Finite Group Databasebeta

← #19147588

Subgroups — #19147588

Order 5504.

372 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583631C211yesmaximal, characteristic, complemented
2#14583618C211yesmaximal, characteristic, complemented
3#14583280C211yesmaximal, characteristic, complemented
4#14583270C211yesmaximal, characteristic, complemented
5#14583123C211yesmaximal, characteristic, complemented
6#14583118C211yesmaximal, characteristic, complemented
7#14583112C211yesmaximal, characteristic, complemented
8#14583111C211yesmaximal, characteristic, complemented
9#14583107C211yesmaximal, characteristic, complemented
10#14583092C211yesmaximal, characteristic
11C8×Dic86C211yesmaximal, characteristic, complemented
12C4×#10621873C211yesmaximal, characteristic, complemented
13SD16×Dic43C211yesmaximal, characteristic, complemented
14SD16×Dic43C211yesmaximal, characteristic, complemented
15C43×#495C211yesmaximal, characteristic, complemented
16C2×#10621885C2211yescharacteristic
17C2×#10621873C2211yescharacteristic
18C2×#10621883C2211yescharacteristic
19C2×#10621884C2211yescharacteristic
20C2×#10621882C2211yescharacteristic
21#13063323C2211yescharacteristic
22#13063321C2211yescharacteristic
23#13063318—21no—
24#13063318—21no—
25#13063314C2211yescharacteristic
26#13063312C2211yescharacteristic
27#13063311—21no—
28#13063309—21no—
29#13063307—21no—
30#13063302—21no—
31Q8×Dic43C2211yescharacteristic
32Q8×Dic43C2211yescharacteristic
33C4×Dic86C2211yescharacteristic
34C4×Dic86C2211yescharacteristic
35C4×D172C2211yescharacteristic
36D4×Dic43C2211yescharacteristic
37D4×Dic43C2211yescharacteristic
38(C22⋊D43)⋊C4—21no—
39#13063281—21no—
40#13063257C2211yescharacteristic
41C4⋊(C43⋊C8)C2211yescharacteristic
42Dic43⋊C8C2211yescharacteristic
43Dic43⋊C8C2211yescharacteristic
44#13063250C2211yescharacteristic
45#13063249C2211yescharacteristic
46#13063249C2211yescharacteristic
47#13063247C2211yescharacteristic
48#13063246C2211yescharacteristic
49#13063246C2211yescharacteristic
50C8×Dic43C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C2×Q16×C43C2211yescharacteristic
53C2×SD16×C43C2211yescharacteristic
54C2×SD16×C43C2211yescharacteristic
55C2×D8×C43C2211yescharacteristic
56#124×C43C2211yescharacteristic
57#124×C43C2211yescharacteristic
58C4×C8×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60C2×Q8×C43C2311yescharacteristic
61C2×D4×C43C2311yescharacteristic
62C2×D4×C43C2311yescharacteristic
63C2×C22⋊D43—21no—
64C2×C22⋊D43—21no—
65C22×Dic43—21no—
66C22×Dic43—21no—
67C2×D172C2311yescharacteristic
68C2×C4×D43—21no—
69C2×Dic86D411yescharacteristic
70C2×Dic86C2311yescharacteristic
71Q16×C43—41no—
72SD16×C43—22no—
73SD16×C43—22no—
74D8×C43—41no—
75C2×C8×C43C2311yescharacteristic
76C2×C8×C43C2311yescharacteristic
77C22⋊C4×C43—21no—
78C22⋊C4×C43—21no—
79C22⋊C4×C43—21no—
80C22⋊C4×C43—21no—
81C42×C43C2311yescharacteristic
82C22⋊Dic43—21no—
83C22⋊Dic43—21no—
84C22⋊Dic43—21no—
85C22⋊Dic43—21no—
86#10621885—41no—
87#10621884—41no—
88#10621883—41no—
89#10621882—41no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93C4⋊Dic43—21no—
94C4⋊Dic43—21no—
95C4⋊Dic43D411yescharacteristic
96C4⋊Dic43C2311yescharacteristic
97C4⋊Dic43C2311yescharacteristic
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101Dic43⋊C4D411yescharacteristic
102Dic43⋊C4D411yescharacteristic
103C4×Dic43—21no—
104C4×Dic43—21no—
105C4×Dic43—21no—
106C4×Dic43C2311yescharacteristic
107C4×Dic43C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110#10621873—22no—
111C23×C43—21no—
112C23×C43—21no—
113C22×D43—21no—
114Q8×C43—21no—
115Q8×C43—21no—
116Q8×C43—21no—
117Q8×C43—21no—
118D4×C43—21no—
119D4×C43—21no—
120D4×C43—21no—
121D4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43C2×D411yescharacteristic
125C2×C4×C43C2×D411yescharacteristic
126C2×C4×C43C2411yescharacteristic
127C22⋊D43—42no—
128C22⋊D43—81no—
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—42no—
133C2×Dic43—81no—
134C2×Dic43C2×D411yescharacteristic
135C2×Dic43C2×D411yescharacteristic
136C2×Dic43C2×D411yescharacteristic
137C2×Dic43C2×D411yescharacteristic
138D172—21no—
139D172—21no—
140C4×D43—81no—
141Dic86—22no—
142Dic86—21no—
143Dic86—21no—
144C8×C43—21no—
145C8×C43#4112yes—
146C43⋊C8—21no—
147C43⋊C8—21no—
148C22×C43—41no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43—41no—
