Finite Group Databasebeta

← #19146447

Subgroups — #19146447

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#14583595C211yesmaximal, characteristic, complemented
2#14583545C211yesmaximal, characteristic, complemented
3#14583254C211yesmaximal, characteristic, complemented
4#14583235C211yesmaximal, characteristic, complemented
5#14583224C211yesmaximal, characteristic, complemented
6#14583200C211yesmaximal, characteristic, complemented
7#14583135C211yesmaximal, characteristic, complemented
8#14583128C211yesmaximal, characteristic, complemented
9#14583115C211yesmaximal, characteristic, complemented
10#14583046C211yesmaximal, characteristic, complemented
11#14583035C211yesmaximal, characteristic, complemented
12C4×D344C211yesmaximal, characteristic, complemented
13#14582896C211yesmaximal, characteristic, complemented
14C2×#13063247C211yesmaximal, characteristic, complemented
15C8×D4×C43C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C22×D172C2211yescharacteristic
18C2×#10621873C2211yescharacteristic, complemented
19C2×D344C2211yescharacteristic
20C2×D344C2211yescharacteristic
21#13063320—21no—
22#13063317C2211yescharacteristic, complemented
23#13063313C2211yescharacteristic
24#13063310—21no—
25#13063307—21no—
26#13063304C2211yescharacteristic
27#13063299C2211yescharacteristic
28#13063299C2211yescharacteristic
29#13063299C2211yescharacteristic, complemented
30#13063298—21no—
31#13063297—21no—
32#13063293—21no—
33C4×D172C2211yescharacteristic
34C4×D172C2211yescharacteristic, complemented
35(C22⋊D43)⋊C4—21no—
36#13063284C2211yescharacteristic, complemented
37C2×C4⋊Dic43C2211yescharacteristic
38C22⋊C4×D43—21no—
39#13063259C2211yescharacteristic, complemented
40#13063259C2211yescharacteristic, complemented
41#13063257C2211yescharacteristic, complemented
42#13063250C2211yescharacteristic, complemented
43#13063250C2211yescharacteristic, complemented
44#13063250C2211yescharacteristic, complemented
45#13063247C2211yescharacteristic
46#13063247C2211yescharacteristic
47#13063247C2211yescharacteristic
48#13063247C2211yescharacteristic
49#13063247C2211yescharacteristic
50#13063247C2211yescharacteristic
51#13063247C2211yescharacteristic, complemented
52C22×C8×C43C2211yescharacteristic
53C22×C8×C43C2211yescharacteristic, complemented
54C4×D4×C43C2211yescharacteristic
55C4⋊C8×C43C2211yescharacteristic, complemented
56C22⋊C8×C43C2211yescharacteristic
57C22⋊C8×C43C2211yescharacteristic, complemented
58C4×C8×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60C2×D4×C43D411yescharacteristic
61C22×C4×C43C2311yescharacteristic
62C22×C4×C43C2311yescharacteristic
63C2×C22⋊D43—21no—
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C22×Dic43—21no—
68#10621898—22no—
69#10621898—41no—
70C2×D172—21no—
71C2×D172—22no—
72C2×D172—41no—
73C2×D172C2311yescharacteristic
74C2×D172C2311yescharacteristic
75C2×D172C2311yescharacteristic
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C4×D43—21no—
79C2×Dic86C2311yescharacteristic
80C2×C8×C43—41no—
81C2×C8×C43—41no—
82C2×C8×C43C2311yescharacteristic
83C2×C8×C43C2311yescharacteristic
84C2×C8×C43C2311yescharacteristic
85C2×C8×C43C2311yescharacteristic
