Finite Group Databasebeta

← #19147059

Subgroups — #19147059

Order 5504.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583553C211yesmaximal, characteristic, complemented
2#14583309C211yesmaximal, characteristic, complemented
3#14583223C211yesmaximal, characteristic, complemented
4#14583217C211yesmaximal, characteristic, complemented
5#14583215C211yesmaximal, characteristic, complemented
6#14583210C211yesmaximal, characteristic, complemented
7#14583196C211yesmaximal, characteristic, complemented
8#14583189C211yesmaximal, characteristic, complemented
9#14583150C211yesmaximal, characteristic, complemented
10#14583133C211yesmaximal, characteristic, complemented
11#14583009C211yesmaximal, characteristic, complemented
12#14582971C211yesmaximal, characteristic, complemented
13#14582942C211yesmaximal, characteristic, complemented
14C2×#13063256C211yesmaximal, characteristic, complemented
15C43×#553C211yesmaximal, characteristic, complemented
16C2×#10621900—21no—
17C2×#10621882C2211yescharacteristic
18C2×#10621877C2211yescharacteristic
19C22×C43⋊C8C2211yescharacteristic
20#13063325C2211yescharacteristic
21#13063309—21no—
22#13063309—21no—
23#13063305—21no—
24#13063299C2211yescharacteristic
25#13063299C2211yescharacteristic
26C4×D172C2211yescharacteristic
27C2×C4⋊Dic43C2211yescharacteristic
28C2×C4⋊Dic43C2211yescharacteristic
29#13063258C2211yescharacteristic
30#13063258C2211yescharacteristic
31#13063258C2211yescharacteristic
32#13063256C2211yescharacteristic
33#13063256C2211yescharacteristic
34#13063256C2211yescharacteristic
35#13063256C2211yescharacteristic
36#13063256C2211yescharacteristic
37#13063256C2211yescharacteristic
38C4⋊(C43⋊C8)C2211yescharacteristic
39#13063246C2211yescharacteristic
40#13063246C2211yescharacteristic
41#13063246C2211yescharacteristic
42#13063245C2211yescharacteristic
43#13063245C2211yescharacteristic
44#13063245C2211yescharacteristic
45C22⋊(C43⋊C8)C2211yescharacteristic
46C22⋊(C43⋊C8)C2211yescharacteristic
47#13063236C2211yescharacteristic
48#126×C43—21no—
49#125×C43C2211yescharacteristic
50#123×C43—21no—
51#121×C43—21no—
52#121×C43C2211yescharacteristic
53#121×C43C2211yescharacteristic
54C4×D4×C43—21no—
55C4×D4×C43C2211yescharacteristic
56C4×D4×C43C2211yescharacteristic
57#117×C43C2211yescharacteristic
58C2×C4⋊C4×C43C2211yescharacteristic
59C2×D4×C43—21no—
60C2×D4×C43—21no—
61C2×D4×C43D411yescharacteristic
62C2×D4×C43C2311yescharacteristic
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43C2311yescharacteristic
66C22×C4×C43C2311yescharacteristic
67C2×C22⋊D43—21no—
68C2×C22⋊D43—21no—
69C22×Dic43—21no—
70C22×Dic43—21no—
71#10621900—44no—
72C2×D172C2311yescharacteristic
73C2×C4×D43—21no—
74C2×Dic86—21no—
75C4⋊C4×C43—21no—
76C4⋊C4×C43—21no—
77C4⋊C4×C43—21no—
78C4⋊C4×C43D411yescharacteristic
79C4⋊C4×C43C2311yescharacteristic
80C4⋊C4×C43C2311yescharacteristic
81C4⋊C4×C43C2311yescharacteristic
82C22⋊C4×C43—21no—
83C22⋊C4×C43—21no—
84C22⋊C4×C43—21no—
85C22⋊C4×C43—21no—
86C22⋊C4×C43D411yescharacteristic
87C22⋊C4×C43D411yescharacteristic
88C42×C43—21no—
89C42×C43C2311yescharacteristic
90#10621882—22no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94C4⋊Dic43—21no—
95C4⋊Dic43—21no—
96C4⋊Dic43—21no—
97C4⋊Dic43C2311yescharacteristic
98C4⋊Dic43C2311yescharacteristic
99C4⋊Dic43C2311yescharacteristic
100#10621877—22no—
101C2×C43⋊C8—22no—
102C2×C43⋊C8C2311yescharacteristic
103C2×C43⋊C8C2311yescharacteristic
104C2×C43⋊C8C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106C23×C43—21no—
107C23×C43C2×D411yescharacteristic
108C23×C43C2×D411yescharacteristic
109C22×D43—21no—
110D4×C43—22no—
111D4×C43—21no—
112D4×C43—21no—
113D4×C43—42no—
114D4×C43—81no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—81no—
123C2×C4×C43—81no—
124C2×C4×C43C2×D411yescharacteristic
125C2×C4×C43C2×D411yescharacteristic
126C2×C4×C43C2×D411yescharacteristic
127C2×C4×C43C2×D411yescharacteristic
128C2×C4×C43C2411yescharacteristic
129C22⋊D43—42no—
130C22⋊D43—42no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—42no—
135C2×Dic43—42no—
136D172—21no—
137D172—21no—
138C4×D43—42no—
139Dic86—42no—
140C43⋊C8—21no—
141C43⋊C8—21no—
142C43⋊C8—21no—
143C43⋊C8#4112yescomplemented
144C22×C43—21no—
145C22×C43—21no—
146C22×C43—21no—
147C22×C43—21no—
