Finite Group Databasebeta

← #19146608

Subgroups — #19146608

Order 5504.

404 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583599C211yesmaximal, characteristic, complemented
2#14583569C211yesmaximal, characteristic, complemented
3#14583263C211yesmaximal, characteristic, complemented
4#14583222C211yesmaximal, characteristic, complemented
5#14583211C211yesmaximal, characteristic, complemented
6#14583207C211yesmaximal, characteristic, complemented
7#14583149C211yesmaximal, characteristic, complemented
8#14583132C211yesmaximal, characteristic, complemented
9#14583041C211yesmaximal, characteristic, complemented
10#14583041C211yesmaximal, characteristic, complemented
11#14582999C211yesmaximal, characteristic, complemented
12#14582969C211yesmaximal, characteristic, complemented
13#14582897C211yesmaximal, characteristic, complemented
14#14582892C211yesmaximal, characteristic, complemented
15C43×#459C211yesmaximal, characteristic, complemented
16C2×#10621900C2211yescharacteristic
17C2×#10621900C2211yescharacteristic
18C2×#10621883C2211yescharacteristic
19C2×#10621872C2211yescharacteristic
20C2×C8×D43C2211yescharacteristic
21#13063321—21no—
22#13063318—21no—
23#13063317C2211yescharacteristic
24#13063308—21no—
25#13063298—21no—
26#13063297—21no—
27#13063297—21no—
28#13063296C2211yescharacteristic
29#13063296C2211yescharacteristic
30#13063296C2211yescharacteristic
31#13063296C2211yescharacteristic
32C4×Dic86C2211yescharacteristic
33C4×D172C2211yescharacteristic
34D4×Dic43—21no—
35C4×C22⋊D43—21no—
36#13063283C2211yescharacteristic
37C4⋊C4×D43C2211yescharacteristic
38#13063259C2211yescharacteristic
39#13063258C2211yescharacteristic
40#13063257C2211yescharacteristic
41#13063250C2211yescharacteristic
42#13063250C2211yescharacteristic
43#13063248C2211yescharacteristic
44#13063246C2211yescharacteristic
45#13063246C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063246C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51#13063236C2211yescharacteristic
52C2×D8×C43C2211yescharacteristic
53C2×D8×C43C2211yescharacteristic
54#127×C43C2211yescharacteristic
55C4×D4×C43C2211yescharacteristic
56C4⋊C8×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic
59C2×D4×C43—21no—
60C2×D4×C43—21no—
61C2×D4×C43C2311yescharacteristic
62C2×D4×C43C2311yescharacteristic
63C2×D4×C43C2311yescharacteristic
64C22×C4×C43—21no—
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C2×C22⋊D43—21no—
68C2×C22⋊D43—21no—
69C2×C22⋊D43—21no—
70C2×C22⋊D43—21no—
71C22×Dic43—21no—
72C22×Dic43—21no—
73#10621900—22no—
74#10621900—22no—
75#10621900—41no—
76#10621900—41no—
77C2×D172D411yescharacteristic
78C2×C4×D43—21no—
79C2×C4×D43C2311yescharacteristic
80C2×C4×D43C2311yescharacteristic
81C2×Dic86C2311yescharacteristic
82D8×C43—41no—
83D8×C43—41no—
84C2×C8×C43C2311yescharacteristic
85C2×C8×C43C2311yescharacteristic
86C4⋊C4×C43C2311yescharacteristic
87C22⋊C4×C43—21no—
88C42×C43C2311yescharacteristic
89C22⋊Dic43—21no—
90C22⋊Dic43—21no—
