Finite Group Databasebeta

← #19146789

Subgroups — #19146789

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#14583601C211yesmaximal, characteristic, complemented
2#14583537C211yesmaximal, characteristic, complemented
3#14583255C211yesmaximal, characteristic, complemented
4#14583239C211yesmaximal, characteristic, complemented
5#14583213C211yesmaximal, characteristic, complemented
6#14583197C211yesmaximal, characteristic, complemented
7#14583150C211yesmaximal, characteristic, complemented
8#14583142C211yesmaximal, characteristic, complemented
9#14583116C211yesmaximal, characteristic, complemented
10#14583031C211yesmaximal, characteristic, complemented
11D8×Dic43C211yesmaximal, characteristic, complemented
12#14582974C211yesmaximal, characteristic, complemented
13#14582902C211yesmaximal, characteristic, complemented
14#14582900C211yesmaximal, characteristic, complemented
15C43×#449C211yesmaximal, characteristic, complemented
16C2×D4×D43C2211yescharacteristic
17C2×#10621882C2211yescharacteristic
18C2×#10621877C2211yescharacteristic, complemented
19C2×#10621872C2211yescharacteristic
20#13063318—21no—
21#13063316C2211yescharacteristic, complemented
22#13063314C2211yescharacteristic
23#13063309—21no—
24#13063308—21no—
25#13063301C2211yescharacteristic
26#13063299C2211yescharacteristic
27#13063297—21no—
28#13063297—21no—
29#13063296C2211yescharacteristic
30#13063293—21no—
31D4×Dic43—21no—
32D4×Dic43C2211yescharacteristic
33D4×Dic43C2211yescharacteristic, complemented
34C4×C22⋊D43C2211yescharacteristic
35#13063283C2211yescharacteristic
36C2×C4⋊Dic43C2211yescharacteristic, complemented
37C2×(C2×D43)⋊C4—21no—
38#13063259C2211yescharacteristic, complemented
39#13063259C2211yescharacteristic, complemented
40#13063256C2211yescharacteristic, complemented
41Dic43⋊C8C2211yescharacteristic, complemented
42#13063249C2211yescharacteristic, complemented
43#13063249C2211yescharacteristic, complemented
44#13063247C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063246C2211yescharacteristic, complemented
49#13063245C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51C8×Dic43C2211yescharacteristic, complemented
52C2×#41×C43C2211yescharacteristic
53C2×SD16×C43C2211yescharacteristic, complemented
54C2×D8×C43C2211yescharacteristic
55#121×C43C2211yescharacteristic, complemented
56#103×C43C2211yescharacteristic, complemented
57#102×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60#41×C43—22no—
61#41×C43—41no—
62C2×Q8×C43C2311yescharacteristic
63C2×D4×C43—21no—
64C2×D4×C43—21no—
65C2×D4×C43C2311yescharacteristic
66C2×D4×C43C2311yescharacteristic
67C22×C4×C43—21no—
68C22×C4×C43C2311yescharacteristic
69C2×C22⋊D43—21no—
70C2×C22⋊D43—21no—
71C2×C22⋊D43—21no—
72C2×C22⋊D43D411yescharacteristic
73C22×Dic43—21no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76D4×D43—22no—
77D4×D43—41no—
78C2×D172C2311yescharacteristic
79C2×C4×D43C2311yescharacteristic
80SD16×C43—41no—
81D8×C43—22no—
82C2×C8×C43C2311yescharacteristic
83C2×C8×C43C2311yescharacteristic
84C4⋊C4×C43C2311yescharacteristic
85C22⋊C4×C43—21no—
86C22⋊Dic43—21no—
87C22⋊Dic43—21no—
88C22⋊Dic43—21no—
89C22⋊Dic43D411yescharacteristic
90#10621882—41no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4D411yescharacteristic
97C4⋊Dic43—21no—
98C4⋊Dic43—21no—
99C4⋊Dic43C2311yescharacteristic
100C4⋊Dic43C2311yescharacteristic
101C4⋊Dic43C2311yescharacteristic
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104Dic43⋊C4D411yescharacteristic
105C4×Dic43—21no—
106C4×Dic43C2311yescharacteristic
107#10621877—41no—
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110#10621872—41no—
111C23×C43—21no—
112C23×C43—21no—
113C23×C43C2×D411yescharacteristic
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—21no—
124D4×C43—42no—
125D4×C43—42no—
126D4×C43#4112yes—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—42no—
132C2×C4×C43C2×D411yescharacteristic
133C2×C4×C43C2411yescharacteristic
134C22⋊D43—41no—
135C22⋊D43—42no—
136C22⋊D43—81no—
137C22⋊D43—81no—
138C2×Dic43—21no—
139C2×Dic43—21no—
140C2×Dic43—21no—
141C2×Dic43—81no—
142C2×Dic43—81no—
143C2×Dic43—81no—
144C2×Dic43C2×D411yescharacteristic
145C2×Dic43C2×D411yescharacteristic
146C2×Dic43C2×D411yescharacteristic
147D172—21no—
148D172—21no—
149C4×D43—21no—
150C4×D43—21no—
151C8×C43—21no—
152C8×C43—21no—
153C43⋊C8—21no—
154C43⋊C8—21no—
155C22×C43—22no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—41no—
160C22×C43—41no—
161C22×C43—41no—
162C22×C43—41no—
163C22×C43—41no—
164C22×C43C22×D411yescharacteristic
165C2×D43—21no—
166C2×D43—21no—
167C2×D43—21no—
168C2×D43—41no—
