Finite Group Databasebeta

← #19144944

Subgroups — #19144944

Order 5504.

404 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583526C211yesmaximal, characteristic, complemented
2#14583462C211yesmaximal, characteristic
3#14583263C211yesmaximal, characteristic, complemented
4#14583262C211yesmaximal, characteristic, complemented
5#14583261C211yesmaximal, characteristic, complemented
6#14583257C211yesmaximal, characteristic, complemented
7#14583254C211yesmaximal, characteristic, complemented
8#14583252C211yesmaximal, characteristic, complemented
9#14583244C211yesmaximal, characteristic, complemented
10#14582902C211yesmaximal, characteristic, complemented
11#14582897C211yesmaximal, characteristic, complemented
12#14582892C211yesmaximal, characteristic, complemented
13#102×D43C211yesmaximal, characteristic, complemented
14#14582853C211yesmaximal, characteristic, complemented
15C43×#486C211yesmaximal, characteristic, complemented
16C2×#10621900C2211yescharacteristic
17C2×D4×D43C2211yescharacteristic
18C2×#10621872C2211yescharacteristic
19C2×C8×D43C2211yescharacteristic
20#13063324C2211yescharacteristic, complemented
21#13063323—21no—
22#13063321C2211yescharacteristic
23#13063317C2211yescharacteristic, complemented
24#13063316C2211yescharacteristic, complemented
25#13063315—21no—
26#13063313C2211yescharacteristic
27#13063312C2211yescharacteristic
28#13063303—21no—
29#13063301—21no—
30#13063297—21no—
31#13063297—21no—
32#13063293—21no—
33#13063293—21no—
34#13063283C2211yescharacteristic
35#13063282C2211yescharacteristic
36C4⋊C4×D43C2211yescharacteristic
37#13063250C2211yescharacteristic, complemented
38#13063250C2211yescharacteristic, complemented
39#13063248C2211yescharacteristic, complemented
40#13063248C2211yescharacteristic, complemented
41#13063247C2211yescharacteristic
42#13063247C2211yescharacteristic
43#13063246C2211yescharacteristic
44#13063246C2211yescharacteristic
45#13063246C2211yescharacteristic, complemented
46#13063246C2211yescharacteristic, complemented
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49#13063236C2211yescharacteristic, complemented
50#13063235C2211yescharacteristic, complemented
51C8×Dic43C2211yescharacteristic, complemented
52C4⋊Q8×C43C2211yescharacteristic, complemented
53#127×C43C2211yescharacteristic
54#102×C43C2211yescharacteristic
55#102×C43C2211yescharacteristic
56#102×C43C2211yescharacteristic, complemented
57#102×C43C2211yescharacteristic, complemented
58C4×C8×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60C2×Q8×C43—21no—
61C2×D4×C43—21no—
62C2×D4×C43—21no—
63C2×D4×C43C2311yescharacteristic
64C2×D4×C43C2311yescharacteristic
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C2×C22⋊D43—21no—
68C2×C22⋊D43—21no—
69C22×Dic43—21no—
70#10621900—22no—
71#10621900—22no—
72D4×D43—22no—
73D4×D43—22no—
74C2×D172C2311yescharacteristic
75C2×C4×D43—21no—
76C2×C4×D43C2311yescharacteristic
77C2×Dic86—21no—
78C2×Dic86C2311yescharacteristic
79C2×C8×C43C2311yescharacteristic
80C2×C8×C43C2311yescharacteristic
81C4⋊C4×C43—21no—
82C4⋊C4×C43C2311yescharacteristic
83C4⋊C4×C43C2311yescharacteristic
84C42×C43C2311yescharacteristic
85C22⋊Dic43—21no—
86C22⋊Dic43—21no—
87(C2×D43)⋊C4—21no—
