Finite Group Databasebeta

← #19144788

Subgroups — #19144788

Order 5504.

396 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#14583379C211yesmaximal, characteristic, complemented
2#14583215C211yesmaximal, characteristic, complemented
3#14583210C211yesmaximal, characteristic, complemented
4#14583203C211yesmaximal, characteristic, complemented
5#14583196C211yesmaximal, characteristic, complemented
6#14583096C211yesmaximal, characteristic, complemented
7#14583091C211yesmaximal, characteristic, complemented
8#14583042C211yesmaximal, characteristic, complemented
9#14583042C211yesmaximal, characteristic, complemented
10#14583009C211yesmaximal, characteristic, complemented
11#14582999C211yesmaximal, characteristic, complemented
12C4×#10621883C211yesmaximal, characteristic, complemented
13C4×#10621882C211yesmaximal, characteristic, complemented
14#14582960C211yesmaximal, characteristic, complemented
15C43×#540C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×#10621883C2211yescharacteristic
18C2×#10621883C2211yescharacteristic
19C2×#10621882C2211yescharacteristic
20C2×#10621882C2211yescharacteristic
21C4×Dic86C2211yescharacteristic
22C4×Dic86C2211yescharacteristic
23C4×D172C2211yescharacteristic
24C4×D172C2211yescharacteristic
25(C22⋊D43)⋊C4—21no—
26(C22⋊D43)⋊C4—21no—
27#13063283—21no—
28C2×C4⋊Dic43C2211yescharacteristic
29C4⋊C4×D43—21no—
30#13063258C2211yescharacteristic
31#13063258C2211yescharacteristic
32#13063256C2211yescharacteristic
33#13063256C2211yescharacteristic
34C4⋊(C43⋊C8)C2211yescharacteristic
35C4⋊(C43⋊C8)C2211yescharacteristic
36#13063248C2211yescharacteristic
37#13063248C2211yescharacteristic
38#13063246C2211yescharacteristic
39#13063246C2211yescharacteristic
40#13063246C2211yescharacteristic
41#13063246C2211yescharacteristic
42#13063245C2211yescharacteristic
43#13063245C2211yescharacteristic
44C22⋊(C43⋊C8)C2211yescharacteristic
45C22⋊(C43⋊C8)C2211yescharacteristic
46#13063236C2211yescharacteristic
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—
69C22×Dic43—21no—
70#10621898—22no—
71#10621898—22no—
72C2×D172C2311yescharacteristic
73C2×C4×D43—21no—
74C2×C4×D43—21no—
75C2×C4×D43—21no—
76C2×Dic86C2311yescharacteristic
77C4⋊C4×C43—21no—
78C4⋊C4×C43—21no—
79C4⋊C4×C43D411yescharacteristic
80C4⋊C4×C43D411yescharacteristic
81C4⋊C4×C43C2311yescharacteristic
82C4⋊C4×C43C2311yescharacteristic
83C22⋊C4×C43—21no—
84C22⋊C4×C43—21no—
85C22⋊C4×C43—21no—
86C22⋊C4×C43—21no—
87C22⋊C4×C43D411yescharacteristic
88C22⋊C4×C43D411yescharacteristic
89C42×C43C2311yescharacteristic
90C42×C43C2311yescharacteristic
91#10621883—22no—
92#10621883—22no—
93#10621882—22no—
94#10621882—22no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4—21no—
97C4⋊Dic43—21no—
98C4⋊Dic43C2311yescharacteristic
99C4⋊Dic43C2311yescharacteristic
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102C4×Dic43—21no—
103C4×Dic43—21no—
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—24no—
133C2×Dic43—21no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—81no—
137D172—21no—
138D172#4112yes—
139C4×D43—24no—
140C4×D43—81no—
141C4×D43—81no—
142Dic86—21no—
143Dic86#4112yes—
144C43⋊C8—21no—
145C43⋊C8—21no—
146C43⋊C8—21no—
147C43⋊C8—21no—
148C22×C43—21no—
149C22×C43—21no—
150C22×C43—21no—
151C22×C43—41no—
152C22×C43—41no—
153C22×C43—41no—
154C22×C43—41no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43C22×D411yescharacteristic
158C2×D43—22no—
159C2×D43—41no—
160C2×D43—41no—
161C4×C43—21no—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43—41no—
167C4×C43—41no—
168C4×C43C2×#4111yescharacteristic
169C4×C43C2×#4111yescharacteristic
170Dic43—22no—
171Dic43—41no—
172Dic43—41no—
173#3119—431nomaximal, Sylow
174C2×C43—41no—
175C2×C43—81no—
176C2×C43—81no—
177C2×C43#52511yescharacteristic
178C2×C43#57611yescharacteristic
