Finite Group Databasebeta

← #19146920

Subgroups — #19146920

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#14583550C211yesmaximal, characteristic, complemented
3#14583244C211yesmaximal, characteristic, complemented
4#14583219C211yesmaximal, characteristic, complemented
5#14583183C211yesmaximal, characteristic, complemented
6#14583153C211yesmaximal, characteristic, complemented
7#14583150C211yesmaximal, characteristic, complemented
8#14583093C211yesmaximal, characteristic, complemented
9#14583046C211yesmaximal, characteristic, complemented
10#14583045C211yesmaximal, characteristic, complemented
11#14582986C211yesmaximal, characteristic, complemented
12#14582974C211yesmaximal, characteristic, complemented
13#14582898C211yesmaximal, characteristic, complemented
14#14582897C211yesmaximal, characteristic, complemented
15C43×#481C211yesmaximal, characteristic, complemented
16C2×#10621898—21no—
17C2×#10621898C2211yescharacteristic
18C2×#10621900C2211yescharacteristic
19C2×#10621873C2211yescharacteristic
20C2×D344C2211yescharacteristic
21C2×#10621882C2211yescharacteristic
22C2×#10621877C2211yescharacteristic
23C2×#10621872C2211yescharacteristic
24#13063324C2211yescharacteristic
25#13063321—21no—
26#13063321C2211yescharacteristic
27#13063310—21no—
28#13063308—21no—
29#13063303—21no—
30#13063300C2211yescharacteristic
31#13063300C2211yescharacteristic
32#13063299C2211yescharacteristic
33#13063298—21no—
34#13063297—21no—
35#13063290C2211yescharacteristic
36#13063287C2211yescharacteristic
37C4×C22⋊D43C2211yescharacteristic
38(C22⋊D43)⋊C4—21no—
39C4⋊C4×D43C2211yescharacteristic
40#13063256C2211yescharacteristic
41Dic43⋊C8C2211yescharacteristic
42#13063250C2211yescharacteristic
43#13063248C2211yescharacteristic
44#13063248C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49#13063245C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52#121×C43C2211yescharacteristic
53C2×C4⋊C4×C43C2211yescharacteristic
54#106×C43C2211yescharacteristic
55#106×C43C2211yescharacteristic
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59C2×D4×C43—21no—
60C2×D4×C43C2311yescharacteristic
61C22×C4×C43—21no—
62C22×C4×C43C2311yescharacteristic
63C2×C22⋊D43—21no—
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C2×C22⋊D43—21no—
68C2×C22⋊D43D411yescharacteristic
69C22×Dic43—21no—
70#10621900—22no—
71#10621900—41no—
72#10621898—22no—
73#10621898—41no—
74#10621898—44no—
75C2×D172—21no—
76C2×D172—21no—
77C2×D172C2311yescharacteristic
78C2×D172C2311yescharacteristic
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×C4×D43—21no—
82C2×C4×D43C2311yescharacteristic
83C2×Dic86—21no—
84C2×Dic86C2311yescharacteristic
85C2×C8×C43C2311yescharacteristic
86C2×C8×C43C2311yescharacteristic
87C4⋊C4×C43—21no—
88C4⋊C4×C43C2311yescharacteristic
89C4⋊C4×C43C2311yescharacteristic
90C4⋊C4×C43C2311yescharacteristic
91C22⋊C4×C43—21no—
92C22⋊Dic43D411yescharacteristic
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)⋊C4D411yescharacteristic
99C4⋊Dic43C2311yescharacteristic
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103Dic43⋊C4D411yescharacteristic
104C4×Dic43—21no—
105C4×Dic43C2311yescharacteristic
106#10621877—41no—
107C2×C43⋊C8C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109D344—41no—
110#10621873—22no—
111#10621872—41no—
112C23×C43—21no—
113C23×C43C2×D411yescharacteristic
114C22×D43—21no—
115C22×D43—21no—
116C22×D43C2×D411yescharacteristic
117D4×C43—21no—
118D4×C43—21no—
119D4×C43—81no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—42no—
126C2×C4×C43C2×D411yescharacteristic
127C2×C4×C43C2411yescharacteristic
128C22⋊D43—22no—
129C22⋊D43—42no—
130C22⋊D43—42no—
131C22⋊D43—42no—
132C22⋊D43—42no—
133C22⋊D43—81no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—42no—
137C2×Dic43C2×D411yescharacteristic
138C2×Dic43C2×D411yescharacteristic
139C2×Dic43C2×D411yescharacteristic
140D172—21no—
141D172—21no—
142D172—21no—
143D172—21no—
144D172—42no—