86C4⋊C4×C43D411yescharacteristic
87C22⋊C4×C43D411yescharacteristic
88C22⋊C4×C43D411yescharacteristic
89C42×C43C2311yescharacteristic
90C22⋊Dic43—21no—
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—
99C4⋊Dic43—21no—
100C4⋊Dic43C2311yescharacteristic
101C4⋊Dic43C2311yescharacteristic
102C4⋊Dic43C2311yescharacteristic
103C4⋊Dic43C2311yescharacteristic
104Dic43⋊C4—21no—
105Dic43⋊C4—21no—
106Dic43⋊C4—21no—
107C4×Dic43—21no—
108D344—22no—
109D344—41no—
110#10621873—41no—
111C23×C43C2×D411yescharacteristic
112C23×C43C2×D411yescharacteristic
113C22×D43—21no—
114C22×D43—21no—
115C22×D43—21no—
116C22×D43—42no—
117C22×D43—42no—
118C22×D43—81no—
119D4×C43—22no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
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×C43C2411yescharacteristic
129C22⋊D43—42no—
130C22⋊D43—42no—
131C22⋊D43—81no—
132C22⋊D43—81no—
133C2×Dic43—21no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—21no—
138C2×Dic43—81no—
139D172—21no—
140D172—21no—
141D172—21no—
142D172—21no—
143D172—21no—
144D172—42no—
145D172#4112yes—
146C4×D43—42no—
147C4×D43—81no—
148C4×D43—81no—
149Dic86—21no—
150Dic86—21no—
151C8×C43—21no—
152C8×C43—21no—
153C8×C43—21no—
154C8×C43—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43#13512yes—
161C22×C43C22×D411yescharacteristic
162C2×D43—22no—
163C2×D43—41no—
164C2×D43—41no—
165C2×D43—41no—
166C2×D43—41no—
167C2×D43—41no—
168C2×D43—41no—
169C2×D43—41no—
170C2×D43—41no—
171C2×D43—84no—
172C4×C43—21no—
173C4×C43—21no—
174C4×C43—21no—
175C4×C43—21no—
176C4×C43C2×#4111yescharacteristic
177C4×C43H(5,𝔽2)11yescharacteristic
178Dic43—41no—
179Dic43—41no—
180Dic43—41no—
181Dic43—41no—
182Dic43—41no—
183#3297—431nomaximal, Sylow
184C2×C43—22no—
185C2×C43—41no—
186C2×C43#54611yescharacteristic
187C2×C43C2×#13511yescharacteristic
188C2×C43#57611yescharacteristic
189D43—42no—
190D43—81no—
191D43—81no—
192#553—431no—
193#546—431no—
194#488—431no—
195#484—431no—
196#482—431no—
197#478—431no—
198#466—431no—
199#465—431no—
200#463—431no—
201#449—431no—
202#447—431no—
203C4×D8—431no—
204C8×D4D4311yescharacteristic, complemented
205#416—431no—
206C2×#102—431no—
207C43#329711yescharacteristic, complemented, Sylow
208C2×#41—431no—
209C22×D4—431no—
210C2×SD16—431no—
211C2×D8—431no—
212C2×D8—431no—
213C22×C8C2×D4311yescharacteristic
214C22×C8C2×D4311yescharacteristic, complemented
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—431no—
224#121—861no—
225#121—861no—
226#120—861no—
227C4×D4—431no—
228C4×D4—431no—
229C4×D4—861no—
230C4×D4C2×D4311yescharacteristic
231#117—431no—
232C2×C4⋊C4—431no—
233C2×C22⋊C4—861no—
234#107—431no—
235#107—431no—
236#106—431no—
237C4⋊C8C2×D4311yescharacteristic, complemented
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#102—431no—
247#102—431no—
248C22⋊C8C2×D4311yescharacteristic
249C22⋊C8C2×D4311yescharacteristic, complemented
250C4×C8C2×D4311yescharacteristic, complemented
251C24—861no—
252#41—862no—
253#41—1721no—
254C2×Q8—431no—
255C2×D4—431no—
256C2×D4—431no—
257C2×D4—431no—
258C2×D4—862no—
259C2×D4—861no—
260C2×D4—861no—
261C2×D4—861no—
262C2×D4—861no—
263C2×D4—861no—
264C2×D4—1721no—
265C2×D4D17211yescharacteristic
