Finite Group Databasebeta

← #19146678

Subgroups — #19146678

Order 5504.

410 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583606C211yesmaximal, characteristic, complemented
2#14583545C211yesmaximal, characteristic
3#14583259C211yesmaximal, characteristic, complemented
4#14583235C211yesmaximal, characteristic, complemented
5#14583213C211yesmaximal, characteristic, complemented
6#14583180C211yesmaximal, characteristic, complemented
7#14583145C211yesmaximal, characteristic, complemented
8#14583140C211yesmaximal, characteristic, complemented
9#14583122C211yesmaximal, characteristic, complemented
10#14583063C211yesmaximal, characteristic, complemented
11#14583052C211yesmaximal, characteristic, complemented
12#14583001C211yesmaximal, characteristic, complemented
13#14582901C211yesmaximal, characteristic, complemented
14C2×#13063247C211yesmaximal, characteristic, complemented
15C43×#435C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C22×D172C2211yescharacteristic
18C2×Dic172C2211yescharacteristic, complemented
19C2×#10621873C2211yescharacteristic
20C2×#10621873C2211yescharacteristic
21#13063325C2211yescharacteristic, complemented
22#13063316—21no—
23#13063313C2211yescharacteristic
24#13063310—21no—
25#13063304C2211yescharacteristic
26#13063304C2211yescharacteristic
27#13063304C2211yescharacteristic, complemented
28#13063302—21no—
29#13063302—21no—
30#13063299C2211yescharacteristic
31#13063298—21no—
32#13063293—21no—
33C4×Dic86C2211yescharacteristic, complemented
34C4×D172C2211yescharacteristic
35D4×Dic43—21no—
36C2×C4⋊Dic43C2211yescharacteristic
37C2×C4⋊Dic43C2211yescharacteristic, complemented
38C22⋊C4×D43—21no—
39#13063259C2211yescharacteristic, complemented
40#13063259C2211yescharacteristic, complemented
41#13063259C2211yescharacteristic, complemented
42#13063250C2211yescharacteristic, complemented
43#13063250C2211yescharacteristic, complemented
44#13063250C2211yescharacteristic, complemented
45#13063250C2211yescharacteristic, complemented
46#13063247C2211yescharacteristic
47#13063247C2211yescharacteristic
48#13063247C2211yescharacteristic
49#13063247C2211yescharacteristic
50#13063247C2211yescharacteristic
51#13063247C2211yescharacteristic
52C2×M16×C43C2211yescharacteristic, complemented
53C22×C8×C43C2211yescharacteristic
54C4×D4×C43C2211yescharacteristic
55C4⋊C8×C43C2211yescharacteristic, complemented
56C22⋊C8×C43C2211yescharacteristic
57C22⋊C8×C43C2211yescharacteristic, complemented
58#97×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60C2×D4×C43D411yescharacteristic
61C22×C4×C43C2311yescharacteristic
62C22×C4×C43C2311yescharacteristic
63C2×C22⋊D43—21no—
64C2×C22⋊D43—21no—
65C22×Dic43—21no—
66C22×Dic43—21no—
67#10621898—22no—
68#10621898—41no—
69C2×D172—21no—
70C2×D172—22no—
71C2×D172—41no—
72C2×D172C2311yescharacteristic
73C2×D172C2311yescharacteristic
74C2×C4×D43—21no—
75C2×C4×D43—21no—
76C2×Dic86—21no—
77C2×Dic86C2311yescharacteristic
78C2×Dic86C2311yescharacteristic
79M16×C43—41no—
80C2×C8×C43—41no—
81C2×C8×C43C2311yescharacteristic
82C2×C8×C43C2311yescharacteristic
83C2×C8×C43C2311yescharacteristic
84C2×C8×C43C2311yescharacteristic
85C4⋊C4×C43D411yescharacteristic
86C22⋊C4×C43D411yescharacteristic
87C22⋊C4×C43D411yescharacteristic
