—
119D4×C43—21no—
120D4×C43#4112yes—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—81no—
125C2×C4×C43C2×D411yescharacteristic
126C2×C4×C43C2×D411yescharacteristic
127C2×C4×C43C2411yescharacteristic
128C22⋊D43—42no—
129C22⋊D43—42no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—42no—
134C2×Dic43C2×D411yescharacteristic
135C2×Dic43C2×D411yescharacteristic
136D172—22no—
137D172—21no—
138D172—21no—
139D172—81no—
140C4×D43—21no—
141C4×D43—21no—
142C4×D43—21no—
143C4×D43—21no—
144C4×D43—81no—
145C4×D43—81no—
146Dic86—21no—
147Dic86—21no—
148Dic86—21no—
149Dic86—21no—
150C8×C43—21no—
151C8×C43—21no—
152C43⋊C8—21no—
153C43⋊C8—21no—
154C22×C43—22no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43C22×D411yescharacteristic
158C2×D43—21no—
159C2×D43—21no—
160C2×D43—21no—
161C2×D43—21no—
162C2×D43—21no—
163C2×D43—41no—
164C2×D43—41no—
165C2×D43—41no—
166C2×D43—84no—
167C2×D43#13712yes—
168C4×C43—21no—
169C4×C43—21no—
170C4×C43—41no—
171C4×C43—41no—
172C4×C43—41no—
173C4×C43C2×#4111yescharacteristic
174C4×C43H(5,𝔽2)11yescharacteristic
175Dic43—21no—
176Dic43—21no—
177Dic43—41no—
178Dic43—41no—
179Dic43—41no—
180#3314—431nomaximal, Sylow
181C2×C43—42no—
182C2×C43#54611yescharacteristic
183C2×C43C2×#13711yescharacteristic
184C2×C43#57611yescharacteristic
185D43—22no—
186D43—41no—
187D43—81no—
188#554—431no—
189#546—431no—
190#489—431no—
191#484—431no—
192#480—431no—
193#474D4311yescharacteristic, complemented
194#468—431no—
195#467—431no—
196#464—431no—
197#452—431no—
198#450—431no—
199#440—431no—
200#435—431no—
201#417—431no—
202C2×#102—431no—
203C43#331411yescharacteristic, complemented, Sylow
204C2×#41—431no—
205C22×D4—431no—
206C2×Q16—431no—
207C2×SD16—431no—
208C2×SD16—431no—
209C2×M16—431no—
210C22×C8—431no—
211C4⋊Q8C2×D4311yescharacteristic, complemented
212#125—861no—
213#124—431no—
214#123—861no—
215C22⋊Q8—431no—
216C22⋊Q8—431no—
217C22⋊Q8—431no—
218C22⋊Q8—861no—
219C22⋊Q8—861no—
220#121—431no—
221#121—861no—
222#120—861no—
223C4×Q8—431no—
224C4×D4—431no—
225C4×D4—861no—
226C4×D4C2×D4311yescharacteristic
227C2×C4⋊C4—431no—
228C2×C4⋊C4—431no—
229C2×C22⋊C4—861no—
230#107—431no—
231#107C2×D4311yescharacteristic, complemented
232#107C2×D4311yescharacteristic, complemented
233C4⋊C8C2×D4311yescharacteristic, complemented
234#103—431no—
235#103—431no—
236#103—431no—
237#103—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—
246#97—431no—
247C24—861no—
248#41—862no—
249#41—1721no—
250C2×Q8—21no—
251C2×Q8—431no—
252C2×Q8—431no—
253C2×D4—431no—
254C2×D4—431no—
255C2×D4—861no—
256C2×D4—861no—
257C2×D4—862no—
258C2×D4—861no—
259C2×D4—1721no—
260C2×D4C22×D4311yescharacteristic
261C22×C4—21no—
262C22×C4—431no—
263C22×C4—431no—
264C22×C4—861no—
265C22×C4—861no—
266C22×C4—861no—
267Q16—1721no—
268SD16—862no—
269SD16—1721no—
270M16—1721no—
271C2×C8—431no—
272C2×C8—431no—
273C2×C8—1721no—
