Finite Group Databasebeta

← #19145508

Subgroups — #19145508

Order 5504.

402 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583480C211yesmaximal, characteristic, complemented
2#14583478C211yesmaximal, characteristic, complemented
3#14583231C211yesmaximal, characteristic, complemented
4#14583229C211yesmaximal, characteristic, complemented
5#14583219C211yesmaximal, characteristic, complemented
6#14583158C211yesmaximal, characteristic, complemented
7#14583151C211yesmaximal, characteristic, complemented
8#14583129C211yesmaximal, characteristic, complemented
9#14583127C211yesmaximal, characteristic, complemented
10#14583063C211yesmaximal, characteristic, complemented
11#14583062C211yesmaximal, characteristic, complemented
12#14583045C211yesmaximal, characteristic, complemented
13#14583042C211yesmaximal, characteristic, complemented
14#14582864C211yesmaximal, characteristic, complemented
15C43×#481C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×#10621898C2211yescharacteristic
18C2×#10621900C2211yescharacteristic
19C2×Dic172C2211yescharacteristic
20C2×#10621873C2211yescharacteristic
21C2×#10621883C2211yescharacteristic
22C2×#10621882C2211yescharacteristic
23C2×#10621872C2211yescharacteristic
24C2×C8×D43C2211yescharacteristic
25#13063305—21no—
26#13063305C2211yescharacteristic
27#13063305C2211yescharacteristic
28#13063305C2211yescharacteristic
29#13063304C2211yescharacteristic
30#13063302—21no—
31#13063300—21no—
32#13063300C2211yescharacteristic
33#13063300C2211yescharacteristic
34#13063299—21no—
35#13063299—21no—
36#13063298—21no—
37#13063297—21no—
38#13063296—21no—
39#13063296C2211yescharacteristic
40C4⋊C4×D43C2211yescharacteristic
41#13063256C2211yescharacteristic
42#13063256C2211yescharacteristic
43#13063250C2211yescharacteristic
44#13063248C2211yescharacteristic
45#13063248C2211yescharacteristic
46#13063248C2211yescharacteristic
47#13063247C2211yescharacteristic
48#13063245C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51(C2×D43)⋊C8C2211yescharacteristic
52#121×C43C2211yescharacteristic
53C2×C4⋊C4×C43C2211yescharacteristic
54#106×C43C2211yescharacteristic
55#106×C43C2211yescharacteristic
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59C2×D4×C43—21no—
60C2×D4×C43C2311yescharacteristic
61C22×C4×C43—21no—
62C22×C4×C43C2311yescharacteristic
63C2×C22⋊D43—21no—
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66C2×C22⋊D43D411yescharacteristic
67C2×C22⋊D43D411yescharacteristic
68C22×Dic43—21no—
69#10621900—41no—
70#10621900—41no—
71#10621898—41no—
72#10621898—41no—
73#10621898—41no—
74#10621898—41no—
75C2×D172—21no—
76C2×D172—21no—
77C2×D172D411yescharacteristic
78C2×D172C2311yescharacteristic
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×C4×D43C2311yescharacteristic
82C2×C4×D43C2311yescharacteristic
83C2×Dic86D411yescharacteristic
84C2×Dic86C2311yescharacteristic
85C2×Dic86C2311yescharacteristic
86C2×C8×C43C2311yescharacteristic
87C2×C8×C43C2311yescharacteristic
88C4⋊C4×C43—21no—
89C4⋊C4×C43C2311yescharacteristic
90C4⋊C4×C43C2311yescharacteristic
