Finite Group Databasebeta

← #19146440

Subgroups — #19146440

Order 5504.

420 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#14583596C211yesmaximal, characteristic, complemented
2#14583546C211yesmaximal, characteristic, complemented
3#14583252C211yesmaximal, characteristic, complemented
4#14583236C211yesmaximal, characteristic, complemented
5#14583220C211yesmaximal, characteristic, complemented
6#14583202C211yesmaximal, characteristic, complemented
7#14583127C211yesmaximal, characteristic, complemented
8#14583112C211yesmaximal, characteristic, complemented
9#14583042C211yesmaximal, characteristic, complemented
10#14583031C211yesmaximal, characteristic, complemented
11#14582979C211yesmaximal, characteristic, complemented
12C8×C22⋊D43C211yesmaximal, characteristic, complemented
13#14582896C211yesmaximal, characteristic, complemented
14#102×D43C211yesmaximal, characteristic, complemented
15C43×#466C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×D4×D43C2211yescharacteristic
18C2×#10621883C2211yescharacteristic, complemented
19C2×#10621882C2211yescharacteristic
20C2×C8×D43C2211yescharacteristic
21#13063318—21no—
22#13063316C2211yescharacteristic, complemented
23#13063312C2211yescharacteristic
24#13063307—21no—
25#13063306—21no—
26#13063305C2211yescharacteristic
27#13063296—21no—
28#13063296—21no—
29#13063296C2211yescharacteristic
30#13063293—21no—
31D4×Dic43C2211yescharacteristic, complemented
32#13063287C2211yescharacteristic
33C4×C22⋊D43C2211yescharacteristic
34(C22⋊D43)⋊C4—21no—
35#13063284C2211yescharacteristic, complemented
36C4⋊C4×D43C2211yescharacteristic
37C22⋊C4×D43—21no—
38#13063258C2211yescharacteristic, complemented
39#13063256C2211yescharacteristic, complemented
40Dic43⋊C8C2211yescharacteristic, complemented
41#13063250C2211yescharacteristic, complemented
42#13063250C2211yescharacteristic, complemented
43#13063248C2211yescharacteristic, complemented
44#13063247C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063245C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic, complemented
50(C2×D43)⋊C8C2211yescharacteristic
51C8×Dic43C2211yescharacteristic, complemented
52C2×D8×C43C2211yescharacteristic
53C22×C8×C43C2211yescharacteristic, complemented
54#121×C43C2211yescharacteristic
55#121×C43C2211yescharacteristic, complemented
56#107×C43C2211yescharacteristic, complemented
57#102×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60C2×D4×C43—21no—
61C2×D4×C43—21no—
62C2×D4×C43C2311yescharacteristic
63C2×D4×C43C2311yescharacteristic
64C22×C4×C43C2311yescharacteristic
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C2×C22⋊D43—21no—
68C2×C22⋊D43D411yescharacteristic
69C22×Dic43—21no—
70D4×D43—22no—
71D4×D43—41no—
72#10621898—22no—
73#10621898—41no—
74C2×D172C2311yescharacteristic
75C2×C4×D43—21no—
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C4×D43C2311yescharacteristic
79C2×Dic86C2311yescharacteristic
80D8×C43—41no—
81C2×C8×C43—41no—
82C2×C8×C43C2311yescharacteristic
83C2×C8×C43C2311yescharacteristic
84C4⋊C4×C43C2311yescharacteristic
85C4⋊C4×C43C2311yescharacteristic
86C22⋊C4×C43—21no—
87C22⋊C4×C43—21no—
88C22⋊Dic43—21no—
89C22⋊Dic43—21no—
90C22⋊Dic43—21no—
91C22⋊Dic43—21no—
92C22⋊Dic43—21no—
93C22⋊Dic43D411yescharacteristic
94#10621883—41no—
95#10621882—22no—
96(C2×D43)⋊C4—21no—
97(C2×D43)⋊C4—21no—
98(C2×D43)⋊C4D411yescharacteristic
99C4⋊Dic43—21no—
100C4⋊Dic43—21no—
101C4⋊Dic43C2311yescharacteristic
102C4⋊Dic43C2311yescharacteristic
103Dic43⋊C4—21no—
104Dic43⋊C4—21no—
105Dic43⋊C4D411yescharacteristic
106C4×Dic43—21no—
107C4×Dic43C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110C8×D43—41no—
111C23×C43—21no—
112C23×C43—21no—
113C23×C43C2×D411yescharacteristic
114C22×D43—21no—
115C22×D43—42no—
116C22×D43—42no—
117C22×D43—81no—
118C22×D43C2×D411yescharacteristic
119D4×C43—21no—
120D4×C43—21no—
121D4×C43—21no—
122D4×C43—21no—
123D4×C43—81no—
124D4×C43—81no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43C2×D411yescharacteristic
130C2×C4×C43C2411yescharacteristic
131C22⋊D43—22no—
132C22⋊D43—42no—
133C22⋊D43—42no—
134C22⋊D43—42no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—21no—
138C2×Dic43—81no—
139C2×Dic43C2×D411yescharacteristic
140C2×Dic43C2×D411yescharacteristic
141C2×Dic43C2×D411yescharacteristic
142D172—21no—
143D172#4112yes—
144C4×D43—21no—
145C4×D43—21no—
146C4×D43—42no—
147C4×D43—81no—
148C4×D43—81no—
149Dic86—21no—
150Dic86—21no—
151C8×C43—21no—
152C8×C43—21no—
153C43⋊C8—21no—
154C43⋊C8—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43—41no—
161C22×C43—41no—
162C22×C43—41no—
