Finite Group Databasebeta

← #19145691

Subgroups — #19145691

Order 5504.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583520C211yesmaximal, characteristic, complemented
2#14583468C211yesmaximal, characteristic, complemented
3#14583288C211yesmaximal, characteristic, complemented
4#14583283C211yesmaximal, characteristic, complemented
5#14583259C211yesmaximal, characteristic, complemented
6#14583246C211yesmaximal, characteristic, complemented
7#14583122C211yesmaximal, characteristic, complemented
8#14583115C211yesmaximal, characteristic, complemented
9#14583100C211yesmaximal, characteristic, complemented
10#14583095C211yesmaximal, characteristic, complemented
11#14583063C211yesmaximal, characteristic, complemented
12#14583052C211yesmaximal, characteristic, complemented
13#14583046C211yesmaximal, characteristic, complemented
14#14583035C211yesmaximal, characteristic, complemented
15C43×#433C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C22×D172C2211yescharacteristic
18C2×Dic172C2211yescharacteristic, complemented
19C2×#10621873C2211yescharacteristic
20C2×#10621873C2211yescharacteristic
21C2×#10621873C2211yescharacteristic, complemented
22C2×#10621873C2211yescharacteristic, complemented
23C2×D344C2211yescharacteristic
24C2×D344C2211yescharacteristic
25C2×D344C2211yescharacteristic, complemented
26#13063325C2211yescharacteristic, complemented
27#13063322C2211yescharacteristic
28#13063322C2211yescharacteristic
29#13063320—21no—
30#13063313C2211yescharacteristic
31#13063313C2211yescharacteristic
32#13063313C2211yescharacteristic, complemented
33#13063311—21no—
34#13063307—21no—
35#13063304C2211yescharacteristic
36#13063303—21no—
37#13063300—21no—
38#13063300—21no—
39#13063299C2211yescharacteristic
40#13063295—21no—
41#13063295—21no—
42C4×Dic86C2211yescharacteristic, complemented
43C4×D172C2211yescharacteristic, complemented
44#13063250C2211yescharacteristic, complemented
45#13063250C2211yescharacteristic, complemented
46#13063247C2211yescharacteristic
47#13063247C2211yescharacteristic
48#13063247C2211yescharacteristic
49#13063247C2211yescharacteristic
50#13063247C2211yescharacteristic, complemented
51#13063247C2211yescharacteristic, complemented
52#117×C43C2211yescharacteristic
53C4⋊C8×C43C2211yescharacteristic, complemented
54C4⋊C8×C43C2211yescharacteristic, complemented
55C22⋊C8×C43C2211yescharacteristic
56C22⋊C8×C43C2211yescharacteristic
57#97×C43C2211yescharacteristic, complemented
58C4×C8×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60C22×C4×C43C2311yescharacteristic
61C2×C22⋊D43—21no—
62C2×C22⋊D43—21no—
63#10621898—41no—
64#10621898—41no—
65C2×D172—21no—
66C2×D172—21no—
67C2×D172—21no—
68C2×D172—21no—
69C2×D172—21no—
70C2×D172—41no—
71C2×D172—41no—
72C2×D172C2311yescharacteristic
73C2×D172C2311yescharacteristic
74C2×D172C2311yescharacteristic
75C2×D172C2311yescharacteristic
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×Dic86—21no—
79C2×Dic86C2311yescharacteristic
80C2×Dic86C2311yescharacteristic
81C2×C8×C43C2311yescharacteristic
82C2×C8×C43C2311yescharacteristic
83C2×C8×C43C2311yescharacteristic
84C2×C8×C43C2311yescharacteristic
85C4⋊C4×C43D411yescharacteristic
86C4⋊C4×C43D411yescharacteristic
87C22⋊C4×C43D411yescharacteristic
88C22⋊C4×C43D411yescharacteristic
89C42×C43C2311yescharacteristic
90C42×C43C2311yescharacteristic
91C22⋊Dic43—21no—
92(C2×D43)⋊C4—21no—
