Finite Group Databasebeta

← #19146703

Subgroups — #19146703

Order 5504.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583610C211yesmaximal, characteristic, complemented
2#14583561C211yesmaximal, characteristic
3#14583261C211yesmaximal, characteristic, complemented
4#14583231C211yesmaximal, characteristic, complemented
5#14583219C211yesmaximal, characteristic, complemented
6#14583158C211yesmaximal, characteristic, complemented
7#14583129C211yesmaximal, characteristic, complemented
8#14583122C211yesmaximal, characteristic, complemented
9#14583064C211yesmaximal, characteristic, complemented
10#14583056C211yesmaximal, characteristic, complemented
11#14583004C211yesmaximal, characteristic, complemented
12#14582969C211yesmaximal, characteristic, complemented
13#14582899C211yesmaximal, characteristic, complemented
14#103×D43C211yesmaximal, characteristic, complemented
15C43×#475C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×Q8×D43C2211yescharacteristic
18C2×Dic172C2211yescharacteristic
19C2×#10621885C2211yescharacteristic
20C2×#10621873C2211yescharacteristic
21C2×#10621872C2211yescharacteristic
22C2×C8×D43C2211yescharacteristic
23#13063316—21no—
24#13063313—21no—
25#13063313C2211yescharacteristic
26#13063305—21no—
27#13063305C2211yescharacteristic
28#13063305C2211yescharacteristic
29#13063305C2211yescharacteristic
30#13063301—21no—
31#13063301—21no—
32#13063300—21no—
33#13063300C2211yescharacteristic
34C4×Dic86C2211yescharacteristic
35C4×D172—21no—
36C4×D172C2211yescharacteristic
37#13063287—21no—
38C4⋊C4×D43C2211yescharacteristic
39C4⋊C4×D43C2211yescharacteristic
40#13063256C2211yescharacteristic
41#13063250C2211yescharacteristic
42#13063249C2211yescharacteristic
43#13063248C2211yescharacteristic
44#13063248C2211yescharacteristic
45#13063248C2211yescharacteristic
46#13063247C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51#13063236C2211yescharacteristic
52C4⋊Q8×C43C2211yescharacteristic
53C4×Q8×C43C2211yescharacteristic
54#106×C43C2211yescharacteristic
55#106×C43C2211yescharacteristic
56C4⋊C8×C43C2211yescharacteristic
57#103×C43C2211yescharacteristic
58#103×C43C2211yescharacteristic
59C2×Q8×C43—21no—
60C2×Q8×C43C2311yescharacteristic
61#10621902—22no—
62#10621902—41no—
63Q8×D43—22no—
64Q8×D43—41no—
65C2×D172—21no—
66C2×D172—21no—
67C2×D172D411yescharacteristic
68C2×D172C2311yescharacteristic
69C2×C4×D43—21no—
70C2×C4×D43—21no—
71C2×C4×D43—21no—
72C2×C4×D43—21no—
73C2×C4×D43C2311yescharacteristic
74C2×C4×D43C2311yescharacteristic
75C2×Dic86—21no—
76C2×Dic86C2311yescharacteristic
77C2×Dic86C2311yescharacteristic
78C2×C8×C43C2311yescharacteristic
79C2×C8×C43C2311yescharacteristic
80C4⋊C4×C43—21no—
81C4⋊C4×C43—21no—
82C4⋊C4×C43C2311yescharacteristic
83C4⋊C4×C43C2311yescharacteristic
84C4⋊C4×C43C2311yescharacteristic
85C42×C43—21no—
86C42×C43C2311yescharacteristic
