Finite Group Databasebeta

← #19146596

Subgroups — #19146596

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#14583601C211yesmaximal, characteristic, complemented
2#14583567C211yesmaximal, characteristic, complemented
3#14583262C211yesmaximal, characteristic, complemented
4#14583225C211yesmaximal, characteristic, complemented
5#14583210C211yesmaximal, characteristic, complemented
6#14583209C211yesmaximal, characteristic, complemented
7#14583134C211yesmaximal, characteristic, complemented
8#14583092C211yesmaximal, characteristic, complemented
9#14583042C211yesmaximal, characteristic, complemented
10#14583041C211yesmaximal, characteristic, complemented
11#14582996C211yesmaximal, characteristic, complemented
12#14582968C211yesmaximal, characteristic, complemented
13#14582901C211yesmaximal, characteristic, complemented
14#14582892C211yesmaximal, characteristic, complemented
15C43×#469C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×#10621900C2211yescharacteristic
18C2×#10621883C2211yescharacteristic
19C2×#10621882C2211yescharacteristic
20C2×C8×D43C2211yescharacteristic
21#13063321—21no—
22#13063321C2211yescharacteristic
23#13063318—21no—
24#13063316C2211yescharacteristic
25#13063309—21no—
26#13063300C2211yescharacteristic
27#13063298—21no—
28#13063297—21no—
29#13063297—21no—
30#13063296C2211yescharacteristic
31#13063290C2211yescharacteristic
32D4×Dic43—21no—
33D4×Dic43C2211yescharacteristic
34C4×C22⋊D43C2211yescharacteristic
35(C22⋊D43)⋊C4—21no—
36#13063283C2211yescharacteristic
37C2×C4⋊Dic43C2211yescharacteristic
38#13063258C2211yescharacteristic
39#13063258C2211yescharacteristic
40Dic43⋊C8C2211yescharacteristic
41#13063250C2211yescharacteristic
42#13063250C2211yescharacteristic
43#13063248C2211yescharacteristic
44#13063247C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063245C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51#13063235C2211yescharacteristic
52C2×D8×C43C2211yescharacteristic
53C2×M16×C43C2211yescharacteristic
54#121×C43C2211yescharacteristic
55#121×C43C2211yescharacteristic
56#106×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic
59C2×D4×C43—21no—
60C2×D4×C43—21no—
61C2×D4×C43C2311yescharacteristic
62C2×D4×C43C2311yescharacteristic
63C22×C4×C43C2311yescharacteristic
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C2×C22⋊D43—21no—
68C2×C22⋊D43—21no—
69C2×C22⋊D43D411yescharacteristic
70C22×Dic43—21no—
71C22×Dic43—21no—
72C22×Dic43—21no—
73#10621900—22no—
74#10621900—41no—
75#10621898—22no—
76#10621898—41no—
77C2×D172—21no—
78C2×D172C2311yescharacteristic
79C2×C4×D43—21no—
80C2×C4×D43C2311yescharacteristic
81C2×Dic86C2311yescharacteristic
82D8×C43—41no—
83M16×C43—41no—
84C2×C8×C43C2311yescharacteristic
85C2×C8×C43C2311yescharacteristic
86C4⋊C4×C43C2311yescharacteristic
87C4⋊C4×C43C2311yescharacteristic
88C22⋊C4×C43—21no—
89C22⋊C4×C43—21no—
90C22⋊Dic43—21no—
91C22⋊Dic43—21no—
92C22⋊Dic43D411yescharacteristic
93#10621883—22no—
94#10621882—41no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4—21no—
97(C2×D43)⋊C4D411yescharacteristic
98C4⋊Dic43—21no—
99C4⋊Dic43—21no—
100C4⋊Dic43C2311yescharacteristic
101C4⋊Dic43C2311yescharacteristic
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104Dic43⋊C4D411yescharacteristic
105C4×Dic43—21no—
106C4×Dic43—21no—
107C4×Dic43C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110C8×D43—41no—
111C23×C43—21no—
112C23×C43—21no—
113C23×C43C2×D411yescharacteristic
114C22×D43—21no—
115C22×D43C2×D411yescharacteristic
116D4×C43—21no—
117D4×C43—21no—
118D4×C43—21no—
119D4×C43—21no—
120D4×C43—42no—
121D4×C43—81no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43C2×D411yescharacteristic
127C2×C4×C43C2411yescharacteristic
128C22⋊D43—41no—
129C22⋊D43—42no—
130C22⋊D43—42no—
131C22⋊D43—42no—
132C22⋊D43—81no—
133C22⋊D43—81no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—42no—
138C2×Dic43—81no—
139C2×Dic43—81no—
140C2×Dic43C2×D411yescharacteristic
141C2×Dic43C2×D411yescharacteristic
142C2×Dic43C2×D411yescharacteristic