274C2×C8C22×D4311yescharacteristic
275C2×C8C22×D4311yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—431no—
278C4⋊C4—431no—
279C4⋊C4—861no—
280C4⋊C4—861no—
281C4⋊C4—861no—
282C4⋊C4—861no—
283C4⋊C4—861no—
284C4⋊C4—861no—
285C4⋊C4C22×D4311yescharacteristic
286C4⋊C4C22×D4311yescharacteristic
287C4⋊C4C22×D4311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—431no—
290C22⋊C4—431no—
291C22⋊C4—861no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C22⋊C4—861no—
295C22⋊C4—861no—
296C22⋊C4—861no—
297C42—861no—
298C42C22×D4311yescharacteristic
299C23—21no—
300C23—431no—
301C23—431no—
302C23—861no—
303C23—3441no—
304C23—1722no—
305C23—1722no—
306Q8—81no—
307Q8—861no—
308Q8—861no—
309Q8—861no—
310Q8—861no—
311D4—21no—
312D4—862no—
313D4—861no—
314D4—861no—
315D4—3441no—
316D4—1722no—
317D4—1722no—
318D4#1062190212yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—81no—
323C2×C4—431no—
324C2×C4—431no—
325C2×C4—861no—
326C2×C4—861no—
327C2×C4—861no—
328C2×C4—861no—
329C2×C4—861no—
330C2×C4—861no—
331C2×C4—861no—
332C2×C4—3441no—
333C2×C4—3441no—
334C2×C4—1722no—
335C2×C4D4×D4311yescharacteristic
336C2×C4D4×D4311yescharacteristic
337C2×C4C23×D4311yescharacteristic
338C8—21no—
339C8—21no—
340C8—861no—
341C8—861no—
342C22—22no—
343C22—41no—
344C22—41no—
345C22—432no—
346C22—861no—
347C22—861no—
348C22—861no—
349C22—861no—
350C22—861no—
351C22—3444no—
352C22—1721no—
353C22—1721no—
354C22—1721no—
355C22C2×D4×D4311yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—861no—
362C4—861no—
363C4—1721no—
364C4—1721no—
365C4—1721no—
366C4C2×#1062190211yescharacteristic
367C4#1306337111yescharacteristic
368C2—42no—
369C2—862no—
370C2—3441no—
371C2—1721no—
372C2#1458354011yescharacteristic
373C2#137×D4311yescharacteristic
374C2#1458370011yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#474C2
socleC22×C43C22×D4
hypercenter#474D43
hypocenterC43#3314
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #14583610C2semidirect
3. #14583261C2semidirect
4. #14583236C2semidirect
5. #14583214C2semidirect
6. #14583146C2semidirect
7. #14583141C2semidirect
8. #14583122C2semidirect
9. #14583062C2semidirect
10. #14583051C2semidirect
11. #14582999C2semidirect
12. #14582969C2semidirect
13. #14582897C2semidirect
14. #102×D43C2semidirect
15. C43×#474C2semidirect
18. C2×Dic172C22semidirect
21. C2×#10621872C22semidirect
28. #13063305C22semidirect
34. C4×Dic86C22semidirect
38. C4⋊C4×D43C22semidirect
40. #13063258C22semidirect
41. #13063250C22semidirect
42. #13063248C22semidirect
43. #13063248C22semidirect
44. #13063248C22semidirect
50. (C2×D43)⋊C8C22semidirect
51. #13063236C22semidirect
52. C4⋊Q8×C43C22semidirect
54. #107×C43C22semidirect
55. #107×C43C22semidirect
56. C4⋊C8×C43C22semidirect
193. #474D43semidirect
203. C43#3314semidirect
211. C4⋊Q8C2×D43semidirect
231. #107C2×D43semidirect
232. #107C2×D43semidirect
233. C4⋊C8C2×D43semidirect