Finite Group Databasebeta

← #19145159

Subgroups — #19145159

Order 5504.

380 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#14583433C211yesmaximal, characteristic, complemented
2#14583298C211yesmaximal, characteristic, complemented
3#14583281C211yesmaximal, characteristic, complemented
4#14583256C211yesmaximal, characteristic, complemented
5#14583253C211yesmaximal, characteristic, complemented
6#14583138C211yesmaximal, characteristic, complemented
7#14583133C211yesmaximal, characteristic
8#14583130C211yesmaximal, characteristic, complemented
9#14583126C211yesmaximal, characteristic, complemented
10C4×#10621885C211yesmaximal, characteristic, complemented
11C4×#10621884C211yesmaximal, characteristic, complemented
12C4×#10621883C211yesmaximal, characteristic, complemented
13C4×#10621882C211yesmaximal, characteristic, complemented
14C2×C4×C43⋊C8C211yesmaximal, characteristic, complemented
15C43×#529C211yesmaximal, characteristic, complemented
16C2×#10621885C2211yescharacteristic
17C2×#10621883C2211yescharacteristic
18C2×#10621884C2211yescharacteristic
19C2×#10621882C2211yescharacteristic
20C22×C43⋊C8C2211yescharacteristic
21C22×C43⋊C8C2211yescharacteristic
22#13063319—21no—
23#13063317C2211yescharacteristic
24#13063313C2211yescharacteristic
25#13063308—21no—
26#13063304C2211yescharacteristic
27#13063299C2211yescharacteristic
28C4×Dic86C2211yescharacteristic
29C4×D172C2211yescharacteristic
30C4×C22⋊D43—21no—
31#13063282—21no—
32#13063258C2211yescharacteristic
33#13063258C2211yescharacteristic
34#13063256C2211yescharacteristic
35#13063256C2211yescharacteristic
36#13063249C2211yescharacteristic
37#13063249C2211yescharacteristic
38#13063248C2211yescharacteristic
39#13063248C2211yescharacteristic
40#13063246C2211yescharacteristic
41#13063246C2211yescharacteristic
42#13063245C2211yescharacteristic
43#13063245C2211yescharacteristic
44C4×C43⋊C8C2211yescharacteristic
45C4×C43⋊C8C2211yescharacteristic
46C4×C43⋊C8C2211yescharacteristic
47C4×C43⋊C8C2211yescharacteristic
48#126×C43—21no—
49#125×C43C2211yescharacteristic
50#124×C43C2211yescharacteristic
51#123×C43—21no—
52C22⋊Q8×C43C2211yescharacteristic
53#121×C43C2211yescharacteristic
54C4×Q8×C43C2211yescharacteristic
55C4×D4×C43—21no—
56C4×D4×C43C2211yescharacteristic
57#117×C43—21no—
58C2×C42×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60C2×D4×C43—21no—
61C2×D4×C43C2311yescharacteristic
62C22×C4×C43—21no—
63C22×C4×C43D411yescharacteristic
64C22×C4×C43D411yescharacteristic
65C22×C4×C43C2311yescharacteristic
66C2×C22⋊D43—21no—
67C2×D172C2311yescharacteristic
68C2×C4×D43—21no—
69C2×Dic86C2311yescharacteristic
70C4⋊C4×C43—21no—
71C4⋊C4×C43—21no—
72C4⋊C4×C43—21no—
73C4⋊C4×C43—21no—
74C4⋊C4×C43C2311yescharacteristic
75C4⋊C4×C43C2311yescharacteristic
76C22⋊C4×C43—21no—
77C22⋊C4×C43—21no—
78C22⋊C4×C43—21no—
79C22⋊C4×C43—21no—
80C22⋊C4×C43—21no—
81C42×C43—21no—
82C42×C43D411yescharacteristic
83C42×C43D411yescharacteristic
84C42×C43C2311yescharacteristic
85C42×C43C2311yescharacteristic
86C22⋊Dic43—21no—
87#10621885—22no—
88#10621884—22no—
89#10621883—22no—
90#10621882—22no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4—21no—
95C4⋊Dic43C2311yescharacteristic
96C4⋊Dic43C2311yescharacteristic
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101C4×Dic43—21no—
102C2×C43⋊C8—22no—
103C2×C43⋊C8—22no—
104C2×C43⋊C8C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108C23×C43—21no—
109C23×C43C2×D411yescharacteristic
110C22×D43—21no—
111Q8×C43—21no—
112Q8×C43—21no—
113D4×C43—21no—
114D4×C43—21no—
115D4×C43—42no—
116C2×C4×C43—22no—
117C2×C4×C43—22no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—42no—
124C2×C4×C43C2×D411yescharacteristic
125C2×C4×C43C2×D411yescharacteristic
126C2×C4×C43C2×D411yescharacteristic
127C2×C4×C43C2×D411yescharacteristic
128C2×C4×C43C2×D411yescharacteristic
129C2×C4×C43C2411yescharacteristic
130C22⋊D43—42no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134D172—21no—
135D172—21no—
136C4×D43—42no—
137Dic86—21no—
138Dic86—21no—
139C43⋊C8—21no—
140C43⋊C8—21no—
141C43⋊C8#4112yes—
142C43⋊C8#4112yes—
143C22×C43—21no—
144C22×C43—21no—
145C22×C43—41no—
146C22×C43—41no—
