Finite Group Databasebeta

← #19147638

Subgroups — #19147638

Order 5504.

418 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583632C211yesmaximal, characteristic, complemented
2#14583570C211yesmaximal, characteristic, complemented
3#14583288C211yesmaximal, characteristic, complemented
4#14583287C211yesmaximal, characteristic, complemented
5#14583274C211yesmaximal, characteristic, complemented
6#14583114C211yesmaximal, characteristic, complemented
7#14583113C211yesmaximal, characteristic, complemented
8#14583098C211yesmaximal, characteristic, complemented
9#14583094C211yesmaximal, characteristic, complemented
10#14583093C211yesmaximal, characteristic, complemented
11#14583093C211yesmaximal, characteristic, complemented
12#14583027C211yesmaximal, characteristic, complemented
13#14583010C211yesmaximal, characteristic, complemented
14#14582986C211yesmaximal, characteristic, complemented
15C43×#442C211yesmaximal, characteristic, complemented
16C2×#10621898—21no—
17C2×#10621873C2211yescharacteristic
18C2×#10621873C2211yescharacteristic
19C2×#10621883C2211yescharacteristic
20C2×D344C2211yescharacteristic
21C2×D344C2211yescharacteristic
22C2×#10621882C2211yescharacteristic
23C2×#10621882C2211yescharacteristic
24C2×#10621882C2211yescharacteristic
25#13063322C2211yescharacteristic
26#13063321C2211yescharacteristic
27#13063321C2211yescharacteristic
28#13063321C2211yescharacteristic
29#13063313C2211yescharacteristic
30#13063312C2211yescharacteristic
31#13063311—21no—
32#13063308—21no—
33#13063307—21no—
34#13063299—21no—
35#13063298—21no—
36#13063298—21no—
37C4×Dic86C2211yescharacteristic
38#13063290C2211yescharacteristic
39#13063287C2211yescharacteristic
40#13063287C2211yescharacteristic
41#13063287C2211yescharacteristic
42C4×C22⋊D43—21no—
43C4⋊(C43⋊C8)C2211yescharacteristic
44Dic43⋊C8C2211yescharacteristic
45Dic43⋊C8C2211yescharacteristic
46#13063248C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49#13063245C2211yescharacteristic
50#13063235C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C2×D8×C43C2211yescharacteristic
53C4×D4×C43C2211yescharacteristic
54C4×D4×C43C2211yescharacteristic
55#106×C43C2211yescharacteristic
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58#97×C43C2211yescharacteristic
59C2×D4×C43C2311yescharacteristic
60C2×D4×C43C2311yescharacteristic
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C2×C22⋊D43—21no—
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C2×C22⋊D43—21no—
68C2×C22⋊D43—21no—
69#10621898—44no—
70C2×D172—21no—
71C2×D172—21no—
72C2×D172C2311yescharacteristic
73C2×D172C2311yescharacteristic
74C2×D172C2311yescharacteristic
75C2×C4×D43—21no—
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×Dic86D411yescharacteristic
79C2×Dic86C2311yescharacteristic
80D8×C43—22no—
81C2×C8×C43C2311yescharacteristic
82C2×C8×C43C2311yescharacteristic
83C4⋊C4×C43C2311yescharacteristic
84C4⋊C4×C43C2311yescharacteristic
85C22⋊C4×C43—21no—
86C22⋊C4×C43—21no—
87C42×C43C2311yescharacteristic
88C22⋊Dic43—21no—
89C22⋊Dic43—21no—
