Finite Group Databasebeta

← #19145453

Subgroups — #19145453

Order 5504.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583479C211yesmaximal, characteristic, complemented
2#14583468C211yesmaximal, characteristic, complemented
3#14583223C211yesmaximal, characteristic, complemented
4#14583219C211yesmaximal, characteristic, complemented
5#14583214C211yesmaximal, characteristic, complemented
6#14583153C211yesmaximal, characteristic, complemented
7#14583148C211yesmaximal, characteristic, complemented
8#14583136C211yesmaximal, characteristic, complemented
9#14583131C211yesmaximal, characteristic, complemented
10#14583049C211yesmaximal, characteristic, complemented
11#14583047C211yesmaximal, characteristic, complemented
12#14583047C211yesmaximal, characteristic, complemented
13#14583035C211yesmaximal, characteristic, complemented
14#14582864C211yesmaximal, characteristic, complemented
15C43×#485C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic, complemented
17C2×#10621898C2211yescharacteristic
18C22×D172C2211yescharacteristic
19C2×#10621884C2211yescharacteristic
20C2×#10621884C2211yescharacteristic
21C2×D344C2211yescharacteristic
22C2×D344C2211yescharacteristic
23C2×#10621872C2211yescharacteristic, complemented
24C2×C8×D43C2211yescharacteristic, complemented
25#13063322—21no—
26#13063313—21no—
27#13063303—21no—
28#13063301C2211yescharacteristic, complemented
29#13063300—21no—
30#13063300C2211yescharacteristic
31#13063300C2211yescharacteristic
32#13063300C2211yescharacteristic
33#13063300C2211yescharacteristic
34#13063300C2211yescharacteristic, complemented
35#13063299C2211yescharacteristic
36#13063298—21no—
37#13063298—21no—
38#13063295—21no—
39#13063295—21no—
40C4⋊C4×D43C2211yescharacteristic, complemented
41#13063258C2211yescharacteristic, complemented
42#13063256C2211yescharacteristic, complemented
43#13063247C2211yescharacteristic
44#13063247C2211yescharacteristic
45#13063245C2211yescharacteristic
46#13063245C2211yescharacteristic
47#13063245C2211yescharacteristic, complemented
48#13063245C2211yescharacteristic, complemented
49C22⋊(C43⋊C8)C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic, complemented
51(C2×D43)⋊C8C2211yescharacteristic, complemented
52C22⋊Q8×C43C2211yescharacteristic
53#117×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic, complemented
55#106×C43C2211yescharacteristic, complemented
56#103×C43C2211yescharacteristic, complemented
57#103×C43C2211yescharacteristic, complemented
58C22⋊C8×C43C2211yescharacteristic
59C23×D43—21no—
60C2×Q8×C43C2311yescharacteristic
61C22×C4×C43C2311yescharacteristic
62C2×C22⋊D43—21no—
63C2×C22⋊D43D411yescharacteristic
64C2×C22⋊D43D411yescharacteristic
65#10621902—41no—
66#10621902—41no—
67#10621898—41no—
68#10621898—41no—
69C2×D172—21no—
70C2×D172—21no—
71C2×D172—21no—
72C2×D172—21no—
73C2×D172—21no—
74C2×D172—21no—
75C2×D172—21no—
76C2×D172—41no—
77C2×D172—41no—
78C2×D172D411yescharacteristic
79C2×D172C2311yescharacteristic
80C2×D172C2311yescharacteristic
81C2×D172C2311yescharacteristic
82C2×C4×D43—21no—
83C2×C4×D43—21no—
84C2×C4×D43C2311yescharacteristic
85C2×C4×D43C2311yescharacteristic
86C2×Dic86D411yescharacteristic
87C2×C8×C43C2311yescharacteristic
88C2×C8×C43C2311yescharacteristic
89C4⋊C4×C43—21no—
90C4⋊C4×C43C2311yescharacteristic
91C4⋊C4×C43C2311yescharacteristic
92C4⋊C4×C43C2311yescharacteristic
93C22⋊C4×C43—21no—
