Finite Group Databasebeta

← #19146598

Subgroups — #19146598

Order 5504.

404 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583602C211yesmaximal, characteristic, complemented
2#14583571C211yesmaximal, characteristic, complemented
3#14583265C211yesmaximal, characteristic, complemented
4#14583225C211yesmaximal, characteristic, complemented
5#14583214C211yesmaximal, characteristic, complemented
6#14583153C211yesmaximal, characteristic, complemented
7#14583136C211yesmaximal, characteristic, complemented
8#14583095C211yesmaximal, characteristic, complemented
9#14583047C211yesmaximal, characteristic, complemented
10#14583047C211yesmaximal, characteristic, complemented
11#14582997C211yesmaximal, characteristic, complemented
12#14582969C211yesmaximal, characteristic, complemented
13#14582899C211yesmaximal, characteristic, complemented
14#14582894C211yesmaximal, characteristic, complemented
15C43×#479C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×#10621902C2211yescharacteristic
18C2×#10621884C2211yescharacteristic
19C2×D344C2211yescharacteristic
20C2×D344C2211yescharacteristic
21C2×#10621872C2211yescharacteristic
22C2×C8×D43C2211yescharacteristic
23#13063322—21no—
24#13063322C2211yescharacteristic
25#13063320—21no—
26#13063310—21no—
27#13063300—21no—
28#13063300—21no—
29#13063300—21no—
30#13063300C2211yescharacteristic
31#13063300C2211yescharacteristic
32#13063300C2211yescharacteristic
33#13063300C2211yescharacteristic
34C4×D172—21no—
35C4×D172C2211yescharacteristic
36C4×D172C2211yescharacteristic
37#13063287—21no—
38#13063283C2211yescharacteristic
39C4⋊C4×D43C2211yescharacteristic
40#13063258C2211yescharacteristic
41#13063249C2211yescharacteristic
42#13063247C2211yescharacteristic
43#13063247C2211yescharacteristic
44#13063245C2211yescharacteristic
45#13063245C2211yescharacteristic
46#13063245C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51#13063236C2211yescharacteristic
52#125×C43C2211yescharacteristic
53C4×Q8×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic
55#106×C43C2211yescharacteristic
56C4⋊C8×C43C2211yescharacteristic
57#103×C43C2211yescharacteristic
58#103×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60#10621902—22no—
61#10621902—22no—
62#10621902—41no—
63#10621902—41no—
64C2×D172—21no—
65C2×D172—21no—
66C2×D172—21no—
67C2×D172—21no—
68C2×D172—21no—
69C2×D172—21no—
70C2×D172—21no—
71C2×D172—21no—
72C2×D172D411yescharacteristic
73C2×D172C2311yescharacteristic
74C2×D172C2311yescharacteristic
75C2×D172C2311yescharacteristic
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C4×D43—21no—
79C2×C4×D43—21no—
80C2×C4×D43C2311yescharacteristic
81C2×C4×D43C2311yescharacteristic
82C2×C8×C43C2311yescharacteristic
83C2×C8×C43C2311yescharacteristic
84C4⋊C4×C43—21no—
85C4⋊C4×C43—21no—
86C4⋊C4×C43—21no—
87C4⋊C4×C43C2311yescharacteristic
88C4⋊C4×C43C2311yescharacteristic
89C4⋊C4×C43C2311yescharacteristic
90C42×C43—21no—
91C42×C43C2311yescharacteristic
92#10621884—22no—
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⋊Dic43D411yescharacteristic
102C4⋊Dic43C2311yescharacteristic
103Dic43⋊C4—21no—
104C4×Dic43—21no—
105C2×C43⋊C8C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107D344—41no—
108D344—41no—
109#10621872—41no—
110C8×D43—41no—
111C22×D43—21no—
112C22×D43—21no—
113C22×D43—21no—
114C22×D43C2×D411yescharacteristic
115C22×D43C2×D411yescharacteristic
116Q8×C43—21no—
117Q8×C43#4112yes—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43C2×D411yescharacteristic
123C2×C4×C43C2×D411yescharacteristic
124C2×C4×C43C2411yescharacteristic
125C2×Dic43—21no—
126C2×Dic43C2×D411yescharacteristic
127C2×Dic43C2×D411yescharacteristic
128D172—21no—
129D172—21no—
130D172—21no—
131D172—21no—
132D172—21no—
133D172—21no—
134D172—41no—
135D172—42no—
136D172—42no—
137D172—42no—
138D172—42no—
139D172—81no—
140D172—81no—
141D172—81no—
142D172—81no—
143C4×D43—21no—
144C4×D43—21no—
145C4×D43—21no—
146C4×D43—21no—
147C4×D43—42no—
148C4×D43—42no—
149C4×D43—81no—
150C4×D43—81no—
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—21no—
162C2×D43—41no—
163C2×D43—41no—
164C2×D43—41no—
165C2×D43—41no—
166C2×D43—41no—
167C2×D43—41no—
168C2×D43—41no—
169C2×D43—41no—
170C2×D43—41no—
171C4×C43—22no—
172C4×C43—21no—
173C4×C43—21no—
174C4×C43—41no—
175C4×C43—41no—
176C4×C43—41no—
