Finite Group Databasebeta

← #19146580

Subgroups — #19146580

Order 5504.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583558C211yesmaximal, characteristic, complemented
2#14583261C211yesmaximal, characteristic, complemented
3#14583234C211yesmaximal, characteristic, complemented
4#14583212C211yesmaximal, characteristic, complemented
5#14583191C211yesmaximal, characteristic, complemented
6#14583143C211yesmaximal, characteristic, complemented
7#14583133C211yesmaximal, characteristic, complemented
8#14583114C211yesmaximal, characteristic, complemented
9#14583042C211yesmaximal, characteristic, complemented
10#14583037C211yesmaximal, characteristic, complemented
11#14582999C211yesmaximal, characteristic, complemented
12#14582971C211yesmaximal, characteristic, complemented
13#14582898C211yesmaximal, characteristic, complemented
14C2×#13063248C211yesmaximal, characteristic, complemented
15C43×#547C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C22×Dic86C2211yescharacteristic
18C2×#10621883C2211yescharacteristic
19C2×#10621883C2211yescharacteristic
20C2×#10621882C2211yescharacteristic
21C2×#10621877C2211yescharacteristic
22C22×C43⋊C8C2211yescharacteristic
23#13063313C2211yescharacteristic
24#13063311—21no—
25#13063304C2211yescharacteristic
26#13063303—21no—
27#13063299C2211yescharacteristic
28#13063297—21no—
29C4×Dic86C2211yescharacteristic
30(C22⋊D43)⋊C4—21no—
31#13063258C2211yescharacteristic
32#13063258C2211yescharacteristic
33#13063258C2211yescharacteristic
34C4⋊(C43⋊C8)C2211yescharacteristic
35#13063248C2211yescharacteristic
36#13063248C2211yescharacteristic
37#13063248C2211yescharacteristic
38#13063248C2211yescharacteristic
39#13063248C2211yescharacteristic
40#13063248C2211yescharacteristic
41#13063246C2211yescharacteristic
42#13063245C2211yescharacteristic
43#13063245C2211yescharacteristic
44#13063245C2211yescharacteristic
45C22⋊(C43⋊C8)C2211yescharacteristic
46C22⋊(C43⋊C8)C2211yescharacteristic
47#13063236C2211yescharacteristic
48C2×#41×C43—21no—
49C4⋊Q8×C43C2211yescharacteristic
50#123×C43—21no—
51#123×C43—21no—
52C22⋊Q8×C43—21no—
53#121×C43C2211yescharacteristic
54#121×C43C2211yescharacteristic
55C4×D4×C43C2211yescharacteristic
56C4×D4×C43C2211yescharacteristic
57C2×C4⋊C4×C43C2211yescharacteristic
58C2×C4⋊C4×C43C2211yescharacteristic
59#41×C43—44no—
60C2×Q8×C43—21no—
61C2×D4×C43—21no—
62C2×D4×C43—21no—
63C2×D4×C43D411yescharacteristic
64C2×D4×C43C2311yescharacteristic
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43C2311yescharacteristic
69C22×C4×C43C2311yescharacteristic
70C2×C22⋊D43—21no—
71C2×C22⋊D43—21no—
72C22×Dic43—21no—
73#10621898—22no—
74#10621898—41no—
75C2×D172C2311yescharacteristic
76C2×C4×D43—21no—
77C2×Dic86—22no—
78C2×Dic86—21no—
79C2×Dic86—41no—
80C2×Dic86C2311yescharacteristic
81C2×Dic86C2311yescharacteristic
82C4⋊C4×C43—21no—
83C4⋊C4×C43—21no—
84C4⋊C4×C43—21no—
85C4⋊C4×C43D411yescharacteristic
86C4⋊C4×C43C2311yescharacteristic