179C2×C43#57711yescharacteristic
180D43—42no—
181#540D4311yescharacteristic, complemented
182#520—431no—
183#481—431no—
184#480—431no—
185#479—431no—
186#478—431no—
187#460—431no—
188#459—431no—
189#449—431no—
190#449—431no—
191#442—431no—
192#440—431no—
193C4×SD16—431no—
194C4×D8—431no—
195#433—431no—
196C43#311911yescharacteristic, complemented, Sylow
197C2×#41—431no—
198C2×SD16—431no—
199C2×SD16—431no—
200C2×D8—431no—
201C2×D8—431no—
202#127C2×D4311yescharacteristic
203#125C2×D4311yescharacteristic
204#123—21no—
205#123—21no—
206#121—21no—
207#121—21no—
208#121C2×D4311yescharacteristic
209#121C2×D4311yescharacteristic
210C4×Q8—431no—
211C4×Q8—431no—
212C4×D4—431no—
213C4×D4—431no—
214C4×D4—861no—
215C4×D4—861no—
216C4×D4C2×D4311yescharacteristic
217C4×D4C2×D4311yescharacteristic
218#117—861no—
219#117C2×D4311yescharacteristic
220C2×C4⋊C4—431no—
221C2×C4⋊C4—861no—
222#107—431no—
223#107—431no—
224#106—431no—
225#106—431no—
226C4⋊C8—431no—
227C4⋊C8—431no—
228#103—431no—
229#103—431no—
230#102—431no—
231#102—431no—
232#102—431no—
233#102—431no—
234#102—431no—
235#102—431no—
236C22⋊C8—431no—
237C22⋊C8—431no—
238#97—431no—
239C4×C8—431no—
240#41—862no—
241#41—862no—
242C2×Q8—431no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—431no—
248C2×D4—861no—
249C2×D4C22×D4311yescharacteristic
250C2×D4C22×D4311yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—861no—
254C22×C4—861no—
255C22×C4—861no—
256C22×C4—861no—
257C22×C4C22×D4311yescharacteristic
258SD16—862no—
259SD16—862no—
260D8—862no—
261D8—862no—
262C2×C8—431no—
263C2×C8—431no—
264C2×C8—431no—
265C2×C8—431no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—431no—
269C4⋊C4—431no—
270C4⋊C4—861no—
271C4⋊C4—861no—
272C4⋊C4—861no—
273C4⋊C4C22⋊D4311yescharacteristic
274C4⋊C4C22⋊D4311yescharacteristic
275C4⋊C4C22×D4311yescharacteristic
276C4⋊C4C22×D4311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—861no—
282C22⋊C4—861no—
283C22⋊C4C22⋊D4311yescharacteristic
284C22⋊C4C22⋊D4311yescharacteristic
285C42—861no—
286C42—861no—
287C42C22×D4311yescharacteristic
288C42C22×D4311yescharacteristic
289C23—21no—
290C23—21no—
291C23—861no—
292C23C2×C22⋊D4311yescharacteristic
293Q8—432no—
294Q8—861no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—81no—
301D4—81no—
302D4—81no—
303D4—432no—
304D4—864no—
305D4—861no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—864no—
313C2×C4—861no—
314C2×C4—861no—
315C2×C4—861no—
316C2×C4—3441no—
317C2×C4—3441no—
318C2×C4—3441no—
319C2×C4C2×C22⋊D4311yescharacteristic
320C2×C4C2×C22⋊D4311yescharacteristic
321C2×C4C2×C22⋊D4311yescharacteristic
322C2×C4C2×C22⋊D4311yescharacteristic
323C2×C4C2×C22⋊D4311yescharacteristic
324C2×C4C23×D4311yescharacteristic
325C8—861no—
326C8—861no—
327C8—861no—
328C8—861no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—862no—
339C22—1721no—
340C22—1721no—
341C22C22×C22⋊D4311yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—862no—
350C4—1721no—
351C4—1721no—
352C4#41×D4311yescharacteristic
353C4#41×D4311yescharacteristic
354C2—41no—
355C2—81no—
356C2—81no—
357C2—1722no—
358C2#1458340611yescharacteristic
359C2#1458370211yescharacteristic
360C2#1458371011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#540C2
socleC22×C43C22×D4
hypercenter#540D43
hypocenterC43#3119
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. #14583379C2semidirect
2. #14583215C2semidirect
3. #14583210C2semidirect
4. #14583203C2semidirect
5. #14583196C2semidirect
6. #14583096C2semidirect
7. #14583091C2semidirect
8. #14583042C2semidirect
9. #14583042C2semidirect
10. #14583009C2semidirect
11. #14582999C2semidirect
12. C4×#10621883C2semidirect
13. C4×#10621882C2semidirect
14. #14582960C2semidirect
15. C43×#540C2semidirect
181. #540D43semidirect
196. C43#3119semidirect