91C22⋊Dic43—21no—
92C22⋊Dic43—21no—
93#10621883—22no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4D411yescharacteristic
96(C2×D43)⋊C4D411yescharacteristic
97C4⋊Dic43D411yescharacteristic
98C4⋊Dic43C2311yescharacteristic
99C4⋊Dic43C2311yescharacteristic
100C4⋊Dic43C2311yescharacteristic
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104Dic43⋊C4—21no—
105C4×Dic43—21no—
106C4×Dic43—21no—
107C2×C43⋊C8C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109#10621872—41no—
110C8×D43—41no—
111C23×C43—21no—
112C23×C43—21no—
113C23×C43—21no—
114C22×D43C2×D411yescharacteristic
115C22×D43C2×D411yescharacteristic
116D4×C43—21no—
117D4×C43—21no—
118D4×C43—21no—
119D4×C43—21no—
120D4×C43—21no—
121D4×C43—21no—
122D4×C43—42no—
123D4×C43—81no—
124C2×C4×C43—21no—
125C2×C4×C43—81no—
126C2×C4×C43C2×D411yescharacteristic
127C2×C4×C43C2×D411yescharacteristic
128C2×C4×C43C2411yescharacteristic
129C22⋊D43—42no—
130C22⋊D43—42no—
131C22⋊D43—42no—
132C22⋊D43—81no—
133C22⋊D43—81no—
134C22⋊D43—81no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—21no—
138C2×Dic43—21no—
139C2×Dic43—42no—
140C2×Dic43—42no—
141C2×Dic43C2×D411yescharacteristic
142C2×Dic43C2×D411yescharacteristic
143D172—41no—
144C4×D43—21no—
145C4×D43—21no—
146C4×D43—21no—
147C4×D43—21no—
148C4×D43—81no—
149Dic86—21no—
150Dic86#4112yes—
151C8×C43—21no—
152C8×C43—21no—
153C43⋊C8—21no—
154C43⋊C8—21no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43—41no—
161C22×C43—41no—
162C22×C43—41no—
163C22×C43—41no—
164C22×C43C22×D411yescharacteristic
165C2×D43—21no—
166C2×D43—21no—
167C2×D43—21no—
168C2×D43—21no—
169C2×D43—21no—
170C2×D43—21no—
171C4×C43—21no—
172C4×C43—21no—
173C4×C43—41no—
174C4×C43C2×#4111yescharacteristic
175C4×C43H(5,𝔽2)11yescharacteristic
176Dic43—22no—
177Dic43—21no—
178Dic43—21no—
179Dic43—41no—
180Dic43—41no—
181Dic43—41no—
182#3309—431nomaximal, Sylow
183C2×C43—81no—
184C2×C43—81no—
185C2×C43—81no—
186C2×C43#54611yescharacteristic
187C2×C43#57511yescharacteristic
188C2×C43#57611yescharacteristic
189D43—41no—
190D43—41no—
191#553—431no—
192#550—431no—
193#490—431no—
194#482—431no—
195#480—431no—
196#479—431no—
197#469—431no—
198#466—431no—
199#459D4311yescharacteristic, complemented
200#449—431no—
201#449—431no—
202#440—431no—
203#435—431no—
204#417—431no—
205#416—431no—
206C43#330911yescharacteristic, complemented, Sylow
207C2×#41—431no—
208C2×#41—431no—
209C2×SD16—431no—
210C2×D8C2×D4311yescharacteristic
211C2×D8C2×D4311yescharacteristic
212C2×M16—431no—
213C22×C8—431no—
214#127—861no—
215#127C2×D4311yescharacteristic
216#126—861no—
217#125—431no—
218#123—861no—
219#121—431no—
220#121—431no—
221#121—431no—
222#121—431no—
223#121—861no—
224#121—861no—
225#121—861no—
226C4×Q8—431no—
227C4×D4—431no—
228C4×D4—861no—
229C4×D4—861no—
230C4×D4C2×D4311yescharacteristic
231#117—431no—
232C2×C4⋊C4—431no—
233#107—431no—
234#107—431no—
235#106—431no—
236C4⋊C8C2×D4311yescharacteristic
237#103—431no—
238#103—431no—
