Finite Group Databasebeta

← #19147684

Subgroups — #19147684

Order 5504.

380 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583634C211yesmaximal, characteristic, complemented
2#14583632C211yesmaximal, characteristic, complemented
3#14583288C211yesmaximal, characteristic, complemented
4#14583285C211yesmaximal, characteristic, complemented
5#14583280C211yesmaximal, characteristic, complemented
6#14583124C211yesmaximal, characteristic, complemented
7#14583121C211yesmaximal, characteristic, complemented
8#14583117C211yesmaximal, characteristic, complemented
9#14583113C211yesmaximal, characteristic, complemented
10#14583094C211yesmaximal, characteristic, complemented
11#14583093C211yesmaximal, characteristic, complemented
12#14583027C211yesmaximal, characteristic, complemented
13#14582998C211yesmaximal, characteristic, complemented
14#14582981C211yesmaximal, characteristic, complemented
15C43×#440C211yesmaximal, characteristic, complemented
16C2×#10621885C2211yescharacteristic
17C2×#10621873C2211yescharacteristic
18C2×#10621873C2211yescharacteristic
19C2×#10621884C2211yescharacteristic
20C2×D344C2211yescharacteristic
21C2×D344C2211yescharacteristic
22C2×#10621882C2211yescharacteristic
23C2×#10621882C2211yescharacteristic
24#13063322C2211yescharacteristic
25#13063321C2211yescharacteristic
26#13063314C2211yescharacteristic
27#13063314C2211yescharacteristic
28#13063313—21no—
29#13063313C2211yescharacteristic
30#13063312C2211yescharacteristic
31#13063311—21no—
32#13063310—21no—
33#13063310—21no—
34#13063308—21no—
35#13063307—21no—
36C4×Dic86C2211yescharacteristic
37#13063290C2211yescharacteristic
38C4×D172—21no—
39#13063287C2211yescharacteristic
40#13063287C2211yescharacteristic
41#13063287C2211yescharacteristic
42C4×C22⋊D43—21no—
43C4⋊(C43⋊C8)C2211yescharacteristic
44Dic43⋊C8C2211yescharacteristic
45Dic43⋊C8C2211yescharacteristic
46#13063248C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49#13063245C2211yescharacteristic
50#13063235C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C2×SD16×C43C2211yescharacteristic
53C4×Q8×C43C2211yescharacteristic
54C4×D4×C43C2211yescharacteristic
55#107×C43C2211yescharacteristic
56#103×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58#97×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60C2×D4×C43C2311yescharacteristic
61C22×C4×C43—21no—
62C2×C22⋊D43—21no—
63C2×C22⋊D43—21no—
64C2×D172—21no—
65C2×D172—21no—
66C2×D172C2311yescharacteristic
67C2×D172C2311yescharacteristic
68C2×D172C2311yescharacteristic
69C2×C4×D43—21no—
70C2×C4×D43—21no—
71C2×C4×D43—21no—
72C2×Dic86D411yescharacteristic
73C2×Dic86C2311yescharacteristic
74SD16×C43—22no—
75C2×C8×C43C2311yescharacteristic
76C2×C8×C43C2311yescharacteristic
77C4⋊C4×C43—21no—
78C4⋊C4×C43C2311yescharacteristic
79C4⋊C4×C43C2311yescharacteristic
80C22⋊C4×C43—21no—
81C42×C43—21no—
82C42×C43C2311yescharacteristic
83C22⋊Dic43—21no—
84C22⋊Dic43—21no—
85#10621885—41no—
86#10621884—41no—
87#10621882—41no—
88#10621882—41no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
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)⋊C4—21no—
97(C2×D43)⋊C4—21no—
98C4⋊Dic43D411yescharacteristic
99Dic43⋊C4—21no—
100Dic43⋊C4D411yescharacteristic
101Dic43⋊C4D411yescharacteristic
102C4×Dic43—21no—
103C4×Dic43C2311yescharacteristic
104C4×Dic43C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107D344—22no—
108D344—41no—
109#10621873—22no—
110#10621873—41no—
111C23×C43—21no—
112C22×D43—21no—
113C22×D43—21no—
114C22×D43—21no—
115Q8×C43—21no—
116Q8×C43—21no—
117D4×C43—21no—
118D4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—81no—
123C2×C4×C43C2×D411yescharacteristic
124C2×C4×C43C2×D411yescharacteristic
125C2×C4×C43C2411yescharacteristic
126C22⋊D43—42no—
127C22⋊D43—81no—
128C2×Dic43—21no—
129C2×Dic43C2×D411yescharacteristic
130C2×Dic43C2×D411yescharacteristic
131C2×Dic43C2×D411yescharacteristic
132C2×Dic43C2×D411yescharacteristic
133D172—21no—
134D172—21no—
135D172—21no—
136D172—21no—
137D172—21no—
138D172—21no—
139D172—42no—
140D172—81no—
141C4×D43—81no—
142C4×D43—81no—
143C4×D43—81no—
144Dic86—21no—
145Dic86—21no—
146Dic86—41no—
147C8×C43—21no—
148C8×C43#4112yes—
149C43⋊C8—21no—
150C43⋊C8—21no—
151C22×C43—41no—
152C22×C43—41no—
153C22×C43—41no—
154C22×C43C22×D411yescharacteristic
155C2×D43—41no—
156C2×D43—41no—
157C2×D43—41no—
158C2×D43—41no—
