Finite Group Databasebeta

← #19146404

Subgroups — #19146404

Order 5504.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583550C211yesmaximal, characteristic, complemented
2D4×C22⋊D43C211yesmaximal, characteristic, complemented
3#14583244C211yesmaximal, characteristic, complemented
4#14583212C211yesmaximal, characteristic, complemented
5#14583211C211yesmaximal, characteristic, complemented
6#14583177C211yesmaximal, characteristic, complemented
7#14583135C211yesmaximal, characteristic, complemented
8#14583134C211yesmaximal, characteristic, complemented
9#14583093C211yesmaximal, characteristic, complemented
10#14583034C211yesmaximal, characteristic, complemented
11#14583033C211yesmaximal, characteristic, complemented
12#14582979C211yesmaximal, characteristic, complemented
13C8×C22⋊D43C211yesmaximal, characteristic, complemented
14#102×D43C211yesmaximal, characteristic, complemented
15C2×#102×C43C211yesmaximal, characteristic, complemented
16C2×#10621898—21no—
17C22×C22⋊D43—21no—
18C2×D4×D43C2211yescharacteristic
19C2×D344C2211yescharacteristic, complemented
20C2×#10621882C2211yescharacteristic
21C2×#10621882C2211yescharacteristic, complemented
22C2×C8×D43C2211yescharacteristic, complemented
23#13063324C2211yescharacteristic, complemented
24#13063321C2211yescharacteristic
25#13063310—21no—
26#13063308—21no—
27#13063303—21no—
28#13063300C2211yescharacteristic, complemented
29#13063299C2211yescharacteristic
30#13063299C2211yescharacteristic, complemented
31#13063297—21no—
32#13063296C2211yescharacteristic
33#13063294—21no—
34#13063293—21no—
35D4×Dic43C2211yescharacteristic
36#13063287C2211yescharacteristic, complemented
37C4×C22⋊D43C2211yescharacteristic
38C4⋊C4×D43C2211yescharacteristic, complemented
39#13063259C2211yescharacteristic, complemented
40#13063258C2211yescharacteristic, complemented
41#13063258C2211yescharacteristic, complemented
42Dic43⋊C8C2211yescharacteristic, complemented
43#13063247C2211yescharacteristic, complemented
44#13063247C2211yescharacteristic, complemented
45#13063246C2211yescharacteristic
46#13063246C2211yescharacteristic, complemented
47#13063245C2211yescharacteristic, complemented
48#13063245C2211yescharacteristic, complemented
49C22⋊(C43⋊C8)C2211yescharacteristic, complemented
50(C2×D43)⋊C8C2211yescharacteristic, complemented
51C8×Dic43C2211yescharacteristic, complemented
52C22×D4×C43C2211yescharacteristic
53C22×C8×C43C2211yescharacteristic, complemented
54C2×C4⋊C4×C43C2211yescharacteristic, complemented
55#102×C43C2211yescharacteristic
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic, complemented
58#102×C43C2211yescharacteristic, complemented
59C24×C43—21no—
60C23×D43—21no—
61C2×D4×C43—21no—
62C2×D4×C43—22no—
63C2×D4×C43—41no—
64C2×D4×C43C2311yescharacteristic
65C2×D4×C43C2311yescharacteristic
66C22×C4×C43—21no—
67C22×C4×C43C2311yescharacteristic
68C2×C22⋊D43—21no—
69C2×C22⋊D43—21no—
70C2×C22⋊D43—21no—
71C2×C22⋊D43—21no—
72C2×C22⋊D43—21no—
73C2×C22⋊D43—21no—
74C2×C22⋊D43—44no—
75C2×C22⋊D43D411yescharacteristic
76C22×Dic43—21no—
77D4×D43—22no—
78D4×D43—41no—
79#10621898—44no—
80C2×D172—21no—
81C2×D172C2311yescharacteristic
82C2×D172C2311yescharacteristic
83C2×C4×D43—21no—
84C2×C4×D43—21no—
85C2×C4×D43C2311yescharacteristic
86C2×Dic86—21no—
87C2×C8×C43—41no—
88C2×C8×C43C2311yescharacteristic
89C2×C8×C43C2311yescharacteristic
90C4⋊C4×C43—21no—
91C4⋊C4×C43C2311yescharacteristic
92C4⋊C4×C43C2311yescharacteristic
93C22⋊Dic43—21no—
94C22⋊Dic43—21no—
95C22⋊Dic43D411yescharacteristic
96#10621882—22no—
97#10621882—41no—
98(C2×D43)⋊C4—21no—
99(C2×D43)⋊C4—21no—