90#10621883—41no—
91#10621882—41no—
92#10621882—41no—
93#10621882—41no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4—21no—
97(C2×D43)⋊C4—21no—
98(C2×D43)⋊C4—21no—
99C4⋊Dic43D411yescharacteristic
100Dic43⋊C4—21no—
101Dic43⋊C4D411yescharacteristic
102Dic43⋊C4D411yescharacteristic
103C4×Dic43—21no—
104C4×Dic43C2311yescharacteristic
105C4×Dic43C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108D344—22no—
109D344—41no—
110#10621873—22no—
111#10621873—41no—
112C23×C43—21no—
113C23×C43—21no—
114C22×D43—21no—
115C22×D43—21no—
116C22×D43—21no—
117D4×C43—21no—
118D4×C43—21no—
119D4×C43—21no—
120D4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—42no—
124C2×C4×C43—81no—
125C2×C4×C43C2×D411yescharacteristic
126C2×C4×C43C2×D411yescharacteristic
127C2×C4×C43C2411yescharacteristic
128C22⋊D43—42no—
129C22⋊D43—42no—
130C22⋊D43—42no—
131C22⋊D43—81no—
132C22⋊D43—81no—
133C22⋊D43—81no—
134C2×Dic43—21no—
135C2×Dic43C2×D411yescharacteristic
136C2×Dic43C2×D411yescharacteristic
137C2×Dic43C2×D411yescharacteristic
138C2×Dic43C2×D411yescharacteristic
139D172—21no—
140D172—21no—
141D172—21no—
142D172—21no—
143D172—21no—
144D172—21no—
145D172—42no—
146D172—81no—
147C4×D43—42no—
148C4×D43—42no—
149C4×D43—81no—
150Dic86—22no—
151Dic86—21no—
152Dic86—21no—
153C8×C43—21no—
154C8×C43#4112yescomplemented
155C43⋊C8—21no—
156C43⋊C8—21no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43—41no—
161C22×C43—41no—
162C22×C43—41no—
163C22×C43C22×D411yescharacteristic
164C2×D43—41no—
165C2×D43—41no—
166C2×D43—41no—
167C2×D43—41no—
168C2×D43—41no—
169C2×D43—41no—
170C2×D43—41no—
171C2×D43—41no—
172C2×D43—41no—
173C4×C43—21no—
174C4×C43—21no—
175C4×C43—41no—
176C4×C43—41no—
177C4×C43C2×#4111yescharacteristic
178C4×C43H(5,𝔽2)11yescharacteristic
179Dic43—21no—
180Dic43—21no—
181Dic43—21no—
182Dic43—41no—
183Dic43AGL(1,ℤ/8)12yes—
184#3399—431nomaximal, Sylow
185C2×C43—81no—
186C2×C43—81no—
187C2×C43#55011yescharacteristic
188C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
189C2×C43#57611yescharacteristic
190D43—81no—
191D43—81no—
192D43—81no—
193#559—431no—
194#550—431no—
195#496—431no—
196#496—431no—
197#493—431no—
198#463—431no—
199#463—431no—
200#460—431no—
201#459—431no—
202#459—431no—
203#459—431no—
204#446—431no—
205#442—431no—
206#442D4311yescharacteristic, complemented
207C4×SD16—431no—
208C43#339911yescharacteristic, complemented, Sylow
209C2×#41—861no—
210C2×SD16—431no—
211C2×SD16—431no—
212C2×SD16—431no—
213C2×D8—431no—
214C2×D8—431no—
215C2×D8—431no—
216C2×D8—431no—
217C2×D8—431no—
218C2×D8C2×D4311yescharacteristic
219#127—431no—
220#127—431no—
221#127—431no—
222#127—431no—
223#124—431no—
224#124—431no—
225#124—861no—
226#123—861no—
227#123—861no—
228#121—861no—
229#121—861no—
230#121—861no—
231C4×Q8—431no—
232C4×Q8—431no—
233C4×D4—431no—
234C4×D4—431no—
235C4×D4—431no—
236C4×D4—861no—
237C4×D4C2×D4311yescharacteristic
238C4×D4C2×D4311yescharacteristic
239#106C2×D4311yescharacteristic
240C4⋊C8—431no—
241C4⋊C8—431no—
242C4⋊C8—431no—
243#103—431no—
244#102—431no—
245#102—431no—
