Finite Group Databasebeta

← #19145572

Subgroups — #19145572

Order 5504.

400 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583448C211yesmaximal, characteristic, complemented
2#14583434C211yesmaximal, characteristic, complemented
3#14583283C211yesmaximal, characteristic, complemented
4#14583281C211yesmaximal, characteristic, complemented
5#14583256C211yesmaximal, characteristic, complemented
6#14583108C211yesmaximal, characteristic, complemented
7#14583103C211yesmaximal, characteristic, complemented
8#14583098C211yesmaximal, characteristic, complemented
9#14583093C211yesmaximal, characteristic, complemented
10#14583064C211yesmaximal, characteristic, complemented
11#14583062C211yesmaximal, characteristic, complemented
12#14583047C211yesmaximal, characteristic, complemented
13#14583045C211yesmaximal, characteristic, complemented
14#14582950C211yesmaximal, characteristic, complemented
15C43×#488C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×#10621900C2211yescharacteristic
18C2×Dic172C2211yescharacteristic
19C2×#10621885C2211yescharacteristic
20C2×#10621873C2211yescharacteristic
21C2×#10621873C2211yescharacteristic
22C2×#10621883C2211yescharacteristic
23C2×#10621884C2211yescharacteristic
24C2×D344C2211yescharacteristic
25C2×#10621882C2211yescharacteristic
26#13063323C2211yescharacteristic
27#13063321C2211yescharacteristic
28#13063320—21no—
29#13063313C2211yescharacteristic
30#13063313C2211yescharacteristic
31#13063310—21no—
32#13063305C2211yescharacteristic
33#13063300C2211yescharacteristic
34#13063298—21no—
35#13063298—21no—
36#13063290C2211yescharacteristic
37#13063287—21no—
38#13063287C2211yescharacteristic
39(C22⋊D43)⋊C4—21no—
40(C22⋊D43)⋊C4—21no—
41#13063283—21no—
42C42×D43C2211yescharacteristic
43Dic43⋊C8C2211yescharacteristic
44Dic43⋊C8C2211yescharacteristic
45#13063248C2211yescharacteristic
46#13063248C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51C4×C43⋊C8C2211yescharacteristic
52#125×C43C2211yescharacteristic
53#124×C43C2211yescharacteristic
54#103×C43C2211yescharacteristic
55#103×C43C2211yescharacteristic
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58C4×C8×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60C2×D4×C43C2311yescharacteristic
61C2×C22⋊D43—21no—
62C2×C22⋊D43—21no—
63C2×C22⋊D43—21no—
64C22×Dic43—21no—
65#10621902—41no—
66#10621902—41no—
67#10621900—41no—
68#10621900—41no—
69C2×D172—21no—
70C2×D172—21no—
71C2×D172C2311yescharacteristic
72C2×D172C2311yescharacteristic
73C2×C4×D43—21no—
74C2×C4×D43—21no—
75C2×C4×D43D411yescharacteristic
76C2×C4×D43D411yescharacteristic
77C2×C4×D43C2311yescharacteristic
78C2×Dic86C2311yescharacteristic
79C2×Dic86C2311yescharacteristic
80C2×C8×C43C2311yescharacteristic
81C2×C8×C43C2311yescharacteristic
82C4⋊C4×C43—21no—
83C4⋊C4×C43—21no—
84C4⋊C4×C43C2311yescharacteristic
85C4⋊C4×C43C2311yescharacteristic
86C22⋊C4×C43—21no—
87C22⋊C4×C43—21no—
88C42×C43C2311yescharacteristic
89#10621885—41no—
90#10621884—41no—
91#10621883—41no—
92#10621882—41no—
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)⋊C4—21no—
100C4⋊Dic43—21no—
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104C4×Dic43—21no—
105C4×Dic43D411yescharacteristic
106C4×Dic43D411yescharacteristic
107C4×Dic43C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110Dic172—41no—
111D344—41no—
112#10621873—41no—
113#10621873—41no—
114C23×C43—21no—
115C22×D43—21no—
116C22×D43—21no—
117C22×D43C2×D411yescharacteristic
118Q8×C43—21no—
119Q8×C43—21no—
120D4×C43—21no—
121D4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43C2×D411yescharacteristic
126C2×C4×C43C2×D411yescharacteristic
127C2×C4×C43C2411yescharacteristic
128C22⋊D43—42no—
129C22⋊D43—42no—
130C22⋊D43—42no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—42no—
134C2×Dic43C2×D411yescharacteristic
135C2×Dic43C2×D411yescharacteristic
136C2×Dic43C2×D411yescharacteristic
137D172—21no—
138D172—21no—
139D172—21no—
140D172—21no—
141D172—42no—
142D172—42no—
143C4×D43—21no—
144C4×D43—21no—
145C4×D43—22no—
146C4×D43—41no—
147C4×D43—42no—
148C4×D43—42no—
149Dic86—21no—
150Dic86—21no—
151Dic86—21no—
152Dic86—21no—
153C8×C43—21no—
154C8×C43—21no—
155C43⋊C8—21no—
156C43⋊C8—21no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43C22×D411yescharacteristic
161C2×D43—21no—
162C2×D43—21no—
163C2×D43—21no—
164C2×D43—41no—
165C2×D43—41no—
166C2×D43—41no—
167C2×D43—41no—
168C2×D43—41no—