159C2×D43—41no—
160C2×D43—41no—
161C2×D43—41no—
162C2×D43—41no—
163C2×D43—41no—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43—41no—
167C4×C43—41no—
168C4×C43—41no—
169C4×C43C2×#4111yescharacteristic
170C4×C43H(5,𝔽2)11yescharacteristic
171Dic43—21no—
172Dic43—21no—
173Dic43—21no—
174Dic43—21no—
175Dic43—41no—
176#3403—431nomaximal, Sylow
177C2×C43—81no—
178C2×C43#55011yescharacteristic
179C2×C43#57511yescharacteristic
180C2×C43#57611yescharacteristic
181D43—81no—
182D43—81no—
183D43—81no—
184#559—431no—
185#559—431no—
186#496—431no—
187#496—431no—
188#495—431no—
189#464—431no—
190#464—431no—
191#463—431no—
192#463—431no—
193#459—431no—
194#459—431no—
195#446—431no—
196#440—431no—
197#440D4311yescharacteristic, complemented
198C4×D8—431no—
199C43#340311yescharacteristic, complemented, Sylow
200C2×Q16—431no—
201C2×SD16—431no—
202C2×SD16—431no—
203C2×SD16—431no—
204C2×SD16C2×D4311yescharacteristic
205C2×D8—431no—
206C2×D8—431no—
207C2×D8—431no—
208C2×D8—431no—
209#127—431no—
210#127—431no—
211#124—431no—
212#124—431no—
213#124—431no—
214#124—431no—
215#124—861no—
216#124—861no—
217#123—861no—
218#123—861no—
219#123—861no—
220#123—861no—
221C4×Q8—431no—
222C4×Q8—431no—
223C4×Q8C2×D4311yescharacteristic
224C4×D4—431no—
225C4×D4—431no—
226C4×D4—431no—
227C4×D4—861no—
228C4×D4—861no—
229C4×D4C2×D4311yescharacteristic
230#107C2×D4311yescharacteristic
231C4⋊C8—431no—
232C4⋊C8—431no—
233C4⋊C8—431no—
234#103—431no—
235#103C2×D4311yescharacteristic
236#102—431no—
237#102—431no—
238#102—431no—
239#102C2×D4311yescharacteristic
240#97—431no—
241#97C2×D4311yescharacteristic
242C4×C8—431no—
243C2×Q8—431no—
244C2×Q8—431no—
245C2×Q8C22×D4311yescharacteristic
246C2×D4—431no—
247C2×D4—431no—
248C2×D4—431no—
249C2×D4—861no—
250C2×D4—861no—
251C2×D4—861no—
252C2×D4—861no—
253C2×D4C22×D4311yescharacteristic
254C22×C4—21no—
255C22×C4—861no—
256C22×C4—861no—
257C22×C4—861no—
258Q16—1721no—
259SD16—22no—
260SD16—862no—
261SD16—1721no—
262SD16—1721no—
263D8—862no—
264D8—1721no—
265D8—1721no—
266D8—1721no—
267C2×C8—431no—
268C2×C8—431no—
269C2×C8C22×D4311yescharacteristic
270C2×C8C22×D4311yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—431no—
273C4⋊C4—431no—
274C4⋊C4—431no—
275C4⋊C4—861no—
276C4⋊C4C22×D4311yescharacteristic
277C4⋊C4C22×D4311yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—861no—
280C22⋊C4—861no—
281C22⋊C4—861no—
282C22⋊C4—861no—
283C22⋊C4—861no—
284C22⋊C4—861no—
285C22⋊C4—861no—
286C22⋊C4—861no—
287C22⋊C4—861no—
288C22⋊C4—861no—
289C22⋊C4—861no—
290C42—21no—
291C42—431no—
292C42—431no—
293C42—861no—
294C42C22×D4311yescharacteristic
295C23—21no—
296C23—861no—
297C23—861no—
298C23—861no—
299Q8—21no—
300Q8—21no—
301Q8—861no—
302Q8—861no—
303Q8—1721no—
304D4—21no—
305D4—21no—
306D4—861no—
307D4—861no—
308D4—861no—
309D4—861no—
310D4—861no—
311D4—861no—
312D4—3441no—
313D4—3441no—
314D4—1722no—
315D4—1722no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—431no—
321C2×C4—431no—
322C2×C4—431no—
323C2×C4—431no—
324C2×C4—861no—
325C2×C4—3441no—
326C2×C4—3441no—
327C2×C4—3441no—
328C2×C4D4×D4311yescharacteristic
329C2×C4D4×D4311yescharacteristic
330C2×C4C23×D4311yescharacteristic
331C8—21no—
332C8—861no—
333C8—861no—
334C8#1062189812yes—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—1721no—
339C22—1721no—
340C22—1721no—
341C22—1721no—
342C22—1721no—
343C22—1721no—
344C22—1721no—
345C22—1721no—
346C22—1721no—
347C22C2×D4×D4311yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—861no—
354C4—861no—
355C4—861no—
356C4—861no—
357C4—1721no—
358C4C2×#1062189811yescharacteristic
359C4#1306337111yescharacteristic
360C2—81no—
361C2—3441no—
362C2—3441no—
363C2—3441no—
364C2#1458357011yescharacteristic
365C2#1458369811yescharacteristic
366C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#440C2
socleC22×C43C22×D4
hypercenter#440D43
hypocenterC43#3403
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #14583634C2semidirect
2. #14583632C2semidirect
3. #14583288C2semidirect
4. #14583285C2semidirect
5. #14583280C2semidirect
6. #14583124C2semidirect
7. #14583121C2semidirect
8. #14583117C2semidirect
9. #14583113C2semidirect
10. #14583094C2semidirect
11. #14583093C2semidirect
12. #14583027C2semidirect
13. #14582998C2semidirect
14. #14582981C2semidirect
15. C43×#440C2semidirect
197. #440D43semidirect
199. C43#3403semidirect