Finite Group Databasebeta

← #19146033

Subgroups — #19146033

Order 5504.

370 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583505C211yesmaximal, characteristic, complemented
2#14583500C211yesmaximal, characteristic, complemented
3#14583202C211yesmaximal, characteristic, complemented
4#14583198C211yesmaximal, characteristic, complemented
5#14583196C211yesmaximal, characteristic, complemented
6#14583153C211yesmaximal, characteristic, complemented
7#14583151C211yesmaximal, characteristic, complemented
8#14583136C211yesmaximal, characteristic, complemented
9#14583134C211yesmaximal, characteristic, complemented
10#14583095C211yesmaximal, characteristic, complemented
11#14583094C211yesmaximal, characteristic, complemented
12#14583093C211yesmaximal, characteristic, complemented
13#14583093C211yesmaximal, characteristic, complemented
14#14582924C211yesmaximal, characteristic, complemented
15C43×#478C211yesmaximal, characteristic, complemented
16C2×D344C2211yescharacteristic
17C2×D344C2211yescharacteristic
18C2×#10621882C2211yescharacteristic
19C2×#10621882C2211yescharacteristic
20C2×#10621872C2211yescharacteristic
21C2×C8×D43C2211yescharacteristic
22#13063322C2211yescharacteristic
23#13063321C2211yescharacteristic
24#13063316C2211yescharacteristic
25#13063310—21no—
26#13063310—21no—
27#13063308—21no—
28#13063307—21no—
29#13063300—21no—
30#13063300—21no—
31#13063300C2211yescharacteristic
32#13063300C2211yescharacteristic
33#13063300C2211yescharacteristic
34#13063299—21no—
35#13063298—21no—
36#13063296C2211yescharacteristic
37C4×D172C2211yescharacteristic
38#13063287C2211yescharacteristic
39#13063287C2211yescharacteristic
40#13063282C2211yescharacteristic
41#13063258C2211yescharacteristic
42#13063256C2211yescharacteristic
43C4⋊(C43⋊C8)C2211yescharacteristic
44Dic43⋊C8C2211yescharacteristic
45Dic43⋊C8C2211yescharacteristic
46#13063247C2211yescharacteristic
47#13063247C2211yescharacteristic
48#13063245C2211yescharacteristic
49#13063245C2211yescharacteristic
50#13063245C2211yescharacteristic
51#13063245C2211yescharacteristic
52#125×C43C2211yescharacteristic
53C4×D4×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic
55#106×C43C2211yescharacteristic
56C4⋊C8×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic
59C2×D4×C43C2311yescharacteristic
60C22×C4×C43—21no—
61C2×C22⋊D43—21no—
62C2×C22⋊D43—21no—
63C2×C22⋊D43—21no—
64C2×D172—21no—
65C2×D172—21no—
66C2×D172—21no—
67C2×D172—21no—
68C2×D172—21no—
69C2×D172C2311yescharacteristic
70C2×D172C2311yescharacteristic
71C2×D172C2311yescharacteristic
72C2×C4×D43—21no—
73C2×C4×D43—21no—
74C2×C4×D43—21no—
75C2×C4×D43C2311yescharacteristic
76C2×C8×C43C2311yescharacteristic
77C2×C8×C43C2311yescharacteristic
78C4⋊C4×C43—21no—
79C4⋊C4×C43—21no—
80C4⋊C4×C43C2311yescharacteristic
81C4⋊C4×C43C2311yescharacteristic
82C4⋊C4×C43C2311yescharacteristic
83C22⋊C4×C43—21no—
84C42×C43C2311yescharacteristic
85C22⋊Dic43—21no—
86#10621882—41no—
87#10621882—41no—
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⋊Dic43C2311yescharacteristic
98Dic43⋊C4—21no—
99Dic43⋊C4D411yescharacteristic
100Dic43⋊C4D411yescharacteristic
101C4×Dic43C2311yescharacteristic
102C2×C43⋊C8C2311yescharacteristic
103C2×C43⋊C8C2311yescharacteristic
104D344—41no—
105D344—41no—
106#10621872—41no—
107C8×D43—41no—
108C23×C43—21no—
109C22×D43—21no—
110C22×D43—21no—
111C22×D43—21no—
112C22×D43C2×D411yescharacteristic
113D4×C43—21no—
114D4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—81no—
119C2×C4×C43C2×D411yescharacteristic
120C2×C4×C43C2×D411yescharacteristic
121C2×C4×C43C2411yescharacteristic
122C22⋊D43—81no—
123C22⋊D43—81no—
124C22⋊D43—81no—
125C2×Dic43—21no—
126C2×Dic43C2×D411yescharacteristic
127C2×Dic43C2×D411yescharacteristic
128C2×Dic43C2×D411yescharacteristic
129D172—21no—
130D172—21no—
131D172—21no—
132D172—21no—
133D172—21no—
134D172—21no—
135D172—81no—
136D172—81no—
137D172—81no—
138D172—81no—
139D172—81no—
140C4×D43—21no—
141C4×D43—21no—
142C4×D43—81no—
143C4×D43—81no—
144C4×D43—81no—
145C8×C43—21no—
146C8×C43—21no—
147C43⋊C8—21no—
148C43⋊C8—21no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43C22×D411yescharacteristic
153C2×D43—21no—
154C2×D43—21no—
155C2×D43—21no—
156C2×D43—41no—
157C2×D43—41no—
158C2×D43—41no—
159C2×D43—41no—
160C2×D43—41no—
161C2×D43—41no—
