Finite Group Databasebeta

← #19147663

Subgroups — #19147663

Order 5504.

368 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#14583634C211yesmaximal, characteristic, complemented
2#14583622C211yesmaximal, characteristic, complemented
3#14583293C211yesmaximal, characteristic, complemented
4#14583288C211yesmaximal, characteristic
5#14583283C211yesmaximal, characteristic, complemented
6#14583122C211yesmaximal, characteristic, complemented
7#14583122C211yesmaximal, characteristic, complemented
8#14583115C211yesmaximal, characteristic, complemented
9#14583115C211yesmaximal, characteristic, complemented
10#14583105C211yesmaximal, characteristic, complemented
11#14583100C211yesmaximal, characteristic, complemented
12#14583012C211yesmaximal, characteristic, complemented
13#14583007C211yesmaximal, characteristic, complemented
14C4×#10621873C211yesmaximal, characteristic, complemented
15C43×#446C211yesmaximal, characteristic, complemented
16C2×Dic172C2211yescharacteristic
17C2×Dic172C2211yescharacteristic
18C2×#10621873C2211yescharacteristic
19C2×#10621873C2211yescharacteristic
20C2×#10621873C2211yescharacteristic
21C2×#10621873C2211yescharacteristic
22C2×#10621873C2211yescharacteristic
23C2×D344C2211yescharacteristic
24C2×D344C2211yescharacteristic
25#13063325C2211yescharacteristic
26#13063322C2211yescharacteristic
27#13063320—21no—
28#13063320—21no—
29#13063314—21no—
30#13063313C2211yescharacteristic
31#13063313C2211yescharacteristic
32#13063313C2211yescharacteristic
33#13063313C2211yescharacteristic
34#13063310—21no—
35#13063310—21no—
36#13063301—21no—
37C4×Dic86C2211yescharacteristic
38C4×Dic86C2211yescharacteristic
39C4×Dic86C2211yescharacteristic
40C4×D172C2211yescharacteristic
41C4×D172C2211yescharacteristic
42C4×D172C2211yescharacteristic
43#13063287—21no—
44#13063283—21no—
45#13063257C2211yescharacteristic
46#13063250C2211yescharacteristic
47#13063250C2211yescharacteristic
48#13063250C2211yescharacteristic
49#13063247C2211yescharacteristic
50#13063247C2211yescharacteristic
51#13063247C2211yescharacteristic
52C4×Q8×C43C2211yescharacteristic
53C4⋊C8×C43C2211yescharacteristic
54C4⋊C8×C43C2211yescharacteristic
55C4⋊C8×C43C2211yescharacteristic
56#97×C43C2211yescharacteristic
57#97×C43C2211yescharacteristic
58C4×C8×C43C2211yescharacteristic
59C2×Q8×C43D411yescharacteristic
60C2×D172—21no—
61C2×D172—21no—
62C2×D172C2311yescharacteristic
63C2×D172C2311yescharacteristic
64C2×D172C2311yescharacteristic
65C2×C4×D43—21no—
66C2×C4×D43—21no—
67C2×C4×D43—21no—
68C2×Dic86C2311yescharacteristic
69C2×Dic86C2311yescharacteristic
70C2×Dic86C2311yescharacteristic
71C2×C8×C43C2311yescharacteristic
72C2×C8×C43C2311yescharacteristic
73C2×C8×C43C2311yescharacteristic
74C2×C8×C43C2311yescharacteristic
75C4⋊C4×C43D411yescharacteristic
76C4⋊C4×C43D411yescharacteristic
77C4⋊C4×C43D411yescharacteristic
78C42×C43C2311yescharacteristic
79C42×C43C2311yescharacteristic
