Finite Group Databasebeta

← #19146917

Subgroups — #19146917

Order 5504.

430 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583567C211yesmaximal, characteristic, complemented
2#14583549C211yesmaximal, characteristic, complemented
3#14583244C211yesmaximal, characteristic, complemented
4#14583219C211yesmaximal, characteristic, complemented
5#14583215C211yesmaximal, characteristic, complemented
6#14583183C211yesmaximal, characteristic, complemented
7#14583151C211yesmaximal, characteristic, complemented
8#14583092C211yesmaximal, characteristic, complemented
9#14583042C211yesmaximal, characteristic, complemented
10#14583041C211yesmaximal, characteristic, complemented
11#14582990C211yesmaximal, characteristic, complemented
12#14582975C211yesmaximal, characteristic, complemented
13#14582901C211yesmaximal, characteristic, complemented
14#14582897C211yesmaximal, characteristic, complemented
15C43×#469C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×#10621900—21no—
18C2×#10621900C2211yescharacteristic
19C2×#10621883C2211yescharacteristic
20C2×#10621882C2211yescharacteristic
21C2×#10621872C2211yescharacteristic
22#13063324C2211yescharacteristic
23#13063321—21no—
24#13063321C2211yescharacteristic
25#13063307—21no—
26#13063306—21no—
27#13063302—21no—
28#13063300C2211yescharacteristic
29#13063298—21no—
30#13063297—21no—
31#13063296C2211yescharacteristic
32#13063290C2211yescharacteristic
33D4×Dic43C2211yescharacteristic
34C4×C22⋊D43C2211yescharacteristic
35(C22⋊D43)⋊C4—21no—
36C2×C4⋊Dic43C2211yescharacteristic
37C4⋊C4×D43C2211yescharacteristic
38#13063256C2211yescharacteristic
39#13063256C2211yescharacteristic
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
51C8×Dic43C2211yescharacteristic
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#10621900—44no—
76#10621898—22no—
77#10621898—41no—
78C2×D172—21no—
79C2×D172C2311yescharacteristic
80C2×C4×D43—21no—
81C2×C4×D43—21no—
82C2×C4×D43C2311yescharacteristic
83C2×Dic86—21no—
84C2×Dic86C2311yescharacteristic
85D8×C43—41no—
86M16×C43—41no—
87C2×C8×C43C2311yescharacteristic
88C2×C8×C43C2311yescharacteristic
89C4⋊C4×C43C2311yescharacteristic
90C4⋊C4×C43C2311yescharacteristic
91C22⋊C4×C43—21no—
92C22⋊C4×C43—21no—
93C22⋊Dic43—21no—
94C22⋊Dic43—21no—
95C22⋊Dic43D411yescharacteristic
96#10621883—22no—
97#10621882—41no—
98(C2×D43)⋊C4—21no—
99(C2×D43)⋊C4D411yescharacteristic
100C4⋊Dic43—21no—
101C4⋊Dic43C2311yescharacteristic
102C4⋊Dic43C2311yescharacteristic
103Dic43⋊C4—21no—
104Dic43⋊C4—21no—
105Dic43⋊C4—21no—
106Dic43⋊C4D411yescharacteristic
107C4×Dic43—21no—
108C4×Dic43C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111#10621872—41no—
112C23×C43—21no—
113C23×C43—21no—
114C23×C43C2×D411yescharacteristic
115C22×D43—21no—
116C22×D43C2×D411yescharacteristic
117D4×C43—21no—
118D4×C43—21no—
119D4×C43—21no—
120D4×C43—21no—
121D4×C43—42no—
122D4×C43—81no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43C2×D411yescharacteristic
128C2×C4×C43C2411yescharacteristic
129C22⋊D43—22no—
130C22⋊D43—42no—
131C22⋊D43—42no—
132C22⋊D43—42no—
133C22⋊D43—42no—
134C22⋊D43—81no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—21no—
138C2×Dic43—42no—
139C2×Dic43—42no—
140C2×Dic43—42no—
141C2×Dic43C2×D411yescharacteristic
142C2×Dic43C2×D411yescharacteristic
143C2×Dic43C2×D411yescharacteristic
144D172—21no—
145D172—21no—
146D172—81no—
147C4×D43—21no—
148C4×D43—21no—
149C4×D43—42no—
150C4×D43—42no—
151Dic86—21no—
152Dic86—42no—
153Dic86#4112yescomplemented
154C8×C43—21no—
155C8×C43—21no—
156C43⋊C8—21no—
157C43⋊C8—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—41no—
162C22×C43—41no—
163C22×C43—41no—
164C22×C43—41no—
165C22×C43—41no—
166C22×C43—41no—
167C22×C43C22×D411yescharacteristic
168C2×D43—21no—
169C2×D43—21no—
170C2×D43—21no—
171C2×D43—41no—
172C2×D43—41no—
173C2×D43—41no—
174C4×C43—21no—
175C4×C43—41no—
176C4×C43—41no—
177C4×C43C2×#4111yescharacteristic
178C4×C43H(5,𝔽2)11yescharacteristic
179Dic43—22no—
180Dic43—21no—
181Dic43—21no—
182Dic43—41no—
183Dic43—41no—
184Dic43AGL(1,ℤ/8)12yes—
185#3332—431nomaximal, Sylow
186C2×C43—41no—
187C2×C43—81no—
