Finite Group Databasebeta

← #19146749

Subgroups — #19146749

Order 5504.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583612C211yesmaximal, characteristic, complemented
2#14583546C211yesmaximal, characteristic, complemented
3#14583257C211yesmaximal, characteristic, complemented
4#14583243C211yesmaximal, characteristic, complemented
5#14583178C211yesmaximal, characteristic, complemented
6#14583146C211yesmaximal, characteristic, complemented
7#14583133C211yesmaximal, characteristic, complemented
8#14583113C211yesmaximal, characteristic, complemented
9#14583046C211yesmaximal, characteristic, complemented
10#14583034C211yesmaximal, characteristic, complemented
11#14583010C211yesmaximal, characteristic, complemented
12#14582967C211yesmaximal, characteristic, complemented
13#14582902C211yesmaximal, characteristic, complemented
14#14582893C211yesmaximal, characteristic, complemented
15C43×#482C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×D4×D43C2211yescharacteristic
18C2×#10621873C2211yescharacteristic, complemented
19C2×D344C2211yescharacteristic
20C2×#10621882C2211yescharacteristic
21C2×#10621872C2211yescharacteristic
22C22×C43⋊C8C2211yescharacteristic, complemented
23#13063324C2211yescharacteristic, complemented
24#13063313—21no—
25#13063312C2211yescharacteristic
26#13063311—21no—
27#13063307—21no—
28#13063305C2211yescharacteristic
29#13063300C2211yescharacteristic
30#13063299C2211yescharacteristic, complemented
31#13063298—21no—
32#13063296—21no—
33#13063293—21no—
34#13063287C2211yescharacteristic
35#13063287C2211yescharacteristic, complemented
36C4×C22⋊D43C2211yescharacteristic
37#13063283C2211yescharacteristic
38#13063282—21no—
39C22⋊C4×D43—21no—
40#13063258C2211yescharacteristic, complemented
41Dic43⋊C8C2211yescharacteristic, complemented
42#13063250C2211yescharacteristic, complemented
43#13063248C2211yescharacteristic, complemented
44#13063248C2211yescharacteristic, complemented
45#13063247C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49#13063245C2211yescharacteristic, complemented
50(C2×D43)⋊C8C2211yescharacteristic
51#13063235C2211yescharacteristic, complemented
52#121×C43C2211yescharacteristic
53#117×C43C2211yescharacteristic, complemented
54#107×C43C2211yescharacteristic, complemented
55#106×C43C2211yescharacteristic, complemented
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60C2×D4×C43—21no—
61C2×D4×C43C2311yescharacteristic
62C22×C4×C43C2311yescharacteristic
63C2×C22⋊D43—21no—
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66C2×C22⋊D43D411yescharacteristic
67D4×D43—22no—
68D4×D43—41no—
69#10621898—22no—
70#10621898—41no—
71C2×D172—21no—
72C2×D172C2311yescharacteristic
73C2×D172C2311yescharacteristic
74C2×C4×D43—21no—
75C2×C4×D43—21no—
76C2×C4×D43—21no—
77C2×C4×D43C2311yescharacteristic
78C2×Dic86—21no—
79C2×Dic86C2311yescharacteristic
80C2×C8×C43C2311yescharacteristic
81C2×C8×C43C2311yescharacteristic
82C4⋊C4×C43C2311yescharacteristic
83C4⋊C4×C43C2311yescharacteristic
84C4⋊C4×C43C2311yescharacteristic
85C22⋊C4×C43—21no—
86C22⋊C4×C43—21no—
87C42×C43—21no—
88C22⋊Dic43—21no—
89C22⋊Dic43—21no—
90C22⋊Dic43D411yescharacteristic
91#10621882—41no—
