Finite Group Databasebeta

← #19146583

Subgroups — #19146583

Order 5504.

420 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#14583561C211yesmaximal, characteristic, complemented
2#14583552C211yesmaximal, characteristic, complemented
3#14583261C211yesmaximal, characteristic, complemented
4#14583236C211yesmaximal, characteristic, complemented
5#14583214C211yesmaximal, characteristic, complemented
6#14583146C211yesmaximal, characteristic, complemented
7#14583136C211yesmaximal, characteristic, complemented
8#14583115C211yesmaximal, characteristic, complemented
9#14583047C211yesmaximal, characteristic, complemented
10#14583039C211yesmaximal, characteristic, complemented
11#14582997C211yesmaximal, characteristic, complemented
12#14582969C211yesmaximal, characteristic, complemented
13#14582899C211yesmaximal, characteristic, complemented
14#103×D43C211yesmaximal, characteristic, complemented
15C43×#477C211yesmaximal, characteristic, complemented
16C2×#10621902—21no—
17C2×#10621902C2211yescharacteristic
18C2×Q8×D43C2211yescharacteristic
19C2×#10621873C2211yescharacteristic
20C2×#10621884C2211yescharacteristic
21C2×D344C2211yescharacteristic
22C2×#10621872C2211yescharacteristic
23C2×C8×D43C2211yescharacteristic
24#13063313—21no—
25#13063313C2211yescharacteristic
26#13063310—21no—
27#13063310—21no—
28#13063305—21no—
29#13063305C2211yescharacteristic
30#13063301—21no—
31#13063300—21no—
32#13063300C2211yescharacteristic
33#13063300C2211yescharacteristic
34#13063300C2211yescharacteristic
35C4×D172—21no—
36C4×D172C2211yescharacteristic
37C4×D172C2211yescharacteristic
38C4⋊C4×D43C2211yescharacteristic
39C4⋊C4×D43C2211yescharacteristic
40#13063258C2211yescharacteristic
41#13063250C2211yescharacteristic
42#13063249C2211yescharacteristic
43#13063248C2211yescharacteristic
44#13063248C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063245C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51#13063236C2211yescharacteristic
52C4⋊Q8×C43C2211yescharacteristic
53C4×Q8×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic
55#107×C43C2211yescharacteristic
56C4⋊C8×C43C2211yescharacteristic
57#103×C43C2211yescharacteristic
58#103×C43C2211yescharacteristic
59C2×Q8×C43—21no—
60C2×Q8×C43C2311yescharacteristic
61#10621902—22no—
62#10621902—41no—
63#10621902—44no—
64Q8×D43—22no—
65Q8×D43—41no—
66C2×D172—21no—
67C2×D172—21no—
68C2×D172—21no—
69C2×D172—21no—
70C2×D172D411yescharacteristic
71C2×D172C2311yescharacteristic
72C2×D172C2311yescharacteristic
73C2×C4×D43—21no—
74C2×C4×D43—21no—
75C2×C4×D43—21no—
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C4×D43C2311yescharacteristic
79C2×C4×D43C2311yescharacteristic
80C2×Dic86—21no—
81C2×Dic86C2311yescharacteristic
82C2×C8×C43C2311yescharacteristic
83C2×C8×C43C2311yescharacteristic
84C4⋊C4×C43—21no—
85C4⋊C4×C43—21no—
86C4⋊C4×C43C2311yescharacteristic
87C4⋊C4×C43C2311yescharacteristic
88C4⋊C4×C43C2311yescharacteristic
89C42×C43—21no—
