Finite Group Databasebeta

← #19146799

Subgroups — #19146799

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#14583597C211yesmaximal, characteristic, complemented
2#14583546C211yesmaximal, characteristic, complemented
3#14583252C211yesmaximal, characteristic, complemented
4#14583242C211yesmaximal, characteristic, complemented
5#14583202C211yesmaximal, characteristic, complemented
6#14583150C211yesmaximal, characteristic, complemented
7#14583146C211yesmaximal, characteristic, complemented
8#14583113C211yesmaximal, characteristic, complemented
9#14583046C211yesmaximal, characteristic, complemented
10#14583034C211yesmaximal, characteristic, complemented
11#14582981C211yesmaximal, characteristic, complemented
12#14582974C211yesmaximal, characteristic, complemented
13#14582902C211yesmaximal, characteristic, complemented
14#14582898C211yesmaximal, characteristic, complemented
15C43×#480C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×D4×D43C2211yescharacteristic
18C2×#10621873C2211yescharacteristic, complemented
19C2×D344C2211yescharacteristic
20C2×#10621882C2211yescharacteristic
21C2×#10621877C2211yescharacteristic, complemented
22C2×#10621872C2211yescharacteristic
23#13063320—21no—
24#13063316C2211yescharacteristic, complemented
25#13063312C2211yescharacteristic
26#13063310—21no—
27#13063307—21no—
28#13063305C2211yescharacteristic
29#13063300C2211yescharacteristic
30#13063299—21no—
31#13063299C2211yescharacteristic, complemented
32#13063296—21no—
33#13063293—21no—
34#13063287C2211yescharacteristic
35#13063287C2211yescharacteristic, complemented
36C4×C22⋊D43—21no—
37C4×C22⋊D43C2211yescharacteristic
38#13063283C2211yescharacteristic
39C22⋊C4×D43—21no—
40#13063256C2211yescharacteristic, complemented
41Dic43⋊C8C2211yescharacteristic, complemented
42#13063250C2211yescharacteristic, complemented
43#13063248C2211yescharacteristic, complemented
44#13063248C2211yescharacteristic, complemented
45#13063247C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49#13063245C2211yescharacteristic, complemented
50(C2×D43)⋊C8C2211yescharacteristic
51C8×Dic43C2211yescharacteristic, complemented
52#121×C43C2211yescharacteristic
53C2×C4⋊C4×C43C2211yescharacteristic, complemented
54#107×C43C2211yescharacteristic, complemented
55#107×C43C2211yescharacteristic, complemented
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60C2×D4×C43—21no—
61C2×D4×C43C2311yescharacteristic
62C22×C4×C43—21no—
63C22×C4×C43C2311yescharacteristic
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C2×C22⋊D43D411yescharacteristic
68D4×D43—22no—
69D4×D43—41no—
70#10621898—22no—
71#10621898—41no—
72C2×D172—21no—
73C2×D172C2311yescharacteristic
74C2×D172C2311yescharacteristic
75C2×C4×D43—21no—
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C4×D43C2311yescharacteristic
79C2×Dic86C2311yescharacteristic
80C2×C8×C43C2311yescharacteristic
81C2×C8×C43C2311yescharacteristic
82C4⋊C4×C43—21no—
83C4⋊C4×C43C2311yescharacteristic
84C4⋊C4×C43C2311yescharacteristic
85C4⋊C4×C43C2311yescharacteristic
86C22⋊C4×C43—21no—
87C22⋊Dic43—21no—
88C22⋊Dic43—21no—
89C22⋊Dic43D411yescharacteristic
90#10621882—41no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4—21no—
97(C2×D43)⋊C4D411yescharacteristic
98C4⋊Dic43—21no—
99C4⋊Dic43—21no—
100C4⋊Dic43C2311yescharacteristic
101Dic43⋊C4—21no—
102Dic43⋊C4D411yescharacteristic
103C4×Dic43—21no—
104C4×Dic43C2311yescharacteristic
105#10621877—41no—
106C2×C43⋊C8C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108D344—22no—
109#10621873—41no—
110#10621872—41no—
111C23×C43—21no—
112C23×C43C2×D411yescharacteristic
113C22×D43—21no—
114C22×D43—21no—
115C22×D43—42no—
116C22×D43—42no—
117C22×D43—81no—
118C22×D43C2×D411yescharacteristic
119D4×C43—21no—
120D4×C43—21no—
121D4×C43—81no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—81no—
128C2×C4×C43C2×D411yescharacteristic
129C2×C4×C43C2411yescharacteristic
130C22⋊D43—41no—
131C22⋊D43—42no—
132C22⋊D43—42no—
133C22⋊D43—42no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43C2×D411yescharacteristic
137C2×Dic43C2×D411yescharacteristic
138C2×Dic43C2×D411yescharacteristic
139D172—21no—
140D172—21no—
141D172—21no—
142D172—81no—
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×C43C22×D411yescharacteristic
162C2×D43—22no—
163C2×D43—21no—
164C2×D43—21no—
165C2×D43—21no—
166C2×D43—41no—
167C2×D43—41no—
168C2×D43—41no—
169C2×D43—41no—
170C2×D43—41no—
171C2×D43—84no—
172C4×C43—21no—
