Finite Group Databasebeta

← #19146752

Subgroups — #19146752

Order 5504.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583612C211yesmaximal, characteristic, complemented
2#14583543C211yesmaximal, characteristic, complemented
3#14583257C211yesmaximal, characteristic, complemented
4#14583240C211yesmaximal, characteristic, complemented
5#14583221C211yesmaximal, characteristic, complemented
6#14583177C211yesmaximal, characteristic, complemented
7#14583145C211yesmaximal, characteristic, complemented
8#14583134C211yesmaximal, characteristic, complemented
9#14583113C211yesmaximal, characteristic, complemented
10#14583045C211yesmaximal, characteristic, complemented
11#14583033C211yesmaximal, characteristic, complemented
12#14583008C211yesmaximal, characteristic, complemented
13#14582968C211yesmaximal, characteristic, complemented
14#14582892C211yesmaximal, characteristic, complemented
15C43×#418C211yesmaximal, characteristic, complemented
16C2×#10621900C2211yescharacteristic
17C2×#10621873C2211yescharacteristic, complemented
18C2×#10621882C2211yescharacteristic
19C2×#10621882C2211yescharacteristic
20C2×C8×D43C2211yescharacteristic, complemented
21#13063324C2211yescharacteristic, complemented
22#13063313—21no—
23#13063312C2211yescharacteristic
24#13063311—21no—
25#13063306—21no—
26#13063304C2211yescharacteristic
27#13063300C2211yescharacteristic, complemented
28#13063299C2211yescharacteristic
29#13063298—21no—
30#13063297—21no—
31#13063296C2211yescharacteristic
32#13063294—21no—
33D4×Dic43C2211yescharacteristic
34#13063287C2211yescharacteristic, complemented
35C4×C22⋊D43C2211yescharacteristic
36#13063283C2211yescharacteristic, complemented
37#13063282—21no—
38C2×C22⋊Dic43—21no—
39#13063259C2211yescharacteristic, complemented
40#13063258C2211yescharacteristic, complemented
41#13063256C2211yescharacteristic, complemented
42Dic43⋊C8C2211yescharacteristic, complemented
43#13063250C2211yescharacteristic, complemented
44#13063248C2211yescharacteristic, complemented
45#13063248C2211yescharacteristic, complemented
46#13063247C2211yescharacteristic, complemented
47#13063246C2211yescharacteristic
48#13063246C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic, complemented
51#13063235C2211yescharacteristic, complemented
52C22×D4×C43C2211yescharacteristic
53C2×M16×C43C2211yescharacteristic
54#117×C43C2211yescharacteristic
55#102×C43C2211yescharacteristic
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic
59C24×C43—21no—
60C2×D4×C43—21no—
61C2×D4×C43—22no—
62C2×D4×C43—41no—
63C2×D4×C43C2311yescharacteristic
64C2×D4×C43C2311yescharacteristic
65C22×C4×C43C2311yescharacteristic
66C2×C22⋊D43—21no—
67C2×C22⋊D43—21no—
68C2×C22⋊D43—21no—
69C2×C22⋊D43D411yescharacteristic
70C22×Dic43—21no—
71C22×Dic43—21no—
72#10621900—22no—
73#10621900—41no—
74C2×D172—21no—
75C2×D172C2311yescharacteristic
76C2×C4×D43—21no—
77C2×C4×D43C2311yescharacteristic
78C2×Dic86—21no—
79C2×Dic86C2311yescharacteristic
80M16×C43—41no—
81C2×C8×C43C2311yescharacteristic
82C2×C8×C43C2311yescharacteristic
83C4⋊C4×C43C2311yescharacteristic
84C4⋊C4×C43C2311yescharacteristic
85C22⋊C4×C43—21no—
86C42×C43—21no—
87C22⋊Dic43—21no—
88C22⋊Dic43—21no—
89C22⋊Dic43—21no—
90C22⋊Dic43—21no—