100(C2×D43)⋊C4—21no—
101(C2×D43)⋊C4—21no—
102(C2×D43)⋊C4D411yescharacteristic
103C4⋊Dic43C2311yescharacteristic
104C4⋊Dic43C2311yescharacteristic
105Dic43⋊C4—21no—
106Dic43⋊C4—21no—
107Dic43⋊C4D411yescharacteristic
108C4×Dic43C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111D344—41no—
112C8×D43—41no—
113C23×C43—21no—
114C23×C43—21no—
115C23×C43—42no—
116C23×C43—42no—
117C23×C43—81no—
118C23×C43C2×D411yescharacteristic
119C22×D43—21no—
120C22×D43—21no—
121C22×D43—42no—
122C22×D43—42no—
123C22×D43—81no—
124C22×D43C2×D411yescharacteristic
125D4×C43—21no—
126D4×C43—21no—
127D4×C43—21no—
128D4×C43—42no—
129D4×C43#4112yescomplemented
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—42no—
135C2×C4×C43C2×D411yescharacteristic
136C2×C4×C43C2411yescharacteristic
137C22⋊D43—42no—
138C22⋊D43—42no—
139C22⋊D43—42no—
140C22⋊D43—42no—
141C22⋊D43—42no—
142C22⋊D43—81no—
143C22⋊D43D814yescomplemented
144C2×Dic43—21no—
145C2×Dic43—21no—
146C2×Dic43—42no—
147C2×Dic43C2×D411yescharacteristic
148C2×Dic43C2×D411yescharacteristic
149C2×Dic43C2×D411yescharacteristic
150D172—21no—
151D172—21no—
152D172—21no—
153D172—21no—
154D172—42no—
155C4×D43—21no—
156C4×D43—21no—
157C4×D43—42no—
158C4×D43—42no—
159Dic86—42no—
160C8×C43—21no—
161C8×C43—21no—
162C43⋊C8—21no—
163C43⋊C8—21no—
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—22no—
167C22×C43—41no—
168C22×C43—41no—
169C22×C43—41no—
170C22×C43—41no—
171C22×C43—41no—
172C22×C43—84no—
173C22×C43C2×D812yes—
174C22×C43C22×D411yescharacteristic
175C2×D43—21no—
176C2×D43—21no—
177C2×D43—41no—
178C2×D43—41no—
179C2×D43—41no—
180C2×D43—41no—
181C2×D43—41no—
182C2×D43—41no—
183C2×D43—84no—
184C2×D43C2×D812yes—
185C4×C43—21no—
186C4×C43—41no—
187C4×C43—41no—
188C4×C43C2×#4111yescharacteristic
189C4×C43H(5,𝔽2)11yescharacteristic
190Dic43—21no—
191Dic43—21no—
192Dic43—41no—
193Dic43—41no—
194Dic43C2×D812yes—
195#3294—431nomaximal, Sylow
196C2×C43—22no—
197C2×C43—42no—
198C2×C43—81no—
199C2×C43#54611yescharacteristic
200C2×C43C22×D811yescharacteristic
201C2×C43#57711yescharacteristic
202D43—22no—
203D43—81no—
204D43—81no—
205#547—431no—
206D42—431no—
207#486—431no—
208#480—431no—
209#480—431no—
210#474—431no—
211#466—431no—
212#466—431no—
213#459—431no—
214#447—431no—
215#447—431no—
216C4×D8—431no—
217C8×D4—431no—
218C2×#102—431no—
219C2×#102D4311yescharacteristic, complemented
220C43#329411yescharacteristic, complemented, Sylow
221C2×#41—861no—
222C22×D4—431no—
223C22×D4—861no—
224C22×D4C2×D4311yescharacteristic
225C2×D8—431no—
226C2×D8—431no—
227C2×D8—431no—
228C22×C8—431no—
229C22×C8C2×D4311yescharacteristic, complemented
230C4⋊Q8—431no—
231#127—431no—
232#123—861no—
233#123—861no—
234C22⋊Q8—861no—
235#121—431no—
236#121—431no—
237#121—431no—
238#121—431no—
239#121—861no—
240#120—861no—
241#120—861no—
242C4×D4—431no—
243C4×D4—431no—
244C4×D4—431no—
245C2×C4⋊C4—431no—
246C2×C4⋊C4C2×D4311yescharacteristic, complemented
247#107—431no—
248#107—431no—
249#107—431no—
250C4⋊C8—431no—
251#102—431no—
252#102—431no—
253#102—431no—
254#102—431no—
255#102—431no—
256#102—431no—
257#102C2×D4311yescharacteristic
258#102C2×D4311yescharacteristic
259#102C2×D4311yescharacteristic, complemented
260#102C2×D4311yescharacteristic, complemented
261C22⋊C8—431no—
262C22⋊C8—431no—
263C4×C8—431no—
264C24—21no—
265C24—861no—
266#41—1724no—
267C2×Q8—861no—
268C2×D4—22no—
269C2×D4—21no—
270C2×D4—41no—
271C2×D4—431no—
272C2×D4—431no—
273C2×D4—431no—
274C2×D4—861no—
275C2×D4—861no—
276C2×D4—861no—
277C2×D4—861no—
278C2×D4—862no—
279C2×D4—861no—
280C2×D4—861no—
281C2×D4—861no—
282C2×D4—1721no—
283C2×D4—1724no—