148C22×C43—21no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43AGL(1,ℤ/8)12yes—
153C22×C43C22×D411yescharacteristic
154C2×D43—41no—
155C2×D43—41no—
156C2×D43—41no—
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—41no—
162C4×C43—41no—
163C4×C43—41no—
164C4×C43C2×#4111yescharacteristic
165C4×C432−1+411yescharacteristic
166Dic43—41no—
167Dic43—41no—
168Dic43—41no—
169#3345—431nomaximal, Sylow
170C2×C43—22no—
171C2×C43—41no—
172C2×C43—81no—
173C2×C43#54711yescharacteristic
174C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
175C2×C43#57711yescharacteristic
176D43—81no—
177#553D4311yescharacteristic, complemented
178#547—431no—
179#501—431no—
180#482—431no—
181#481—431no—
182#481—431no—
183#480—431no—
184#478—431no—
185#476—431no—
186#469—431no—
187#466—431no—
188#442—431no—
189#435—431no—
190#428—431no—
191C2×#106—431no—
192C43#334511yescharacteristic, complemented, Sylow
193C2×#41—861no—
194C2×D8—431no—
195C2×M16—431no—
196C22×C8—431no—
197C4⋊Q8—431no—
198#126—21no—
199#125C2×D4311yescharacteristic
200#123—21no—
201#123—861no—
202#123—861no—
203C22⋊Q8—861no—
204#121—21no—
205#121—431no—
206#121—431no—
207#121C2×D4311yescharacteristic
208#121C2×D4311yescharacteristic
209C4×D4—21no—
210C4×D4—431no—
211C4×D4C2×D4311yescharacteristic
212C4×D4C2×D4311yescharacteristic
213#117C2×D4311yescharacteristic
214C2×C4⋊C4—431no—
215C2×C4⋊C4—431no—
216C2×C4⋊C4C2×D4311yescharacteristic
217#107—431no—
218#107—431no—
219#107—431no—
220#106—431no—
221#106—431no—
222#106—431no—
223#106—431no—
224#106—431no—
225#106—431no—
226C4⋊C8—431no—
227#102—431no—
228#102—431no—
229#102—431no—
230#102—431no—
231#102—431no—
232#102—431no—
233C22⋊C8—431no—
234C22⋊C8—431no—
235#97—431no—
236#41—1724no—
237C2×Q8—861no—
238C2×D4—21no—
239C2×D4—21no—
240C2×D4—431no—
241C2×D4—861no—
242C2×D4—861no—
243C2×D4C22⋊D4311yescharacteristic
244C2×D4C22×D4311yescharacteristic
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—861no—
248C22×C4—861no—
249C22×C4—861no—
250C22×C4C22×D4311yescharacteristic
251C22×C4C22×D4311yescharacteristic
252D8—862no—
253M16—862no—
254C2×C8—431no—
255C2×C8—431no—
256C2×C8—431no—
257C2×C8—431no—
258C2×C8—862no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—431no—
263C4⋊C4—431no—
264C4⋊C4—431no—
265C4⋊C4—861no—
266C4⋊C4—861no—
267C4⋊C4—861no—
268C4⋊C4C22⋊D4311yescharacteristic
269C4⋊C4C22×D4311yescharacteristic
270C4⋊C4C22×D4311yescharacteristic
271C4⋊C4C22×D4311yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—861no—
277C22⋊C4—861no—
278C22⋊C4—861no—
279C22⋊C4C22⋊D4311yescharacteristic
280C22⋊C4C22⋊D4311yescharacteristic
281C42—21no—
282C42C22×D4311yescharacteristic
283C23—21no—
284C23—861no—
285C23C2×C22⋊D4311yescharacteristic
286C23C2×C22⋊D4311yescharacteristic
287Q8—1722no—
288D4—22no—
289D4—21no—
290D4—21no—
291D4—42no—
292D4—81no—
293D4—861no—
294D4—861no—
295D4—1722no—
296D4—1722no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—861no—
307C2×C4—861no—
308C2×C4—861no—
309C2×C4—1722no—
310C2×C4—1722no—
311C2×C4—1722no—
312C2×C4C2×C22⋊D4311yescharacteristic
313C2×C4C2×C22⋊D4311yescharacteristic
314C2×C4C2×C22⋊D4311yescharacteristic
315C2×C4C2×C22⋊D4311yescharacteristic
316C2×C4C23×D4311yescharacteristic
317C8—432no—
318C8—861no—
319C8—861no—
320C8—861no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—1721no—
330C22—1721no—
331C22—1721no—
332C22#1306335012yes—
333C22C22×C22⋊D4311yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—1721no—
342C4—1721no—
343C4—1721no—
344C4#41×D4311yescharacteristic
345C4#1306337211yescharacteristic
346C2—22no—
347C2—41no—
348C2—81no—
349C2—3441no—
350C2#1458354811yescharacteristic
351C2C2×#1306335011yescharacteristic
352C2#1458371011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#553C2
socleC22×C43C22×D4
hypercenter#553D43
hypocenterC43#3345
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #14583553C2semidirect
2. #14583309C2semidirect
3. #14583223C2semidirect
4. #14583217C2semidirect
5. #14583215C2semidirect
6. #14583210C2semidirect
7. #14583196C2semidirect
8. #14583189C2semidirect
9. #14583150C2semidirect
10. #14583133C2semidirect
11. #14583009C2semidirect
12. #14582971C2semidirect
13. #14582942C2semidirect
14. C2×#13063256C2semidirect
15. C43×#553C2semidirect
143. C43⋊C8#41semidirect
177. #553D43semidirect
192. C43#3345semidirect