87C4⋊C4×C43C2311yescharacteristic
88C4⋊C4×C43C2311yescharacteristic
89C22⋊C4×C43—21no—
90C22⋊C4×C43—21no—
91C22⋊C4×C43—21no—
92C22⋊C4×C43D411yescharacteristic
93C22⋊C4×C43D411yescharacteristic
94C42×C43C2311yescharacteristic
95C22⋊Dic43—21no—
96#10621883—22no—
97#10621883—41no—
98#10621882—41no—
99(C2×D43)⋊C4—21no—
100(C2×D43)⋊C4—21no—
101(C2×D43)⋊C4—21no—
102C4⋊Dic43C2311yescharacteristic
103Dic43⋊C4—21no—
104Dic43⋊C4—21no—
105C4×Dic43—21no—
106#10621877—41no—
107C2×C43⋊C8—41no—
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111C2×C43⋊C8C2311yescharacteristic
112C23×C43—21no—
113C23×C43C2×D411yescharacteristic
114C23×C43C2×D411yescharacteristic
115C22×D43—21no—
116Q8×C43—42no—
117D4×C43—22no—
118D4×C43—21no—
119D4×C43—21no—
120D4×C43—42no—
121D4×C43—42no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—42no—
130C2×C4×C43—42no—
131C2×C4×C43—42no—
132C2×C4×C43C2×D411yescharacteristic
133C2×C4×C43C2×D411yescharacteristic
134C2×C4×C43C2×D411yescharacteristic
135C2×C4×C43C2×D411yescharacteristic
136C2×C4×C43C2411yescharacteristic
137C22⋊D43—42no—
138C22⋊D43—42no—
139C2×Dic43—21no—
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43—42no—
143D172—21no—
144D172—21no—
145C4×D43—42no—
146Dic86—21no—
147Dic86—21no—
148Dic86—21no—
149Dic86—42no—
150Dic86#4112yescomplemented
151C43⋊C8—21no—
152C43⋊C8—21no—
153C43⋊C8—21no—
154C43⋊C8—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—41no—
161C22×C43—41no—
162C22×C43—41no—
163C22×C43AGL(1,ℤ/8)12yes—
164C22×C43C22×D411yescharacteristic
165C2×D43—41no—
166C2×D43—41no—
167C2×D43—41no—
168C4×C43—21no—
169C4×C43—21no—
170C4×C43—21no—
171C4×C43—21no—
172C4×C43—41no—
173C4×C43—41no—
174C4×C43—41no—
175C4×C43C2×#4111yescharacteristic
176C4×C43H(5,𝔽2)11yescharacteristic
177Dic43—22no—
178Dic43—41no—
179Dic43—41no—
180#3308—431nomaximal, Sylow
181C2×C43—22no—
182C2×C43—41no—
183C2×C43—81no—
184C2×C43#54611yescharacteristic
185C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
186C2×C43#57811yescharacteristic
187D43—81no—
188#548—431no—
189#547D4311yescharacteristic, complemented
190#489—431no—
191#484—431no—
192#480—431no—
193#477—431no—
194#468—431no—
195#466—431no—
196#463—431no—
197#449—431no—
198#448—431no—
199#440—431no—
200#435—431no—
201#417—431no—
202C2×#103—431no—
203C43#330811yescharacteristic, complemented, Sylow
204C2×#41—21no—
205C2×#41—431no—
206C22×Q8—431no—
207C2×SD16—431no—
208C2×SD16—431no—
209C2×D8—431no—
210C2×M16—431no—
211C22×C8—431no—
212C4⋊Q8C2×D4311yescharacteristic
213#124—431no—
214#124—861no—
215#123—21no—
216#123—21no—
217C22⋊Q8—21no—
218C22⋊Q8—431no—
219C22⋊Q8—861no—
220#121—431no—
221#121—861no—
222#121C2×D4311yescharacteristic
223#121C2×D4311yescharacteristic
224C4×Q8—431no—
225C4×D4—861no—
226C4×D4C2×D4311yescharacteristic
227C4×D4C2×D4311yescharacteristic
228C2×C4⋊C4C2×D4311yescharacteristic
229C2×C4⋊C4C2×D4311yescharacteristic
230#107—431no—
231#107—431no—
232#107—431no—
233C4⋊C8—431no—