239#103—431no—
240#102—431no—
241#102—431no—
242#102—431no—
243#102—431no—
244#102—431no—
245#102C2×D4311yescharacteristic
246#102C2×D4311yescharacteristic
247C22⋊C8—431no—
248C22⋊C8—431no—
249#97—431no—
250#41—862no—
251#41—862no—
252#41—1721no—
253#41—1721no—
254C2×Q8—431no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—431no—
258C2×D4—861no—
259C2×D4—861no—
260C2×D4—861no—
261C2×D4—861no—
262C2×D4—861no—
263C2×D4—861no—
264C2×D4C22×D4311yescharacteristic
265C2×D4C22×D4311yescharacteristic
266C2×D4C22×D4311yescharacteristic
267C22×C4—21no—
268C22×C4—431no—
269C22×C4—431no—
270C22×C4—861no—
271C22×C4—861no—
272C22×C4—861no—
273SD16—862no—
274D8—41no—
275D8—41no—
276M16—1721no—
277C2×C8—431no—
278C2×C8—431no—
279C2×C8—1721no—
280C2×C8C22×D4311yescharacteristic
281C2×C8C22×D4311yescharacteristic
282C4⋊C4—431no—
283C4⋊C4—431no—
284C4⋊C4—431no—
285C4⋊C4—431no—
286C4⋊C4—861no—
287C4⋊C4—861no—
288C4⋊C4—861no—
289C4⋊C4—861no—
290C4⋊C4C22×D4311yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—431no—
293C22⋊C4—431no—
294C22⋊C4—861no—
295C22⋊C4—861no—
296C22⋊C4—861no—
297C22⋊C4—861no—
298C22⋊C4—861no—
299C42—861no—
300C42—861no—
301C42C22×D4311yescharacteristic
302C23—21no—
303C23—21no—
304C23—21no—
305C23—431no—
306C23—431no—
307Q8—432no—
308Q8—861no—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—21no—
315D4—42no—
316D4—81no—
317D4—3441no—
318D4—3441no—
319D4—3441no—
320D4—1721no—
321D4—1722no—
322D4—1722no—
323D4—1722no—
324C2×C4—21no—
325C2×C4—81no—
326C2×C4—431no—
327C2×C4—431no—
328C2×C4—861no—
329C2×C4—861no—
330C2×C4—861no—
331C2×C4—861no—
332C2×C4—861no—
333C2×C4—861no—
334C2×C4—861no—
335C2×C4—861no—
336C2×C4—3441no—
337C2×C4—1722no—
338C2×C4—1722no—
339C2×C4D4×D4311yescharacteristic
340C2×C4D4×D4311yescharacteristic
341C2×C4C23×D4311yescharacteristic
342C8—21no—
343C8—21no—
344C8—861no—
345C8—861no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—861no—
356C22—861no—
357C22—861no—
358C22—861no—
359C22—861no—
360C22—861no—
361C22C2×D4×D4311yescharacteristic
362C4—21no—
363C4—21no—
364C4—41no—
365C4—861no—
366C4—861no—
367C4—862no—
368C4—1721no—
369C4—1721no—
370C4—1721no—
371C4#41×D4311yescharacteristic
372C4#1306337011yescharacteristic
373C2—81no—
374C2—81no—
375C2—81no—
376C2—1721no—
377C2—1721no—
378C2#1458354611yescharacteristic
379C2#1458369511yescharacteristic
380C2#1458370011yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#459C2
socleC22×C43C22×D4
hypercenter#459D43
hypocenterC43#3309
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #14583599C2semidirect
2. #14583569C2semidirect
3. #14583263C2semidirect
4. #14583222C2semidirect
5. #14583211C2semidirect
6. #14583207C2semidirect
7. #14583149C2semidirect
8. #14583132C2semidirect
9. #14583041C2semidirect
10. #14583041C2semidirect
11. #14582999C2semidirect
12. #14582969C2semidirect
13. #14582897C2semidirect
14. #14582892C2semidirect
15. C43×#459C2semidirect
199. #459D43semidirect
206. C43#3309semidirect