147C22×C43—41no—
148C22×C43#13512yes—
149C22×C43C22×D411yescharacteristic
150C2×D43—41no—
151C2×D43—41no—
152C2×D43—41no—
153C4×C43—21no—
154C4×C43—21no—
155C4×C43—21no—
156C4×C43—21no—
157C4×C43—41no—
158C4×C43—41no—
159C4×C43—41no—
160C4×C43#13512yes—
161C4×C43C2×#4111yescharacteristic
162C4×C43C2×#4111yescharacteristic
163Dic43—41no—
164Dic43—41no—
165Dic43—41no—
166#3168—431nomaximal, Sylow
167C2×C43—22no—
168C2×C43—81no—
169C2×C43#53211yescharacteristic
170C2×C43C2×#13511yescharacteristic
171C2×C43C2×#13511yescharacteristic
172D43—81no—
173#529—431no—
174#529D4311yescharacteristic, complemented
175#499—431no—
176#495—431no—
177#488—431no—
178#488—431no—
179#467—431no—
180#466—431no—
181#465—431no—
182#465—431no—
183C4×Q16—431no—
184C4×SD16—431no—
185C4×SD16—431no—
186C4×D8—431no—
187C2×C4×C8—431no—
188C43#316811yescharacteristic, complemented, Sylow
189C2×Q16—431no—
190C2×SD16—431no—
191C2×SD16—431no—
192C2×D8—431no—
193C22×C8—431no—
194C22×C8—431no—
195#126—21no—
196#126—861no—
197#125—431no—
198#125C2×D4311yescharacteristic
199#124—431no—
200#124C2×D4311yescharacteristic
201#123—21no—
202#123—861no—
203C22⋊Q8—431no—
204C22⋊Q8C2×D4311yescharacteristic
205#121—431no—
206#121C2×D4311yescharacteristic
207C4×Q8—431no—
208C4×Q8C2×D4311yescharacteristic
209C4×D4—21no—
210C4×D4—431no—
211C4×D4—861no—
212C4×D4C2×D4311yescharacteristic
213#117—21no—
214#117—861no—
215C2×C42C2×D4311yescharacteristic
216#107—431no—
217#107—431no—
218#106—431no—
219#106—431no—
220#103—431no—
221#103—431no—
222#103—431no—
223#103—431no—
224#102—431no—
225#102—431no—
226#102—431no—
227#102—431no—
228C4×C8—431no—
229C4×C8—431no—
230C4×C8—431no—
231C4×C8—431no—
232C2×Q8—431no—
233C2×Q8C22×D4311yescharacteristic
234C2×D4—21no—
235C2×D4—431no—
236C2×D4—861no—
237C2×D4C22×D4311yescharacteristic
238C22×C4—21no—
239C22×C4—861no—
240C22×C4C22⋊D4311yescharacteristic
241C22×C4C22⋊D4311yescharacteristic
242C22×C4C22×D4311yescharacteristic
243Q16—862no—
244SD16—862no—
245SD16—862no—
246D8—862no—
247C2×C8—431no—
248C2×C8—431no—
249C2×C8—431no—
250C2×C8—431no—
251C2×C8—862no—
252C2×C8—862no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—431no—
258C4⋊C4—431no—
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—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—861no—
271C22⋊C4—861no—
272C22⋊C4—861no—
273C22⋊C4—861no—
274C22⋊C4—861no—
275C42—21no—
276C42—861no—
277C42C22⋊D4311yescharacteristic
278C42C22⋊D4311yescharacteristic
279C42C22×D4311yescharacteristic
280C42C22×D4311yescharacteristic
281C23—21no—
282C23—861no—
283C23C2×C22⋊D4311yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—861no—
287Q8—861no—
288D4—21no—
289D4—21no—
290D4—42no—
291D4—861no—
292D4—861no—
293D4—1722no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—42no—
302C2×C4—861no—
303C2×C4—861no—
304C2×C4—861no—
305C2×C4—1722no—
306C2×C4C2×C22⋊D4311yescharacteristic
307C2×C4C2×C22⋊D4311yescharacteristic
308C2×C4C2×C22⋊D4311yescharacteristic
309C2×C4C2×C22⋊D4311yescharacteristic
310C2×C4C2×C22⋊D4311yescharacteristic
311C2×C4C23×D4311yescharacteristic
312C8—432no—
313C8—432no—
314C8—861no—
315C8—861no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—1721no—
322C22—1721no—
323C22—1721no—
324C22#1306334512yes—
325C22C22×C22⋊D4311yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—1721no—
334C4—1721no—
335C4—1721no—
336C4#1306334512yes—
337C4#41×D4311yescharacteristic
338C4#41×D4311yescharacteristic
339C2—22no—
340C2—81no—
341C2—3441no—
342C2#1458344511yescharacteristic
343C2C2×#1306334511yescharacteristic
344C2C2×#1306334511yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#529C2
socleC22×C43C22×D4
hypercenter#529D43
hypocenterC43#3168
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #14583433C2semidirect
2. #14583298C2semidirect
3. #14583281C2semidirect
4. #14583256C2semidirect
5. #14583253C2semidirect
6. #14583138C2semidirect
8. #14583130C2semidirect
9. #14583126C2semidirect
10. C4×#10621885C2semidirect
11. C4×#10621884C2semidirect
12. C4×#10621883C2semidirect
13. C4×#10621882C2semidirect
14. C2×C4×C43⋊C8C2semidirect
15. C43×#529C2semidirect
174. #529D43semidirect
188. C43#3168semidirect