Finite Group Databasebeta

← #19146818

Subgroups — #19146818

Order 5504.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583590C211yesmaximal, characteristic, complemented
2#14583542C211yesmaximal, characteristic
3#14583253C211yesmaximal, characteristic, complemented
4#14583239C211yesmaximal, characteristic, complemented
5#14583216C211yesmaximal, characteristic, complemented
6#14583200C211yesmaximal, characteristic, complemented
7#14583154C211yesmaximal, characteristic, complemented
8#14583142C211yesmaximal, characteristic, complemented
9#14583060C211yesmaximal, characteristic, complemented
10#14583048C211yesmaximal, characteristic, complemented
11C4×#10621884C211yesmaximal, characteristic, complemented
12#14582976C211yesmaximal, characteristic, complemented
13#14582902C211yesmaximal, characteristic, complemented
14#14582899C211yesmaximal, characteristic, complemented
15C43×#464C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×D4×D43C2211yescharacteristic
18C2×#10621884C2211yescharacteristic
19C2×#10621872C2211yescharacteristic
20C2×#10621872C2211yescharacteristic, complemented
21#13063319—21no—
22#13063317C2211yescharacteristic, complemented
23#13063315—21no—
24#13063310—21no—
25#13063307—21no—
26#13063301C2211yescharacteristic
27#13063301C2211yescharacteristic
28#13063301C2211yescharacteristic, complemented
29#13063298—21no—
30#13063296C2211yescharacteristic
31#13063295—21no—
32C4×D172C2211yescharacteristic
33C4×D172C2211yescharacteristic
34#13063283C2211yescharacteristic
35#13063282—21no—
36C4⋊C4×D43C2211yescharacteristic, complemented
37C22⋊C4×D43—21no—
38#13063259C2211yescharacteristic, complemented
39#13063257C2211yescharacteristic, complemented
40#13063256C2211yescharacteristic, complemented
41#13063249C2211yescharacteristic, complemented
42#13063249C2211yescharacteristic, complemented
43#13063249C2211yescharacteristic, complemented
44#13063247C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063245C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic, complemented
51C4×C43⋊C8C2211yescharacteristic, complemented
52C2×Q16×C43C2211yescharacteristic, complemented
53C2×SD16×C43C2211yescharacteristic
54#124×C43C2211yescharacteristic
55C4×Q8×C43C2211yescharacteristic, complemented
56C4⋊C8×C43C2211yescharacteristic, complemented
57#103×C43C2211yescharacteristic, complemented
58#102×C43C2211yescharacteristic
59C23×D43—21no—
60C2×Q8×C43C2311yescharacteristic
61C2×Q8×C43C2311yescharacteristic
62C2×D4×C43C2311yescharacteristic
63C2×C22⋊D43—21no—
64C2×C22⋊D43—21no—
65#10621902—22no—
66#10621902—41no—
67D4×D43—22no—
68D4×D43—41no—
69C2×D172—21no—
70C2×D172D411yescharacteristic
71C2×D172C2311yescharacteristic
72C2×C4×D43—21no—
73C2×C4×D43—21no—
74C2×C4×D43—21no—
75C2×C4×D43C2311yescharacteristic
76C2×C4×D43C2311yescharacteristic
77Q16×C43—41no—
78SD16×C43—41no—
79C2×C8×C43C2311yescharacteristic
80C2×C8×C43C2311yescharacteristic
81C4⋊C4×C43—21no—
82C4⋊C4×C43C2311yescharacteristic
83C22⋊C4×C43—21no—
84C22⋊C4×C43—21no—
85C42×C43—21no—
86C42×C43C2311yescharacteristic
87C22⋊Dic43—21no—
88#10621884—22no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4D411yescharacteristic
