Finite Group Databasebeta

← #19144114

Subgroups — #19144114

Order 5504.

490 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063357C211yesmaximal, characteristic, complemented
2C2×SD16×D43C211yesmaximal, characteristic, complemented
3#14583467C211yesmaximal, characteristic
4#14583375C211yesmaximal, characteristic, complemented
5#14583124C211yesmaximal, characteristic, complemented
6#14583123C211yesmaximal, characteristic, complemented
7#14583118C211yesmaximal, characteristic, complemented
8#14583100C211yesmaximal, characteristic, complemented
9#14583099C211yesmaximal, characteristic, complemented
10#14583098C211yesmaximal, characteristic, complemented
11#14583097C211yesmaximal, characteristic, complemented
12#14582924C211yesmaximal, characteristic, complemented
13#14582902C211yesmaximal, characteristic, complemented
14#14582894C211yesmaximal, characteristic, complemented
15C43×#464C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×Q8×D43C2211yescharacteristic
18C2×D4×D43C2211yescharacteristic
19#13063357—24no—
20C2×#10621885C2211yescharacteristic, complemented
21C2×#10621873C2211yescharacteristic
22C2×#10621873C2211yescharacteristic, complemented
23C2×#10621883C2211yescharacteristic
24C2×#10621884C2211yescharacteristic
25C2×#10621884C2211yescharacteristic, complemented
26SD16×D43—24no—
27C2×#10621872C2211yescharacteristic
28C2×C8×D43C2211yescharacteristic
29#13063322C2211yescharacteristic
30#13063321C2211yescharacteristic
31#13063314C2211yescharacteristic
32#13063298—21no—
33#13063298—21no—
34#13063295—21no—
35#13063295—21no—
36Q8×Dic43C2211yescharacteristic, complemented
37C4×Dic86—21no—
38C4×Dic86C2211yescharacteristic, complemented
39#13063290—21no—
40#13063290C2211yescharacteristic, complemented
41#13063283—21no—
42#13063283C2211yescharacteristic
43#13063282—21no—
44#13063282C2211yescharacteristic
45C4⋊(C43⋊C8)C2211yescharacteristic, complemented
46Dic43⋊C8C2211yescharacteristic, complemented
47Dic43⋊C8C2211yescharacteristic, complemented
48#13063249C2211yescharacteristic, complemented
49#13063247C2211yescharacteristic
50#13063247C2211yescharacteristic, complemented
51#13063246C2211yescharacteristic
52#13063245C2211yescharacteristic
53#13063245C2211yescharacteristic, complemented
54C2×Q16×C43C2211yescharacteristic, complemented
55C2×SD16×C43C2211yescharacteristic
56#124×C43C2211yescharacteristic
57C4×Q8×C43C2211yescharacteristic, complemented
58C4⋊C8×C43C2211yescharacteristic, complemented
59#103×C43C2211yescharacteristic, complemented
60#102×C43C2211yescharacteristic
61C23×D43—21no—
62C2×Q8×C43C2311yescharacteristic
63C2×Q8×C43C2311yescharacteristic
64C2×D4×C43C2311yescharacteristic
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C2×C22⋊D43—21no—
68#10621902—22no—
69#10621902—22no—
70Q8×D43—22no—
71Q8×D43D414yescomplemented
72D4×D43—22no—
73D4×D43—22no—
74C2×D172—21no—
75C2×D172—21no—
76C2×D172—21no—
77C2×D172C2311yescharacteristic
78C2×D172C2311yescharacteristic
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×C4×D43C2311yescharacteristic
82C2×Dic86—21no—
83C2×Dic86C2311yescharacteristic
84Q16×C43—22no—
85SD16×C43—22no—
86C2×C8×C43C2311yescharacteristic
87C2×C8×C43C2311yescharacteristic
88C4⋊C4×C43—21no—
89C4⋊C4×C43C2311yescharacteristic
90C22⋊C4×C43—21no—
91C22⋊C4×C43—21no—
92C42×C43—21no—
93C42×C43C2311yescharacteristic
94#10621885—22no—
95#10621884—22no—
96#10621884—22no—
97#10621883—22no—
