Finite Group Databasebeta

← #19145280

Subgroups — #19145280

Order 5504.

374 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583520C211yesmaximal, characteristic, complemented
2#14583309C211yesmaximal, characteristic, complemented
3#14583286C211yesmaximal, characteristic, complemented
4#14583256C211yesmaximal, characteristic, complemented
5#14583245C211yesmaximal, characteristic, complemented
6#14583150C211yesmaximal, characteristic, complemented
7#14583143C211yesmaximal, characteristic, complemented
8#14583133C211yesmaximal, characteristic, complemented
9#14583126C211yesmaximal, characteristic, complemented
10#14583009C211yesmaximal, characteristic, complemented
11#14582999C211yesmaximal, characteristic, complemented
12C4×#10621883C211yesmaximal, characteristic, complemented
13C4×#10621882C211yesmaximal, characteristic, complemented
14#14582855C211yesmaximal, characteristic, complemented
15C43×#540C211yesmaximal, characteristic, complemented
16C2×#10621883C2211yescharacteristic
17C2×#10621883C2211yescharacteristic
18C2×#10621882C2211yescharacteristic
19C2×#10621882C2211yescharacteristic
20C2×#10621877C2211yescharacteristic
21C22×C43⋊C8C2211yescharacteristic
22#13063325C2211yescharacteristic
23#13063320—21no—
24#13063313C2211yescharacteristic
25#13063311—21no—
26#13063307—21no—
27#13063304C2211yescharacteristic
28#13063303—21no—
29#13063299C2211yescharacteristic
30C4×Dic86C2211yescharacteristic
31C4×D172C2211yescharacteristic
32#13063258C2211yescharacteristic
33#13063258C2211yescharacteristic
34#13063256C2211yescharacteristic
35#13063256C2211yescharacteristic
36#13063248C2211yescharacteristic
37#13063248C2211yescharacteristic
38#13063246C2211yescharacteristic
39#13063246C2211yescharacteristic
40#13063246C2211yescharacteristic
41#13063246C2211yescharacteristic
42#13063245C2211yescharacteristic
43#13063245C2211yescharacteristic
44#13063236C2211yescharacteristic
45#13063236C2211yescharacteristic
46C4×C43⋊C8C2211yescharacteristic
47C4×C43⋊C8C2211yescharacteristic
48#127×C43C2211yescharacteristic
49#125×C43C2211yescharacteristic
50#123×C43—21no—
51#123×C43—21no—
52#121×C43—21no—
53#121×C43—21no—
54#121×C43C2211yescharacteristic
55#121×C43C2211yescharacteristic
56C4×D4×C43C2211yescharacteristic
57C4×D4×C43C2211yescharacteristic
58#117×C43C2211yescharacteristic
59C2×D4×C43—21no—
60C2×D4×C43—21no—
61C2×D4×C43—21no—
62C2×D4×C43—21no—
63C2×D4×C43C2311yescharacteristic
64C2×D4×C43C2311yescharacteristic
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43C2311yescharacteristic
68C2×C22⋊D43—21no—
69C2×D172C2311yescharacteristic
70C2×C4×D43—21no—
71C2×Dic86—21no—
72C2×Dic86C2311yescharacteristic
73C4⋊C4×C43—21no—
74C4⋊C4×C43—21no—
75C4⋊C4×C43D411yescharacteristic
76C4⋊C4×C43D411yescharacteristic
77C4⋊C4×C43C2311yescharacteristic
78C4⋊C4×C43C2311yescharacteristic
79C22⋊C4×C43—21no—
80C22⋊C4×C43—21no—
81C22⋊C4×C43—21no—
82C22⋊C4×C43—21no—
83C22⋊C4×C43D411yescharacteristic
84C22⋊C4×C43D411yescharacteristic
85C42×C43C2311yescharacteristic
86C42×C43C2311yescharacteristic
87C22⋊Dic43—21no—
88#10621883—22no—
89#10621883—22no—
90#10621882—22no—
91#10621882—22no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4—21no—
96C4⋊Dic43—21no—
97C4⋊Dic43C2311yescharacteristic
98C4⋊Dic43C2311yescharacteristic
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101C4×Dic43—21no—
102#10621877—22no—
103C2×C43⋊C8—22no—
104C2×C43⋊C8C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108C23×C43—21no—
109C23×C43—21no—
110C23×C43C2×D411yescharacteristic
111C22×D43—21no—
112D4×C43—21no—
113D4×C43—21no—
114D4×C43—21no—
115D4×C43—21no—
116D4×C43—81no—
117D4×C43—81no—
118D4×C43—81no—
119D4×C43—81no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—81no—
125C2×C4×C43—81no—
126C2×C4×C43C2×D411yescharacteristic
127C2×C4×C43C2×D411yescharacteristic
128C2×C4×C43C2×D411yescharacteristic
129C2×C4×C43C2×D411yescharacteristic
130C2×C4×C43C2×D411yescharacteristic
131C2×C4×C43C2411yescharacteristic
132C22⋊D43—81no—
133C2×Dic43—21no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136D172—21no—
137D172—21no—
138C4×D43—81no—
139Dic86—21no—
140Dic86—21no—
141Dic86—81no—
142C43⋊C8—21no—
143C43⋊C8—21no—
144C43⋊C8#4112yes—
145C43⋊C8#4112yes—
146C22×C43—21no—
147C22×C43—21no—
148C22×C43—21no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43—41no—