91C22⋊Dic43—21no—
92C22⋊Dic43D411yescharacteristic
93#10621882—22no—
94#10621882—41no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4—21no—
97(C2×D43)⋊C4—21no—
98(C2×D43)⋊C4—21no—
99(C2×D43)⋊C4D411yescharacteristic
100C4⋊Dic43C2311yescharacteristic
101C4⋊Dic43C2311yescharacteristic
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104Dic43⋊C4D411yescharacteristic
105C4×Dic43—21no—
106C4×Dic43C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109#10621873—41no—
110C8×D43—41no—
111C23×C43—21no—
112C23×C43—21no—
113C23×C43—42no—
114C23×C43—42no—
115C23×C43—81no—
116C23×C43C2×D411yescharacteristic
117C22×D43—21no—
118C22×D43C2×D411yescharacteristic
119D4×C43—21no—
120D4×C43—21no—
121D4×C43—21no—
122D4×C43—42no—
123D4×C43#4112yes—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43C2×D411yescharacteristic
129C2×C4×C43C2411yescharacteristic
130C22⋊D43—41no—
131C22⋊D43—42no—
132C22⋊D43—81no—
133C22⋊D43—81no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—42no—
138C2×Dic43—81no—
139C2×Dic43C2×D411yescharacteristic
140C2×Dic43C2×D411yescharacteristic
141C2×Dic43C2×D411yescharacteristic
142D172—21no—
143D172—21no—
144D172—81no—
145C4×D43—21no—
146C4×D43—21no—
147C4×D43—42no—
148Dic86—21no—
149Dic86—21no—
150Dic86—81no—
151C8×C43—21no—
152C8×C43—21no—
153C43⋊C8—21no—
154C43⋊C8—21no—
155C22×C43—22no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—41no—
160C22×C43—41no—
161C22×C43—41no—
162C22×C43—41no—
163C22×C43—41no—
164C22×C43—84no—
165C22×C43C22×D411yescharacteristic
166C2×D43—21no—
167C2×D43—21no—
168C2×D43—21no—
169C2×D43—41no—
170C2×D43—41no—
171C2×D43—41no—
172C4×C43—21no—
173C4×C43—41no—
174C4×C43—41no—
175C4×C43C2×#4111yescharacteristic
176C4×C43H(5,𝔽2)11yescharacteristic
177Dic43—21no—
178Dic43—21no—
179Dic43—21no—
180Dic43—41no—
181Dic43—41no—
182Dic43—41no—
183#3319—431nomaximal, Sylow
184C2×C43—41no—
185C2×C43—42no—
186C2×C43—81no—
187C2×C43#54611yescharacteristic
188C2×C43#57511yescharacteristic
189C2×C43#57611yescharacteristic
190D43—41no—
191D43—81no—
192#555—431no—
193#546—431no—
194#489—431no—
195#485—431no—
196#482—431no—
197#474—431no—
198#468—431no—
199#466—431no—
200#463—431no—
201#449—431no—
202#447—431no—
203#442—431no—
204#435—431no—
205#418D4311yescharacteristic, complemented
206#416—431no—
207C43#331911yescharacteristic, complemented, Sylow
208C2×#41—431no—
209C22×D4C2×D4311yescharacteristic
210C2×SD16—431no—
211C2×D8—431no—
212C2×D8—431no—
213C2×M16C2×D4311yescharacteristic
214C22×C8—431no—
215C4⋊Q8—431no—
216#124—431no—
217#124—861no—
218#124—861no—
219#123—861no—
220C22⋊Q8—431no—
221#121—431no—
222#121—431no—
223#121—431no—
224#121—861no—
225#121—861no—
226#120—861no—
227C4×D4—431no—
228C4×D4—431no—
229C4×D4—431no—
230#117—431no—
231#117—861no—
232#117C2×D4311yescharacteristic
233C2×C22⋊C4—861no—
234#107—431no—
235#107—431no—
236#106—431no—
237C4⋊C8—431no—
238#103—431no—
239#103—431no—
240#103—431no—
241#102—431no—
242#102—431no—
243#102—431no—
244#102C2×D4311yescharacteristic
245#102C2×D4311yescharacteristic
246#102C2×D4311yescharacteristic
247#102C2×D4311yescharacteristic
248C22⋊C8—431no—
249C22⋊C8—431no—
250#97—431no—
251C24—21no—
252#41—862no—
253#41—1721no—
254C2×Q8—431no—