94C22⋊C4×C43—21no—
95C42×C43—21no—
96#10621884—41no—
97#10621884—41no—
98(C2×D43)⋊C4—21no—
99(C2×D43)⋊C4—21no—
100(C2×D43)⋊C4—21no—
101(C2×D43)⋊C4—21no—
102(C2×D43)⋊C4—21no—
103(C2×D43)⋊C4—21no—
104(C2×D43)⋊C4—21no—
105C4⋊Dic43C2311yescharacteristic
106Dic43⋊C4—21no—
107Dic43⋊C4—21no—
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110D344—41no—
111D344—41no—
112#10621872—41no—
113C8×D43—41no—
114C23×C43C2×D411yescharacteristic
115C22×D43—21no—
116C22×D43—21no—
117C22×D43—21no—
118C22×D43—42no—
119C22×D43—81no—
120C22×D43—81no—
121C22×D43C2×D411yescharacteristic
122C22×D43C2×D411yescharacteristic
123Q8×C43—21no—
124Q8×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43C2×D411yescharacteristic
132C2×C4×C43C2411yescharacteristic
133C22⋊D43—41no—
134C22⋊D43—41no—
135C22⋊D43—81no—
136C2×Dic43—21no—
137C2×Dic43C2×D411yescharacteristic
138C2×Dic43C2×D411yescharacteristic
139D172—21no—
140D172—21no—
141D172—21no—
142D172—21no—
143D172—21no—
144D172—21no—
145D172—41no—
146D172—42no—
147D172—42no—
148D172—81no—
149D172—81no—
150D172—81no—
151D172—81no—
152D172—81no—
153C4×D43—21no—
154C4×D43—21no—
155C4×D43—21no—
156C4×D43—21no—
157C4×D43—42no—
158C4×D43—81no—
159Dic86—41no—
160C8×C43—21no—
161C8×C43—21no—
162C43⋊C8—21no—
163C43⋊C8—21no—
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—21no—
167C22×C43C22×D411yescharacteristic
168C2×D43—21no—
169C2×D43—21no—
170C2×D43—21no—
171C2×D43—21no—
172C2×D43—21no—
173C2×D43—21no—
174C2×D43—41no—
175C2×D43—41no—
176C2×D43—41no—
177C2×D43—41no—
178C2×D43—41no—
179C2×D43—41no—
180C2×D43—41no—
181C2×D43—41no—
182C2×D43—41no—
183C2×D43—84no—
184C4×C43—21no—
185C4×C43—41no—
186C4×C43—41no—
187C4×C43—41no—
188C4×C43—41no—
189C4×C43H(5,𝔽2)11yescharacteristic
190C4×C43H(5,𝔽2)11yescharacteristic
191Dic43—21no—
192Dic43—21no—
193Dic43—41no—
194#3198—431nomaximal, Sylow
195C2×C43—41no—
196C2×C43#53411yescharacteristic
197C2×C43#57611yescharacteristic
198C2×C43#57711yescharacteristic
199D43—41no—
200D43—41no—
201D43—81no—
202D43—81no—
203D43—81no—
204#537—431no—
205#535—431no—
206#485D4311yescharacteristic, complemented
207#482—431no—
208#481—431no—
209#480—431no—
210#469—431no—
211#468—431no—
212#466—431no—
213#465—431no—
214#450—431no—
215#449—431no—
216#449—431no—
217#447—431no—
218#408—431no—
219C43#319811yescharacteristic, complemented, Sylow
220C2×#41—431no—
221C2×#41—431no—
222C22×D4—431no—
223C2×SD16—431no—
224C2×SD16—431no—
225C2×D8—431no—
226C2×D8—431no—
227C2×M16—431no—
228C22×C8—431no—
229#127—861no—
230#124—861no—
231C22⋊Q8—431no—
232C22⋊Q8—861no—
233C22⋊Q8C2×D4311yescharacteristic
234#121—431no—
235#121—431no—
236#121—431no—
237#121—431no—
238#121—431no—
239#121—431no—
240#121—861no—
241#121—861no—
242#121—861no—
243#120—861no—
244#120—861no—
245#117C2×D4311yescharacteristic
246C2×C4⋊C4—431no—
247#107—431no—
248#107C2×D4311yescharacteristic, complemented
249#106—431no—
250#106C2×D4311yescharacteristic, complemented
251#103C2×D4311yescharacteristic, complemented
252#103C2×D4311yescharacteristic, complemented
253#102—431no—
254#102—431no—
255#102—431no—
256#102—431no—
257#102—431no—
258#102—431no—
259C22⋊C8—431no—
260C22⋊C8—431no—
261C22⋊C8—431no—
262C22⋊C8C2×D4311yescharacteristic
263C24—861no—
264#41—1721no—
265#41—1721no—
266#41—1721no—
267#41—1721no—
268C2×Q8—431no—
269C2×Q8C22×D4311yescharacteristic
270C2×D4—431no—
271C2×D4—431no—
272C2×D4—431no—