88(C2×D43)⋊C4—21no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4D411yescharacteristic
91(C2×D43)⋊C4D411yescharacteristic
92C4⋊Dic43—21no—
93C4⋊Dic43C2311yescharacteristic
94C4⋊Dic43C2311yescharacteristic
95Dic43⋊C4—21no—
96Dic43⋊C4—21no—
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4D411yescharacteristic
101Dic43⋊C4D411yescharacteristic
102C4×Dic43—21no—
103C4×Dic43C2311yescharacteristic
104C2×C43⋊C8C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106#10621872—22no—
107C8×D43—22no—
108C23×C43—21no—
109C23×C43—21no—
110C22×D43—21no—
111C22×D43—42no—
112C22×D43—81no—
113C22×D43—81no—
114C22×D43C2×D411yescharacteristic
115Q8×C43—81no—
116D4×C43—21no—
117D4×C43—21no—
118D4×C43—21no—
119D4×C43—21no—
120D4×C43—81no—
121D4×C43—81no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43C2×D411yescharacteristic
125C2×C4×C43C2×D411yescharacteristic
126C2×C4×C43C2411yescharacteristic
127C22⋊D43—42no—
128C22⋊D43—42no—
129C22⋊D43—81no—
130C22⋊D43—81no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—42no—
135C2×Dic43C2×D411yescharacteristic
136C2×Dic43C2×D411yescharacteristic
137C2×Dic43C2×D411yescharacteristic
138D172—21no—
139D172—21no—
140C4×D43—81no—
141C4×D43#4112yes—
142C4×D43#4112yes—
143Dic86—21no—
144Dic86—21no—
145Dic86—81no—
146C8×C43—21no—
147C8×C43—21no—
148C43⋊C8—21no—
149C43⋊C8—21no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43—41no—
153C22×C43—41no—
154C22×C43—41no—
155C22×C43—41no—
156C22×C43C22×D411yescharacteristic
157C2×D43—21no—
158C2×D43—21no—
159C2×D43—41no—
160C2×D43—41no—
161C2×D43—41no—
162C2×D43—84no—
163C2×D43#12412yes—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43—41no—
167C4×C43—41no—
168C4×C43C2×#4111yescharacteristic
169C4×C43C2×#4111yescharacteristic
170Dic43—21no—
171Dic43—21no—
172Dic43—41no—
173Dic43—41no—
174Dic43—41no—
175Dic43#12412yes—
176#3136—431nomaximal, Sylow
177C2×C43—81no—
178C2×C43—81no—
179C2×C43C2×#12411yescharacteristic
180C2×C43#57611yescharacteristic
181C2×C43#57711yescharacteristic
182D43—22no—
183D43—81no—
184#544—431no—
185#535—431no—
186#490—431no—
187#490—431no—
188#489—431no—
189#489—431no—
190#488—431no—
191#488—431no—
192#486—431no—
193#486D4311yescharacteristic, complemented
194#418—431no—
195#417—431no—
196#416—431no—
197C2×#102—431no—
198#405—431no—
199C43#313611yescharacteristic, complemented, Sylow
200C2×#41—431no—
201C22×D4—431no—
202C2×M16—431no—
203C22×C8—431no—
204C4⋊Q8—431no—
205C4⋊Q8—861no—
206C4⋊Q8C2×D4311yescharacteristic, complemented
207#127—431no—
208#127C2×D4311yescharacteristic
209#125—431no—
210#125—431no—
211#125—861no—
212#124—431no—
213#124—431no—
214C22⋊Q8—861no—
215C22⋊Q8—861no—
216#121—861no—
217#121—861no—
218#120—861no—
219#120—861no—
220#117—431no—
221#117—431no—
222C2×C4⋊C4—431no—
223#103—431no—
224#103—431no—
225#103—431no—
226#103—431no—
227#102—431no—
228#102—431no—
229#102—431no—
230#102—431no—
231#102—431no—
232#102—431no—
233#102—431no—
234#102—431no—
235#102C2×D4311yescharacteristic
236#102C2×D4311yescharacteristic
237#102C2×D4311yescharacteristic, complemented
238#102C2×D4311yescharacteristic, complemented
239#97—431no—
240#97—431no—
241C4×C8—431no—
242C4×C8C2×D4311yescharacteristic, complemented
243C24—861no—
