Finite Group Databasebeta

← #19147680

Subgroups — #19147680

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#14583635C211yesmaximal, characteristic, complemented
2#14583631C211yesmaximal, characteristic, complemented
3#14583287C211yesmaximal, characteristic, complemented
4#14583280C211yesmaximal, characteristic, complemented
5#14583119C211yesmaximal, characteristic, complemented
6#14583118C211yesmaximal, characteristic, complemented
7#14583116C211yesmaximal, characteristic, complemented
8#14583112C211yesmaximal, characteristic, complemented
9#14583092C211yesmaximal, characteristic, complemented
10#14583091C211yesmaximal, characteristic, complemented
11#14583027C211yesmaximal, characteristic, complemented
12#14583001C211yesmaximal, characteristic, complemented
13#14583000C211yesmaximal, characteristic, complemented
14D8×Dic43C211yesmaximal, characteristic, complemented
15C43×#496C211yesmaximal, characteristic, complemented
16C2×#10621885C2211yescharacteristic
17C2×#10621873C2211yescharacteristic
18C2×#10621883C2211yescharacteristic
19C2×#10621882C2211yescharacteristic
20C2×#10621882C2211yescharacteristic
21#13063321C2211yescharacteristic
22#13063314C2211yescharacteristic
23#13063312—21no—
24#13063312C2211yescharacteristic
25#13063312C2211yescharacteristic
26#13063311—21no—
27#13063309—21no—
28#13063307—21no—
29#13063306—21no—
30#13063306—21no—
31Q8×Dic43C2211yescharacteristic
32C4×Dic86C2211yescharacteristic
33C4×Dic86C2211yescharacteristic
34C4×D172C2211yescharacteristic
35D4×Dic43—21no—
36D4×Dic43C2211yescharacteristic
37D4×Dic43C2211yescharacteristic
38D4×Dic43C2211yescharacteristic
39(C22⋊D43)⋊C4—21no—
40#13063259C2211yescharacteristic
41C4⋊(C43⋊C8)C2211yescharacteristic
42Dic43⋊C8C2211yescharacteristic
43Dic43⋊C8C2211yescharacteristic
44#13063250C2211yescharacteristic
45#13063249C2211yescharacteristic
46#13063247C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063246C2211yescharacteristic
49#13063246C2211yescharacteristic
50#13063235C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C2×SD16×C43C2211yescharacteristic
53C2×SD16×C43C2211yescharacteristic
54C2×D8×C43C2211yescharacteristic
55C2×D8×C43C2211yescharacteristic
56#127×C43C2211yescharacteristic
57#124×C43C2211yescharacteristic
58#97×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60C2×D4×C43—21no—
61C2×D4×C43—21no—
62C2×D4×C43C2311yescharacteristic
63C2×D4×C43C2311yescharacteristic
64C2×D4×C43C2311yescharacteristic
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C22×Dic43—21no—
68C22×Dic43—21no—
69C22×Dic43—21no—
70C2×D172C2311yescharacteristic
71C2×C4×D43—21no—
72C2×Dic86D411yescharacteristic
73C2×Dic86C2311yescharacteristic
74SD16×C43—22no—
75SD16×C43—41no—
76D8×C43—22no—
77D8×C43—41no—
78C2×C8×C43C2311yescharacteristic
79C2×C8×C43C2311yescharacteristic
80C22⋊C4×C43—21no—
81C22⋊C4×C43—21no—
82C42×C43C2311yescharacteristic
83C22⋊Dic43—21no—
84C22⋊Dic43—21no—
85C22⋊Dic43—21no—
86C22⋊Dic43—21no—
87C22⋊Dic43—21no—
88C22⋊Dic43—21no—
89C22⋊Dic43—21no—
90#10621885—41no—
91#10621883—41no—
92#10621882—41no—
93#10621882—41no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4—21no—
97C4⋊Dic43—21no—
98C4⋊Dic43D411yescharacteristic
99C4⋊Dic43C2311yescharacteristic
100C4⋊Dic43C2311yescharacteristic
101Dic43⋊C4—21no—
102Dic43⋊C4D411yescharacteristic
103Dic43⋊C4D411yescharacteristic
104C4×Dic43—21no—
105C4×Dic43—21no—
106C4×Dic43C2311yescharacteristic
107C4×Dic43C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110#10621873—22no—
111C23×C43—21no—
112C23×C43—21no—
113C23×C43—21no—
114C22×D43—21no—
115Q8×C43—21no—
116Q8×C43—21no—
117D4×C43—21no—
118D4×C43—21no—
119D4×C43—21no—
120D4×C43—21no—
121D4×C43—21no—
122D4×C43—21no—
123D4×C43—42no—
124D4×C43—81no—
125C2×C4×C43—21no—
126C2×C4×C43C2×D411yescharacteristic
127C2×C4×C43C2×D411yescharacteristic
128C2×C4×C43C2411yescharacteristic
129C22⋊D43—42no—
130C22⋊D43—81no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—81no—
135C2×Dic43—81no—
136C2×Dic43—81no—
137C2×Dic43C2×D411yescharacteristic
138C2×Dic43C2×D411yescharacteristic
139C2×Dic43C2×D411yescharacteristic