153C22×C43—41no—
154C22×C43—41no—
155C22×C43C22×D411yescharacteristic
156C2×D43—41no—
157C2×D43—41no—
158C2×D43—41no—
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—21no—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—41no—
165C4×C43—41no—
166C4×C43C2×#4111yescharacteristic
167C4×C43C2×#4111yescharacteristic
168Dic43—41no—
169Dic43—41no—
170Dic43—41no—
171#3179—431nomaximal, Sylow
172C2×C43—41no—
173C2×C43—81no—
174C2×C43—81no—
175C2×C43#53211yescharacteristic
176C2×C43#57611yescharacteristic
177C2×C43#57711yescharacteristic
178D43—81no—
179#542—431no—
180#540D4311yescharacteristic, complemented
181#501—431no—
182#496—431no—
183#488—431no—
184#486—431no—
185#469—431no—
186#468—431no—
187#466—431no—
188#465—431no—
189#442—431no—
190#440—431no—
191C4×SD16—431no—
192C4×D8—431no—
193#405—431no—
194C43#317911yescharacteristic, complemented, Sylow
195C2×SD16—431no—
196C2×SD16—431no—
197C2×D8—431no—
198C2×D8—431no—
199C2×M16—431no—
200C22×C8—431no—
201C4⋊Q8—431no—
202#127C2×D4311yescharacteristic
203#126—861no—
204#125C2×D4311yescharacteristic
205#124—431no—
206#124—861no—
207#123—21no—
208#123—21no—
209#123—861no—
210C22⋊Q8—431no—
211C22⋊Q8—861no—
212#121—21no—
213#121—21no—
214#121—431no—
215#121C2×D4311yescharacteristic
216#121C2×D4311yescharacteristic
217C4×Q8—431no—
218C4×D4—431no—
219C4×D4C2×D4311yescharacteristic
220C4×D4C2×D4311yescharacteristic
221#117C2×D4311yescharacteristic
222#107—431no—
223#107—431no—
224#106—431no—
225#106—431no—
226#103—431no—
227#103—431no—
228#102—431no—
229#102—431no—
230#102—431no—
231#102—431no—
232#102—431no—
233#102—431no—
234#97—431no—
235#97—431no—
236C4×C8—431no—
237C4×C8—431no—
238C2×Q8—431no—
239C2×Q8—861no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—431no—
245C2×D4—861no—
246C2×D4C22×D4311yescharacteristic
247C2×D4C22×D4311yescharacteristic
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—861no—
251C22×C4C22×D4311yescharacteristic
252SD16—862no—
253SD16—862no—
254D8—862no—
255D8—862no—
256M16—862no—
257C2×C8—431no—
258C2×C8—431no—
259C2×C8—431no—
260C2×C8—431no—
261C2×C8—862no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—431no—
265C4⋊C4—431no—
266C4⋊C4—861no—
267C4⋊C4—861no—
268C4⋊C4—861no—
269C4⋊C4C22⋊D4311yescharacteristic
270C4⋊C4C22⋊D4311yescharacteristic
271C4⋊C4C22×D4311yescharacteristic
272C4⋊C4C22×D4311yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—861no—
278C22⋊C4—861no—
279C22⋊C4—861no—
280C22⋊C4—861no—
281C22⋊C4—861no—
282C22⋊C4C22⋊D4311yescharacteristic
283C22⋊C4C22⋊D4311yescharacteristic
284C42—861no—
285C42C22×D4311yescharacteristic
286C42C22×D4311yescharacteristic
287C23—21no—
288C23—21no—
289C23—861no—
290C23C2×C22⋊D4311yescharacteristic
291Q8—861no—
292Q8—861no—
293Q8—3441no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—81no—
299D4—81no—
300D4—81no—
301D4—81no—
302D4—861no—
303D4—861no—
304D4—3441no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—861no—
312C2×C4—861no—
313C2×C4—861no—
314C2×C4—3441no—
315C2×C4C2×C22⋊D4311yescharacteristic
316C2×C4C2×C22⋊D4311yescharacteristic
317C2×C4C2×C22⋊D4311yescharacteristic
318C2×C4C2×C22⋊D4311yescharacteristic
319C2×C4C2×C22⋊D4311yescharacteristic
320C2×C4C23×D4311yescharacteristic
321C8—432no—
322C8—432no—
323C8—861no—
324C8—861no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—1721no—
335C22—1721no—
336C22—1721no—
337C22C22×C22⋊D4311yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—1721no—
346C4—1721no—
347C4—1721no—
348C4#41×D4311yescharacteristic
349C4#41×D4311yescharacteristic
350C2—41no—
351C2—81no—
352C2—81no—
353C2—3441no—
354C2#1458344511yescharacteristic
355C2#1458370211yescharacteristic
356C2#1458371011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#540C2
socleC22×C43C22×D4
hypercenter#540D43
hypocenterC43#3179
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #14583520C2semidirect
2. #14583309C2semidirect
3. #14583286C2semidirect
4. #14583256C2semidirect
5. #14583245C2semidirect
6. #14583150C2semidirect
7. #14583143C2semidirect
8. #14583133C2semidirect
9. #14583126C2semidirect
10. #14583009C2semidirect
11. #14582999C2semidirect
12. C4×#10621883C2semidirect
13. C4×#10621882C2semidirect
14. #14582855C2semidirect
15. C43×#540C2semidirect
180. #540D43semidirect
194. C43#3179semidirect