88C42×C43C2311yescharacteristic
89C22⋊Dic43—21no—
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—
96C4⋊Dic43—21no—
97C4⋊Dic43—21no—
98C4⋊Dic43—21no—
99C4⋊Dic43C2311yescharacteristic
100C4⋊Dic43C2311yescharacteristic
101C4⋊Dic43C2311yescharacteristic
102C4⋊Dic43C2311yescharacteristic
103Dic43⋊C4—21no—
104Dic43⋊C4—21no—
105Dic43⋊C4—21no—
106Dic43⋊C4—21no—
107C4×Dic43—21no—
108Dic172—41no—
109#10621873—22no—
110#10621873—41no—
111C23×C43C2×D411yescharacteristic
112C23×C43C2×D411yescharacteristic
113C22×D43—21no—
114C22×D43—21no—
115C22×D43—42no—
116C22×D43—42no—
117C22×D43—81no—
118D4×C43—22no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43C2×D411yescharacteristic
124C2×C4×C43C2×D411yescharacteristic
125C2×C4×C43C2×D411yescharacteristic
126C2×C4×C43C2×D411yescharacteristic
127C2×C4×C43C2411yescharacteristic
128C22⋊D43—42no—
129C22⋊D43—81no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—81no—
137C2×Dic43—81no—
138D172—21no—
139D172—21no—
140D172—21no—
141D172—42no—
142D172#4112yes—
143C4×D43—42no—
144C4×D43—81no—
145Dic86—21no—
146Dic86—21no—
147Dic86—21no—
148Dic86—21no—
149Dic86—81no—
150C8×C43—21no—
151C8×C43—21no—
152C8×C43—21no—
153C8×C43—21no—
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—21no—
159C22×C43#13712yes—
160C22×C43C22×D411yescharacteristic
161C2×D43—22no—
162C2×D43—41no—
163C2×D43—41no—
164C2×D43—41no—
165C2×D43—41no—
166C2×D43—41no—
167C2×D43—84no—
168C4×C43—21no—
169C4×C43—21no—
170C4×C43—21no—
171C4×C43—21no—
172C4×C43C2×#4111yescharacteristic
173C4×C43H(5,𝔽2)11yescharacteristic
174Dic43—41no—
175Dic43—41no—
176Dic43—41no—
177Dic43—41no—
178Dic43—41no—
179Dic43—41no—
180#3314—431nomaximal, Sylow
181C2×C43—22no—
182C2×C43—41no—
183C2×C43#54611yescharacteristic
184C2×C43C2×#13711yescharacteristic
185C2×C43#57611yescharacteristic
186D43—42no—
187D43—81no—
188#554—431no—
189#546—431no—
190#489—431no—
191#484—431no—
192#480—431no—
193#474—431no—
194#468—431no—
195#467—431no—
196#464—431no—
197#452—431no—
198#450—431no—
199#440—431no—
200#435D4311yescharacteristic, complemented
201#417—431no—
202C2×#102—431no—
203C43#331411yescharacteristic, complemented, Sylow
204C2×#41—431no—
205C22×D4—431no—
206C2×Q16—431no—
207C2×SD16—431no—
208C2×SD16—431no—
209C2×M16C2×D4311yescharacteristic, complemented
210C22×C8C2×D4311yescharacteristic
211C4⋊Q8—431no—
212#125—861no—
213#124—431no—
214#123—861no—
215C22⋊Q8—431no—
216C22⋊Q8—431no—
217C22⋊Q8—431no—
218C22⋊Q8—861no—
219C22⋊Q8—861no—
220#121—431no—
221#121—861no—
222#120—861no—
223C4×Q8—431no—
224C4×D4—431no—
225C4×D4—861no—
226C4×D4C2×D4311yescharacteristic
227C2×C4⋊C4—431no—
228C2×C4⋊C4—431no—
229C2×C22⋊C4—861no—
230#107—431no—
231#107—431no—
232#107—431no—
233C4⋊C8C2×D4311yescharacteristic, complemented
234#103—431no—
235#103—431no—
236#103—431no—
237#103—431no—
238#102—431no—
239#102—431no—
240#102—431no—
241#102—431no—
242#102—431no—
243#102—431no—
244C22⋊C8C2×D4311yescharacteristic
245C22⋊C8C2×D4311yescharacteristic, complemented
246#97C2×D4311yescharacteristic, complemented
247C24—861no—
248#41—862no—
249#41—1721no—
250C2×Q8—431no—
251C2×Q8—431no—
252C2×Q8—861no—
253C2×D4—431no—
254C2×D4—431no—
255C2×D4—862no—
256C2×D4—861no—
257C2×D4—861no—
258C2×D4—861no—
259C2×D4—1721no—