162C2×D43—41no—
163C2×D43—41no—
164C2×D43—41no—
165C4×C43—21no—
166C4×C43—21no—
167C4×C43—41no—
168C4×C43—41no—
169C4×C43—41no—
170C4×C43H(5,𝔽2)11yescharacteristic
171C4×C432−1+411yescharacteristic
172Dic43—21no—
173Dic43—21no—
174Dic43—21no—
175Dic43—41no—
176#3259—431nomaximal, Sylow
177C2×C43—81no—
178C2×C43#53711yescharacteristic
179C2×C43#57611yescharacteristic
180C2×C43#57611yescharacteristic
181D43—41no—
182D43—81no—
183D43—81no—
184D43—81no—
185#540—431no—
186#540—431no—
187#478—431no—
188#478—431no—
189#478—431no—
190#478D4311yescharacteristic, complemented
191#469—431no—
192#469—431no—
193#466—431no—
194#466—431no—
195#459—431no—
196#459—431no—
197#459—431no—
198#459—431no—
199#424—431no—
200C43#325911yescharacteristic, complemented, Sylow
201C2×D8—431no—
202C2×D8—431no—
203C2×D8—431no—
204C2×D8—431no—
205C2×M16—431no—
206C22×C8—431no—
207#127—431no—
208#127—431no—
209#125—431no—
210#125C2×D4311yescharacteristic
211#123—861no—
212#123—861no—
213#123—861no—
214#123—861no—
215#121—431no—
216#121—431no—
217#121—431no—
218#121—431no—
219#121—861no—
220#121—861no—
221#121—861no—
222#121—861no—
223C4×D4—431no—
224C4×D4—431no—
225C4×D4—431no—
226C4×D4C2×D4311yescharacteristic
227#117—431no—
228#107—431no—
229#107C2×D4311yescharacteristic
230#106—431no—
231#106C2×D4311yescharacteristic
232C4⋊C8—431no—
233C4⋊C8—431no—
234C4⋊C8—431no—
235C4⋊C8C2×D4311yescharacteristic
236#102—431no—
237#102—431no—
238#102—431no—
239#102—431no—
240#102—431no—
241#102—431no—
242#102C2×D4311yescharacteristic
243#102C2×D4311yescharacteristic
244C2×D4—431no—
245C2×D4—431no—
246C2×D4—431no—
247C2×D4—861no—
248C2×D4—861no—
249C2×D4—861no—
250C2×D4—861no—
251C2×D4—861no—
252C2×D4—861no—
253C2×D4—861no—
254C2×D4—861no—
255C2×D4C22×D4311yescharacteristic
256C22×C4—21no—
257C22×C4—431no—
258C22×C4—861no—
259C22×C4—861no—
260C22×C4—861no—
261D8—1721no—
262D8—1721no—
263D8—1721no—
264D8—1721no—
265M16—1721no—
266C2×C8—431no—
267C2×C8—431no—
268C2×C8—1721no—
269C2×C8C22×D4311yescharacteristic
270C2×C8C22×D4311yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—431no—
274C4⋊C4—431no—
275C4⋊C4—431no—
276C4⋊C4—861no—
277C4⋊C4—861no—
278C4⋊C4C22×D4311yescharacteristic
279C4⋊C4C22×D4311yescharacteristic
280C4⋊C4C22×D4311yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—431no—
283C22⋊C4—431no—
284C22⋊C4—861no—
285C22⋊C4—861no—
286C22⋊C4—861no—
287C22⋊C4—861no—
288C22⋊C4—861no—
289C22⋊C4—861no—
290C22⋊C4—861no—
291C42—431no—
292C42C22×D4311yescharacteristic
293C23—21no—
294C23—431no—
295C23—861no—
296C23—861no—
297C23—861no—
298D4—21no—
299D4—21no—
300D4—861no—
301D4—861no—
302D4—861no—
303D4—861no—
304D4—861no—
305D4—861no—
306D4—3441no—
307D4—3441no—
308D4—3441no—
309D4—3441no—
310D4—3441no—
311D4—3441no—
312D4—3441no—
313D4—3441no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—81no—
318C2×C4—431no—
319C2×C4—431no—
320C2×C4—431no—
321C2×C4—861no—
322C2×C4—861no—
323C2×C4—861no—
324C2×C4—3441no—
325C2×C4—3441no—
326C2×C4—3441no—
327C2×C4D4×D4311yescharacteristic
328C2×C4D4×D4311yescharacteristic
329C2×C4C23×D4311yescharacteristic
330C8—21no—
331C8—21no—
332C8—861no—
333C8—861no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—861no—
338C22—861no—
339C22—861no—
340C22—1721no—
341C22—1721no—
342C22—1721no—
343C22—1721no—
344C22—1721no—
345C22—1721no—
346C22—1721no—
347C22—1721no—
348C22—1721no—
349C22C2×D4×D4311yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—861no—
356C4—861no—
357C4—861no—
358C4—1721no—
359C4#1306337111yescharacteristic
360C4#1306337311yescharacteristic
361C2—81no—
362C2—3441no—
363C2—3441no—
364C2—3441no—
365C2—1721no—
366C2#1458347911yescharacteristic
367C2#1458370111yescharacteristic
368C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#478C2
socleC22×C43C22×D4
hypercenter#478D43
hypocenterC43#3259
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #14583505C2semidirect
2. #14583500C2semidirect
3. #14583202C2semidirect
4. #14583198C2semidirect
5. #14583196C2semidirect
6. #14583153C2semidirect
7. #14583151C2semidirect
8. #14583136C2semidirect
9. #14583134C2semidirect
10. #14583095C2semidirect
11. #14583094C2semidirect
12. #14583093C2semidirect
13. #14583093C2semidirect
14. #14582924C2semidirect
15. C43×#478C2semidirect
190. #478D43semidirect
200. C43#3259semidirect