87#10621885—22no—
88(C2×D43)⋊C4—21no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4D411yescharacteristic
95(C2×D43)⋊C4D411yescharacteristic
96C4⋊Dic43—21no—
97C4⋊Dic43—21no—
98C4⋊Dic43—21no—
99C4⋊Dic43D411yescharacteristic
100C4⋊Dic43C2311yescharacteristic
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104C4×Dic43—21no—
105C2×C43⋊C8C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107Dic172—41no—
108#10621873—41no—
109#10621872—41no—
110C8×D43—41no—
111C22×D43—21no—
112C22×D43C2×D411yescharacteristic
113C22×D43C2×D411yescharacteristic
114Q8×C43—21no—
115Q8×C43—81no—
116Q8×C43#4112yes—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43C2×D411yescharacteristic
122C2×C4×C43C2×D411yescharacteristic
123C2×C4×C43C2411yescharacteristic
124C2×Dic43—21no—
125C2×Dic43—21no—
126C2×Dic43—21no—
127C2×Dic43C2×D411yescharacteristic
128C2×Dic43C2×D411yescharacteristic
129D172—22no—
130D172—21no—
131D172—21no—
132D172—42no—
133D172—42no—
134C4×D43—21no—
135C4×D43—21no—
136C4×D43—21no—
137C4×D43—21no—
138C4×D43—42no—
139C4×D43—42no—
140C4×D43—81no—
141C4×D43—81no—
142Dic86—21no—
143Dic86—21no—
144Dic86—21no—
145Dic86—21no—
146Dic86—42no—
147C8×C43—21no—
148C8×C43—21no—
149C43⋊C8—21no—
150C43⋊C8—21no—
151C22×C43C22×D411yescharacteristic
152C2×D43—21no—
153C2×D43—21no—
154C2×D43—21no—
155C2×D43—21no—
156C2×D43—21no—
157C2×D43—41no—
158C2×D43—41no—
159C2×D43—41no—
160C2×D43#13712yes—
161C4×C43—22no—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—41no—
165C4×C43—41no—
166C4×C43—41no—
167C4×C43C2×#4111yescharacteristic
168C4×C43H(5,𝔽2)11yescharacteristic
169Dic43—21no—
170Dic43—21no—
171Dic43—41no—
172Dic43—41no—
173Dic43—41no—
174#3316—431nomaximal, Sylow
175C2×C43#54611yescharacteristic
176C2×C43C2×#13711yescharacteristic
177C2×C43#57711yescharacteristic
178D43—22no—
179D43—41no—
180D43—81no—
181#554—431no—
182#548—431no—
183#489—431no—
184#483—431no—
185#481—431no—
186#475D4311yescharacteristic, complemented
187#470—431no—
188#465—431no—
189#464—431no—
190#452—431no—
191#451—431no—
192#441—431no—
193#435—431no—
194#417—431no—
195C2×#103—431no—
196C43#331611yescharacteristic, complemented, Sylow
197C2×#41—431no—
198C22×Q8—431no—
199C2×Q16—431no—
200C2×Q16—431no—
201C2×SD16—431no—
202C2×M16—431no—
203C22×C8—431no—
204C4⋊Q8C2×D4311yescharacteristic
205#125—861no—
206#124—431no—
207#124—861no—
208C22⋊Q8—431no—
209C22⋊Q8—431no—
210C22⋊Q8—431no—
211C22⋊Q8—861no—
212C22⋊Q8—861no—
213C22⋊Q8—861no—
214#121—431no—
215#121—861no—
216C4×Q8—431no—
217C4×Q8C2×D4311yescharacteristic
218C4×D4—431no—
219C4×D4—861no—
220C4×D4—861no—
221C2×C4⋊C4—431no—
222C2×C4⋊C4—431no—
223#106—431no—
224#106C2×D4311yescharacteristic
225#106C2×D4311yescharacteristic
226C4⋊C8C2×D4311yescharacteristic
227#103—431no—
228#103—431no—
229#103—431no—
230#103—431no—
231#103—431no—