91C4⋊C4×C43C2311yescharacteristic
92C22⋊C4×C43—21no—
93C22⋊Dic43—21no—
94C22⋊Dic43—21no—
95#10621883—41no—
96#10621882—41no—
97(C2×D43)⋊C4—21no—
98(C2×D43)⋊C4—21no—
99(C2×D43)⋊C4—21no—
100(C2×D43)⋊C4—21no—
101(C2×D43)⋊C4—21no—
102C4⋊Dic43—21no—
103C4⋊Dic43—21no—
104C4⋊Dic43—21no—
105C4⋊Dic43C2311yescharacteristic
106Dic43⋊C4—21no—
107Dic43⋊C4—21no—
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110Dic172—41no—
111#10621873—41no—
112#10621872—41no—
113C8×D43—41no—
114C23×C43—21no—
115C23×C43C2×D411yescharacteristic
116C22×D43—21no—
117C22×D43C2×D411yescharacteristic
118C22×D43C2×D411yescharacteristic
119D4×C43—21no—
120D4×C43—21no—
121D4×C43—81no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—81no—
128C2×C4×C43C2×D411yescharacteristic
129C2×C4×C43C2411yescharacteristic
130C22⋊D43—41no—
131C22⋊D43—41no—
132C22⋊D43—42no—
133C22⋊D43—42no—
134C22⋊D43—81no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—21no—
138C2×Dic43—42no—
139C2×Dic43C2×D411yescharacteristic
140C2×Dic43C2×D411yescharacteristic
141D172—21no—
142D172—21no—
143D172—41no—
144D172—81no—
145D172—81no—
146C4×D43—21no—
147C4×D43—21no—
148C4×D43—21no—
149C4×D43—21no—
150C4×D43—42no—
151C4×D43—81no—
152Dic86—21no—
153Dic86—21no—
154Dic86—21no—
155Dic86—21no—
156Dic86—41no—
157C8×C43—21no—
158C8×C43—21no—
159C43⋊C8—21no—
160C43⋊C8—21no—
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—21no—
164C22×C43—41no—
165C22×C43—41no—
166C22×C43—41no—
167C22×C43C22×D411yescharacteristic
168C2×D43—21no—
169C2×D43—21no—
170C2×D43—21no—
171C2×D43—21no—
172C2×D43—21no—
173C2×D43—21no—
174C2×D43—41no—
175C2×D43—41no—
176C2×D43—41no—
177C4×C43—21no—
178C4×C43—41no—
179C4×C43—41no—
180C4×C43—41no—
181C4×C43H(5,𝔽2)11yescharacteristic
182C4×C43H(5,𝔽2)11yescharacteristic
183Dic43—21no—
184Dic43—21no—
185Dic43—41no—
186Dic43—41no—
187Dic43—41no—
188#3204—431nomaximal, Sylow
189C2×C43—41no—
190C2×C43—81no—
191C2×C43#53411yescharacteristic
192C2×C43#57711yescharacteristic
193C2×C43#57711yescharacteristic
194D43—41no—
195D43—41no—
196D43—81no—
197#537—431no—
198#537—431no—
199#483—431no—
200#483—431no—
201#481—431no—
202#481D4311yescharacteristic, complemented
203#470—431no—
204#469—431no—
205#465—431no—
206#465—431no—
207#452—431no—
208#452—431no—
209#449—431no—
210#449—431no—
211#408—431no—
212C43#320411yescharacteristic, complemented, Sylow
213C2×#41—431no—
214C2×#41—431no—
215C2×#41—431no—
216C2×Q16—431no—
217C2×SD16—431no—
218C2×SD16—431no—
219C2×D8—431no—
220C2×M16—431no—
221C22×C8—431no—
222C22⋊Q8—431no—
223C22⋊Q8—431no—
224C22⋊Q8—431no—
225C22⋊Q8—431no—
226C22⋊Q8—861no—
227C22⋊Q8—861no—
228#121—431no—
229#121—431no—
230#121—431no—
231#121—861no—
232#121—861no—
233#121—861no—
234#121—861no—
235#121—861no—
236#121—861no—
237#121C2×D4311yescharacteristic
238C2×C4⋊C4—431no—
239C2×C4⋊C4C2×D4311yescharacteristic
240#106—431no—
241#106—431no—
242#106C2×D4311yescharacteristic
243#106C2×D4311yescharacteristic
244#103—431no—
245#103—431no—
246#103—431no—
247#103—431no—
248#102—431no—
249#102—431no—
