Finite Group Databasebeta

← #19146700

Subgroups — #19146700

Order 5504.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583558C211yesmaximal, characteristic
2#14583261C211yesmaximal, characteristic, complemented
3#14583229C211yesmaximal, characteristic, complemented
4#14583217C211yesmaximal, characteristic, complemented
5#14583181C211yesmaximal, characteristic, complemented
6#14583155C211yesmaximal, characteristic, complemented
7#14583130C211yesmaximal, characteristic, complemented
8#14583121C211yesmaximal, characteristic, complemented
9#14583059C211yesmaximal, characteristic, complemented
10#14583054C211yesmaximal, characteristic, complemented
11#14583004C211yesmaximal, characteristic, complemented
12#14582971C211yesmaximal, characteristic, complemented
13#14582898C211yesmaximal, characteristic, complemented
14C2×#13063248C211yesmaximal, characteristic, complemented
15C43×#554C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C22×Dic86C2211yescharacteristic
18C2×#10621885C2211yescharacteristic
19C2×#10621885C2211yescharacteristic
20C2×#10621884C2211yescharacteristic
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#13063256C2211yescharacteristic
32#13063256C2211yescharacteristic
33#13063256C2211yescharacteristic
34C4⋊(C43⋊C8)C2211yescharacteristic
35#13063249C2211yescharacteristic
36#13063248C2211yescharacteristic
37#13063248C2211yescharacteristic
38#13063248C2211yescharacteristic
39#13063248C2211yescharacteristic
40#13063248C2211yescharacteristic
41#13063248C2211yescharacteristic
42#13063245C2211yescharacteristic
43#13063245C2211yescharacteristic
44#13063245C2211yescharacteristic
45C22⋊(C43⋊C8)C2211yescharacteristic
46C22⋊(C43⋊C8)C2211yescharacteristic
47#13063236C2211yescharacteristic
48C4⋊Q8×C43C2211yescharacteristic
49#125×C43—21no—
50C22⋊Q8×C43—21no—
51C22⋊Q8×C43—21no—
52C22⋊Q8×C43C2211yescharacteristic
53C22⋊Q8×C43C2211yescharacteristic
54C4×Q8×C43C2211yescharacteristic
55C4×D4×C43—21no—
56C4×D4×C43C2211yescharacteristic
57C2×C4⋊C4×C43C2211yescharacteristic
58C2×C4⋊C4×C43C2211yescharacteristic
59C2×Q8×C43—21no—
60C2×Q8×C43C2311yescharacteristic
61C2×D4×C43D411yescharacteristic
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43C2311yescharacteristic
65C22×C4×C43C2311yescharacteristic
66C2×C22⋊D43—21no—
67C2×C22⋊D43—21no—
68C22×Dic43—21no—
69#10621898—22no—
70#10621898—41no—
71C2×D172C2311yescharacteristic
72C2×C4×D43—21no—
73C2×Dic86—22no—
74C2×Dic86—21no—
75C2×Dic86—41no—
76C2×Dic86C2311yescharacteristic
77C2×Dic86C2311yescharacteristic
78C4⋊C4×C43—21no—
79C4⋊C4×C43—21no—
80C4⋊C4×C43—21no—
81C4⋊C4×C43—21no—
82C4⋊C4×C43—21no—
83C4⋊C4×C43—21no—
84C4⋊C4×C43D411yescharacteristic
85C4⋊C4×C43C2311yescharacteristic
86C4⋊C4×C43C2311yescharacteristic
87C4⋊C4×C43C2311yescharacteristic
88C22⋊C4×C43—21no—
89C22⋊C4×C43—21no—
90C22⋊C4×C43D411yescharacteristic
91C22⋊C4×C43D411yescharacteristic
92C42×C43—21no—
93C42×C43C2311yescharacteristic
94C22⋊Dic43—21no—
95#10621885—22no—
96#10621885—41no—
97#10621884—41no—
98(C2×D43)⋊C4—21no—
99(C2×D43)⋊C4—21no—
100(C2×D43)⋊C4—21no—
101C4⋊Dic43C2311yescharacteristic
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104C4×Dic43—21no—
105#10621877—41no—
106C2×C43⋊C8—41no—
107C2×C43⋊C8C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111C23×C43C2×D411yescharacteristic
112C23×C43C2×D411yescharacteristic
113C22×D43—21no—
114Q8×C43—21no—
115Q8×C43—21no—
116Q8×C43—81no—
117D4×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—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—81no—
127C2×C4×C43—81no—
128C2×C4×C43C2×D411yescharacteristic
129C2×C4×C43C2×D411yescharacteristic
130C2×C4×C43C2×D411yescharacteristic
131C2×C4×C43C2×D411yescharacteristic
132C2×C4×C43C2411yescharacteristic
133C22⋊D43—42no—
134C22⋊D43—42no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—21no—
138C2×Dic43—42no—
139D172—21no—
140D172—21no—
141C4×D43—42no—
142Dic86—21no—
143Dic86—21no—
144Dic86—21no—
145Dic86—42no—
146Dic86#4112yes—
147C43⋊C8—21no—
148C43⋊C8—21no—
149C43⋊C8—21no—
150C43⋊C8—21no—
151C22×C43—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—21no—
156C22×C43#13712yes—
157C22×C43C22×D411yescharacteristic
158C2×D43—41no—
159C2×D43—41no—
160C2×D43—41no—
