Finite Group Databasebeta

← #19146797

Subgroups — #19146797

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#14583537C211yesmaximal, characteristic, complemented
3#14583255C211yesmaximal, characteristic, complemented
4#14583238C211yesmaximal, characteristic, complemented
5#14583212C211yesmaximal, characteristic, complemented
6#14583201C211yesmaximal, characteristic, complemented
7#14583152C211yesmaximal, characteristic, complemented
8#14583148C211yesmaximal, characteristic, complemented
9#14583117C211yesmaximal, characteristic, complemented
10#14583044C211yesmaximal, characteristic, complemented
11#14583034C211yesmaximal, characteristic, complemented
12#14582979C211yesmaximal, characteristic, complemented
13#14582975C211yesmaximal, characteristic, complemented
14#14582902C211yesmaximal, characteristic, complemented
15C43×#417C211yesmaximal, characteristic, complemented
16C2×D4×D43C2211yescharacteristic
17C2×#10621884C2211yescharacteristic, complemented
18C2×D344C2211yescharacteristic
19C2×#10621882C2211yescharacteristic
20C2×#10621872C2211yescharacteristic
21#13063320—21no—
22#13063316C2211yescharacteristic, complemented
23#13063314C2211yescharacteristic
24#13063310—21no—
25#13063308—21no—
26#13063301C2211yescharacteristic
27#13063300C2211yescharacteristic
28#13063299—21no—
29#13063299C2211yescharacteristic
30#13063299C2211yescharacteristic, complemented
31#13063297—21no—
32#13063293—21no—
33D4×Dic43C2211yescharacteristic
34#13063287C2211yescharacteristic, complemented
35C4×C22⋊D43—21no—
36C4×C22⋊D43C2211yescharacteristic
37#13063283C2211yescharacteristic
38C2×(C2×D43)⋊C4—21no—
39#13063258C2211yescharacteristic, complemented
40#13063258C2211yescharacteristic, complemented
41#13063257C2211yescharacteristic, complemented
42Dic43⋊C8C2211yescharacteristic, complemented
43#13063249C2211yescharacteristic, complemented
44#13063247C2211yescharacteristic
45#13063247C2211yescharacteristic, complemented
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⋊D43—21no—
71C2×C22⋊D43D411yescharacteristic
72C22×Dic43—21no—
73D4×D43—22no—
74D4×D43—41no—
75C2×D172—21no—
76C2×D172C2311yescharacteristic
77C2×D172C2311yescharacteristic
78C2×C4×D43—21no—
79C2×C4×D43C2311yescharacteristic
80M16×C43—41no—
81C2×C8×C43C2311yescharacteristic
82C2×C8×C43C2311yescharacteristic
83C4⋊C4×C43—21no—
84C4⋊C4×C43C2311yescharacteristic
85C4⋊C4×C43C2311yescharacteristic
86C22⋊Dic43—21no—
87C22⋊Dic43D411yescharacteristic
88#10621884—41no—
89#10621882—22no—
90(C2×D43)⋊C4—21no—
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)⋊C4—21no—
98(C2×D43)⋊C4D411yescharacteristic
99C4⋊Dic43—21no—
100C4⋊Dic43C2311yescharacteristic
101C4⋊Dic43C2311yescharacteristic
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104Dic43⋊C4D411yescharacteristic
105C4×Dic43—21no—
106C4×Dic43C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109D344—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
119Q8×C43—21no—
120Q8×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×C43—21no—
129C2×C4×C43—42no—
130C2×C4×C43—81no—
131C2×C4×C43C2×D411yescharacteristic
132C2×C4×C43C2411yescharacteristic
133C22⋊D43—41no—
134C22⋊D43—42no—
135C22⋊D43—42no—
136C22⋊D43—81no—
137C2×Dic43—21no—
138C2×Dic43—21no—
139C2×Dic43—81no—
140C2×Dic43C2×D411yescharacteristic
141C2×Dic43C2×D411yescharacteristic
142C2×Dic43C2×D411yescharacteristic
143D172—21no—
144D172—21no—
145D172—21no—
146D172—21no—
147D172—81no—
148C4×D43—21no—
149C4×D43—21no—
150C4×D43—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×C43C22×D411yescharacteristic