188C2×C43—81no—
189C2×C43#54611yescharacteristic
190C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C43#57711yescharacteristic
192D43—41no—
193D43—81no—
194#550—431no—
195#547—431no—
196#486—431no—
197#481—431no—
198#481—431no—
199#475—431no—
200#469—431no—
201#469D4311yescharacteristic, complemented
202#459—431no—
203#449—431no—
204#449—431no—
205C4×SD16—431no—
206#436—431no—
207#417—431no—
208#417—431no—
209C43#333211yescharacteristic, complemented, Sylow
210C2×#41—431no—
211C2×#41—431no—
212C2×#41—861no—
213C2×SD16—431no—
214C2×D8—431no—
215C2×D8C2×D4311yescharacteristic
216C2×M16—431no—
217C2×M16C2×D4311yescharacteristic
218C4⋊Q8—431no—
219#127—431no—
220#127—861no—
221#123—861no—
222#123—861no—
223C22⋊Q8—861no—
224#121—431no—
225#121—431no—
226#121—861no—
227#121—861no—
228#121C2×D4311yescharacteristic
229#121C2×D4311yescharacteristic
230C4×Q8—431no—
231C4×D4—431no—
232C4×D4—431no—
233C4×D4—861no—
234C2×C4⋊C4—431no—
235C2×C4⋊C4—431no—
236#106—431no—
237#106—431no—
238#106C2×D4311yescharacteristic
239C4⋊C8—431no—
240#103—431no—
241#103—431no—
242#103—431no—
243#102—431no—
244#102—431no—
245#102—431no—
246#102—431no—
247#102—431no—
248#102C2×D4311yescharacteristic
249#102C2×D4311yescharacteristic
250C22⋊C8—431no—
251C22⋊C8—431no—
252C4×C8—431no—
253#41—862no—
254#41—862no—
255#41—1721no—
256#41—1721no—
257#41—1724no—
258C2×Q8—431no—
259C2×Q8—861no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—431no—
263C2×D4—431no—
264C2×D4—861no—
265C2×D4—861no—
266C2×D4—861no—
267C2×D4—861no—
268C2×D4—861no—
269C2×D4—861no—
270C2×D4C22×D4311yescharacteristic
271C2×D4C22×D4311yescharacteristic
272C22×C4—431no—
273C22×C4—861no—
274C22×C4—861no—
275C22×C4—861no—
276C22×C4—861no—
277C22×C4—861no—
278C22×C4C22×D4311yescharacteristic
279SD16—862no—
280D8—41no—
281D8—1721no—
282M16—41no—
283M16—1721no—
284C2×C8—431no—
285C2×C8—431no—
286C2×C8C22×D4311yescharacteristic
287C2×C8C22×D4311yescharacteristic
288C4⋊C4—431no—
289C4⋊C4—431no—
290C4⋊C4—431no—
291C4⋊C4—861no—
292C4⋊C4—861no—
293C4⋊C4—861no—
294C4⋊C4—861no—
295C4⋊C4C22×D4311yescharacteristic
296C4⋊C4C22×D4311yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—431no—
300C22⋊C4—431no—
301C22⋊C4—861no—
302C22⋊C4—861no—
303C22⋊C4—861no—
304C42—431no—
305C42—861no—
306C23—21no—
307C23—21no—
308C23—431no—
309C23—861no—
310C23D4×D4311yescharacteristic
311Q8—432no—
312Q8—861no—
313Q8—1722no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—21no—
318D4—42no—
319D4—81no—
320D4—862no—
321D4—861no—
322D4—861no—
323D4—3441no—
324D4—3441no—
325D4—1722no—
326D4—1722no—
327D4—1722no—
328D4—1722no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—431no—
334C2×C4—431no—
335C2×C4—431no—
336C2×C4—861no—
337C2×C4—861no—
338C2×C4—861no—
339C2×C4—861no—
340C2×C4—861no—
341C2×C4—1722no—
342C2×C4—1722no—
343C2×C4—1722no—
344C2×C4—1722no—
345C2×C4—1722no—
346C2×C4D4×D4311yescharacteristic
347C2×C4C23×D4311yescharacteristic
348C8—21no—
349C8—21no—
350C8—861no—
351C8—861no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—861no—
362C22—861no—
363C22—861no—
364C22—1721no—
365C22—1721no—
366C22—1721no—
367C22C2×D4×D4311yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—432no—
372C4—861no—
373C4—861no—
374C4—862no—
375C4—1721no—
376C4—1721no—
377C4#41×D4311yescharacteristic
378C4#1306337011yescharacteristic
379C2—41no—
380C2—81no—
381C2—81no—
382C2—3441no—
383C2—1721no—
384C2#1458353811yescharacteristic
385C2AGL(1,ℤ/8)×D4311yescharacteristic
386C2#1458370911yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#469C2
socleC22×C43C22×D4
hypercenter#469D43
hypocenterC43#3332
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. #14583567C2semidirect
2. #14583549C2semidirect
3. #14583244C2semidirect
4. #14583219C2semidirect
5. #14583215C2semidirect
6. #14583183C2semidirect
7. #14583151C2semidirect
8. #14583092C2semidirect
9. #14583042C2semidirect
10. #14583041C2semidirect
11. #14582990C2semidirect
12. #14582975C2semidirect
13. #14582901C2semidirect
14. #14582897C2semidirect
15. C43×#469C2semidirect
153. Dic86#41semidirect
201. #469D43semidirect
209. C43#3332semidirect