273C2×D4—431no—
274C2×D4—431no—
275C2×D4—431no—
276C2×D4—861no—
277C2×D4—861no—
278C2×D4—861no—
279C2×D4—861no—
280C2×D4—861no—
281C2×D4—861no—
282C2×D4—861no—
283C2×D4—861no—
284C2×D4—1721no—
285C2×D4—1721no—
286C22×C4—431no—
287C22×C4—431no—
288C22×C4—861no—
289C22×C4—861no—
290C22×C4C22×D4311yescharacteristic
291SD16—1721no—
292SD16—1721no—
293D8—1721no—
294D8—1721no—
295M16—1721no—
296C2×C8—431no—
297C2×C8—431no—
298C2×C8—1721no—
299C2×C8C22×D4311yescharacteristic
300C2×C8C22×D4311yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—431no—
303C4⋊C4—861no—
304C4⋊C4—861no—
305C4⋊C4C22×D4311yescharacteristic
306C4⋊C4C22×D4311yescharacteristic
307C4⋊C4C22×D4311yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—861no—
311C22⋊C4—861no—
312C22⋊C4—861no—
313C22⋊C4—861no—
314C22⋊C4—861no—
315C22⋊C4—861no—
316C22⋊C4—861no—
317C42—21no—
318C23—431no—
319C23—431no—
320C23—861no—
321C23—861no—
322C23—861no—
323C23—3441no—
324C23—3441no—
325C23—1722no—
326C23D4×D4311yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—1721no—
330D4—861no—
331D4—861no—
332D4—861no—
333D4—861no—
334D4—861no—
335D4—861no—
336D4—3441no—
337D4—3441no—
338D4—3441no—
339D4—3441no—
340D4—3441no—
341D4—3441no—
342D4—1721no—
343D4—1722no—
344D4—1722no—
345D4—1721no—
346D4—1721no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—431no—
354C2×C4—431no—
355C2×C4—861no—
356C2×C4—861no—
357C2×C4—861no—
358C2×C4—861no—
359C2×C4—861no—
360C2×C4—3441no—
361C2×C4—1722no—
362C2×C4D4×D4311yescharacteristic
363C2×C4C23×D4311yescharacteristic
364C8—21no—
365C8—21no—
366C8—861no—
367C8—861no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—861no—
372C22—861no—
373C22—861no—
374C22—861no—
375C22—861no—
376C22—861no—
377C22—3444no—
378C22—1721no—
379C22—1721no—
380C22—1721no—
381C22—1721no—
382C22—1721no—
383C22—1721no—
384C22—1721no—
385C22—1721no—
386C22—1721no—
387C22C2×D4×D4311yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—41no—
393C4—861no—
394C4—861no—
395C4—1721no—
396C4#1306337111yescharacteristic
397C4#1306337111yescharacteristic
398C2—41no—
399C2—3441no—
400C2—3441no—
401C2—3441no—
402C2—1721no—
403C2—1721no—
404C2#1458346011yescharacteristic
405C2#1458370111yescharacteristic
406C2#1458370811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#485C2
socleC22×C43C22×D4
hypercenter#485D43
hypocenterC43#3198
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #14583479C2semidirect
2. #14583468C2semidirect
3. #14583223C2semidirect
4. #14583219C2semidirect
5. #14583214C2semidirect
6. #14583153C2semidirect
7. #14583148C2semidirect
8. #14583136C2semidirect
9. #14583131C2semidirect
10. #14583049C2semidirect
11. #14583047C2semidirect
12. #14583047C2semidirect
13. #14583035C2semidirect
14. #14582864C2semidirect
15. C43×#485C2semidirect
16. C2×#10621902C22semidirect
23. C2×#10621872C22semidirect
24. C2×C8×D43C22semidirect
28. #13063301C22semidirect
34. #13063300C22semidirect
40. C4⋊C4×D43C22semidirect
41. #13063258C22semidirect
42. #13063256C22semidirect
47. #13063245C22semidirect
48. #13063245C22semidirect
50. (C2×D43)⋊C8C22semidirect
51. (C2×D43)⋊C8C22semidirect
54. #107×C43C22semidirect
55. #106×C43C22semidirect
56. #103×C43C22semidirect
57. #103×C43C22semidirect
206. #485D43semidirect
219. C43#3198semidirect
248. #107C2×D43semidirect
250. #106C2×D43semidirect
251. #103C2×D43semidirect
252. #103C2×D43semidirect