173C4×C43—41no—
174C4×C43—41no—
175C4×C43—41no—
176C4×C43C2×#4111yescharacteristic
177C4×C43H(5,𝔽2)11yescharacteristic
178Dic43—21no—
179Dic43—21no—
180Dic43—21no—
181Dic43—41no—
182Dic43—41no—
183#3322—431nomaximal, Sylow
184C2×C43—41no—
185C2×C43—81no—
186C2×C43#54611yescharacteristic
187C2×C43#57511yescharacteristic
188C2×C43#57611yescharacteristic
189D43—41no—
190D43—42no—
191D43—81no—
192#553—431no—
193#546—431no—
194#488—431no—
195#485—431no—
196#480D4311yescharacteristic, complemented
197#478—431no—
198#469—431no—
199#468—431no—
200#463—431no—
201#449—431no—
202#447—431no—
203C4×D8—431no—
204#436—431no—
205#418—431no—
206#417—431no—
207C43#332211yescharacteristic, complemented, Sylow
208C2×#41—431no—
209C22×D4—431no—
210C2×SD16—431no—
211C2×D8—431no—
212C2×D8—431no—
213C2×M16—431no—
214C2×M16—431no—
215#126—861no—
216#125—431no—
217#124—431no—
218#123—861no—
219#123—861no—
220C22⋊Q8—431no—
221#121—431no—
222#121—431no—
223#121—861no—
224#121—861no—
225#121C2×D4311yescharacteristic
226#120—861no—
227C4×D4—431no—
228C4×D4—431no—
229C4×D4—431no—
230C4×D4—861no—
231#117—431no—
232C2×C4⋊C4C2×D4311yescharacteristic, complemented
233C2×C22⋊C4—861no—
234#107C2×D4311yescharacteristic, complemented
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
248C22⋊C8—431no—
249C22⋊C8C2×D4311yescharacteristic, complemented
250C4×C8—431no—
251C24—861no—
252#41—862no—
253#41—1721no—
254C2×Q8—431no—
255C2×D4—21no—
256C2×D4—431no—
257C2×D4—431no—
258C2×D4—431no—
259C2×D4—861no—
260C2×D4—861no—
261C2×D4—862no—
262C2×D4—861no—
263C2×D4—861no—
264C2×D4—1721no—
265C2×D4C22×D4311yescharacteristic
266C22×C4—21no—
267C22×C4—431no—
268C22×C4—861no—
269C22×C4—861no—
270C22×C4—861no—
271C22×C4C22×D4311yescharacteristic
272SD16—1721no—
273D8—862no—
274D8—1721no—
275M16—1721no—
276M16—1721no—
277C2×C8—431no—
278C2×C8—431no—
279C2×C8C22×D4311yescharacteristic
280C2×C8C22×D4311yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—431no—
283C4⋊C4—431no—
284C4⋊C4—861no—
285C4⋊C4—861no—
286C4⋊C4—861no—
287C4⋊C4C22×D4311yescharacteristic
288C4⋊C4C22×D4311yescharacteristic
289C4⋊C4C22×D4311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—431no—
292C22⋊C4—431no—
293C22⋊C4—861no—
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—431no—
305C23—861no—
306C23—861no—
307C23—3441no—
308C23—1722no—
309C23—1722no—
310C23D4×D4311yescharacteristic
311Q8—861no—
312Q8—861no—
313D4—21no—
314D4—21no—
315D4—81no—
316D4—432no—
317D4—861no—
318D4—861no—
319D4—861no—
320D4—3441no—
321D4—1721no—
322D4—1722no—
323D4—1722no—
324D4—1722no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—81no—
331C2×C4—431no—
332C2×C4—431no—
333C2×C4—431no—
334C2×C4—861no—
335C2×C4—861no—
336C2×C4—861no—
337C2×C4—861no—
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—861no—
354C22—861no—
355C22—861no—
356C22—862no—
357C22—3444no—
358C22—1721no—
359C22—1721no—
360C22—1721no—
361C22—1721no—
362C22—1721no—
363C22C2×D4×D4311yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—861no—
369C4—861no—
370C4—861no—
371C4—1721no—
372C4—1721no—
373C4#41×D4311yescharacteristic
374C4#1306337111yescharacteristic
375C2—41no—
376C2—81no—
377C2—3441no—
378C2—1721no—
379C2—1722no—
380C2#1458354111yescharacteristic
381C2#1458369811yescharacteristic
382C2#1458370011yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#480C2
socleC22×C43C22×D4
hypercenter#480D43
hypocenterC43#3322
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #14583597C2semidirect
2. #14583546C2semidirect
3. #14583252C2semidirect
4. #14583242C2semidirect
5. #14583202C2semidirect
6. #14583150C2semidirect
7. #14583146C2semidirect
8. #14583113C2semidirect
9. #14583046C2semidirect
10. #14583034C2semidirect
11. #14582981C2semidirect
12. #14582974C2semidirect
13. #14582902C2semidirect
14. #14582898C2semidirect
15. C43×#480C2semidirect
18. C2×#10621873C22semidirect
21. C2×#10621877C22semidirect
24. #13063316C22semidirect
31. #13063299C22semidirect
35. #13063287C22semidirect
40. #13063256C22semidirect
41. Dic43⋊C8C22semidirect
42. #13063250C22semidirect
43. #13063248C22semidirect
44. #13063248C22semidirect
49. #13063245C22semidirect
51. C8×Dic43C22semidirect
53. C2×C4⋊C4×C43C22semidirect
54. #107×C43C22semidirect
55. #107×C43C22semidirect
58. C22⋊C8×C43C22semidirect
196. #480D43semidirect
207. C43#3322semidirect
232. C2×C4⋊C4C2×D43semidirect
234. #107C2×D43semidirect
235. #107C2×D43semidirect
249. C22⋊C8C2×D43semidirect