169C2×D43—41no—
170C2×D43—41no—
171C2×D43—84no—
172C4×C43—21no—
173C4×C43—41no—
174C4×C43—41no—
175C4×C43C2×#4111yescharacteristic
176C4×C43H(5,𝔽2)11yescharacteristic
177Dic43—21no—
178Dic43—21no—
179Dic43—21no—
180Dic43—41no—
181Dic43—41no—
182Dic43—41no—
183#3322—431nomaximal, Sylow
184C2×C43—42no—
185C2×C43—41no—
186C2×C43—81no—
187C2×C43#54611yescharacteristic
188C2×C43#57511yescharacteristic
189C2×C43#57611yescharacteristic
190D43—41no—
191D43—81no—
192#553—431no—
193#546—431no—
194#488—431no—
195#485—431no—
196#480—431no—
197#478—431no—
198#469—431no—
199#468—431no—
200#463—431no—
201#449D4311yescharacteristic, complemented
202#447—431no—
203C4×D8—431no—
204#436—431no—
205#418—431no—
206#417—431no—
207C43#332211yescharacteristic, complemented, Sylow
208C2×#41C2×D4311yescharacteristic
209C22×D4—431no—
210C2×SD16C2×D4311yescharacteristic, complemented
211C2×D8—431no—
212C2×D8C2×D4311yescharacteristic
213C2×M16—431no—
214C2×M16—431no—
215#126—861no—
216#125—431no—
217#124—431no—
218#123—861no—
219#123—861no—
220C22⋊Q8—431no—
221#121—431no—
222#121—431no—
223#121—861no—
224#121—861no—
225#121C2×D4311yescharacteristic, complemented
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#106—431no—
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
248C22⋊C8—431no—
249C22⋊C8C2×D4311yescharacteristic, complemented
250C4×C8—431no—
251C24—861no—
252#41—22no—
253#41—41no—
254C2×Q8C22×D4311yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—431no—
258C2×D4—431no—
259C2×D4—861no—
260C2×D4—862no—
261C2×D4—861no—
262C2×D4—861no—
263C2×D4—1721no—
264C2×D4C22×D4311yescharacteristic
265C2×D4C22×D4311yescharacteristic
266C22×C4—21no—
267C22×C4—431no—
268C22×C4—861no—
269C22×C4—861no—
270C22×C4—861no—
271C22×C4C22×D4311yescharacteristic
272SD16—41no—
273D8—22no—
274D8—1721no—
275M16—1721no—
276M16—1721no—
277C2×C8—431no—
278C2×C8—431no—
279C2×C8C22×D4311yescharacteristic
280C2×C8C22×D4311yescharacteristic
281C4⋊C4—431no—
282C4⋊C4—431no—
283C4⋊C4—431no—
284C4⋊C4—431no—
285C4⋊C4—861no—
286C4⋊C4—861no—
287C4⋊C4—861no—
288C4⋊C4—861no—
289C4⋊C4C22×D4311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—431no—
292C22⋊C4—431no—
293C22⋊C4—861no—
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—21no—
305C23—431no—
306C23—861no—
307C23—3441no—
308C23—1722no—
309C23—1722no—
310C23D4×D4311yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—42no—
317D4—42no—
318D4—861no—
319D4—861no—
320D4—3441no—
321D4—3441no—
322D4—1721no—
323D4—1722no—
324D4#1062190012yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—431no—
331C2×C4—431no—
332C2×C4—431no—
333C2×C4—861no—
334C2×C4—861no—
335C2×C4—861no—
336C2×C4—861no—
337C2×C4—861no—
338C2×C4—3441no—
339C2×C4—3441no—
340C2×C4—3441no—
341C2×C4D4×D4311yescharacteristic
342C2×C4C23×D4311yescharacteristic
343C8—21no—
344C8—21no—
345C8—861no—
346C8—861no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—22no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—861no—
357C22—861no—
358C22—861no—
359C22—3444no—
360C22—1721no—
361C22—1721no—
362C22—1721no—
363C22C2×D4×D4311yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—861no—
368C4—861no—
369C4—861no—
370C4—1721no—
371C4—1721no—
372C4—1721no—
373C4C2×#1062190011yescharacteristic
374C4#1306337011yescharacteristic
375C2—41no—
376C2—42no—
377C2—81no—
378C2—3441no—
379C2—1721no—
380C2#1458353611yescharacteristic
381C2#1458369511yescharacteristic
382C2#1458370111yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#449C2
socleC22×C43C22×D4
hypercenter#449D43
hypocenterC43#3322
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #14583601C2semidirect
2. #14583537C2semidirect
3. #14583255C2semidirect
4. #14583239C2semidirect
5. #14583213C2semidirect
6. #14583197C2semidirect
7. #14583150C2semidirect
8. #14583142C2semidirect
9. #14583116C2semidirect
10. #14583031C2semidirect
11. D8×Dic43C2semidirect
12. #14582974C2semidirect
13. #14582902C2semidirect
14. #14582900C2semidirect
15. C43×#449C2semidirect
18. C2×#10621877C22semidirect
21. #13063316C22semidirect
33. D4×Dic43C22semidirect
36. C2×C4⋊Dic43C22semidirect
38. #13063259C22semidirect
39. #13063259C22semidirect
40. #13063256C22semidirect
41. Dic43⋊C8C22semidirect
42. #13063249C22semidirect
43. #13063249C22semidirect
48. #13063246C22semidirect
51. C8×Dic43C22semidirect
53. C2×SD16×C43C22semidirect
55. #121×C43C22semidirect
56. #103×C43C22semidirect
58. C22⋊C8×C43C22semidirect
201. #449D43semidirect
207. C43#3322semidirect
210. C2×SD16C2×D43semidirect
225. #121C2×D43semidirect
240. #103C2×D43semidirect
249. C22⋊C8C2×D43semidirect