143D172—21no—
144D172—21no—
145D172—81no—
146C4×D43—21no—
147C4×D43—21no—
148C4×D43—42no—
149Dic86—21no—
150Dic86#4112yes—
151C8×C43—21no—
152C8×C43—21no—
153C43⋊C8—21no—
154C43⋊C8—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—21no—
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—41no—
169C2×D43—41no—
170C2×D43—41no—
171C4×C43—21no—
172C4×C43—41no—
173C4×C43—41no—
174C4×C43C2×#4111yescharacteristic
175C4×C43H(5,𝔽2)11yescharacteristic
176Dic43—22no—
177Dic43—21no—
178Dic43—21no—
179Dic43—21no—
180Dic43—41no—
181Dic43—41no—
182#3309—431nomaximal, Sylow
183C2×C43—41no—
184C2×C43—81no—
185C2×C43—81no—
186C2×C43#54611yescharacteristic
187C2×C43#57511yescharacteristic
188C2×C43#57611yescharacteristic
189D43—41no—
190D43—81no—
191#553—431no—
192#550—431no—
193#490—431no—
194#482—431no—
195#480—431no—
196#479—431no—
197#469D4311yescharacteristic, complemented
198#466—431no—
199#459—431no—
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×D8—431no—
211C2×D8C2×D4311yescharacteristic
212C2×M16C2×D4311yescharacteristic
213C22×C8—431no—
214#127—431no—
215#127—861no—
216#126—861no—
217#125—431no—
218#123—861no—
219#121—431no—
220#121—431no—
221#121—861no—
222#121—861no—
223#121—861no—
224#121C2×D4311yescharacteristic
225#121C2×D4311yescharacteristic
226C4×Q8—431no—
227C4×D4—431no—
228C4×D4—431no—
229C4×D4—861no—
230C4×D4—861no—
231#117—431no—
232C2×C4⋊C4—431no—
233#107—431no—
234#107—431no—
235#106C2×D4311yescharacteristic
236C4⋊C8—431no—
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—431no—
259C2×D4—861no—
260C2×D4—861no—
261C2×D4—861no—
262C2×D4—861no—
263C2×D4—861no—
264C2×D4—861no—
265C2×D4C22×D4311yescharacteristic
266C2×D4C22×D4311yescharacteristic
267C22×C4—431no—
268C22×C4—861no—
269C22×C4—861no—
270C22×C4—861no—
271C22×C4—861no—
272C22×C4C22×D4311yescharacteristic
273SD16—862no—
274D8—41no—
275D8—1721no—
276M16—41no—
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—861no—
286C4⋊C4—861no—
287C4⋊C4—861no—
288C4⋊C4—861no—
289C4⋊C4C22×D4311yescharacteristic
290C4⋊C4C22×D4311yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—431no—
294C22⋊C4—431no—
295C22⋊C4—861no—
296C22⋊C4—861no—
297C22⋊C4—861no—
298C22⋊C4—861no—
299C42—431no—
300C42—861no—
301C42—861no—
302C23—21no—
303C23—21no—
304C23—431no—
305C23—861no—
306C23D4×D4311yescharacteristic
307Q8—432no—
308Q8—861no—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—42no—
314D4—81no—
315D4—861no—
316D4—861no—
317D4—3441no—
318D4—3441no—
319D4—3441no—
320D4—1721no—
321D4—1722no—
322D4—1722no—
323D4—1722no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—431no—
329C2×C4—431no—
330C2×C4—431no—
331C2×C4—861no—
332C2×C4—861no—
333C2×C4—861no—
334C2×C4—861no—
335C2×C4—861no—
336C2×C4—3441no—
337C2×C4—3441no—
338C2×C4—1722no—
339C2×C4—1722no—
340C2×C4D4×D4311yescharacteristic
341C2×C4C23×D4311yescharacteristic
342C8—21no—
343C8—21no—
344C8—861no—
345C8—861no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—861no—
356C22—861no—
357C22—861no—
358C22—1721no—
359C22—1721no—
360C22—1721no—
361C22C2×D4×D4311yescharacteristic
362C4—21no—
363C4—41no—
364C4—41no—
365C4—861no—
366C4—861no—
367C4—861no—
368C4—862no—
369C4—1721no—
370C4—1721no—
371C4#41×D4311yescharacteristic
372C4#1306337011yescharacteristic
373C2—41no—
374C2—81no—
375C2—81no—
376C2—3441no—
377C2—1721no—
378C2#1458353811yescharacteristic
379C2#1458369511yescharacteristic
380C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#469C2
socleC22×C43C22×D4
hypercenter#469D43
hypocenterC43#3309
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #14583601C2semidirect
2. #14583567C2semidirect
3. #14583262C2semidirect
4. #14583225C2semidirect
5. #14583210C2semidirect
6. #14583209C2semidirect
7. #14583134C2semidirect
8. #14583092C2semidirect
9. #14583042C2semidirect
10. #14583041C2semidirect
11. #14582996C2semidirect
12. #14582968C2semidirect
13. #14582901C2semidirect
14. #14582892C2semidirect
15. C43×#469C2semidirect
197. #469D43semidirect
206. C43#3309semidirect