80C42×C43C2311yescharacteristic
81(C2×D43)⋊C4—21no—
82(C2×D43)⋊C4—21no—
83(C2×D43)⋊C4—21no—
84(C2×D43)⋊C4—21no—
85(C2×D43)⋊C4—21no—
86(C2×D43)⋊C4—21no—
87(C2×D43)⋊C4—21no—
88(C2×D43)⋊C4—21no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92C4⋊Dic43—21no—
93C4⋊Dic43—21no—
94C4⋊Dic43C2311yescharacteristic
95C4⋊Dic43C2311yescharacteristic
96Dic43⋊C4—21no—
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99C4×Dic43—21no—
100C4×Dic43—21no—
101C4×Dic43—21no—
102Dic172—22no—
103Dic172—41no—
104D344—22no—
105D344—41no—
106#10621873—22no—
107#10621873—41no—
108#10621873—41no—
109#10621873—41no—
110#10621873—41no—
111C22×D43—21no—
112C22×D43—21no—
113C22×D43—21no—
114Q8×C43—41no—
115C2×C4×C43C2×D411yescharacteristic
116C2×C4×C43C2×D411yescharacteristic
117C2×C4×C43C2×D411yescharacteristic
118C2×C4×C43C2×D411yescharacteristic
119C2×C4×C43C2×D411yescharacteristic
120C2×C4×C43C2×D411yescharacteristic
121C2×C4×C43C2411yescharacteristic
122C2×Dic43—21no—
123C2×Dic43—21no—
124C2×Dic43—21no—
125C2×Dic43—21no—
126C2×Dic43—21no—
127D172—21no—
128D172—21no—
129D172—21no—
130D172—21no—
131D172—21no—
132D172—21no—
133D172—42no—
134D172—81no—
135C4×D43—42no—
136C4×D43—81no—
137C4×D43—81no—
138Dic86—21no—
139Dic86—21no—
140Dic86—21no—
141Dic86—21no—
142Dic86—21no—
143Dic86—21no—
144C8×C43—21no—
145C8×C43—21no—
146C8×C43—21no—
147C8×C43#4112yes—
148C22×C43C22×D411yescharacteristic
149C2×D43—41no—
150C2×D43—41no—
151C2×D43—41no—
152C2×D43—41no—
153C2×D43—41no—
154C2×D43—41no—
155C2×D43—41no—
156C2×D43—41no—
157C2×D43—41no—
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—21no—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43C2×#4111yescharacteristic
165C4×C43H(5,𝔽2)11yescharacteristic
166Dic43—41no—
167Dic43—41no—
168Dic43—41no—
169Dic43—41no—
170Dic43—41no—
171#3401—431nomaximal, Sylow
172C2×C43#55011yescharacteristic
173C2×C43#57511yescharacteristic
174C2×C43#57711yescharacteristic
175D43—81no—
176D43—81no—
177D43—81no—
178#559—431no—
179#556—431no—
180#497—431no—
181#496—431no—
182#495—431no—
183#464—431no—
184#464—431no—
185#463—431no—
186#463—431no—
187#461—431no—
188#460—431no—
189#446D4311yescharacteristic, complemented
190#442—431no—
191#441—431no—
192C4×SD16—431no—
193C43#340111yescharacteristic, complemented, Sylow
194C2×Q16—431no—
195C2×Q16—431no—
196C2×SD16—431no—
197C2×SD16—431no—
198C2×SD16—431no—
199C2×SD16—431no—
200C2×SD16—431no—
201C2×D8—431no—
202C2×D8—431no—
203C4⋊Q8—431no—
204#127—431no—
205#126—861no—
206#126—861no—
207#124—431no—
208#124—431no—
209#124—431no—
210#124—431no—
211#124—861no—
212#123—861no—
213#123—861no—
214C22⋊Q8—861no—
215C4×Q8—431no—
216C4×Q8—431no—
217C4×Q8—431no—
218C4×Q8C2×D4311yescharacteristic
219C4×D4—431no—
220C4×D4—431no—
221C4×D4—431no—
222C4×D4—861no—
223#117—861no—
224#106—431no—
225C4⋊C8C2×D4311yescharacteristic
226C4⋊C8C2×D4311yescharacteristic
227C4⋊C8C2×D4311yescharacteristic
228#103—431no—
229#103—431no—
