Finite Group Databasebeta

← #19146812

Subgroups — #19146812

Order 5504.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583584C211yesmaximal, characteristic, complemented
2#14583537C211yesmaximal, characteristic
3#14583255C211yesmaximal, characteristic, complemented
4#14583239C211yesmaximal, characteristic, complemented
5#14583217C211yesmaximal, characteristic, complemented
6#14583197C211yesmaximal, characteristic, complemented
7#14583156C211yesmaximal, characteristic, complemented
8#14583145C211yesmaximal, characteristic, complemented
9#14583124C211yesmaximal, characteristic, complemented
10#14583061C211yesmaximal, characteristic, complemented
11#14583051C211yesmaximal, characteristic, complemented
12#14582990C211yesmaximal, characteristic, complemented
13#14582975C211yesmaximal, characteristic, complemented
14#14582902C211yesmaximal, characteristic, complemented
15C43×#417C211yesmaximal, characteristic, complemented
16C2×D4×D43C2211yescharacteristic
17C2×#10621885C2211yescharacteristic, complemented
18C2×#10621873C2211yescharacteristic
19C2×#10621883C2211yescharacteristic
20C2×#10621872C2211yescharacteristic
21#13063320—21no—
22#13063316C2211yescharacteristic, complemented
23#13063315—21no—
24#13063314C2211yescharacteristic
25#13063308—21no—
26#13063308—21no—
27#13063305C2211yescharacteristic
28#13063304C2211yescharacteristic, complemented
29#13063301C2211yescharacteristic
30#13063299C2211yescharacteristic
31#13063297—21no—
32#13063293—21no—
33#13063290C2211yescharacteristic, complemented
34D4×Dic43C2211yescharacteristic
35C4×C22⋊D43C2211yescharacteristic
36#13063284—21no—
37#13063283C2211yescharacteristic
38C2×(C2×D43)⋊C4—21no—
39#13063259C2211yescharacteristic, complemented
40#13063256C2211yescharacteristic, complemented
41#13063256C2211yescharacteristic, complemented
42Dic43⋊C8C2211yescharacteristic, complemented
43#13063250C2211yescharacteristic, complemented
44#13063249C2211yescharacteristic, complemented
45#13063247C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic, complemented
50(C2×D43)⋊C8C2211yescharacteristic
51C8×Dic43C2211yescharacteristic, complemented
52C2×#41×C43C2211yescharacteristic
53C2×M16×C43C2211yescharacteristic, complemented
54C2×C4⋊C4×C43C2211yescharacteristic, complemented
55#103×C43C2211yescharacteristic, complemented
56#103×C43C2211yescharacteristic, complemented
57#102×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic
59C23×D43—21no—
60#41×C43—22no—
61#41×C43—41no—
62C2×Q8×C43C2311yescharacteristic
63C2×D4×C43—21no—
64C2×D4×C43C2311yescharacteristic
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43C2311yescharacteristic
68C2×C22⋊D43—21no—
69C2×C22⋊D43—21no—
70C2×C22⋊D43D411yescharacteristic
71C22×Dic43—21no—
72D4×D43—22no—
73D4×D43—41no—
74C2×D172C2311yescharacteristic
75C2×C4×D43C2311yescharacteristic
76C2×Dic86C2311yescharacteristic
77M16×C43—41no—
78C2×C8×C43C2311yescharacteristic
79C2×C8×C43C2311yescharacteristic
80C4⋊C4×C43—21no—
81C4⋊C4×C43C2311yescharacteristic
82C4⋊C4×C43C2311yescharacteristic
83C22⋊Dic43—21no—
84C22⋊Dic43—21no—
85C22⋊Dic43D411yescharacteristic
86#10621885—41no—
