Finite Group Databasebeta

← #19146451

Subgroups — #19146451

Order 5504.

420 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#14583601C211yesmaximal, characteristic, complemented
2#14583540C211yesmaximal, characteristic, complemented
3#14583255C211yesmaximal, characteristic, complemented
4#14583232C211yesmaximal, characteristic, complemented
5#14583225C211yesmaximal, characteristic, complemented
6#14583198C211yesmaximal, characteristic, complemented
7#14583134C211yesmaximal, characteristic, complemented
8#14583116C211yesmaximal, characteristic, complemented
9#14583043C211yesmaximal, characteristic, complemented
10#14583032C211yesmaximal, characteristic, complemented
11#14582979C211yesmaximal, characteristic, complemented
12C8×C22⋊D43C211yesmaximal, characteristic, complemented
13#14582894C211yesmaximal, characteristic, complemented
14C2×#13063247C211yesmaximal, characteristic, complemented
15C43×#465C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C22×D172C2211yescharacteristic
18C2×#10621882C2211yescharacteristic
19C2×#10621882C2211yescharacteristic
20C2×C8×D43C2211yescharacteristic, complemented
21#13063318—21no—
22#13063316C2211yescharacteristic, complemented
23#13063314C2211yescharacteristic
24#13063310—21no—
25#13063309—21no—
26#13063300—21no—
27#13063300C2211yescharacteristic
28#13063297—21no—
29#13063296C2211yescharacteristic, complemented
30#13063295—21no—
31D4×Dic43—21no—
32D4×Dic43C2211yescharacteristic, complemented
33#13063287C2211yescharacteristic
34C4×C22⋊D43C2211yescharacteristic
35#13063283C2211yescharacteristic, complemented
36C2×C4⋊Dic43C2211yescharacteristic
37C22⋊C4×D43—21no—
38#13063258C2211yescharacteristic, complemented
39#13063258C2211yescharacteristic, complemented
40Dic43⋊C8C2211yescharacteristic, complemented
41#13063249C2211yescharacteristic, complemented
42#13063249C2211yescharacteristic, complemented
43#13063247C2211yescharacteristic
44#13063247C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063247C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic, complemented
51C8×Dic43C2211yescharacteristic, complemented
52C2×SD16×C43C2211yescharacteristic, complemented
53C22×C8×C43C2211yescharacteristic
54C22⋊Q8×C43C2211yescharacteristic
55#121×C43C2211yescharacteristic
56#106×C43C2211yescharacteristic, complemented
57#103×C43C2211yescharacteristic, complemented
58#102×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60C2×Q8×C43C2311yescharacteristic
61C2×D4×C43—21no—
62C2×D4×C43C2311yescharacteristic
63C22×C4×C43C2311yescharacteristic
64C2×C22⋊D43—21no—
65C2×C22⋊D43D411yescharacteristic
66C22×Dic43—21no—
67C22×Dic43—21no—
68#10621902—22no—
69#10621902—41no—
70C2×D172—21no—
71C2×D172—21no—
72C2×D172—21no—
73C2×D172—22no—
74C2×D172—41no—
75C2×D172C2311yescharacteristic
76C2×D172C2311yescharacteristic
77C2×C4×D43—21no—
78C2×C4×D43—21no—
79C2×C4×D43C2311yescharacteristic
80SD16×C43—41no—
81C2×C8×C43—41no—
82C2×C8×C43C2311yescharacteristic
83C2×C8×C43C2311yescharacteristic
84C4⋊C4×C43—21no—
85C4⋊C4×C43C2311yescharacteristic
86C4⋊C4×C43C2311yescharacteristic
87C22⋊C4×C43—21no—
88C22⋊C4×C43—21no—
89C22⋊Dic43—21no—
90C22⋊Dic43—21no—
91C22⋊Dic43D411yescharacteristic
92#10621882—22no—
93#10621882—41no—
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)⋊C4D411yescharacteristic
100C4⋊Dic43—21no—
101C4⋊Dic43—21no—
102C4⋊Dic43C2311yescharacteristic
103C4⋊Dic43C2311yescharacteristic
104Dic43⋊C4—21no—
105Dic43⋊C4D411yescharacteristic
106C4×Dic43—21no—
107C4×Dic43C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110C8×D43—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
119Q8×C43—21no—
120Q8×C43—21no—
121D4×C43—21no—
122D4×C43—21no—
123D4×C43—42no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43C2×D411yescharacteristic
130C2×C4×C43C2411yescharacteristic
131C22⋊D43—22no—
132C22⋊D43—81no—
133C2×Dic43—21no—
134C2×Dic43—21no—
135C2×Dic43—81no—
136C2×Dic43—81no—
137C2×Dic43C2×D411yescharacteristic
138C2×Dic43C2×D411yescharacteristic
139C2×Dic43C2×D411yescharacteristic
140D172—21no—
141D172—21no—
142D172—21no—
143D172—42no—
144D172—42no—
145D172—81no—
146D172#4112yes—
147C4×D43—21no—
148C4×D43—21no—
149C4×D43—42no—
150C4×D43—81no—
151C8×C43—21no—
152C8×C43—21no—
153C43⋊C8—21no—
154C43⋊C8—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43#13512yes—
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#3297—431nomaximal, Sylow
184C2×C43—22no—
185C2×C43—81no—