145D172—81no—
146C4×D43—21no—
147C4×D43—21no—
148C4×D43—42no—
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×C43C22×D411yescharacteristic
165C2×D43—21no—
166C2×D43—21no—
167C2×D43—21no—
168C2×D43—41no—
169C2×D43—41no—
170C2×D43—41no—
171C2×D43—41no—
172C2×D43—41no—
173C2×D43—41no—
174C4×C43—21no—
175C4×C43—41no—
176C4×C43—41no—
177C4×C43—41no—
178C4×C43C2×#4111yescharacteristic
179C4×C43H(5,𝔽2)11yescharacteristic
180Dic43—22no—
181Dic43—21no—
182Dic43—21no—
183Dic43—41no—
184Dic43AGL(1,ℤ/8)12yes—
185#3332—431nomaximal, Sylow
186C2×C43—41no—
187C2×C43—81no—
188C2×C43#54611yescharacteristic
189C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C43#57711yescharacteristic
191D43—41no—
192D43—81no—
193D43—81no—
194#550—431no—
195#547—431no—
196#486—431no—
197#481—431no—
198#481D4311yescharacteristic, complemented
199#475—431no—
200#469—431no—
201#469—431no—
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×D8—431no—
216C2×M16—431no—
217C2×M16—431no—
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—431no—
227#121—861no—
228#121—861no—
229#121C2×D4311yescharacteristic
230C4×Q8—431no—
231C4×D4—431no—
232C4×D4—431no—
233C4×D4—861no—
234C2×C4⋊C4—431no—
235C2×C4⋊C4C2×D4311yescharacteristic
236#106—431no—
237#106C2×D4311yescharacteristic
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⋊C8C2×D4311yescharacteristic
252C4×C8—431no—
253#41—862no—
254#41—862no—
255#41—1721no—
256#41—1724no—
257#41—1721no—
258C2×Q8—431no—
259C2×Q8—861no—
260C2×D4—21no—
261C2×D4—431no—
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×D4—861no—
271C2×D4C22×D4311yescharacteristic
272C22×C4—21no—
273C22×C4—431no—
274C22×C4—861no—
275C22×C4—861no—
276C22×C4—861no—
277C22×C4—861no—
278C22×C4C22×D4311yescharacteristic
279SD16—862no—
280D8—1721no—
281D8—1721no—
282M16—1721no—
283M16—1721no—
284C2×C8—431no—
285C2×C8—431no—
286C2×C8C22×D4311yescharacteristic
287C2×C8C22×D4311yescharacteristic
288C4⋊C4—21no—
289C4⋊C4—431no—
290C4⋊C4—431no—
291C4⋊C4—861no—
292C4⋊C4—861no—
293C4⋊C4—861no—
294C4⋊C4C22×D4311yescharacteristic
295C4⋊C4C22×D4311yescharacteristic
296C4⋊C4C22×D4311yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—431no—
299C22⋊C4—431no—
300C22⋊C4—861no—
301C22⋊C4—861no—
302C22⋊C4—861no—
303C22⋊C4—861no—
304C42—431no—
305C42—861no—
306C23—21no—
307C23—431no—
308C23—861no—
309C23—861no—
310C23D4×D4311yescharacteristic
311Q8—432no—
312Q8—861no—
313Q8—1722no—
314D4—21no—
315D4—21no—
316D4—81no—
317D4—862no—
318D4—861no—
319D4—861no—
320D4—861no—
321D4—861no—
322D4—3441no—
323D4—3441no—
324D4—1722no—
325D4—1722no—
326D4—1722no—
327D4—1722no—
328D4—1722no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—42no—
335C2×C4—431no—
336C2×C4—431no—
337C2×C4—431no—
338C2×C4—861no—
339C2×C4—861no—
340C2×C4—861no—
341C2×C4—861no—
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—861no—
359C22—861no—
360C22—861no—
361C22—1721no—
362C22—1721no—
363C22—1721no—
364C22—1721no—
365C22—1721no—
366C22—1721no—
367C22C2×D4×D4311yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—432no—
373C4—861no—
374C4—861no—
375C4—862no—
376C4—1721no—
377C4#41×D4311yescharacteristic
378C4#1306337111yescharacteristic
379C2—41no—
380C2—81no—
381C2—3441no—
382C2—3441no—
383C2—1721no—
384C2#1458354111yescharacteristic
385C2AGL(1,ℤ/8)×D4311yescharacteristic
386C2#1458370511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#481C2
socleC22×C43C22×D4
hypercenter#481D43
hypocenterC43#3332
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. #14583567C2semidirect
2. #14583550C2semidirect
3. #14583244C2semidirect
4. #14583219C2semidirect
5. #14583183C2semidirect
6. #14583153C2semidirect
7. #14583150C2semidirect
8. #14583093C2semidirect
9. #14583046C2semidirect
10. #14583045C2semidirect
11. #14582986C2semidirect
12. #14582974C2semidirect
13. #14582898C2semidirect
14. #14582897C2semidirect
15. C43×#481C2semidirect
153. Dic86#41semidirect
198. #481D43semidirect
209. C43#3332semidirect