87#10621883—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
95C4⋊Dic43—21no—
96C4⋊Dic43—21no—
97C4⋊Dic43C2311yescharacteristic
98C4⋊Dic43C2311yescharacteristic
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103Dic43⋊C4D411yescharacteristic
104C4×Dic43—21no—
105C4×Dic43—21no—
106C4×Dic43C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109#10621873—41no—
110#10621872—41no—
111C23×C43—21no—
112C23×C43C2×D411yescharacteristic
113C22×D43—21no—
114C22×D43—42no—
115C22×D43—42no—
116C22×D43—81no—
117C22×D43C2×D411yescharacteristic
118Q8×C43—21no—
119Q8×C43—21no—
120D4×C43—21no—
121D4×C43—42no—
122D4×C43#4112yes—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—42no—
129C2×C4×C43—42no—
130C2×C4×C43C2×D411yescharacteristic
131C2×C4×C43C2411yescharacteristic
132C22⋊D43—41no—
133C22⋊D43—42no—
134C22⋊D43—81no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—21no—
138C2×Dic43—81no—
139C2×Dic43C2×D411yescharacteristic
140C2×Dic43C2×D411yescharacteristic
141C2×Dic43C2×D411yescharacteristic
142D172—21no—
143D172—21no—
144C4×D43—21no—
145C4×D43—21no—
146Dic86—21no—
147Dic86—21no—
148C8×C43—21no—
149C8×C43—21no—
150C43⋊C8—21no—
151C43⋊C8—21no—
152C22×C43—22no—
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—41no—
157C22×C43—41no—
158C22×C43C22×D411yescharacteristic
159C2×D43—21no—
160C2×D43—21no—
161C2×D43—21no—
162C2×D43—41no—
163C2×D43—41no—
164C2×D43—41no—
165C2×D43—84no—
166C4×C43—21no—
167C4×C43—41no—
168C4×C43—41no—
169C4×C43—41no—
170C4×C43C2×#4111yescharacteristic
171C4×C43H(5,𝔽2)11yescharacteristic
172Dic43—21no—
173Dic43—21no—
174Dic43—21no—
175Dic43—41no—
176Dic43—41no—
177Dic43—41no—
178#3323—431nomaximal, Sylow
179C2×C43—42no—
180C2×C43—41no—
181C2×C43#54611yescharacteristic
182C2×C43#57511yescharacteristic
183C2×C43#57711yescharacteristic
184D43—41no—
185D43—81no—
186#552—431no—
187#546—431no—
188#488—431no—
189#485—431no—
190#481—431no—
191#478—431no—
192#470—431no—
193#468—431no—
194#464—431no—
195#452—431no—
196#450—431no—
197C4×SD16—431no—
198#436—431no—
199#418—431no—
200#417D4311yescharacteristic, complemented
201C43#332311yescharacteristic, complemented, Sylow
202C2×#41C2×D4311yescharacteristic
203C22×D4—431no—
204C2×Q16—431no—
205C2×SD16—431no—
206C2×SD16—431no—
207C2×M16—431no—
208C2×M16C2×D4311yescharacteristic, complemented
209#126—861no—
210#125—431no—
211#125—861no—
212#124—431no—
213#123—861no—
214#123—861no—
215C22⋊Q8—431no—
216C22⋊Q8—431no—
217C22⋊Q8—431no—
218#121—431no—
219#121—861no—
220#120—861no—
221C4×Q8—431no—
222C4×D4—431no—
223C4×D4—431no—
224#117—431no—
225#117—861no—
226C2×C4⋊C4C2×D4311yescharacteristic, complemented
227C2×C22⋊C4—861no—
228#107—431no—
229#106—431no—
230#106—431no—
231C4⋊C8—431no—
232#103—431no—
233#103—431no—
234#103C2×D4311yescharacteristic, complemented
235#103C2×D4311yescharacteristic, complemented
236#102—431no—
237#102—431no—
238#102—431no—
239#102—431no—
240#102C2×D4311yescharacteristic
241#102C2×D4311yescharacteristic
242C22⋊C8—431no—
243C22⋊C8—431no—
244C4×C8—431no—
245C24—861no—
246#41—22no—
247#41—41no—
248C2×Q8—431no—
249C2×Q8C22×D4311yescharacteristic
250C2×D4—21no—
251C2×D4—431no—