244#41—862no—
245#41—862no—
246C2×Q8—21no—
247C2×Q8—431no—
248C2×Q8—861no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—431no—
252C2×D4—862no—
253C2×D4—862no—
254C2×D4—861no—
255C2×D4—861no—
256C2×D4—861no—
257C2×D4—861no—
258C2×D4C22×D4311yescharacteristic
259C2×D4C22×D4311yescharacteristic
260C22×C4—431no—
261C22×C4—861no—
262C22×C4—861no—
263M16—862no—
264C2×C8—431no—
265C2×C8—431no—
266C2×C8—862no—
267C2×C8C22×D4311yescharacteristic
268C2×C8C22×D4311yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—431no—
271C4⋊C4—431no—
272C4⋊C4—431no—
273C4⋊C4—431no—
274C4⋊C4—861no—
275C4⋊C4—861no—
276C4⋊C4—861no—
277C4⋊C4—861no—
278C4⋊C4—861no—
279C4⋊C4—861no—
280C4⋊C4C22×D4311yescharacteristic
281C4⋊C4C22×D4311yescharacteristic
282C22⋊C4—431no—
283C22⋊C4—431no—
284C22⋊C4—861no—
285C22⋊C4—861no—
286C22⋊C4—861no—
287C22⋊C4—861no—
288C22⋊C4—861no—
289C42—431no—
290C42—861no—
291C42C22×D4311yescharacteristic
292C23—21no—
293C23—21no—
294C23—431no—
295C23—861no—
296C23—3441no—
297C23—3441no—
298C23—1722no—
299Q8—81no—
300Q8—861no—
301Q8—861no—
302Q8—3441no—
303D4—21no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—81no—
308D4—81no—
309D4—861no—
310D4—861no—
311D4—3441no—
312D4—3441no—
313D4—1722no—
314D4—1722no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—431no—
318C2×C4—432no—
319C2×C4—432no—
320C2×C4—431no—
321C2×C4—431no—
322C2×C4—861no—
323C2×C4—861no—
324C2×C4—861no—
325C2×C4—3441no—
326C2×C4—1722no—
327C2×C4D4×D4311yescharacteristic
328C2×C4D4×D4311yescharacteristic
329C2×C4C23×D4311yescharacteristic
330C8—21no—
331C8—21no—
332C8—861no—
333C8—861no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—432no—
341C22—861no—
342C22—861no—
343C22—3444no—
344C22—1721no—
345C22—1721no—
346C22—1721no—
347C22C2×D4×D4311yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—432no—
353C4—861no—
354C4—861no—
355C4—1721no—
356C4—1721no—
357C4—1721no—
358C4#41×D4311yescharacteristic
359C4#41×D4311yescharacteristic
360C2—81no—
361C2—81no—
362C2—862no—
363C2—3441no—
364C2#124×D4311yescharacteristic
365C2#1458370011yescharacteristic
366C2#1458370511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#486C2
socleC22×C43C22×D4
hypercenter#486D43
hypocenterC43#3136
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #14583526C2semidirect
3. #14583263C2semidirect
4. #14583262C2semidirect
5. #14583261C2semidirect
6. #14583257C2semidirect
7. #14583254C2semidirect
8. #14583252C2semidirect
9. #14583244C2semidirect
10. #14582902C2semidirect
11. #14582897C2semidirect
12. #14582892C2semidirect
13. #102×D43C2semidirect
14. #14582853C2semidirect
15. C43×#486C2semidirect
20. #13063324C22semidirect
23. #13063317C22semidirect
24. #13063316C22semidirect
37. #13063250C22semidirect
38. #13063250C22semidirect
39. #13063248C22semidirect
40. #13063248C22semidirect
45. #13063246C22semidirect
46. #13063246C22semidirect
49. #13063236C22semidirect
50. #13063235C22semidirect
51. C8×Dic43C22semidirect
52. C4⋊Q8×C43C22semidirect
56. #102×C43C22semidirect
57. #102×C43C22semidirect
58. C4×C8×C43C22semidirect
193. #486D43semidirect
199. C43#3136semidirect
206. C4⋊Q8C2×D43semidirect
237. #102C2×D43semidirect
238. #102C2×D43semidirect
242. C4×C8C2×D43semidirect