260C2×D4D17211yescharacteristic
261C22×C4—861no—
262C22×C4—861no—
263C22×C4—861no—
264C22×C4—861no—
265C22×C4C22×D4311yescharacteristic
266C22×C4C22×D4311yescharacteristic
267Q16—1721no—
268SD16—862no—
269SD16—1721no—
270M16—41no—
271C2×C8—41no—
272C2×C8C22×D4311yescharacteristic
273C2×C8C22×D4311yescharacteristic
274C2×C8C22×D4311yescharacteristic
275C2×C8C22×D4311yescharacteristic
276C4⋊C4—431no—
277C4⋊C4—431no—
278C4⋊C4—431no—
279C4⋊C4—431no—
280C4⋊C4—861no—
281C4⋊C4—861no—
282C4⋊C4—861no—
283C4⋊C4—861no—
284C4⋊C4—861no—
285C4⋊C4—861no—
286C4⋊C4—861no—
287C4⋊C4D17211yescharacteristic
288C22⋊C4—861no—
289C22⋊C4—861no—
290C22⋊C4—861no—
291C22⋊C4—861no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C22⋊C4—861no—
295C22⋊C4D17211yescharacteristic
296C22⋊C4D17211yescharacteristic
297C42—861no—
298C42C22×D4311yescharacteristic
299C23—861no—
300C23—861no—
301C23—3441no—
302C23—1722no—
303C23—1722no—
304C23C2×D17211yescharacteristic
305C23C2×D17211yescharacteristic
306Q8—861no—
307Q8—861no—
308Q8—861no—
309Q8—861no—
310Q8—3441no—
311D4—22no—
312D4—432no—
313D4—861no—
314D4—861no—
315D4—861no—
316D4—3441no—
317D4—1722no—
318D4—1722no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—861no—
324C2×C4—861no—
325C2×C4—861no—
326C2×C4—861no—
327C2×C4—861no—
328C2×C4—861no—
329C2×C4—3441no—
330C2×C4—3441no—
331C2×C4—3441no—
332C2×C4—1722no—
333C2×C4C2×D17211yescharacteristic
334C2×C4C2×D17211yescharacteristic
335C2×C4C2×D17211yescharacteristic
336C2×C4C2×D17211yescharacteristic
337C2×C4C23×D4311yescharacteristic
338C8—21no—
339C8—21no—
340C8—21no—
341C8—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—862no—
348C22—3444no—
349C22—1721no—
350C22—1721no—
351C22—1721no—
352C22—1721no—
353C22—1721no—
354C22#1306335812yes—
355C22C22×D17211yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—1721no—
361C4—1721no—
362C4—1721no—
363C4—1721no—
364C4—1721no—
365C4—1721no—
366C4#41×D4311yescharacteristic
367C4#1306337011yescharacteristic
368C2—22no—
369C2—41no—
370C2—3441no—
371C2—1722no—
372C2#1458354411yescharacteristic
373C2C2×#1306335811yescharacteristic
374C2#1458370411yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#435C2
socleC22×C43C22×D4
hypercenter#435D43
hypocenterC43#3314
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #14583606C2semidirect
3. #14583259C2semidirect
4. #14583235C2semidirect
5. #14583213C2semidirect
6. #14583180C2semidirect
7. #14583145C2semidirect
8. #14583140C2semidirect
9. #14583122C2semidirect
10. #14583063C2semidirect
11. #14583052C2semidirect
12. #14583001C2semidirect
13. #14582901C2semidirect
14. C2×#13063247C2semidirect
15. C43×#435C2semidirect
18. C2×Dic172C22semidirect
21. #13063325C22semidirect
27. #13063304C22semidirect
33. C4×Dic86C22semidirect
37. C2×C4⋊Dic43C22semidirect
39. #13063259C22semidirect
40. #13063259C22semidirect
41. #13063259C22semidirect
42. #13063250C22semidirect
43. #13063250C22semidirect
44. #13063250C22semidirect
45. #13063250C22semidirect
52. C2×M16×C43C22semidirect
55. C4⋊C8×C43C22semidirect
57. C22⋊C8×C43C22semidirect
58. #97×C43C22semidirect
200. #435D43semidirect
203. C43#3314semidirect
209. C2×M16C2×D43semidirect
233. C4⋊C8C2×D43semidirect
245. C22⋊C8C2×D43semidirect
246. #97C2×D43semidirect