98(C2×D43)⋊C4—21no—
99(C2×D43)⋊C4—21no—
100(C2×D43)⋊C4—21no—
101(C2×D43)⋊C4D411yescharacteristic
102(C2×D43)⋊C4D411yescharacteristic
103C4⋊Dic43—21no—
104C4⋊Dic43C2311yescharacteristic
105Dic43⋊C4—21no—
106Dic43⋊C4—21no—
107Dic43⋊C4D411yescharacteristic
108Dic43⋊C4D411yescharacteristic
109C4×Dic43—21no—
110C4×Dic43—21no—
111C4×Dic43—21no—
112C4×Dic43—21no—
113C4×Dic43C2311yescharacteristic
114C2×C43⋊C8C2311yescharacteristic
115C2×C43⋊C8C2311yescharacteristic
116#10621873—22no—
117#10621873—22no—
118#10621872—22no—
119C8×D43—22no—
120C23×C43—21no—
121C22×D43—21no—
122C22×D43—21no—
123C22×D43—42no—
124C22×D43—81no—
125C22×D43—81no—
126C22×D43C2×D411yescharacteristic
127Q8×C43—21no—
128Q8×C43—21no—
129Q8×C43—21no—
130Q8×C43C2×D412yes—
131D4×C43—21no—
132D4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43C2×D411yescharacteristic
137C2×C4×C43C2×D411yescharacteristic
138C2×C4×C43C2411yescharacteristic
139C22⋊D43—42no—
140C22⋊D43—81no—
141C22⋊D43—81no—
142C2×Dic43—21no—
143C2×Dic43—21no—
144C2×Dic43C2×D411yescharacteristic
145C2×Dic43C2×D411yescharacteristic
146C2×Dic43C2×D411yescharacteristic
147D172—21no—
148D172—21no—
149D172—21no—
150D172—21no—
151D172—42no—
152D172—81no—
153D172—81no—
154C4×D43—24no—
155C4×D43—42no—
156C4×D43C2×D412yes—
157C4×D43#4112yes—
158Dic86—21no—
159Dic86—24no—
160Dic86C2×D412yes—
161C8×C43—21no—
162C8×C43—21no—
163C43⋊C8—21no—
164C43⋊C8—21no—
165C22×C43—41no—
166C22×C43—41no—
167C22×C43—41no—
168C22×C43C22×D411yescharacteristic
169C2×D43—21no—
170C2×D43—21no—
171C2×D43—41no—
172C2×D43—41no—
173C2×D43—41no—
174C2×D43—41no—
175C2×D43—41no—
176C2×D43—41no—
177C2×D43—84no—
178C2×D43#12112yes—
179C4×C43—22no—
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—41no—
183C4×C43—41no—
184C4×C43C22×D411yescharacteristic
185C4×C43C2×#4111yescharacteristic
186Dic43—22no—
187Dic43—21no—
188Dic43—21no—
189Dic43—41no—
190Dic43#12112yes—
191#3043—431nomaximal, Sylow
192C2×C43—81no—
193C2×C43C2×#12111yescharacteristic
194C2×C43#57711yescharacteristic
195C2×C43#57711yescharacteristic
196D43—22no—
197D43—81no—
198D43—81no—
199C2×#137—431no—
200C22×SD16—431no—
201#535—431no—
202#519—431no—
203#464—431no—
204#464—431no—
205#464—431no—
206#464D4311yescharacteristic, complemented
207#460—431no—
208#460—431no—
209#460—431no—
210#460—431no—
211#424—431no—
212#418—431no—
213#416—431no—
214C43#304311yescharacteristic, complemented, Sylow
215C2×#41—431no—
216C22×Q8—431no—
217C22×D4—431no—
218#137—864no—
219C2×Q16—431no—
220C2×Q16C2×D4311yescharacteristic, complemented
221C2×SD16—431no—
222C2×SD16—431no—
223C2×SD16—431no—
224C2×SD16—431no—
225C2×SD16—431no—
226C2×SD16—864no—
227C2×SD16C2×D4311yescharacteristic
228C2×M16—431no—
229C22×C8—431no—
230#127—431no—
231#127—431no—
232#124—431no—
233#124C2×D4311yescharacteristic
234#121—861no—
235#121—861no—
236#120—861no—
237#120—861no—
238C4×Q8—431no—
239C4×Q8—431no—
240C4×Q8—431no—
241C4×Q8—861no—
242C4×Q8—861no—
243C4×Q8C2×D4311yescharacteristic, complemented
244#117—431no—
245#117—431no—
246#117—861no—
247#117—861no—
248C4⋊C8—431no—
249C4⋊C8—431no—
250C4⋊C8—431no—
251C4⋊C8C2×D4311yescharacteristic, complemented
252#103—431no—
253#103C2×D4311yescharacteristic, complemented
254#102—431no—
255#102—431no—
256#102—431no—
257#102—431no—
258#102—431no—
259#102C2×D4311yescharacteristic
260C24—861no—
261#41—862no—
262#41—862no—
263C2×Q8—434no—
264C2×Q8—431no—
265C2×Q8—861no—
