Finite Group Databasebeta

← #19145268

Subgroups — #19145268

Order 5504.

350 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583523C211yesmaximal, characteristic
2#14583512C211yesmaximal, characteristic, complemented
3#14583293C211yesmaximal, characteristic, complemented
4#14583256C211yesmaximal, characteristic, complemented
5#14583251C211yesmaximal, characteristic, complemented
6#14583158C211yesmaximal, characteristic, complemented
7#14583146C211yesmaximal, characteristic
8#14583141C211yesmaximal, characteristic, complemented
9#14583129C211yesmaximal, characteristic
10#14583005C211yesmaximal, characteristic, complemented
11#14582998C211yesmaximal, characteristic, complemented
12#14582993C211yesmaximal, characteristic, complemented
13#14582986C211yesmaximal, characteristic, complemented
14#14582856C211yesmaximal, characteristic, complemented
15C43×#501C211yesmaximal, characteristic, complemented
16C2×Dic172C2211yescharacteristic
17C2×Dic172C2211yescharacteristic
18C2×#10621873C2211yescharacteristic
19C2×#10621873C2211yescharacteristic
20C2×#10621872C2211yescharacteristic
21C2×C8×D43C2211yescharacteristic
22#13063325C2211yescharacteristic
23#13063320—21no—
24#13063320—21no—
25#13063320—21no—
26#13063316—21no—
27#13063316—21no—
28#13063314—21no—
29#13063313C2211yescharacteristic
30#13063310—21no—
31#13063305C2211yescharacteristic
32#13063305C2211yescharacteristic
33#13063305C2211yescharacteristic
34#13063301—21no—
35#13063300C2211yescharacteristic
36#13063290C2211yescharacteristic
37#13063290C2211yescharacteristic
38#13063290C2211yescharacteristic
39#13063287C2211yescharacteristic
40#13063282C2211yescharacteristic
41#13063248C2211yescharacteristic
42#13063248C2211yescharacteristic
43#13063248C2211yescharacteristic
44#13063248C2211yescharacteristic
45#13063248C2211yescharacteristic
46#13063248C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49#13063235C2211yescharacteristic
50C4×C43⋊C8C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C4⋊Q8×C43C2211yescharacteristic
53#125×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic
55#107×C43C2211yescharacteristic
56#106×C43C2211yescharacteristic
57#106×C43C2211yescharacteristic
58#97×C43C2211yescharacteristic
59C2×Q8×C43—21no—
60C2×D172—21no—
61C2×D172C2311yescharacteristic
62C2×C4×D43—21no—
63C2×C4×D43C2311yescharacteristic
64C2×Dic86C2311yescharacteristic
65C2×Dic86C2311yescharacteristic
66C2×Dic86C2311yescharacteristic
67C2×C8×C43C2311yescharacteristic
68C2×C8×C43C2311yescharacteristic
69C4⋊C4×C43—21no—
70C4⋊C4×C43—21no—
71C4⋊C4×C43—21no—
72C4⋊C4×C43C2311yescharacteristic
73C4⋊C4×C43C2311yescharacteristic
74C4⋊C4×C43C2311yescharacteristic
75C4⋊C4×C43C2311yescharacteristic
76C42×C43C2311yescharacteristic
77(C2×D43)⋊C4—21no—
78(C2×D43)⋊C4—21no—
79(C2×D43)⋊C4—21no—
80(C2×D43)⋊C4—21no—
81(C2×D43)⋊C4—21no—
82(C2×D43)⋊C4—21no—
83(C2×D43)⋊C4—21no—
84(C2×D43)⋊C4D411yescharacteristic
85(C2×D43)⋊C4D411yescharacteristic
86C4⋊Dic43—21no—
87C4⋊Dic43—21no—
88C4⋊Dic43—21no—
89C4⋊Dic43—21no—
90C4⋊Dic43—21no—
91Dic43⋊C4—21no—
92Dic43⋊C4—21no—
93Dic43⋊C4—21no—
94Dic43⋊C4D411yescharacteristic
95Dic43⋊C4D411yescharacteristic
96C4×Dic43—21no—
97C4×Dic43—21no—
98C4×Dic43—21no—
99C4×Dic43C2311yescharacteristic
100C2×C43⋊C8C2311yescharacteristic
101C2×C43⋊C8C2311yescharacteristic
102Dic172—22no—
103Dic172—22no—
104#10621873—22no—
105#10621873—22no—
106#10621872—22no—
107C8×D43—22no—
108C22×D43—21no—
109C22×D43C2×D411yescharacteristic
110Q8×C43—81no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43C2×D411yescharacteristic
116C2×C4×C43C2×D411yescharacteristic
117C2×C4×C43C2411yescharacteristic
118C2×Dic43—21no—
119C2×Dic43—21no—
120C2×Dic43—21no—
121C2×Dic43C2×D411yescharacteristic
122C2×Dic43C2×D411yescharacteristic
123C2×Dic43C2×D411yescharacteristic
124D172—21no—
125D172—21no—
126D172—81no—
127C4×D43—21no—
128C4×D43—21no—
129C4×D43—81no—
130Dic86—21no—
131Dic86—21no—
132Dic86—21no—
133Dic86—21no—
134Dic86—21no—
135Dic86—21no—
136C8×C43#4112yes—
137C8×C43#4112yes—
138C43⋊C8—21no—
139C43⋊C8—21no—
