Finite Group Databasebeta

← #19145211

Subgroups — #19145211

Order 5504.

362 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583523C211yesmaximal, characteristic, complemented
2#14583518C211yesmaximal, characteristic, complemented
3#14583295C211yesmaximal, characteristic, complemented
4#14583281C211yesmaximal, characteristic, complemented
5#14583259C211yesmaximal, characteristic, complemented
6#14583156C211yesmaximal, characteristic, complemented
7#14583151C211yesmaximal, characteristic
8#14583131C211yesmaximal, characteristic, complemented
9#14583127C211yesmaximal, characteristic, complemented
10#14583008C211yesmaximal, characteristic, complemented
11#14583003C211yesmaximal, characteristic, complemented
12#14582990C211yesmaximal, characteristic, complemented
13#14582984C211yesmaximal, characteristic, complemented
14#14582856C211yesmaximal, characteristic, complemented
15C43×#489C211yesmaximal, characteristic, complemented
16C2×#10621885C2211yescharacteristic
17C2×#10621883C2211yescharacteristic
18C2×#10621884C2211yescharacteristic
19C2×#10621882C2211yescharacteristic
20C2×#10621872C2211yescharacteristic
21C2×C8×D43C2211yescharacteristic
22#13063325C2211yescharacteristic
23#13063320—21no—
24#13063318—21no—
25#13063314—21no—
26#13063313C2211yescharacteristic
27#13063311—21no—
28#13063310—21no—
29#13063309—21no—
30#13063305C2211yescharacteristic
31#13063302—21no—
32#13063301—21no—
33#13063301C2211yescharacteristic
34#13063300C2211yescharacteristic
35#13063296C2211yescharacteristic
36Q8×Dic43C2211yescharacteristic
37#13063290C2211yescharacteristic
38D4×Dic43C2211yescharacteristic
39#13063287C2211yescharacteristic
40#13063282C2211yescharacteristic
41#13063256C2211yescharacteristic
42#13063256C2211yescharacteristic
43#13063256C2211yescharacteristic
44#13063256C2211yescharacteristic
45#13063250C2211yescharacteristic
46#13063250C2211yescharacteristic
47#13063247C2211yescharacteristic
48#13063247C2211yescharacteristic
49#13063235C2211yescharacteristic
50C4×C43⋊C8C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C4⋊Q8×C43C2211yescharacteristic
53#124×C43C2211yescharacteristic
54#103×C43C2211yescharacteristic
55#103×C43C2211yescharacteristic
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58#97×C43C2211yescharacteristic
59C2×Q8×C43—21no—
60C2×Q8×C43C2311yescharacteristic
61C2×D4×C43C2311yescharacteristic
62C2×C22⋊D43—21no—
63C22×Dic43—21no—
64C2×D172—21no—
65C2×D172C2311yescharacteristic
66C2×C4×D43—21no—
67C2×C4×D43C2311yescharacteristic
68C2×Dic86—21no—
69C2×Dic86C2311yescharacteristic
70C2×C8×C43C2311yescharacteristic
71C2×C8×C43C2311yescharacteristic
72C4⋊C4×C43—21no—
73C4⋊C4×C43C2311yescharacteristic
74C4⋊C4×C43C2311yescharacteristic
75C22⋊C4×C43—21no—
76C22⋊C4×C43—21no—
77C42×C43C2311yescharacteristic
78C22⋊Dic43—21no—
79C22⋊Dic43—21no—
80#10621885—22no—
81#10621884—22no—
82#10621883—22no—
83#10621882—22no—
84(C2×D43)⋊C4—21no—
85(C2×D43)⋊C4—21no—
86(C2×D43)⋊C4—21no—
87(C2×D43)⋊C4—21no—
88(C2×D43)⋊C4—21no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4D411yescharacteristic
91(C2×D43)⋊C4D411yescharacteristic
92C4⋊Dic43—21no—
93C4⋊Dic43—21no—
94C4⋊Dic43—21no—
95C4⋊Dic43C2311yescharacteristic
96C4⋊Dic43C2311yescharacteristic
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99Dic43⋊C4D411yescharacteristic
100Dic43⋊C4D411yescharacteristic
101C4×Dic43—21no—
102C4×Dic43—21no—
103C4×Dic43C2311yescharacteristic
104C2×C43⋊C8C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106#10621872—22no—
107C8×D43—22no—
108C23×C43—21no—
109C22×D43—21no—
110C22×D43C2×D411yescharacteristic
111Q8×C43—21no—
112Q8×C43—21no—
113Q8×C43—81no—
114D4×C43—21no—
115D4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43C2×D411yescharacteristic
120C2×C4×C43C2×D411yescharacteristic
121C2×C4×C43C2411yescharacteristic
122C22⋊D43—81no—
123C2×Dic43—21no—
124C2×Dic43—21no—
125C2×Dic43—21no—
126C2×Dic43—81no—
127C2×Dic43C2×D411yescharacteristic
128C2×Dic43C2×D411yescharacteristic
129C2×Dic43C2×D411yescharacteristic
130D172—21no—
131D172—21no—
132D172—81no—
133C4×D43—21no—
134C4×D43—21no—
135C4×D43—81no—
136Dic86—21no—
137Dic86—21no—
138Dic86—81no—
139C8×C43—21no—
140C8×C43—21no—
141C43⋊C8#4112yes—
142C43⋊C8#4112yes—
143C22×C43—41no—