284C2×D4C22×D4311yescharacteristic
285C2×D4C22×D4311yescharacteristic
286C22×C4—21no—
287C22×C4—431no—
288C22×C4—861no—
289C22×C4—861no—
290C22×C4—861no—
291C22×C4C22×D4311yescharacteristic
292D8—862no—
293D8—1721no—
294D8—1721no—
295C2×C8—41no—
296C2×C8—431no—
297C2×C8—431no—
298C2×C8—1721no—
299C2×C8C22×D4311yescharacteristic
300C2×C8C22×D4311yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—431no—
303C4⋊C4—431no—
304C4⋊C4—431no—
305C4⋊C4—861no—
306C4⋊C4—861no—
307C4⋊C4C22×D4311yescharacteristic
308C4⋊C4C22×D4311yescharacteristic
309C22⋊C4—431no—
310C22⋊C4—431no—
311C22⋊C4—861no—
312C22⋊C4—861no—
313C22⋊C4—861no—
314C22⋊C4—861no—
315C22⋊C4—861no—
316C22⋊C4—861no—
317C42—431no—
318C23—21no—
319C23—21no—
320C23—42no—
321C23—42no—
322C23—81no—
323C23—431no—
324C23—861no—
325C23—861no—
326C23—3441no—
327C23—1722no—
328C23—1722no—
329C23D4×D4311yescharacteristic
330Q8—1722no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—42no—
335D4—434no—
336D4—861no—
337D4—861no—
338D4—861no—
339D4—861no—
340D4—3441no—
341D4—1722no—
342D4—1722no—
343D4—1722no—
344D4—1722no—
345D4—1722no—
346D4—1722no—
347D4#1062189812yescomplemented
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—42no—
353C2×C4—431no—
354C2×C4—431no—
355C2×C4—431no—
356C2×C4—861no—
357C2×C4—861no—
358C2×C4—861no—
359C2×C4—861no—
360C2×C4—1722no—
361C2×C4—1722no—
362C2×C4—1722no—
363C2×C4D4×D4311yescharacteristic
364C2×C4C23×D4311yescharacteristic
365C8—21no—
366C8—21no—
367C8—861no—
368C8—861no—
369C22—21no—
370C22—21no—
371C22—22no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—84no—
378C22—432no—
379C22—861no—
380C22—861no—
381C22—3444no—
382C22—1721no—
383C22—1721no—
384C22—1721no—
385C22—1721no—
386C22—1721no—
387C22—1721no—
388C22D8×D4312yes—
389C22C2×D4×D4311yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—432no—
394C4—861no—
395C4—861no—
396C4—1721no—
397C4—1721no—
398C4C2×#1062189811yescharacteristic
399C4#1306337011yescharacteristic
400C2—22no—
401C2—42no—
402C2—81no—
403C2—862no—
404C2—3441no—
405C2—3441no—
406C2#1458353911yescharacteristic
407C2C2×D8×D4311yescharacteristic
408C2#1458370511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC2×#102×C43C2
socleC22×C43C22×D4
hypercenterC2×#102D43
hypocenterC43#3294
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #14583550C2semidirect
2. D4×C22⋊D43C2semidirect
3. #14583244C2semidirect
4. #14583212C2semidirect
5. #14583211C2semidirect
6. #14583177C2semidirect
7. #14583135C2semidirect
8. #14583134C2semidirect
9. #14583093C2semidirect
10. #14583034C2semidirect
11. #14583033C2semidirect
12. #14582979C2semidirect
13. C8×C22⋊D43C2semidirect
14. #102×D43C2semidirect
15. C2×#102×C43C2semidirect
19. C2×D344C22semidirect
21. C2×#10621882C22semidirect
22. C2×C8×D43C22semidirect
23. #13063324C22semidirect
28. #13063300C22semidirect
30. #13063299C22semidirect
36. #13063287C22semidirect
38. C4⋊C4×D43C22semidirect
39. #13063259C22semidirect
40. #13063258C22semidirect
41. #13063258C22semidirect
42. Dic43⋊C8C22semidirect
43. #13063247C22semidirect
44. #13063247C22semidirect
46. #13063246C22semidirect
47. #13063245C22semidirect
48. #13063245C22semidirect
49. C22⋊(C43⋊C8)C22semidirect
50. (C2×D43)⋊C8C22semidirect
51. C8×Dic43C22semidirect
53. C22×C8×C43C22semidirect
54. C2×C4⋊C4×C43C22semidirect
57. #102×C43C22semidirect
58. #102×C43C22semidirect
129. D4×C43#41semidirect
143. C22⋊D43D8semidirect
219. C2×#102D43semidirect
220. C43#3294semidirect
229. C22×C8C2×D43semidirect
246. C2×C4⋊C4C2×D43semidirect
259. #102C2×D43semidirect
260. #102C2×D43semidirect
347. D4#10621898semidirect