153C22×C43—41no—
154C22×C43C22×D411yescharacteristic
155C2×D43—41no—
156C2×D43—41no—
157C2×D43—41no—
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—41no—
161C4×C43—41no—
162C4×C43C2×#4111yescharacteristic
163C4×C43H(5,𝔽2)11yescharacteristic
164Dic43—21no—
165Dic43—21no—
166Dic43—21no—
167Dic43—41no—
168Dic43—41no—
169Dic43—41no—
170Dic43#13512yes—
171#3394—431nomaximal, Sylow
172C2×C43—81no—
173C2×C43—81no—
174C2×C43#55011yescharacteristic
175C2×C43C2×#13511yescharacteristic
176C2×C43#57711yescharacteristic
177D43—81no—
178#559—431no—
179#556—431no—
180#495—431no—
181#495D4311yescharacteristic, complemented
182#492—431no—
183#464—431no—
184#464—431no—
185#463—431no—
186#463—431no—
187#462—431no—
188#459—431no—
189C8×Q8—431no—
190C4×SD16—431no—
191C4×SD16—431no—
192C4×SD16—431no—
193C43#339411yescharacteristic, complemented, Sylow
194C2×Q16—431no—
195C2×Q16C2×D4311yescharacteristic
196C2×SD16—431no—
197C2×SD16—431no—
198C2×SD16—431no—
199C2×SD16C2×D4311yescharacteristic
200C2×SD16C2×D4311yescharacteristic
201C2×D8—431no—
202C2×D8C2×D4311yescharacteristic
203C4⋊Q8—431no—
204#127—431no—
205#126—861no—
206#126—861no—
207#124—431no—
208#124—431no—
209#124—861no—
210#124C2×D4311yescharacteristic
211#124C2×D4311yescharacteristic
212#123—861no—
213#123—861no—
214C22⋊Q8—861no—
215C4×Q8—431no—
216C4×Q8—431no—
217C4×Q8—431no—
218C4×Q8—431no—
219C4×D4—431no—
220C4×D4—431no—
221C4×D4—431no—
222C4×D4—861no—
223#117—861no—
224#106—431no—
225C4⋊C8—431no—
226C4⋊C8—431no—
227C4⋊C8—431no—
228#103—431no—
229#103—431no—
230#103—431no—
231#102—431no—
232#102—431no—
233#102—431no—
234C4×C8—431no—
235C4×C8—431no—
236C4×C8C2×D4311yescharacteristic
237C2×Q8—431no—
238C2×Q8—431no—
239C2×Q8C22×D4311yescharacteristic
240C2×Q8C22×D4311yescharacteristic
241C2×D4—431no—
242C2×D4—861no—
243C2×D4—861no—
244C2×D4C22×D4311yescharacteristic
245C2×D4C22×D4311yescharacteristic
246C22×C4—861no—
247C22×C4—861no—
248C22×C4—861no—
249Q16—41no—
250Q16—1721no—
251SD16—22no—
252SD16—22no—
253SD16—862no—
254SD16—1721no—
255SD16—1721no—
256D8—41no—
257D8—1721no—
258C2×C8—431no—
259C2×C8—431no—
260C2×C8C22×D4311yescharacteristic
261C2×C8C22×D4311yescharacteristic
262C4⋊C4—431no—
263C4⋊C4—431no—
264C4⋊C4—431no—
265C4⋊C4—431no—
266C4⋊C4—431no—
267C4⋊C4—861no—
268C4⋊C4—861no—
269C4⋊C4—861no—
270C4⋊C4—861no—
271C4⋊C4—861no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—861no—
277C22⋊C4—861no—
278C22⋊C4—861no—
279C22⋊C4—861no—
280C22⋊C4—861no—
281C22⋊C4—861no—
282C22⋊C4—861no—
283C42—431no—
284C42—431no—
285C42—861no—
286C42—861no—
287C42—861no—
288C42C22×D4311yescharacteristic
289C23—21no—
290C23—21no—
291C23—861no—
292Q8—21no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—862no—
297Q8—861no—
298Q8—861no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—861no—
304D4—861no—
305D4—3441no—
306D4—1722no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—431no—
310C2×C4—431no—
311C2×C4—431no—
312C2×C4—431no—
313C2×C4—861no—
314C2×C4—861no—
315C2×C4—861no—
316C2×C4—3441no—
317C2×C4—3441no—
318C2×C4—1722no—
319C2×C4D4×D4311yescharacteristic
320C2×C4D4×D4311yescharacteristic
321C2×C4C23×D4311yescharacteristic
322C8—21no—
323C8—861no—
324C8—861no—
325C8#1062190012yes—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—1721no—
333C22—1721no—
334C22—1721no—
335C22C2×D4×D4311yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—432no—
341C4—861no—
342C4—861no—
343C4—861no—
344C4—1721no—
345C4—1721no—
346C4—1721no—
347C4C2×#1062190011yescharacteristic
348C4#1306337011yescharacteristic
349C2—81no—
350C2—81no—
351C2—3441no—
352C2#1458356911yescharacteristic
353C2#135×D4311yescharacteristic
354C2#1458370611yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#495C2
socleC22×C43C22×D4
hypercenter#495D43
hypocenterC43#3394
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #14583631C2semidirect
2. #14583618C2semidirect
3. #14583280C2semidirect
4. #14583270C2semidirect
5. #14583123C2semidirect
6. #14583118C2semidirect
7. #14583112C2semidirect
8. #14583111C2semidirect
9. #14583107C2semidirect
11. C8×Dic86C2semidirect
12. C4×#10621873C2semidirect
13. SD16×Dic43C2semidirect
14. SD16×Dic43C2semidirect
15. C43×#495C2semidirect
181. #495D43semidirect
193. C43#3394semidirect