255C2×Q8—861no—
256C2×D4—22no—
257C2×D4—21no—
258C2×D4—41no—
259C2×D4—431no—
260C2×D4—431no—
261C2×D4—861no—
262C2×D4—861no—
263C2×D4—861no—
264C2×D4—861no—
265C2×D4C22×D4311yescharacteristic
266C2×D4C22×D4311yescharacteristic
267C22×C4—431no—
268C22×C4—861no—
269C22×C4—861no—
270C22×C4—861no—
271C22×C4C22×D4311yescharacteristic
272SD16—1721no—
273D8—862no—
274D8—1721no—
275M16—41no—
276C2×C8—431no—
277C2×C8—431no—
278C2×C8—1721no—
279C2×C8C22×D4311yescharacteristic
280C2×C8C22×D4311yescharacteristic
281C4⋊C4—431no—
282C4⋊C4—431no—
283C4⋊C4—431no—
284C4⋊C4—861no—
285C4⋊C4—861no—
286C4⋊C4C22×D4311yescharacteristic
287C4⋊C4C22×D4311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—431no—
290C22⋊C4—431no—
291C22⋊C4—861no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C22⋊C4—861no—
295C22⋊C4—861no—
296C22⋊C4—861no—
297C22⋊C4—861no—
298C22⋊C4—861no—
299C22⋊C4—861no—
300C42—21no—
301C42—431no—
302C42—861no—
303C23—21no—
304C23—21no—
305C23—42no—
306C23—42no—
307C23—81no—
308C23—431no—
309C23—861no—
310C23D4×D4311yescharacteristic
311Q8—861no—
312Q8—861no—
313Q8—3441no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—42no—
318D4—861no—
319D4—861no—
320D4—3441no—
321D4—3441no—
322D4—3441no—
323D4—1721no—
324D4—1722no—
325D4#1062189812yes—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—431no—
331C2×C4—431no—
332C2×C4—431no—
333C2×C4—861no—
334C2×C4—861no—
335C2×C4—861no—
336C2×C4—861no—
337C2×C4—861no—
338C2×C4—3441no—
339C2×C4—1722no—
340C2×C4—1722no—
341C2×C4D4×D4311yescharacteristic
342C2×C4C23×D4311yescharacteristic
343C8—21no—
344C8—21no—
345C8—861no—
346C8—861no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—22no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—84no—
357C22—861no—
358C22—861no—
359C22—861no—
360C22—1721no—
361C22—1721no—
362C22—1721no—
363C22C2×D4×D4311yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—861no—
368C4—861no—
369C4—861no—
370C4—1721no—
371C4—1721no—
372C4—1721no—
373C4C2×#1062189811yescharacteristic
374C4#1306337011yescharacteristic
375C2—41no—
376C2—42no—
377C2—81no—
378C2—3441no—
379C2—1721no—
380C2#1458353911yescharacteristic
381C2#1458369511yescharacteristic
382C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#418C2
socleC22×C43C22×D4
hypercenter#418D43
hypocenterC43#3319
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #14583612C2semidirect
2. #14583543C2semidirect
3. #14583257C2semidirect
4. #14583240C2semidirect
5. #14583221C2semidirect
6. #14583177C2semidirect
7. #14583145C2semidirect
8. #14583134C2semidirect
9. #14583113C2semidirect
10. #14583045C2semidirect
11. #14583033C2semidirect
12. #14583008C2semidirect
13. #14582968C2semidirect
14. #14582892C2semidirect
15. C43×#418C2semidirect
17. C2×#10621873C22semidirect
20. C2×C8×D43C22semidirect
21. #13063324C22semidirect
27. #13063300C22semidirect
34. #13063287C22semidirect
36. #13063283C22semidirect
39. #13063259C22semidirect
40. #13063258C22semidirect
41. #13063256C22semidirect
42. Dic43⋊C8C22semidirect
43. #13063250C22semidirect
44. #13063248C22semidirect
45. #13063248C22semidirect
46. #13063247C22semidirect
50. (C2×D43)⋊C8C22semidirect
51. #13063235C22semidirect
205. #418D43semidirect
207. C43#3319semidirect