Finite Group Databasebeta

← #19144875

Subgroups — #19144875

Order 5504.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583516C211yesmaximal, characteristic, complemented
2#14583380C211yesmaximal, characteristic, complemented
3#14583229C211yesmaximal, characteristic, complemented
4#14583188C211yesmaximal, characteristic, complemented
5#14583183C211yesmaximal, characteristic, complemented
6#14583120C211yesmaximal, characteristic, complemented
7#14583113C211yesmaximal, characteristic, complemented
8#14583063C211yesmaximal, characteristic, complemented
9#14583042C211yesmaximal, characteristic
10#14583008C211yesmaximal, characteristic, complemented
11#14583005C211yesmaximal, characteristic, complemented
12#14582990C211yesmaximal, characteristic, complemented
13#14582986C211yesmaximal, characteristic, complemented
14#14582957C211yesmaximal, characteristic, complemented
15C43×#481C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×Dic172C2211yescharacteristic
18C2×#10621873C2211yescharacteristic
19C2×#10621883C2211yescharacteristic
20C2×#10621882C2211yescharacteristic
21#13063324C2211yescharacteristic
22#13063318—21no—
23#13063312—21no—
24#13063312C2211yescharacteristic
25#13063306—21no—
26#13063304C2211yescharacteristic
27#13063302—21no—
28#13063290C2211yescharacteristic
29#13063290C2211yescharacteristic
30#13063290C2211yescharacteristic
31D4×Dic43C2211yescharacteristic
32#13063287C2211yescharacteristic
33#13063287C2211yescharacteristic
34C4×C22⋊D43—21no—
35C4×C22⋊D43—21no—
36#13063284C2211yescharacteristic
37#13063283—21no—
38C4⋊C4×D43—21no—
39#13063256C2211yescharacteristic
40#13063256C2211yescharacteristic
41Dic43⋊C8C2211yescharacteristic
42Dic43⋊C8C2211yescharacteristic
43#13063250C2211yescharacteristic
44#13063248C2211yescharacteristic
45#13063248C2211yescharacteristic
46#13063248C2211yescharacteristic
47#13063247C2211yescharacteristic
48#13063245C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50#13063235C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
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—
64C22×Dic43—21no—
65#10621898—22no—
66#10621898—22no—
67C2×D172C2311yescharacteristic
68C2×C4×D43—21no—
69C2×C4×D43—21no—
70C2×C4×D43—21no—
71C2×Dic86—21no—
72C2×Dic86C2311yescharacteristic
73C2×Dic86C2311yescharacteristic
74C2×C8×C43C2311yescharacteristic
75C2×C8×C43C2311yescharacteristic
76C4⋊C4×C43—21no—
77C4⋊C4×C43C2311yescharacteristic
78C4⋊C4×C43C2311yescharacteristic
79C4⋊C4×C43C2311yescharacteristic
80C22⋊C4×C43—21no—
81C22⋊Dic43—21no—
82C22⋊Dic43—21no—
83C22⋊Dic43—21no—
84C22⋊Dic43—21no—
85C22⋊Dic43D411yescharacteristic
86C22⋊Dic43D411yescharacteristic
87#10621883—22no—
88#10621882—22no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91C4⋊Dic43D411yescharacteristic
92C4⋊Dic43D411yescharacteristic
93C4⋊Dic43C2311yescharacteristic
94Dic43⋊C4—21no—
95Dic43⋊C4—21no—
96Dic43⋊C4—21no—
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99C4×Dic43—21no—
100C4×Dic43—21no—
101C4×Dic43—21no—
102C4×Dic43C2311yescharacteristic
103C4×Dic43C2311yescharacteristic
104C2×C43⋊C8C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106Dic172—22no—
107#10621873—22no—
108C23×C43—21no—
109C23×C43C2×D411yescharacteristic
110C22×D43—21no—
111D4×C43—21no—
112D4×C43—21no—
113D4×C43—81no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—81no—
120C2×C4×C43C2×D411yescharacteristic
121C2×C4×C43C2411yescharacteristic
122C22⋊D43—24no—
123C2×Dic43—21no—
124C2×Dic43—21no—
125C2×Dic43—21no—
126C2×Dic43—81no—
127C2×Dic43C2×D411yescharacteristic
128C2×Dic43C2×D411yescharacteristic
129C2×Dic43C2×D411yescharacteristic
130C2×Dic43C2×D411yescharacteristic
131D172—21no—
132D172#4112yes—
133C4×D43—24no—
134C4×D43—81no—
135C4×D43—81no—
136Dic86—21no—
137Dic86—21no—
138Dic86—21no—
139Dic86—81no—
140Dic86#4112yes—
141C8×C43—21no—
142C8×C43—21no—
143C43⋊C8—21no—
144C43⋊C8—21no—
145C22×C43—21no—
146C22×C43—21no—
147C22×C43—21no—
148C22×C43—41no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43C22×D411yescharacteristic
152C2×D43—22no—
153C2×D43—41no—
154C2×D43—41no—