232#103C2×D4311yescharacteristic
233#103C2×D4311yescharacteristic
234#102—431no—
235#102—431no—
236#102—431no—
237C22⋊C8—431no—
238C22⋊C8—431no—
239#97—431no—
240#41—862no—
241#41—1721no—
242C2×Q8—21no—
243C2×Q8—431no—
244C2×Q8—431no—
245C2×Q8—861no—
246C2×Q8—862no—
247C2×Q8—1721no—
248C2×Q8C22×D4311yescharacteristic
249C2×D4—431no—
250C2×D4—431no—
251C2×D4—861no—
252C2×D4—861no—
253C22×C4—431no—
254C22×C4—431no—
255C22×C4—861no—
256C22×C4—861no—
257C22×C4—861no—
258C22×C4—861no—
259Q16—862no—
260Q16—1721no—
261SD16—1721no—
262M16—1721no—
263C2×C8—431no—
264C2×C8—431no—
265C2×C8—1721no—
266C2×C8C22×D4311yescharacteristic
267C2×C8C22×D4311yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—431no—
271C4⋊C4—431no—
272C4⋊C4—861no—
273C4⋊C4—861no—
274C4⋊C4—861no—
275C4⋊C4—861no—
276C4⋊C4—861no—
277C4⋊C4—861no—
278C4⋊C4C22×D4311yescharacteristic
279C4⋊C4C22×D4311yescharacteristic
280C4⋊C4C22×D4311yescharacteristic
281C22⋊C4—431no—
282C22⋊C4—431no—
283C22⋊C4—861no—
284C22⋊C4—861no—
285C22⋊C4—861no—
286C22⋊C4—861no—
287C22⋊C4—861no—
288C22⋊C4—861no—
289C42—21no—
290C42—861no—
291C42C22×D4311yescharacteristic
292C23—431no—
293C23—431no—
294C23—861no—
295Q8—21no—
296Q8—81no—
297Q8—861no—
298Q8—861no—
299Q8—861no—
300Q8—861no—
301Q8—1722no—
302Q8#1062190212yes—
303D4—862no—
304D4—861no—
305D4—861no—
306D4—1722no—
307D4—1722no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—431no—
313C2×C4—431no—
314C2×C4—861no—
315C2×C4—861no—
316C2×C4—861no—
317C2×C4—861no—
318C2×C4—861no—
319C2×C4—861no—
320C2×C4—861no—
321C2×C4—3441no—
322C2×C4—3441no—
323C2×C4—1722no—
324C2×C4—1722no—
325C2×C4D4×D4311yescharacteristic
326C2×C4D4×D4311yescharacteristic
327C2×C4C23×D4311yescharacteristic
328C8—21no—
329C8—21no—
330C8—861no—
331C8—861no—
332C22—432no—
333C22—861no—
334C22—861no—
335C22—861no—
336C22—861no—
337C22—861no—
338C22—1721no—
339C22—1721no—
340C22—1721no—
341C22C2×D4×D4311yescharacteristic
342C4—21no—
343C4—21no—
344C4—22no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—861no—
349C4—861no—
350C4—1721no—
351C4—1721no—
352C4—1721no—
353C4C2×#1062190211yescharacteristic
354C4#1306337111yescharacteristic
355C2—862no—
356C2—3441no—
357C2—1721no—
358C2#1458354011yescharacteristic
359C2#137×D4311yescharacteristic
360C2#1458370511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#475C2
socleC22×C43C22×D4
hypercenter#475D43
hypocenterC43#3316
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. #14583610C2semidirect
3. #14583261C2semidirect
4. #14583231C2semidirect
5. #14583219C2semidirect
6. #14583158C2semidirect
7. #14583129C2semidirect
8. #14583122C2semidirect
9. #14583064C2semidirect
10. #14583056C2semidirect
11. #14583004C2semidirect
12. #14582969C2semidirect
13. #14582899C2semidirect
14. #103×D43C2semidirect
15. C43×#475C2semidirect
186. #475D43semidirect
196. C43#3316semidirect