90C42×C43C2311yescharacteristic
91#10621884—22no—
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—
99(C2×D43)⋊C4D411yescharacteristic
100(C2×D43)⋊C4D411yescharacteristic
101C4⋊Dic43—21no—
102C4⋊Dic43D411yescharacteristic
103C4⋊Dic43C2311yescharacteristic
104Dic43⋊C4—21no—
105Dic43⋊C4—21no—
106C2×C43⋊C8C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108D344—41no—
109#10621873—41no—
110#10621872—41no—
111C8×D43—41no—
112C22×D43—21no—
113C22×D43—21no—
114C22×D43C2×D411yescharacteristic
115C22×D43C2×D411yescharacteristic
116Q8×C43—21no—
117Q8×C43—42no—
118Q8×C43#4112yescomplemented
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×C43C2411yescharacteristic
126C2×Dic43—21no—
127C2×Dic43—21no—
128C2×Dic43C2×D411yescharacteristic
129C2×Dic43C2×D411yescharacteristic
130D172—22no—
131D172—21no—
132D172—21no—
133D172—21no—
134D172—21no—
135D172—42no—
136D172—42no—
137D172—42no—
138D172—42no—
139C4×D43—21no—
140C4×D43—21no—
141C4×D43—21no—
142C4×D43—21no—
143C4×D43—42no—
144C4×D43—42no—
145C4×D43—42no—
146C4×D43—42no—
147C4×D43—42no—
148Dic86—21no—
149Dic86—21no—
150Dic86—42no—
151C8×C43—21no—
152C8×C43—21no—
153C43⋊C8—21no—
154C43⋊C8—21no—
155C22×C43C22×D411yescharacteristic
156C2×D43—21no—
157C2×D43—21no—
158C2×D43—21no—
159C2×D43—21no—
160C2×D43—21no—
161C2×D43—41no—
162C2×D43—41no—
163C2×D43—41no—
164C2×D43—41no—
165C2×D43—41no—
166C2×D43—41no—
167C2×D43AGL(1,ℤ/8)12yes—
168C4×C43—22no—
169C4×C43—21no—
170C4×C43—21no—
171C4×C43—41no—
172C4×C43—41no—
173C4×C43—41no—
174C4×C43C2×#4111yescharacteristic
175C4×C43H(5,𝔽2)11yescharacteristic
176Dic43—21no—
177Dic43—21no—
178Dic43—41no—
179Dic43—41no—
180#3308—431nomaximal, Sylow
181C2×C43#54611yescharacteristic
182C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
183C2×C43#57811yescharacteristic
184D43—22no—
185D43—41no—
186D43—81no—
187D43—81no—
188#548—431no—
189#547—431no—
190#489—431no—
191#484—431no—
192#480—431no—
193#477D4311yescharacteristic, complemented
194#468—431no—
195#466—431no—
196#463—431no—
197#449—431no—
198#448—431no—
199#440—431no—
200#435—431no—
201#417—431no—
202C2×#103—431no—
203C43#330811yescharacteristic, complemented, Sylow
204C2×#41—431no—
205C2×#41—861no—
206C22×Q8—431no—
207C2×SD16—431no—
208C2×SD16—431no—
209C2×D8—431no—
210C2×M16—431no—
211C22×C8—431no—
212C4⋊Q8C2×D4311yescharacteristic
213#124—431no—
214#124—861no—
215#123—861no—
216#123—861no—
217C22⋊Q8—431no—
218C22⋊Q8—861no—
219C22⋊Q8—861no—
220#121—431no—
221#121—431no—
222#121—431no—
223#121—861no—
224C4×Q8C2×D4311yescharacteristic
225C4×D4—431no—
226C4×D4—431no—
227C4×D4—861no—
228C2×C4⋊C4—431no—
229C2×C4⋊C4—431no—
230#107—431no—
231#107C2×D4311yescharacteristic
232#107C2×D4311yescharacteristic
233C4⋊C8C2×D4311yescharacteristic
234#103—431no—
235#103—431no—
236#103—431no—
237#103—431no—
238#103C2×D4311yescharacteristic
239#103C2×D4311yescharacteristic
240#102—431no—
241#102—431no—
242#102—431no—
243#102—431no—
244C22⋊C8—431no—