140C2×Dic43C2×D411yescharacteristic
141D172—21no—
142D172—21no—
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×C43—41no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43C22×D411yescharacteristic
161C2×D43—41no—
162C2×D43—41no—
163C2×D43—41no—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43—41no—
167C4×C43C2×#4111yescharacteristic
168C4×C43H(5,𝔽2)11yescharacteristic
169Dic43—21no—
170Dic43—21no—
171Dic43—21no—
172Dic43—21no—
173Dic43—41no—
174Dic43—41no—
175Dic43—41no—
176#3403—431nomaximal, Sylow
177C2×C43—81no—
178C2×C43—81no—
179C2×C43—81no—
180C2×C43#55011yescharacteristic
181C2×C43#57511yescharacteristic
182C2×C43#57611yescharacteristic
183D43—81no—
184#559—431no—
185#559—431no—
186#496—431no—
187#496D4311yescharacteristic, complemented
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#440—431no—
198C4×D8—431no—
199C43#340311yescharacteristic, complemented, Sylow
200C2×Q16—431no—
201C2×SD16—431no—
202C2×SD16—431no—
203C2×SD16C2×D4311yescharacteristic
204C2×SD16C2×D4311yescharacteristic
205C2×D8—431no—
206C2×D8—431no—
207C2×D8C2×D4311yescharacteristic
208C2×D8C2×D4311yescharacteristic
209#127—431no—
210#127C2×D4311yescharacteristic
211#124—431no—
212#124—431no—
213#124—431no—
214#124—861no—
215#124—861no—
216#124C2×D4311yescharacteristic
217#123—861no—
218#123—861no—
219#123—861no—
220#123—861no—
221C4×Q8—431no—
222C4×Q8—431no—
223C4×Q8—431no—
224C4×D4—431no—
225C4×D4—431no—
226C4×D4—431no—
227C4×D4—431no—
228C4×D4—861no—
229C4×D4—861no—
230#107—431no—
231C4⋊C8—431no—
232C4⋊C8—431no—
233C4⋊C8—431no—
234#103—431no—
235#103—431no—
236#102—431no—
237#102—431no—
238#102—431no—
239#102—431no—
240#97—431no—
241#97C2×D4311yescharacteristic
242C4×C8—431no—
243C2×Q8—431no—
244C2×Q8—431no—
245C2×Q8C22×D4311yescharacteristic
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—431no—
249C2×D4—861no—
250C2×D4—861no—
251C2×D4C22×D4311yescharacteristic
252C2×D4C22×D4311yescharacteristic
253C2×D4C22×D4311yescharacteristic
254C22×C4—861no—
255C22×C4—861no—
256C22×C4—861no—
257C22×C4—861no—
258Q16—1721no—
259SD16—22no—
260SD16—41no—
261SD16—862no—
262SD16—1721no—
263D8—22no—
264D8—41no—
265D8—1721no—
266D8—1721no—
267C2×C8—431no—
268C2×C8—431no—
269C2×C8C22×D4311yescharacteristic
270C2×C8C22×D4311yescharacteristic
271C4⋊C4—431no—
272C4⋊C4—431no—
273C4⋊C4—431no—
274C4⋊C4—431no—
275C4⋊C4—431no—
276C4⋊C4—861no—
277C4⋊C4—861no—
278C22⋊C4—21no—
279C22⋊C4—21no—
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—431no—
291C42—431no—
292C42—861no—
293C42—861no—
294C42C22×D4311yescharacteristic
295C23—21no—
296C23—21no—
297C23—21no—
298C23—861no—
299Q8—21no—
300Q8—21no—
301Q8—861no—
302Q8—861no—
303Q8—1721no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—21no—
310D4—42no—
311D4—81no—
312D4—861no—
313D4—861no—
314D4—3441no—
315D4—1722no—
316C2×C4—21no—
317C2×C4—431no—
318C2×C4—431no—
319C2×C4—431no—
320C2×C4—431no—
321C2×C4—861no—
322C2×C4—861no—
323C2×C4—861no—
324C2×C4—3441no—
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#1062190012yes—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—1721no—
345C22—1721no—
346C22—1721no—
347C22C2×D4×D4311yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—861no—
352C4—861no—
353C4—861no—
354C4—861no—
355C4—1721no—
356C4—1721no—
357C4—1721no—
358C4C2×#1062190011yescharacteristic
359C4#1306337011yescharacteristic
360C2—81no—
361C2—81no—
362C2—81no—
363C2—3441no—
364C2#1458356911yescharacteristic
365C2#1458369511yescharacteristic
366C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#496C2
socleC22×C43C22×D4
hypercenter#496D43
hypocenterC43#3403
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #14583635C2semidirect
2. #14583631C2semidirect
3. #14583287C2semidirect
4. #14583280C2semidirect
5. #14583119C2semidirect
6. #14583118C2semidirect
7. #14583116C2semidirect
8. #14583112C2semidirect
9. #14583092C2semidirect
10. #14583091C2semidirect
11. #14583027C2semidirect
12. #14583001C2semidirect
13. #14583000C2semidirect
14. D8×Dic43C2semidirect
15. C43×#496C2semidirect
187. #496D43semidirect
199. C43#3403semidirect