163C22×C43—41no—
164C22×C43C22×D411yescharacteristic
165C2×D43—21no—
166C2×D43—21no—
167C2×D43—22no—
168C2×D43—41no—
169C2×D43—41no—
170C2×D43—84no—
171C2×D43#13512yes—
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#3297—431nomaximal, Sylow
184C2×C43—41no—
185C2×C43—81no—
186C2×C43—81no—
187C2×C43#54611yescharacteristic
188C2×C43C2×#13511yescharacteristic
189C2×C43#57611yescharacteristic
190D43—22no—
191D43—42no—
192#553—431no—
193#546—431no—
194#488—431no—
195#484—431no—
196#482—431no—
197#478—431no—
198#466D4311yescharacteristic, complemented
199#465—431no—
200#463—431no—
201#449—431no—
202#447—431no—
203C4×D8—431no—
204C8×D4—431no—
205#416—431no—
206C2×#102—431no—
207C43#329711yescharacteristic, complemented, Sylow
208C2×#41—431no—
209C22×D4—431no—
210C2×SD16—431no—
211C2×D8—431no—
212C2×D8C2×D4311yescharacteristic
213C22×C8—431no—
214C22×C8C2×D4311yescharacteristic, complemented
215#126—861no—
216#125—431no—
217#124—431no—
218#123—861no—
219#123—861no—
220C22⋊Q8—431no—
221#121—431no—
222#121—861no—
223#121—861no—
224#121C2×D4311yescharacteristic
225#121C2×D4311yescharacteristic, complemented
226#120—861no—
227C4×D4—431no—
228C4×D4—431no—
229C4×D4—431no—
230C4×D4—861no—
231#117—431no—
232C2×C4⋊C4—431no—
233C2×C22⋊C4—861no—
234#107—431no—
235#107C2×D4311yescharacteristic, complemented
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#102—431no—
245#102—431no—
246#102C2×D4311yescharacteristic
247#102C2×D4311yescharacteristic, complemented
248C22⋊C8—431no—
249C22⋊C8—431no—
250C4×C8—431no—
251C24—861no—
252#41—862no—
253#41—1721no—
254C2×Q8—431no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—431no—
258C2×D4—431no—
259C2×D4—861no—
260C2×D4—862no—
261C2×D4—861no—
262C2×D4—861no—
263C2×D4—1721no—
264C2×D4C22×D4311yescharacteristic
265C2×D4C22×D4311yescharacteristic
266C22×C4—431no—
267C22×C4—861no—
268C22×C4—861no—
269C22×C4—861no—
270C22×C4—861no—
271C22×C4C22×D4311yescharacteristic
272SD16—1721no—
273D8—41no—
274D8—862no—
275C2×C8—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⋊C4—861no—
287C4⋊C4—861no—
288C4⋊C4C22×D4311yescharacteristic
289C4⋊C4C22×D4311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—431no—
293C22⋊C4—431no—
294C22⋊C4—861no—
295C22⋊C4—861no—
296C22⋊C4—861no—
297C22⋊C4—861no—
298C22⋊C4—861no—
299C22⋊C4—861no—
300C22⋊C4—861no—
301C42—431no—
302C42—861no—
303C23—21no—
304C23—21no—
305C23—431no—
306C23—861no—
307C23—3441no—
308C23—1722no—
309C23—1722no—
310C23D4×D4311yescharacteristic
311Q8—861no—
312Q8—861no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—81no—
318D4—81no—
319D4—432no—
320D4—862no—
321D4—861no—
322D4—1722no—
323D4—1722no—
324D4—1722no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—431no—
330C2×C4—431no—
331C2×C4—431no—
332C2×C4—861no—
333C2×C4—861no—
334C2×C4—861no—
335C2×C4—861no—
336C2×C4—861no—
337C2×C4—3441no—
338C2×C4—3441no—
339C2×C4—3441no—
340C2×C4—1722no—
341C2×C4D4×D4311yescharacteristic
342C2×C4C23×D4311yescharacteristic
343C8—21no—
344C8—21no—
345C8—861no—
346C8—861no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—432no—
357C22—861no—
358C22—861no—
359C22—862no—
360C22—3444no—
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—
373C4#41×D4311yescharacteristic
374C4#1306337011yescharacteristic
375C2—41no—
376C2—81no—
377C2—81no—
378C2—862no—
379C2—1722no—
380C2#1458353811yescharacteristic
381C2#135×D4311yescharacteristic
382C2#1458370011yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#466C2
socleC22×C43C22×D4
hypercenter#466D43
hypocenterC43#3297
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #14583596C2semidirect
2. #14583546C2semidirect
3. #14583252C2semidirect
4. #14583236C2semidirect
5. #14583220C2semidirect
6. #14583202C2semidirect
7. #14583127C2semidirect
8. #14583112C2semidirect
9. #14583042C2semidirect
10. #14583031C2semidirect
11. #14582979C2semidirect
12. C8×C22⋊D43C2semidirect
13. #14582896C2semidirect
14. #102×D43C2semidirect
15. C43×#466C2semidirect
18. C2×#10621883C22semidirect
22. #13063316C22semidirect
31. D4×Dic43C22semidirect
35. #13063284C22semidirect
38. #13063258C22semidirect
39. #13063256C22semidirect
40. Dic43⋊C8C22semidirect
41. #13063250C22semidirect
42. #13063250C22semidirect
43. #13063248C22semidirect
49. C22⋊(C43⋊C8)C22semidirect
51. C8×Dic43C22semidirect
53. C22×C8×C43C22semidirect
55. #121×C43C22semidirect
56. #107×C43C22semidirect
58. #102×C43C22semidirect
198. #466D43semidirect
207. C43#3297semidirect
214. C22×C8C2×D43semidirect
225. #121C2×D43semidirect
235. #107C2×D43semidirect
247. #102C2×D43semidirect