250#102C2×D4311yescharacteristic
251#102C2×D4311yescharacteristic
252C22⋊C8—431no—
253C22⋊C8—431no—
254C22⋊C8—431no—
255C22⋊C8C2×D4311yescharacteristic
256#41—1721no—
257#41—1721no—
258#41—1721no—
259#41—1721no—
260#41—1721no—
261#41—1721no—
262C2×Q8—431no—
263C2×Q8—431no—
264C2×Q8—431no—
265C2×D4—21no—
266C2×D4—431no—
267C2×D4—431no—
268C2×D4—431no—
269C2×D4—431no—
270C2×D4—861no—
271C2×D4—861no—
272C2×D4—861no—
273C2×D4—861no—
274C2×D4—861no—
275C2×D4C22×D4311yescharacteristic
276C22×C4—21no—
277C22×C4—431no—
278C22×C4—431no—
279C22×C4—861no—
280C22×C4—861no—
281C22×C4—861no—
282C22×C4C22×D4311yescharacteristic
283Q16—1721no—
284SD16—1721no—
285SD16—1721no—
286D8—1721no—
287M16—1721no—
288C2×C8—431no—
289C2×C8—431no—
290C2×C8—1721no—
291C2×C8C22×D4311yescharacteristic
292C2×C8C22×D4311yescharacteristic
293C4⋊C4—21no—
294C4⋊C4—431no—
295C4⋊C4—861no—
296C4⋊C4—861no—
297C4⋊C4—861no—
298C4⋊C4—861no—
299C4⋊C4—861no—
300C4⋊C4C22×D4311yescharacteristic
301C4⋊C4C22×D4311yescharacteristic
302C4⋊C4C22×D4311yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—861no—
305C22⋊C4—861no—
306C22⋊C4—861no—
307C22⋊C4—861no—
308C22⋊C4—861no—
309C22⋊C4—861no—
310C22⋊C4—861no—
311C23—21no—
312C23—431no—
313C23—431no—
314C23—861no—
315C23D4×D4311yescharacteristic
316Q8—861no—
317Q8—861no—
318Q8—861no—
319Q8—861no—
320Q8—1721no—
321D4—21no—
322D4—21no—
323D4—81no—
324D4—861no—
325D4—861no—
326D4—3441no—
327D4—3441no—
328D4—3441no—
329D4—1721no—
330D4—1721no—
331D4—1721no—
332D4—1722no—
333D4—1722no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—81no—
340C2×C4—431no—
341C2×C4—431no—
342C2×C4—861no—
343C2×C4—861no—
344C2×C4—861no—
345C2×C4—861no—
346C2×C4—861no—
347C2×C4—861no—
348C2×C4—861no—
349C2×C4—3441no—
350C2×C4—1722no—
351C2×C4—1722no—
352C2×C4D4×D4311yescharacteristic
353C2×C4C23×D4311yescharacteristic
354C8—21no—
355C8—21no—
356C8—861no—
357C8—861no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—861no—
365C22—861no—
366C22—861no—
367C22—861no—
368C22—861no—
369C22—861no—
370C22—1721no—
371C22—1721no—
372C22—1721no—
373C22C2×D4×D4311yescharacteristic
374C4—21no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—861no—
379C4—861no—
380C4—1721no—
381C4—1721no—
382C4—1721no—
383C4#1306337111yescharacteristic
384C4#1306337111yescharacteristic
385C2—41no—
386C2—81no—
387C2—3441no—
388C2—1721no—
389C2—1721no—
390C2#1458346011yescharacteristic
391C2#1458370511yescharacteristic
392C2#1458370911yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#481C2
socleC22×C43C22×D4
hypercenter#481D43
hypocenterC43#3204
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. #14583480C2semidirect
2. #14583478C2semidirect
3. #14583231C2semidirect
4. #14583229C2semidirect
5. #14583219C2semidirect
6. #14583158C2semidirect
7. #14583151C2semidirect
8. #14583129C2semidirect
9. #14583127C2semidirect
10. #14583063C2semidirect
11. #14583062C2semidirect
12. #14583045C2semidirect
13. #14583042C2semidirect
14. #14582864C2semidirect
15. C43×#481C2semidirect
202. #481D43semidirect
212. C43#3204semidirect