230#103—431no—
231#102—431no—
232#102—431no—
233#102—431no—
234#97C2×D4311yescharacteristic
235#97C2×D4311yescharacteristic
236C4×C8C2×D4311yescharacteristic
237C2×Q8—431no—
238C2×Q8—431no—
239C2×Q8—431no—
240C2×Q8D17211yescharacteristic
241C2×D4—431no—
242C2×D4—431no—
243C2×D4—431no—
244C2×D4—861no—
245C2×D4—861no—
246C22×C4—861no—
247C22×C4—861no—
248C22×C4—861no—
249Q16—862no—
250Q16—1721no—
251SD16—862no—
252SD16—1721no—
253SD16—1721no—
254SD16—1721no—
255SD16—1721no—
256D8—862no—
257D8—1721no—
258C2×C8C22×D4311yescharacteristic
259C2×C8C22×D4311yescharacteristic
260C2×C8C22×D4311yescharacteristic
261C2×C8C22×D4311yescharacteristic
262C4⋊C4—431no—
263C4⋊C4—431no—
264C4⋊C4—861no—
265C4⋊C4—861no—
266C4⋊C4—861no—
267C4⋊C4—861no—
268C4⋊C4—861no—
269C4⋊C4D17211yescharacteristic
270C4⋊C4D17211yescharacteristic
271C4⋊C4D17211yescharacteristic
272C22⋊C4—861no—
273C22⋊C4—861no—
274C22⋊C4—861no—
275C22⋊C4—861no—
276C22⋊C4—861no—
277C22⋊C4—861no—
278C22⋊C4—861no—
279C22⋊C4—861no—
280C22⋊C4—861no—
281C22⋊C4—861no—
282C22⋊C4—861no—
283C42—861no—
284C42—861no—
285C42—861no—
286C42C22×D4311yescharacteristic
287C42C22×D4311yescharacteristic
288C42C22×D4311yescharacteristic
289C23—861no—
290C23—861no—
291C23—861no—
292Q8—41no—
293Q8—861no—
294Q8—861no—
295Q8—861no—
296Q8—861no—
297Q8—861no—
298Q8—861no—
299D4—861no—
300D4—861no—
301D4—861no—
302D4—861no—
303D4—861no—
304D4—861no—
305D4—3441no—
306D4—1722no—
307C2×C4—861no—
308C2×C4—861no—
309C2×C4—861no—
310C2×C4—861no—
311C2×C4—861no—
312C2×C4—3441no—
313C2×C4—3441no—
314C2×C4—1722no—
315C2×C4C2×D17211yescharacteristic
316C2×C4C2×D17211yescharacteristic
317C2×C4C2×D17211yescharacteristic
318C2×C4C2×D17211yescharacteristic
319C2×C4C2×D17211yescharacteristic
320C2×C4C2×D17211yescharacteristic
321C2×C4C23×D4311yescharacteristic
322C8—21no—
323C8—21no—
324C8—21no—
325C8#1062190212yes—
326C22—1721no—
327C22—1721no—
328C22—1721no—
329C22—1721no—
330C22—1721no—
331C22—1721no—
332C22—1721no—
333C22—1721no—
334C22—1721no—
335C22C22×D17211yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—1721no—
343C4—1721no—
344C4—1721no—
345C4—1721no—
346C4—1721no—
347C4C2×#1062190211yescharacteristic
348C4#1306337111yescharacteristic
349C2—3441no—
350C2—3441no—
351C2—3441no—
352C2#1458357111yescharacteristic
353C2#1458369911yescharacteristic
354C2#1458371111yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#446C2
socleC22×C43C22×D4
hypercenter#446D43
hypocenterC43#3401
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #14583634C2semidirect
2. #14583622C2semidirect
3. #14583293C2semidirect
5. #14583283C2semidirect
6. #14583122C2semidirect
7. #14583122C2semidirect
8. #14583115C2semidirect
9. #14583115C2semidirect
10. #14583105C2semidirect
11. #14583100C2semidirect
12. #14583012C2semidirect
13. #14583007C2semidirect
14. C4×#10621873C2semidirect
15. C43×#446C2semidirect
189. #446D43semidirect
193. C43#3401semidirect