95(C2×D43)⋊C4D411yescharacteristic
96C4⋊Dic43D411yescharacteristic
97C4⋊Dic43C2311yescharacteristic
98C4⋊Dic43C2311yescharacteristic
99C4⋊Dic43C2311yescharacteristic
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104Dic43⋊C4—21no—
105Dic43⋊C4—21no—
106C4×Dic43—21no—
107C2×C43⋊C8C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109#10621872—41no—
110#10621872—41no—
111C23×C43—21no—
112C22×D43—21no—
113C22×D43—42no—
114C22×D43—42no—
115C22×D43—81no—
116C22×D43C2×D411yescharacteristic
117C22×D43C2×D411yescharacteristic
118Q8×C43—21no—
119Q8×C43—21no—
120Q8×C43—21no—
121Q8×C43—21no—
122D4×C43—21no—
123D4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
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×Dic43C2×D411yescharacteristic
136C2×Dic43C2×D411yescharacteristic
137D172—21no—
138D172—41no—
139D172—42no—
140D172#4112yes—
141C4×D43—21no—
142C4×D43—21no—
143C4×D43—21no—
144C4×D43—21no—
145C4×D43—42no—
146C4×D43—42no—
147C4×D43—81no—
148C8×C43—21no—
149C8×C43—21no—
150C43⋊C8—21no—
151C43⋊C8—21no—
152C22×C43—41no—
153C22×C43—41no—
154C22×C43—41no—
155C22×C43C22×D411yescharacteristic
156C2×D43—22no—
157C2×D43—21no—
158C2×D43—21no—
159C2×D43—21no—
160C2×D43—21no—
161C2×D43—21no—
162C2×D43—21no—
163C2×D43—41no—
164C2×D43—41no—
165C2×D43—84no—
166C4×C43—21no—
167C4×C43—21no—
168C4×C43—41no—
169C4×C43—41no—
170C4×C43—41no—
171C4×C43C2×#4111yescharacteristic
172C4×C43H(5,𝔽2)11yescharacteristic
173Dic43—21no—
174Dic43—21no—
175Dic43—41no—
176Dic43—41no—
177Dic43—41no—
178#3323—431nomaximal, Sylow
179C2×C43—81no—
180C2×C43#54611yescharacteristic
181C2×C43#57511yescharacteristic
182C2×C43#57711yescharacteristic
183D43—41no—
184D43—41no—
185D43—42no—
186#552—431no—
187#546—431no—
188#488—431no—
189#485—431no—
190#481—431no—
191#478—431no—
192#470—431no—
193#468—431no—
194#464D4311yescharacteristic, complemented
195#452—431no—
196#450—431no—
197C4×SD16—431no—
198#436—431no—
199#418—431no—
200#417—431no—
201C43#332311yescharacteristic, complemented, Sylow
202C2×#41—431no—
203C22×D4—431no—
204C2×Q16C2×D4311yescharacteristic, complemented
205C2×SD16—431no—
206C2×SD16C2×D4311yescharacteristic
207C2×M16—431no—
208C2×M16—431no—
209#126—861no—
210#125—431no—
211#125—861no—
212#124C2×D4311yescharacteristic
213#123—861no—
214#123—861no—
215C22⋊Q8—431no—
216C22⋊Q8—431no—
217C22⋊Q8—431no—
218#121—431no—
219#121—861no—
220#120—861no—
221C4×Q8C2×D4311yescharacteristic, complemented
222C4×D4—431no—
223C4×D4—431no—
224#117—431no—
225#117—861no—
226C2×C4⋊C4—431no—
227C2×C22⋊C4—861no—
228#107—431no—
229#106—431no—
230#106—431no—
231C4⋊C8C2×D4311yescharacteristic, complemented
232#103—431no—
233#103—431no—
234#103—431no—
235#103C2×D4311yescharacteristic, complemented
236#102—431no—
237#102—431no—
238#102—431no—
239#102—431no—
240#102—431no—
241#102C2×D4311yescharacteristic
242C22⋊C8—431no—
243C22⋊C8—431no—
244C4×C8—431no—
245C24—861no—
246#41—862no—
247#41—1721no—
248C2×Q8C22×D4311yescharacteristic
249C2×Q8C22×D4311yescharacteristic
250C2×D4—431no—
251C2×D4—431no—
252C2×D4—861no—
253C2×D4—861no—
254C2×D4—862no—