234#103—431no—
235#103—431no—
236#103—431no—
237#103—431no—
238#103—431no—
239#103—431no—
240#102—431no—
241#102—431no—
242#102—431no—
243#102—431no—
244C22⋊C8—431no—
245C22⋊C8—431no—
246#97—431no—
247#41—44no—
248#41—862no—
249#41—1721no—
250C2×Q8—21no—
251C2×Q8—431no—
252C2×Q8—431no—
253C2×Q8—862no—
254C2×Q8—861no—
255C2×Q8—1721no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—431no—
259C2×D4—861no—
260C2×D4—861no—
261C2×D4C22⋊D4311yescharacteristic
262C2×D4C22×D4311yescharacteristic
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—861no—
267C22×C4—861no—
268C22×C4C22×D4311yescharacteristic
269C22×C4C22×D4311yescharacteristic
270SD16—862no—
271SD16—1721no—
272D8—1721no—
273M16—1721no—
274C2×C8—431no—
275C2×C8—431no—
276C2×C8—431no—
277C2×C8—431no—
278C2×C8—1721no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—431no—
283C4⋊C4—861no—
284C4⋊C4—861no—
285C4⋊C4C22⋊D4311yescharacteristic
286C4⋊C4C22×D4311yescharacteristic
287C4⋊C4C22×D4311yescharacteristic
288C4⋊C4C22×D4311yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C22⋊C4—861no—
295C22⋊C4—861no—
296C22⋊C4C22⋊D4311yescharacteristic
297C22⋊C4C22⋊D4311yescharacteristic
298C42—861no—
299C42C22×D4311yescharacteristic
300C23—21no—
301C23—861no—
302C23C2×C22⋊D4311yescharacteristic
303C23C2×C22⋊D4311yescharacteristic
304Q8—42no—
305Q8—432no—
306Q8—861no—
307Q8—861no—
308Q8—861no—
309Q8—1722no—
310D4—22no—
311D4—21no—
312D4—21no—
313D4—42no—
314D4—42no—
315D4—861no—
316D4—861no—
317D4—1722no—
318D4—1722no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—861no—
330C2×C4—861no—
331C2×C4—861no—
332C2×C4—1722no—
333C2×C4—1722no—
334C2×C4C2×C22⋊D4311yescharacteristic
335C2×C4C2×C22⋊D4311yescharacteristic
336C2×C4C2×C22⋊D4311yescharacteristic
337C2×C4C2×C22⋊D4311yescharacteristic
338C2×C4C23×D4311yescharacteristic
339C8—861no—
340C8—861no—
341C8—861no—
342C8—861no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—1721no—
352C22—1721no—
353C22—1721no—
354C22#1306335112yes—
355C22C22×C22⋊D4311yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—41no—
363C4—862no—
364C4—1721no—
365C4—1721no—
366C4#41×D4311yescharacteristic
367C4#1306337111yescharacteristic
368C2—22no—
369C2—41no—
370C2—81no—
371C2—3441no—
372C2#1458353711yescharacteristic
373C2C2×#1306335111yescharacteristic
374C2#1458371411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#547C2
socleC22×C43C22×D4
hypercenter#547D43
hypocenterC43#3308
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #14583558C2semidirect
2. #14583261C2semidirect
3. #14583234C2semidirect
4. #14583212C2semidirect
5. #14583191C2semidirect
6. #14583143C2semidirect
7. #14583133C2semidirect
8. #14583114C2semidirect
9. #14583042C2semidirect
10. #14583037C2semidirect
11. #14582999C2semidirect
12. #14582971C2semidirect
13. #14582898C2semidirect
14. C2×#13063248C2semidirect
15. C43×#547C2semidirect
150. Dic86#41semidirect
189. #547D43semidirect
203. C43#3308semidirect