161C4×C43—21no—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—21no—
165C4×C43—41no—
166C4×C43—41no—
167C4×C43—41no—
168C4×C43—41no—
169C4×C43C2×#4111yescharacteristic
170C4×C43H(5,𝔽2)11yescharacteristic
171Dic43—22no—
172Dic43—41no—
173Dic43—41no—
174#3316—431nomaximal, Sylow
175C2×C43—22no—
176C2×C43—41no—
177C2×C43#54611yescharacteristic
178C2×C43C2×#13711yescharacteristic
179C2×C43#57711yescharacteristic
180D43—81no—
181#554D4311yescharacteristic, complemented
182#548—431no—
183#489—431no—
184#483—431no—
185#481—431no—
186#475—431no—
187#470—431no—
188#465—431no—
189#464—431no—
190#452—431no—
191#451—431no—
192#441—431no—
193#435—431no—
194#417—431no—
195C2×#103—431no—
196C43#331611yescharacteristic, complemented, Sylow
197C2×#41—431no—
198C22×Q8—431no—
199C2×Q16—431no—
200C2×Q16—431no—
201C2×SD16—431no—
202C2×M16—431no—
203C22×C8—431no—
204C4⋊Q8C2×D4311yescharacteristic
205#125—21no—
206#124—431no—
207#124—861no—
208C22⋊Q8—21no—
209C22⋊Q8—21no—
210C22⋊Q8—431no—
211C22⋊Q8—861no—
212C22⋊Q8C2×D4311yescharacteristic
213C22⋊Q8C2×D4311yescharacteristic
214#121—431no—
215#121—861no—
216C4×Q8—431no—
217C4×Q8C2×D4311yescharacteristic
218C4×D4—21no—
219C4×D4—861no—
220C4×D4C2×D4311yescharacteristic
221C2×C4⋊C4C2×D4311yescharacteristic
222C2×C4⋊C4C2×D4311yescharacteristic
223#106—431no—
224#106—431no—
225#106—431no—
226C4⋊C8—431no—
227#103—431no—
228#103—431no—
229#103—431no—
230#103—431no—
231#103—431no—
232#103—431no—
233#103—431no—
234#102—431no—
235#102—431no—
236#102—431no—
237C22⋊C8—431no—
238C22⋊C8—431no—
239#97—431no—
240#41—862no—
241#41—1721no—
242C2×Q8—21no—
243C2×Q8—431no—
244C2×Q8—431no—
245C2×Q8—862no—
246C2×Q8—861no—
247C2×Q8—1721no—
248C2×Q8C22×D4311yescharacteristic
249C2×D4—431no—
250C2×D4—861no—
251C2×D4—861no—
252C2×D4C22⋊D4311yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—861no—
256C22×C4—861no—
257C22×C4C22×D4311yescharacteristic
258C22×C4C22×D4311yescharacteristic
259Q16—862no—
260Q16—1721no—
261SD16—1721no—
262M16—1721no—
263C2×C8—431no—
264C2×C8—431no—
265C2×C8—431no—
266C2×C8—431no—
267C2×C8—1721no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—431no—
275C4⋊C4—861no—
276C4⋊C4—861no—
277C4⋊C4C22⋊D4311yescharacteristic
278C4⋊C4C22×D4311yescharacteristic
279C4⋊C4C22×D4311yescharacteristic
280C4⋊C4C22×D4311yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—861no—
284C22⋊C4—861no—
285C22⋊C4—861no—
286C22⋊C4—861no—
287C22⋊C4C22⋊D4311yescharacteristic
288C22⋊C4C22⋊D4311yescharacteristic
289C42—21no—
290C42—861no—
291C42C22×D4311yescharacteristic
292C23—861no—
293C23C2×C22⋊D4311yescharacteristic
294C23C2×C22⋊D4311yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—81no—
298Q8—432no—
299Q8—861no—
300Q8—861no—
301Q8—861no—
302Q8—1722no—
303D4—22no—
304D4—861no—
305D4—861no—
306D4—1722no—
307D4—1722no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—861no—
319C2×C4—861no—
320C2×C4—861no—
321C2×C4—1722no—
322C2×C4—1722no—
323C2×C4C2×C22⋊D4311yescharacteristic
324C2×C4C2×C22⋊D4311yescharacteristic
325C2×C4C2×C22⋊D4311yescharacteristic
326C2×C4C2×C22⋊D4311yescharacteristic
327C2×C4C23×D4311yescharacteristic
328C8—861no—
329C8—861no—
330C8—861no—
331C8—861no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—1721no—
338C22—1721no—
339C22—1721no—
340C22#1306335612yes—
341C22C22×C22⋊D4311yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—862no—
351C4—1721no—
352C4—1721no—
353C4#41×D4311yescharacteristic
354C4#1306337111yescharacteristic
355C2—22no—
356C2—41no—
357C2—3441no—
358C2#1458353711yescharacteristic
359C2C2×#1306335611yescharacteristic
360C2#1458371011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#554C2
socleC22×C43C22×D4
hypercenter#554D43
hypocenterC43#3316
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #554

Complements

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

NH ≅ G/Ntype
2. #14583261C2semidirect
3. #14583229C2semidirect
4. #14583217C2semidirect
5. #14583181C2semidirect
6. #14583155C2semidirect
7. #14583130C2semidirect
8. #14583121C2semidirect
9. #14583059C2semidirect
10. #14583054C2semidirect
11. #14583004C2semidirect
12. #14582971C2semidirect
13. #14582898C2semidirect
14. C2×#13063248C2semidirect
15. C43×#554C2semidirect
181. #554D43semidirect
196. C43#3316semidirect