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—
99(C2×D43)⋊C4—21no—
100C4⋊Dic43—21no—
101C4⋊Dic43C2311yescharacteristic
102C4⋊Dic43C2311yescharacteristic
103Dic43⋊C4—21no—
104Dic43⋊C4—21no—
105C4×Dic43—21no—
106Dic172—41no—
107D344—41no—
108D344—41no—
109D344—41no—
110#10621873—41no—
111#10621873—41no—
112#10621873—41no—
113#10621873—41no—
114C23×C43C2×D411yescharacteristic
115C22×D43—21no—
116C22×D43—21no—
117C22×D43—21no—
118C22×D43—21no—
119C22×D43—42no—
120C22×D43—81no—
121C22×D43—81no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43C2×D411yescharacteristic
125C2×C4×C43C2×D411yescharacteristic
126C2×C4×C43C2×D411yescharacteristic
127C2×C4×C43C2×D411yescharacteristic
128C2×C4×C43C2×D411yescharacteristic
129C2×C4×C43C2411yescharacteristic
130C22⋊D43—42no—
131C22⋊D43—81no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136D172—21no—
137D172—21no—
138D172—21no—
139D172—21no—
140D172—21no—
141D172—21no—
142D172—21no—
143D172—21no—
144D172—42no—
145D172—81no—
146D172—81no—
147D172—81no—
148D172—81no—
149C4×D43—42no—
150C4×D43—81no—
151Dic86—21no—
152Dic86—21no—
153Dic86—21no—
154Dic86—21no—
155Dic86—81no—
156C8×C43—21no—
157C8×C43—21no—
158C8×C43—21no—
159C8×C43—21no—
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—21no—
163C22×C43C22×D411yescharacteristic
164C2×D43—41no—
165C2×D43—41no—
166C2×D43—41no—
167C2×D43—41no—
168C2×D43—41no—
169C2×D43—41no—
170C2×D43—41no—
171C2×D43—41no—
172C2×D43—41no—
173C2×D43—41no—
174C2×D43—41no—
175C2×D43—41no—
176C2×D43—84no—
177C4×C43—21no—
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—21no—
181C4×C43—21no—
182C4×C43H(5,𝔽2)11yescharacteristic
183C4×C43H(5,𝔽2)11yescharacteristic
184Dic43—41no—
185Dic43—41no—
186Dic43—41no—
187Dic43—41no—
188#3224—431nomaximal, Sylow
189C2×C43—41no—
190C2×C43#53511yescharacteristic
191C2×C43#57611yescharacteristic
192C2×C43#57711yescharacteristic
193D43—81no—
194D43—81no—
195D43—81no—
196D43—81no—
197#542—431no—
198#535—431no—
199#496—431no—
200#495—431no—
201#489—431no—
202#486—431no—
203#464—431no—
204#463—431no—
205#460—431no—
206#459—431no—
207#452—431no—
208#450—431no—
209#449—431no—
210#447—431no—
211#433D4311yescharacteristic, complemented
212C43#322411yescharacteristic, complemented, Sylow
213C2×#41—431no—
214C22×D4—431no—
215C2×Q16—431no—
216C2×SD16—431no—
217C2×SD16—431no—
218C2×SD16—431no—
219C2×SD16—431no—
220C2×D8—431no—
221C2×D8—431no—
222C2×D8—431no—
223C4⋊Q8—431no—
224#127—431no—
225#127—431no—
226#126—861no—
227#124—431no—
228#124—431no—
229#124—431no—
230#124—861no—
231#123—861no—
232C22⋊Q8—431no—
233C22⋊Q8—861no—
234#121—431no—
235#121—861no—
236#121—861no—
237#120—861no—
238#120—861no—
239C4×Q8—431no—
240C4×D4—431no—
241#117C2×D4311yescharacteristic
242C4⋊C8C2×D4311yescharacteristic, complemented
243C4⋊C8C2×D4311yescharacteristic, complemented
244#103—431no—
245#103—431no—
246#102—431no—
247#102—431no—
248#102—431no—
249#102—431no—
250#102—431no—
251#102—431no—
252C22⋊C8C2×D4311yescharacteristic
253C22⋊C8C2×D4311yescharacteristic
254#97C2×D4311yescharacteristic, complemented
255C4×C8C2×D4311yescharacteristic, complemented
256C24—861no—
257#41—1721no—
258#41—1721no—
259C2×Q8—431no—
260C2×Q8—431no—
261C2×Q8—861no—
262C2×D4—431no—
263C2×D4—431no—
264C2×D4—431no—
265C2×D4—431no—
266C2×D4—861no—
267C2×D4—861no—
268C2×D4—861no—
269C2×D4—861no—
270C2×D4—861no—