162C2×D43—21no—
163C2×D43—21no—
164C2×D43—21no—
165C2×D43—41no—
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—42no—
185C2×C43—41no—
186C2×C43#54611yescharacteristic
187C2×C43#57511yescharacteristic
188C2×C43#57611yescharacteristic
189D43—41no—
190D43—81no—
191D43—81no—
192#553—431no—
193#546—431no—
194#488—431no—
195#485—431no—
196#480—431no—
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#417D4311yescharacteristic, complemented
207C43#332211yescharacteristic, complemented, Sylow
208C2×#41C2×D4311yescharacteristic
209C22×D4—431no—
210C2×SD16—431no—
211C2×D8—431no—
212C2×D8—431no—
213C2×M16—431no—
214C2×M16C2×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—431no—
223#121—431no—
224#121—861no—
225#121—861no—
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#107—431no—
235#107—431no—
236#106—431no—
237C4⋊C8—431no—
238#103—431no—
239#103C2×D4311yescharacteristic, complemented
240#103C2×D4311yescharacteristic, complemented
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⋊C8—431no—
250C4×C8—431no—
251C24—861no—
252#41—22no—
253#41—41no—
254C2×Q8C22×D4311yescharacteristic
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—21no—
268C22×C4—431no—
269C22×C4—861no—
270C22×C4—861no—
271C22×C4C22×D4311yescharacteristic
272SD16—1721no—
273D8—862no—
274D8—1721no—
275M16—41no—
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—431no—
285C4⋊C4—861no—
286C4⋊C4—861no—
287C4⋊C4—861no—
288C4⋊C4C22×D4311yescharacteristic
289C4⋊C4C22×D4311yescharacteristic
290C22⋊C4—431no—
291C22⋊C4—431no—
292C22⋊C4—861no—
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—21no—
312Q8—21no—
313D4—21no—
314D4—42no—
315D4—861no—
316D4—861no—
317D4—861no—
318D4—861no—
319D4—3441no—
320D4—3441no—
321D4—1721no—
322D4—1722no—
323D4—1722no—
324D4#1062189812yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—81no—
332C2×C4—431no—
333C2×C4—431no—
334C2×C4—431no—
335C2×C4—861no—
336C2×C4—861no—
337C2×C4—861no—
338C2×C4—861no—
339C2×C4—3441no—
340C2×C4—3441no—
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—861no—
354C22—861no—
355C22—861no—
356C22—3444no—
357C22—1721no—
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—
373C4C2×#1062189811yescharacteristic
374C4#1306337011yescharacteristic
375C2—41no—
376C2—42no—
377C2—3441no—
378C2—3441no—
379C2—1721no—
380C2#1458353911yescharacteristic
381C2#1458369811yescharacteristic
382C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#417C2
socleC22×C43C22×D4
hypercenter#417D43
hypocenterC43#3322
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. #14583597C2semidirect
2. #14583537C2semidirect
3. #14583255C2semidirect
4. #14583238C2semidirect
5. #14583212C2semidirect
6. #14583201C2semidirect
7. #14583152C2semidirect
8. #14583148C2semidirect
9. #14583117C2semidirect
10. #14583044C2semidirect
11. #14583034C2semidirect
12. #14582979C2semidirect
13. #14582975C2semidirect
14. #14582902C2semidirect
15. C43×#417C2semidirect
17. C2×#10621884C22semidirect
22. #13063316C22semidirect
30. #13063299C22semidirect
34. #13063287C22semidirect
39. #13063258C22semidirect
40. #13063258C22semidirect
41. #13063257C22semidirect
42. Dic43⋊C8C22semidirect
43. #13063249C22semidirect
45. #13063247C22semidirect
49. C22⋊(C43⋊C8)C22semidirect
51. C8×Dic43C22semidirect
53. C2×M16×C43C22semidirect
54. C2×C4⋊C4×C43C22semidirect
55. #103×C43C22semidirect
56. #103×C43C22semidirect
206. #417D43semidirect
207. C43#3322semidirect
214. C2×M16C2×D43semidirect
232. C2×C4⋊C4C2×D43semidirect
239. #103C2×D43semidirect
240. #103C2×D43semidirect