144C22×C43—41no—
145C22×C43—41no—
146C22×C43C22×D411yescharacteristic
147C2×D43—21no—
148C2×D43—21no—
149C2×D43—21no—
150C2×D43—41no—
151C2×D43—41no—
152C2×D43—41no—
153C4×C43—21no—
154C4×C43—21no—
155C4×C43—41no—
156C4×C43—41no—
157C4×C43—41no—
158C4×C43C2×#4111yescharacteristic
159C4×C43C2×#4111yescharacteristic
160Dic43—21no—
161Dic43—21no—
162Dic43—21no—
163Dic43—41no—
164Dic43—41no—
165Dic43—41no—
166#3173—431nomaximal, Sylow
167C2×C43—81no—
168C2×C43#53211yescharacteristic
169C2×C43#57711yescharacteristic
170C2×C43#57711yescharacteristic
171D43—41no—
172D43—81no—
173#542—431no—
174#542—431no—
175#498—431no—
176#495—431no—
177#489—431no—
178#489D4311yescharacteristic, complemented
179#470—431no—
180#469—431no—
181#465—431no—
182#465—431no—
183#442—431no—
184#441—431no—
185C4×SD16—431no—
186C4×SD16—431no—
187#405—431no—
188C43#317311yescharacteristic, complemented, Sylow
189C2×Q16—431no—
190C2×SD16—431no—
191C2×SD16—431no—
192C2×D8—431no—
193C2×M16—431no—
194C22×C8—431no—
195C4⋊Q8—431no—
196C4⋊Q8C2×D4311yescharacteristic
197#126—861no—
198#126—861no—
199#124—431no—
200#124—861no—
201#124—861no—
202#124C2×D4311yescharacteristic
203#123—861no—
204#123—861no—
205C22⋊Q8—431no—
206C22⋊Q8—431no—
207C22⋊Q8—861no—
208C22⋊Q8—861no—
209#121—431no—
210#121—431no—
211C4×Q8—431no—
212C4×Q8—431no—
213C4×D4—431no—
214C4×D4—431no—
215#117—431no—
216#106—431no—
217#106—431no—
218#106—431no—
219#106—431no—
220#103—431no—
221#103—431no—
222#103C2×D4311yescharacteristic
223#103C2×D4311yescharacteristic
224#102—431no—
225#102—431no—
226#102C2×D4311yescharacteristic
227#102C2×D4311yescharacteristic
228#97—431no—
229#97C2×D4311yescharacteristic
230C4×C8—431no—
231C4×C8—431no—
232C2×Q8—21no—
233C2×Q8—431no—
234C2×Q8—861no—
235C2×Q8C22×D4311yescharacteristic
236C2×D4—431no—
237C2×D4—861no—
238C2×D4—861no—
239C2×D4C22×D4311yescharacteristic
240C22×C4—431no—
241C22×C4—861no—
242C22×C4—861no—
243Q16—862no—
244SD16—862no—
245SD16—862no—
246D8—862no—
247M16—862no—
248C2×C8—431no—
249C2×C8—431no—
250C2×C8—862no—
251C2×C8C22×D4311yescharacteristic
252C2×C8C22×D4311yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—431no—
255C4⋊C4—431no—
256C4⋊C4—431no—
257C4⋊C4—431no—
258C4⋊C4—861no—
259C4⋊C4—861no—
260C4⋊C4—861no—
261C4⋊C4—861no—
262C4⋊C4—861no—
263C4⋊C4C22×D4311yescharacteristic
264C4⋊C4C22×D4311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—431no—
268C22⋊C4—431no—
269C22⋊C4—861no—
270C22⋊C4—861no—
271C22⋊C4—861no—
272C22⋊C4—861no—
273C22⋊C4—861no—
274C22⋊C4—861no—
275C22⋊C4—861no—
276C22⋊C4—861no—
277C42—431no—
278C42—861no—
279C42—861no—
280C42C22×D4311yescharacteristic
281C23—21no—
282C23—431no—
283C23—861no—
284Q8—21no—
285Q8—21no—
286Q8—81no—
287Q8—861no—
288Q8—861no—
289Q8—3441no—
290D4—21no—
291D4—21no—
292D4—861no—
293D4—861no—
294D4—3441no—
295D4—3441no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—431no—
300C2×C4—431no—
301C2×C4—431no—
302C2×C4—861no—
303C2×C4—861no—
304C2×C4—861no—
305C2×C4—861no—
306C2×C4—861no—
307C2×C4—3441no—
308C2×C4—3441no—
309C2×C4D4×D4311yescharacteristic
310C2×C4D4×D4311yescharacteristic
311C2×C4C23×D4311yescharacteristic
312C8—21no—
313C8—21no—
314C8—432no—
315C8—432no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—861no—
320C22—861no—
321C22—861no—
322C22—1721no—
323C22—1721no—
324C22—1721no—
325C22C2×D4×D4311yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—861no—
332C4—861no—
333C4—861no—
334C4—1721no—
335C4—1721no—
336C4—1721no—
337C4#41×D4311yescharacteristic
338C4#41×D4311yescharacteristic
339C2—81no—
340C2—3441no—
341C2—1721no—
342C2#1458344811yescharacteristic
343C2#1458370811yescharacteristic
344C2#1458370911yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#489C2
socleC22×C43C22×D4
hypercenter#489D43
hypocenterC43#3173
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #14583523C2semidirect
2. #14583518C2semidirect
3. #14583295C2semidirect
4. #14583281C2semidirect
5. #14583259C2semidirect
6. #14583156C2semidirect
8. #14583131C2semidirect
9. #14583127C2semidirect
10. #14583008C2semidirect
11. #14583003C2semidirect
12. #14582990C2semidirect
13. #14582984C2semidirect
14. #14582856C2semidirect
15. C43×#489C2semidirect
178. #489D43semidirect
188. C43#3173semidirect