177C4×C43C2×#4111yescharacteristic
178C4×C43H(5,𝔽2)11yescharacteristic
179Dic43—21no—
180Dic43—21no—
181Dic43—41no—
182#3309—431nomaximal, Sylow
183C2×C43#54611yescharacteristic
184C2×C43#57511yescharacteristic
185C2×C43#57611yescharacteristic
186D43—41no—
187D43—41no—
188D43—81no—
189D43—81no—
190D43—81no—
191#553—431no—
192#550—431no—
193#490—431no—
194#482—431no—
195#480—431no—
196#479D4311yescharacteristic, complemented
197#469—431no—
198#466—431no—
199#459—431no—
200#449—431no—
201#449—431no—
202#440—431no—
203#435—431no—
204#417—431no—
205#416—431no—
206C43#330911yescharacteristic, complemented, Sylow
207C2×#41—431no—
208C2×#41—431no—
209C2×SD16—431no—
210C2×D8—431no—
211C2×D8—431no—
212C2×M16—431no—
213C22×C8—431no—
214#127—431no—
215#127—861no—
216#126—861no—
217#125C2×D4311yescharacteristic
218#123—861no—
219#121—431no—
220#121—431no—
221#121—431no—
222#121—431no—
223#121—861no—
224#121—861no—
225#121—861no—
226C4×Q8C2×D4311yescharacteristic
227C4×D4—431no—
228C4×D4—431no—
229C4×D4—861no—
230C4×D4—861no—
231#117—431no—
232C2×C4⋊C4—431no—
233#107—431no—
234#107C2×D4311yescharacteristic
235#106C2×D4311yescharacteristic
236C4⋊C8C2×D4311yescharacteristic
237#103—431no—
238#103C2×D4311yescharacteristic
239#103C2×D4311yescharacteristic
240#102—431no—
241#102—431no—
242#102—431no—
243#102—431no—
244#102—431no—
245#102—431no—
246#102—431no—
247C22⋊C8—431no—
248C22⋊C8—431no—
249#97—431no—
250#41—862no—
251#41—862no—
252#41—1721no—
253#41—1721no—
254C2×Q8C22×D4311yescharacteristic
255C2×D4—431no—
256C2×D4—431no—
257C2×D4—431no—
258C2×D4—431no—
259C2×D4—861no—
260C2×D4—861no—
261C2×D4—861no—
262C2×D4—861no—
263C2×D4—861no—
264C2×D4—861no—
265C2×D4—861no—
266C2×D4—861no—
267C22×C4—431no—
268C22×C4—431no—
269C22×C4—861no—
270C22×C4—861no—
271C22×C4—861no—
272C22×C4—861no—
273SD16—862no—
274D8—1721no—
275D8—1721no—
276M16—1721no—
277C2×C8—431no—
278C2×C8—431no—
279C2×C8—1721no—
280C2×C8C22×D4311yescharacteristic
281C2×C8C22×D4311yescharacteristic
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—431no—
286C4⋊C4—431no—
287C4⋊C4—861no—
288C4⋊C4C22×D4311yescharacteristic
289C4⋊C4C22×D4311yescharacteristic
290C4⋊C4C22×D4311yescharacteristic
291C22⋊C4—431no—
292C22⋊C4—431no—
293C22⋊C4—861no—
294C22⋊C4—861no—
295C22⋊C4—861no—
296C22⋊C4—861no—
297C22⋊C4—861no—
298C22⋊C4—861no—
299C42—21no—
300C42—861no—
301C42C22×D4311yescharacteristic
302C23—431no—
303C23—431no—
304C23—861no—
305C23—861no—
306C23—861no—
307Q8—21no—
308Q8#1062190212yes—
309D4—861no—
310D4—861no—
311D4—861no—
312D4—861no—
313D4—861no—
314D4—861no—
315D4—3441no—
316D4—3441no—
317D4—3441no—
318D4—3441no—
319D4—1721no—
320D4—1722no—
321D4—1722no—
322D4—1722no—
323D4—1722no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—431no—
329C2×C4—431no—
330C2×C4—861no—
331C2×C4—861no—
332C2×C4—861no—
333C2×C4—861no—
334C2×C4—861no—
335C2×C4—3441no—
336C2×C4—3441no—
337C2×C4—1722no—
338C2×C4—1722no—
339C2×C4D4×D4311yescharacteristic
340C2×C4D4×D4311yescharacteristic
341C2×C4C23×D4311yescharacteristic
342C8—21no—
343C8—21no—
344C8—861no—
345C8—861no—
346C22—861no—
347C22—861no—
348C22—861no—
349C22—861no—
350C22—861no—
351C22—861no—
352C22—1721no—
353C22—1721no—
354C22—1721no—
355C22—1721no—
356C22—1721no—
357C22—1721no—
358C22—1721no—
359C22—1721no—
360C22—1721no—
361C22C2×D4×D4311yescharacteristic
362C4—21no—
363C4—21no—
364C4—22no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—861no—
369C4—861no—
370C4—1721no—
371C4C2×#1062190211yescharacteristic
372C4#1306337111yescharacteristic
373C2—3441no—
374C2—3441no—
375C2—3441no—
376C2—1721no—
377C2—1721no—
378C2#1458354011yescharacteristic
379C2#1458369811yescharacteristic
380C2#1458370111yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#479C2
socleC22×C43C22×D4
hypercenter#479D43
hypocenterC43#3309
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #14583602C2semidirect
2. #14583571C2semidirect
3. #14583265C2semidirect
4. #14583225C2semidirect
5. #14583214C2semidirect
6. #14583153C2semidirect
7. #14583136C2semidirect
8. #14583095C2semidirect
9. #14583047C2semidirect
10. #14583047C2semidirect
11. #14582997C2semidirect
12. #14582969C2semidirect
13. #14582899C2semidirect
14. #14582894C2semidirect
15. C43×#479C2semidirect
196. #479D43semidirect
206. C43#3309semidirect