246#102—431no—
247#102C2×D4311yescharacteristic
248#102C2×D4311yescharacteristic
249#97—431no—
250#97C2×D4311yescharacteristic
251C4×C8—431no—
252#41—1724no—
253C2×Q8—431no—
254C2×Q8—431no—
255C2×D4—431no—
256C2×D4—431no—
257C2×D4—431no—
258C2×D4—861no—
259C2×D4—861no—
260C2×D4—861no—
261C2×D4—861no—
262C2×D4—861no—
263C2×D4—861no—
264C2×D4—861no—
265C2×D4—861no—
266C2×D4C22×D4311yescharacteristic
267C2×D4C22×D4311yescharacteristic
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—861no—
271C22×C4—861no—
272C22×C4—861no—
273SD16—862no—
274SD16—1721no—
275SD16—1721no—
276D8—22no—
277D8—862no—
278D8—1721no—
279D8—1721no—
280D8—1721no—
281D8—1721no—
282C2×C8—431no—
283C2×C8—431no—
284C2×C8C22×D4311yescharacteristic
285C2×C8C22×D4311yescharacteristic
286C4⋊C4—431no—
287C4⋊C4—431no—
288C4⋊C4—431no—
289C4⋊C4—861no—
290C4⋊C4C22×D4311yescharacteristic
291C4⋊C4C22×D4311yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—861no—
295C22⋊C4—861no—
296C22⋊C4—861no—
297C22⋊C4—861no—
298C22⋊C4—861no—
299C22⋊C4—861no—
300C22⋊C4—861no—
301C42—431no—
302C42—431no—
303C42—861no—
304C42C22×D4311yescharacteristic
305C23—21no—
306C23—21no—
307C23—861no—
308C23—861no—
309C23—861no—
310Q8—862no—
311Q8—861no—
312Q8—861no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—861no—
318D4—861no—
319D4—861no—
320D4—861no—
321D4—861no—
322D4—861no—
323D4—3441no—
324D4—3441no—
325D4—3441no—
326D4—3441no—
327D4—1722no—
328D4—1722no—
329D4—1722no—
330D4—1722no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—42no—
334C2×C4—81no—
335C2×C4—431no—
336C2×C4—431no—
337C2×C4—431no—
338C2×C4—431no—
339C2×C4—861no—
340C2×C4—3441no—
341C2×C4—1722no—
342C2×C4—1722no—
343C2×C4D4×D4311yescharacteristic
344C2×C4D4×D4311yescharacteristic
345C2×C4C23×D4311yescharacteristic
346C8—21no—
347C8—861no—
348C8—861no—
349C8#1062189812yescomplemented
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—1721no—
357C22—1721no—
358C22—1721no—
359C22—1721no—
360C22—1721no—
361C22—1721no—
362C22—1721no—
363C22—1721no—
364C22—1721no—
365C22C2×D4×D4311yescharacteristic
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—432no—
371C4—861no—
372C4—861no—
373C4—861no—
374C4—1721no—
375C4C2×#1062189811yescharacteristic
376C4#1306337111yescharacteristic
377C2—81no—
378C2—81no—
379C2—3441no—
380C2—3441no—
381C2—3441no—
382C2#1458357011yescharacteristic
383C2AGL(1,ℤ/8)×D4311yescharacteristic
384C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#442C2
socleC22×C43C22×D4
hypercenter#442D43
hypocenterC43#3399
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #14583632C2semidirect
2. #14583570C2semidirect
3. #14583288C2semidirect
4. #14583287C2semidirect
5. #14583274C2semidirect
6. #14583114C2semidirect
7. #14583113C2semidirect
8. #14583098C2semidirect
9. #14583094C2semidirect
10. #14583093C2semidirect
11. #14583093C2semidirect
12. #14583027C2semidirect
13. #14583010C2semidirect
14. #14582986C2semidirect
15. C43×#442C2semidirect
154. C8×C43#41semidirect
206. #442D43semidirect
208. C43#3399semidirect
349. C8#10621898semidirect