155C4×C43—21no—
156C4×C43—41no—
157C4×C43—41no—
158C4×C43—41no—
159C4×C43C2×#4111yescharacteristic
160C4×C43C2×#4111yescharacteristic
161Dic43—22no—
162Dic43—21no—
163Dic43—21no—
164Dic43—21no—
165Dic43—21no—
166Dic43—41no—
167Dic43—41no—
168#3125—431nomaximal, Sylow
169C2×C43—41no—
170C2×C43—81no—
171C2×C43#52511yescharacteristic
172C2×C43#57711yescharacteristic
173C2×C43#57711yescharacteristic
174D43—42no—
175#542—431no—
176#520—431no—
177#483—431no—
178#481D4311yescharacteristic, complemented
179#476—431no—
180#475—431no—
181#464—431no—
182#463—431no—
183#452—431no—
184#449—431no—
185#442—431no—
186#441—431no—
187C4×SD16—431no—
188C4×SD16—431no—
189#433—431no—
190C43#312511yescharacteristic, complemented, Sylow
191C2×#41—431no—
192C2×Q16—431no—
193C2×SD16—431no—
194C2×SD16—431no—
195C2×D8—431no—
196C4⋊Q8—431no—
197#126—861no—
198#124—431no—
199#124—861no—
200#123—861no—
201C22⋊Q8—431no—
202C22⋊Q8—861no—
203#121C2×D4311yescharacteristic
204C4×Q8—431no—
205C4×Q8—431no—
206C4×Q8—431no—
207C4×D4—431no—
208C4×D4—431no—
209C4×D4—431no—
210C4×D4—861no—
211C4×D4—861no—
212#117—431no—
213#117—861no—
214C2×C4⋊C4—861no—
215C2×C4⋊C4C2×D4311yescharacteristic
216#106—431no—
217#106—431no—
218#106C2×D4311yescharacteristic
219#106C2×D4311yescharacteristic
220C4⋊C8—431no—
221C4⋊C8—431no—
222#103—431no—
223#103—431no—
224#103—431no—
225#103—431no—
226#102—431no—
227#102—431no—
228#102C2×D4311yescharacteristic
229#102C2×D4311yescharacteristic
230C22⋊C8—431no—
231C22⋊C8C2×D4311yescharacteristic
232#97—431no—
233C4×C8—431no—
234#41—862no—
235#41—862no—
236C2×Q8—431no—
237C2×Q8—431no—
238C2×Q8—861no—
239C2×D4—21no—
240C2×D4—431no—
241C2×D4—861no—
242C2×D4C22×D4311yescharacteristic
243C22×C4—21no—
244C22×C4—861no—
245C22×C4—861no—
246C22×C4—861no—
247C22×C4—861no—
248C22×C4C22×D4311yescharacteristic
249Q16—862no—
250SD16—862no—
251SD16—862no—
252D8—862no—
253C2×C8—431no—
254C2×C8—431no—
255C2×C8C22×D4311yescharacteristic
256C2×C8C22×D4311yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—431no—
259C4⋊C4—431no—
260C4⋊C4—431no—
261C4⋊C4—861no—
262C4⋊C4—861no—
263C4⋊C4—861no—
264C4⋊C4—861no—
265C4⋊C4—861no—
266C4⋊C4C22×D4311yescharacteristic
267C4⋊C4C22×D4311yescharacteristic
268C4⋊C4C22×D4311yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—431no—
271C22⋊C4—431no—
272C22⋊C4—861no—
273C22⋊C4—861no—
274C22⋊C4—861no—
275C22⋊C4—861no—
276C22⋊C4—861no—
277C22⋊C4—861no—
278C42—431no—
279C42—431no—
280C42—861no—
281C42—861no—
282C42—861no—
283C23—21no—
284C23—861no—
285C23D4×D4311yescharacteristic
286Q8—432no—
287Q8—861no—
288Q8—861no—
289Q8—861no—
290Q8—3441no—
291D4—21no—
292D4—21no—
293D4—81no—
294D4—432no—
295D4—864no—
296D4—861no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—431no—
304C2×C4—431no—
305C2×C4—431no—
306C2×C4—431no—
307C2×C4—864no—
308C2×C4—861no—
309C2×C4—861no—
310C2×C4—861no—
311C2×C4—3441no—
312C2×C4—3441no—
313C2×C4—3441no—
314C2×C4D4×D4311yescharacteristic
315C2×C4C23×D4311yescharacteristic
316C8—21no—
317C8—21no—
318C8—861no—
319C8—861no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—862no—
327C22—1721no—
328C22—1721no—
329C22C2×D4×D4311yescharacteristic
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—862no—
335C4—861no—
336C4—861no—
337C4—861no—
338C4—861no—
339C4—1721no—
340C4—1721no—
341C4#41×D4311yescharacteristic
342C4#41×D4311yescharacteristic
343C2—41no—
344C2—81no—
345C2—1722no—
346C2#1458340711yescharacteristic
347C2#1458370511yescharacteristic
348C2#1458370911yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#481C2
socleC22×C43C22×D4
hypercenter#481D43
hypocenterC43#3125
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. #14583516C2semidirect
2. #14583380C2semidirect
3. #14583229C2semidirect
4. #14583188C2semidirect
5. #14583183C2semidirect
6. #14583120C2semidirect
7. #14583113C2semidirect
8. #14583063C2semidirect
10. #14583008C2semidirect
11. #14583005C2semidirect
12. #14582990C2semidirect
13. #14582986C2semidirect
14. #14582957C2semidirect
15. C43×#481C2semidirect
178. #481D43semidirect
190. C43#3125semidirect