140C22×C43C22×D411yescharacteristic
141C2×D43—21no—
142C2×D43—21no—
143C2×D43—21no—
144C2×D43—41no—
145C2×D43—41no—
146C2×D43—41no—
147C4×C43—21no—
148C4×C43—21no—
149C4×C43—41no—
150C4×C43—41no—
151C4×C43—41no—
152C4×C43—41no—
153C4×C43C2×#4111yescharacteristic
154C4×C43C2×#4111yescharacteristic
155Dic43—21no—
156Dic43—21no—
157Dic43—21no—
158Dic43—41no—
159Dic43—41no—
160Dic43—41no—
161#3178—431nomaximal, Sylow
162C2×C43#53211yescharacteristic
163C2×C43#57711yescharacteristic
164C2×C43#57811yescharacteristic
165D43—41no—
166D43—81no—
167#542—431no—
168#541—431no—
169#501D4311yescharacteristic, complemented
170#497—431no—
171#488—431no—
172#487—431no—
173#470—431no—
174#468—431no—
175#467—431no—
176#465—431no—
177#441—431no—
178#440—431no—
179C4×Q16—431no—
180C4×SD16—431no—
181#405—431no—
182C43#317811yescharacteristic, complemented, Sylow
183C2×Q16—431no—
184C2×Q16—431no—
185C2×SD16—431no—
186C2×SD16—431no—
187C2×M16—431no—
188C22×C8—431no—
189C4⋊Q8—431no—
190C4⋊Q8C2×D4311yescharacteristic
191#126—861no—
192#126—861no—
193#126—861no—
194#125—861no—
195#125—861no—
196#125C2×D4311yescharacteristic
197#124—431no—
198#124—861no—
199#123—861no—
200C22⋊Q8—431no—
201C22⋊Q8—431no—
202C22⋊Q8—431no—
203C22⋊Q8—861no—
204#121—431no—
205C4×Q8—431no—
206C4×Q8—431no—
207C4×Q8—431no—
208C4×D4—431no—
209#117—431no—
210#107C2×D4311yescharacteristic
211#107C2×D4311yescharacteristic
212#106C2×D4311yescharacteristic
213#106C2×D4311yescharacteristic
214#103—431no—
215#103—431no—
216#103—431no—
217#103—431no—
218#103—431no—
219#103—431no—
220#102—431no—
221#102—431no—
222#97—431no—
223#97C2×D4311yescharacteristic
224C4×C8—431no—
225C4×C8—431no—
226C2×Q8—21no—
227C2×Q8—431no—
228C2×Q8—431no—
229C2×Q8—431no—
230C2×D4—431no—
231C2×D4—861no—
232C22×C4—431no—
233C22×C4—861no—
234Q16—862no—
235Q16—862no—
236SD16—862no—
237SD16—862no—
238M16—862no—
239C2×C8—431no—
240C2×C8—431no—
241C2×C8—862no—
242C2×C8C22×D4311yescharacteristic
243C2×C8C22×D4311yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—431no—
248C4⋊C4—431no—
249C4⋊C4—861no—
250C4⋊C4—861no—
251C4⋊C4—861no—
252C4⋊C4—861no—
253C4⋊C4—861no—
254C4⋊C4—861no—
255C4⋊C4—861no—
256C4⋊C4—861no—
257C4⋊C4C22×D4311yescharacteristic
258C4⋊C4C22×D4311yescharacteristic
259C4⋊C4C22×D4311yescharacteristic
260C4⋊C4C22×D4311yescharacteristic
261C22⋊C4—431no—
262C22⋊C4—431no—
263C22⋊C4—861no—
264C22⋊C4—861no—
265C22⋊C4—861no—
266C22⋊C4—861no—
267C22⋊C4—861no—
268C22⋊C4—861no—
269C22⋊C4—861no—
270C42—431no—
271C42—861no—
272C42—861no—
273C42—861no—
274C42C22×D4311yescharacteristic
275C23—431no—
276C23—861no—
277Q8—81no—
278Q8—861no—
279Q8—861no—
280Q8—861no—
281Q8—861no—
282Q8—861no—
283Q8—861no—
284D4—861no—
285D4—861no—
286D4—3441no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—431no—
292C2×C4—431no—
293C2×C4—431no—
294C2×C4—861no—
295C2×C4—861no—
296C2×C4—861no—
297C2×C4—861no—
298C2×C4—861no—
299C2×C4—3441no—
300C2×C4D4×D4311yescharacteristic
301C2×C4D4×D4311yescharacteristic
302C2×C4C23×D4311yescharacteristic
303C8—861no—
304C8—861no—
305C8#1062190212yes—
306C8#1062190212yes—
307C22—861no—
308C22—861no—
309C22—861no—
310C22—1721no—
311C22—1721no—
312C22—1721no—
313C22C2×D4×D4311yescharacteristic
314C4—21no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—861no—
321C4—861no—
322C4—861no—
323C4—1721no—
324C4—1721no—
325C4—1721no—
326C4C2×#1062190211yescharacteristic
327C4C2×#1062190211yescharacteristic
328C2—3441no—
329C2—1721no—
330C2#1458345011yescharacteristic
331C2#1458370911yescharacteristic
332C2#1458371511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#501C2
socleC22×C43C22×D4
hypercenter#501D43
hypocenterC43#3178
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
2. #14583512C2semidirect
3. #14583293C2semidirect
4. #14583256C2semidirect
5. #14583251C2semidirect
6. #14583158C2semidirect
8. #14583141C2semidirect
10. #14583005C2semidirect
11. #14582998C2semidirect
12. #14582993C2semidirect
13. #14582986C2semidirect
14. #14582856C2semidirect
15. C43×#501C2semidirect
169. #501D43semidirect
182. C43#3178semidirect