252C2×D4—431no—
253C2×D4—861no—
254C2×D4—862no—
255C2×D4—861no—
256C2×D4—1721no—
257C2×D4C22×D4311yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—431no—
261C22×C4—861no—
262C22×C4C22×D4311yescharacteristic
263Q16—1721no—
264SD16—862no—
265SD16—1721no—
266M16—41no—
267M16—1721no—
268C2×C8—431no—
269C2×C8—431no—
270C2×C8C22×D4311yescharacteristic
271C2×C8C22×D4311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—431no—
274C4⋊C4—431no—
275C4⋊C4—431no—
276C4⋊C4—861no—
277C4⋊C4—861no—
278C4⋊C4—861no—
279C4⋊C4—861no—
280C4⋊C4—861no—
281C4⋊C4—861no—
282C4⋊C4C22×D4311yescharacteristic
283C4⋊C4C22×D4311yescharacteristic
284C22⋊C4—431no—
285C22⋊C4—431no—
286C22⋊C4—861no—
287C22⋊C4—861no—
288C22⋊C4—861no—
289C22⋊C4—861no—
290C22⋊C4—861no—
291C22⋊C4—861no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C42—431no—
295C42—861no—
296C42—861no—
297C23—21no—
298C23—431no—
299C23—861no—
300C23—3441no—
301C23—1722no—
302C23—1722no—
303C23D4×D4311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—861no—
307Q8—861no—
308D4—21no—
309D4—42no—
310D4—861no—
311D4—861no—
312D4—3441no—
313D4—1721no—
314D4—1722no—
315D4#1062189812yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—431no—
324C2×C4—431no—
325C2×C4—431no—
326C2×C4—861no—
327C2×C4—861no—
328C2×C4—861no—
329C2×C4—861no—
330C2×C4—861no—
331C2×C4—3441no—
332C2×C4D4×D4311yescharacteristic
333C2×C4C23×D4311yescharacteristic
334C8—21no—
335C8—21no—
336C8—861no—
337C8—861no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—22no—
342C22—41no—
343C22—41no—
344C22—861no—
345C22—861no—
346C22—861no—
347C22—3444no—
348C22—1721no—
349C22—1721no—
350C22—1721no—
351C22C2×D4×D4311yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—861no—
357C4—861no—
358C4—861no—
359C4—1721no—
360C4—1721no—
361C4—1721no—
362C4C2×#1062189811yescharacteristic
363C4#1306337011yescharacteristic
364C2—41no—
365C2—42no—
366C2—3441no—
367C2—1721no—
368C2#1458353911yescharacteristic
369C2#1458369511yescharacteristic
370C2#1458370811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#417C2
socleC22×C43C22×D4
hypercenter#417D43
hypocenterC43#3323
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #14583584C2semidirect
3. #14583255C2semidirect
4. #14583239C2semidirect
5. #14583217C2semidirect
6. #14583197C2semidirect
7. #14583156C2semidirect
8. #14583145C2semidirect
9. #14583124C2semidirect
10. #14583061C2semidirect
11. #14583051C2semidirect
12. #14582990C2semidirect
13. #14582975C2semidirect
14. #14582902C2semidirect
15. C43×#417C2semidirect
17. C2×#10621885C22semidirect
22. #13063316C22semidirect
28. #13063304C22semidirect
33. #13063290C22semidirect
39. #13063259C22semidirect
40. #13063256C22semidirect
41. #13063256C22semidirect
42. Dic43⋊C8C22semidirect
43. #13063250C22semidirect
44. #13063249C22semidirect
49. C22⋊(C43⋊C8)C22semidirect
51. C8×Dic43C22semidirect
53. C2×M16×C43C22semidirect
54. C2×C4⋊C4×C43C22semidirect
55. #103×C43C22semidirect
56. #103×C43C22semidirect
200. #417D43semidirect
201. C43#3323semidirect
208. C2×M16C2×D43semidirect
226. C2×C4⋊C4C2×D43semidirect
234. #103C2×D43semidirect
235. #103C2×D43semidirect