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)⋊C4D411yescharacteristic
99C4⋊Dic43—21no—
100C4⋊Dic43C2311yescharacteristic
101Dic43⋊C4—21no—
102Dic43⋊C4D411yescharacteristic
103C4×Dic43—21no—
104C4×Dic43C2311yescharacteristic
105C2×C43⋊C8—41no—
106C2×C43⋊C8C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108D344—22no—
109#10621873—41no—
110#10621872—41no—
111C23×C43—21no—
112C23×C43C2×D411yescharacteristic
113C22×D43—21no—
114C22×D43—21no—
115C22×D43—42no—
116C22×D43—42no—
117C22×D43—81no—
118C22×D43C2×D411yescharacteristic
119D4×C43—21no—
120D4×C43—21no—
121D4×C43—81no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43C2×D411yescharacteristic
128C2×C4×C43C2411yescharacteristic
129C22⋊D43—41no—
130C22⋊D43—42no—
131C22⋊D43—42no—
132C22⋊D43—81no—
133C2×Dic43—21no—
134C2×Dic43—21no—
135C2×Dic43C2×D411yescharacteristic
136C2×Dic43C2×D411yescharacteristic
137C2×Dic43C2×D411yescharacteristic
138D172—21no—
139D172—21no—
140D172—21no—
141D172—81no—
142D172#4112yes—
143C4×D43—21no—
144C4×D43—21no—
145C4×D43—42no—
146C4×D43—42no—
147C4×D43—81no—
148Dic86—21no—
149Dic86—21no—
150Dic86—81no—
151C8×C43—21no—
152C8×C43—21no—
153C43⋊C8—21no—
154C43⋊C8—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43—41no—
161C22×C43C22×D411yescharacteristic
162C2×D43—22no—
163C2×D43—21no—
164C2×D43—21no—
165C2×D43—21no—
166C2×D43—41no—
167C2×D43—41no—
168C2×D43—41no—
169C2×D43—41no—
170C2×D43—41no—
171C2×D43—84no—
172C4×C43—21no—
173C4×C43—41no—
174C4×C43—41no—
175C4×C43—41no—
176C4×C43C2×#4111yescharacteristic
177C4×C43H(5,𝔽2)11yescharacteristic
178Dic43—21no—
179Dic43—21no—
180Dic43—21no—
181Dic43—41no—
182Dic43—41no—
183#3319—431nomaximal, Sylow
184C2×C43—41no—
185C2×C43—81no—
186C2×C43#54611yescharacteristic
187C2×C43#57511yescharacteristic
188C2×C43#57611yescharacteristic
189D43—41no—
190D43—42no—
191D43—81no—
192#555—431no—
193#546—431no—
194#489—431no—
195#485—431no—
196#482D4311yescharacteristic, complemented
197#474—431no—
198#468—431no—
199#466—431no—
200#463—431no—
201#449—431no—
202#447—431no—
203#442—431no—
204#435—431no—
205#418—431no—
206#416—431no—
207C43#331911yescharacteristic, complemented, Sylow
208C2×#41—431no—
209C22×D4—431no—
210C2×SD16—431no—
211C2×D8—431no—
212C2×D8—431no—
213C2×M16—431no—
214C22×C8—431no—
215C4⋊Q8—431no—
216#124—431no—
217#124—861no—
218#124—861no—
219#123—861no—
220C22⋊Q8—431no—
221#121—431no—
222#121—431no—
223#121—861no—
224#121—861no—
225#121C2×D4311yescharacteristic
226#120—861no—
227C4×D4—431no—
228C4×D4—431no—
229C4×D4—431no—
230#117—431no—
231#117—861no—
232#117C2×D4311yescharacteristic, complemented
233C2×C22⋊C4—861no—
234#107—431no—
235#107C2×D4311yescharacteristic, complemented
236#106C2×D4311yescharacteristic, complemented
237C4⋊C8—431no—
238#103—431no—
239#103—431no—
240#103—431no—
241#102—431no—
242#102—431no—
243#102—431no—
244#102—431no—
245#102—431no—
246#102C2×D4311yescharacteristic
247#102C2×D4311yescharacteristic
248C22⋊C8—431no—
249C22⋊C8C2×D4311yescharacteristic, complemented
250#97—431no—
251C24—861no—
252#41—862no—
253#41—1721no—
254C2×Q8—431no—
255C2×Q8—861no—
256C2×D4—21no—
257C2×D4—431no—
258C2×D4—431no—
259C2×D4—431no—