169C2×D43—41no—
170C4×C43—21no—
171C4×C43—21no—
172C4×C43—41no—
173C4×C43—41no—
174C4×C43—41no—
175C4×C43H(5,𝔽2)11yescharacteristic
176C4×C43H(5,𝔽2)11yescharacteristic
177Dic43—21no—
178Dic43—21no—
179Dic43—41no—
180Dic43—41no—
181Dic43#13512yes—
182#3212—431nomaximal, Sylow
183C2×C43—81no—
184C2×C43#53511yescharacteristic
185C2×C43C2×#13511yescharacteristic
186C2×C43#57511yescharacteristic
187D43—41no—
188D43—81no—
189D43—81no—
190#532—431no—
191#529—431no—
192#495—431no—
193#495—431no—
194#488—431no—
195#488D4311yescharacteristic, complemented
196#462—431no—
197#461—431no—
198#460—431no—
199#459—431no—
200#452—431no—
201#452—431no—
202#449—431no—
203#449—431no—
204#431—431no—
205C43#321211yescharacteristic, complemented, Sylow
206C2×#41—431no—
207C2×#41—431no—
208C2×Q16—431no—
209C2×Q16—431no—
210C2×SD16—431no—
211C2×SD16—431no—
212C2×SD16—431no—
213C2×SD16—431no—
214C2×D8—431no—
215C2×D8—431no—
216C4⋊Q8—431no—
217#127—431no—
218#126—861no—
219#125C2×D4311yescharacteristic
220#124—431no—
221#124—431no—
222#124C2×D4311yescharacteristic
223#123—861no—
224C22⋊Q8—431no—
225#121—431no—
226#121—861no—
227#121—861no—
228C4×Q8—431no—
229C4×D4—431no—
230C4×D4—861no—
231C4×D4—861no—
232C4×D4—861no—
233#117—861no—
234C2×C42—431no—
235C4⋊C8—431no—
236C4⋊C8—431no—
237#103—431no—
238#103—431no—
239#103C2×D4311yescharacteristic
240#103C2×D4311yescharacteristic
241#102—431no—
242#102—431no—
243#102C2×D4311yescharacteristic
244#102C2×D4311yescharacteristic
245C22⋊C8—431no—
246C22⋊C8—431no—
247C4×C8—431no—
248C4×C8C2×D4311yescharacteristic
249#41—1721no—
250#41—1721no—
251#41—1721no—
252#41—1721no—
253C2×Q8—431no—
254C2×Q8—431no—
255C2×Q8C22×D4311yescharacteristic
256C2×D4—431no—
257C2×D4—431no—
258C2×D4—861no—
259C2×D4—861no—
260C2×D4—861no—
261C2×D4—861no—
262C2×D4—861no—
263C2×D4C22×D4311yescharacteristic
264C22×C4—431no—
265C22×C4—431no—
266C22×C4—431no—
267C22×C4—861no—
268C22×C4—861no—
269C22×C4—861no—
270Q16—1721no—
271Q16—1721no—
272SD16—1721no—
273SD16—1721no—
274SD16—1721no—
275SD16—1721no—
276D8—1721no—
277D8—1721no—
278C2×C8—431no—
279C2×C8—431no—
280C2×C8C22×D4311yescharacteristic
281C2×C8C22×D4311yescharacteristic
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—861no—
285C4⋊C4—861no—
286C4⋊C4—861no—
287C4⋊C4—861no—
288C4⋊C4C22×D4311yescharacteristic
289C4⋊C4C22×D4311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C22⋊C4—861no—
295C22⋊C4—861no—
296C22⋊C4—861no—
297C22⋊C4—861no—
298C22⋊C4—861no—
299C42—431no—
300C42—431no—
301C42—431no—
302C42—861no—
303C42C22×D4311yescharacteristic
304C23—21no—
305C23—431no—
306C23—861no—
307C23—861no—
308Q8—21no—
309Q8—21no—
310Q8—861no—
311Q8—861no—
312Q8—861no—
313Q8—861no—
314D4—21no—
315D4—21no—
316D4—861no—
317D4—861no—
318D4—861no—
319D4—861no—
320D4—1722no—
321D4—1722no—
322D4—1722no—
323D4—1722no—
324D4—1722no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—431no—
329C2×C4—431no—
330C2×C4—431no—
331C2×C4—862no—
332C2×C4—861no—
333C2×C4—861no—
334C2×C4—861no—
335C2×C4—861no—
336C2×C4—1721no—
337C2×C4—1722no—
338C2×C4—1722no—
339C2×C4—1722no—
340C2×C4D4×D4311yescharacteristic
341C2×C4D4×D4311yescharacteristic
342C2×C4C23×D4311yescharacteristic
343C8—21no—
344C8—21no—
345C8—861no—
346C8—861no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—861no—
351C22—861no—
352C22—861no—
353C22—1721no—
354C22—1721no—
355C22—1721no—
356C22—1721no—
357C22—1721no—
358C22—1721no—
359C22C2×D4×D4311yescharacteristic
360C4—21no—
361C4—21no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—432no—
366C4—861no—
367C4—861no—
368C4—1721no—
369C4—1721no—
370C4#1306337111yescharacteristic
371C4#1306337111yescharacteristic
372C2—81no—
373C2—3441no—
374C2—3441no—
375C2—1721no—
376C2#1458346711yescharacteristic
377C2#135×D4311yescharacteristic
378C2#1458369611yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#488C2
socleC22×C43C22×D4
hypercenter#488D43
hypocenterC43#3212
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #14583448C2semidirect
2. #14583434C2semidirect
3. #14583283C2semidirect
4. #14583281C2semidirect
5. #14583256C2semidirect
6. #14583108C2semidirect
7. #14583103C2semidirect
8. #14583098C2semidirect
9. #14583093C2semidirect
10. #14583064C2semidirect
11. #14583062C2semidirect
12. #14583047C2semidirect
13. #14583045C2semidirect
14. #14582950C2semidirect
15. C43×#488C2semidirect
195. #488D43semidirect
205. C43#3212semidirect