271C2×D4—861no—
272C2×D4—861no—
273C2×D4—1721no—
274C2×D4—1721no—
275C22×C4—861no—
276C22×C4—861no—
277C22×C4C22×D4311yescharacteristic
278Q16—1721no—
279SD16—1721no—
280SD16—1721no—
281SD16—1721no—
282SD16—1721no—
283D8—1721no—
284D8—1721no—
285D8—1721no—
286C2×C8C22×D4311yescharacteristic
287C2×C8C22×D4311yescharacteristic
288C2×C8C22×D4311yescharacteristic
289C2×C8C22×D4311yescharacteristic
290C4⋊C4—431no—
291C4⋊C4—431no—
292C4⋊C4—861no—
293C4⋊C4—861no—
294C4⋊C4—861no—
295C4⋊C4D17211yescharacteristic
296C4⋊C4D17211yescharacteristic
297C22⋊C4—861no—
298C22⋊C4—861no—
299C22⋊C4—861no—
300C22⋊C4—861no—
301C22⋊C4—861no—
302C22⋊C4—861no—
303C22⋊C4—861no—
304C22⋊C4—861no—
305C22⋊C4—861no—
306C22⋊C4D17211yescharacteristic
307C22⋊C4D17211yescharacteristic
308C42—861no—
309C42C22×D4311yescharacteristic
310C42C22×D4311yescharacteristic
311C23—861no—
312C23—861no—
313C23—861no—
314C23—861no—
315C23—3441no—
316C23—3441no—
317C23—1722no—
318C23C2×D17211yescharacteristic
319Q8—861no—
320Q8—861no—
321Q8—861no—
322Q8—861no—
323Q8—3441no—
324D4—861no—
325D4—861no—
326D4—861no—
327D4—861no—
328D4—861no—
329D4—861no—
330D4—861no—
331D4—861no—
332D4—3441no—
333D4—3441no—
334D4—3441no—
335D4—3441no—
336D4—3441no—
337D4—1722no—
338D4—1722no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—861no—
342C2×C4—861no—
343C2×C4—861no—
344C2×C4—861no—
345C2×C4—3441no—
346C2×C4—1722no—
347C2×C4C2×D17211yescharacteristic
348C2×C4C2×D17211yescharacteristic
349C2×C4C2×D17211yescharacteristic
350C2×C4C2×D17211yescharacteristic
351C2×C4C2×D17211yescharacteristic
352C2×C4C23×D4311yescharacteristic
353C8—21no—
354C8—21no—
355C8—21no—
356C8—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—3444no—
361C22—1721no—
362C22—1721no—
363C22—1721no—
364C22—1721no—
365C22—1721no—
366C22—1721no—
367C22—1721no—
368C22—1721no—
369C22—1721no—
370C22—1721no—
371C22—1721no—
372C22—1721no—
373C22C22×D17211yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—1721no—
380C4—1721no—
381C4—1721no—
382C4—1721no—
383C4#1306337111yescharacteristic
384C4#1306337111yescharacteristic
385C2—41no—
386C2—3441no—
387C2—3441no—
388C2—3441no—
389C2—3441no—
390C2#1458346811yescharacteristic
391C2#1458370411yescharacteristic
392C2#1458371111yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#433C2
socleC22×C43C22×D4
hypercenter#433D43
hypocenterC43#3224
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #14583520C2semidirect
2. #14583468C2semidirect
3. #14583288C2semidirect
4. #14583283C2semidirect
5. #14583259C2semidirect
6. #14583246C2semidirect
7. #14583122C2semidirect
8. #14583115C2semidirect
9. #14583100C2semidirect
10. #14583095C2semidirect
11. #14583063C2semidirect
12. #14583052C2semidirect
13. #14583046C2semidirect
14. #14583035C2semidirect
15. C43×#433C2semidirect
18. C2×Dic172C22semidirect
21. C2×#10621873C22semidirect
22. C2×#10621873C22semidirect
25. C2×D344C22semidirect
26. #13063325C22semidirect
32. #13063313C22semidirect
42. C4×Dic86C22semidirect
43. C4×D172C22semidirect
44. #13063250C22semidirect
45. #13063250C22semidirect
50. #13063247C22semidirect
51. #13063247C22semidirect
53. C4⋊C8×C43C22semidirect
54. C4⋊C8×C43C22semidirect
57. #97×C43C22semidirect
58. C4×C8×C43C22semidirect
211. #433D43semidirect
212. C43#3224semidirect
242. C4⋊C8C2×D43semidirect
243. C4⋊C8C2×D43semidirect
254. #97C2×D43semidirect
255. C4×C8C2×D43semidirect