266C2×Q8—862no—
267C2×Q8C22×D4311yescharacteristic
268C2×Q8C22×D4311yescharacteristic
269C2×D4—431no—
270C2×D4—431no—
271C2×D4—861no—
272C2×D4—862no—
273C2×D4—862no—
274C2×D4—861no—
275C2×D4—861no—
276C2×D4—861no—
277C2×D4—861no—
278C2×D4—861no—
279C2×D4C22×D4311yescharacteristic
280C22×C4—431no—
281C22×C4—861no—
282C22×C4—861no—
283Q16—22no—
284Q16—862no—
285SD16—22no—
286SD16—862no—
287SD16—862no—
288SD16—862no—
289SD16—862no—
290SD16—862no—
291M16—862no—
292C2×C8—431no—
293C2×C8—431no—
294C2×C8—862no—
295C2×C8C22×D4311yescharacteristic
296C2×C8C22×D4311yescharacteristic
297C4⋊C4—21no—
298C4⋊C4—431no—
299C4⋊C4—431no—
300C4⋊C4—431no—
301C4⋊C4—861no—
302C4⋊C4—861no—
303C4⋊C4—861no—
304C4⋊C4C22×D4311yescharacteristic
305C22⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—431no—
308C22⋊C4—431no—
309C22⋊C4—861no—
310C22⋊C4—861no—
311C22⋊C4—861no—
312C42—21no—
313C42—431no—
314C42—861no—
315C42—861no—
316C42—861no—
317C42—861no—
318C42C22×D4311yescharacteristic
319C23—21no—
320C23—431no—
321C23—861no—
322C23—861no—
323C23—3441no—
324C23—3441no—
325C23—1722no—
326Q8—21no—
327Q8—21no—
328Q8—21no—
329Q8—432no—
330Q8—864no—
331Q8—861no—
332Q8D4×D4312yes—
333D4—21no—
334D4—21no—
335D4—861no—
336D4—861no—
337D4—861no—
338D4—861no—
339D4—3441no—
340D4—3441no—
341D4—3441no—
342D4—3441no—
343D4—1722no—
344D4—1722no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—431no—
349C2×C4—432no—
350C2×C4—432no—
351C2×C4—431no—
352C2×C4—431no—
353C2×C4—864no—
354C2×C4—861no—
355C2×C4—861no—
356C2×C4—1722no—
357C2×C4D4×D4311yescharacteristic
358C2×C4D4×D4311yescharacteristic
359C2×C4C23×D4311yescharacteristic
360C8—21no—
361C8—21no—
362C8—861no—
363C8—861no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—432no—
368C22—861no—
369C22—861no—
370C22—3444no—
371C22—1721no—
372C22—1721no—
373C22—1721no—
374C22—1721no—
375C22—1721no—
376C22—1721no—
377C22C2×D4×D4311yescharacteristic
378C4—22no—
379C4—21no—
380C4—21no—
381C4—41no—
382C4—41no—
383C4—432no—
384C4—862no—
385C4—861no—
386C4—861no—
387C4—1721no—
388C4C2×D4×D4311yescharacteristic
389C4#41×D4311yescharacteristic
390C2—81no—
391C2—862no—
392C2—3441no—
393C2—3441no—
394C2#121×D4311yescharacteristic
395C2#1458370611yescharacteristic
396C2#1458370811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#464C2
socleC22×C43C22×D4
hypercenter#464D43
hypocenterC43#3043
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. C2×#13063357C2semidirect
2. C2×SD16×D43C2semidirect
4. #14583375C2semidirect
5. #14583124C2semidirect
6. #14583123C2semidirect
7. #14583118C2semidirect
8. #14583100C2semidirect
9. #14583099C2semidirect
10. #14583098C2semidirect
11. #14583097C2semidirect
12. #14582924C2semidirect
13. #14582902C2semidirect
14. #14582894C2semidirect
15. C43×#464C2semidirect
20. C2×#10621885C22semidirect
22. C2×#10621873C22semidirect
25. C2×#10621884C22semidirect
36. Q8×Dic43C22semidirect
38. C4×Dic86C22semidirect
40. #13063290C22semidirect
45. C4⋊(C43⋊C8)C22semidirect
46. Dic43⋊C8C22semidirect
47. Dic43⋊C8C22semidirect
48. #13063249C22semidirect
50. #13063247C22semidirect
53. #13063245C22semidirect
54. C2×Q16×C43C22semidirect
57. C4×Q8×C43C22semidirect
58. C4⋊C8×C43C22semidirect
59. #103×C43C22semidirect
71. Q8×D43D4semidirect
206. #464D43semidirect
214. C43#3043semidirect
220. C2×Q16C2×D43semidirect
243. C4×Q8C2×D43semidirect
251. C4⋊C8C2×D43semidirect
253. #103C2×D43semidirect