266C22×C4—861no—
267C22×C4—861no—
268C22×C4—861no—
269C22×C4—861no—
270C22×C4C22×D4311yescharacteristic
271C22×C4C22×D4311yescharacteristic
272SD16—1721no—
273D8—862no—
274D8—1721no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8C22×D4311yescharacteristic
278C2×C8C22×D4311yescharacteristic
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⋊C4D17211yescharacteristic
290C22⋊C4—861no—
291C22⋊C4—861no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C22⋊C4—861no—
295C22⋊C4—861no—
296C22⋊C4—861no—
297C22⋊C4—861no—
298C22⋊C4—861no—
299C22⋊C4D17211yescharacteristic
300C22⋊C4D17211yescharacteristic
301C42—861no—
302C42C22×D4311yescharacteristic
303C23—861no—
304C23—861no—
305C23—861no—
306C23—3441no—
307C23—1722no—
308C23—1722no—
309C23C2×D17211yescharacteristic
310C23C2×D17211yescharacteristic
311Q8—861no—
312Q8—861no—
313D4—22no—
314D4—432no—
315D4—861no—
316D4—861no—
317D4—861no—
318D4—861no—
319D4—861no—
320D4—3441no—
321D4—3441no—
322D4—1722no—
323D4—1722no—
324D4—1722no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—861no—
330C2×C4—861no—
331C2×C4—861no—
332C2×C4—861no—
333C2×C4—861no—
334C2×C4—3441no—
335C2×C4—3441no—
336C2×C4—3441no—
337C2×C4—1722no—
338C2×C4C2×D17211yescharacteristic
339C2×C4C2×D17211yescharacteristic
340C2×C4C2×D17211yescharacteristic
341C2×C4C2×D17211yescharacteristic
342C2×C4C23×D4311yescharacteristic
343C8—21no—
344C8—21no—
345C8—21no—
346C8—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—862no—
353C22—3444no—
354C22—1721no—
355C22—1721no—
356C22—1721no—
357C22—1721no—
358C22—1721no—
359C22—1721no—
360C22—1721no—
361C22—1721no—
362C22#1306334712yes—
363C22C22×D17211yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—1721no—
369C4—1721no—
370C4—1721no—
371C4—1721no—
372C4—1721no—
373C4#41×D4311yescharacteristic
374C4#1306337011yescharacteristic
375C2—22no—
376C2—41no—
377C2—3441no—
378C2—3441no—
379C2—1722no—
380C2#1458354411yescharacteristic
381C2C2×#1306334711yescharacteristic
382C2#1458370411yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC8×D4×C43C2
socleC22×C43C22×D4
hypercenterC8×D4D43
hypocenterC43#3297
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #14583595C2semidirect
2. #14583545C2semidirect
3. #14583254C2semidirect
4. #14583235C2semidirect
5. #14583224C2semidirect
6. #14583200C2semidirect
7. #14583135C2semidirect
8. #14583128C2semidirect
9. #14583115C2semidirect
10. #14583046C2semidirect
11. #14583035C2semidirect
12. C4×D344C2semidirect
13. #14582896C2semidirect
14. C2×#13063247C2semidirect
15. C8×D4×C43C2semidirect
18. C2×#10621873C22semidirect
22. #13063317C22semidirect
29. #13063299C22semidirect
34. C4×D172C22semidirect
36. #13063284C22semidirect
39. #13063259C22semidirect
40. #13063259C22semidirect
41. #13063257C22semidirect
42. #13063250C22semidirect
43. #13063250C22semidirect
44. #13063250C22semidirect
51. #13063247C22semidirect
53. C22×C8×C43C22semidirect
55. C4⋊C8×C43C22semidirect
57. C22⋊C8×C43C22semidirect
58. C4×C8×C43C22semidirect
204. C8×D4D43semidirect
207. C43#3297semidirect
214. C22×C8C2×D43semidirect
237. C4⋊C8C2×D43semidirect
249. C22⋊C8C2×D43semidirect
250. C4×C8C2×D43semidirect