186C2×C43#54611yescharacteristic
187C2×C43C2×#13511yescharacteristic
188C2×C43#57611yescharacteristic
189D43—41no—
190D43—42no—
191D43—81no—
192#553—431no—
193#546—431no—
194#488—431no—
195#484—431no—
196#482—431no—
197#478—431no—
198#466—431no—
199#465D4311yescharacteristic, complemented
200#463—431no—
201#449—431no—
202#447—431no—
203C4×D8—431no—
204C8×D4—431no—
205#416—431no—
206C2×#102—431no—
207C43#329711yescharacteristic, complemented, Sylow
208C2×#41—431no—
209C22×D4—431no—
210C2×SD16C2×D4311yescharacteristic, complemented
211C2×D8—431no—
212C2×D8—431no—
213C22×C8—431no—
214C22×C8C2×D4311yescharacteristic
215#126—861no—
216#125—431no—
217#124—431no—
218#123—861no—
219#123—861no—
220C22⋊Q8C2×D4311yescharacteristic
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—
230C4×D4—861no—
231#117—431no—
232C2×C4⋊C4—431no—
233C2×C22⋊C4—861no—
234#107—431no—
235#107—431no—
236#106C2×D4311yescharacteristic, complemented
237C4⋊C8—431no—
238#103—431no—
239#103—431no—
240#103C2×D4311yescharacteristic, complemented
241#102—431no—
242#102—431no—
243#102—431no—
244#102—431no—
245#102—431no—
246#102—431no—
247#102C2×D4311yescharacteristic, complemented
248C22⋊C8—431no—
249C22⋊C8—431no—
250C4×C8—431no—
251C24—861no—
252#41—862no—
253#41—1721no—
254C2×Q8C22×D4311yescharacteristic
255C2×D4—21no—
256C2×D4—431no—
257C2×D4—431no—
258C2×D4—431no—
259C2×D4—862no—
260C2×D4—861no—
261C2×D4—861no—
262C2×D4—861no—
263C2×D4—861no—
264C2×D4—1721no—
265C2×D4C22×D4311yescharacteristic
266C22×C4—431no—
267C22×C4—861no—
268C22×C4—861no—
269C22×C4—861no—
270C22×C4—861no—
271C22×C4C22×D4311yescharacteristic
272SD16—41no—
273D8—862no—
274D8—1721no—
275C2×C8—41no—
276C2×C8—431no—
277C2×C8—431no—
278C2×C8—1721no—
279C2×C8C22×D4311yescharacteristic
280C2×C8C22×D4311yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—431no—
283C4⋊C4—431no—
284C4⋊C4—431no—
285C4⋊C4—861no—
286C4⋊C4—861no—
287C4⋊C4—861no—
288C4⋊C4C22×D4311yescharacteristic
289C4⋊C4C22×D4311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—431no—
293C22⋊C4—431no—
294C22⋊C4—861no—
295C22⋊C4—861no—
296C22⋊C4—861no—
297C22⋊C4—861no—
298C22⋊C4—861no—
299C22⋊C4—861no—
300C22⋊C4—861no—
301C42—431no—
302C42—861no—
303C23—21no—
304C23—431no—
305C23—861no—
306C23—861no—
307C23—3441no—
308C23—1722no—
309C23—1722no—
310C23D4×D4311yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—21no—
315D4—42no—
316D4—432no—
317D4—862no—
318D4—861no—
319D4—861no—
320D4—861no—
321D4—3441no—
322D4—3441no—
323D4—1722no—
324D4—1722no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—431no—
331C2×C4—431no—
332C2×C4—431no—
333C2×C4—861no—
334C2×C4—861no—
335C2×C4—861no—
336C2×C4—861no—
337C2×C4—3441no—
338C2×C4—3441no—
339C2×C4—3441no—
340C2×C4—1722no—
341C2×C4D4×D4311yescharacteristic
342C2×C4C23×D4311yescharacteristic
343C8—21no—
344C8—21no—
345C8—861no—
346C8—861no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—861no—
353C22—861no—
354C22—861no—
355C22—862no—
356C22—3444no—
357C22—1721no—
358C22—1721no—
359C22—1721no—
360C22—1721no—
361C22—1721no—
362C22#1306334612yes—
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#1306337011yescharacteristic
375C2—22no—
376C2—81no—
377C2—3441no—
378C2—1721no—
379C2—1722no—
380C2#1458353811yescharacteristic
381C2C2×#1306334611yescharacteristic
382C2#1458370111yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#465C2
socleC22×C43C22×D4
hypercenter#465D43
hypocenterC43#3297
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #14583601C2semidirect
2. #14583540C2semidirect
3. #14583255C2semidirect
4. #14583232C2semidirect
5. #14583225C2semidirect
6. #14583198C2semidirect
7. #14583134C2semidirect
8. #14583116C2semidirect
9. #14583043C2semidirect
10. #14583032C2semidirect
11. #14582979C2semidirect
12. C8×C22⋊D43C2semidirect
13. #14582894C2semidirect
14. C2×#13063247C2semidirect
15. C43×#465C2semidirect
20. C2×C8×D43C22semidirect
22. #13063316C22semidirect
29. #13063296C22semidirect
32. D4×Dic43C22semidirect
35. #13063283C22semidirect
38. #13063258C22semidirect
39. #13063258C22semidirect
40. Dic43⋊C8C22semidirect
41. #13063249C22semidirect
42. #13063249C22semidirect
50. (C2×D43)⋊C8C22semidirect
51. C8×Dic43C22semidirect
52. C2×SD16×C43C22semidirect
56. #106×C43C22semidirect
57. #103×C43C22semidirect
58. #102×C43C22semidirect
199. #465D43semidirect
207. C43#3297semidirect
210. C2×SD16C2×D43semidirect
236. #106C2×D43semidirect
240. #103C2×D43semidirect
247. #102C2×D43semidirect