255C2×D4—861no—
256C2×D4—1721no—
257C2×D4C22×D4311yescharacteristic
258C22×C4—431no—
259C22×C4—431no—
260C22×C4—861no—
261C22×C4—861no—
262C22×C4—861no—
263Q16—41no—
264SD16—41no—
265SD16—862no—
266M16—1721no—
267M16—1721no—
268C2×C8—431no—
269C2×C8—431no—
270C2×C8C22×D4311yescharacteristic
271C2×C8C22×D4311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—431no—
274C4⋊C4—431no—
275C4⋊C4—431no—
276C4⋊C4—431no—
277C4⋊C4—861no—
278C4⋊C4—861no—
279C4⋊C4—861no—
280C4⋊C4—861no—
281C4⋊C4—861no—
282C4⋊C4—861no—
283C4⋊C4C22×D4311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—431no—
287C22⋊C4—431no—
288C22⋊C4—861no—
289C22⋊C4—861no—
290C22⋊C4—861no—
291C22⋊C4—861no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C42—21no—
295C42—861no—
296C42C22×D4311yescharacteristic
297C23—21no—
298C23—431no—
299C23—431no—
300C23—861no—
301C23—3441no—
302C23—1722no—
303C23—1722no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308D4—21no—
309D4—21no—
310D4—432no—
311D4—861no—
312D4—3441no—
313D4—1721no—
314D4—1722no—
315D4—1722no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—431no—
320C2×C4—431no—
321C2×C4—861no—
322C2×C4—861no—
323C2×C4—861no—
324C2×C4—861no—
325C2×C4—861no—
326C2×C4—861no—
327C2×C4—861no—
328C2×C4—3441no—
329C2×C4—1722no—
330C2×C4—1722no—
331C2×C4D4×D4311yescharacteristic
332C2×C4D4×D4311yescharacteristic
333C2×C4C23×D4311yescharacteristic
334C8—21no—
335C8—21no—
336C8—861no—
337C8—861no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—861no—
342C22—861no—
343C22—861no—
344C22—861no—
345C22—861no—
346C22—861no—
347C22—862no—
348C22—3444no—
349C22—1721no—
350C22—1721no—
351C22C2×D4×D4311yescharacteristic
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—861no—
358C4—861no—
359C4—1721no—
360C4—1721no—
361C4—1721no—
362C4#41×D4311yescharacteristic
363C4#1306337011yescharacteristic
364C2—81no—
365C2—1721no—
366C2—1721no—
367C2—1722no—
368C2#1458354611yescharacteristic
369C2#1458369611yescharacteristic
370C2#1458370811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#464C2
socleC22×C43C22×D4
hypercenter#464D43
hypocenterC43#3323
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. #14583590C2semidirect
3. #14583253C2semidirect
4. #14583239C2semidirect
5. #14583216C2semidirect
6. #14583200C2semidirect
7. #14583154C2semidirect
8. #14583142C2semidirect
9. #14583060C2semidirect
10. #14583048C2semidirect
11. C4×#10621884C2semidirect
12. #14582976C2semidirect
13. #14582902C2semidirect
14. #14582899C2semidirect
15. C43×#464C2semidirect
20. C2×#10621872C22semidirect
22. #13063317C22semidirect
28. #13063301C22semidirect
36. C4⋊C4×D43C22semidirect
38. #13063259C22semidirect
39. #13063257C22semidirect
40. #13063256C22semidirect
41. #13063249C22semidirect
42. #13063249C22semidirect
43. #13063249C22semidirect
50. (C2×D43)⋊C8C22semidirect
51. C4×C43⋊C8C22semidirect
52. C2×Q16×C43C22semidirect
55. C4×Q8×C43C22semidirect
56. C4⋊C8×C43C22semidirect
57. #103×C43C22semidirect
194. #464D43semidirect
201. C43#3323semidirect
204. C2×Q16C2×D43semidirect
221. C4×Q8C2×D43semidirect
231. C4⋊C8C2×D43semidirect
235. #103C2×D43semidirect