260C2×D4—861no—
261C2×D4—861no—
262C2×D4—862no—
263C2×D4—861no—
264C2×D4—861no—
265C2×D4—1721no—
266C2×D4C22×D4311yescharacteristic
267C22×C4—431no—
268C22×C4—861no—
269C22×C4—861no—
270C22×C4—861no—
271C22×C4C22×D4311yescharacteristic
272SD16—1721no—
273D8—862no—
274D8—1721no—
275M16—1721no—
276C2×C8—431no—
277C2×C8—431no—
278C2×C8—1721no—
279C2×C8C22×D4311yescharacteristic
280C2×C8C22×D4311yescharacteristic
281C4⋊C4—431no—
282C4⋊C4—431no—
283C4⋊C4—861no—
284C4⋊C4—861no—
285C4⋊C4C22×D4311yescharacteristic
286C4⋊C4C22×D4311yescharacteristic
287C4⋊C4C22×D4311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—431no—
291C22⋊C4—431no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C22⋊C4—861no—
295C22⋊C4—861no—
296C22⋊C4—861no—
297C22⋊C4—861no—
298C22⋊C4—861no—
299C22⋊C4—861no—
300C42—21no—
301C42—431no—
302C42—861no—
303C23—21no—
304C23—431no—
305C23—861no—
306C23—861no—
307C23—3441no—
308C23—1722no—
309C23—1722no—
310C23D4×D4311yescharacteristic
311Q8—861no—
312Q8—861no—
313Q8—3441no—
314D4—21no—
315D4—21no—
316D4—81no—
317D4—432no—
318D4—861no—
319D4—861no—
320D4—861no—
321D4—3441no—
322D4—3441no—
323D4—1721no—
324D4—1722no—
325D4—1722no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—431no—
332C2×C4—431no—
333C2×C4—431no—
334C2×C4—861no—
335C2×C4—861no—
336C2×C4—861no—
337C2×C4—861no—
338C2×C4—3441no—
339C2×C4—1722no—
340C2×C4—1722no—
341C2×C4D4×D4311yescharacteristic
342C2×C4C23×D4311yescharacteristic
343C8—21no—
344C8—21no—
345C8—861no—
346C8—861no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—861no—
354C22—861no—
355C22—861no—
356C22—862no—
357C22—3444no—
358C22—1721no—
359C22—1721no—
360C22—1721no—
361C22—1721no—
362C22—1721no—
363C22C2×D4×D4311yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—861no—
369C4—861no—
370C4—861no—
371C4—1721no—
372C4—1721no—
373C4#41×D4311yescharacteristic
374C4#1306337111yescharacteristic
375C2—41no—
376C2—81no—
377C2—3441no—
378C2—1721no—
379C2—1722no—
380C2#1458354111yescharacteristic
381C2#1458369611yescharacteristic
382C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#482C2
socleC22×C43C22×D4
hypercenter#482D43
hypocenterC43#3319
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #14583612C2semidirect
2. #14583546C2semidirect
3. #14583257C2semidirect
4. #14583243C2semidirect
5. #14583178C2semidirect
6. #14583146C2semidirect
7. #14583133C2semidirect
8. #14583113C2semidirect
9. #14583046C2semidirect
10. #14583034C2semidirect
11. #14583010C2semidirect
12. #14582967C2semidirect
13. #14582902C2semidirect
14. #14582893C2semidirect
15. C43×#482C2semidirect
18. C2×#10621873C22semidirect
22. C22×C43⋊C8C22semidirect
23. #13063324C22semidirect
30. #13063299C22semidirect
35. #13063287C22semidirect
40. #13063258C22semidirect
41. Dic43⋊C8C22semidirect
42. #13063250C22semidirect
43. #13063248C22semidirect
44. #13063248C22semidirect
49. #13063245C22semidirect
51. #13063235C22semidirect
53. #117×C43C22semidirect
54. #107×C43C22semidirect
55. #106×C43C22semidirect
58. C22⋊C8×C43C22semidirect
196. #482D43semidirect
207. C43#3319semidirect
232. #117C2×D43semidirect
235. #107C2×D43semidirect
236. #106C2×D43semidirect
249. C22⋊C8C2×D43semidirect