245C22⋊C8—431no—
246#97—431no—
247#41—862no—
248#41—1721no—
249#41—1724no—
250C2×Q8—21no—
251C2×Q8—431no—
252C2×Q8—861no—
253C2×Q8—862no—
254C2×Q8—1721no—
255C2×Q8C22×D4311yescharacteristic
256C2×D4—431no—
257C2×D4—431no—
258C2×D4—431no—
259C2×D4—861no—
260C2×D4—861no—
261C2×D4—861no—
262C2×D4—861no—
263C22×C4—431no—
264C22×C4—431no—
265C22×C4—861no—
266C22×C4—861no—
267C22×C4—861no—
268C22×C4—861no—
269C22×C4—861no—
270SD16—862no—
271SD16—1721no—
272D8—1721no—
273M16—1721no—
274C2×C8—431no—
275C2×C8—431no—
276C2×C8—1721no—
277C2×C8C22×D4311yescharacteristic
278C2×C8C22×D4311yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—431no—
282C4⋊C4—431no—
283C4⋊C4—861no—
284C4⋊C4—861no—
285C4⋊C4—861no—
286C4⋊C4C22×D4311yescharacteristic
287C4⋊C4C22×D4311yescharacteristic
288C4⋊C4C22×D4311yescharacteristic
289C22⋊C4—431no—
290C22⋊C4—431no—
291C22⋊C4—861no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C22⋊C4—861no—
295C22⋊C4—861no—
296C22⋊C4—861no—
297C22⋊C4—861no—
298C42—21no—
299C42C22×D4311yescharacteristic
300C23—431no—
301C23—431no—
302C23—861no—
303C23—861no—
304Q8—21no—
305Q8—42no—
306Q8—861no—
307Q8—861no—
308Q8—1722no—
309Q8#1062190212yescomplemented
310D4—862no—
311D4—861no—
312D4—861no—
313D4—861no—
314D4—861no—
315D4—1722no—
316D4—1722no—
317D4—1722no—
318D4—1722no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—431no—
324C2×C4—431no—
325C2×C4—861no—
326C2×C4—861no—
327C2×C4—861no—
328C2×C4—861no—
329C2×C4—861no—
330C2×C4—861no—
331C2×C4—1722no—
332C2×C4—1722no—
333C2×C4—1722no—
334C2×C4—1722no—
335C2×C4—1722no—
336C2×C4D4×D4311yescharacteristic
337C2×C4D4×D4311yescharacteristic
338C2×C4C23×D4311yescharacteristic
339C8—21no—
340C8—21no—
341C8—861no—
342C8—861no—
343C22—432no—
344C22—861no—
345C22—861no—
346C22—861no—
347C22—861no—
348C22—861no—
349C22—1721no—
350C22—1721no—
351C22—1721no—
352C22—1721no—
353C22—1721no—
354C22—1721no—
355C22C2×D4×D4311yescharacteristic
356C4—21no—
357C4—21no—
358C4—22no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—861no—
363C4—861no—
364C4—1721no—
365C4—1721no—
366C4C2×#1062190211yescharacteristic
367C4#1306337111yescharacteristic
368C2—862no—
369C2—3441no—
370C2—3441no—
371C2—1721no—
372C2#1458354011yescharacteristic
373C2AGL(1,ℤ/8)×D4311yescharacteristic
374C2#1458371211yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#477C2
socleC22×C43C22×D4
hypercenter#477D43
hypocenterC43#3308
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
1. #14583561C2semidirect
2. #14583552C2semidirect
3. #14583261C2semidirect
4. #14583236C2semidirect
5. #14583214C2semidirect
6. #14583146C2semidirect
7. #14583136C2semidirect
8. #14583115C2semidirect
9. #14583047C2semidirect
10. #14583039C2semidirect
11. #14582997C2semidirect
12. #14582969C2semidirect
13. #14582899C2semidirect
14. #103×D43C2semidirect
15. C43×#477C2semidirect
118. Q8×C43#41semidirect
193. #477D43semidirect
203. C43#3308semidirect
309. Q8#10621902semidirect